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κζУܻһݡ
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2020410գһɫâէڶҹա
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ȻϮֶʵ˲ܣǡһԼ֮ĺ˧ҲɵĴ˸


 
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ʴͣŵŲ
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Ǳߣվһ˵˵Ǽ尾Ŀ֮ѹСʱǣ˲ѽڵͬг֡
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һܣŵһעĸݡ
ȻŵڱпһϤӰ


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骴һѼñĺɫ˶ǰ͹毺õĹճֵڳŵǰСš
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ǺǡһۣСС̫ĺܡǻﾭƵġ
һΪǡŵͳһԪĴȯŴȯװɵò״ﾭġ


ڶʮ ǹˣ
ڳŵĵȰ˵£ջǲ鲻Ըֻë޵Ĵܡ
ŵһӵѰҺʵġ̯ص㣬ССһ˱һֻë޵Ĵܸڳŵ档СС߳һͷһ׶ߵĴֻǽƽ񵭵ıڻУССͱȽϱˣܼСССȥԶȥһֻڴվߣϲС
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裬ҵطԷȻȥҽԺһ塣
ȥҽԺɶûòĺܡ
裬˭˵ûòͲȥҽԺˣδѣοϴμѾǰǰˡ
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һʤ߼Ӿ˹ĸһĳŵ˵ʼһλ֪ĳֵװĵˣֱӹѳŵʣµȫߣʡ˳ŵܶʱ䡣
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пһһδͬʱԼǧҪΪΪǧԪʧҡŵһ⳵ֱꡣ
ŵȥһġǡԭҲ֪ŵļҵױһٷͿա
죬ŵǧԪ޿ɱ˻

ŵҪ͵顣һֹڼ̣һǹڽڣǼǹڼѧ鼮˵°ͺղ룬գBirch˹άګͨ-Swinnerton-Dyer֮ġ
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ŵڳϣ緢
ں󻰡ǺǣŵÿÿʱԼԼ

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ŵ֪δᷢʲϵԼûд

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ȻֻڵйϵôԶΪʲôѡһɼ룬ƺֻ

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Զе㼤ؿʼӡ
ǲȥձѣȥKTVӣǴսһΣеСأ
ڣϣѰѸˣ100Ԫۣ
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235.35ףƫ11.24ȣ5.24ף6.25ס
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ڳŵѸ㡣ܿ죬һͶ֡
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ʼͶ߶1.52ףǰ38.94ȣȦбǶ18.38ȣ8.82ţ

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һǩֱʣһ߳˵Ҫ͸ܵܡʣµģСС˲٣һЩûҪĳŵװԼĵɽ


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ע٣лָ˶ʱлʶ԰ʱлʵı1METָÿأһӻ3.5
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21Եͬѧһ֡ŵʵ
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ŲˣŵҲΪʲôԼĸĸһֱƲˡ
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16.25ǧˣٶ19.25/Сʱ
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ŵҲͨѸٵļĴһƲͨ졣


ڰʮ ٿ
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ĳҲʵ̫˰ɣǵдųԾͲ⡣
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20.58ף30.25ף뾶6.25ףٶ9.84/η롭
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ܡСɬ촽˵
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һߣŵѳᵽ100/СʱΧгڳŵ
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ۿǱϵ֣60ĵ70ٴ70ĵ100
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ʮʱƾһ֮Ƶ˳ɱ˰ʱ֮󣬽֮ԷͬʱҲǱʡ繫ϵʮѰ֮һʱһͨԱİ׾̽ƾ˰һٳ
֮Ķڣ׾̽ȺƵɱ˰ɱ˰ѩ첻ȴССʮɽֿȵľ̽
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ӳһѰĹһ顣
óŵºĴǸаľ̽
180.25ף82.24ǧˣ78/֣λ543625꣡
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ԼǸĳȿǡ
ˣɲܸǡ
ŵĬĬǸаľ̽һ
ӳҽĿǡѾ³ӳԼϵĽеĿġ
ӳǺһЦԣٰĿǰҺͰ׾̽Э顣ȻгǱߵĴӦʶһ¡˳㣬׾̽һЩҪ


ڰʮ 
ƺҲ֪ӳһڰƵƺЩʵ
ǣĿǰմһش󰸼İ׾̽˹Эӳе顣
Դˣӳûκβ
ӳΪƾԼֻҪٷ¶ţҪһץסǲô򵥡
Ѱɹ顣ӳҲˡ
һǶ˶׾̽СĦ˹ĳƺſɲǰ׸ġа׾̽ЭץסٷĿԴ˺ܶࡣ
һҪһûץסٷҲȫӳһϡ
ӳվߵߣļ򣬡׾̽ȱоˣгѾˣϿȥкɡ
ŶгѾˣãһһЩҪתЩЦ˵
׾̽ã
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Ͱ΢΢֣Ȼĳ˼䣬׾̽ղӳΪѽ
ԽĿޣ嵹ûκǫӣ˵չ¶š
гģȻҰˣٷˣҾԲǰĵң⣡죬ֻҪ죬Ҿܱ֤ץסǣҵ־򣬿ҪΪ񸣶Ħ˹̽
˫ȭգͷޱŵ˵
ǰ׾̽ǷʲôҪ𣿡˫һеʵ
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ȻӳͰ׾̽ûʲôҪļ̶ֳȣȻҪĶ࣡
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һֱվԱĬĬĳŵҲ׼ڽȥеļء
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178.28ףء


ڰʮ ٷ˵ͼ
175.35ף75.24ǧˣŽų22.28ףŽſ8.92ףҽŽų22.04ףҽŽſ9.00ף۳60.12ףұ۳60.35ףȳ93.25ס32꣡
178.28ף65.28ǧˣŽų19.62ס31꣡
174.98ף70.68ǧˡ35꣡
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ŵҲûɨһƬ˵ĸݡһλǽٷ˵Ļ˵λ׾̽ʵǿԵġ

177.50ף73.87ǧˣŽų20.28ףŽſ8.02ס
176.35ף74.21ǧˡ
ˣݶÿߺأŵ֪ˣǽٷˣ
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ˣҵĻɶݷΪѧ˵λ˾λٷ˵Ŀԣߴ˳ɣĹİװĲʲôļǣ׻ġǮ


ھʮ ŵ
ˣҵĻɶݷΪѧ˵λ˾λٷ˵Ŀԣߴ˳ɣĹİװĲʲôļǣ׻ġǮˣ˼˵
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ŵǸղռƬλݵʱ򣬷ʳָĳЩ쳣ֻ2.11ףƶϳ˵ָһڡ
ŵ̨İھԵЩˡ
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ƾƬǿ϶޷֪λٷ˵ߣб۳Ƕ١ǣǿԿ⡣ŵָƬеĵذש˵ذשĹ300*400mmҲǴɰשĳ40ף30ף
ٷ˵ӰӸǵĵذשĿ3.54ôӰӵĳȾ141.60ף
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һʱ䣬ðе㻳ĸо
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ðɣӮˣ
ӲȥˣҲҪԶȥˡΪôԼ߹ˣ


ھʮһ Ǹͬ־
ҵݷλ˵ı۳ͽٷı۳ͬ˵׾̽ҳλУû˵λŽٷˣ
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ǾֺֺǵĸСȥ˹⡣
ŵСĸһ𷢱۵椣Բͬԭ˷̵ĻԷԳŵźСĸĹϵǺܲ


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ĳŵֻԼյһڽ賿෢ʼ
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Σ̣ˣǹȥɡԴԶһ֡


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ˣСŵ㻹ûԷɡſŵ˯ѵӣŤͷڲһߵĳŵı˵Сȥ緹˳

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ǣʱĽһ뵽һδ˿Ĺҵޣ


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²ժĲ˵ĻҶغֵӦ0.3/ңҶƬʾɫӦǹ̡ɿⲤ˵ɫҶض0.2/ˡҶصĺϳɿԷΪĸ裺٢ڢۢܡע٣
ûֲĸϵþԪأҶǸɺϳɡҶʱ޿̲ĵġԣǸողժĻҶغֱ0.1/ˡ
Сŵһָ˵

PSҶصĺϳɲ裺
һ׶Σ8ӵĹȰϳ4ӵĵɫԭ
ڶ׶Σ4ӵĵɫԭϳԭ߲IXٺþγɵϩԭҶa
׶ΣϩԭҶaڹ±NADPHԭҶa
Ľ׶ΣҶaֲγҶa
ܿͿˡ
пῼô


һһʮ ˭˵ֻҪӼ˳ģ
Сŵߵ̯λǰ˷˵ߣȻװģϸ۲һ˵
˴вժʱڶʱڣΪϸδйúͺá6 CO2+12 H2O===C6H12O6+6 O2+6 H2OC6H12O6+6 O2+6 H2O===6 CO2+12 H2O
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ŵߣװơŶԣҪʼˡ
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һ2.10ǧˣ4ǮһĻһ16.8ԪĨȥͷ16.5Ԫɡ׳һֻڵӳϣЦǺǵ˵
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Ƕи18ڡ
ڰǸ߿ʱ֣Ѿڲĸ£1
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18ڣʱȴѻȸһȫͷŽ̨ϵǵӰ
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ʤ
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һٶʮ ȫǸ߿
202067գ
죬˵Ƿһ졣
Ϊڽ죬һһȵȫ߿ʽʼ
˼ʱķչĸ߿Ѿ֮ǰĸʡԵһԾΪȫͳһԾ
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ͳһԣͳһ⣬ͳһ𰸣
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ŵгͣһеĳܼ࿼ʦһϸļ󣬽ԼμӿԵĽҡ203
ŵλڿһߡ
λϣŵŴεգս˫ȭϴһӦеš
߿ҳŵˣ


һٶʮһ ʮ꺮ʣһ֪
ԿĿ
ʱ䣺900~1130
ԽҵĺڰдſԵĿĿʱ䡣
ڿǰСʱԽ뿼ԿʼʮӺֹ뿼
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ϣĿԵĿҪ̫Ѱɡŵ
Ƴŵܱ֤һƣŵֻȡѶˡ
򵥵Ļһ130Ҳûпܡ
ѵĻǾֻһһʮһεˡ
ȫ״Ԫ
˵ʵͷγŵǺϣܵõģ
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ǰӣ࿼ʦַԾ
չʾһԾûо֮󣬲ܷλʦʼַԾ
⿨ԾݸֽЩԽҪϽ
Щطľ߶ڿͳһš
Ҳ˵һЩ֤ϴŵ·ʲôܴ
ÿڶź࿼ʦŽ̽һѧļ顣ܼٿ׵Ŀԡ
ڶž϶һ֮ϵС
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ٶȣǰѡģĶһЩĿһСʱһСʱꡣȻʣµһСʱдġ
ȿĿĻǰĿʱ򣬿һ⣬һ߹˼ġʣһСʱдĵʱͻ
ȻҲһ
ѵĻ̬ͻӿԿʼһֱԽһ˾ı
Ŀġ
ĶĲϣԼĸ룬дһƪ800ֵ£
һСѧĿԳһ⡯Ŀ
һ75ͷţ34ͷʴꣿ
ԣһ޷Ŀ
ɧ⿼⣬ѵ۲һ
Ϊڻȡ裬ϿĿġӦͣ
ҲЩΪܺõѧɾֵù
Ԥ18߿⣬λǲл²ҡ׷Ԥⲻԣ߿ң
⣬ӦɡŵԹԵֹһ䡣
ԣʴⲻ޽ġ
װţ109ͷ500µĴҪб֤飬ְҵҪ48£ѧҪǴרϡ
Դ21+4=25ꡣ
ȥ껪˾6914Ԫ
ţ300ÿ7.5Ԫ80ÿ12Ԫ75ͷţ2250011250kg11.25֡
32ֻ25601280kg1.28ţ12.53֡
һ55m300ţһ16.875һ3.075ţһҪ319.95Ԫ
ڼ16֮ǰ޷׬Ǯģ3199500/6914=462.8463+16=479꣡
˵Ϊ479꣡
ԣд𰸵ĺðɣֻƺλЩ̫ˣ
ˣˣⲻص㡣߿أûд𰸣ȰԾ˵ɡ
εĸ߿ʦᵽļࡣεĸ߿ģǰĺɫ˿ⶹ벻֪˶١
ŵһԺй˼д˼·һ߿ǰĿ
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A.Ű B.ᣬҹ
C.ͼ D.Ȼ˳
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ŵͬԼĴŰٷְǿš
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ǿǿƤ
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ԵĻ˵ľʦԼһĽⲽ裬õĳ֪ʶǷ
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ŵһۣһĲӡ


һٶʮ Ҫǰô򵥾ͺ
ռǿĿУͷʱ򣬳ŵǿαˮӰֱһĴڡ
һֱڿελ࿼ʦҲ˳ŵࡱ
ϾټĽУֻгŵһɵı飬ƺûаⳡԷϡ
ŵһϵоٶΥԹ涨λ࿼ʦԳŵҲ޿κΡ
ĬĬһۡ
λʦװĴӳŵ߹һƳ㿴˳ŵϵĴֽ
Ŵֽϣ鲻Ǹֹʽ֡
ʦȻһʲôûӣɫ糣Ļߵλ곤ļ࿼ʦߡ
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߿ΪʱŵĻ⣬ΪߣȻҪʱ̸
ʱһŰɫӰС߳Уš
˲Ǳˣǳŵ
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˵˵һ⣬õ׳֤ͨʽڼϵ޺Ҽ޺͵һ룬ٽиҶ任˹̣N׵ͣȡ޾ͺˡ
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󣬳ŵ̾һĿʵ̫ˡ
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ݱ̨ոյϢɽǿһʵǿ翼ʱųĹâϹͬȫʦͬѧ۾غĹ㷺ע
֪߳ƣÿڿ֮Ѹ뿼;Ū˸ڿһŮͬѧ˷ָڳУ֮󣬸ȻµؽܲɷãһװƵ۾˲ɷõļߡĿǰÿٵĳ˵µУзɵƲã
ѧԽĵŵӰ˸ýİϡ
һ䡰ô򵥾ͺˡֱһδεսѧǴ񾭡
һЩϵѧܣճŵ˵ЩԲǸзΧѧĸ߿Ŀһ飬ȴǷֳŵ˵Щʽ˵ģȴöӦĹʽ⿪Ӧ⡣
ձѶȵѧĥĿǣصң򿪵׼ɷɵʱ򣬺ȻٿɵӰ絭˵θ߿ѧǶôô򵥣жôô̡
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ĿоԼСܵ1024㱩ĲֱѪ
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˼طȷ֮⣬ʣµĿ100%İԡ
ճŵĹƣķҲ290ҡ
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ԳŵɷõһϣŮõٽ
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ߣðɣףͬѧҵһŮѡŶˣܸʲô𣿡
ŵ²Ҫ֪ĻǾҡĿͬѧɣ


һٶʮ һֽŶִ̼ҫ
һƪΪĿͬѧĸ߿ճһСȳ
ģһУſڣһλĵĸ߿ͬѧǼ߽ĸ߿ճݴλĵĳͬѧڵһѧԺ͵ڶӢ￼Уǵһ뿪ҫ۵ѧԹ⻷࿼硣߲ɷõ֪λĵĳͬѧĿǰ״Ϊԡи߿򵥾ͺˡֵ̬ƺθ߿ѶЩǻ߿ɼ֮ǻἰʱͬѧķҡ
ⷬĿͬһ뷨Բۣôһ
һﲻϹһôһΣ
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챻Ű컹ҪűŰ
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һᣬŵھĸо
ſԣѾȫꡣ
ȻûԴ𰸣ŵоԼû㲻ӵĻС
˵һõȫ״ԪͷΣʲôְҵѧԺԲ԰ѧԺûġ
ɽϣ̫ඣ~~~
ŵСŷ۵糸гӭűϦȾϼʻڿĵ·ϡ
죬׼ȷ˵ǵӢ￼վһ𣬰ŵڵļѾٱΪǡ׼ѧ
ʱʦǻѴѧޱȾʣѧǵ롣
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ⲻ֪̤һ̣ѾԶãģʽս
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СŵԼôһڳ֭ȿʵ
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Զһ㶣ʾԼĪǹ
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Щϰϻǲãţȵӿ߿ʱһҪ׼ϰӦöŶ屶ԶĬ˵
ҲʮͬԼɷ뷨ţӦöһ㡣
һԵĳŵһͷߡ
ǰһܣһٶ౾ĸϰϡ
ŵΪԼδĶĬ룺ӣ㡭~~

㷹˱Իصҡ
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һֵģŵҲԼĶλ˲
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ҡƬ5V5ƥ䣡


һٶʮ ᲻ᳰ
СС
ϷΪƬϷ룬ŵʵ
ССϷIDȷʵǡƬţܷĸԡ
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ԣĿǶԷѡʵĿУ˫սĲġ
ļƷͬʱûһԷֱ档Ҫѡֱȥжϡ



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ѡ֮໥⣬е㲩ĵ˼ˡ
˶ǾеӵߣȻ֪ӵоеˣĸ׵ķֱ͡
ڳʱǱѱ˴ˡ
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200źӦû֧ӴļĻףУҪ
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ҸоپѾʧˡҪʹ嶫ͷͷСĸţһƬŻѹ
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һٰʮһ ĳŵ
ʱ䣬صڶ̩ɭĿֵʱ
ŵüģ첲˶֮󣬱㿴Ļе档
˵һεľ֮󣬳ŵٶȺܿ졣
ڲ߰˷ӵĴ֮󣬳ŵˬĵͺһ˲оȫµëȫſ

ŵ˲ڼ˶Һ壬̵Ŀαϡ
ָоѽ
˵һ֮󣬼ֱʳ֮裬޲һֱȥ
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ڶһʮ 
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ֻǣʱͻȻ֣ס˵ȥ·
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⼸軨ɶҴӹġÿһ裬Ҫü򣡡
ĻЩǰľסˡ̽ѰĿ⣬塣
뿪ڡɳŵǱߣ;ߵһ跢ǰźЩѿףЦĿڣģеʧǾᰴ⳥ġ
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ССʦѧ¼ȡҲھУܾ档
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ڶһʮ 
8.27գѧ
8.28գ9㵽10ۺݾпѧ
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8.29գΪ4ܵľѵʽʼ

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ѧ󣬳ŵоû˶೤ʱ䣬ѧھȻ
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˫λõָ߾0.56ס0.00ףϣ
ŽǶȵŽǶ61.25ȡŽǶ60.00ȣϣ

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廪ҲСôһŵѧܣ㣬סԺˣǧҪʺãмǣмǣһλԸ͸©Աѧʵĸ룡



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ԣĶʽֻ01x^mx-1^m
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ŵĵĿڣһϣλֵܹĻһ㡣ҪŤŤһλȻ廪ǾͲӦõ裡Ŭѧϰ;̨ûУγΪһõĶ֮ţ
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ڶٶʮ ѧ̺һ
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ȴû뵽ߴεĵһ죬ͼ˳ŵ
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֮ޱȵ۹ųŵŹֵĿڣŵͬѧƺǽϵѧɣ
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Ȼҽ廪ѧУлܹڶĸߵȽôҶȻѧϵ츳װʧѧͽڣȰרҵΪʲô߲ɵüأԣҵԺðεͷ
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鷳鷳֮аڰ֣ѵüŵͬѧôϲѧϵγ̵ѧʦ鷳ʲôֻҪѧ֪鷳Ҳֵõģ֪ǽϵĿγ̺ѧϵγеʱǳͻģûϵһ޿α㰲ſγ̵ġ
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Ϊ˴ѧ֮󣬾ͿԲÿ춼ڽѧϰˡ
ڿƵŵҪѽ

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ޱȵڽڸߴΣŵŵԽѡ

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ŶҾø̫ˣһΡǵĿҾû£Žһ£û뵽ͦ򵥵ġˣͬѧӦҲΪǵĿܼ򵥰ɣ

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ҪǼ򵥵Ļʦ̨ʱԼ;ˡ
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Ҳûʲôģ廪ѧڣʮϵʦϽְơЩʮ꣬ܳΪԺʿģǲ
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ɫ̫ÿĳŵͷţʦҡ


ڶٶʮ ίѡ
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ǣҸǿɻģ޵ļϵ㲢ӰĻۡ
ԡֹ۵ɣ
ǰֹ۵ɣ
һѧҪֹ۵һС
лʲôɣеĥѣԹ԰أ

ֿΣѾʮ㡣ŵ绹пΣʳҴҳ緹󣬳ŵһᣬһ·ϹѧԭĿαϿνҡ
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ԬɳŵǲǸѧϵһĿˣ
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νHelmholtẓķȷ̡
һŲԲƫ΢ַ̣Ե¹ѧҺķȵͨ漰ͬʱڿռʱƫ΢̵ַоС
ΪͲ̵Ĺϵ÷ѧеŷ䣬ѧѧоŹ㷺Ӧá
ڷʽԱʾΪfx+k^2fx=gxxʦ
У˹ӣkΪռR^dd=123
Helmholtz̵ֵⷨܶ࣬Ҫ޲ַԪ߽Ԫ񷨵ȡ⼸ڵҪϸҼȽϴ
ԣоĿͨϽ²ָʽCCDHelmholtz̽ɢHelmholtzʽÿ㼫ֵһ׵ֵӶ̩չʽϵͳ
˵һ൱Ҽ俼ĿĿ
ͳŵһЩϰĿȣһѶȲϡԲҪר걨һѴʱо⡣
ڳŵľ֮в÷ЦŵͷȷʵĿĿǰ˵ȷʵЩѶȡҲ޷ɡ
οҲҪһȥ񡣶ҪɵСŶ໥ϡԷԼĳǱС
֮˵Ҫʱμһ仰־ߣ¾ɣƸۣعˣ첻нǧԽ׿⣡
˹һ뼦֮֮жǰı±Сһڡ
̧󣬿˿ֱʱ䡣Ȼվ
ˣ߻¡߾ͽˡ˶ׯŵһҪݣĿǰоȡȻŵҵɶԼС
áλѧӦŵͷĿ֮ȥ
칫ڣճĬ˼ӡ
ѧ˶յһЦҲҪôĬλŵѧܽһ⡣˽һʲô
û⡣һָͳԼıʼǱԣϰ칫ҵͶӰǣųŵһüŵѧܣãСһǶ˫һĨڰɡ
ûϵŴһ֪ʶԻ⣬Ҫܳ͸ѵЩֻҪǴ־ˡ
ѧڣ֤װƴɣظװϢʮ˵仰
ϻˣϿ콲ȻǷһɢˡ˶۾дߴٵ
ϣϣϣٿ꣬㿪һWordĵ
һ£ڣ⣬ʵý²ָʽԶάHelmholtz̽ɢòָʽ׾ȣֺʽص㡭
һ룬ͻȻʲôƵģԳŵʵŵѧܣӦ֪Helmholtz̺ͽ²ָʽԶʲôɣʣƺӦǻûнӴ
Ȼʦǿ飬Ӧö˵ɣЦųŵ
Helmholtz̺ͽ²ָʽ𣿡ŵͷǫĵжš
Ŷһʾŵǳŵѧܣ˵һ⡣óᣬѧ㲹һ©Ķ㳹˽ʡ
Գŵһѧ֪ԳٵʵסҲżȻ˵ѡ󻹲ҪԼ͡
ãᣬڳŵѧš
Ͷллѧˡ鷳ˡŵϿҡ
鷳鷳˳ŵĿޣһ֣ĹЦָѧѧϰΪѧڵ¡ʹ󵨵˵˵Ҳûϵģ
ŵͷ˵һHelmholtz̰ɣɵ¹ѧҺķġָѧϾУ2+k2=fʽ˫ƫ΢ַ̡ʽС2Ϊ˹ӣֱϵΪķȷ̺ķȷ̣Ϊ;k2ΪfΪԴfʱΪκķȷ;fʱΪκķȷ̡
ŵ٩٩̸һFxyztʱг䶯ʱԱFxyzejwtʽʱ/t൱jأ2/t2൱-2롭
Ӻķȷ̵Դʽⷨ任Ӧãŵν㵽ÿһط˵ϸ΢κδ
Helmholtzһʣŵϲʮӵʱ䣬˵ǽһĭɣٴ죬ҵڻûֹͣơ
ڳŵʱѾŵĳ͡
жţ
ôаŻĹ
жŵĻʲô
һǲǶʲô⣿


ڶʮ 
ԣķȷһнģôڲУ߽ƣ̵Ľɢıģʽʾ
˵²ָʽǾ͸ˣһָ߾ȵ޲ַٸӡ
ǣƽɢxiƫĲָʽ漰Ҫȴ˲ָʽضĽ1УʾָʽڽصֵƵɢ²ָʽʾָʽͬxiϵĺֵ֮Ȩƽƽxi㸽ϺƫļȨƽ
ŵ㣬渽Լļ⡣һԵһһ㶵ġ
ĩˣŵʮǫѷ̧ͷһĳҪ̵̬ȿڣѧЩֻҵһ׾ѡ϶಻֮ϣѧͽ̡

ͽ̣ͽ̸ë߰ͽ̣
ʱĿųŵң֪˵ɶǺá
ķȷ̡С²ָʽĿҪؼʡ
ʵڿ·֮ǰλԺѧΣֻжŶѡ
ежţֵֻ֡ǳŵװʽжš
˵ʵɡ˵Ĺжˮƽȫͬġ
ǳŵ˵һѶ;Բáжšĸܸġ
ŵǱ߰˵ʮӣȫ̶ˡ
˵ŵ˵ģûһ˿һĴҲȫ档һЩλѾоһµĶ˽⡣
ڴͽ̡
һƵĿ⿴Լλͬۡ
λϸ磡
ˣƺûоĿһ
ׯʦ֣緹һȥʳһ¥ɣ˵һѡڣζ
˶ţһһȥ
Ǻǡ
˵õĻأ
ѧû°ɣŵһصı飬ʵʵмƿҪ´ҸζػҲС
ڰ֣û£Ǽ
ת˫֣һĪӣʣʵ֪ĻֻƤëѡͽʲôҲ˵ˡΪ˵ˣҲһʱ⡣ѼʽĽҴǲᳫġ
ԣʱ䣬ͺúøĿƿиε⡣
ŵ׼ѧܹʽͷõģѧ
գѧڱסˡ
ĨһѶͷϵ麹
ѧҵľʲôأŵʵ󲹳䣬ˣоȣ
תڳŵ棬ͷЩεĿڣһµʱ䣬Ϊæű飬ʾĿǰֻǽĿĴܴ
ھ䣬սĻ5%
ŵۣʾ
ʮһĽȰ
ĿĿʱ䣬ֻ²ʱ䡣һ¹ȥˣɿĽĿǰֻ5%
ʱ䣬ҪؼҺúù꣬Ǽˡ
˶Ϊĸ鳤һڡ
ĸһˣæǶʱӦùȥˡгŵǴһʱҲԣ
ôڣҾͰѿҷһ°ɡ
˸ӵĿĿȻһ˴ͷβȫֹ໥ЭʱԵúбҪ
˶ŤͷԳŵ˵ղŸҲ˵ˣĿĴ¿Ѿˡ
ĿʵҪΪ֡
һ֣ҲĲ֣ͨһάHelmholtzϽ²ָʽõάHelmholtz̵ϵͳŵ򵥵Ĳ֣ûɣ
ŵͷû⡣
ڶ֣ϵĿһֽóⷽ档
ģҡظ
֣ѭԤӼԷ
Ĳ֣Ԥϵͳ㷨
岿ֵ֣顣
ֿϵһ飬Һһо
ׯͷʾͬ⡣
ʱأϣǶíɾΣȡշɹ
ͣ
˵Ƶһ𣬼͹ľ
ѧǸһȽ𣿡ŵ˵

⣬оǶ٣
һ׼ȷ˵һʮһë
ŵ
ôôأ
ܰɣôҲڹҼĿô㾭ѣ
оѾͲˡڴѧĿѧķѧ⡣ûЩѧĿǮܸô㲻ˡ
ˣҵˡһӿʽóһǧԪŵ͸һȥ꣬嵥ϵ鶼
˶һ֣һƴֵӡ
⣬ҪӡһֱȥͼݽҲ㡣ȻڱĵطòǮǾȥ飡


ڶʮ ⲻ
磬ŵͼɨ
ﴧһǧԪľ޿Եúʮ㡣
ѧйHelmholtzϵͳĹʽˣ
ѧѧаƪڼһάHelmholtz̵ģҲˣ
ߵѧоһ½ڽ˲̵ĸ߽ײָʽ㷨ͳͳ£
갢󡷣Ҫ˸гɼ밢һ˵кܺõѧϰ塣ųŵ˸²ȫס
˳ţһһ׽ŮԵ־鼮ֵҹڴʱϸϸƷ
أ
˵гصһ飬ɿڡ
ˣˣ
ʮ౾飬ܼƻٶԪȻִӸľߵһЩװ塢ݸֽԱ֮ıҪľߡ
˸ԵжųĶ
һǧԪĿѣʣٶࡣ⻹ôһѶĽ
Ȼѧϵ൱ʡǮ
һǧԪĿϣ˻ƲɡɶѧĿ˵ֻҪֽͱʣʱټһ̨ԣܽһС
ʮͷǺܶĨһѶͷϵĺˮվ·Եȳ
ʱ˶˵ĸ
~~
ҵĿ
Եÿ춼~
~~
Եʵݣ
һλƤڣϸǷͣ׵Ĵһ̯ӣǰ
Сˡ
ɢŨͬѧһ¿ˮ
Ǻö
Ǯһߵ̯ǰſˮʵ
ԪһʵݣСҪ
˴ɣˣҲһƿеʡ
еģеġ
罫õϵİ˸һƿϵݸ
أóԣ
ҧһ¶ı飬޲ڵĴָϰ壬⿾֣ζ
̲סҧһڣУӾ׽ڳݲ˵ϰ壬ȻĿôóԣôȥЩѧУſȥǱӦñ׬Ǯɣ
㲻֪ܸ֡ǳ԰ҵĵ˵
ֹͣеľ׽ԼֽʣǸǩӣ
ôҲǸۣ
ѧˣŵӻ֡
ʱپὡˣһߴӿڴǮһʵϰ壬һǮ
һʮˣֱӸҶʮɣˡ
á㡣˵ţһŶʮԪĴ󳮵ݸ磬ŲҴҵߵĳǰϳ
ӣѾʻ˵غԶһڷһ
õģѧϵİȻĿǮ

ΪǮ¼һֱڼΪѧŵһ·϶ԵƲ֡е㻳
صѧУڳŵ֪λѧģѧնʱܴӸղŵĴлֻܰľ߶ŻصԼᡣ
Բۣŵ㲻ǸɣôණɶŵûһѶԬⲻҪС֡
ŵĨһѶͷϺˮЦЦȻѧϰҿɲһڳԼ޷԰ΡҿһλȰѧϰĺѧһ첻ѧϰҾͻܣ
Ԭ
Ǻǡ
Ҳ֪ǰԼʱˣһͨǸ˭
鷳¸缸滹жûаæŵ³ʱѧԼļ͡
û⡣һ̵ĳſһߺͳŵһ¥

졣
ڴ󲿷ѧĹڵʱ򣬿ƵĳŵòͶ뵽ĿоС
ŵĵһ֣ͨһάHelmholtzϽ²ָʽƳάHelmholtz̵ϵͳ
ڿܵУ򵥵Ĳ֡Խ˶񽻸꼶Сĳŵ
ͬʱһҲĲ֡
ŵCCDϽ²֣ʽɢάHelmholtz̵õϵͳûĻĸֵĹɸܿչ
ϾĿĿƣоάHelmholtz̵CCDʽ
ѹɽ󰡣
ǳŵһνӵô߱Ƹ
ǣΪʱµñŵñ岻ݴǵֹԼ
Խ죬ŵһ硣׼ʼһĿճ
ΪװƣŵҪ㾡ȫ
ỷ̫ͼ̫ԶҶ̫࣬ŵԼܲ
ǳŵһѧУһҡɡһ̨ӡ
ȻгԼãĿ£лͳһ
ݸֽԱʣԲ棬Ƥ
ɢѧӦá
֤뷴-ѧзֵ߼
RichardsonƷӦá



ڶʮ ϲ
λ廪ѧҽԵС
ŵһѧʷóȻԱ߼λԼҵһ±ƵĿУ϶󣬴򿪵ԣһwordĵ
άHelmholtz̵Ͻ²ɢԤ
ŵı档
֣ָŤŤӡŵ˶
ֱߣһ߰˱Ĳοϡ
ֱߣǲݸֽԱʣֱߣƤ
¾㱸ֻ
ŵû˿˷ʱ䣬ļƻһʱ䣬ǲֵ20%
ʮһڹҪϿΣҲӷæŵʱ䣬
㿪һסѧȥŶдĶеŵһ߿ʼĿ⹤
ǰϣи˺ܿᡣѧԵ˭·
ѧһֱڿ飬ϲҪܲ

ѧԣѧԣȥѽ쿼Ե׻ῼ
ѧѧ㲻ҪٿҲǲסѽ
ŵһкߺŸʣһ˫ڼžĴš
CCDʽɢһάHelmholtz̵άHelmholtẓҪŪһάHelmholtzεСﵽ׳ʲôģ
һǰиĿרоһάķȵ׽²ַġ
ԹһάHelmholtz̵Щŵֱӽƪġ
ȣDirichlet߽һάHelmholtz̡
f''x+k^2fx=gxxʦ=01
fx=0ʦ
kʾ
ţѶ򻮷Ϊ
ŵĴԷת
ڳŵֱߵ߰˱ҲŵطţѰҪϡ
ֱһݸֽƽŵϲ⡣
ΪǸ߿ѧϵʦϳЩĿ̫򵥣ֵóŵáݸֽѧԵѹױ
ڲһˡ
̶һʱ䣬ŵѾʮŲݸֽ
ÿŲݸֽϣó˿ǹĹʽ
ĽȣҲſϲķչ
ŵȻȳ˸ߣҲδ˵ĳ̶ȡ
ŵֻǴһΣŵûһһõ⣬Դ߿̬ɵĸ㶨
Ŵǿ֧ţŵǳƲϣҲɡ

ڡ
ŵһĴڣﲻ˵ע⡣
ڳŵλþпſڵһ顣ÿ¹˿ţ·ŵǱʱͻע⵽һ꼶꣬һ߿ٷ飬һдд˫ֻʱü˼ʱȻһЦ
ʱʱЦһ䣬ǣԭӦʽɧ٣

ѵҡߴطˡ
Ҫ԰ѼĹ˿һ±ơ
ȻҲ˺棬ߵŵ뿴ŵһﵽڹŪɶ
ŵһ飬ޱȵĹʽ󡭡
УУ
RBQRBQǲ
ǣͣ
ڳŵѧԹ⻷£ѧԶˣ

磬ŵûˣֱӶ˸
ǣҿһᶫȥŵԱǸǵļЦſڡ
ڳŵԱߵǸһݵӣ۾ɫơ
ģһλߣ䳬ġߣѡ
Ǹһ綼ԼӲһԼϷһɡϷ
û⡣ѧԴУԳŵ˸OKƣȻӣֹеˡ
ŵʱ򣬼Ǹ棬Ե㡣
ŵһƨλߣŤͷ˵ǣõֽ벻ġһר˵ġ
Цˣһ棬պ壬ǺǣǸרô쵽ˣں
⻰ŵ޷
˵ˣ˵ˣԷԷ
ŵ֣ſˮĴӡ
桭һͰ档

CCDʽɢһάHelmholtz̵õ£Af=oң/bb;
žžž~~
ڣɵָû̵
ֻ棬ѧ
f=[f1f2fN]^Tf'
ڸ㶨ˣ
ŪߵӣŵCCDʽһάķȷ̸Ūˡֱɾ͸
ʱһάĸŪû뵽״ֱ̬ӽʱһ롣
ô죬ͿԿʼάĹˡ
ҹͽ٣ĽֵϣѾƻͨ
ŵżԼд̫Ͷ룬ûԡ
ŵժ¶һ̧ͷŵм˶ûԣһ̧ͷе̨
ϲŵģLPLְҵܾ
EDG V RNG
ȷ֣12
ʱѾľֵĩβRNGռݾơ
˸ߵţзˣƸߵأ
顪
ˮһ̣˵˻𣺡ǡ
ϲRNG
ɣȫڡ


ڶʮ ֻбΣ
Ϊѧĺܿ
ǵģѧԵĿ󲻵
ժԡŵ¼

죬ѧ½У
廪У԰ָյ
ŵһ飬ԭλãʼһĹ
˵㣬ǿ˵㡣
װƵĸоǡôĺˬ
죬ŵѾCCDʽɢһάķȷ̸ˡ
ǸӸѵһάάĽ׶ˡ
ŵڵǰüͷһתűʣһԺв̽Ѱ߽Ĳ衣
ӴԺвϵĽײ
Сʱ󡭡
ˣ
ŵֱͦ壬ʮָụ̂ԼС
һάתάһx꣬תΪxyƽꡣôڹDirichlet߽ĶάHelmholtz̺󣬽лΪȾ磬õN^2㡭
xiyi=i-1hj-1h
ԺУ˼׷ɡ
⣬ͺñһߴٵŮһֻҪĵһſӽ⿪ʣµ飬ˮɣ
žžžž~~
ŵ˫֣Ŭ
ͷϣ֪ʱѲˮɳŵȴδֹͣ˼ڡ
žžž
ָû̵

ʱ֡
ŵﱬһ죬ƣصҡ
ѧⶫŷʺ봽вͨġ
ֻбΣ
첻Žôѧţİͷ
죬ŵͨ˵ҲҪŲסˡ
صһƿ֮󣬳ŵϴۣϢ
ҪָϿˣŵ״̬Ա飬Ͷ뵽ѧϰΰּ޵ҵС
ڿ⡭
ŵҲʱС
ıΣŵѾһֵĿ50%ҡ
ʣµģһܶʱܹ㶨

գŵڽֹ̨ͣϵһλڽšߵѧݡ
ߵѧǽϵڴһѧ޵ļŹγ֮һ
ſγڴѧеѧγУȻƲ򵥣ȴĿγ̡
еĹרҵҪѧϰ˿γ̡
֮ǰ˵ģſγڽϴá֮ɫ䡣
ɶԳŵ˵
So easy
Ѿѧϵרҵγ̵ĳŵڸСƣʵ᲻ʲôȤ
Ӧú͵Աһ£ǲԺĸγܲϡ
ߵѧ֪ʶڡѧѧ
ߵѧۣԵ֤һԪ΢ֺͻ֣΢֣Ԫ΢ֺͻ֣ȳ΢ַ̣ռΣȡ
ѧʵۣǶȣ½ָףвʵŵģۣԵ֤֤һԪ΢ֺͻ֣Ԫ΢ֺͻ֣ȡ
ǲġ
ֻһעؼ㣬һע֤ѧѧȻҪһЩ
ʵЩĵĳŵ˴Ƿ϶һ֣һ߼ڲݸֽڿļ㹫ʽԼ衣
ڽ̨ϽϰĸʦȻŵľٶС
½̨ŲŲŵߣá
ˣ
ŵŤͷվߵĸʦһ߶µժ¶
ʲô֣
̡ŵ
ãŵǰɣϿβľٶҸʮʱ䣬ѽ̨ϵǵ
ŵ̧ͷڰ塣
ȻںڰϷдһĿ
Cļ귽Ϊr=asin/3^3Cȫ
ŵ΢΢ü
ʦĿĿģΪ̵
ʦŵüģΪǳŵˣڣҲΪ㣬ֻҪҪ㲽衣ʱ
3/2aС
ʦ
ʦǸʼֻδڣͱŵӲС
ôٶȣ
˵ʵŵĴٶȣʦʼδġ
Ŀ򵥣ҲҪ롣
ɳŵˣֻһ벻
ֲ˹
ʦԳŵòĿ࿴

塭
¿졣
ŵһʰһ߿ѧϵĿα
һڸߴ߰˽һڽ⼸
ңһΡ
ڳŵӰʱһӰڳŵǰ
ŵͬѧ𣿡
˵塣
ŶˣĿǰŵǰİ೤ίͷŽΣ
ԣ뽲
Ů죬ŵ֮
һ̬ġϾҪˡѧԺ׼ٰһᡣҪÿҪĿ
߿ԱһĿǻһŵͬѧ˵㳪費ҲһĿ
᣿
ŵĲ֪ҪٰϢ
ңŵָָԼ
ԣЦⰻȻĵͷŵΪίӦģͷáֻͬѧеŻߴ
ңμᣬҲнģһЦ
ŵһѧ𣿡
Цҡͷһָһ±
ŵ
գİٰȰ˵֮£ŵڴӦ̨ݡġ
Ҫһ̨ࡣݳЧﵽܰҽ赽ĻҾʹӦϳ
忪ڣû⣬˵ɣʲôȥѧѧ衣
ŵ³֣


ڶʮ ǰ
ũʮ壬Բ֮գž֮ʱ
ѧУһڣѧԺ¡ٿ
һԺѧղٰ֯أҪĿģʱƯѧһãܵ¶
γŵ2020ϵһĿ
һĸ
һǳŵĶࡣ
ͬѧ½
Ҳô¡أĻ϶ѧֻʦԵúɡ
һһŮλ꼶ˣһ¡صװŻͲ̨
ӭѧԺֳ
ڴˡ
̨ϣνܵҪ
̨£ŵͼλںţ±
ŵ㲻нĿôȥ̨׼Ԭơ
ŵʼ磬ǸĿ󼸸úܣ⿴һ
˵ŵ㵽ױɶѽǽ£Сơ
ŵһЦʱǾ֪ˡ
ŵʲôŤͷ˵ˣӣ£һ̨ϱݵʱֻҪһƣͽһ֪ɣеԽԽã˵ţŵѸֵ̧Ķ
Сһ±ơ
ԣûңǧˡŵѡ
ˣῪʼˣǿĿɡ
Сӻ׷ʣŵһ仰ֱҭס
廪ѧÿѧѧԣⲻζֻӡ
ܸߣԲռ
裬裬СƷӼħϷ
һĿ֣óŵ಻ѡ
һѧᣬӲıŪǴһʡ
Ȼ廪ѧǸԻĵط
棬һϵѽͬѧΪǴǰ̨ϱĻ
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ŵֱ壬̧ͷ̨ϡ
ԱҲߴߴ
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屾һӣھĴһȻ;һѡ
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ҳϳϿҿҡ
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ŵҲжĲҪҪġ
пܵĻҲص˵Ǹǰ
ǰɫ
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Դˣŵʾʮʹ
ŵˣȥ̨׼ɣӺ̨ϯѳŵ
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ŵŶһԼЩŵ顣
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ŵ߳ǰ׼õϡֳֶϡֳٹϡ
Ȼŵˣٹһ
~~~~~
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ˣ˲侪ˣ
̨Щ˯ͬѧǣֱӱһĶѡ
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~~~~~~
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ŵҲѾ賿ֱ࣬ӽоĳɹ
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ͬѧǶʱæдһƪġ
һƪSCIġ
Ҫ֪ĶУѧSCIĵķ൱ġ
һЩУ˲ŵĿSCIĵķһҪĲο׼
һ˵ڴѧ˵ÿһ귢һƪSCIģܹΪһ
һ˲پ롣
һʱ䣬˺ܾãŪһƪSCIġصһʡ
ͷ˽һ٣Ӿһµʱ䣬дһƪΪ൱ģٴͶ嵽ϴͶǸSCIڿAPPLIED MATHEMATICS LETTERS
һĺѧڿ
ӰΪ2.333СѧӦѧ2һ൱ڿ
һƪıķȵƪӰֻ㼸SCIڿ
Ͷ塣
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ΪƬģ꼸һٶûгȥˣһһ⣬ֻдһƪSCIģԼıƸ
ɽ
Ͷ֮յڿ༭ʼظ
ҲûдһξͨSCI塣
˵ССһˣϽڣͶSCIĵʱҲᱻһЩ覴ãСޡ
һƪģСΣ۵ĲҪ֮󣬲ŵ˳
Σ
༭ֱʼָгص߼
Ҳ˵һ߼֤һ֪ǶǴĶ
˵ĸǴޣ
ߡ׷ġ
ܰ൱ܰ
SCIĵˣѧ2༭һѧĴţڣ϶еȥƭСһ
˵ģȷʵ൱ëġ
µѪȻΪһ˭ﶼܡ
۵ǣ༭ûָеĸִ
ֻ˵һ䣬дڽϴ߼󣬲ڿ¼׼
̾˿ֵ֪ѧҵĿദ˰ɣ
ŵĬŮᡣ

ڷߵ飬ŵǱʾ΢еͬġ
SCI˵һУжƪSCI
ȻܶдһƪͶдһƪ
ŵѧ׼ô죿Ǵģֱ
ܸĵĻҵȻİɹؼǣôİҵĿˣûҵ༭˵Ǹ
Ҳơ
пܵĻǲԸƬĵġ
ģٴηĻᡣ
ֱӷĻǿɾûһ˿һĻˡ
ǻصǸʵ⡣
ͬѧ֪еǸ߼󣬳ںδ
ƵͷͷQQϳŵһϢ
ŵѧҪҪҰ㿴
㣿
ŵԣѧܳɲˣ͵հհˡ׼SCIĵɶġ
ǡðɡ
˵꣬ŵյQQϷһļ
ļ⣬ĵơ
һ΢̵ַĽⷨ


ڶʮһ Сּ
һ΢̵ַĽⷨ
ŵ㿪ļϸж
һ̵ĽⷨѧϵһĿγľѾѧ
ŵǵòĻ΢ַ̣Ӧʹó׷⡣
һΪãҲǹΪԼ΢ַⷽ
׷˵΢̶ַӦ΢̵ַĽ⣬ٳ׵õ̵ʾ⡣
磬΢ַd=Ftdt+CtdBȽ̸дΪd-Fldl=CtdBӦ΢ַΪٷճ΢ַеǡӷյõ=ء-`񣩡
ôʵǴ򲻳
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һֱһֱõĳ׷Ľⷨ
˵ⷨı֤ʵʵõĻǾԻ΢һСģ𶯡
˵SCIѧ2ڿѧ1ĶڿԻƬġ
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ڶʮ еĴ
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ŵӿڴͳһʣĵĵڶҳһʽصĻһᡣΣ衣ѧôǰǼʽƵʽӵأ
ŵµǸʽͽⷨʼļƵʽ֮һ
УдһBlack-Scholes΢ַ̣磺dE=E1udt+dB1
д΢̵ַα΢ַ̣dE=EdBʡ
һfx=cte^B*tһ󵼵ĺֵСֱֵԭ̵α΢ַУ⣬Itoʽ΢֡
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Ϊŵ˵ֵǸƬĵкβ֡
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û취ֻʯ£ͼ˺ƴ
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ӽʯǣһſʯ£˫ϥţ˫ֳŵأͷһ˫ȵסҪǣſʯµǸͣǰšһ΢㣬һˬı顣
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пԼˡڵȻ˿
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ڶʮ ڲã
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ŵָһ
һ֣ϵBlack-Scholes΢ַ̣dE=Eudt+dB
ڶ֣ʱϵBlack-Scholes΢ַ̣dE=btEdt+ңtEdB
֣dt=at+btdt+ctdBt΢ַ̡
֡
ĺȻ֪дԵ߼󣬹½ⷨĲ˵ȷŵͲסĺģΪ˼޿εʱ䣬гһƿеĵ·
ۣȻ󽫽ܽᣬóսⷨ
ŵΪ˼·˵һӦα΢ַdt=ҦtdBtʦt=ceBtóףȻItoʽ֡
ڳŵûоʱȥùʽһļ㣬ֻṩһ˼·
˼·ȷ񣬺ܱǸŵҲ޷֤
ѾǳŵĿǰ뵽ģаյһ֤
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ŵ˵˼·ھϻȥһ£ĿеĻƬĻܹȥȻѾ¶͵ı飬˫ȭգɫ˷ܡ
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Ҫǳŵæٸһܵʱ䣬ҲֲдڵĴ
˵һոµ˼·
ŵΪ˸͸Ƭģһҹû˯
ӴĹҪ߰˸СʱŹã
ͷĺѧܣѾټ˰
ĸж
ˣ֮ͶѡŵЦʼ硣
Ϊ˼θУŵⲹһ䣬˵Ҳûöʱ䣬Ҳ˼޿ζѡŶԣ׼ȷ˵һڰΡ

డడ
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ɳŵǱߵãֱһڰθ㶨
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ϣѧԺ߾ͲռϷ硣
ŵһͽ˴˫򣬵һֳվڳŵǰͷԳŵ˵
ң˫򣿡ŵָָԼдɻ
֮ǰѵǰʱһֱǵͻȻȥ򵥴򣬲óŵоЩ⡣
ͷԡ½ˣֻʱȥˡ
е£ǽϴ˫Ĵѧ
ǰͷ
ŵΧһۣȻûзµӰ
ŵЩԥֱӿڣŵֱӸңваɣ
УȻУŵʯվ𣬡ô˵С
İɣһ˫һѶ̬

84֣ѧԺVSѧԺ
~~
˫ѡλڲмϣ
˫һ֣ѧԺɳŵͽս
ͳŵһ죬ͬǽĴһ
ֻŵǽϵǾϵ
ŵֱҪʲô𣿡ϳǰߵŵʵ
ŵ˻еģЦſڣɶɺþС
˵꣬ŵķŵϣأһ°ıӰ

~~
𣬵һС̣ŵߵķȨ
򡣡
ŵûиɵĻᣬԺݼϣ󡭡͵һӣ
顪

ı̬ѡֻ̫٣ССĴѧһʵס
ڶԸѧԺͨ֡
򣬾ӣ
ʽһʱڳŵֻܴķ
ԳŵСʱܼס
飡飡飡
ļֱӴĶƢ
ôٵĳתȥӵûС
ѧԺˣĨһѶͷϵ亹һ³أڽ˵һС̵ļ尾
ֵǵıʱˣ
ѧԺλѡֶһۣЦЦ
ڶ̣ɻѧԺ
ѧԺиǸ߽ϸߵŵеʾΪ191.25ס
߶ȵѡִ˫ʵ൱£Ȼơ
飡
һ򣬱߸
λã롣
ʶǰ
ֻʱһϤɺã


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ɺã
ŵڽʱʹģͣǰĶ
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ãǸ߸ŻָųŵԲд˵У棡
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ԹȺҲɻĿ⿴УǳԵ֪ʶ򲻹ĻӦ㷸İɡ
ŵȻ㣬ǲܵ÷ֵĻƺҲûʲôá
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ղſֱֱĳ߷ΪԼҪأ
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ȴǣڵóǿ϶Ƿ棬ʵûë
˫Уǡδ򣬵ĵȷȷڹķΧ֮ڡ
֪ĳԹȺѾ̾Ŀŵ
ɧ
ͬǾȴΪ㣡

飡
30-0
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̡
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ȫΪŵѵĽȴĺܡ
˰ŵ򣬾͸ɶøɡ
˫Ҫ˫ϳ뵽Աȥˡ
ѧԺ
Ļ뾪̾УŵķڼϣһӰ
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ѧԺıʮڽ
գѧԺ32Ӯ±ǿ
ĽѧԺĶ֡Ժ
ŵαһս
ȣŵıֲԼͽҺãװƿܻٵȱϯ
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ŵˣ
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ŵЦŵͷİɣƱҿһҪõģ

˫ѡ־λ
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飡
򻮹һߣŵߵĳء
ŵһЦһġ

ѧԺ㣡
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̣ȷ4015
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һ̣ǼԺķ֡
ѧԺȫסĿڱϣĽ
飡飡
֮Դһʧ󣬽ߡ
ŵⶸȻһģѸٳǰ
ŵֳģ߸Ծ𡭡
ϸ߾֣Ĵ󺰡
ѽ
꣬ϱ˹⣡

ŵû뵽ѧԺȻܽ·ϣһ߻ֱۣһ˷ܵĶԳŵ˵
ŵЦЦڣȻû⡣
ˣξĵصģỹǸ򳡰ɣ
ҡҡͷȻǡεǻڵϲģȻѧУٰ졣
αĵص㣬ھʯ򳡡ҲǼµ׽ְҵʦĳءͬʱ4000ˣʱ򣬸УԳϯε
룡ͦ߰
ǵȻҲʲôѧ㻹ǵϴθһı𣿡
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ϢѾǴˣѾ֤ʵϢˡ
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Ӯ峡Ҫ
ҪŰĺܲң
ЩְҵѡֲóȫʵԵͺˡ
ŵʼ磬ðɣǾʱʲôʱ򣿡
³֣

һܺ
ʯ򳡣λھйģǰͶʹã򳡵Ӳʩκһǿȫģ򳡹ݡ
죬廪ѧһ5000ݾС
ͬʱ̨ʵʱֱ


ڶʮ ھ
5000ֳڣӾ̨ȫֱ
̣˵ʵŵǵһ
֮ǰڡǿԡϵǴΣҲֻмλڶѣһ¼
һΣʵʵڵֱֳ

˵㿪ʼǾ½½Ӹʯ򳡡
ȵŵʮ֣ʽʼʮӵʱ䣬ǧλѾ˾ųɡ
ǧڣ󲿷ֿɲΪλְҵѡֶ
ǡ廪ѧ
廪ѧѧڣε˶Ĺǰ

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һţҽѧԺᵽС
ÿһҽѧԺѧһηѿ̬
ˣǲƴɱõᡣ
ŻɫӷҽѧԺɫӷľѧԺȺ볡
˫վڳ࣬Ѻ֡
ͬʱ̨ͷ׼򳡣ʵʱֱ
֧ԻصϢ
ŵһ㻹һϡҪǴ򵽾ʤ֣ȫˡ
ݸŵһƿˮڳŵ߿ڡ
ŵЦŵͷû⡣
Ҳұֻ֤ҪϳǾ;Բ䣡
áͷǽˡ
Ľ̺ܿ졣
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ڶ˫ҽѧԺʤ
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ŵ̤򳡣̧ͷŹϯѹѹĹڣԼʱʱĻвп
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һ̣ɾѧԺŵ򡣡
Ĳһƣһ˵
ŵĶ֣ҽѧԺһ۾ĸ߸۾ӣý׼
ˣ
һ򣬳ŵֱһϡ
ȻҽѧԺλ۾УȫûӦ֮
֮ǰ˵Ҫס򣬼ְҵѡ֣Ҳ޷
˸֮⣬廪ѧЩֻҵ༶ѡ֣ȻǺм֮
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⡭
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ɵڶĿųŵٴδ
ûˣȷȷʵʵ
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ŵ򶼽Ӳסⳡˡ۾ű
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ѧԺӵˣͶԳŵƵϤĲϤ
ԣڳŵ򣬲þȣĺ޲Ѷ
ڹϯϵˣûбֵ㵭Ȼ
ǿ򰦣
ӵƷ򰡣
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ʲôܳ𣿡һŮͷơ
㲻Ǵģһഺһ̾

ʯϣڼѾû̫
˵ŵ޷סĻǸûô
ֱֳڼֳмǧ˿أŵͲҽѧԺǱŰ̫ҡ
ŵֻˡһܣֳڴŵó򼼵Ĺޱȡ
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佱´ǣ
ŵ˰佱廪ѧĸУԾǰιѧԺĸԺ

Уº͵Ŀڼλϻɨ˵˼䲻֮󣬱㽫ݵŵС
ĳŵļ򣬡ûǴǽгŵǰɣ
ŵû뵽У˾Ȼ֪Լ֣еС
ͷţϣԳΪԽǰŵ
ˣ

Խǰŵ
УʲôǳЦĳŵļ򣬡ǽĸ߿״Ԫ廪ѧȻһѧϰΪѧУ棬ҲϣѧǶ룬ǿ塣һģͷãܲԺ֡
ŵԹԵͷ
ˣһбúü͡
һ
˵꣬У˳
̨ΪŻͲ佱õĸ̨ϡ
λż뿪ϣǼбαĹھ飬λְҵѡɵְҵеľʶԾ
棬λְҵѡֵǳ
λְҵѡ֣ڴν
ԻӢ׹޲-ж˹ı-˹塭


ڶʮ սְҵѡ
λְҵѡ֣λԻλԵʣλֱԵµ롣
ϣλŵϺŵ
꽻Ʊ
ݵĳɷԶھĳɷ֡
ãᣬΪµ׾ٰʦơ

һ֣ѧԺɽɵ˫϶󻪹λְҵѡ֡

лأ
ڻλְҵѡֿˮ£˴Ĳֺһְֺҵѡһϸµ˼
λְҵѡҲʮ˵װƱݡ
װƵңڱݡ
ֱˮʮʱѡֲóְҵʵ
ϣǿĻ򣬾׼ԤС
ҵѡְֺҵѡֵĲడ迴ϱĻĽ£̲סЦŤͷԳŵ˵
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öߵ㷢ŵһֵˣѵһ㲻ĵ𣿡
ŵһĪɶ
ȻǵıŰ̫Ұѵ㻹ְָҵѡִ忪
ǵǡ

忪̫ˣʮ㿪ɡ
Ųһ䣬ʮ
ˣѧ㣬εĶ˭
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ŵһ
ǰĳȻְҵѡȡʤȻ˵ǷˮҲܷˮҵѡ֡
ŵϳˣͰǰĳŵļ򣬡ˣһŰ̫ҵĻǧ203ְ
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λְҵѡϢеָʾϵƺֲһĨ⡣
´ϵĺסͷһߵģȽϱء
ƺֲĿ⣬򳡶ǸɢӰϣǹһĨмЦݡ
廪ѧѧ
뵱꣬ҲڵĶѧſԱ500״AVĿģ
ˮڵģ
AVĿ鼸ľ飬ˮǿŮ˵רܡ

ǰ˫Ѻ֡
ŵƺֲߵǰ
ֱһóʵˮƺֲӸµĿųŵӢ˵
ŶŵֻǵӦһ
ڵھšƺֲΪŵԼʵ
ͦáŵһ֡СҺܿ㡱Ŀ⿴ƺֲ
ûʲô˵𣿡ƺְֲȭ޻ĸо
ȴһ£㡭ز𣿡
زɶ
ǿûˡȻˣҲˮˡ
˵꣬ŵصأ΢΢ףýơ
򳡶棬ߴƺֲ˦˦ֱۡ
ˮǺǣԼʲôˡֱ
飡
ƺֲޱһ򣬾óóĸٻ
⡭ƺ򣡡
ְҵѡϢ˶һۣԿƺֲһǺޱһ
ˣ
λְҵѡͬʱðһ뷨
ٻ򣬿ƺֲƷʽϣҲֻвɵİܽס
öֻһҵ༶Ĵѧ򣬸ûܡ
ɶȻ
˵ͫ͵һ
ϣ΢΢׵ĳŵ͵һ̧ͷ
࡭
ŵٶȿ쵽˼˻Ӱ
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ƺֲʱ򣬸ٲأ𣬶ֱŵܡ
ƺֲһ±ƵĿŹԼµһʱ仹ûת
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ҵĸٻôܱһѧɴ
ɺϣһɺϣ
ƺֲ˶𽥱
һα߸
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Ǹٻ
ŵЦЦһ໹
໹ػػ֮һ淢ĸٻãɸ򣬴ʹغٵ𣬶ֱŵܡ
⡭
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ңǲԼʵ
ɣ
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飡

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ڣ
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飡
ߴһػ򱻳ŵ߸𣬷򳡡
ӷй켣صڵ߸
򡣡
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ɡ
Ѹأصĵص㣬ֻھֻһֻλá
ǡ½ػ
ŵ÷֣ȷ֣400


ڶʮ Զأ
ôܣ
ƺֲͫ͵һ
ǳ򣬿Ϊʲô
ƺֲһȻĿ⿴ŵ緭ˣþòƽ
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˵½ػܹġ
ֽһ֮ͻľ׼ؾ룬ȵƿأ̵˵ĳ̶ȡ
ӦáҲɺϰɡ
ƺֲɬ촽˫ֽģֻοԼ
һӮģһӮģ


ŵϥأƺֲȣֱӽĿɱ֮ǰػ
ػػڶʽ
ƺֲĿޱȵĿɱ򣬱ŵԸػ
~~~
ĲĦ
ʮĻƺֲҧɫǺ죬þȫɡֻͽ͡
ŵ÷֣ȷ450ŵӮõһ̣
~~
ƺֲŴȻĿʱʱڳŵɨ
໹½ػ
еʽ
Ƕְҵѡ˵ѧһȦռһϯ֮ء
ɳŵֻһС̵ıͳ
ͻȻƺֲԺðһֲͷ
ʽǸһᶼɣ

ڶ̣˫أŵķ֡
ƺֲһѶͷϵĺˮģӣԴ
ڵ״̬һǰμܾʱҪš
Ͼڻ֪ԼԵĶ֣Ǹʲô֡
һߣŵдиָ󣬽
ڣٹڽ΢΢ǰ㣬Աܹϵһһ
Ǻܺ棬һ򣬳ŵǷó
ˡ˵ôڿأõģ˵ȥ
ȻˣǾóһаɡ
ţŵ߻ģ߸
飡
ת͵ҵأͣĦ֮ȵͣڵ档
ʽֽ
ƺֲǰ׼壬ǱͣһֱӾͶ
亹ֹסĴĶͷ䡣
ʼӵ塣
ʱϯҲһƬڡ
֪ǣȻ֪ŵһζʲô
ʽУΪ޽ķû֮һ

ƺֲѡ֣صߴλ
ֱѣƺֲѹ
һھŵְҵѡ֣ôܻһҵĴѧ
Ϊ˴󵺵۹ҫһģ
Բᣡ
ƺֲԼ
Ըڻһǵеʽѧ׵׵Ļܡ
ָоȥһ֮ʧȥھʱҪ

أأأ
ϣͣ
ԳŵĿǰʽʹõĴ˹ࡣ
ԣһóʽƺֲһ֮󣬳ŵͺƺֲս
ǰ취
ŵػƺֲһ򣬲ɽüͷ
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ͣȥŵĵĺܿ졣һְҵѡֱ϶֮١
ˣҲֻʹˡ
Уֻԭĳŵ˵ߴųŵأҽڵ滮һԲ
ƺֲ򣬳ŵŵһЦվԭزһŵء
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ƺֲܵһ࣬ء
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򣬳ŵĽء
ҾͲˣ
ƺֲа뽫ŵĻ롣
ɡǱһεǣţٴھŵһλá
ǡڣ
ϯϣѾϳŵõС
ڣ˵ͨԼתĽǶȺƶֵĻתǶȺȡͨȴȵҰڶһȦڣʹеĻΪһתĽǶȺصһ
ʵеͨģ˵ıУû˿ôȷļתĽǶȺȣӶǡŵԣ
ƺֲˡ
ŵÿһλ򣬶⽫ֱұ߽紦Ҫƺֲزͣܶϱġ
ŵֻҪվԭػľͺˡ
һȫͣܣһվԭز
Ƚ֮£ƺֲбȳŵ£Ҳߵķݡ
ʮӺ󡭡
~~~
ƺֲڴڵĴŴˮֹסĴջ䣬Ҳѱˮ͸ߣҲѱģ塣
һѾһٶغϡ
ûǴʮӣһٶغϡ
ɣƺֲδƵŵڣ
ÿһ򣬶תǶȵԭٴλصŵڣڡ
ʵǰѾ˲༫޵ĵز
ڣֶֻѡ
ˣ
֪ԼѾˡԴһٶûƵŵڣʱԤϵԼˡ
飡
һƺֲѾȡ
ʮӣŵվԭؾû
ǶȻһ̣ŵˡ
μǰ壬̧ģȻ͵س
Bֳ
һԲ׽ٶȣԾһBֵĻߣ͵ƺֲűߡ
ƺֲĿǰ״̬Ӧ
žણ
ء
ߣһ˲䳹ױ
䡣
ƺֲԲ˵󣬱ֱ͸֧ڵϡ
룬ŵ
ƺֲѡ䣬һεʤǡ
廪ѧĳŵͬѧ
~~
ϡ
ʱͷŵһ
⡭ⲻװƷ𣿣
ԣԶԣ˵ǿ֮װƷ廪ˣû뵽⿴
¹ȥˣװƷǸװƷ
ϯϲϳ˳ŵ
ͷУŵƳһ̱ڵصƺֲķڼϡ
Զأ


ڶʮ һܵʱ䣡
廪ѧһƺֲ䣬ʽĻ
ֵģȻװƷŵڳŰ֮س
ȻװƵĿ˶Ϊ˶Ϥζͬĸо
˱ʾŵǸŵǸװƷ
һܺ
廪ѧһС͵Ļڡ
˽һ̵Ŀ̻飬νڲûвμӡ
ڣ֮жڳŵǿĸˣȫһַ̬ˡ
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νڵĻ˵Ŀøõġ
ѶȵĿĿɲˣǻؼֵأ
һֻܾ֮ܿԼ㶨

Ѿʮһµףµİ¶Ҫԡټϸϰʱ䣬ԣҪںٲУĻ֮Ūꡣ
˶óӡõһA4ָֽˡ
ڵǣŵ㸺Ŀĵһ֣ҲǶάHelmholtz̵ϵͳĹѾɡ˲µʱŪġٶȷʵǳҵԤϡ
ҲǱŵٶȸһءһԴǻ
ȱ˵ˡ˶Ƴһۣ㸺ڶ֣ϵĿɵôˣ
ǸǸЩεͷѧҲ֪ǰʱһֱ޸ҵƪSCIġڿĽȣĸǵĿŪһ롣
һ룿㡭˶͵һӣö˵ʲôˡ
ϴϴ󣬱ŵöһ£Ͻϴ㱣֤һ֮ڣŪꡣ
˶ɫΪֱֱֻĶ
Щš
˵ƪıSCIڿ¼ˣѵףһ𣿡ׯѡ
ŶԶԶԣһĴȣЦŶԽ˶˵ѧŵѧܣǽͣףһ£˳ǸλǸ
Ƴһ۽˶ɫݺҧҧʴͣ
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ԣֻmatlab岽ֵʵ飡
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ûǴĻӦǡJournal of putational ahematicsڿ༭
Ҳǳŵһǰƪ̩չʽжɢԵӦáͶSCIڿ
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ȻԼкܴģĽûг֮ǰŵҲ˵Űٷ֮ٵİա
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Dear Chen
We are very honored to receive your contribution.

Your thesis aboutApplication of Taylor formula in determining convergence and divergence of staggered seriesis very goodbut in my opion
SoI suggest that you should revise this place.

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Your paper has been accepted
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ҲˣŵֱûзĸߴԾԾʲôġֱóһſհ׵A4ֽһ֣Ǹɣ
֪HΪGȺPΪGһSYLOWȺHʾʽΪ˻󡭡
֪۰ȺĶָM۰ȺָһMڰŵλԪҾ߷ԣxyNx*yNӼ NԵأNǸ۰ȺڵMĶԪ֮¡һMڵԪeĸʽ
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󣬳ŵӭĸߵѧԡ
¬Ǳ߰룬֮γŵͼûȥڿ֪ʶ㡢ϰϰɶĳŵһŲ֪ġⲻӰֵľġ
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y=arcsin1-x^2+1/1+x^2ĶΪ_______
y=e^2+xϵ㣨10߷_______
fxx0ɵҡ

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Ψһ΢еѶȵһ⡣
fx[ab]ĵfa=fb=0ҡ
˼·ͨfx[ab]Χڵ֣֤fxʵһʹæԪʽ⡣


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ŵͷЦҲûɶΪ߸ߴˮƽʶԼĲ㣬ӦģҲܵſлҡ

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һȺĺ203ڣŵڴз̰
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ڼǰѲúą̃ϸ߹ź
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ڣȫޣӦѧĶţ
ֵ廪ѧѧԺѧϵһְ
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2018ٰĵڶʮѧҴϣ̨45ӵѧ档
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ĵص㣬廪Уڷڵס
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СſڵǳŵͬѧǵĻɡڴһԴϵȴʮ
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ϸһ룬ԼԺҲΪ˵ըǷݲɢ˲٣η֮飬Ծɴڡ
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ͣųҪȳŵ꣬ȴûκεļ
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ŵ˵ллʾ顣
ǡãʱһ̲˴ӳ߳
һǴŹǷڲ輸ϣ˲ͷϵ㺹Իվŵĳŵ˵ǼվŸɶϿ³Էɡ
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شʦ˵ˣ־ͽйp-Laplacianӵ˫ͷ΢̵ַĵԷ
йp-Laplacianӵ˫ͷ΢̵ַĵԷŵСֹ
ǲǸоһ±ƣ˵ʵҪһûоʱ֣ҲԻȦڣоҲɡڳŵųԼһμСѧǰĬĬװ˸ơ
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ʵ¬Ǹ󣬳ŵȥ˽һ֪ⷽʶ
Խ˽⣬ŵҲ֪ΪʲôѧԺ¶оĿôҪ
p-LaplacianӺͼȷʵоȵ㲻ӦѧҲȳչĿйⷽҲһƪһƪ
ǣ˵ʵڻĿǰЩйһĿģܹõĳֵ֮١ܹŵѧͬѧϰĳɹǷëǡ
ʴˣ廪ͱУŻѵõһp-LaplacianӷΪǰصĿ⡣
Ȼǰص⣬Ҳû̫ϿԲοһУȫԼ
ӺأǶԻڱ׶εĳŵ˵
ȻҺŷִȵĴڡ
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ǶԺйp-LaplacianӵķԲ̺﷽оƹ.ͬʱ˶Ψһĳ󵥵֮ĹϵȻЩ֪ʶҵһЩ룬ʵʲУõַҲܸһۡȼ򵥽Ҫо˵һ顣
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ҡҡͷ˵λͬѧùѧƾһȽţƵ֡
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ڵĻ򵥸Ļóŵĸ˲ţͿĿһݵĴսλڣ䵱ԵOBɫ


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λϷֵҫ̵ϴ˯ֻгŵһڵǰһƪƪġ
Observation and characterization of the effect of electron cyclotron waves on toroidal rotation in EAST L-mode discharges5%

Electron Cyclotron Harmonic Wave Heating in Tokamak Plasmas with Different Polarization Modes18%

Dependence of synergy current driven byfor Tokamaks72%



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ŵQQ˽ѧѾѲҪݶժˣ㿴ʲôҪ޸ĵû
ô죿һ𾪵ı飬㲻ңѾʮƪȫ˰ɣ
ŵʲô𣿡

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ʱ䣬񽻽ӣƽֻҪ¾Ҫظһ֣ʱ䲻գҲ˵Ͽԣ
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⼸죬һпʱ䣬ŵͺѧλάFokker-Planck̽㼸ʮ飬һٶݣתɺѧԡ
ͬʱĩŵŴӡõĹڹp-Laplacianӿо棬ٴڼС


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ڹԢڣȳŵŶʱλжѧųź͹ڿɳ˵Ц졣
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ŵзʮҳA4ֽĿⱨ棬ߵ鷿ǰš
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ŵʶƳһۣ淢ֹ֡
ŶŵͬѧıϾͺãһҿǼٿģ̇ͷһ۳ŵЦʾŵֻҪоϡ
ǡڣҾȳȥˣȻѾ͵ŵҲ˼鷿ŷڡ
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ڵĸڵһ裬Сһڡ
еķݱ棬ЦеĿڣķо棬Ѿȫˡ
ܵ˵ڿųţˣ˵ı棬ûʧǣͬҲûиҾϲ
ڴƪгһݣо档
˵÷λΪоͨLipschitzǵԶݳp-Laplacianӵ˫ͷ΢̵ַĵԷڰѱ淭һҳڡ
ʦӦáӦǿеİɣԭԱĹôһ˵ҲǺȷ
·ͨûκһо⣬ֻΨһһо
ڴѧһ򣬸ˡ
ϴμʱ򣬷Ѿ޵ĵ˳ŵоԵĿԣBanachռΪ㣬ͨBanachռͷBanachռϵӼнһp-Laplacianӵݡ
ҪȵĻֱ˳ųŵ˼·ɢ׫дһƪġ
ĵĽùֽܾԵ
ȥ󣬹죬48Сʱҹδߵʱ䣬ϣ뵽ڴλӵķ
ʵעҪһˮ
ԹʣֻҡҡͷȻƪдĺ棬跽ҲϸҪǣķС
׻촽
ʱŵҲڲ輸Ϲо棬һҳҳ
ĬãŻ³һĿָƽ򷽽ڣϿңʦ֪Ҵ𣿡
ʱŵϱһҳδȷ˵ŵЦſڵ
ɷλ֣LipschitzĳЩʣȷʵԹһֽToeplitzӵӣp-LaplacianӺҲȷʵһûв𡣡
ŵƽĿŹǣѧԵһ㣬ToeplitzӵʶڸӴͿռ²еġ
⣬о˵ľͿռ½۵ġ
ŵЦʼ磬ѧӦûǵͿռĶʲôɣ
Ϳռ䣨XḍָXϸһԳƵdһǸBorelȡЦ̣Bx2rBxr&lt;.Bxr={yXdxy}˵
ŵһָͿռ䣬ָһڶԳĿռ䡣ǣp-Laplacian˵ȴû޶ĿռΪԳռ䡣
ڴˡ
ŵѾɽ͵ĺԹ̲ⲻˡ
Ȼŵ˵⻰󣬹ϵɫ仯һ󣬿ЦĿ˳ŵһۣܽˡ
Ǹ򷽽ڣʦȷʵҿǲܣһ÷Ĵ󡣡
ڰڰ֣Ҫô˵Ȼƪἰо򲢲߱ʵʩĿܣ滹ɺܶණнģںĿойƻõ
ţֵһųźĿⱨ棬͹һ߱ʵʩĿܡ
󣬷Ŀ˳ŵһۡ
ŵͬѧģǻBanachռΪо̵ı棬۴ӿԣǼ˵ĸõġ
ԣҾ鸱鳤λãóŵΣ𣿡ʵ
ûС˻شĺܸɴࡣ
ԳŵĹҲûа㷴Ե
˵һֻдһͣСѧܣĶͷ˾˵ȥЩˡ
ѧȦеְλ߾֮
ʵˣķڷ


һʮ ݴѧУ
йp-Laplacionӵ˫߷΢̵ַĵԷ
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鸱鳤ŵ
Աų
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ڴϣŵҪƿءΪһԱҲҪλжѧѧһͶ뵽岿ֵо
Գŵ˵һȫµĳԡ

ѧ¥һСڣŵٿһμ̵Ŀⱨ顣
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Ǻáŵһ飬Ժноݹһ飬ֱӣĿڣҼ򵥰ѿоֳĸ֣ĸÿ˸һҸܽᡣȣһ֣BanachռӼGǿհ

Сʱ󣬻
ŵüģ߳ң췱ǵǿգЦһ£ѧԲ

תۼ䣬ʱѮ
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һp-LaplacianӵķԷ΢̵ַԵо
ŵǵо⣬Ǻйp-Laplacionӵ˫߷΢̵ַĵԷ
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˵ѧ㣬һ¹ųţǿһʱ顣̣


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οٿĵص㣬ǼСҡ
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ԭʱоǵĽȿ˵ʮϲˣ󳬳ԭоʱ滮
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ŵһЦȻһսݣ
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ûбһѧû̵ս
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οp-LaplacianӣĿǰţоѶȴų̶ȼƥ
ЩصĴڣŵҪȥһ
˭Ǹ־ҪΪ˰
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ڶλǳĸǿѧҪǹڷԷйص⡣
Ȼ̨ϸǿĳŵĳһ仰ǣĿⶸȻһ


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ǿѧҪ漰ΪԷеķߵ˫ϡ
ԣ̨ϷıݣȻ˫йء
ŵѧϰ̬ȣ̨ޱ棬´ʲôϸڡ
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ǸǿܰΪʵû˻ѹע档
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긶ǿǶλɫһȻһƺԭʺڰǰеĽŲǴֿɼĹ
˫̡p-Laplacianӣ˫̣
Ժһ˼·˲Ȼʡ
һֱĿׯǰ
һʱ䣬ŵһֱĥôٶӿp-Laplacianӿоٶȡ
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ţŵ˵Ӹղ̨ϸǿеóУһ̶ȵļ
ҵ뷨һCxt=0gxuou/atDu=|u|^p-2uô̡˻Ϊp-Laplacianӵ˫߷̡
Ҫ׵Ķܶ࣬ŵ˲ӵʱſԼ˼·һ顣
˵꣬ƽ߻ûھѾ̲ס̾
ϾŵǸµģеƣѾŵ˼·Ҫ壬Ǳƽٵġ
ŵ˼·ȷʵ԰ѿĺεоٴһʱ䡣ȥ֮ϰ˼·һ£ʲôĶȥҾСһĵͷ̾һ߿ڶԳŵ˵
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ȻϲǹȻ׼ԼκһϢʱ䡣
ⳡ佱ʱ㣬һʱŵϢ
ڿԼǷҪǸ˰
ŵģȿĿŪ֮ԼһҪ˯ҹ췭ظʱǷľȫ
佱С
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һЩѧȽ֪ʶҲóŵࡣ
Ȼлμһ˶ѧһ۵˼ײѧ飬Գŵ˵൱һƸ
ͷϷʡѧĻ
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˵ĹУλʮ꣬ѧѧң̨콱
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СӣûȤתǸѧѧϵ


һʮ ǽ
СӣûȤתǸѧѧϵ
ƽڳŵ߻ص
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ڷλѧϵĸεǰܻˡ
ŵǸѧѧϵʵԲ廪ѧϵңӦĻֵѧѧԺԵбһЩԴѡһλΪ㱾׶εĵʦƽЦ˵ܸŵġ
ŵɫԵıЩŹ
ڸŵǰǻƵĽŵ
ƣʲô˼
һֱĺƵķڣԼѧѵǽţҲõȥ
ⲻŵͬѧһõѡƽû˿ӣ˵ŵͬѧǻѧѼĺӣ廪û츳õõĻǻһõѡǸѧѧϵ
٣ǵĻٲĵڡҲˣμӻٶλѧңûһʶСһ˭
ȷڵȷʵСӦȥڸĹâѵ룬óŵؾصʱ걾ѧҵ
жξжͬҲǡҿϣгһգۿһλĻˣѧڵĽ
ƽڵһ仰΢΢һ
ǵУƺһֽεĶ
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ڣҲһǰŷֳŵӡ
ƣģŵͬѧҿ϶߾ܵҺһҲܹۿǸһ̰
תȥǸѧͲˡŵע廪ѧѧҲὫǸ仰˵İʮ㡣
ƽŷڡ
ʮһЦʮˣЦ红ͯһ㣬Ǻãϣܻһ죡
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Ҳ˵һ򣬳пԺǼɽļλ»û˭ܱȹҵġ
˵꣬ŵлĻᣬڰ֣Լλʿ󿪿ڣˣ
ҪŬ˰ȺѧĻƽһò˶ãͻᱻһȺȥˣʱ򣬺Ǻǡ
һһٵӰнԶģ̸󳹵ʧ
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ãŵԺĴӦ

㣬ŵϻᡣ
λѶڣ˵СŮװһѵõᣬλ̵ͬȥˡ
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źȦĳŵwordڰ佱ϲͬʱͨʽԡ
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ŵϵԣ˯ʵ˫ۣϴȻе㲻ԾôĵڣλѶû
ŵǳʲô£æӴ绰ֱʣιģ
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ŵڴϣ컨壬ĬĬ᣺ôĻǸأ
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ĽȣҲһǷٵĽǰš
55ţ58%
58ţ67%
511ţ81%
515ţ100%
ͬʱҲ515һ죬Զ֮ļݴѧУ



һʮ ˹MMP
ݴѧУλ׹ɽɽСΪһѧǰʮʷУȻ߳൱ѧ֪׶˹ٷҡ˹÷ȡ
ͬʱѧңʡҲйڴУν̵ľ
ЩͶڲУѧǣЩһһǣΪǵѧУеҫš
Ȼҫˣٵģһָ߰
ƺֻʡ˹УѧǲŻƽȵ۹п
ݴѧУУһ칫ڣһŮͷڲݸֽ֪ʲô
ʱһŲҴҵ߽
˹ǿ鷳ߵеΨһλǰڡ
Ŷʲô£ǹǿ𣿡ǸΪ˹ķ±ʣתЦſڡ
ͷҸղżȻ鵽һѧоƵĿ⣬֣йp-Laplacionӵ˫߷΢̵ַĵԷңǵоҪϰ¡
ѧ˹ɫһӱ
廪ѧ
Ŷġ˹ɫɣһЦֲЦ飬ҵѣҿЦ𣿡
ҿôŵ߽Ϊߵ¹Źѧ߼ʿѧҶӿǼĿȡ
ǣңǵĶǡ廪ѧ˹һʮֻĵ顣
ĿҲλļЦſڣ鷳鱨֮ǰȲһȥ廪ѧѧϵðɡ
ǵĶ֣ǰʮѧУһǰʮȥĶѧ
ˣˣǼ˹ڰ֣λŮǵĹתԿЦңǵĿԤòһµʱͿԸ㶨ˡԻǰѧˮƽڶµʱ䣬Ҳ˵ܸǵĽȡ
ȻײǴˣ廪ѧײĶ˭ãҪǡ˵ţ˹ʼ磬ǲ˼ֻǰ˵Բˡ
˵ľǻ˹ڵ̬
ҪǶ˹٣߹ѧĶ֣Լ߿Ȱ£ǻûκηıҪˡΪûκ
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ǣҪ˵ĲͷðͳָֻһƪţԻ˹ڣ˹˵ǣ廪ѧڽ賿Ѿڡйp-Laplacionӵ˫߷΢̵ַĵԷĿı棡
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֮Уǰһ֮⣬μǹŵͬѧĽܡ
Ȼڻ˹Ĺעص㣬ڲǸֶû˵ĳŵϣǡ⣡
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Ŀǰ˵һѾɶ֡
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˹ɫɫȻͷͳȥ֪ͨһ˿÷ɰɣˡ
˵꣬˹Ĺţͷڴϣĥ죡

һҷڡΪףڽ˵ǿӣŵ󷽵˳Է
ʱ°£ڸ㶨
ԭָʱҪǰһҪֹ
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Ӯøɴ࣬ף


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ŵ˸㶨飬ڲ֪ܲ
ȻƹʵеǷԣԿȵȫŲˡ
˵ĳɼʾ϶֮ڵڶ죬Ҳǳŵ˽ĵڶ죬սһΰѳŵеĹԢС
ڣûѧһŽյĿԼվǰ΢Цŵսڣŵʵ
ΪηڽǺ˵һ¿ݽо֮һЩ飬û뵽ֻзһˡ
ںǺһЦкŵ
ҽ鷿
ŵͷСһͷһ鷿
ڵ鷿ŵǵһνϴγŵͿⱨʱʵ̫ڽţûлϸ۲鷿ڵװΡ
ŵĿ鷿ɨһܡ
ǽڣһһ׸ߵܣһһܣǽǹܡ
ʱڵϣɢҵķżŲݸֽ
棬Ĺʽ
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塭ʮſγ̣ŵɴ۾Ĳš
ѧʱǲѾȥһ꣬Ҫǰշ˵еѧϵƿγ̵Ļǡ
δһҪʮſΰ
Ҫ֪޵ѧϵγֻšѾ꣬õѧֵģһûУ
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ˣŵͬѧѧĿγѾѧˣʡ
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ڵĵͷһ˵꣬˵ڶ¡
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ȫѧѧģɽߵȽ˾ͻҵӦЭᣨCSIAMϾٰһȫѧAѧƾ
ǴӹģǴӾˮƽȳŵ֮ǰμӵȫѧѧҪһΡ
ѡʽȻҲѧе
ͬǷѧǷΪ;ģЩѧУоٰУѡ⣬ıֻҪμһ֡
еĽһȽȫһȽѡȡȫƾһύı
ģСʽбѡõĽҲͬʱ·Сڵˡ
涨ÿģСɡһ˵˸Ըģ̣֣ڹ涨ʱ䣬72СʱڣдһƪдίĽģġȻзֹ⣬ҲһϷֺ˶ǿӵЩҲᡣ
֮һ仰ѧģҹߣͬʱѶˮƽҲһѧ
ңýˣлμȫĶѧһչҵĽ档
ڣ롭ҲμӣһڣŵͲ³⡣
ѧģӦѧһ൱Ҫķ֧
νѧģǽѧԺͷͨ󡢼򻯽ܽƿ̻ʵһǿѧֶΡһĴţ
λڵѧμӹģȡùһĳɼ
ֱûκīĵͷϣڣģڵ˵ЩãĺܶණҽòμӲһ¡
ʣµλѵĻSCI㶼дģȻ⣬ֻҪһ̵ĶѾˡ
ŵڣڣʵҲmetlab
Ǹã·ȥӱˣĽһڿЦ˵
ĳŵӻ᲻ý⡣
ѧģɲʲôMOBAϷ1V3ֲ
¾ô˵ˣģıʱʵѮǵùעһ¡˵ںȻɫһ࣬ݸֽڣ棬˵Ҫһ¡
ĿƵĶųŵʣŵͬѧ˵BSD𣿡


ٶʮ BSD
ѧʦϣ190088ڰٿĵڶѧҴϵݽ23ѧ⡣
ϣڹȥмѧҵǻָۣѧǰķѧչӰƶǾ޴ģ޷ġ
ʮһѧоĿѧίԱѡ߸ǧ⡱
ѧоȻûһǰϣѧһ޶ĺؾ⡰߸ǧ⡱ȫҲûжѧȥǡ˼Ǯ
ѧоĶ»߰ԪĴ󽱻ÿǧ⡱ĽɻһԪĽ
ЩѧĶţںСǮѧУԣӽǮ˱Ͼ
ǡѧң߸ǧѧ⣬㵱һ׷ѰĿꡣȻǧѾȥ˶ʮǰʱ䣬߸⣬ǱֻСӼ롱һʣµģǽΪ
¸͵֮ǰܷ߸ǧһ룬Ǹδ֪

߸ǧ⣬ֱǣNPȫ⡢롢Ӽ롢衢-׶˹Ժȱڡ-˹пɷ̡BSD롣
ȻᵽBSD룬ȻҲڴС
Էڵѯʣŵͷ
Ϊѧ߸ǧ⣬ŵȻûɻ᲻
˽һЩBSD룬ȫǲ˹ɶ-Ų롣
ΪEǶڴKϵԲߣEKEϵļϣѾ֪EKɽȺLsEEHasse-Weil L˵EKǡõLEss=1ĽסҺߵTaylorչĵһϵߵĴʾȷ
BSDǸӵһ룬ѧ綦ĸ°ͺղļ׶̶ȸûȡ
ڳŵѧͦġ
˵BSD˰ص֮ϵǧδ˽һ룬һʵõĶ
ڣǣŵɻ
΢΢һЦҸ㣬ڲ֤أ
ʲʲôŵȵŴ졣
˫ѹЦſڣҪ̫ȡ֤ߴвʲô˵¡ܰǧ֤ǲ˲ĳɾ͡
οĹ֤ϵBSD룬ڽΪ1µBSD롣
Ϊ1µBSD룿ŵס
ԡڵͷڽ͵BSD룬ָһϵİأġɲλԼɳȺоȷĵʽϵǰ벿ָ֣ľBSD롣
ǰ͵¹Źλѧң֤˵Ϊ0µBSD룬ҾȷBSD2
ҲǰſʼһоĿǰĽȡ˵⣬еĲݸֽЦһ£ǧⲻΪǧ⣬Ȼֻǹһ룬ʱ䣬ܵóöֻôһ㡣BSD֤ҿٷ֮һ·Ӷûꡣ
˵꣬ڰѲݸֽݸŵ
ŵԥһ£ûнӹڣѪҿʰɣ
ȻһЦݸֽŵУֲʲôļģȥɡ˵Ұһ£ǺBSDйء
㣬ҹڽΪ1µBSD֣ͬBSD룡
ڳŵսӹڵݹŲݸʱ򣬶ͬװϢ
ңBSD룿
ŵڵеκġ
ʵϢеͻȻ
˵ʵ֮ǰõܵǶʱ䣬ŵҲȥѧ⣬֣ԼӲ豸ʵǲ
һִ廹ûҵĲ񣬾ȥսBOSSһ999ҲǺ޻֮Ժ󣬳ŵͺȥսѧˣǲ϶ۡ
մ㣬ŵ׼Ʊҵо˶ʿʿʱȥһ¡ȴû뵽ھȻԼ뵽BSD֤
֮ǰŵŪͨѧС⣬ͻȻһǧѧ⡣
̫󣬻᲻ᳶ
ŵͬѧŵͬѧ
ֱڳŵ˼ŵ˼Żصʵ
Ŷڣ˵ŵع
ڵŵЦ⣬ŵͬѧҵ飬оô
ŵ룬ݺݵͷɣ
СҲ൱ģ⼸Ųݸ壬ûȥȻ̸顣
֤һһϦ˲һƴĸʱ䡣ѭ򽥽ͺá



ٶʮһ 
ӷڹԢڻص󣬳ŵһЩBSDйϢ
Ȼ鵽ǰȷʵһλղѧңһλ˹ٵĵ¹Źѧң˹ڽΪ£֤BSD룬ǶԹBSDһͻԽչ
Ժѧٳ˷BSD֤Ҫĳɹоһ衣
еΪ1£BSD롱֤ǿBSDδ֤һ롣
ֻҪܹ֤Ϊ1£BSD2͵Ͼȫ֤BSD롣
ⲢûǮã
ѧоǳ׽BSD롣BSD룬ֻBOSSԱߵһСBOSSѣֻǸθˣƷֻоֵûнҡ
ԽϹBSDϢŵԽе㷢š
˵Դӵ0BSDоɹ֮һЩ緶ΧڵѧţͼҪһBSD룬ΪⲢһôԸ㶨顣
ǿֻҪղ˹ٵƶϷѽΪ1´ȥƵһOKˡ
û뵽Ҫղ˹ͬķһƵ֤ĻΪʲôֱӵBSDȫ֤Ϻơǻ͹עȡ
ûôֻ֤µBSD֤ʺͬһϵ
ˣʱȥˣBSDоϷһδ˻
Ǹ鷳Ķأŵϵԣǰϣ˫֣ૡ
Ƴһ۷ϣǰȥǼŲݸ塣
ⶫڹBSDоѪˡ
ݸֽһʮҳ̶ȿȴ쳣
Ϊŵϸǡôĺܶණ͸İ
ǡԲߵLءĪһϵе֪ʶȻԣҪۼӦú͹ʽƵԻЩ
鵽ʱ٣
ŵھĸо
йĽݸϣʱ׼ȥˡٿҲǿ˷Ѵϸ洦飬һЩBSDרҵ֪ʶ
˵֤ż
ȫгǧϰѧС˼ڤ֤BSD룬õһԪĽ𡣵˵ʵģվֻǼˣҲ˵˭о磬ͻȽ
һУԵ֡
Եֵˣ㼴оһ꣬Ҳܱоʮ˸뵽֤

һʱ䣬ŵ廪ѧͼݵĳ͡
ʲôִѧԲߵıעЩǺBSDйص鼮ڿŵӹһ顣
ǰǳŵûϵͳѧϰһ֪ʶһȫһܵʱȥֵĴ鱾мȡ֪ʶǽݡ
һܺ󣬳ŵҲѾܿڲݸϹʽľ󲿷֡ͬʱŵһδĿ⣬άFokker-Planck̵ĵӻģ⡷ҲѾβ
ԺĵӻĿ⣬оֻ˳ݡ˸տʼһʱС鷳⣬ʣµĶ˳
ԺԺβֻͣоı߶Ը˸ѧԺӣһõ񣬶ǿҩһ־Ŀʼ
ԭоڣҲ̵ĸ¡
죡
죡
칦ϣЦ֡
ּңԺĿкܶ࣬˵˲ٽͬһ顣ͨκԺλѧǶԳŵ˳ֵʶ
ǳŵǿ֪֮⣬ŵѧԺһеεĸ鳤ĹǸ飬ѾͼݴѧУǳʱ侺ǶҲһЩ
㲻ϣȷȷʵʵϿɳŵλһ꼶ѧܡ´κĻĻǲѳŵ
ŵҲʱȥ칦󣬳ŵȥԺ¥ڵİ칫ң֤ˡ
ֵḶ́Ƿ˵ŵ
Է˴ţһᵽĶȻǳŵֻа²İˮƽȵġ
Ѫ⵽һʱ䣬𲽾ĸŵBSD֤ĸԣԼģһBSD֤˼·
ȻǴԲ֣ٽShafarevich-TateȺԣóEһи˵ԲߣôLE10rE=0õһBloch-Kato conjectureϣƳBSD2
ܽᡣ


ٶʮ һ߿ʱ
ʱֵ£һ߿ʱ
ȥʱ򣬳ŵڸ߿Ŀװƣ
ڣڳΪĵ·ʸ־š
ֻ̨ǴӸл˴ѧ
ڳŵһԾĿĳѶȣƷ˲ٸ߿Ŀԭ򣬽߿Ѷȥ꣬ǽ˲١
ѧɸʦԲٵձ鷴ӳ򵥵š
˵Ⱥɵĸ߿⣬һѧѧѪỻġ
ףͳŵ޹ءĿѻǼ򵥣˵û
ǣθ߿Գŵ˵˵һϵûС
Ǹԭ򣬳ŵϾȥĸ߿״Ԫ
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ļ򿪣һͷһ߽оĿƣԼKaup-Newell̵Darboux任ķԻ
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Ц꣬ʰöˡ
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ûκԥֱӰ¡ȷ
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ύǸ汾ȻǾһһ޸Ĺİ汾һֽܹƬԭѧģ͡
ˣѧģ֮ʽ
ߵʱŵصؿһۣͬѧڱΣһ־սͷ
Ȼƴŵ̾һ䡣
ҪټεĳŵһɵĻصᣬȻ̣ͷ˯

գ峿
û˯ĽģԱԺ½߽
Ҳ⣬˯СʱĨϷ;Լ֮󣬱ʶŵλӵķһۡ
ţûѵ찾̫ˡ룬ͷæԼ¡
ٴ̧ͷʱѾʮ㡣
ٿŵķ򣬿ǿյλɻ
ǡʲô


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ǣ˵ãģڼʣµ⼸ٷȥʳô
Уȥ
ͷ̹һ֮󣬱ŲҴҵ߳
ӵĹ򣬻𼱻ǵѸٸϵʳãһһ˼׷ĴǰŶӡ
ȻŶӵĶУоվԼ
ʶŤͷȥһϤӰ
㣿ס
ڵͷˢֻɻ̧ͷǣ
ԣǡĲˣӡġˮ顱еһˡ塣
Ȼʱ֪֡
֪ԼЩͻˣֽ͵ҽ棬ǼԺһѧǲ11¥203μѧģ
԰ͷǳɻ
ԥһ£ʳеɻ󣬡ҽ翴һ˶ûһ£ǲʲô鷳ˣ
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˵ȻΪ˵ϾͰѽģĿ㶨ˣ֮Ͳȥ˰
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澪㵵ĳͣеĻ
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ݴߵĻ˼׷һŤͷʵͬѧܰλͬѧָ𣿡
֣ͷһ֣ûǴĻŵ

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򵥵ϴһ£緹ŵһڵı
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ŵʼЦЦģѾǰŪˣʱ䣬صع
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ڳŵ֮ǰ׸Чʿܵ·£ÿĿѾβ׶Ρ
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ԱҪУϺķѰļ˴ΪϲáϾ˭ҲԼʱ಻ǡ
ڳŵģǰ볡¼ֻǾһ֮һƽȥ
ԳŵĿǰֵʵȷʵҲ
ڰ칫ҴһһЩڿⷽľݺ󣬳ŵͼ˸
鸺ѾɣֻҪܽʱһξͺá

715Ű˵㡣
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뿪ʱѾʮСʱû۵棬ԭŵڵλãҵҪһˣߵһ

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ڣھѮУʽĻλԱظҡ
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Ҫ֪ͨŵ㶼˻أ
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ŵΪǹڲ֤飬ԱҴҸϹȥ
~~
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ɣ
Ŷŵ֣칫ڲֻзһˡ
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ЦǺǵĿڣŵ£λԻԺ˾ƵΡ


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˸ϿѧԺһλڷ޽ڵİ칫ҡ
ǣԺ˱ˡ
ŵŮϲԽڼ뵽˹ͬμӽģ£ȷͽģйء
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ʣλǷڽģѡĿB⣬ֽƬƴӸԭһ⣿
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ν˵ʵģÿĿǻѧҵӦЭһЩǿлһЩȵоѵ⣬һ̶ȵļ򻯶
ǱĿһڽܲţһ˾š
ʵֽƬԶƴӼ˾˵ǷǳҪһ˵һЩ˾ѾɹоһרŵĴǹңȴһֱ׶Ρ
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ǣǰҲĵ죬ȻӵһλμξBίļͬµĵ绰˵һƪģģѾˣһҪ
յģǳŵƪġ
Уŵȷд׽ģ򣬲ֻںкеֽƬκʽֽƬĸԭ
ʱͺĴ𣬽һλֽŸԭĿԱճŵṩ㷨򣬽вԡ
һεõԽ
ܹ500ݣ갸ЩԱ˹ԭ
Խδһ
׼ȷ98.57%
֣߳εԤ̫̫࣡
ͬʱҲʶ׳ĳ֣ζʲô
õڶ죬Ҳǽ죬αŵڵ廪ѧ
ż˵棬һذըλͬѧǿ۾ֽƬԭרŸȫ˾ʹá
֪һ׳̶ȵȫΧƹ㣬Ƕڰƣϵܽʡʱ䡣
ϢԤϵĳŵɫ糣͹˷Ʒһ˫ǳ𺳡
֮ǰҪȷһ顣λڣ׳Ƿֻλоɣ
͹˷Ʒҡͷ
ֵ±ˣѵ׳˲з
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ǣǡڰ֣æͣǵ˼ǣ׳˺зģǣɳŵһ˸㶨ģ
ζ˶ǿʹԼɫƽĽЩȻϢ
ǼȻֻҪǰСӵͷͺˡ
Գŵ֣΢΢һЦͬѧԸʮԪ׳̶ȵר֪Ρ
ŵЦź֣ΪҵһȻ֮
٣û뵽μ˽ģиʮạ̣̃


ʮ 鷳
̶ר飬αǡ
ѾҪ˳ŵпţʱ䣬ʮרѱ򵽳ŵ˻ϡ
ۣ
ȥظһ˫ųŵ̾
˷ƷҲ࣬˫ֵ°ϣġ
ȻǴ񰡣ȻԺ˶רܵרǸˣ
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Ȼ֪ڽģз׳ףֱû뵽ܾԺ
Ҳã֤ʮСʱ޸ĳûа׷ѡ

ǴûĻ˰
ڰ칫һ֮ǡ
ڼ䣬ŵҲƽʮרѵ뷨Ͼܾˡ
ܱŵĴ˫ѾĪˣרѣ˻ûôʶ̧ٵͳŵƽ֡
Ͼ׳ȫѪڳŵһˡ
ңڿȻԺɳŵĽģζţģСзǳļõһ
͹˷ƷѾãҪõģһȽĻǱóµѣŵһٴͣ
͹˷Ʒƣ칫ֻʣ³ŵһֱڰ칫Цߵķڡ
ڵһЦдһ˿٩Ϊμνģøһˣû뵽Ū̵ͦ󣡡
ŵЦһ£ڣҲģû취
˵ţŵ̾һ䣬Ҫֻ֣̫㣡
ڣ
˵֣㻹洭ˡ
ˡҡͷһЦȻ㶼ˣǾ˳һBSD֤ɡ
ŵɫһ࣬һڷڰ칫档šڣȷʵ֤һЩ⣬˳һ¡
˵
ڰص㣬γһɽȺ˾ֲ㼯

һһ٣ҵľ硣
ȳŵѧλذߵʱһ̧ͷִѾϦ¡
ҴҸ˷ڣŵ뿪Ժ¥

֮һµʱ⣬ŵÿĿγ֮⣬ǰʣʱȫעBSD֤ϡ
ȡõĳɹϲ
׼ȷ˵һܣо̿ô粽Ϊݡ
֤һֱ56%ȥ
õģһϢûг嵭ŵͷǡ
ǹ죬ˡ
ģںͳŵʶ˵о򣬿ܳ˴

ص㣺ѧԺڰ칫ҡ
ʱ䣺2021112710㡣
ޣŵ
칫ϣĲֽЩʱBSDȫѪ
ĵƹ£ɫЩ㲵ĳŵڣڣ˵ĸǳ⣿
ϻ̾˵ѧ֤һǺ֪ǰĸڳ⣬档
ˣҪ֤ȥĻֻôβͷŲһ顣
˵һ鷳ڵΪЧĽ
ŵЦŵͷʾ֪
Ȼ֪缶Ĳ֤лʵķǰʱЩԽܡ
ʵֹϽܹʱķ֤дڵĴܹһ¡
ܱЩһףѲ֤ȴ̴֤شҪúܶࡣ
Ȼ޷Ǿֹԡ
Ǳŵ£
һļŲݸ壬ŵͷ濴
LEsԲEӦHasse-Weil L-functionʵBSD conjecture.LEsڴTaylorչĽ׵ԲߵMordell-Weil rankôLE1=0~L'E1\not=0 Rightarrow rE1

һ̡֤
ôLE1=0~L'E1\not=0rE=1.Kolyvaginá

ŵĴһ̨תĻ
һѶѵĹʽַڴڽϣ㣬߼
·֪ƣ㣬ŵβͷҳ

ʱ䣬Ѿ賿㡣
ŵеһҳݸֽŤŤӣһ̧ͷֶķѾſ˯š
ŵЦЦڰ칫һԵĹһë̺ڸϣȻ󣬱ǼдʽֽżͷѰŴ㡣
ʱ䣬һһš
ŵĿһɨӡ
ͻȻĿһʽϡ
p11£Բsemi-stableģordLE1/c=ordShaEGL2Ϊ
ΪʲôGL2Ĳּ֤ȥĵóһ֤Ĺؼ
ԣӦ
GL2ʽȫûҪҪ߼ϵõKolyvagin conjectureĻӦá
һ˲䣬ŵѣ


ʮ ô֪ģ
CL2ʽⲢǱҪĻôƵ̣δһŻ
һ˵
뷨ڳŵԺײ֡
ģŬץסһŵ⡣
Eisenstein seriesۣԣ
ŵԺͻȻðʻ㣬Ȼ˱ΪЩ΢΢
ʲôȫά1еEisensteinڷȫʵһرģδֱдչĶһģȺ
һΦһϸ϶鲿ȫEisensteinG2kӣ2kk2һϵɣ
G2ka=1/m+na^2k
ϵоȫ.ϰƽFourierչʽչһȫa=i.
ͦӵģʵǡȷʵ쳣ɬѶ
ŵҲһۡȫά1еEisensteinڷȫ鼮Уϵͳȫ˽⵽֪ⷽʶ
ʱǡEisenstein seriesۺBSD֤ƴһЩߵĹϵǰѧҹBSDоУδߵ״ںֹϵ
б޻̬ŵǰ֪ʶǵ
û뵽Ȼõʱ
Уŵ˼ά̷ɢ
ģȺȫģʽдɶʽG4G6رǸ߽G2kG4G6ͨݹϵdk=2k+3kG2k+4磬d0=3G4d1=5G6Ȼdkϵƣnk=2n+9/3n+6
q=e2IӣG2ka=2ˣ2k1+
BnBernoulliƣzZetaͦpnǳͺܺpȻȻ󡭡
ٶȿ첻ˡ
ŵһſհ׵ĲݸֽһʽԾȻֽϡ
ڼ˷״̬Ѿʱ䣬ƣУֻʣѧʽ
Գŵ˵һҹ
ͬʱBSDоʷУҲԱ¼ʷһҹ

峿ʮ֡
ԶнһĨǰס
ҹδߵĳŵڲݸֽϣдһйʽ
Nq=-1-504n^5q^n/1-q^n
ڸ㶨˰
ŵЩ͵۾ŲӣԼˮ
˯߽ǳķҲŵķѡ
̧ͷоԼϵë̺ųŵ
һû˯ųŵ㲵ɫʵ
ŵͷ
üһû˯Ȼ㻹ᣬҲƴˣӦø廹ծˣ
ڣֲǾͨżһλûϵġŵЦ
ЦǺǵİڰ֣ˣ֪绹пΡϿᲹҪΪ߹͵ѧҵ
ףŵߵ칫űߵ¼ףֺͷڸ𣬡ǽڣҾȻ˰
š߰ɡڳŵת뿪ʱ򣬷ڽסŵˣ㰾ҹһϣûʲôչ
Уŵĵͷ΢΢ЦнչһкܴĽչ嶫ǼŲݸֽϣԿ
˵꣬ŵ뿪
˳ŵɻŵǰŲݸֽ
ʮӣʮӣʮӡ
Сʱڵμûж
ֻ΢΢ָʾĵļƽ
ὫļŲֽŻ棬˿αϣָɵû棬ϣ¶쳣ο顣
ŵϣԺҵľϲԽԽ󣡡
칫ڣ𷽽ƵĻ

ڣŵһ˯ʮ㡣
Ԭæʳô緹ŵˢ΢š
ţǱȫһϵŮѵ̬֪ŵæƽʱҲϢ
һŮȴƵƵ΢Ϻͳŵ
Ǿǳŵ½СѧùѼѣڿѧӭǸͬҵǶУȴȳŵСһŮ
ѼѾͶԳŵλѧĺܣڼϽѧ֮󣬸һЩڳŵѧĹ¼
һͷSCIģĸĿ֮
ǰθ˳ŵڹѼĿе
ڳŵײβԹѼֻʱ΢̳ŵ⡣
ŵҲǱ˵뷨ûµʱǾָ㼸Ρ
ŹѼѵ΢ͼʾϢŵʶĵȥΪѧĿû뵽ֻԼڲڡ
Ѽѣѧѧ𣿡
ŵڡ
Ѽѣѧ벻뿴ҵдƬ
룬ôŵ
ŵȻܾ뿴
ѼѣѧĲ뿴
ŵԥһ£ǿɡ
Ѽѣѧ˵ĹȻûѧ־ᶨУ
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Сɶʱˣڸʲô
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Ѽѣѧ벻뿴ҵдƬ
ŵ뿴
Ѽѣѧ治뿴
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Ѽѣߣѧ˵ĹȻѧһȺУ
ŵۡ۲ô֪ģ
Ѽѣ
ǹӡ
ѼѣѧǸղȥϴˣԻѡ[][]ѧû뵽㲻ϲŮˡ
ŵ


ʮ һ
һĿγ̣ŵٴζһڰ칫ҡ
һŽŵΣڰ칫ǰɫĶ
ЩŵͷڨڨЦڣûʲôɣ
ҡҡͷԳŵ֡
ŵһӣڷڰ칫棬˫ַϥϣһϤģ
ڽ˳ŵ룬漴ɫѩڻŲóһЦ⡣
ָųŵСӵı֣Զ֪ļﰡ
ڣ˼ָ
֮ǰ˵ҿһ㰾ҹһķܶɹдڲݸֽϵЩƵѾˡʱ򣬻Ĳòϣ츳ҪȾã
ڼҪĻ˳ɲ뵽áEisenstein seriesۡΪӾEisenstein seriesۺBSD벢δ߼ϵܹϵȴ뵽ˣЩƵ裬Ҳȷʵ֤Ĳȷģ
ȻԤԼƵڵ׿ڿ϶ֳɾ͸п϶ǲһġ
ŵϸһĨϲɫǽڣĺ֤
̧̧֣˳ŵһ԰ơ
󣬲ĻڣǷоʱ֤ĽѾе56%ѡ߼ѡEisenstein series۵Ľȵ48%ҡ
ˣ֮ǰ8%ĽȣᱻȫҲ˵ٴķ˷һµʱ䡣ֵһǣŵEisenstein seriesƵĸνۣۺԤۣͬŻǺһЩƵ衣
Ҵһ£52%֤ݣ20%ҵƵ̱һ룡
ϢǺϢ
Ȼ֮ǰװ˷һµʱ䣬Ḷ́Ҳ԰һµĽȸˣ
ң賿Ǵο֮󣬳ŵоԼԺƺֳһۣȴʮ֤·ߡ
ʵ֤·֪յ㡣
·֤ͨһֱֻŽ⣬Ψһ⡣
ŵͷģǲ֪ߵغҵŽ⣬ǣٳһͨյ·߱á

ŵ࣬˰ͰĽš
ѧڣǸУĿ⣬ŵûмκεĿС顣
ҪѧԺʦ֪ŵĿǰǸŷڹġ
ϲûеʦѧϵЩҪѳŵĽǣҪȺͷһ£󣬱ڶһһؾ
ڷڿԳŵĿǰټЩоѶһĿĿ˷ʱûκ塣
ЩѶˮƽͺϸߵĿĿô廪ѧԺһѧҲʮӣңЩĿԱѡҲϳŵ
ѧڷеǸT1Ŀһɲ
ˣŵôǲýæȥϿˡ
ѧҵBSD֤Ϊʱ򣬻дƪģͶSCIڿ
һƪԼӷСݶȷһƪǡKazhdan-Lusztingе淴ʽ
ƪϾŵҲûָ˻öƪͶһѧšĶSCIڿˢˢ
ȻҪµʱ֪Ƿ¼Ľŵġ
ƪĳŵøǰүӵĻ˵ŵƪģͶЩһĴڿϵļʱ¼ڶһЩڿȻǺ⡣

202112311150֡
գۼ䣬ʱʱ
ŴѤõ̻ŵĿЩ㱡
һ˰
һ꣬ŵѧ˺ܶ࣬Ҳ˺ܶ࣬һǰԸȴûʵ֡
Ϊ
·Ȼ̫ˣ
һ̣ŵȭͷٴ˺ȥͬԸ
ҪΪ

ʱת2022ꡣ
ڶʮ籭11·ݵĿٰ죬ѾǰȷС̭
ڶʮĽ춬»Ҳڽ·ڻ׶ٰ죬ǻ״γа춬»ᣬؽʷᡣ
Ȼһ鲻ֹôࡣ
ѧ˵ҲһҪ
һķƶȽڽӭĵ20ΰ佱
ƶȵ壬زö˵ѧҶԸý֮ͣɹģмˡ
2022꣬ƽ꣬ͳŵ˵ûаëǮϵ
ڵˮƽƶȽľ뻹֮ң
ŵᣬҲıǮ
רĸ£ǰڸϿBSD֤Ū꣡
ƺڣŵ鷳
Ϊ¥£һλ֮͡
Ŷ׼ȷ˵һһСλ֮ͣ


ʮ Ҷӵ
һλɽΡĸߴӣһλ۵СŮ
ŵˣͻȻһ㶣ϴųЦ߹ȥ
ǸСŮͷ΢Цŵôˣ
ûСŮǳŵһûİŵСͯЬˡ
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ԻһеĴڣ
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ѧѧģ۹ȻҪȻѧģҪһΡ
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Ҫ֪ĿǰѾBSD֤ؼԽ׶ΣֻҪμȹˣĵ·һƽ
ŵȥμӱǴȥģʮصȽ㶼ҪһǷڸŵԭ
˵ףѧԺ쵼Ҫ
廪ѧԺ쵼ԼĿ
ŵѧȦҲСڵĵӡƺžΪĿ⣬ڼΪڵ֣BSD룬Ǿ˸ӿسŵ֡
ǵ򲻵ѵĵزҲԸȥǿȷڵİͽ
Ŀǰȷʵ˷ǳϾĳ̶ȡ
֪һֱڲμĹбȽϻ֡վٰǼ꣬һٵʱ򣬻ռݶʮصȽеʮң廪ѧҲʱһģСõһȽ
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˶вμӹľ飬ڸѧԺǴмĴڣ񱻸֪ǰλĶ飬Ҫָӣ˵ʵЩġ
ֲŵֻǼ򵥵˵֣ңнã
ԺѧԺμӹ3%ĻȻꪳɳ
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ڣıҵĺͱҵ綼û׼
˿ģǡȷʵæˣ
ڸ㶨BSD֮ҪץʱŪҵˡ


ʮ ִͼ
ѧУ¶ʮ壬˷ڣŵһϻؼҵķɻ
ӷſգʲôBSD밡ЩȫԺ
δһΨһܷϢ·ŵļˣԳŵϧ
Ժ֣ʱ⡣
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ӽԼܸλԱʱһλСŮͷеĶԳŵʺһã
ŵʱһߣһͺͳŵʶİŵڿֱЦ

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һʮһ·ɻסڱظһҾƵꡣ
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Ѱ͸⡣һһٵӼ㣬λ˷λͣÿѶɲͬķֵܷ500֡
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Ҫܵĵõ߷֣ǱҪģԵԽԽáΪڻⷽ棬һڲ߼ࡣ
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2010꣬ѡʹܷ1052ֵļ¼˴ƣ


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2010꣬ɻѡʹ1052ֵĸּܷ¼
Ŀǰӽһ¼903֣ȥǽһСŮ졣
˵ǸΪСħСŮ֪ʲôԭ򣬲ûвμӽһ
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ڱǰһϣǾ͸֪ͨԼĶԱǣһҪϺúñ֣ӳ200%ʵܻӣΪǹҵʵ
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100⣬ȻС⡱ˣǿ϶Ŀ
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5117+2387-1475+3144-1225+=
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22178+58712-87100+84712=
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58711232*54712=
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Һã𰸱ϾҪдģǹԳŵΨһƣҪֱˡ
ৣৣ
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100֣дĻŵ߷ֶӡ
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ÿݸԾ50ѶĿÿֵһ֡
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飬˵ȥǶеСŮûвμӽıΪʲôҪ֪ȥıֿʮۡϻĻ᳤Цʡ
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Ҫ֪ΪӦⳡص׼1000Ŀɵĸ⡣
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Ҫ֪ʷ߼¼ߣҲԻֻͣ587Ŀõ552ֵĸӷֶѡ
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ʵϻ᳤û˵ǣŵ֮õ1500֣Ϊʵֻ1
500֣ǡ
׼Ŀķֵֻ1500ְ
500ֵĻ⣬1000ֵĸ⣬Ϊ׼Ѿ㹻֣ȴûԤϵгŵ̬ļһֱ֣Ӵ⣬һֲ
󣬱ǰ佱ڡ
ϻ᳤ԽھĽ͸һĽƸŵϣĳŵļ򣬡ͬѧϣһ컹ܿӰһúģһĽС
ϻ᳤һı飬ŵЩЦãķ˼䣬´ʱμӵģ

磬佱һ˻صƵʰøԵĶͼϷɻؾķɻ
ز죬ҶԱǴԻδСӣĻǳʲôӣԺ佱ʽһͷ̡
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һȺСѧȻû˼
ţڴ󼴽е
ϣβμЩѡ֣ʧɣ޵еҲû˼İ


ʮ ֤ϣ
Ͼŵ㣬ɻȵͣھʻ
˷ɻܾ˺һԷףһµ룬һŵϻѧУ
ѧУԱߵС͹˶ӣŵͣʦԢڵļС
֮ôżϻΪҪ׼顣
ŻῪʼɲż
֮ҪæΪһǳҪǾBSDβ
ûںͳŵҹԼյĲиУ֤Ȼﵽ97%ֻʣһЩ㸴ӵβ
ＸһͷɣƺҲصƿӭջļڡ
Ŀ˵ǳŵѧѶˮƽߵоĿ
ϾҪɹʱ̣ŵô᲻ż֤һ̡
~~
ŵǰ֪˷ԼϢԼվ΢΢ЩϢĳŵڵûκ⡣
ЦкŵһˮôջΣ
ŵͷڵĹϵѾս㵱ƽʱаɡǹҵʵʦҲ֪ȥĻֻǽѡ
ңһȺСӲμӵıӮҲûеʲôɾ͸Сŵһ䡣
ںǺһЦĦеı±ǳɡ
Уٹ죬ҪʼˣʱȫУ˲μӣʱͻӮгɾ͸Щˡ
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Eisenstein series۵һʵǰ۵໥νӣһй̾൱ˮɡҲˣںʱоУǼûʲô谭
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ȷʵEisenstein seriesۡBSD֤ӵòԶ˵ΪԭƵʽ̻
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˵ǺͳŵƽʱֲиĻйء
귽ڵĻ󣬳ŵ¶ϲɫڣ˼˵ϾҪ깤ˣ
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СŵüģûӲ񣬡ʦҾȻȥˣμҾ͹㡣
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ϴβμӹʱҹսһ죬žɸ㶨˰ɣ
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ʮ ĿꡭO
214գŦԼʱ20ʱ8ڶʮȫѧѧģʽ
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ѡDEFĻĬϲμICMInterdisciplinary Contest In Modelingѧƽģ
ӲҪ˵MCMICMĻһMCMĿϾ壬࣬Ҫȷ
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Oƽ䵽ÿѡ⣬ߵ֮˳20OȫһѡҲڿܡ
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ϸϸĿĿŵûżһʱͿʼģ
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Ϊû㣬Ҳû⡣
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ԺеĲݣûԪϸԶؿ޷һģۡСӰ졣
ȣҪ˶̺ͽӦģcar-generationģͣʻĳҪһģͺͳģ͡
˵ҪͬµģͣĿҪĳѧģ͡
ģͣģ漴ٹ··ڴĳÿһǰϸԪԶΪvehicle-generation
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Ժݡһ飬ŵ˼·
ģͣģͣģͣģͣŵܹСʱʱͨʽ佨ģɡ
ƹģ⳵˶ģ͡
ŵ׹CAģ͡
һǿʻĹһףʻĹ
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λʱΣϵ
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ˣŵĽģ幤ȫɡ
˿ʱ䣬ҲŲʮ㡣
ڳŵģ͹һ̣㽫ݷԺλѣʼ̡
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Ǵһ˸˵ĻȻҪ
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ڶŵŴλԺѿQQͼһ£ʶĴ򿪣㿴ŵļ
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ŵͷOK
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緹󣬽ԼĳŵһߴŹǷһ߿һô룬һġ
һ󣬳ŵĥ
˵ٶҪŪ꣬Ҫˡ˵ҪһȻͷһBSDĵġ
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ԱߣŵҲһ̨ԣĻžûš
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ŵȥʳóԶûϴβμӹҹҲûᲹ
Աĳŵ̤¹⣬ٴڵĽڹԢ

һɵĲ߶źȦ߳
ĳŵʱڷڼС
죬һֱͷڹͬв֤
ĲиŬŵͷڽΪ1£BSD֤̣һٶҳġ
⻹ǾĴμ򻯵Ľ
Ҫ֪ԭĲݸ壬ٶҳ֤ʽ
ڣͶĸڿŵɫ˷ܵʡ
ڵһЦȻڣInventiones mathematicae


ʮ ҵ
Inventiones mathematicae͡Annals of MathematicsѧڿΪѧġȻ롶ѧ
߶һڿӰҲ10ϡ
Ȼ롶Ȼ͡ѧ40ӰӻЩ࣬ѧڣȻߵڿ
ȻӰԽߣͶڿ¼ѶԽ
ڡInventiones mathematicaeϿĵģ඼緶Χʢѧţ
񷽽ڻӦѧ򶥼ѧңҲδڿϷһƪġ
η֮ƶĽ֤Ͷ嵽ڿȻʮš
BSD֤̺Ѷ˵Ǿʸ񽫾֤̿档
ĵǷںͳŵ˹֣ͬûκʡ
ȻӰȲЩѧţ緶ΧҲСзҲƪ֤Ļֱʯ󺣡
һٶҳתΪPDFʽ롶Inventiones mathematicaeڿĹ˳Ͷ塣
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񣿡ŵһ˲
䣬ڷȡ֪ʶĽ׶Σиһ¿ԣһֱиȥĻɾͰһֶ˷ѵˣЦеĿڡ
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Ѿǰͳŵͨһ˵Ҫ˳ͨҵĻ׼һƪѧˮƽ൱ıҵģ򣬴Ǽʦ²ô׵óŵõҵ֤
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дһƪˮƽSCIĻˮͨҵѾһ̫ʵ顣
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ŵն񣬿⣬ʵԺڲͣĸת
ԺԵһƪչ۲٣ѧֵûжߣԶûдﵽŵҪˮƽ
̵Ŀռۣ
С֪ⷽʶ̫򵥣ʲôļ⡣
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ҲУƫ΢ַĿǰԼе

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û˼·
ŤŤӣǱԵ㷭һҳ
ҳı⣺Bertrand衣
ŵĿͷʼ
Bertrand裬ǣȻn2ٴһpʹn&lt;p&lt;2n
1845ɷѧJoseph BertrandΪһġBertrand3000000ڵν֤1850꣬ѧPafnuty Chebyshev1821-1894˸üĵһϸ֤BertrandʱҲΪChebyshev
Сʱʱ䣬ŵŰChebyshevľ֤̿꣬Ȼüͷ
ӣʵ̫ˣ
Chebyshev֤̣˸Ӷ֣ŵҲҲκεۡ
һѶѵĹʽַĳŵϰߵ˶ЩͷƤ顣
ڳŵʰ飬׼ҳʱеĶͻȻͣסԺƺ뵽ʲô


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ŵ΢΢һҳԭһҳ
ȻChebyshevбѩ򣩸Bertrand֤˸ӣôԼսһ£ǷܹøӼѧ֤Bertrandɡ
˳㣬֤һ£һУԼ˺ֵز
Bertrandļ֤
ĿԱƵһˮƽġȻǰǳŵܹ̽򵥵Ľⷨ
ŵ֮ǰġѧÿһ߼̶֤ߵյḶ́е·ۣе·ֱ߱
бѩֵȽ۵·ߣŵҪǰ˵ĻϣٳһӼݵĵ·
ȴȵ֤BertrandҪ򵥡
Ͼվھ˵ļϿ⣬бѩλߡ֤ŵٵҲܴмȡʲôж⡣
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ŵôԥˡʱԣݵóŵڷ֡·ͨѰһķ
ҪӼķҪǰ֤˼·͸
ûл𼱻ǵֱӿʼԼУǵͷͷβĶйBertrandʮҳݡ
Сʱ󣬳ŵ顣
ۻζ˼룬ͳһհ׵Ĳݸֽϵĺɫ̼رʣ۾ĿʼԼݣ
Ҫ֤Bertrand裬ͱ֤⡣
һ1nΪһȻpΪһnpݴΪs=i1floorn/piʽfloorxΪx
Ҫ1nУnȻһֱϣÿϵһsiǺţȻǺŵs
ϵʽs=1in siʾȼеļǺsiͣɴ˵õĹϵ1
nΪȻpΪpn p&lt;4n
ѧɷn=1n=2ʱȻn&lt;NN&gt;2֤n=NΡ
NΪżpN p=pN-1 pȻ
NΪN=2m+1m1ע⵽m+1&lt;p2m+12m+1/mm+1ӣһ2m+1/mm+1ڶʽչ1+12m+1гΣ2m+1/mm+1ܣ1+12m+1/2=4m.
ˣܡ
ŵ˼·˳ûѶ󹦷򣬱Լķ֤
Ȼⲻǲһѡ
бѩ˼·滹Ҫͨ뵽Bertrand֤ȥ
бѩõķӲգûӲգ
ͨʽĲתBertrandĳĳһĳҪתΪһʽڽл⡣
Ȼŵ϶ô
Ϊ֤Ļ˵ǳŵϣ֤Ҳбѩ򵥶١ˣҪת˼·
Ǿôһת
ŵûá
ۿͷбֵ˳극ʱ䣬ŵһԺ˼һʳá

ͬʱԶڴ˰׹
Inventiones mathematicae־ܲ׹ɼ
ΪѧڶSCIڿ֮һÿǴŻյȫѧҵͶ塣
лõصĵģȴֻвƪ
ңƪѧĵУм֮ĵķݶǼλѧռݡ
Peter Scholze
΢ּRichard Hamilton
ѧJean Bourgain
ȵȵȵȡ
ԣ༭ʱ򣬲ǰͶ˳ģǰߵѧˮΪ׼
ϾѧˮƽԽߵߣﵽڿ¼׼ĿԽߡÿڿ¼¸һֵ
Ļܴʡ༭ʱ䡣
ѧ綥ڿ༭ҲǼ֮
˵Inventiones mathematicae༭֮һ-˵öΪùŬ𽱵֪ѧҡ
Ŀǰڿ༭⣬μݴѧɼУĿڣۡ
ΪһλͷμѧţÿϰƵĳĴڰ칫ĸ
һ˵ÿܳһʱ䣬ԼҵĹԢЩͨ༭ģƪѧҵͶ壬һЩ̫֪ѧҷΪ¼ʵͶ塣
£ͨ༭ѧˮƽߵԭЩѡʼֻкٲַڿ¼׼
˵㡣
˵öеһȣ̨ϣһűʼǱʾͶ壬һԵõСਡ
ʱѧеƽ쳶һƪģС̾һ䡣
⼸£ABC֮Ļѧ綼һƪƽ˽ʮһ·ƽ䷢ʱ򣬲Żٴɡ
ƣʱʮһ㡣
λѧͶƪѾȫꡣУƪĵˮƽ¼׼ߡ˵öע˼طϵ߽΢ޡ
ʹĹͣǲż緹
ȻˣǾٿϼƪɡ
˵öٿ꣬㿪һʼ
ĵı⣺Ϊ1ʱBSD֤


ʮ ش
ף
Ŀ
˵öüͷ΢΢𿧷ȵֱڰС
BSD룬ڱ˵öо
ΪһλԹ㷺ѧţȻ֪BSD̡֤
ԴӾǰ͵¹Źλѧ֤Ϊ0ʱBSD֮BSD򣬱ҲûʲôͻԵĳɹ
ԭ򲢷ΪоBSDѧ̫١
Ϊǧߴѧ֮һټ100ļôٵͶڴѧҡ
ͱ˵öԼ˽ģȺվѧ˵ѧңоݰBSDģͲʮˡ
ѣĿǰμݴѧУѧԺԺЪڣǳBSD򳤴ʮĶѧ֮һ
񣬿һƪĿΪΪ1ʱBSD֤Ͷʱñȵ¶еЩȡ
λBSDʿ֪һе֤̱֤ΪȷĻǶBSD֤𵽾޴ƽá
˶񣬱˵öڽеǱȷŻ棬ϻƬ۾Уѵõ¶ޱɫ
ԹĿ֮ƪĵߡ
ޣŵ
ˣ
˵öԴ˲֡
ѧĵλߣżλѧҵͷԡ
׹Ϊ׵ļѧŬˮƽѧңһ񣬾ͻᱻӭͷϡ
˵öһֱԴѧ綼ûκӵ̬ȣԴѧҵͶһͬʵ̬ȡ
ң֮УһȽ϶֣ޡ
ǰȥѧһʱ䣬ͷмν̸лطȻǲԻ
Ƿڣ˵öûκͷ
λѧңܸѧϲҲ˵
˵ö΢΢ʧ˼룬ԥһеġ
δ~δ~
һԣʱ벻ͣת
˵ǫ̈ϣɫޱжеݣ·ʱš
ڿ輸ϵֻһֱ죬˵ö˿δ
ʱ仺ţǽϵʱӣҲʮ֡
֪䣬˵öѾƪĸСʱ
˵ڱ˵öڿ༭δйġ
̨ϣƺоӵʹ˵öڴǲʽбקʵ
˵öЩɬĲӣ̧󣬿һʱ䡣
Ѿ˳أ˵仰˵öƺ뵽ʲôæվҴܵ輸ϵֻ
ʮδӵ绰ʾֻĻϡ
ohmy god˵öյһԴ
ԽҪͳԷû뵽ƪĵУ⵵¡
ص绰Ǹʮӣ˺üٴ͵ĴۣŻ˵ԭ¡
Ҷϵ绰˵öֻص̨ŵĻɴµġסЦһ£ѧղܰ
ĸСʱȻƪ100ҳĵȫ˵öҲ࿴֮ĽȣҲһԼС
˵ʱ俴޾׵һƪġ
ǡEisenstein seriesۡһ㣬ֱ֮ʣʱʱ̲סȽкã
Ǻεȴϻ۵ĴԣŻ뵽ͻƿڣ
amazing
˵öѹסԼٵĺֻͨһ绰롣
ݴѧУЪڡ
ҲλоBSDʮĶѧҡ
ޣ˵öôҴ绰ˣżСһæһ⣬ûʱ졣Ъͨ󣬱Цʵ
˵öſڣҵѣҴ绰ɲΪ˺ģҵʱҲͬ󡣡
Ŷʲô£
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ʲô绰ǱߵЪھȵĳƪİBSD֤ˣ
һδȫĿǰ˵ⲻ󡣡˵öǿѹסҪǰҫĸоῪڣҪҰķһݸ˳ҰѰѹء
˵öôΥ涨ʱȷʵһЩͶģ޷жĳЩطרҵǷȷʱ򣬾ҪרóѧԮ
ο漰ĳߴ̡֤
绰ͷĬá
ã˵öǱߴһ̾ɡ
OK˵öˬӦ
Ҷϵ绰˵öԼû緹ֻ˸˵öصǰǽĿһݷЪȻδݡ
һ߿һ̾


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һߣ
һҹ˼ŵڶԼıҵµ˼·
ãŵԼļ⡣
ԣĿһŵҴҸϵͼݣһû˵λãóֽʣ֤Լ뷨
ȻǿӽBertrand֤вͨǳŵǣܷóۣȻӦõBertrandС
ĻȻ˸䣬ƱбѩķҪ鷳١Ľ֮ǰ˭ҲҰٷְپ˵
ŵûӦóһ¡
ѱãһ󣬿ʼڲݸֳֽԡ
вϵۣܺȷ֪ͨó۾ĸãĸûá׵ķһһԡ
ʱ㹻ŵż
~~
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ϣ1nΪһȻpΪһ2n/nnpݴΪs=i1[floor2n/pi-2floorn/pi]
Ϊn32n/3&lt;pnp2&gt;2nֻi=1һs=floor2n/p-2floorn/p2n/3&lt;pn1n/p&lt;3/2s=floor2n/p-2floorn/p=2-2=0
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һУһС
ϿΣŵһ춼ͼ
ȵʮչݵʱ򣬳ŵű뿪
ŵĲݸֽϣѾʮۡ
Ͷһĳɹ
ŵĹǴʮУѰҳBertrand֤õۡ

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գģůһ졣
³ڸŵһ¼ڻʣʮʱ䡣
ŵ㹻ʱȥˡŶȥıҵġ
ĵĽȰճŵ滮ķУһ죬ƵʮѰҳ֤BertrandҪõۡ
æµһ죬ڶ죬ŵͣĿʼʽBertrand֤
ɲǸɵĹ
ŵûжһʱ㶨
һŻ˵ĺãһٶ˥ߡͷ㣬һ¡
ʱ򣬳ŵòٴ׼ɴ󷨡
ŵҲ׼ϡ
ΰɣ꣡
ŵ̼رʣʼһѹء
жѩ֤Bertrandʱȡķֱӽ֪ӲƵ˿ûκμԿԡ
ŵȻô
Bertrand裬׼ʹ÷֤
ǳֱƵ֤֮õ֤ʱǳҪ
ǡ֤ĳ벻ʱ
ŵڵʱҪѰҷ֤Bertrand費
жѩȻ֤һĳʹ÷֤޷ǽ֤м򻯡
ŵ
һ÷֤ⲻĳn2n2n֮û
ڶ2n/nnķֽ⣨2n/nn=pspspΪpݴΡ
5֪p&lt;2nɷ֤֪pn3֪p2n/3ˣ2n/nn=p2n/3 psp

߲8ɵã2n/nnܦpܡ2n psp2n&lt;p2n/3 pܦpܡ2n pspp2n/3 p
˼·ͨŵһ·дκһСʱұһ֤衣
ŵˣ˺һ
ԭڣ֪Ѿô˰
ŵһ
󣬱ǵͷƵ֤ʽ
ڰ˲ڳ˻еĵһıĿΪ2nڵĿڡ2n/2-1ż1ɴ˵õ2n/nn&lt;2n2n/2-142n/3
ھŲ2n/nnǣ1+12nչʽһչʽ2nǽĩ1ϲΪ2ˣ2n/nn22n/2n=4n/2nȡһɵã2n ln4&lt;3 ln2n
棬һ
ݺ2nnٶԶڶln2nʽ㹻nȻܳ
ˣ˵Bertrand
ĵĲݸ岿֣ʽ깤
깤ʱ䣬ȳŵԤҪһʱ䡣
ĻܳȵĽҵĵĵ
㣡㣡㣡
žžž~~
ŵָûẓ̇ĸСʱ󣬱ҵʽ塣
ŵһPPTҵʱõ
ڴĸ壬ŵû׼
ʱˮھǡ
ҪԸˮƽһҵ綼ˣǻֱҿ鶹ײˡ
Ŷˣһ¡
ŵһԴ·ʲô
һ󣬳ŵתΪӢĵPDFʽͶλڵ¹ŹһѧڿѧͨѶš
SCIڿ֮һλһ
Ӱ5.21һѧ־Уеƫϵˮƽ


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µʱ䣬Ҵҹȥ
ҵĳ׸㶨ŵҲȴһ׮¡
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һ죬ȹһĳŵⱻڵһֽټ˻
Ǽ칫ңŵŽ
ڰ칫һɳϣǵȴá
кŵԼߣЦǺǵĿڣһ¹Ļңɣ
ŵЦ԰ɡ֪ҵϾҪͷˣ
νԼ϶ʲôµԼ
Ŀⲻ̫ܣ
֮ǰ˵T1T2ѧԺĿóŵȥΪֻ˷ʱ䣬Գŵѧˮƽߺ塣
ȻĿ⣬Ǹûʲôأ
òᡭ
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λĸ
룬ǻ룿
ŵѾԿ֮һԼٴΰҹκĿƾ
óŵıԹٿŵԽԽɫɹЦŵҪôۣһΣҸҵ飬һɵĹ
Ŷŵ۾һĴ
˸ӣŵ벻һѣʦĸо
ʦ˼ǣŵЩͷԡ
˵㵣ѧҵ̣ɫĿڡ
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һʱ䣬ŵЩɡ
Ȼ뵽ֿܣ˸°ͺղֿԶûϵڻֱӸһ𰸡
ְλɲô򵥵ġ
ȻֻڴѧĽʦְλͶ˵ĳƺǺôʦְƲǡ
ڻһЩѧҪõڡڵְƣǱҪһ
һ˵ҪΪ̣ѧˮƽУ˶ʿʸ
񷽽ֵλĽڣ붼ӦλѧˮƽμĲʿ
ɳŵأһССıѡ
ѧˮƽϣŵȻǹġ
ϣŵλ̡ȷʵЩϹء
ȻⲢҪŵȥǵġ
ڼȻô˵ȻǺѧԺк
ڳŵͷˡ
ŵûȥܾ
ңڸһȺͬˣһЩԼҪ˵ʦ£ģȷʵеСڴ
ŵԱãڿЦôԸ⣿ƣÿ»йõģ
ʲôйʣɾ֮ϲˡ
ţߣÿ°˰١ЦǺǵ
ûϵǮþСŵĲǹʵĶ٣Ǹ׬ǮĹ̡
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ʦʲôʱϸڣŵ˫ȭԵ²
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ͦɣҲȷʵͦɵġôʱͳŵһBSD롣
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֮󣬷ѳŵһ䡣
ŵͷû⣬ǵһεʦЩš
ȻǴƴǴεĻ
ŵвһ䡣

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ŵҪģǽеۣжͲͬѶȵϰ⡣
Գŵ˵ֱСkiss
Ȿ飬Ҫ۵Ļʷֲļ޶ͳʷֲƺͼ顢عƷݡ
ڵĽѾͳʷֲ
һϣŵеϰϡ
׼ʱ򣬽Ⱥѧúðһ£
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һãһ˾ȡ
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棬ŵ̸˵䡣ڸŵʹʹɫͬʱơ
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Ϊһ̣ŵͦġ
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ŵִ˲ƣһγΪ̵У¿˰Сʱҵʱһһͬѧǵɻ
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˵ͬĿγظ˵ʮ꣬ѾʼĸɾĿ﷦ζ
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㣬ӵְƵʱֻ¡

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һˮһŽţһˢֻ
΢ţĳȺѾһƬ֡
΢ȺͳƽȺ
ǽսһ΢ȺǷſγ̵ĽȺĳԱſεѧ
񷽽ʹʦQQ΢ණԾһֱûнȺ컹Ǿһλͬѧ飬ŵ֯΢Ⱥ
Ⱥ֮ʲôʱ򣬶϶Ỷһġ
ʷȺϢѾ99+ŵֻ
ӦݣۣǷûе˧ңᣡ
Ϣŵ΢̡
ͷ˵ʵ˲ˣ
ͬѧҼסˣԺڿϽشģ
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ƿƻұҸоðŵȻǶҪСѧˮƽֹǸǼΡģһͼصĿãҿǴǱ˵ȥһʱ䣬ŵڸŷŪһĿйʲôҲ֪϶ӦýӴġ
ҿǺܿóŵδܳΪһˮƽѧңѧҵѧӦòǶ˰ɣ
λͬѧ۹⵹ͦ
ŵĬĬ˸ޡ
ŵӦóˣǷһȺ档
ȺΪճѧϰ֮ãʶˮȺֹͼֹˢֹƶĶֹ棬ֹƴӣѧĿɻ󡢹ճ˧
OK༭ϣ
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Ӧݣۣ̣ҿ˧ҷ
˧ǻ۲̣ԡ
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ŵȺǳƣ˷׷
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ԣ콵
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Ҫôȣһû˵أκԺЦһ䣬ƪģô˵أһʧƷΪдŷ֣һִ߼󡣡
κԺɫһŵͬѧҸĲǣСʱ֮ڣƬĴڵ߼֮ҵ
Ȼ㻹ܸ⴦߼ʹƪ߼ͨ˳εıҵ磬ֱӸ֣


ʮ Ѿ㶨ˣ
κԺЦĻһŵɫɱ˱䡣
һƪ֤߼ģ
ԼڰСʱ֮ҵдڵѧ߼
ŵüͷ˼˼κԺѶȡ
ûͨƪ֮ǰѸһ׼ȷĶۡ
ܲɣҪһʺţ
˿̣ûСܾѡ
κԺЦⰻȻӣŵصͷãԡ
κԺָۣŴҺŵһλǴɣǼѧ
Сʱʱ䣬ĸʦȻŵȳŵϡ
óʱ䣬һλҵ
κԺҲĳŵֻϡ
ƪı׫дǷѸ壬ûκƽ̨Ϸ
ڸдڵǴ߼󣬾͸ֶͨε֪
һУֻܿŵԼ
ҲǶԳŵѧˮƽľ顣
Ȼ˵ŵûгɹκԺҲܲŵҵ֤ǣŵеķԻۿۡ
ںԴϣҲµ
ŵκԺƪģҺŵһλϡ
λĳ붴һĲݸֽ̼ر֮ĸľߡ
κԺԤı
ŵЦһ£Լ֮ǰֻ֪֪ε
ܹ34ҳȳŵϽϼҳ
Ŀ֤Ҳͳŵһģһ֤Bertrand衣
Ψһģǳŵ֤Ϊһȷе֤
κԺģһִ֤

ĻȷʵǺܶˣ
ŵͷǱκԺƵһɨա
ָ֮ǰһֱά΢ЦЩͷʼκԺġ
۾һ㽫еݽ顣
ǰλʦʹҵûв
ȻκԺĴƪĺͳŵıҵѡ֤֤ͬȴǧ
ŵΰѧжѩ֤BertrandʱǲƵķ
κԺƪУȴ辶ȡһֽȻ֤ͬ˼·
Euler˻ʽ뷨
ŵô
УκԺ̵֤һʼEuler˻ʽͨEuler˻ʽBertrandѧ߼ϵƵ
νEuler˻ʽ
ѧնĹڸֲ֮һΪ⸴sRes&gt;1򣺦n n-s=p1-p-s-1
һ൱ŵѧʽѧѧомõ
û뵽κԺͻ룬Ϊ֤Bertrandһ㣬ȻΪĻѧĴţֻƺ
ʮӵʱ䣬ŵƪġ
ȻָĲǳŵļ34ҳݡ
ͳŵύıҵһʵϵģֻҳݰˡ
֮󣬳ŵκԺ֤˼·Ҳ˽⡣
ȣfnΪfn1fn2=fn1n2Ҧn|fn|&lt;޵ĺn1n2ΪȻ˳Ƶnfn=p[1+fp+fp2+fp3+...]
óһƵ֤ĵһ
棬ڦn|fn|&lt;ޣ1+fp+fp2+fp3+...˻p&lt;NĲ֣޳˻fnĳ˻ʿɵãp&lt;N[1+fp+fp2+fp3+...]='fn
1+fp+fp2+fp3+...=1+fp+fp2+fp3+...=[1-fp]-1
Ĳ

һɣ2n/nn=p2n/3 psp˷ֽΪpܡ2n2n&lt;p2n/3֡ɴˣ֤Bertrand
һһ߼ܡ
˼·棬ƺȴڳ֮С
һ飬ŵδҳдڵκ覴á
ŵüͷһ¡
Ȼûô򵥡
ŵûʱȥͨһ飬ų߼Ƶ򵥵Ĳֱ֣ӺԲ
Ǹ߼ĳֵͼ߼ƵϣκԺܻ䵱ŵĴĿ
Ϊ̫ˡ
дӴƵĵطһ崦
ŵһŲ顣
һEuler˻ʽҶͺͨ޻ȣʽҶк2fnȥȻ󡭡
ڶķֲԼȷ

ĴfnʵĴ룬f2nfn=f2+f4+f6+...
ȻһݵĳŵĿⶸȻһ
һйʽƣҳȻǸһĨЦݡ
ңҵˣ
ŵ̼رʣڲݸֽддһصĵйʽ»һߡ
ϵĹʽp[1-fp]nfn=f1=12n/nn=pܡ2n pspnfn=p[1-fp]-1
ûˡ
ʽǰʽֻ߼ϵһϰԵĴ
ʽҲƪ֤мĹʽ֮һҲˣʽĴ󣬵ƪĳΪһƪѸ塣
ŵʱޱȺá
ΪҵκԺҪǴ߼󣬲ңԺѾ
̧ͷһλʦǰĴϯûˡ
ŵģϽ̨
Ȼλʦ΢΢㵵ĿУһЦʦѾ㶨ˣ


ʮ 
ŵͬѧ뿪ʼıݣ
̨£κԺʾŵԿʼ˱ݡ
ŵһڣκԺҵƪĵ֤˼·ͨEuler˻ʽBertrand֤
ŵλڲûȶκԺƪģԳŵ򵥽κԺв˼·򵥵Ľһ顣
κԺҪѰҵǴ߼ҲѾҵ
λʦԷĵĵڶʮһҳʮеǴʽǱƪеǴ߼ڡκԺ֪ѧ˵ĶԲԣŵŵš
κԺЦǺǵĵͷǲڵĺ룬شûŵͬѧɺʹ˵°ɣ
ŵȻӦʡ
ںڰдһеʽp[1-fp]nfn=f1=12n/nn=pܡ2n pspnfn=p[1-fp]-1
Ĭ룬̨¼λʦɨ֮ٴοڣӱƪеĹʽۺ͹ʽ?УɵĿƵһʽһûκ⡣ڶʽҲɶݺ͹ʽࡢʽ?ó
ؼǣʽӺBertrandĹʽӦǱƪĵĺĹʽ֮һùʽȷֱӹغƪǷǣҵļ֣ʽһȷĹʽ
˵֮ǰĹʽУͨƵõʽƲ⣬κԺ֮ԻὫʽǰ޻Ƶ͹ʽΪǵʽ޻͵ӡ
ŵͬѧκԺѾ̲סơ
ŵ˵û
ʱڹڸʱ䣬ûȥĥ⣬һʽƵ
ҲǵƪĳΪһƪѸ壬װ˷ʱ䡣
ãκԺֱӷãŵĿ⣬˳һ³ŵˮ׼
ŵĴֹĿǰκԺȽ⡣
ŵѾҳҪǴ߼ȲʳǸʵ⣬ǳŵͬѧ⴦߼оķ𣿡
κԺ֪ġ
ʵκԺǵڻû뵽ҲὫѪΪһƪѸ塣
ŵһϲҲ˵
ѧˮƽû̫Ĺϵǣһ˲ԺС
κԺʣŵһЦȻ
˵꣬ŵŤͷںڰϱд˵
ǿԽRiemannƺڷ⡣
ȣһRes=aEuler˻ʽƣs|=p|1-p-s|-1ݦp1+p-a-1=exp[-pln1+p-a]
ʽǿ֪κεx&gt;0ln1+x&lt;xʽɽһƵã|ƣs|exp[-pp-a]&gt;0Ȼ͸㶨ˣ
꣬ŵŵת΢Цλʦ
ȫ֪κԺĵľݣڵλʦǿһͷһŤͷ۾ֱźڰ岻ƿκԺ
ڹİ˼ʮ롣
ãκԺĽںڰƿ
ʵκԺ̲סһĴȣŵĿһϡ
̾ŵͬѧ˼·ȷʵ̾ѣ
ŵǫ飬һ㣬һ㡣
κԺһЦ˵ϲŵͬѧǫѧ
ŵͷ˵һֻǻǫ顣
κԺ˲䱻ҭһ¡
ʻڽܽ´֮󣬳ŵıαҵʽ
ŵͬѧֵĺܺãȥһλͬѧɣκԺڡ
ŵ֣վŲ˵κԺǲʲô
κԺһȻı飬ָųŵЦһûôƤģƪڷʱ򣬻λüһֵģ
ŵ֣κԺָĲ˵ҵĴɼ
ǣСӣκԺ̧Ц

ס
ŵװпյ̵ĺһƿ⡣
ҵĳɼѾŵϵõ֡
ˣı׶Ǹһ䡣
֮ҵĵ·ŵҲ滮á
׼ȷ˵ǷڸԼİš

һǰԺ¥
ǼϤİ칫ңһ̸ʼ
̸۵⣬ǹڳŵҵȥ⡣
ȻŵѾѡ·ǰǰֻѡ
Ҫôڹڡ
Ҫôȥ⡣
ŵͷ˫СʱĽվѡڶ·
ǹڵѧˮƽͷΧʼձȲϹ⣬óŵഺ껪ȥѧϰȽ֪ʶЧ
ŵǹڵĵͼѾɲԼװˣʱ󣬻ͼʼԼΪĵڶˣ
װҪ磬ԼᣬЩȥĴ̨Ҳá
Ĺ磬ңˣ


ʮһ С籩
ѮŵĴѧУŴ廪һʱ⡣
ⲻ֪һѧС籩
ԺԺغ͵İ칫ڡ
ԺѾʮ꣬ΪҵһѧߣпԺԺʿְƵĻߣĿǰѧļһ֮һ
Ȼ⼸Ѿ˾Ļ󣬼ڹڿϷѧɹ󲿷ʱרעڽˣѧȴ˺λĴڡ
ڹڿϷ壬ԺʱĶڿϰߡ
󣬵ظ֪ѧһʼˮƽŲࡣʦĳܿٷչ
Inventiones mathematicaeڿΪѧڿ֮һԺȻÿڶ
~~
ڰ칫еƷԺ

Ժ²豭ڡ
칫űƿһЩ߽Ŷƺһ顣
ʦҰһڵġInventiones mathematicaeùˡ˿Ŀڡ
ΰչԺĵѧ
ʱԺһڡʮȥˣѡ˽ʦҵΪԺһλڡؽڣҲΪڵԺ
Ժͷʾΰչ£ЦǺǵĿڣڿ⼸շ
ΰչͷšʱҪϰҡ˵ţѻδڿݸԺ
Ժ⿪棬¶ָڿ־
ǼڿĺȻ¿Щ־
ϰߣԺʶڿķ档
ǳɫķϣڿƺͷз֮⣬мӴһӢ塣
𾪣˾ȻBSD£
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ǻUC壬ɶʱ׹Сѧȥˣ
Ժһʮ󣬲Žƽ͡
ع
ˣBSD룿
˵ֱⷽʽ̫ϲۻȤ
BSD룬Ժһ򣬵Ϊѧ֮һȻǧߴ˽⡣
ߴ룬Ժûгȥ˹
Щ꣬ͺйߴĻ룬ȴ飬Ͷ뵽ҲͶⷽ롣
BSD룬ΪͻͬȼĴڣѶȻ˵
Ժ֪ڿݾԲȫBSD̡֤
ҪInventiones mathematicae־Ǳ߿϶İϢ֮ڣ浽·
ԺȤĲ㣬Ǳᵽˣ
˰
Ѿж೤ʱûпɻдĵλˣ뵱ꡭ
ԺԺһԴBGMĻɱǶλѧķʱ
ȻɻдģȻҪƷһġ
ȣļȻܵλã϶˳㣬ѧңдġ
ڿĿ¼ɨһۺ󣬱ҵƪĵλãȻ󷭵ҳ
һߡ
ޡŵ
֣һϤһİ
ǿǺͬһʱǴǸѧһëʱն߳ġ
ʵ˵ԺԷʮһβоѧʷľ塣
޵ֻ֣Ծһ£ָɫ
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ģԺͷݡ
ҪһͨĽڴˣйBSDרҵƵһ±ƣԺȴ˿õЩ
ԶżУԹ㷺ɲֻ˵˵ѵġ
ݲֻ̫ǵ֤ĻСʱʱ㹻
ΰչԺ棬ĵš
һֻͨѧԺһЩһ߹۲Լʦɫ
ȻԺе־ɫ任һ
ϷΣǸһ鰡κԺЦһ䡣
ʦôˣΰչƼӺʵ
ԺԼѧĿ䣬ȦӣӦҪˣ

ԺһУĽڣԺʿҲǵһʱõ˸շInventiones mathematicae־
ӡڷǴ⣬϶᲻ע⵽
ȻȻģҲƪġ
Ϊ1ʱBSD֤
ȻֻBSD汾Գ֮õBSD֤עһ֧ǿļ
BSD֤ɹһ󲽵ĿԽ
һѧңҲϣǰ
οƪĵߣˡ
֤BSD룬㲢̫𾪣ݹɻѧʱǾֵˣ
ѧλġ
ǣѧƶ


ʮ ͨ
η粨Ĳ󣬳ŵҲ˵ߡ
ΪλͷͬһʱԵѧҡ
һȴ֣ԭŵһѧ
ǳԾˣ
ָˮƽѧģǳΪѧ֮֡
ôĻһλ
ֱûɶʱ򱾿ôţˣ
һ̣֪жٵĻѧңڿķ氬̾
ͬʱͨ绰Ҳŷڴ
һףطϲᶥڿƣһȻһ³ŵ
ŶΣ˵ŵȥյһѧӺ⡣ţԣƪֻдġûУûУûе¡ҪСֻһЩȴӵĻƣһһд֡ʵɣƪ֮˳ɣкܴĹͣҪڳŵСӣҸ˵
ҶһλѴĵ绰ڶ豭̵һСڡ
ָоȷʵͦˬģ
ֲóŵǸСʱʱľϲװơ
Ѿǽӵĵʮ绰д󲿷Ǻͬһʱѧһ
ڳŵġ󱲡ע
귽ڽŵֳ¼ɲʵͷ
ͷŵϻۣϲװƵԺܺˣ
ŵͱ£Щֻۺ죬ȴûκΰ취
ȻҲûǽǵͷ뵱ǽʡѧİ佱ϣѧƽھɹȻûгɹˡ
ڰ칫ڻδϢӵķڣϵĵ绰
û취
һ߿Цҡͷһ߽ͨ绰
ãǷޡ޿ڡ
غ͡绰Ǳߴһϣɤ
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찡Ҵ绰ʲô
̸һ³ŵ顣ڻδüʣԺڡ˵ŵѾҵˣ
һ
Ժ⻰˼ѵ롭ǽţ
ڻش𣬡ţʣƽ׶ʱ㹻
ѧԺӦǶԳŵҵĵ·˰ɡԺʵ
ڳĬ룬Ѿ滮ˡ
Ժܷ𣿡
ڼĬ
绰ǱߣԺƺ͸˷ڵ뷨ǺһЦģҲǽšóŵڹڣңѧ磬ûκκôֻһ£Ǹŵŵĸѧ
ڳ˼룬֮ͨ󣬻ڣ˹ٴѧѾдһŹȥŵGPAҲ㹻㣬Ӧúܿͻõ˹ٵoffer
廪ѧԺŵŵĵ·
˹ٴѧʿѧλ֮ٽһİš
ԺһЦ˹𣿻ԡһ飬֪ûȤ
ϴڡ
Ūһ˲ųƻһ֧ǰŹڵһЩоȥЩѧĴţ֡Ժڡ
ЩѧĴţͬ⣿ʡ
ԺһЦǮˣȻʲôû⡣
ðɣ޻˵
ԺЩѧĴţ￴˭
ںϣ˭
׹ʡѧķ-׶ڣԺһһ˵֡
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ʮʱڹѧȦչ¶ͷǣڷ˼ƪԿռͶԳƿռĸģС󣬶ʮʱ÷ƶȽ
⻹ģ
ʮ꣬Ҳ2005ʱ3ݹؼĵָճarXiv.orgרſѧԤӡĵվϡĵݣӼ֤
Ӽ룬ǧߴѧ֮һҲǽֹĿǰߴΨһ֤Ĳ룡
ѧߵļɽ֮һ˵ľʱĵλˣ
˼ǣڸоЩ١
зһ룬ܲܰԺЦǺǣһѧң߲·
֪Ժͼͷ֪ˣԺģ
Ҷϵ绰üͷԥӣ󣬲ͨһ룬ιԺңһ¡

һںö
ŵòʸ
ûֻһʸѡ
ϾڵȳŵõõݰŵѧҲ
ɸѡȷξΪ12ˣ
һܺ󣬻ͨһ飬ȷĹ


ʮ 
Ϣ֪ͨŵʱǱѾյ˹ٵoffer
ΪѧϵǰĴѧܳΪеһѧѧߵ롣
13λƶȽλȫλ
ѧţҲڴУν̣ѧΧŨ
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ڳŵ˵ѧѡǺν
ֻҪѡʡѧĻõһƶȽְλټϷڵĽ飬ŵ˼һ֮󣬻ѡѡ
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ŵǸġ
ЩߣŲʿˮƽѡҪ˻㲻ɶӱ

սһܺڷڵĴ£ŵвԵһ䡣
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ŵĿ⵭ɨһۡ
ŮձҪȳŵꡣ
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ŮʿͬĴ硣ľƬԺβյ
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ҲӦðҪߺŽģһһȺʿûɶð
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־ȴĿ⣬һ໥ű˴ˡ
Ȼűƿһ󸹱һİ߽
ɨһ۽ңˣӹİͳһԾһһȥ
ӹԾŵһۡ
ԾֻܹĿ
ĿԽ٣˵ĿѶԽߣǹϵһ
Ծ󸹱ӿһڣԣʱĸСʱǰ
˵꣬һӵǰֻ
ŵʼ磬Ծǰ棬ϸĶ
ȻֲԣԵĿ϶ӦĿ൱
ѶȣҪȲʿҵĵˮƽƽ
Ͼѡηڵ֡
һ⣺裨Ngһn+1άΣMnάΣNϵĸ⻬ǷǶգMNʹfx=.
Ŀ٣ҲǼ̵ĲС
Ѷȣɱһѣ龰µѧĿȫͬһƽ档
ĿĵһۣŵһָоǸӲ磡
ԣһĿ
ڷǼѧ򣬳ĿҲ֮С
νΣ
ָ΢ԼУһǾ΢Σ仰˵䱸һԳĶЭ༴ÿһпռ䱸һ͡˶ԺǾͿȼѧһȣ
nάŷϿռȻĶds^2=dx_1^2+...+dx_n^2ľʾǵλ
ŷϿռеεȻҲȻյһߺ΢ּǶǰΪάռΣȻ˶ṹ
ԾϵĿŵ˼
ѡڶĿóֻҴææϣŵ
һϸѵȷ𰸣йεϣѾӡ
һܵıսʱ䣬ŵҲǺ׼
һӣӣӡ
ԺУŵ˼ת
һ鹫ʽ໥ϴγһ֤
ʮӺ󣬳ŵյ˫
Ȼִʿд
⣬ŵ׼εĳԤ⣬⡣
գMյµΪk=k1k2k3fһԳƵĺرģfk=kifk=ki.
N=R^n+1NʱnάΣMd^2Ϳ΢hIR^2ʹN=I*MNĶдds^2=dt^2+h^2

ʱεδţŵҲһйʽдԾϡ
˼·˳ŵдޱ
˿ŵûо˼ƵģһʽԾȻֽš
һnάM΢ͬߣI=abRĿ䣬abR
㶨
ʶĴһָ
Ȼ󣬽˶¶ɵĿ⡣
ŵ˫ֺʮ˶תͷȥ󣬱ҡͷһЦ
˵ʵĿĿĲչһƬĵĻȥμ˶ʿıҵȫ⡣
Ҳ˵һʿµһоݣŵ˰Сʱɸ㶨
Ӳʵ
ŵ΢̣ڶ⡣


ʮ ټо
ڶĿŵɨһۣ֪Ҫݡ
ͬڼѧΪΡ
εĴͬǼѧн͹˵
гռ䣬ŵԴΪ㣬ڶĿ
BSDĶŵѲ°ɡ
һǰΪĿֻСkissѡ
̵ĺŸ裬ŵдµڶĽ⹫ʽ
һ⻬MΪдռ䣬Ͼһ1-γɦǺһͨ⻬ʸƺһ1-1㣺ǣƣ=-1^2X=X+ǣX.
MϸһȶgʹgTpM*Tp*MRһзŵķ˻ڻgxy=gXY+ǣXǣYgXƣ=ǣX.ơ

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ŵùĿһ顣
֤2nNʱʽ
2345n3/2^n-1n+2ܡ1+21+31+41++n-11+n
ŵ֪Ϊʲô֮ǰ˵Ŭʽۡ
ԭĿһŬʽıΡ
νŬʽָһΰѧŬһʽ
ʽΪ3=1+21+31+41+51+n
úʽֱȽ֤ڴ˾Ͳһһ׸
֮ŵĿŬʽء
ͬѧŵݸŵһֽдѧʽΣ³ͬѧ֤衣Ϊ֤ȷģû⡣Ϊ֤ǴģΪǾͳˣ
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ΪǸˣŵʡ
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ѶȵĿЩΪˡ
ŵָСͬѧɫǿӲ졣
ɫǺ죬ָָųŵ㲻Ǻǿ𣬱ʸ㣬д
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֤࣬3kNʱɲŬʽɵã2*3/2^k-2=2*1+1/2^k-22*1+k-2/2=k.k&lt;2*3/2^k-2k=34nǣ2345̡nܡ22*3/22*3/2^22*3/2^3
֤Ҳ࣬Ϊk=1+k-1k+1k=3453=1+2*41+2*1+3*5=1+21+31+4*6==1+21+31+41++n-11-nn-2


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ţŵһ㶣ɷڶԼ
㻹Ҫ֤𣿼ֱ򵥵ĺ壬ΪʵrȻǴx-r=0ĸ
ŵ⡣
ҺãڽŲ䣬ȻĿһ޶Ǿÿһϵֻ
ˣһƺĴȷеؽӦΪϵĴ̡
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ڰ칫˼άɢ뵽˼֤ԺѾһ֤ķ
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ڡʵǷǴ̸⡯Ҫȷȷһ㡣qǴx-q=0ĸңֻҪѧһԪη̵˶֪ȻϵΪ̵ĸȴһ
x2-2=02-2
ͣ˼룬ŵɤӣ˵
ʵȰҲԽ2ǴӣeͦǳԽӡǵһ
ͨ˵ĻʵҲܼ򵥡
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ѧݸֽҪԾͬϲʱֽҪԣ
ն򿪵ϵһĵΪŵϸĿǰĿ
ŵһһԣĿ˽⡣
Ŀǰо칫ҡŵ˳ƺԷΪĵоС顣
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ĿǹһѧУо񣬶Ƿ˽½ӵһĿ
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һ⣬ԸĿĹ˾
ˣÿһʱ䣬ڶϼԼ۱ȽϸߵĿļȥʽһ֣Ҳø
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ϵͳʧȣֲٽڽϵͳѧģ͵ķʵֶֽϵͳĿơ
ն˵Ľģ˼·Ҳܳ档
ȣϵͳѧķһӿ飬ң֤ȯӿͶӿɵĽϵͳ
һϵͳڳΪ޹Լ״ֵ̬Ͳ仯ļԣǲᵽĻ
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ܿģؿѧѧߵѧۡдĿѧģȫĻѯƸϢͬʱ㻹ܹѧԴȫ˿ѧרҡѧ߼С¿гɹѧ
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ڵġϰ塱ڣһƽģ۽С
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ResearchGate̳ϣе֪ȡ
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һ⡣һнĿĿ飬һЩԭѾɢǸĿȻܼȥ
ǣǹ˾ҵҡϣо칫ңһĿ


ʮ ҿ
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Ŀ˳ŵļ룬ƽÿϵĽ١
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⻰һڣ˵г˳ŵ⣬˽һıڡ
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ԭԤھõڹ˾͸Ͷʵģ͡Ȼ˾Ϳʽ졣
û뵽⵵ӵ飬аĿĿֱӽɢˣǿһ޴Ĵ
ˣĿǰڹ˾ֻо칫ǣǷܽĿǰİ취
һٴοڣҰǽһ¡ĿǽӲӡӵĻͱҪһɡ
ˣһǹ˾Ǳ˵ˣĿĳаԭȻҷǵĽҲԭ˫
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ԣŵͷڣΪǿ԰ĿĹӶ۸ɲ
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ڵƢն֪Ҫ³ŵĸҵĻǽŵ¾ı乬ˡ
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һäĿɾԼ㷨ʽ㷨ɲѧ1982꿪Ե
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ŵһʱ䣬Ƚڸ֮ȵLogisticƵ
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̷΢΢ɫһ죬Ȼһһѧӣģͬһרҵֶǻˣպһչġ
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ŵ˼Ļش𣬡νFritz JohnҪָminfxst.{gx0hx=0xMıҪ
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Ƴһ۳ŵĿһ˿ͣ׼ȷ˵ǾֲLipschitz
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ŵУѾĿڵʲôˡ
ڼ۽⣬ʽУǿ԰MһmάΡ
ٿɵƪHilbertռMPģӦжɣ
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ڶ۹ݶȵʡ
ǰĻϣ⣨MPFritz John
Ĳ
ѱڴá
ŵڿһȻĹ̲裬һඥĸо
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˵ϸLipsehitzĹ巽͹ݶȵĸ
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ͬʱ֤˶ϵĺȡСֵıҪǹݶȰԪءЩʸѧ滮Fritz John
ڴĿĿǰƲƣΪľĻƻҪʱоľжƵĿܣҲǳŵĿǰĪġ
пһŵòڼѧ裬ǳԼһΡ
кܳ·Ҫ߰ŵ̾һ䡣
ŵĿУŵֲΪҪоԱϵĹࡣ
һΣǱѧϰĿģ뵽صѧĿоС
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ڽǵȻ϶ѶȽСϵϵ͵Щڷڿ
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Һã뻹гŵţʹ΢Щ
ֻԱ߳ŵϵı飬ôû˿ĵӣ
ŵЦЦնģзںڣµĿӵģ
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ŵţûͺնˣڵһ˾ڸ㶨⡣
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ŵֻбĺȣϱ˺ȵĵ
ͣŵûô˼ĺնЦ߻ذ칫
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裨MgmάΣÿһxMпTxMһguv=&lt;uv&gt;?uvTxM||v||x=&lt;vv&gt;ʾvTxMڵxķпռ䶨һȼ۷
ˣÿһxgTxMTnxM֮յһȾͬv*=gxvnv*u=gxvu?uTxM.
ռT*xMķΪ||v*||=||v||=gxvv˱иʽ&lt;v*u&gt;||v*||||u||?uTxM.
һٲ绢ŵָҪڼϷɳӰ
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һ׶оLipschitzһЩʺFritz JohnתϵѶȷͳŵõࡣ
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ŵҡͷЦЦתӣͶ뵽С

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ŵŶڿİ칫ϣŵĻźӣЦǺǵֵ
ŵȻɫһصڲŵƵ
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⵹ã˵ԼǸС֮⣬౻һ
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صңѾϾŵࡣ
оеĺܣԡۣ뿿ɳϣһ߳ʳһ߶ŵӡ
ŵҲϽϴһԼɳϣ
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ŵͷûУ˸ĿֲҪϷҶ޲öʮСʱת
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Χо˵Ȼֲһ䣬֮Χ
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ٰʮ һ䡭
ͦİŵ輸ϵһ㣬Цſڡ
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ŵ͵һ顣ĺĺ
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ŵ۾Ժ˼ת
v||x=&lt;vv&gt;fx;oTxMR
Xyһ&lt;Xy&gt;o=&lt;Xy&gt;DһXy^n

Ȼŵһ̡
յ˫˷ܣ֪ôˣ
ѹסĵļŵڼžžžóһйʽ
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ˮһ˼·ͨŵֵҰޣֵҰһʰ

󣬳ŵ飬ƿڸš
ڣĲиŬҰ㽻ҵŪˡŵڰ칫һỤõ˵
ٶȺܿ찡˵˺ϴͬĻ
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ںǺһЦųŵٶȺܿ찡
ŵɫľȻĿڣڣ˵ɣηָʲô񣿡
ڰڰ֣ûˡ
ŵ¶ɵı顣
˵ûˡӦ˰ɣʡѧԺоѧӣ١
죿ѧŵһ㶣Ӧ
ʱæͷ˶ѧҪӶˣ


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˺٣ͬѧĹҲûжôæ±һλ걨󣬲ͬѧͷˢֻ
ResearchGate̳ѧ飬Ƴöƪһظŵӣ¶һ˿ɫ
Ѿʮˣ֪ȥˣĺòã
ͬѧ˼ĲȻͷһϤ
Ŷ˵һ֡ͬѧ̧ͷҹ˼ʱ
㣬㡭
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磬ѧУһ俧ȵڡ
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ԥһ˿ĭµ˵㲻ǲʿ
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ȣĿǰ˵ܻϸδδûбɲǱ
ĬĬģͬѧһ

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ȵıǿγ̵ļ٣ʵϰĿʱࡣ̿ΡҿʲôģֻҪ̫֣˹ܡ
Уһ༶һĻᣬֻһѧıҵΡ
2022ѧϵоϳŵһֻжʮˡ
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ѡһΣʱʱɵĵʦһĵʦѧ֮·Ϳ˵˴룡
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⣬ֻһȺоĵʦѡ




پʮ дģ
ʮλڣǰһλݷͺİڡ
ڽֻʮ꣬͡ȲЩϽϾ˼ѧѧҵҲָ顣
ڼŬ𽱵ļӳɣʹðһͳΪоѡ
ںλҲȫѧСѧҡ
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ʮλʦ֮ЩѾ˽࣬⻹Ϊҽһ飡
-֣ȥʮŬ𽱵Ļߣ۷굣оʦ굣βʿʦľ顣ڡAnnals of Mathematicsƪģڶͼʹ۵ȷͻף
ǰһ˺ЦЦ
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λǱ-սڣۣ
ʮλڣÿ˶оڸоҪĳɾ͡
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ȻΪѧǰĴѧʦۺԶѰѧУȵġ
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Ҫ˵ӭģʢİڡ棬λѧŶӵŽ̸Ļᡣ
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תۼ䣬ǰֻʣ³ŵһˡ
ŵҲ̫Уԥһº󣬴λվߵš
ò˵ܽʡѧԺѧϵһǵ֮ں͵ʦĽУʦѧһЩ⣬󲿷˶Դ
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ںǰһλڷɫ˽š
ŵһ󣬲ɵɴ۾
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ѧͷŵԣҴʮ꿪ʼѾòоУѾʮʱ䣡
Ҹ˵һУ˶BSDоң
ŵһ顣
˫ֽ棬ϴһ˿Ц⣬BSDʲôǡãҲһλBSDʵоߣ
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ڣͨӦĳȺṹĴEǴоs=1ΪLsĽΪr=RankEΪZ-ģrank㣬limL/s-1^r=......һ漰ּʽ
EisensteinseriesۣƵ漰ɳȺIII=kerH^1&gt;ֲ H^1֮͡ԼEtorsion-partȻ󡭡
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ͬѧûиܵͷ⣬ŵ˵ǿԷdk=2k+3kG2k+4磬d0=3G4d1=5G6Ȼdkϵƣnk=2n+9/3n+6
q=e2IӣG2k=2ˣ2k1+

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ղλͬѧ˵ɳȺֱֲͣͨԼEtorsion-partġEisensteinseries۵ãɲ򵥵Ϊ˼򻯲ãŵЦſڡ
ͬѧɫһʲôˣ
ŵûлش⣬Ƿʵλͬѧ㽲ЩӦǴӡΪ1ʱBSD֤ƪİɣϧûƪµľ裡
˵ţŵ̾Ϣҡҡͷ
ͬѧɫ䣬㡭ô֪
ŵһЦʼ磬Ϊƪģдİ


پʮһ 
ΪƪģдİŵʼһЦ
ͬѧŵ⻰ɫȴԭȵĽű
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ô̫ˣһۣѡʦ£ȫԸģѵǿ˲ɣǣ㿴ҵĵʦ
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ŵҲ˷Դ
ԳŵһֱšԺ߶ڵĴ٣


پʮ 
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Ҵˣº󣬽оһΧ磬Ͱгŵͬѧˣ


پʮ Ŀ
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ǲǰʱ䰲Ÿŵ̫࣬ѹ̫󣬰ŪñɶMˡ
վ¶ĺͰЦݣŵͬѧĿʱ仹ǳԣµޣڲŹȥ²Ѿ֮һĽȡ㲻̫Լٻ񣡡
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ŵȱϯѧʢ硣
ŵɫȻ࣬ڣͺնѧܶڿеĵһߣΪĿ깤ԷʳΪĿһԱܶСңͶ뵽ΰĿҵоУ
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ŵ̵ȥ
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ǿȱ֮ǰ˲٣ŵȴԵøɾʮ㡣
ǰѧҴջ£ŵȻǰѰٷ֮һٶľ͸¶ĿоС
˳һµʱڸ㶨ÿ⣬ҪһʮļڣӦòɣ
˵һĿǰοĽȡ
һ׶εɣڻFritz JohnҪLipschitzĹϵƵԼLipschitzʵȫó
ڽеǵڶ׶Ρ
ںնͷڹ˵һ׶ʱŵڹ̫ǰѾһֵڶ׶εݡõڵڶ׶εݡ
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1躯rM-Rڵ㹤MֲLipschitzUգǰz꿨ڵzطvLMĹ巽Ϊ
fxv=limyգxsupf*^-1y+txv-f*^-1y/t=f*^-1գx*xv.
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iifxvΪvĺTxMLipschitz
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¼ļѾէʼĳԾڵľޱȡ
һή⾫ֻⳡôʲôʱǺҪؼ˯
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پʮ β
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ЩеûˣϿԻȥŸдȥɣһλܺͰ㲻µҵ֣ǸŰ

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ڳŵͷѾɵĲ࣬Կ˴š
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HelloλŵԺ˵
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ԱߵλһֱһԲ
ƳһʦɫֲûκŴԿս˵Ȼ˰æȫҲԲ׷
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ѧרҵоλһ㶣ҡͷЦЦƪ£ɲһоܶġ
ŵҡͷǿδأ
ŶһЦĿֱӳŵɫƽӣЦҿɾĿԴˣ
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ŵûλ꣬ǵͷλһֱһԲϡ
ŵ΢ӣЦǺǵĵƪ£ӦҪĴεĸӰռŷϿռԶ㹹ɵĿռеعʽƵڣ˵ûɣ
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û뵽λɽ©ˮġѧ㡱Ȼһλ
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ҵ뷨ǣҺ͹øҪԱݣȻǾͿɳ룬ʩΪ
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ˣѧҴ180ʮλѧңǴѧʮŸоĶѧҾɸѡѡγġ
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Ҫ֪ڶʮһͳھٰǼѧҴᣬĻѧֻˡܵ˳̶ȣʵס

һһٶೡѧ棬ȺѧҲÿȥμӣοеѧͬʱ
һٶೡѧİűŵʱ̷ͨ΢΢ĹϵѾõ֡
ܵ˵ʱźܽաΪ滹нѧĻڡ
ŵ϶Ҳеѧ涼ꡣ
ҪģԼȤЩԼо򣬻뱨Ǻܸߵѧ棬ŵȻֱԹˡ
ֵһǣ뱾ѧҴʮλƽŶ׼ȷ˵ʮλ
ʮλƽУʮλΪѧˡ
һλоѧķƽıͳŵое֮⣬ľų棬ŵҪȥһġ
Ϊ͵հһ´еӢˡ

һŵȥһλ׹˹ٴѧƽڵѧ档
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ٶ˵Сã˺ŵһλȫ
ѮıһλĲ»Ͻ̨ԭվýĳŵ׼ʱһŵĿλϡ
мλѧע⵽ŵ߷û⣬ֻǸվˣпЪ
ԺѳǳĻǲҽ𿭴ƵסΪá
͵͵͵ؾƵķҲ
̷΢΢ĹøôҲ֪Ϊ¾ͽ˼λѧҶǾƵۣ֪ˣҲ⡣ƴ
ڣǴ۷Ķţ
꣬ҲΪȺۺͬشףűΪƶȽ
ˣѧĺǴѧֻ΢˵εһЩ
ѧƣSome results on affine Deligne-Lusztig varietiesǡһDLƷֵĽ
νķDLأڴһࡣأָǴѧ϶ʽϵĹļϡ
DLһǰ׹ѧҵ-һһʱķչѾĿǰоȵ֮һ
ŵ֮ǰںʹѧⷽĽӴĽ٣ֻ֪DLشǸʲôʣŵ˽ݲࡣ
̨ϵıȶѧݣԴѧеȺΪ㣬ܷͨDLص½չ
һţ޷ǰŻУŵ̧ͷýζ
ŵļλѧңд󲿷ֶΪհȶڶרҵԿڵԭ򣬶佲ڵݲûͶ̫ྫȥ
;֮ʣʶһƳ㿴λֱŲӡ
һ㶣漴ȻʧЦ
ѵΪһѧһѧеѬգܳΪһѧ
˵ȶڽݣǸʮ֮һŶٷ֮һȺѧ߾ͿԼ鶹ײˡ
뽫ЩʲôʵĻֱӾʣȻҲ԰дСֽϴңַʽԡȶڽPPTϵݽ꣬Ц˵
ΪƽУȶλ뱨ȻǽеһСʱѧ棬϶һСʱ
ĿǰѾȥʮӣʣµʮң˵ʱ䡣
һջĳŵһ߳űݣһѹסĵļ
ͶԸ÷˽ⲻĳŵȻӵ
ĿŵʣֻôıʼǱ˺°ֽдҪʵݺվװ·ӣݸǰλѧҡǰ
ŶáλѧʶĽӹݸǰˡ
˼λѧƺ뵽ʲô͵һŤͷ
տҲλλѧҼһ


İ ֽƬ
ѧβݽ̨ϵıȶڽӹǰŵݹļдֽһһ
ŵվڽȻЩף쳣档
ûֵҵⰡһ󣬼û⣬ŵСֹ
һλһţŵѧ˳ŵҡͷЦЦԳŵ֣Աһ£
һȻŵ˽зԱڻδ뵽ɫȥûӦԼ
Աһ£
ֱλѧҽ˵ڶ飬ŵһ£ϹŷԱʽЦߵλѧǰң
ѧҵͷһʵҾƵķԱɣ
ǵģҸսƵ깤û죬ʲôĵط뺣ŵλѧӦǿԼλˣ˵
ҿղţȶѧ棿ѧҺЦʵ˶٣
ŵڰ֣˵ЦˣֻĽȶķƽմְˣô١
ֻ˰ٷ־ʮѡŵﲹһ䡣
ѧһȻ˵ı飬ЦȻһķΧҲͦõġ
Ȼѳŵеġû١ʶΪˡһû
Գŵڰ֣鷳ñϰɡ
ȻвԸΪ̨֪ϵıȶʲôʱشԼ⣬Ϊ˱Ⱪ¶ЦŵͷõģԵȣϡ
˵⻰󣬳ŵżҴҵĲõĺ߳

ڣվ̨ϵıȶڸջشһ⣬򵥵ĺȿˮһֽ
ȶɨһۣǺЦе˼
ţͲ̨˽͵һ˼⣬ҿһ
ǣȺӳ㲻ɲ£DLصkֵ
⣬˵ҸղŽѾȫ⡣Ϊʲô˵Ŀ˼ģʵϣע⵽˻֣ᷢٸղŽʱһʴġ
оһֱûһֻۣܸһĴ𰸡
ŵʱҲϴӺ߽Ѿ⣬ͣ˽Ųפ
ȶڽ˵֪ȺǾȺṹʵλ߸ΣȺеļӷԪеĽӳ䡣һkΪ򣬲A^nΪkϵnάռ䡣
ɴˣ׵ófk[X1X2X3Xn]ZS={xA^n|fx=0fS}
SʹVA^nV=ZSһǿմVԼIVΪVȡֵĺɵ룬IV={fk[x1x2x3xn]|fx=0V껷Ƕʽ̡
ôˡ
⣬ȶƺ顣ǰشļⶼһ£ѾֶӣͣϢͷ
⣬ľЩˣȻҽĲһԣвһģǿ˽ۡ
ðһ£֪λ⣬ɷʶһ£ȶڸ߸߾ֽ̽ѰĿ̨¡
һ룬룬롭
һֹİУʮȥ̨²δ˾֡
һŵλѧҿűȶھİֽ֪ΪʲôһϤĸо
ȶڵɫҲЩΣڨڨЦȻλͬвԸ¶棬˽̸˽̸
˵꣬һֽ⡣
̨£ǼλǰѧҲ۷׷ס
Ǹô£ôȥӴȶڵĻᣬȻôˣôģһŵλѧûпѹֹ
ŵЦһ¡û뵽ֻһѣȶھȻôӡ
ҲǰŻаʵֻա
Ͱ£һܰɡ
ҪϡŵԻֹѧҿ˵
ѧҽӹŵϣ˵һ䣬ôá
ŵǸ˵սʱȶڽһ˼⣬оͣһ
˼ѧҺߺһ˵ֻ˼ѡ壬ûô򵥡
ŵվһԣû˵
ѧҰڰ֣ˡȥæİɡ
ȥˣʲôĻ˵ѧҲ˵ŵҲ׼ˡ
һСʱѧϾҪˣԼģʵҲȫˣջν࣬ҪҸطһ£Ȼȥ³
ŵҪٴδǸѧҵЬˡ
ŵͷһŶлл
ŵϵЬ첽뿪ã˿ûע⵽ֽƬӿڴе
ѧҿһĻҪѳŵһȴƺ뵽ʲôԾ
ûмǴĻλİֽƬ̨ϱȶչʾǵֽƬ˺Ѵ·ȫǺϡ
Ӧǡͬһֽ
ǣ˵


İ ICMϵĻ
ܱѧıˣ϶һӹңѧ˵ݣҲǰط
磬һĹѧҴᣬûлͣЪüʮѧǰѧо
ȶڵһ棬ŵͿνջࡣ
еһϯɱȳŵԼͷ쳵оһڵջҪࡣ
ŵȻǸϧᡣ
ͣĴ᳡ϵǸ᳡æòֺ
ھһ麣һϵļȡźе֪ʶʵ
ڳŵ̷΢΢Եķ̷ͬ΢΢ĿǰȥĴЩеĽгŵĻɡ
ŵȥ۷Ľ⣬Ҳȥʮೡ棬Ҳˣϣŵһƣڷ̷΢΢غϡ
õôƴ𣿡̷΢΢һ֭Цʵ
ŵһƨɳϣѵãƴа
̷΢΢ʵջô
ķᡣŵͷҸоһջĶһ߶˿ĿջҪ࣡
ŵ˵ʵ
ڴƼĹѧҴᣬŵÿģѧģǸŷһ¹ȵġ
ۺͷͬһĴţʮˡ
ѧҴҪٰʮʱ䣬ŵžϴ֮ѧˮƽߵߵһΡ
ϧģѧʱֻʮ죬ҪһصĻ
ðɣ̰ãĳһأŵҲޡ
ڵǿȣÿһѧ󣬳ŵҪһ
̷΢΢½ջ񣬰컹Ǽͷж⣬ŵصԼ䡣

գڶ졣
ڵһ쿪ĻʽʱǧλѧͬʱԾھƵѧҾ˲ࡣ
ŵûйٵȺ˵׸ʲôȥˣʱȥѧ档
ŵһվȥƫ΢ַֻ᳡
ｫĳʮӵѧ棬PEDѧҹ񫡣
ֽڱ漸ηݣڽˮ̳ʱԣŵ½ڱڼβPDEԷеӦãڶָԼʽȷExp LebesgueռйƵĽ⡣
λĿǰƫ΢ַѧңŵҲûдλᣬĳ漸һ㲻ꡣ
ŵӡΪ̵ǽڵı棬˼·ƽȷѵڣٽЩѵ㡣
ͨ滻̷˫ϵͳѣͨ켫ODEϵͳĽSobolevʽĹƣӶúɢϵͳL-ģҪ˥
Щ˼·ŵܴĵ㲦

磬ŵǻںۡۡѧֻ᳡˼λеı档
ϣ׼һµĳŵȥ˻λ뱨˵Ľ
֮ǰᵽ칲ʮλѧΪ뱨ˣڸԷֻ᳡һСʱʮѧ档
ʮУԺʿˣʮˣλ缶Уڵݡ
ŵƽ֮ԺʿĽΪһλԺƽ֮Ժʿʮ꣬ǻûйѧоĻƽ䡣
ͬʱƽ֮ԺʿǳѧߵĻߣڹѧȷ޽ڻҪһЩ
Ϊδ׹ӣƽ֮Ժʿʮλѧңͬ˹ѧҴϵĻ
ʶڵĻѾϸڽͶ˵ĽĬĬš
ѧһįΪеϷÿҫ۵ıҹԼյĿ˼ڤ룬ǵĥӵеһŸƽִŵģˣȱЩ
ƽ֮ԺʿǡInteraction between singularity theory and the minimal model programлع˹۵оص뼫Сģ͸Ĺϵ˶żεĹʣ䷶ֵ֤Լkltġֲȶۡ½չ
ۿ壬ƽ֮Ժʿ˿ǼλƽѧֵͶ٣ǰѧҴС
ͬʱʣ¼λԻ뱨ҲȺ󿪽
ʱγʡѧоʱΪQuantitative almost reducibility and its applicationsоŶڽƿɻԭԵ½չһά׼SchrodingerеӦá־Żоʽ׷ϹȽˮƽ
ʡѧԺڵΰѧҸ³˹չʽع˹ڻֵĲͶ־ϵȦԼǶL-䵼ֵϵԼʽоɹͨƵȫֵGan-Gross-Prasad֤Сĺ䶯
ΰͬ͵Ļ֮һԻߵGross-Zagierʽϵرʾоһ߷塣
֪УѾΪѧоչУһСĴڡ


İ 
109ţ졣
һٶೡѧĻ㱨Ѿȫ
ڼ䣬ŵ˶ʮ峡ѧ棬漰ۡۡΡ΢֡Ӧѧѧ߸
ӽ쿪ʼʣʱ䣬㰲ݽۺͽ
μЩߴ඼ڵεѧңҪҪСһ㣬Ҳ˳ŵȥͣĲͬ᳡ܡ
ٶೡܶ࣬ݽߴ඼ŵڷɻλڲˮƽ
ȻҲдڵһηƽû£ٰһСͽ
˷ƶȽ佱񣬲˶ʮೡ綥˵ѧ棬ŵѧҴĿѾ˴롣
ʣʱ䣬ŵһ֮ǰʱδ͸ݣһ߼żȥ
СҲ⡣
Ȼ˵ջ϶Ȳ֮ǰѧ棬ֻҪһѧ˼ķʽǾûȥ
ڣŵҳA4ֽӡĽűһϹ
ĴGauss͵Ĵξֵһŵ㸴ӵļⶼܱѧͨ㲻㲻
صHardyռToplitzӵĽԡѾϸ͵Ķ˰ɣ˷ȥȥ
NAȫȷԵһݽĻǰ½ڣǾ͸һҪȥˡ

ɸѡһ󣬳ŵȷʮ峡һҪȥĽʣµģȫԵɡ
һȫˣĸþĸá
ˣŵһĶͷͻȻʲô
ǵãƺӦǸڣҪȥš
ʲôţ
ŵùǼŽűݽһ֡
ҵˡŵĿڱһϡ
⣺κѧϵ
ݽˣ-˹ֿ
ʱ䣺1091400~1600
ôһͨͨĿȻڳŵʮ峡ڡ
ŵһԼĽűţʱ䲢ͻ
ȻˣǾȥֲʧʲô
ö˼ƻŵϷ·һ̣װͲ͵˳ĵһվ

ˬ
緹ʱ䣬һţڷ̻ʵĳŵ
һóŵջֻΨһźǣĶɻҲҴյλݽѧǰʡ
ûļ˯ŵŴ󲿷ݻм䣬ջ֪ʶдרΪѧҴ׼һʼǱϡ
ԭոµıʼǱڳŵ²ͣĴݲ£Ѿһѹʽ֮
㣬ŵڽСڡ
ŵǲʱģ˵ѧҴѾǳŵһɨȥһٶ˵СڣŵĽȶʮ˶ѡ
ţ
еͰҹбҪġŵСһ䣬ûκι˼ɵһŵĿϡ
Σܹûע⵽Լ˰ɡ
վݽ̨ϵڣ̨µĴèСèֻɫҲЩѿ
ЩƽеĽ˵öϯɵ⣬ſȸΪ
û취ȺеѧɾԶԶССһѧܹȽϵġ
Ѹٵϼһ˿΢ЦһԵʾ⡣
λ꣬ŶҲǳŵڷɻѧס
׵ͶӰǣ򿪽õǷPPT
ţú޼ڽȣӭλڰæ֮ҵⳡݽ⣬ǡκѧϵ
ڽ֮ǰұҪҽܼڵ㿪һҳPPTһzata
ʲôҲù׸Ҫļʣҽйصʡ
ƣsɽΪƽϵǴs=1е㡣Ǧƣs걸ƣs=^-s/2s/2ƣsΪGammaƣs㺯̦ƣs=ƣ1-s
ͬʱÿżǦƣs㣬ЩΪƣsƽ㣬⣬ƣsķƽȫֱDis=1/2ϡ

˵ͨоFqϵĴXZetaZxTͦxsĸ|XFq^n|ȻоߺͰ£ZxTʡ
ⲻʲôĶֻһȽӱĹ۵ȥ⡣
̨ڸɰͰ͵Ľţ̨£ĳŵڽеһʱͷ˯ȥ
ֳŵʵڽ̫Ȥ
̨ϣѾPPTݣڴ̨¶ʮˣڴʵĻԾʣһ֪޲ԡ
žһƬ
ޱΣڨڨû𣿡
һͺãҲһ
п
һţŵԺչһ壬˸ĹǷ
ŵ֫չƲ
̨ڵУ˾ˣһֻ֡
һ
ֻ֣˵ǿҰ
ЦĿڣһŵλܷվ˵⣿
ո˯ѵĳŵһ¡
ɶɶ


İ ʵڵС
һŵλܲվ˵ץסһ˿ϵľݡŵٳûзӦٴο˵
κ״̬ĳŵںǰŶʮλȫĿ۽Լϣһ±Ƶվ
㣿
̨ϵķڿԱĳŵ۾Ӻվͫ͵һ
׸̲ס
ŵӣٹʮ꣬Ҳǡ
ֻû뵽ǻʱ䣬ٴ˵ڻŵ˵Ҫȥŵܻ볡ʸֻǰѳŵĻ׵Ļˡ
ŵˡ
ɨһ³ŵĴ磬˲ˡŵӦǴɷĻģھƵԱûвͲڸÿǵˡ
ǶԳŵĵĸм
λСͦʵڰ˵Ϊ˸רװһղżԼӦΪ뾽˫ӦԼ
ʱӳʵ˿ɲˣ
ȿȣںݺݵһۣһЦǺǵĶԳŵ˵˵ɣһ֪޲ԣ޲
ڻһŵûκζǰǶʮλѧҾЩסˡ
ǿۿǸˣֻǾƵһλԱˡ
һҾƵķԱûѧ⣬ǡЦأ
ȶţٻҪ֡
Ϲˣۻˣ
ûǾһҺ᳡ҲӦվˣֻϢһͱˡ
ǸһǸһΪʲô1+1=2⣬ǺΡ
һôճɡ

ţŵڴԺ״̬ѹʶʲô顣
ҲҾѣôͱΪˣ
Ҳ߯ʹ˰ɡ
ǹǹȳİһǴԼݵľȳ
ŵˣɶֻ··ǼȥԱߵĻ᳡ʲô󡣡
ŵͷһ˵һ⳷
ߣڴסŵˣˡҵǵ棬ɶȫָˡ
ЦĵλҾ;ѧϰѧ֡ʶһλѣ֮ʣʦӷڣҾãлĻҲԴȥԱݣȥʡѧԺʦڡ
δһλѧһ԰ɣֻϧҵλûᣬлĻʶһ¡
ŵɫһڡ
вԼһæȳͻὫŵݹ֮ڡ
ⲻ֪ŵȳҲȥˡ
ŵĿ̨Цеһ䡣
ȻˣǱԸֻϣ㲻Ҫڲźá
ŵżˣƵ߻ԭλЦſڣѧȷʵһɻҪĽ𡣡
ɫһɵĵ뽲
ʮλҲ䣬λʳʲô⡣
ŵԺһݽݣһЦͨоFqϵĴXZetaZxTͦxsߺͰص£ZxTʣ
٣ZxT
ڣ㺯
һ仰ڽݣӦûɣ
ڶʮλ򲻽⣬ɻĿУڻͷ
⡣ͼʶŵʵ˶һ仰ܽᣬûκεľȡ
ʾŵ
ŵף˵ǰ벿ֵݣǱȽͬģǶZxTʣвͬĹ۵㡣
ZxT㺯⣬ҸΪһʡZxT㣬ĳԵʽ
ĳضʽֹһ䣬˼һУ̧ͷʵΪʲôôΪ
ŵ̧̧֣ʾ԰꣬ҽٽ͡
Ǵɻ⣬һкһͬĹ۵㡣˵ֻߺͰ¡
ǿǶĶõ̫ڿ̣ʵԼΪ㡣ǰչصzataϣձԺʵüֵߡǡ
ܣֱӴ˳ŵ
ʵĵóоFqϵĴXZetaZxTͦxsӦľߺͰأôܵóһձԵĽ۳ڴ
ŵû֤ô֪ܣ
֤ˣʡûݣͲҪ쿪ļ裡
ŵʼ磬Цɣһ֤ˡ


İ ˸飡
ɣһ֤ˡ
ŵصڿտСڣ˶ݵʧ
ǣʲô˵顣
̨ڵĺ͵һͣųŵͦεӰĬʮ롣
ǺЦλڿЦ԰ɣ
ŵ˵֮ǰ˵Ƿûȷʵ֤ݣֻͣڡ롱׶ΣǾͶ֤ŵԶ㹻ѡ
Ҫ֪еĲ붼°ͺղѧӵгߵĵλο߻ֻһλо
ŵȷʵ֮һ㣬зȥ֤˵Ǹ롱ǾʾͱˣǾͱˡ
롱͡ȫͬĸ
롱ʵԵ͵ĿһǸô򵥣ӦܶҪȡ롱ǿ١
ңŵɲʲôôֵĻɫ
ձϵķصZataĹͬʡ
ⲻʾ϶Ĵص͸ص֮һϵ˵˿ռϵͬͬڴغ͸Ρ
Ϊѧѧң֪ĳζʲô
ѧܹͨѧͬԱʾۺͬչεо
ͬʱһֱFrobenius̬ͬĻӳ⽫õ˺ʹεmotive߻ٴӡ
⣬ڸöоĺZataô֤Ҳṩһ˼·
ֻ֮ҪŵֻҪ֤һǾԻڼѧһɷ籩
Цŵʼ磬˵ҿûпЦ˼
üͷ𣬡㡭
鷳ŵֱǰ̨ȥһһ˵ˣһ֤ǿɡ
˵ţŵ̨ϣԱ߻˵з۱𣿡
ŶУС׶·˼룬ԺĴһԵݸŵһз۱ʡ
Ϊ˷㣬Ƶ귽ý̨ǽװĺڰ塣
ŵ̨¶ʮλѧҴ͵ԹԵںڰд
XFqϵdά⻬ӰأZataZxTһZxtQTȷģZxTд޽ʽ
ZxT=PiT^-1^i+1=P1TP3TP2d-1T/p0TP2TP2dTP0T=1-TP2dT=1-q^dT.
1i2d-1PiT1+TZ[T]ϵʽPiTC[T]пɷֽΪǣ1-aijTaijZ.

ZataZxTº̣Zx1/q^dT=q^dx/2T^xZxTЀ=1xXŷʾȼ۵ģZxT=ZxTT^x/2ͦƣs=Zxq^-s򡭡
ϿɵãһӰϵZataӵʣ
٣ZxT
ڣ㺯
ۣZxTӵĳضʽ.
֤ϣ
ৣʮӵʱ䣬ŵĸڰȫд
ͬʱڽβŵд´ġ֤ϡ֡
һƬž
һֹİУš
̨¶ʮλѧңӣ𺳵񣬽Ķųŵ
ںݺݵһĭǲ֪ЦǸÿ޵ı顣ɳƵʵô뵽Щģ
ŵ̯֣ȻȻľ뵽İѵʲôѶϵ
ڣ
ô˵Ļȷ˰ɣŵʵ
ڣʱ̫̣Ҫһʱ֤
ŵӻ֣Ǽ֤ȳˡ
㲻֤
ˡûҪ
ȵȡ
£
ܲ֡
ҽгŵ
˵ĸֺ󣬳ŵҴҵĴ뿪Сá
ǶʮλѧųŵıӰо̶̵ʮھݻ١
һƵķôֲһֱһȺڼѧΪְҵѧҰڵϷĦ
ڵĽҪ⣬֤ŵĶǷȷ
ӺڰϽ֤ǸоǺпܻΪʷļ֤ߡ

̷΢΢ƿŵʱŵʰ·
̷΢΢ƵǸʲôأ
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·̷΢΢ɻˣѧҴỹкüŽأȥʲô
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İ Һܻţ
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1016գΪʮĹѧʽĻ
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ƶȽĹһٶೡ߶ѧ棬µʮϿɸѡСŵͻ
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İһʮ ѡһ
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УΪο鳤ĲȺ﷢һļȻֵķǹڱοȫĵȻȥһǿ绰һоܺ䡣
ʡķOKû⡣

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¼ResearchGateŵ俴ʲôȵ㻰֡
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һĵɽδ׹ѲѧĿչټ10ԪĽ֮£׹ѧߣʼʶһֱõĲ롣
ݴţѧоⶨټһһABCйеĶѧң֮µļBOINCֲʽƽ̨ABCԪЩķֲӶѧҽ룬ϣ֮ڽ⡣
ŵԴ˲̫ڱֹ۵̬ȡ
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ResearchGateЩˣȻûʸȥѧҴϹ䣬ֻܸƬ󷢸пָ㽭ɽ
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ŵʮӵʱ佫ÿԶĬĬޡ
ڵ۾Ȼѩģ


İһʮ 绰
˳ResearchGateĳŵ°ͷ
ϵֻŵ׼ȥ䣬Ƴֻһ绰
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ŵһʼûӦ˭󣬲ǸСԵܡ
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üͷĸһʱҲͼλƳһ۲ԶĳŵңΪһˡ
ͬѧһ顣
ԼͬѧҪݺݴŻʵ
ǻǣһ²֪ˡͬѧ˵ȻˣҲܾϻȥɣ
ͬѧһı飬æ˵Ҫһ͸ƴ
ЭˣĵǾһ°ɣҪʦڣֺڴˡ
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Ҳǲͬѧ뵽˰ȱ⣬ΪٻǵλȼѧûϵһС
˲оǰ;谵
ǱߣѾƨƨߵĻصŵǰõˡ
ŵҡҡͷЦϰˣ´γŵʱҶ°ճһˡ
ˣȥ鷳ɣ£ؼҳԷŵ̧һʱ䣬
Ŷáͬѧѳŵ칫ǰóһA4ֽݸŵоеĽȴ˽һ£ٽһ¾⡣
ŵӹͬѧݹһA4ֽ
˿СоĿƣ׵ķ΢ֵַ̱⡷Ѷˮƽʡооˮƽ
ںͳŵҪĹڼͬԵĿ⣬Ȼû취ȵġ
ϾһǼĿ⣬һоֵĿ⡣ڿоɹʵʵӦ壬ԼԲơ
˵ڵĳŵһǰȼĿ⣬ҲκȤǲԼʵԵܿԼŵҲĵ˾硣
⣬о׵ķ΢ֵַ̱⡣
ͨȷ綨͵н綨Ϲ췽й죬ڸ׵£ŶGreenԷ׵΢ַ̻ӣBanachѹӳۣ֤ռڷ׵ķ΢ֵַ̱Ψһ⡣
ŵ򵥵ɨһA4ֽݣľоܡ
ڣǾǿ֤ռڷ׵ķ΢ֵַ̱Ψһϡ


İһʮ 
ʵ׻׻ֺ͵ͨΪ΢΢ճѧͳ̡ѧϵͳƺ͹ѧźŴȷӦãзḻں
飬Ba nac hѹӳۣо׵ķ΢ֵַ̱ڽ⡣
Ҫ̫˽⣬ŵֻҪ֪ţܹݵӦκ⡣
ŵһҳҳţȻŵûпӿٶȣڲλͬԱУǼ˹һ
濴ڷǣ
ţǸĿٴڲͬѧϣǰԹ˼˵ŵļһСģ
ٴᡣ
ʱһһţʮӺ󣬳ŵеA4ֽŻ棬ЦҸղŴͷβǵоݿһ飬ҲµĲĻӦBanachѹӳ΢ֵַ̱鷳˰ɣ
˽Ŀˢˢڲͬѧϡ
Ϊɶң
һۣĵҪңֻǺʹ˵æû˵ľ⡣ŵĻʴ񣿡
ŵһߵùſհ׵Ĳݸֽһ˵ȷʵûиἰݡҲѲ£ǵо棬ıֵǲ֣ȱʧ˺ܴ󲿷ֵ֤̣Ӧòǿ©İɡ
ǸͷϿɵĳŵĻȷʵⲿ֣Ȼ֪ҪĽʲôṆ̀Ǽ˺ü죬ûŪɹ
ոճŵı֣ѾԳŵӡĹһЩ
ѧܣƺôѰ
̽ʵȻ֪鷳а취𣿡
ŵЦЦһָ˰ڣ³֣ѣ
ͬѧɫһϲ
һ顣
Ϊɶһ֣ۿֱֳĸо
˵棬ųŵڡ
룬֮īôʱ䣬кܴһԭô˷
ô˷
ԣŵññû棬һ⣬ʲôǷ׵ķ΢ַ̣
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ŵʮĵͷ˵ûǷ񻹼ǵãֽ׵Ĵ
һ㶡
ŵ͵Di ri chle tֵһ£ֽ׵΢ַ̾ͻһĴ
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ųŵдµһйʽ˳˼
ɳŵûи˼ʱ䡣ֲǼ˵ʦûбҪǵĽߡ
ŲԼĹ۵㣬ͼȥ֤׵ķ΢ֵַ̱ΨһķֱͨʽƵBa nac hѹӳ۵ó
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ǡ̲סڡ
ŵ˫ѹЦеĵͬѧҪôżƽƽȷ֤Ͼͽ
ŵڲݸֽдؼʣGreenLipschitzѹBanac hռ䡣
ҵ֤ܼ򵥣ʵֻҪǶؼʣҲֻʱ⣬Ϊ˽ʡ˫ʱ䣬һֱƵһɡŵƽԺе˼·ǽΰһ߽д
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ͨ弰֤׵ķ΢ֵַ̱Ψһ⣡
˵дģŵ˽ӽʮӵʱ䣬ֵ֤Ψһ˴ͷβƵһ顣
˲ѾĴڣλǴӵ״̬
͡
뵱ĸαֵҹҲûоȻ
ɵ˳ŵ⣬ôͳ˶ʮӵأ
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ߵǰɬʵλѽʲô֣ôû˵ѧԺ
ʼ磬ûģΪѾûȤѧУڸ÷ӿǸĳŵ֪ɣǴģ
˻
Ȼ


İһʮ 
˵ľЩˣƵ̾⣬ǵˮƽ࿴ͶˣҲöིˡŵλվ𣬡ȳˣԺ£ֱӰĿˣʵ¥ͦԶġ
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ԲҸղŲӦʵԳŵǸ
ŵνİڰ֣ѾϰˣҲûмǺ˼
Ųţû·ϡŵת˻ӻ֣
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İ壬ȻˣǾͰҺķЩͬϸڣʱ˭ķ̼һЩ˭ľС
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һʱ䣬ڳŵȺ󣬿ڱãͬʱҲϡ
պͲУŵȻǱͬһȼѧңˣʱûռκαˡ
Լбһŵָ


İһʮ 
оڣԤµ֮ڡ
ԼλڼĳԱ˵ʱȻ˵϶೤Ҳ쳣ա
ͬĳŵһĴս
ȻŵڵѧˮƽѾ޷УѧˮƽѧרҵǰĴѧ˹ٴѧְڣһξĲࡣ
ҲˣŵΪ˲ȣʡѧԺֻܱĬĬӰాҹˡ
Ǳ
ŵι࣬Ҳϰˡ

һߣ˹ٴѧѧϵһ칫ڡ
ԣ˵ʼɣһ໥ôҲҪķǱ߿졣
򣬶¶ҪЦѧУܡ
ͬΪУѧУľҲԶټѧУѧϵһֱʱҶᣬá
ˣȻʡѧԺѧϵ˹ٴѧѧϵĹϵǺÿλʦѧǰıһϣһĳµѹԷһͷ
޷ѹסҲܱȶԷҪ硣
ԺĿʱ˫ÿí˾Ҫһ¡
Ŀǰ⣬ȻϸϺʡѧԺѧϵĿУĿ˳ŵһУڡڻպ͹˴ʮֵľ
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ʡѧԺѧϵ37λûķ
֮ӿȣص˵УڣųŵȶȻڣԽɹӰԽ󣡡
ѧҵȼļܼ򵥣Ǽ򵥵ĿѧӰʵеѧ߶á
ģо⣬μѧ飬ȡֽͨϵˢԼҵڵӰ
߻ʣȨ
ͬڣڼνƴʽͨӰʵֵġ
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չѧңӰػǺܿصġ
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ȻУҲѳŵͬˮƽĽ
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ߣ˹ĳŵڡȻǼҿȵŶвŵഺҡ壬
ǷƶȽĿʡֻгŵһ˲룬˳ŵʱ䵹ûбǿҪ󵽰칫Ұ칫
칫ǵط̫ѹխҳŵһָ˵Ĵ˻ѡȽɵĹصȽʡ
绹ʣµǵʱ䣬ŵԼб¹滮һ¡
ĸȼߣĸȼͣ
֮Ⱥϵ
ЩŵһһǵԺУԼδµĿй˰š
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ڳŵ֮ǰǼ⣬εҪϲ١ŵôЩ
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ҡҡͷŵֲʵʵ뷨
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ÿһҪѴľʱ䡣
ŵһĹǰ뷽ʽLefschetz㶨һϵļ⣬תΪһε⡣
žž~~
ŵƺûиоʱţֱȵϰڹʱѳŵѾá
ŵŴ״̬һ۵ʾʱ䣬ЦһѾʮһ˰


İһʮ һȺбļһ
ҹڵƹɵУ԰СŵҰҰ죬Щɺ
˰
ղųѧʽе˿ûвʱţڹʱűȵϰѡ
ζҵĸоǷǳˬġҹЧʣҲɡ
͵ĳŵĴҴҵĻصԢûʱڿɳϿӵĺокһͰֱ߽ҹš
òײŽҵľ磬ŻеоŵȻץһʱ䣬ЧʵĹ
˹ٵλڣûһʡ͵ĵơ
ڵ棬ŵʼҹè


峿۵£ŵͰеһ֭һݴһĵȺ
ʡķڽ˼תΪεĹѾŪ꣬λԼһ¡@˹ٲ@˹@˹ٹ档
ʱŲ࣬ŵΪλʱӦûûѣ׼Ȳһٿ˵Ļظ
û뵽ŵϢŷȥ룬ȺڵϢ͵εεε
˹ٲϴһļ
˹ϴһļ
˹ٹϴһļ
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˹ٹ棺ҵٶȶһΪҵһŪأû뵽ķģ
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ŵȻƺţȴһ㶼˲
Ŀǰ״˵оٶȿһ㶼ԼҪҪ졣
ϾһŪֻ꣬ǴԵļһֱϴˡ
ŵüͷɵĸоЩ鷳

ǱߣҲûжá
ŵǸĵֻǴԵļһ飬˻Ҫ硣ΪŵȺϴĵʱֻſŪһѡ
Ҫ鼸оɹͷֻεһ죬ŵǵϢӳС
Ҵææģ飬ֱϴȥ
˽գǻһ㰡
պһߵĿȣǿ񣬿ЦŴ֣û뵽ô찡Ҹϸ鼸ʹȥˡ
ڣ˭أξˣһǣһΣҪǰϸСʱ
մ˴ǷһεĻҿû¹˭
뵱Ϊ˸Ͽȣ߲ݵĹҹ鶼ɳ
ˡռϢͨӻ˼ϣ˵ԱЧҪҪԣ
һɣʹˣ쵽˸βͣ֡ҩһ
ҲȥһЩɣһʱ䣬ǿɲܵӣڲ䡣

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ŵ˸OKغĵԵļ
Сʱ󣬳ŵֵû⣡
˶ʱ䣬ҲȺ˾䡰û⡱
Ȼû⣬Ǽɣȡսоͣ
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Fighting
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æһ˯һģڵ
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λTop5УĽҸĶ

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ûH^iX=00i2d
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Kunnenthʽе䷶ͬH*X*H*YH*X*Y
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ֻѧУӶѣ
ŵȺųһеķļ޵ĳ嶯


İһʮ լ
±ˮƽߣ¾ˮƽߵ˻ڷܣ
ŵھ˹ĸо
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˸ߵĹЧʣѾѧˮƽķ룬۵һµأΣ
ҪüߵĹЧʣѧˮƽʱڲܾ޴£αΨһЧ;
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ŵǰѧУڵĿȹڰ칫⣬ʱ䣬ֱӰѰ칫صƵԼҡ
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оڳŵߣŵûıԱ߳˳εĵõô𣿡
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ʥڣŵһ²ŷӦ
һֱĽЩ̫ðףŵҲ˼һ£Ż˵ǱӦðʲôɣնѧһ졣
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ŵһʱ䣬Ӧû⡣
OKȳȥˣæоԵúá
һ¡ǼѾˣæٴӻɡŵڽƿĻо
оһЦû⡣׹̵⣬ҸǱѾٺ˾̸ҷ֣ȷʵȺרŸоȺЧ
һڴĶԳŵ˵ҿǵһ찡ʱ˾ԣ

ҹƬأǵƹĵطȴڹš
˹ٽڹԢ¥սڵǰּһ̣ڼžûš
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ڣķͬChark=0XĵķͬΪH^idRXk=H^ix/k.
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ܣͬ
ڿŪˡսڵ̣ͷԵõЦӦİɡ
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սڸߵ칫ſڣֻһϢ
սƺ뵽ʲôɫ͵һ䣬ֻȺ
ʡķϴһļ
ȻϢսɫ¶Ϊյɫ
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ԺһǽϹŵʱʱ䣬Ѿϰ˵ࡣ
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İһʮ 
1220š
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İٶʮ 
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İٶʮ 
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ʡһ൱ɵѧУǿŰӲλΣֻǻѧƲϸʱѧѡ
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ʵϸʮʼйصĵ·ѧ߿ʼ۷ᴩṹУ𲽷չйؽṹɿȵĴͳۡ
ơʩʹõ·ṹ·ﵽ涨ۼƱ׼ôʱڣ·ͲӦֱ𲻳ֵĸʣǳ˵·ṹɿȡ
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ǣʦȥߵʱ˳Ѱ칫ҵŸˡ
칫ڣֻʣ˺ͳŵˡ
ǰ̽дһСӣ˵ģԺ󻹻ġûƭ˰ɣ
ŵЦֲҸյѧУûãͱڽ˹ԭϵ˼
û뵽ǽоŵЦ
ۣЦǺǵĵҲû뵽·һСӣǰʱ׹˵Ǹһ
ҿ׹Ǳ߲ٽ˵ΪСӣǵĹűռһ಻ԡ
ඣ˹ڴͷֻӶѣôͳ˱Ǹˣ
֣֮Щ˲˹ڣֻص˱̰ŵҧгݵĵ
Ӧŵŵδûʱܱܷͷ˼ڡ
ѧĵλܲ˶λеĴݲС
˲ȥ⡣
ڳŵǲǱԩ¶ں
ǣΰѳŵоƿԼ¡
ŵСȻᣬһĶĲȴ˿ڳ˵ʮԼ
̶Ĵڵѧ©󲿷е㳣ʶѧҶ֪
֪һ¶©ӮǮȴһ¶
ڼŵ֮ǰ¶֪κһѧ
˵ŵǸ
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˲ţȻҪԼߡ
˫赣¶еĺɨĳָտɴ
ţ¶˫ųŵѾŹ⡣
ŵ䲻Ĵ˸顣
ǿ񣬳ŵʶĺ˼
¶֪ǳŵţﶼһӰԼ̬Ȳ̫ǿӲ
úѵЦ˵İӢѾÿ˻תȥˣӦյ˰ɡ
ŵ㲻ŪĳͷѾյˡ
ǳŵ㻹벻׬һ㡣ȻʱоȽ϶࣬ǿһʱȥ׬ġ
롣ŵĻش
Ǯãûɲɡ
ŵЦЦǮþͺã̫෴һ׸
ǵȱǮʱģ
ԼȥͺãͲͷˡ
Ϊʲô
ϼ׼ȷʡе͡ŵãһࡣ
ˣ
εķŶͷ
Ȼʵҵԭ
̫ôΪ׼ȷ̫˺𣿣
˹̹ʽ15%Ӯʣʹ΢ͼµĽֻİ¶һֻܰӮά5%ҾͲˡ
ɳŵأ13%ϡ
޵ð¶Ҫ˿ŵԿǿǲһ̨΢ͼ
ãǻ⡣ŵȻǽŴѧûȤоһʱ䡣
һˣû߹ʱ䣬ǲе̫ϧˣ
׹ŵüëһ
㲻İӢ𣬻ںСǮ¶Щ
İӮ̫Ѹ٣ûйгɾ͸С

һһӢѾͨڵнˡ˵
ŵʼ磬OKֻҪܸһʽоԱݣҺоȹҵĽġ
Ŵѧоݳŵ֪ǲУʽоԱġܻһоֵݡ
ŵɲڱĽ±ȥġ
ΪоӦûа취ġ
û˿ԥĵͷӦ͵һӣǾô˵ˣСӿɲڣ
˵ͷӰ칫ĳóһűóŵǩֻѺ
ŵڡϰӡЦݲͣųŵļԺǸݺĳԽ
ŵæԱһʵʲôʱʼ
ڵãԵĻھͿԡ
ʲô񣿡ŵоȫѪҺڷڡ
ѾһûֺͶ뵽оеĸоˡ
һоС飬һֱҪһѧҹȥǣоеѧҶиԵ񡣼ȻˣҾȰǿɡ˫ʮָ棬Գŵ˵
Ŵѧоֳѧо
оģֻѧҲռ˼ıء


İʮ 嶯ѧʵ
ŴѧоĳԣΪЩѧרңڷæĽѧ֮⣬һʱר־ش¿й
оĳԱ󶼳еѧصĿĿѧԼĿ
ʮ䣬ʤĿйڼ˺ܺõĹùָѧֲ֧֯ʽĹʡѧֻᣬѧҺѧǰѧѧǰؽ
˵ŴѧһƪѧѧģаʮƪԽŴѧо
ͳŵʡǸֻɷڳһССо칫ҲͬŴѧоȫһٶλоԱĹͬŬ£Ż۳˳Ȼĵλ
ȥ꣬оʼҿѧԺʮһĿ
¶ѳŵǲȥĿ飬ǽʼҿѧԺ·ȫѧһٸһĿ֮һ
оֻĲ㣬˵Ĳ㵱칫ֻ⣬ȫǴССʵҡ
ѧֻҪڱдд㲻ͬо󲿷ֶҪʵΪ֧ţʵҴ󲿷ֶʵҡ
Ȼ¶ѧϵˣûжϵдѹǰÿʽİ˳ɶͶĿ
ѧȣоʽͶߵĿ¡
ѧĿֻҪ򵥵ֽʣټһ̨ԡ
ĿɲͬҪͱҪʵ飬ҪʵҪ豸
һ̨ʵ豸˵ĿܾͼټǧӢĿԴﵽʮӢǻʼҿѧԺǵоȫãҪоԼϡ
ҪһټʵʧܣǸѪ
оһĿоȿסˣҪһѧϵ˹ȥæ¶û˿ãǾøְĳŵһʱ䡣
¶ѿڽųŵȥǸ鱨
ڰѳŵ¥203ʵҡ
дš嶯ѧʵҡ֡
ֱ߽ȥ
嶯ѧʵҵһƽҵӡϾֻһѧ͵綯ѧ֮ıԵѧƣҪ͵ʵ豸
ʱλʵʵ顣
˴Űɫʵվҵĸֻǰһ˲һ˼¼ݡ
ڣëϸ콫ںBi~ZnϽͲм󣬱ͷųǿĵѹŵܿԾĵ绨
һλоԺϵİťҺɢҺ½Ĺбȴĵϡ
̱еƳңһλоԺȡڵ΢¹۲һ󣬱һҡҡͷ
ʧˡдΡ
ŵͿվһĬĬһС
ֱλоԱʵתſվʵõˡ
ʧˣüͷˡ
λоԱ곤λЦһ£ԣѾ޸Ĺʮˣ޷õϹ涨ĳ΢ۡ
ʲôԭ𣿡
ǲ²ӦǶݵļ̳⣬ⲻҪһλѧҹǡô˵ʲôʱ򵽣
ƳһĳŵǸһĨȤЦݣѾǴˡ
ˣģоԱһ£վڿĳŵͻһ¡
Ц˵ģվλɡ
оԱһ͵񣬡ûһλʦջноԱŵ
ĹֵĳŵһۣҡͷЦ
ڰѳŵקǰܵλˣɵ½ں˹ɭڣѧңҪоѧרҡ
λáŵ΢ЦĿڡ
ڶλڽ͵λҪŵĳԻȻֻǸѧѧˮƽԽǵǰˡʦǷ˲پӦæ
ʲôǸѧ
λѾ²ˡ
Ϊʵ̫ΣķԴ׷˰ɡ
Ƕлĺˡɫ׵˵
ҾͲˣ̸ȡѿ⡣˵󣬱Ҵȥ
ʵֻʣ³ŵλڴ۵Сۡ
ߣ곤λоԱһŤͷŵߵ칫ǰһʵݷ
һλоԱҲûкͳŵ˵ߵǰüͷĥĳ⡣
ŵҲÿڣǱйæģǱġ
һӣŵŶȣеֻ
Ӻ곤оԱƳһֻСϷĳŵɫȴƳĬǸ˭æһЩЩݡ



İʮ 
ѧϵϵ
һѧƵĻһȻѧĴͷѧƣǵλȻ
ΪѧһֱǴұ㣬ң˭Ҳ˭ìܹϵ
ʵϣѧԴʼʹһѺõĺϵ
ϸһҲȷʵѧооͬһƧСϣͬȡ
㲻ʲôǶͼ㶮̬ľʲôݡ
˶ѧһѧ˵ԷΪӵйͬԵͬߡ
ӢϧӢۣ˵Ĵűָо
߲Ϊѧλ򣬻ߴֵ
λڶڳŵĲڳŵġѧҡݣɳŵѧˮƽ
ʵǸ㲻¶Ϊʲôǳŵһ⿴ò;ò׵ļһ
ŵϾˣλҲһֱѳŵһߣպܻܿĹϵֵúܽ
ԥһ곤λоԱһŵǸ˭æһЩЩݡ
ŵ̧̧Ƥһ곤ڵķ򣬼ͷֻ
곤Σվλڶһۣеһʵúãŵߡ
ŵҲȻҲ֪ǿĿʲôҪǣеĿǻʼҿѧԺһĿûаʱĻβֻϡ
ŵֻ̧ͷ곤ڵ۾˵¶⣬˵鷳صҹæġġһ˵ѧˮƽѵŴѧĽڣԴ˱˵ô˵ڽһ߰ʮؤǶҪΪѧ̩ඣ
㡭곤ĽúӶˡ
ܳΪǸʲô¶ӵç򡣳ŵ仰Լŭʧȥǡ
곤ЩǺɫָܿ糣ƳһЦԼĳŵһ˵ҳҸղ˵ĻЩϣ˵Щǳ
곤ڽһ¼ʵA4ֽݸŵһ֮ڷʵʧܵԭ򣬱֤ͻƳ֮ˡʱǶλȻΪ֮ǰϵǸ
ŵЦˡ곤нӹһʵݣЦĺܿġ
һûҪһСʱӡ
ŵŵ곤ڵﲻͣĴġ
Ϊ˱ⱻ˵ԮŵֱӾʵڷһʵݡ
ݺܶ࣬ʮʵ¼һٶA4ֽ
ʮʵʵݲͬһΪʧˡ
ŵλʱʱ˼׳ʵС

嶯ѧƱ׳΢۵оǸĿȫơ
˵õ嶯ѧۣӦƱ׳΢ۡ
׳΢һֽԭӡ֮䴦м̬Ĺϡڣܶȴż¼ϡӲϡȽĵص缫ϵʵ
ͳƱ΢ֵķɱߣҶԻͲ϶൱̵ҪʹԴΧƹʵá
һõ綯ѧƱ׳΢۵оʵɹֻҪͨ򵥵ʯӢëϸܣӳǿѹͿɽƱ׳΢ۣɱԭһɡңƱ׳΢۵ĲҲûô̵Ҫ
ѹĿѶϵ̫ߣȴʼҿѧԺһٸһĿ֮һ
ⶫһŪܴļֱֵҪ̫
ͨһ㣬ŵ֪λΪɶôżˡ
ʮӣŵеݷһ飬㽫еݼ¼ԺС
ţŵ˫ۣԺй񣬽ʵһС
λڵĿΪƱҪ׳΢ۣʮʵõķĩȲ׳΢۵Ҫ
ÿʵ飬ֻʮ֮һķĩܱ֤100£ֻɹʵĻȫûноıҪ
ŵҪľͨƵҵڡ
Ʊ΢۵ʵ£Աܶ࣬Գ΢۵ӰľֻôֱѹĵѹֱѹƵʡʵ¶ȡëϸֱС쳤ȡѹëϸʱس
вݸֽ𣿡ŵͻȻ̧ͷ˵
곤ָʵҵһ䣬ǱȫA4ֽá
ųŵıӰ곤Ľ°˼
עһʱ䣬ӳŵõʵݵڣŹȥСʱѡ
ѵô˼·ˣ
ŵɲ곤ôģ˼A4ֽӿڴͳŵıʣ㿪ʼֽϼݣ
rΪ΢Сƽ뾶oΪҺoΪµĽ糣Ϊ볡ǿйصϵGΪλʱγɵҺUΪֱѹ


İʮ ն
rΪ΢Сƽ뾶oΪҺoΪµĽ糣Ϊ볡ǿйصϵGΪλʱγɵҺUΪֱѹIΪ·΢۵ƽ뾶ֱѹйزĹʽϵΪr=60G/̦0IU+2ң30GI/U.
ëϸʱسΪPΪسϵdΪܾlΪëϸܳ.vΪƽ٣PΪܶȡճҺëϸʱ෢ϽëϸеΪȶDar c yʽϽëϸʱسP1ΪP1=l/dpv^2/2򡭡

ŵֽгʵԱó΢ȵĹϵʽ
һʽгŵ˼·
ֱѹĴСֲ£׳΢۵ĳߴӦҺηƵʵӶʷ˥ҺηƵӵ57Ⱥ󣬳ߴԹϵӡ
ѹͬϽëϸѹʱʯӢëϸǰγҺ׶ʱĸѹҲ֮ӣ֮ϵCʹʽ˵ô
һŵ˫ӵ
ͷһֱߵʵݼ¼ŵ΢΢һ
룬Ѿ֪ںδˡŵĬĬ
һߣ곤ڼŵѾû㲻ٰעڳŵǱߡ
ŵʵ˽ĿǰҲ˿ΪŵһСʱڰĵ
ʱ侲곤ҲøղŵĻȷʵЩˡ
ô˵ŵҲһλʴӱ꣬ǿʤǳ¡ǶλΪǰȷʵӦˡ
Һøղû˵һҪǳŵʧ˸ΣҲǣҲǣѵľء
áʱһԼȥͰοһίĸԵ˴Σ˹˼ŵӡ
Ѿ˹滮ãԺѾֳ档
곤ڸ׼ԼɤӣϵĲѿգ׼ȥһ
һ룬һŤͷͻأֵӰ㱻ŵֱһƨϣҲѵһڵϡ
ŵʲôʱģôһûУ
һˣڣҸղż񣬲֪ʲôûĴ㡣
곤һЩ΢΢졣
Ȼܸ߳ŵǹһߵ̬̻塱ŵ
ܹ⣬곤һ߰ѵϵĲһʵŵǱ߼ʵôңѵѾˣ
곤ڵЦ⡣
ʱŹȥʮӲɲΪŵֵʵдڵ⡣
Ҫ֪λȽĽڣȻѧңּң˵ˮƽܴﵽ˸ߵ裬ѧˮƽҲ̫ٱ֮ѧѧרҵĲʿ˿ġ
ɼˣĥûĥκͷ
ڳŵʮӾ͸
ɲΪԼô
곤ڲ룬ŵ˳Ǽʱ佫ʤ⽫赭дһʴ
ĻԼҲŵһӣ´δ
˼ŵ˳ҪоһʱˡԺ̧ͷͷģûбҪ⽻
Ȼһжֻ곤ԼĲ²ѡ
곤Դ͵£ŵͷݸֽƵ곤ǰһЦûʵʧܵԭѾҵˡ
곤ûзӦŵ͵ѾӰ׳΢ȵԱйʽƵó˸ϵʽԵ÷Χ
ȻҰҵʵ¼ݶһ£ڡ
ŵָڲݸֽԲȦȦǼϡ
նȣ곤˷Ӧ
ŵͷûնȡҷ֣ȻڵնȶԺϽڵ׳΢۹̵ֱӰԼԺԲƣնȿԼӰëϸܵѹ糣߰˸
նȣ˵ʹ״̬µϡ̶ȡ
һȷʵûע⵽곤ڳһ£ϸĥһŵĻҲ˵֮ǰʧܵԭ򣬾ΪնӰء
ô˵
ȻѾڣһҵ˺ʵĽ취˰ɣ
ҵļ㣬ֻҪڵնȵ1.3mPa~1.5mPa䣬ƳϹ淶׳΢ۡ
ˣ곤ѾЩʼ˳ŵĻ
벻ǣʵһ²֪𣿡ŵЦ
곤ΪȻĵͷ
λȥʵҽձãڵնȵ1.3mPaֵֵ롣
ŵųҫ۵ĹâϽﱻֽΪϸϸĿ
õ΢¹۲죬һæµ֮յóƽΪ84ȫ׳΢۵ı׼


İʮ Ҳ۸˰
ʵóݣλ곤ϲֱ
ϲʵڳɹˣǽͷһ¡
˵ʵĳɹͬҲ֤һԸţòϵʵ
ǾǳŵƲͼ㣬ûһ˿һĴ
ŵһСʱʱʵڣһĽ
֮ǰ˵µģҪΪ֮ǰŵǸ
곤ڵɫ任һҧҧ׵׵˵ŵΪҸղŵĻǸ
ȻЩԸ˵ϿҵŵǸ
ŵҲֵ˵ˡ
곤ڵǸŵЦŰڰ֣һڲˣҶϣʵ˳С¾͵δպ󶨵Эʵ顣
ӦõģӦõġ곤ĨĨͷϲڵĺˮ
õ嶯ѧ΢Ʊɹ˴롣ʣµģֻҪüֺϽ𣬽һЩݲƣͿֱдˡ
һѧĿҪŵȥͲࡣ
Ҫ鷳˵Ҫŵ˾ܵ㶨һĿ
ŵҲ뽫ȫĹȥ
򵥽Ĺʽһ곤ڣŵԼ˫ֲŶ߳ʵҡ

ˣ

ƿ¥칫ҵţŵ¶һļüͷ
ǳŵ¶дЦʵôÿհ͹ȥôͻˣѵǱ˰ϻģ
ŵɳϣ˵ûôҡǸʵѾˣƺҲûҵʲô¶ˣֱӻϸˡ
ô죡¶Ĵָ̾һ䣬ȻҿеˣٶȿԵģ
ŵ֪ڿֻʼЦЦ
ǲʱûйˣĬ˼󣬳ŵʵҽձֱӱˣûкúùһУ԰ûİŵĻҾͳȥˡ
ȱߡŵƨɸ뿪ɳ㱻¶һ仰ֱӱȥ
¶칫ϵǷļŤͷŵ¶ˡաЦݡ
ţڳŵ˵Цжվжա
¶ЦеĶųŵСӣ»Ҫʱȥͽŵˡ
ָҰʲôֱ˵ɣŵżɽ
ҾϲʶȤĺ¶Цһ䣬ΰŸŵ񣬡󣬽һĵѧѧʱ¹Źʮѧѧμλ
һѧٰĵص㣬ͶǽŴѧÿεѧɲǰѧһ飬ǣȻĳ裬Էա
ÿεĽɶǴдζڵġ֮д裬дѧ֮д衣ڼĴžζСһгΣй档
ͳ˸Уƴѧˮƽ̨ԼѧУοǰȻܼӵһѧУʵʴˣÿθѧУԴѡΪѧμӽǽŴѧҲ⡣
ŵָָԼԣҲμʮѧѧ
û¶Լĺ룬ѧרҵĻÿѧУɳ˲μӣҴռһ
һܱ󰡣
ŵ˼룬°͵ܲһ⣿
¶ڰ֣ʰɣ
νǲֻѧμӣŵʵ
¶ͷֻӵѧУʦ඼ѧȻԸѧУѧˮƽһ˶ʿȻûлμӡĴ󲿷ӦöǸѧУĶⲩʿ
ֻѧμ
ŵʱеɺ
ΪЩڼʦҲΪأ
ȷȥŵ¶
¶صͷ㣬벻κθõѡ
е۸˰ŵҡͷ̾Ϣһ
۸СҪİȺ԰ļһ۸ˣԺĲһɡ¶Ц
ŵҡҡͷ˵ˣĲǲȥˡ
Ȳ̸£֮ĽһҪһѧУöˣʱҸӣһĲ㡣
ңҡ
ȻûмҲûκսѶȣŶ渺̬ϣŵͷڴӦ
۸һȺʿ£ŵȷʵЩġ
ǶһȺӰ
˼ҲԶǧĹֻǼ򵥵ҪΪУ⣬ŴѧΪˣ˵Ӧ˼ССԸǡ
¶ȻԼɽǣεȵĺİ


İʮ УƼ
ѧѧ36ڽŴѧС
Ե¹ŹĹʮѧһǧλѧʱʷƾõĽСչĽġѧ
μӽһǧλѧǸѧУרҵһˣȻö˵ѧǲһ𲽡
ÿѧУÿרҵֻν쳣ҡ
ȺѧõĿҳ㷹һĲʿҲ˵õһ
˶ʿ
˼£ûԸƽ˷һ
¶ڵõϢĵһʱ䣬ҪһǿŵһŸոѧ˶ʿ
Ҫò˿һĻһ˵¶˽һҪһ˶ʿ
¶̹ŵѧˮƽ
ô˵ͳŵдһȺڼѧңŵҲϵİջʤ
ᣬȺδ߳У԰ѧˡ
ңѧֻᶼҪ¶ȴ³ŵӦֱ˸ն࣬öٸ߳ŵ
¶ԺҡҵʱȻ̫󣬵װ˷ֺϵϣ㡣ŵε˵
Ϊ¶ҪŸԼʲôҪûֻǹȥ۸˰ˣŵεĺܡ
ǱԹˡ¶ڰ֣ǺЦҲΪѧУ𡣡
ֻҪǽŴѧνбֳɫԴͻǽбʱ㻹ûĿ
ŵڵתһ£ڵҪһô
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ҰνʣҵһĿΣŵЦ˵
ÿĿŵһеݣԼΪĿĿ廪ʱйһ֮⣬ʣµĶǱ˰ɶԼɶ
˵ʵŵҲһһĿĸо
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ŵʾ⣬ҾԼ⣬ʱоʽ鷳ˡ
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֣ô۵֪ʶ֤ôֶ֤ĳ֮һνŷպ
һnŷպȡֵգnΪգn=nnصĸһpգp=p-1Ϊ1...p-1p-1pȻpء
Ȼ󣬶ͬp1p2գp1p2=p1-1p2-1Ϊ


İʮ Ÿ
Ϊ1p1p2p1p2Уp12p1...p2p1p2p1p2йͬp1p22p2...p1p2p1p1p2йͬp2ȫp1p2ء
ɴˣԵõգp1p2Ϊp1p2-p2-p1ظ
ӵʱ䣬ŵѾͣЪ˵·֤λѲ۽硣
Ҫ֤ŷＸ֤ıֵĻλΪŵŷＸ֤оѣκγ֮⡣
֤ȫͬŷＸӼ֤辶ֱáСֲۡȫͬķչ
ŵ˵֤̫ӣ˵Ǽ򵥵Ĺ֡
Խ򵥣Խ˳Ծѡ
һ֤̣ĸѧңϣȻԽԽá
ߴϵѧ̶֤ޱȸӣȺѧҲԸ
ΪҲӼ򵥵֤
Խ򵥣Խ⡣ѧҵҪԽߡ
ͬһһһҳĽ֤ѧң֮ҪҳĲ֤ܽѧңѧˮƽҪһ
Ҳˣڿŵǿһֻ
һֻһо
ΪŵʵֻǺڲ֮ѡоͳŵڱֳʵѧУθڶ˰ɣ
ˮеڿˡ˻˼֮ʣŵɤʵ
ŶŶˮһ˼æһƿȪˮ˹ȥ
лˡ
ŵ˹˺˰ƿɤֲʸйȥ֮ǰ˵ˣŶҽ֤ˣ˵ĸ
ŵһձ׼¼Ķѵ˵Ļ㡣
˵꣬ŵ濪ʼ
ĸý۵֤ô۵֤֮ͬǶ֪ŷ˻ʽǣnn-s=p1-p-s-1s&gt;1ྭغ󣬿ɱΪмҪĺƺƣs
s=1ŷ˻ʽǱΪͼķɢ
ŵɤӣ˵⼸Ǻйصģ˵֤
Ŀ£ŵ˵֤ķ֤˼·ģκNдN=rs2ʽrǲܱκδ1ƽs2ƽӵĳ˻ֻnrֽС
ŵܲٽһ顣¼λѧͷε˵ҸղŹ˵˼¼ˡ
ŵεʼ磬ðɣ˵һ飬ǿҪ
ĻӳڳŵϣԵùޱȡ
ŵλʿԱͷһѧ̵̬ܽ
˵ķ֤
˶ʱ
ŵɻС񣬹ЦЦеɻѧƺܲɵΪʲôȴô˵ҽ꣬Ǿˡ
ǿԶϵһˣ俪ҽɿռoaz+ba0bΪĲɡ֤˶Ŀ˵Ķ壬
ɴˣ֪𣿡
СװͷвϻζųŵĻ
ŵû̫ζʱ䡣
Ժм򵥹һ˼·ŵ㽲һ֤
СʱʱѾȥһ룬ץʱĻпܽꡣ
߸ϢӦý֤̺ܼ򵥣NɷֽΪ˻N=p1m1p2m2...
ڰ˸úķ֤fNΪNĲͬĸֻ޶˻ΪPȻNfN=fN+P
ھŸҽΪĵ֤бʽΪ0sin/p=sinУ1+2p/pֻ޶ֻ޶ʽࡰ&lt;Ҷ˻еsinԱ/pȫ0֮ͦ䣬sin/p&gt;0
-
˵ھŸ֤󣬳ŵ;ÿڸʣİƿȪˮ˹ȫȥ
һ˺ʶȤֵݸŵһƿȪˮ
ŵû˶Ǹ¼ͬѧ˷ԼдҳĹʽĭСʵ𣿡
ŵڰ֣Ц·֤뵽ֻŸˣ빴ɶٶ֤ǲ̫Զ
ŵЦҲڿЦ
ɶٶ֤ǧʷʮѧҵķչ²γɵġ
ŵڰСʱʱľ֤Ѿķ롣
ŵƺͦ⡣
⡭
ǻ˵ɶ


İʮ ʮһ֤
ǾͽŸɡ¼λͬѧ˷¼µЩ֤̣˵
ţŸ㹻ˡò˵һĻ˵Ｗһ涳һҶһ˵ͷ˵
ŵ㿴أ˴һµǰյľȨŵ
ŵ룬ʱ仹ϼɣܾþŸס
ڣŵ֮ǰ˵Ȼ·֤ûˣֻŷＸ֤ıεĻǲѵġ
ͬʱɫϲ
ȻǿŸ֤Ѿ㹻ѹѧУĻҲûоܾĵ
û˻Ӷģ
Сʱʱ仹ʣӣŵѧУѧѾʼ
ŵǵ׹ĵ֤ʨӲȫ뷨ŵɲ׼κε֡
ŷＸ֤ı࣬䲻ڣĶǽһӼ֤ˡҾͼ򵥵˵
ֻ޶p1...pnN=p1pnpii=1...nNӡp1...pnȫбһN-1ӣΪpr1rnprͬʱNN-1ӣӶҲ֮Ҳ1ǲܵģ
һ͸ˣn+1ӱضnn+11ӣnģҵҵģ
ŵһ˵λͬѧ৵ֽϼ¡
ڴͷβػصļ鼸飬ʮӵʱҲ͸պùȥ
»֣һʱ䵽ˣǸɳһֳ֤̽ңһжϷȷ񣬲гΡͬȡ
סҪдѧУ֡Ҫһʱ䣬ȿʼͣӣͽһ
ʮѧУĴ󣬰»ŲӣݴĴҴһص
ΧԵڼž˼󣬱óʳ￪ʼ͡
͵ձӦǿֵģʱȴԵһһǵɫǼڴֽš
飬ѧʱȴŷʱûκ
ζޱȵʳȴζͬʱʱ򰮵»ڵϡ
ȻһѧУ⡣
ŵڲݵϣһֻʶ죬͵̿š
ҲǳԵĽζȫǡ
ŵǹɻȣǵز㳢
ϺŵţţѾˣŵҲ
ΪͷŹ˲ͣĶԳŵڡ
һ߳Էŵһ߲˵ۡ
ˣˣѧУô֤
ֻ࣬࣬ˣǰе
ƨҸղһȦҲһѣ󲿷ֶĸҲ֪ѧУĸܲƾȡʤôˡ
ҲʮþȣҪһһֵֻЦˡ
Ȼô˵ɫȴ˼֮⡣
֪󲿷ѧУֻ֤ѧУȽǰˡ
٣ǽŴѧô˿ĸιǽҪˡ˵ţѧһλѧյЦǺǵ˵
٣ҲǸ¼ѧֻǵһЦġǲġ
Ŷ˭ôģѵλͬѧȻòϣڵһֱȷʵۣǱϾֻħѣǵпвٵħ֣ħռˡ
βһˣǴѧ⣬Ͷȡܹʤġںڴڴԭα¶һ졣˹Ц
ո꣬㡭ۿҪվոһ
ŵЦǺǿڣѧˣ»ˡ
Ȼ»һֽ߳
˿ϵĺ䣬»ˣѾˡ
ڸλϽĴһǱȽġλΪ֮ӣĶ飬ҲڰСʱ֤֤
ǼֻϽ֤ĴҵѧУɫһס
»˵Ǿ˵ѾȫûκλʤĻᡣ
ĻҲ˵̫࣬ظλԽڴѾˣֱΡ
»ֱӴӵʼ۹ѧ֤ȫȷ
ţѧ֤һΪ󣡡
ŵǸոţѧɫһ
ȻҲӮˣǵĿǳŵһȥģֻ˸ܲŹ֡
ڶѧ֤ȫȷ
ոƳһ۽ŴѧˣͻȻֺ
õȻ̫ˣŴѧǰĶŲȥƾһɨˡ
ո˼֮ʣ»ü߰
һŴѧʮһ֤ȫȷ


İʮ 
һŴѧʮһ֤ȫȷ
»߿صڿտĲݵʱֳİʮӡ
ֱһ󺮷紵ѣ˲ŷ׷׻ع
ģʮһûɣ
ŶҲֱģ̫ˣ
ʮһѧУֻĸѣҳѧУͽŴѧв࣬Ҳڲôɣ
࣬ѾǺ蹵ˣǵ
̾
Ϊѧǽʮ꣬ΣǵıŴѧǸʮһִϡ顣
̫ˣʵ̫ˡ
ڶĲѧҲ֤ѣĲȻ󣬵֪ĿѶȵ˵Ǿ
οڰ»˻ع֮һ˸𺳵Ϣ
Ŵѧύʮһֻ֤ŷＸ֤ı֣Ÿ·֤
Ÿ·֤
֪ζʲô
ΪЩѧУСʱʱ϶ŷＸ֤ı¹
ˣֻĥˡ
·֤ȻǸһµʱ䣬Ҳ˵Ÿɣ
һŤͷڵķ򣬾ǿһ㡣
һô쵽ģ
ⲻ룬ţѧոҲ롣
ڴʱ·˼ʮ֮ɫŤǸճһɫ仯һԼƺʽŴѧˣôܣ
ŵۣôʧܵļһ
»˹æվ
ӭȥ֣ЦǺǵĶ԰»˵»ʲôʱǵ񡣡
õģٲǵġ»˵һ䣬ҹҪ
˵˵
»ŵϽĴٴνУʮһ֤ܸߣȥ֮ŪһƪģֱͶSCI
SCIڿģҽͶʼѧоĿӡġѧԡڿﵣ༭ֱ廷ڣǵھܷ
ʱֱ˵֣ҿᰲŵġ»󽻴һ䡣
ٵͷѸҡͷ»ƪֻҪϳŵͬѧ־ͺˣˡ
Ϊʲô»дΪ棬ʮһ֤ͬҪӦ˹ͬŶԣŵĹ״Ǿһ߾ǣֻһֵĵ
»ЩߣΪ˴Ӧ˳ŵһЩʲôƽȵԼ
ټæ֣ЦĽ͵»ҲЦϽʮһ֤ȫɳŵͬѧһġǵĹֻǸ¼ѡ
Ȼ֪ƪĵܸߣƤûк񵽽˵оɹΪеĳ̶ȡ
굤ٵĽͣ»ǴΪȡ
üͷȷϵ˵ʮһ֤ȫǳŵһģ
ٿЦͷȻе㶪ˣȷʵ
»Ŷͷò
Ҫʮһ֤ǽŴѧ˺ģȻЩϣôĳܷΧڡ
ѧѧУѧŲ
ȫڳŵһϵĻ
˵ʵѲڰ»֪Χˡ
ĿųŵǸѧ
ŵóԼѧ֤ʥѧԺѧϵоŵٰ
»̾һҡͷЦŴѧǴһ
˵꣬㲻ˣȥ
ٴӰ»һΧԹ֧кŵһλѽȥȡů
Ҳ׷֧񣬲Ը˼һ˯ȥ

һҹ޻
գǰ׵էֳһĨصĹâʰõͽӸٺ߻ѧУ
ճÿνŻĵξ
ĿǰϷ֣ӮǽŴѧ
ǵڶ֣Ŵѧǳ˷ͷ
ŵ֣Ϊ˵ʡ
ǰǵССģ˺ķ顣
ڻȥ·ϣ˶ŽŴѧߵġ
־ڽڶС
۵⣬ԺЧӦΪѧоۡ
ȫʵ⣬ŵǵĽŴѧԻΪݣٴΰεͷ
Ϣһ󣬽ѧУһСýһ־
ǰ治һγϯĲֻǰ»λʮѧУҵѧҪʮˣԵֳйĦ


İʮ 
Ŵѧɳ¹ŶλоԵԳŴѧνӡ
Ϊѧеһڼ˶ĴֳĦĿѶȿ϶Ǹ
ѧУΪλÿѧУһ֧СŶӣʽڽģǸһʵʵѧԽ˼ͽ
ֻǱľݣŵ˻֪
볡ʱ򣬳ŵ˰¶
һЦеģŵ֣⼸ıҶ˵ˣֺܲȻûйҶڴ
ŵʼЦЦû˵
¶˵һˣСӾٿǣҲǧҪġʮλѧҵѧУ棬ǲб£
ŵüʣ֪һĿʲô
¶ͷ֪֪ǰ͸¶ǡȻʱ֪ˡ
ֻ˵αĿеѶȡ˳СӴе㼬֡
һļƻеĿģǸѶҪһֹǰյıֺһ¾ͰĿĳСӣ֪Ϊʲô𣿡
ŵԵЩĿ⣬ָָԼЦϱΪҡ
СŪã¶Цһ䣬ֵʵ̫ǿЩļһﵣĿɸ㶨Ҳס棬֮ѶȵΡ
ŵЩӣҾãΣҲûʲôɣ
ڳŵţ¶ָֻųŵ̾Ҳ˵ʲôˣʱҪ˼ʶǽŴѧѧϵʵǣ
˵껰ŵͰ¶һ߽Сá
ŵҵԼλѣٺǣÿλõȴűĿʼ
Ȼ쵼ܶ࣬ûʲôĽڡ
Ȱ»ʮѧѾ룬ǰŵ쵼ʺһ򿪶ý壬ĿͶĻϡ
»һݺҪдˣֻǿһ㣬ǵʱֻСʱСʱύȨ
˵󣬰»½̨
ŵ˲ŷӦ׷׿Ļ鿴ݡ
ŸóĳڻӭһµķչʱڣڻΪĽڹóԽԽҪĽɫ֮ڻгĽΪ֤ڻгմڵĺγɻƣ˶ڵڻгпּܳ۸ߵ󣬲ڸڻóγɲĭ۸񡱵ӦԲԼͬʱͨʽʵƽԴﵽܷյķ
Ŀ˶ͬʱסˡ
ŵҲĦ°ͣüͷ
ֲð¶˵εĿѶȺܸߣʵȻ
Ŀ˵ʹѧķڻгγɣԼܷյķ
էֻһѧģˡ
ʵˡ
ȣоѾȷǾǹڻг
ڻгصʲôӡ
ȫɶٶҺ͵ɣдҲСǿҲһЩҴս֮У÷ոߵĿ£˫óսĹң۸̫ͬߡ
кͬգټϻʷգͳͳҪڡ
ҪǵĶʵ̫࣬ൽֱ޴ֵĳ̶ȡ
ЩѧҺ;ýڷѧңҲڻго˶Ȼһ֪ĳ̶ȡ
ǳ
Ǵʱ󲿷ѧ뷨
ǰĽȻûвμӹݴѧѧģһֵĿȻѣҲӦѵ̶ֳȡ
ǵʱֻСʱ
ʮӿȥˣȴԾץסһ˿˿ͷ
ŴѧǱߡ
ٺλҲǺһץ
ǰֽŴѧѹȣһ֣Ҳؼһ֣ҪǵӵĻǰŬɾǰˡ
ţǲɰĿͶһĳŵ
ŵĿ˼˶쳣ĬĲȥš
ɴˣǶһ·ն
ǿΣõƶţŵһΣ֮ǣͬǰһ
ŵҲȷʵ˼
ڻгĹܶ䣬ʹúѶԵĽ仯ѧԽо
ǣһȫڻг֮ڷǳϵҪѰһڻյĽϼѡ
ǣܹҵһƽ㡣
ˣƽ㣡
ŵ˼·˲û
ƺѾҵȷķ
ڵٺ˵Уŵ˫ۣâһš
ټеʣ뵽𣿡
ŵЦŵͷѾҵˡ
ʲô̲סʵ
ŵһЦ³֣ۣ


İʮ Ͳ
ۣʿºܶ˶İ
ʷѾ޷֤Ϊѧ˳ѧһ֣ʱĲϱǨѾγһ׳ķõúóսС
Ǻеʲ⣬ȫϢгеİ޷Ʒг۵ȡ
ͬڹڻгܹӳǿ
ˣŵھʱ˼֮󣬾ʹò۵ķ⡣
ȣڻгиǵͲľ֡
͵ĲľУҪߡԼ衢Żѡ֤󻯡ĵԼϢĵҪԡһЭѡγɲԼǵͲгıҪء
ڻгǸ֮ϢΪģڹڻгԼͨͶΪγɲԽĽڳ
һ㣬ڻгǵ͵ġͲġ
ʲôͲģ
־ͿԿͲָڽ׹иΪ㣬һһʧڻгһ㶼ǡͲġڻ۸ʱ۸ʱͷͷʧ֮Ȼ
һ㣬гϢгҲ˵ڻгдϢԳԡ
֪㣬ʣµĶͺܼˡ
ٻǻĥνۺڻгϵߵĳŵѾùʺͲݸֽ֤Լ뷨
˼ŵѾʼʣ˼ڳŵµĹʽϡ
ŵ㷽ܼ򵥡
Ȼ֪ڻгͲģǾͿԽ溯Ϊ=-ɱ=۲ɱ-ʽɱ+׷ã
ʽó̶ȣ״ϢĸĲйʽ㡣
󣬳룬ͷŵ৵ֽдţ
P0۸P1Ϊ۸񣬼۸Pͨһǵ°ĺP'Q0P''Q0
QmaxΪгڻгͶʱӦļ۸񡣳ٽ罻۸ڡĭ۸񡱡ڻгֻһ״ʱùܿг۸񣬴ʱ⣺
R1Q1=P*Q=PtQ1-P0*Q1
ʽR1棬PtڵĿǰڻг۸P0ڻг۸񡣡

ŵڵٺ˳ݵĿˮŹʽ
һߣǰŵȺǲûǴеĿģľһš
֮ԹĦһɲΪ˼򵥵ĹСʱһ½
ʮλѧѧһ˲š
Ҳ֪ȺҵѪҺֳֵܱʵ
Ųۼ
˴ԹĦһ˽Ĺ̡
¶ЦǺǵľһߡ
ܺͰ¶ߵһĿ϶ҲͨλˣһλʼҿѧԺѧԺĸԺһλǵ¹ŹѧѧԺԺ
۵λ˿ڰ¶λŴѧо
ͬʱλҲǽαеλߵλ
ʮ֧УŴѧڱȽϿλá
λߵȽϿǰĲѧСԡ
ѧλʿڼҵۺ˷ֹǲõѧģķͨڻгѧģнһ⡣
פԱ߿˼ӣߡ
ⷽȻ棬ģ˼·Ƚ棬ȳ淽Ҫһʱ䣬¶е
ԱߵĻʼҿѧԺѧԺĸԺź룬Ҳͷвʧ£ҵϣǽ̳һȺѧ
ѧѧԺԺҵҲλѶԼѧۼߣҲһɵĸоȻλģѧУĸߣ˱֣Ҳǲǵ
ҵԺŤͷ¹Ŷ¹Ŷ˵ǽŴѧλѧεĽбֵĺۣǲȥ
Ȼԡ¶תһȦҵŵ˵λãλָǱߣǹȥ
˵꣬ߵŵߡ
ŵǳŵһдٺһ߶ſûһ˵ֽϵɳɳûʲô
ŴѧߵĹ״̬¶˶Щɻ
ŵֽеĹʽ󣬱ܿȥ
ŵ֪ԼλſɰԼĽдţ
гֻһʱĬϽѼ۸ٽ۸Ӷ׬ȡۡڻгϴڶʱڻгmm&gt;1ʱn溯Ϊ
RQm=QaPtQm-P
PtQmгϵnʱļ۸QmдܺͣiʱΪQaµʽ
Ra/Qa=Qa*Pt'Qm*+PtQm*-P0=0.


İʮ ſ˱Ȳ
ף
ŵеЩʽѧѧԺķҵԺһ
õǲ۰ҵԺСλ˵
ʼҿѧԺԺԺ˹ĿĵͷΪĳͣõڻгҲΪ档
˹Ժһתֻ뵽һ£ܲһ¡ҿǵĽ˼·Ͳĵԣӯ̣ҵĹ۵ٵķ
Ҳ˿ѷɫЩͨӽģóĽ¶Բһ䡣
ҵԺ°ͣ˼˼룬ͷȷʵǵʱֻСʱͨͳѧģķȻܹЧ̫ϣҪóĽҪʮСʱ۵ķܴʱѹڲҪģЩӵĲ裬Сʱʱǿ㹻
ֻ֪뷨˭ġҵԺǺһЦ
˹Ժź룬ۣʵҲȽϺһ㡣
¶˫֣ĿͣڳŵıӰϣ⡣
λɻ˭ò˼·ȴһ㶼ɡ
ٺλȻǽŴѧеٮٮߣʵʵ˵ŵĲࡣ
Ǹ뷨ߣ˳ŵ¶벻Ŀܡ
һޱƶ
ߣŵɳԼ޷԰ΣƽԼĽȣ¶ĵ̸ֱӱ⡣
ٺǶȻ˱վŵλС
ƺǾֻóŵдԼԱֻǹɿЩ˼
ǴŵļСʵŵҪʲô𣿡
ͻȻ˼·ŵ˵һۣڵʱҪиǽʱ䣬ԼͰŪˡ
ͣһ£ŵѾдһЩݵݸ٣û¸ɵģͰҰдЩ¼뵽ϰɡӦԵӰĵķʽύ
ٿЦŵͷûа㼼ĹȻŤͷλһεı顣
¶λѧŵ𣿡ҵԺЦѵΪһ˿˵Ĺ
ǴȤһ仰û뵽¶ȴĵͷ޷˵ˣȷʵǸ
һԵ˹ԺȻ˵Ǹŵɣ˵ǰֵıֵʮۡһģ
¶һЦɺϣɺ϶ѡ
һߣҵԺѾóֻŵϡ
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KaehlerϵĳȫۺClifford
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ŵҵоĶ󡪡KaehlerΣһڵ͸ṹ²ĸΡ
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ŵεĿЦֻܵǲڣÿĶƻ
Ϳɣֲٿ⡣ŵΪԼֵܾڵļġ

ҵηӿŵֻǰĴУ԰ƾ档
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ڵʦʸϣŵȲμκοˣòʿʦʸҲ˵ŵ˴ʿȨ
档
нʿ϶޷ʡѧԺȵġ
ʱŵнаʮ𣬵ʱнѾһٶʮ
廪ѧнֻ60RMB
ŵЩҲûطᡣ
ͬʱ60RMB֮⣬ᵥŵ200RMBİҷѡ
ȻǮ廪ѧ¥̵һ𣬵Һã廪ѧڽڹԢŵס


İʮ ع
810ա
ŵҪعϢѾʡѧԺ
λͳŵϵĽҲȰŵһѾı䲻˳ŵ뷨
ʵ˵ŵûټڹıҪ
ѧĿģΪ˽ӴϵĶѧ˼롣
ڡ
ŵȻѾΪ˼֮һ
ڿĿڹҲ
޷ǣĿʵȹһЩ
ŵţԼȥЩ⡣

о칫ҡ
ƿŵǼСš
æ칫ĳŵվڣ칫ҽ͸ճ
ڰڰ֣ƺûȤ⡣
ڵʧ䣬ʲôʱߣ
ɡ
Ĭʮ룬ڳ̾ڣ֮ǰҺȱɡ
ŵͷʰõӰᵽϣЦȥϴ֡
ˮ䣬ʵ¥Ķ㡣
һʮֺĹ˵ƣʱЩںоԱȱ򿧷ȣ͸شľɫߺ̸䣬滺顣
֨ѽ-
ŵͷ߽
Ҹ˿еλã¡ԱС鲽߹
tea or coffe
tea.
Ų豭ССڵĺš
ŵ֪鲻ãʶȤڡ
գ˴˳Ĭš
ŵڡһӰڳŵ࣬ڳŵЩĿ£شŵһֱڳŵǰ
֣Цһΰѧң̽ڣ
ŵ΢Ц֡
ţһλŵǰ¸ֱʣԳŵ΢΢ͷʾ⡣
ŵѾЩ¡
ʵ˻ڼ
ûκνһλλںѧߣĽԼĸֱʷڳŵǰͷʾת뿪
̶̲һʱ䣬ŵǰѾİڷʮֱ֧ʡ
ŵۿЩʪ
Щֱζʲô
֮ѧߣ罣֮սʿҲ
ΪԼһֱ֧ʣѧ磬Ƕѧ׵ϿɣԼߵľ⡣
Ҳѧʿһߵ
ڡŵۿڡ
ڷ²豭΢΢һЦ°ɣ㵣Щ
պεأҪԼһλѧңѧҵķչҪĹףڵ¡
ŵصͷڣ֪

Ҳ812š
ʽ߲˲ƻǧ˼ƻʽ
ּ߶˼˲ţƶѧķչ
űĵһʱ䣬廪ѧڹϷϢ
ٷƸʡѧԺڣά׽ѧѧ߳ŵΪ廪ѧڣ
ȻʱһֱںͳŵнӴŵعϢѾڱ״̬
ˣ廪Ϣһųѧ綼ϲա
ʵΪŵһʱʵ̫
ſ˱Ȳ룬β룬ȻʱзļСģ͸⡣
ŵȻڹ⣬ڹѧӰȴЩڽ
ټά׽Ϳѧѧļӳ֡
ѧλϣŵڹֻһЩһѧҡ
ͬʱҲ֤ˣǻ޷һѧţ
Ԥŵһ϶һǿڻѧϣʹʼЩήҵѧö־
ѧ˸⣬廪ѧѧϵѧӵĸˡ
ŵְ廪ѧֱӵ߱ǡ
Գŵܸߡ
ֱӵı֣ǳŵ·ϣֻһεεε죬˼ʮʼ
У󲿷ΪһЩոտ廪ѧϵĲʿ
ŵѾòʿʦʸȻϣһʱסŵȣеմӵݡ
⼸⣬ԹڵļλͬС
ʼҲͬС죬˵ǱһʲôĿֿŵ롣
ʿ飬ŵԿǡ
عĿ֮һΪѧһЩѪҺ
ѡҪѧУʵʿ
Ŀ룬ŵֱһһίĻؾˡ
ع֮󣬳ŵ׼ԼһĿټϻҪѧŵû̫ʱ䡣
ŵûֱӷɻؾ
Сʱг̺󣬷ɻͣǵĳͤ
Ѿһʱûлؼңŵһֽӵĸо
Һãһĸŵе˲ɢ
ϾԼļ硣
Ư˶ã޷ıʵ
λ󣬾Ͳ˰ɣĸڷʵ
ŵһǴŹǣһҧ£Ϥζţˡ廪ѧǱѾƸҵڣԺʹڱ
ҺҲŰȥĻӺҲչ˺ӡĸ׽˵Լ뷨
ŵüǵĹ
ֱܲͺãҲֱӽС͡
ŵͷȻĻûˡ
ÿӣųŵСŵһ׼ţʲôʱ鰡ҿżˡ
ŵЩΣҡ


İʮ һƻ
һϮɫĳȹվ㳡ܼУĴ
ԶһϤӰǸһĨ˵Ц⣬Ѹٱ
ŵܹĨһѶͷϵĺˮЦԼʮڲžŵ룬ô磿
ݺݵ˳ŵһۣͷ¶ѩ׵Ĳ⡣
ŵӣ˸ûȤ
ţȥ򼸼·緹ȥӰ߰ɡŵʶҪסĸ첲
ϣóŵ§˸ա
߰ɡƳ˳ŵһۣȻǰȥ
Թŵ֪㬵ĸ档
Ǹ䣬£緹ʱ򣬳ŵԥãʵ
̧ͷ¿ӣʲô£
ʲôʱ飿ŵӲͷƤʡ
һɫһĨ졣
Щ̵ӣЩ΢㣬ͻȻʲô
ûʲôһ¡ŵڡ
Ŀݺݹ˳ŵһۡ
ʲôУһ£
ư͵ĴӦģڿ
£һû뵽ңڻѧȹʱ˵ɡش
ŵһڹ֭ţպ飬պ顣

ڼһܡ
ʱµף廪ѧǱѾߴ١
ΪϾҪѧˣһЩİҪòǡ
û취ŵֻܸ˸ĸ
ֵһǣŵǴһϷɻġ
ǽոսѧҵľͶĿǰ׼ྩѧ졣
Ҫ廪оɣҿԴ㡣ŵ顣
Ҫҡͷϵıʾܾ
Ұ㵱ѣȻʦ
ңҪŵĵĵʦĻԶҪͳŵһͷ
ԸྩѧҲԸȥںͳŵʲôʦ
ĲǿǣҪ֪Ը⵱ѧо˳ӡŵǺЦ
䱧Ÿ첲ͷŤһߣϡ㣬Ҳܾ
ŵһ㶣ȷʵһ

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һ·ѧǡ
һεĿųŵ߽ྩѧŵ̾ҡҡͷ߽ڵ廪ѧ
廪ѧŵ˽ڹԢܴ󣬳ŵһ壬һס
˳㣬ʡһס޷ѡ
ŵĿĺܵƺ䲢Ǻ飬ÿ޵Ŀ˳ŵһۺ󣬱ת뿪
˵ʵŵеСʹ
ѧУĽڹԢ¥λ廪ѧ
ⶰ¥ŵĲһΣϾھסⶰ¥ϡ
Ѿһʱûع廪ѧУļڳŵԺδĥ
ŵĹԢλڶ¥¥ϣǡþǷڵס
ţŵɨһȦĵͷ
ҾߡҵʲôĶȱֻǻûסԭ򣬷Щ塣
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ŵˣ
źܿ챻򿪣ֲϼֵӳڳŵ
šһˡλ֮ҾͲˣĬһ£ŵЦ˵
֪֪ĳŵļ򣬡ڹ飬ȫ˵ˡû뵽ĻҪ㣡
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СӾͱˣԼʲôˮƽﻹĺܵġ
վſˡǽȥġ
ɳŵͷ¡
ʱ䣬ڹʼνķͷ˵һʱҴڹڶʱʱϢЦǺǵĿڣôλ󣬻Ǽ׼оη򣿡
ˡŵҡҡͷҲѾ쵽Ｋˣֻڹչϣǰһѡ
ԣλعҴһġ
ʲôۣǴȤ
BSD룡
ɫһ㶡
ŵﲻݣҪ֤ȫBSD룡
ڵһ£ֱӴɳվ
BSD룬ǧߴѧ֮һ
˵룬һ㶼İ
ǰĵʱǱĳŵʱһʱ䣬֤ļ򻯰桪BSD룡
BSD룬ѶȵȼϣȫBSDȫһϡ
򵥵ĺһ£BSDֻſ˱Ȳһ룬ȫBSD룬ȴſ˱Ȳ屶Ҫֹ
аգڽųŵ
˵ʵûС
ŵĻش÷һҭ
ŵͣûаٷְٰգҾãҿԳһ¡
ǱϾBSD밡
ߴѧУBSDҲ򵥵һ
ʵɽ壬ʵһ£ŵûж˵һܹԽ
ңѧңŵһơ
Ǿ֤BSD룬ɻһĺô
ߴѧ밡
ֻҪһǾĪҫ
ŵãڣ׼ʼ


İʮ BSD֤ƻ
ˣһķڹBSDϣʡ
ŵͷˣȫBSD֤е㲻ġοһᣬһ²Ϊ˷ѵʱҲûʲô󰭡
ŵһֱ׷
ǰںͷڹͬBSDʱ򣬳ŵһȫBSDֱӸ֤뷨
κΣʱʵֻܾʹա
һˣѧˮƽŵѾΪһСˡ
ڱ˿УҲǡţĴڡ
ʱ죬ŵԼԳһˡ
BSDȻѣûѵóŵηĳ̶ȡ
һĦС
ңһſ˱Ȳ롢ϸ롢ɽ־롢Сģ͸ĳŵͷ͵ʱ㣬ʹӵһǰ
ǳŵõĻᣡ
֪ŵ뷨Ѹı䣬ҲͲȰ裬ʣ׼һ˸ɣ
ԵĻϣʦܹҡŵĿϣ
ڿЦҡͷʦѾˣ⼸Ҹоҵ˼˻ңаĺˡ
õģȻﲻ㣬˿԰㡣
˭
ΰȥ꣬ѾƸΪѧԺĽڡһԼʱ䣬Ǽһ档֮䣬๲ͬԡǺЦ
ΰŵ֪λ
ͳŵһΰƱҵ廪ѧоڼѧڸױǴѧרǰŬ𽱣ΪѧƽһĴ֮һ
ȻڳŵѾΪƽһ
˺ͷڵ̸ŵδ߳Ԣ¥ӵ廪ѧѧԺԺ˵ĵ绰ѧ칫¥һˡ
ƸʽŵԺĽ󣬳죬֣ԺҪ˰ɣҲϲôߵ
ѧԺԺԺʿݷ˵ⲻԸԸ⣬ͬͬ⣬ƸʽҪ죡Ҫĵİ죡
ŵŵҪġֻǺúϾˡ
ŵ֮ڻѧ磬ҪãԺʿҲ
ŵûκԥľʹӦ廪ѧ廪ν̣֪öٸУͿлۺ졣
ˣƸʽ廪һҪ㹻̬ȡ
ͬʱҪǽŵĻ롣
ðɡȫƾԺšŵδ
͵벻ͷԺͬ⡣
Σǲͷˣ
꣬갡
Ժ̸顣ŵֵ
Ժʿȿڲ裬Цúӣֱ˵
׼һ¿⣬Ŀѷ桭
㲻õġԺһӣǧ˼ƻ˲ţڸ棬ÿһĿоѣǮӡ
Ҳ֪оѧģһоѾ㹻ˣⷽ㲻õġ
ŵ˿Ǿͺãҹݽġ
ô鷳ֱѧоǱоѾУ⻹ҪһȦӡԺʿ豭ˣˣĿоʲô
BSD֤ŵʵش
ۡ
Ժʿһڲˮֱ
ͷڵķӦһԺʿҲǡڡһֱվ
˵һ飿Ժʿųŵ
BSD֤ʲô𣿡
⣬кܴ⣡Ժʿߵŵǰң㲻úоļ⣬ܹȥBSDʲô
ҾãѾҪߵһʱҪѣԾ뻻򡣡ŵһ޹
BSD룿
ԺʿһҪ˵ĳ嶯
BSDǸӣǸӣǼʮѧѪܵľ֤һʵ
֪ѧңҲû
ŵھպȽȽǰ;
ԺʿĳŵһBSDӣһĻǾʧ̫ˡ
ŵεЦԺҪģȻûʮɵİգɵİջеġ
Ժʿڰ칫ⲽ
˼ãŶԳŵ˵֪ǸƢҲûȨֹΪδĻѧ磬Ҫ죬ҲĿԼľװ˷档
ɣһʱ䣬һ֮BSDоûͻԽչĻϰͣ𣿡
һʱ䣬㹻ˡ
ŵһ£ЦŵӦԺû⡣
ԺҲͬɿ
һʱ䣬ڳŵŶʮѧ˵ȫǻӻġ
Ƹʽ飬һϽаţһڽУߵϢͺáԺʿ˵ǸBSDĿҪΪˡоǱа칫ңҲԶֱǱ߰칫ͺá


İʮ ռѧ
ա
ڷڵǣߴ£ŵѧУһȵԼΰ
͵ģΰһ򵥵ĸӳ
ŵеĺΰ֡
ʦ֣á
ŵҼ㡣
ŵ÷Աȣ˱ߺȱġ
򵥵ĺѼ󣬱㿪żɽֱ⡣
ŵ˵ҪоBSD룿
ΰʹӷǱߵ֪ŵԼԼĿģ˵ɴ΢΢𺳡

ǿBSD밡
֤BSD룬ΰֻϾʱѣȥʵĻ
˵ʵΰûҲûģ
ţһ׶εĿ꣬BSD룡ŵЦҡҡͷҲҵһִɡһ£Ҳĵġ
ŵΰĿ¿ңԣϣʦܹҡ
ΰĬ룬ʣмɰգ
ɣɣ
ãҼ룡
ΰûκԥ
ɰգѾԵˣ
ǰĿǰһɰնûУǿĿİˡ
ȽɵĿԣֵȥһ
һBSD֤ɹŵ棬ڻѧĵλҲˮǴߡ
ʧܵĻʧҲһЩʱˡ
ʦ֣죡
죡

ΰʦóŵɲ١
Լ̸ΰ磬ŵֱ廪ѧѧо
ѧоÿ곣פоԱԼʮλҡ
ټһЩоԱоʹﵽһٶˡ
оһλλɡ
ǡɽһλݣŵֱӿսλ
ŵûдģоһλоĴ£ֱԼ칫ҡ
һʱ䣬ŵд뱨档
ֻ߸ʽŵܿ㶨ȻԼоݵݽȻᣬоѡ
Ҫ߼죬ŵҲż
óʱ䣬ŵѡһԼҪĲʿ
ֹڣŵѾյһٶѧʼ
ĿҲȷóŵǣڽһʱڳŵ¶
ŵոջòʸ
ճֵһòʸĽڣ󲿷ֲʿԵô飬ǳǵĹ״̬
һ˵ԸⱨʿѧֻдèСèֻ
ſȸŻơ
ŵһ
Ĳ˵һά׽ߣóŵѹٷ֮ʮŵĲʿʦ
οЩмڵβʿʦԺʿĴУڼη򣬳ŵڻܳҡ
ң˵ŵѧҲɾͷǷ
Ϊŵ²ʿĻܵά׽еԽ̵ԳŵڹѧĵλҰĻǺġ
꼸ݼ󣬳ŵûļȥˡ
̫˷ʱˣ
ҼϵݴͬС죬ƾŵҲ޷жĳѧľѧˮƽ
һԵĻǸ鷳BSD֤Ŀ󣬳ŵ׼ѴľͶȥûǸʱ䡣
ɣ
˼ãŵǾ򵥴ֱķʽ
ʮʱ䣬ŵһײ⣬һٶλѧʼȥ
ĿѶȴоˮƽʿˮƽȡ
ݺѧĸ򣬵ڳŵǺܻĿѶϵ
ҪԼʿһȫĿ
ǣоյŵʼ󣬱ΪǳŵǴӦѧʼЦݱϡ
󣬱㼱ķֽͱʣͷܱʼ顣

ŵޱȣҪֱֶͨɸѡ󲿷ѧͬ
һߣ廪ѧٵĲʿʦǷǳơ
е㲻԰
ڱһλ
꣬ڲʿѧǰʱ䣬ͨʼѧʮλ
ܹ꣬յʼֻݣ
ڰ˼⣬е㻳
ʼ˼Լ
ǲԼԴѧ̫ϸϢȥˣ
ǣԼе̫ɷˣ
~~
ڻʱֻ졣
ֻڷԼ˼ʼ
ʼǹ켴ѧоģݣȻǳϿҵϣܵǵĲʿʦ
һʮһ
ڱֻһ顣
ʮһʼǰ⣬ܹʮķ⡣
սѧлܻӭڷеĵģ֮ǰҲһɨա
ֻޱƵǣΪʲôʮһʼǼͬһʱ䷢ģϵڡ
Щѧ֮ǰڸʲô

ˢ˰Ŀ̫ˣҺͳ̽ԵˣֻתͶڵĻˣһλƵ˵һ£Ѱǰͱ༭õʼ͵䡣


İʮ Ŭ
칫ڡ
ŵŵ˵°ͳ˼
ͨԣֵλѧ
˵ʵȳŵҪࡣ
Ҳóŵľüࡣ
ѡ
ŵǵһ굣βʿʦ
Ҫ˵оЩŵȻǵʲáҪ˵ˣҽ̵Ǽλʿ
ŵһ࣬԰գ׹˴ʧˡ
ԣǰ򵥵ģһֻ꣬ѧͺˡ
λͨоһŮ
ŵһ˵ļԸն
廪ѧ˶η
ڣ˶ʿ׶ξͶڽѧ΢ּκѧ
ܿ죬ŵ˷ʼԼϵʽ
ʱ䣬ŵ93š

ϡ
Ժʿ绰֪ŵƸʽٰʱ䡣
ʱ䶨827ʮ㡣
ڵص㣬ͼݵı
Ƹʽ졣
ŵһڶԺʿĴߴͼݱһӭһվſڣÿһλȥĹԱͷʺá
Ժóŵǰϸ컨ϲһ㡣
鱻ĳŵԴǼҵĲˡ
ѧԺνеƸʽȻܴ
廪ѧѧԺλԺʿȫ
ڸڣ˳ɵļλҲݰֳ
ߣԺʿλ
ſϷŴĺ
廪ѧǧ˼ƻŵƸʽ
棬Ժʿѫʽ
ƸʽɶԺ֡
ʽ߳ǶԺԽ廪ѧƸڵƸ齻ŵϡ
̨ҡ
ЩĸڸĽޱȡ
һѧרΪһˣٰ˴͵Ƹʽ٣κ˴һӡ
Ƕ֪Գŵĵλȷʵֵ١
ԺЦеİѻͲݵŵϡ
̣ǳŵķʱ䡣
ܵ廪ѧƸڣ͸λ¡ϣԺǸλܹŽΪ˲ŵԼǰһɽ˵ɽѹסյָɽĵġ
ƸʽڳŵķԲ
ڳŵȡлĻ˼룬λڱʾ߶ȵ

828ա
һŵյһϢ
Ŀ룬Ѿͨ
ʮĿоѣҲѾˡ
ȻѧЧʿνǳѸ١
Ȼ󲿷ԭǿɳŵԵʡ
Ѿ
˵оѾԿʼˡ
ȻǵһһĿŵڵޱȡ
ϾԵĶ֣BSD룡
ǧ˿ԻܵBSD롣
ڣŵϾҪˡ
ŵһѪڵĸо
ŵ̴绰ΰоһ¾İš
Сʱΰϵ
ֻˣ齻Ҳǳ㡣
ŵռλ
ڲݸֽддһ󣬳ŵ̧ͷ˵ʦӦ֪ǰҺͷʦ֤BSD룬⼸꣬Ҳûз¶BSD̽룬һ뷨ġ
ΰͷԳŵʾ⣬ţ˵
BSD룬ľǣEǶڴKϵԲߣEKEϵļϣѾ֪EKɽȺLsEEHasseWeil L
˵ǣEKǡõLEss=1ĽףҺߵ̩չĵһϵߵĴʾȷ
ϸϣBSD벢ѧκһ
ΪȺۡΣְӦѧϹϵʮӡ
룬ŵڣҿĿǰڵѧۣ֤ȫBSD롣
ΪĪΤΪֻǶ˰أ߽ȺûκεĽ͡
ΰüԣŵ˼ǣ
ŵĿҪ죡
һȫµĶߣһ
ΰ˿ĭڳŵ뷨
Ϊ֤һ룬ȥһȫµѧ
뷨ƺֻǰλɣ
ǵһҪʲôΰ̽Ѱʡ
ܣŵɫָƽ
һ־սҪһ֤BSD룬׼ʱɡ
ŵûżǴ켸˼·ʵ
һҪģȰѿܴ
棬ֻҪͺá

91š
ŵڰ칫ǿҪ깤Ŀܡ
Ȼһ죬յһʼ
ʼӡȿƼģŵμ93žеŬ𽱰佱
ŵŬʽ
ңŵľֲǿɹҲͳŵǰʱ㶨ļСģ͸൱
Ҳ˵ŵкܴܶýŬ𽱡


İʮ ٣ȥ콱
ǲȥҲˡڵǰŵ̾
ֻǹȥո¿ʼ׶ΣҪԷǳŵδػȥμӡ
ȻȻҪ䷢ȥĿһˡ
ǣʵ˵ŵĲȥ
̫˷ʱˣһһأټϰ佱֮кüһʱƽ˷ѵˡ
û뵽һ죬Ϊý̫Ƶա
ңɺϵǣ93һ죬ĵʦӡ
ӣҲҪƳˡ
ŵͰԼѧһ΢Ⱥ
ŵͻȻм£3ļҿ²ˣѼƳһܰɡ@@ڡ
ðݡ
û⣬ܲ΢͸©һȥʲô𣿡
ŵŬ𽱰佱3žٰ졣
ۣڣ˼ǣΪŬ𽱵
ŵųɰհɣϾ˵ʮɰе̫ˡ
ʵҪǵýϣȽϴҲ˷ʱĵĵϡû취ֻˡ
ĤݴУ
ڣĤݴУ
죬ŵ򵥵ʰ󣬱ֱɻӡȡ
ŬӡȿƼа졣
93ա
Ŭ𽱰佱죬λѧݰֳ
Ŭ𽱣Ҳһ൱֪Ĺѧ
ۺȳŵ֮ǰõά׽ҪЩһѧоҪǿ١
ͬŬÿֻһߡ
Щѧ󽱣ƶȽַ򽱡ѧңѴ˽ΪĿꡣ
ŬȻǸԵĽڸָӵԭ򣬽һΪǷѧҡ
ŷѧңȴ˻øýĻᶼ޼
֪һǣǷѧˮƽȷʵŷڽϴࡣ
ˣŬҲǴӰ߸
ŵǸ߸
һǺȺ֡
صĻŵѧˮƽŷ͸ѧƽһȣֻ˵ǲֲ١
׹ЩҵĻƽһ϶ùƶȽȳŵҪǿơ
ǷЩңŵֻ˵߸֣޵Ƕôį
ߴʤ
ȥЩһѧңÿһܴġ
ҲˣŬ𽱵ľϣŵûκε
ǧУӡȿƼѧֲĲֱӲŷ⣬˱Ŭ𽱵֡ŵ
Щϣϸ룬ƺ֮С
ϲ̾

97գŵع
ĲǻŬ𽱽СŬ𽱵ĳƺš
ܾ˶ԺΪŵٰӷĺ⣬ŵͣĻص칫Һ󣬱ֱΰʦֺԼһ档
һССŬ𽱣ڳŵȷʵûоٰӷ磬ıҪ
ʲôʱõ˷ƶȽΪ칦
칫ڡ
ΰһƿţ㿴һϺά׽ƣѧо°һŬ𽱽
ϷſЦ£û뵽ôͰġ
ΰȻ֪Ŭ𽱵ĽԼλʦУֻʱˡ
û뵽ŵŸջع죬ֱ
ŵڰ֣˵һСѣʦֲ⡣ǻץʱ̸̸֤BSD顣
ΰ͵س˳顣
СС
뵱ΪŵеСƴ֮á
뵽ŵӣΰϵЩ
ȡһ£ΰɫ˵ȥʱ䣬Ѿ˼·֤Ĵܴˡ
ȵȣҷ䡣
ΰóֻһ󣬳ŵʾյһʼ
ʮʱ䣬ŵԵĿꡣ
ĵͷţĿǰѾҪˡ
ʦ֣ǰһ·ֹ
ţֱӷԸͺá
ŵָû棬ڣʦ֣һ׶ΣҪǸԲϰص߼Ƶ
ŵϴЦ볢һ£ܷݳһϴйصĶ
ݶΰĿ¶ǣŵǲ̫ðˡ
ŵɴЦݣʦ֡һԤУճƵ޷֤BSDģԣǱҪգ
ƵһµĶֲûʦͲõˡ
ŵΰſġ
ΰͷ
ŵĳϸ룬ڵĳϸԼλʦġ
˵ƵһµĶŵȷʵС
ҵĺϢɣµʱ䣬һһµĶʦϡŵ


İʮ ϵķӦ
ΰʦ֣ŵüĿαϡ
Ƶһ¶飬ΰ˵ô򵥣ŵΪΰģȫȫİѾעоȥ
ʵƵ²ŵ˵ɡ
ѹҲܴ
֮ǰ϶гϸʱǶô⡣
ֶͳŵҪĶűʵ
ڻԵɺ£һżȻķ֣ŵƵֵġ
Ҳ˵ݾԣͺܴĲȷԡ
оʱżȻһĶҲǺпܵġ
ڣŵѾ̶˿ܡ
ŵɷӵĿռСѶȣȻҲ֮
Ҫһ£
ŵֱӣùһݸֽʼ

ͬʱ
ŵڹBSD룬Ϣŵûп˸տʼ廪ѧȦСΧĴ
ܿ죬ϵһѧұ֪ŵ¶̬
ϾΪǧչֳǱѧңҵĴжԳŵͶ˼Ĺע
ˣϢһ̣ѧԺﶼðͬһͷҵ
ǺͶԺĿͬȻŵڼνѾƴټǼЩйӰա
Īģȥߴɶ
仹BSDӣ
㣬һʱ䣬ŵѾչ¶ɣɲΪԳŵһ޵̵ѧңԺBSDɽ
ⳡսעǳŵʧܵĽ֡
ѧ磬ϧҲֻ
⼸꣬ѾչֳҪѧľģֻһֱûһ쵼ߵĽɫ֣Ŀʱʵ֡
ŵǿҿ˻ѧ糹ϣ
ЩԸ⿴ѧңֻ۰Ͱ͵Ŀţȴûȥֹʲô
ڣŵԸʶ䣬ʵʵİѾͶ뵽BSDϣһܴ죬Գŵԣ·Ҫࡣ
ʮġ

磬۷׷ס
϶ŵðģֻ൱һٲˡ
ڣҲ಻г˵ŵֲ̫Ű
ԺʿרҹŵһΣóŵЩ
ŵȻ⡣
ɵˣŵᣬʱʵ֤˭ȷġ
׷ţŵȴĵĴ廪У԰Լо
ŵɡ
¶УŵѾһЩ
BSDҪĹؼʣءĪȺԲߡ
ŵΰֽ׶εоĿԲߡ
׼ȷ˵Բߡ
ʵĪУԲߵĽ
BSDϣЩʺˡ
ҲǱȳŵò辶ԭ

ʱͷæµĹǵʦʱ䡣
Ŭ𽱰佱鵢󣬱ڽС
ĵص㱻ѧУһһꡣ
ŵΪڷϣǴٽķʽ
ŵ󵽵ģʱλѧѾˡ
ŵ˼ϵƬԲڷֲ˭˭
ǸɫT߸˧˧
һŴ۾ƤںڵǷڡ
ֵһǣŵѧҲ22꣬ͳŵһ
Ȼͺͳŵ࣬˿Σŵӭ
̬ȣǶԴһͬˣһλѧŵϽڡ
֮ǰŵһֱΪԭ򱻸ӡ
񣬳ŵĲǿʶѾþ󲿷ֵǵ䡣
ԴѧŵûϣңҲϡ
ôнЩʲô㣬͡
ŵȻǵһν̵ѧҲѭ򽥽ĵ
ңŵҲӡ
򵥵üĬСЦһ¹ϵ󣬳ŵЦǺǵĿ˵ֽ׶ڸʲôѧУѾķԷҲö˵˰ɡ
ǸԾӣʣڣڹBSD룿
ţĿǰȻ˳ŵͷ
ɫ̱˷ǽڣܲܡ
ܣŵ֪Ҫ˵ʲôֱӴϡ
BSDѶʵ̫ߣ˵ȽĵĻǹдĹʽʲô˼
ڣǻ֪֮ġЦ
BSDĲʵ̫ߣԶǲʿͿ漰ġ
ң룬˾
ڣһ֮롣۾⡣
ŵһţһպһ߿ڣ˵
֤BSDʱܲܰѵһԤӡһݡ˫ȭȻҲܴʷһһʷļ֤ߣ
ŵüͷһŶô֤BSD룿
ȻڣУܵģ
ųŵϡ


İʮ ¶
ƨ
ŵŶͷ
ܿ죬ŵǰԼתصʦĽɫ
һ£ŵ˵ǼȻյѧȻǷ֮ܡʲô⣬Թҡѧϰ棬Ҳ档
ȻҲϣǲҪҶǵ
ŵҶǵҪ󣬵һ꣬ǾҪɲʿҵĵ׫дʣʱ䣬һѡ񡣡
ٹ֪ѧҲ٣ҿƼȥǵ¹ߣһѡ񣬸Ŀ
һʱ䣬ɲʿģ
Ҫ󣬿˵൱Ŀ̡
Ҫ֪ǲʿҵģˮˮͨıҵġ
ɨ˽üͷŵ΢΢һЦûգ
ɫԥҧݺݵصУ
ҲԱصͷ
˵ѧˮƽҲһٶӱŵѡϡ
ͨУѾ˵еš
ڳŵһʱһƪʿҵģλѧ˵ȫǲġ
ؼǣԸԸⲻϱƽԼļޣԸȥƴ
ڹ⣬ڵĿл̫ڰˣҲ˵һƴ
ͷ˲ʡѧԺĴ󲿷ֲʿ㡣
ʡѧԺ󲿷ֲʿɵ񣬷ǶȻҲԡ
ңԼԮ
ŵ޷ıڵд󻷾ıһԼߵˣŵġ
һμᣬڳԳԺȺнβ
˱ҵĵѡ⣬ŵûָֻ̫˵оԼȤǸͺá
ȷѡ֪һͺá

£ʮ£ʮһ¡
µʱ䣬ŵ̤廪Уš
Ԣ¥оһߣŵԼȫͶ뵽BSDоС
죬ΰʦǱѾѵһ׶ΣҲԲֵ߲Ƶݷŵϡ
ŵ濴һ顣
ƵͳŵԤϵĲࡣ
ҪõĽһСξ롣
Ҳΰʦֽ׶ܹļޡ
һСһǵǰŲһ㣬ǧѡ
ԭǿɹ۴ڵġ
ΪеѧϵУڿһСĹڡ
ͬ
һߵһߣֱ߾Ȼǳ̣мȴһҪȥֻҵľͷȻƹȥ
ʷϣѧҳôãҲûߵľͷ
ŵô
ǳԵĵҵľͷǻҪƺܳԶ·
ƹȥŵϰһ򵥴ֱķţ
ŵݶһŵĹ̡
һһСξ룬׾ܹꡣ
ڣŵţˣ
칫ڣŵչһӣĿĻϵļйʽޱ泩
ڣҸ˰
ҪӰоڵˣŵĺ볤Хһ
£Ϊŵķµʱ䣡
ڼ䣬ŵĸΣ߲·ĴʮΣһ·Ŀİóŵֱӷ
ŵҲǺѵõ鵽пݽߵĸо
ڣһжȥˡ
űŵ֮ǰеŬֵõġ
ŵֱӴ绰ΰʦ֣ѾƵˣҰ칫һ˰ɡ
úúãԺ¥ǱߣһϵǱΰϢҲ쳣
ӺΰҴҵĸϵ
ˮȣ㼱ٵĶԳŵʵ¶أ
ŵЦеİһA4ֽݹȥ
ΰӹͷȥ
KϵԲߣ棨R/Z^2ȻAbelȺṹԲߦǶ뵽Ӱƽ棬Բ߷¼ζ
٣ԶֱߵĽOAbelԪ
ڣR=xy-R=xy
ۣPQPQֱĽڵPP+Q=-R

ΰϸ̧ͷŵĿУѾȫǺȻ
⣬
ΰһ֣һ˯ͷĸо
ŵ¶еݣֱҲʲ
ѩ̿ԭǰ·ͻȻûȻʡ
ΰһϲõͬʱͬʱҲھȡ
ŵȻظ֤һݳһ¶
ʱƣΰBSD֪ӣͬʱҲʶŵ񾿾Ƕôļޡ
ΰѾĿʧܸյ׼ˡ
û뵽Ʋܵ񣬳ŵ˵һ㣬ڰһµĶϡ
¶Ҳ൱ߵѧ塣
򵥵˵ǲBSD룬ѳŵƵ¶óҲǵڶݶѧˮƽ
ʢŵΰûԸܹ
ΰʶԼǰ꣬Ƕôֲһһ


İٰʮ ʲô˵Ķ
ŵʱƵĶΪԲȺ
ԲȺBSDֿ֤ԼС
ʦ֣鷳ˡ
šһܣŶʱ䣬Ұѽ㡣
ԲȺĳ֣ΰеĿ˹BSDϣ
ѾƵԼһݹȫľBSDϡ
ϾһBSD뱻֤ܻõ棬ҪһĿҪǧٱ

BSD֤ɵĽš
ŵΰʦֵܶˣճоĹ⣬ʣľȫ档
ÿڰ칫ûбҪš
ֹ̬ȣ֮У廪ѧ޵ѹ
һߣǳŵΰʦֵܣæȥʳóԷСȥ
һߣȺеڰ칫̵ĺȲ졣
˲䣬У
ˣǶ̶̼ʱ䣬ĿʱͻȻû
־Υƴٴγϡ
ѧУĿзڳŵӰת֮ʣŵΰڰ칫ڼҵš
ϸĻBSD֤Ŀ⣬Ѿȥĸµʱ䡣
ĸµʱڣŵΰˣ㶨BSDĵһƴͼ
֤BSDռĿ꣬1/3
ƴͼֱǰأĪȺ
տܣһҪ㶨ƴͼĪȺ
ĪȺBSDһɵĽȺԲһͬĴϡ
۵ǣ½׶ε뷽ʲô
ΰΪӦôĪȺģоѧоBSDһʱԴνо
ŵĹ۵㲻һ
BSDչоѧǵĹ۵㣬ŵϣҲͬ
Ȼû֤Ǿ˵ǰδȷġ
ǰǵ·辶߳һԼĿׯ
ģŵΪͬ⣬һõ뷽
۵սǳŵ˵ΰ
µʱ䣬Ϊ˸㶮ڶƴͼŬ

ʢģһҲƽ峿
廪ٳܽܵϣŵŶܡ
ڣϺð
һ𣬽űһӰڳŵһС
˲ǱˣǳŵǸϲƨѧ
ѧԼӡ󣬳ŵֻݡ
šŵͷǴк
û뿪ӣһߺͳŵţһ¶ݵı˵ڣû뵽ôæʱ壬ֲܳΪά׽ʦΪᱲģ
ŵЩ˼ЦЦ˵ıҵҪˣͦİ
ԶһƪҵģǧѣУֻǶӵѣСǰֵһᡣ
д׼ȥĹѧϰһ£Ŀ
Ȼͽһ𡣡ԥĻش𣬡ҿЩѧûһȽģУѧĴУҲȥ⣬߾ͺã
ȻӣŵЩò׼Щ򣬻ķԷθ
ҵдøҿض˵Ļǲμӱҵġŵһ䣬Һϸ񣡡
֪Ҿϲϸʦ¶һ׵ݣԴѧԽϸԽ˵ѧ̬ȣڣһֵþʦҺܳΪѧ
ŵ
ЩʵܲˣŵͷһԲȦصԢϴ󣬱ֱо칫ҡ
ŵʱΰʦҲյ
ʦ֣簡
磡
ˡŵҪƽӵ⣬Ѿļ㿴ûʲô⡣
ŵ򵥷һ£ʦ֣ĺܺáǱ棬Ϲˣҡ
ŵΰЩԥ
ŵ˵㹹⣬ǵڶƴͼؼǸ֣ͬҲѵһ֡
ŵΰĵǣɵʼʦ֣ҾͺãѾһЩ뷨ʵƵһ£Ӧò⡣
Ǿͣ鷳ŵˡ

ŵñڲݸֽ㡣
оĪȺͬϽཻʱõıʾʽ
һ൱ӵ⣬ҺãŵЩС
Щǳŵ⼸ڲٳܲʱֵġ
ÿȥٳȦϰߡ
ٶDƽӣ򵥵ĳȿʾDΪͬȼԲE_D:y^2=x^3-D^2xĳy\neq 0㡣֤ĵ㲻TDΪֵͬȼr_D&gt;0ͬDʹr_D&gt;0Ȼ󡭡ȷǡ
ȵȣ
ȻŵıͣסĿ΢
һ̣ƺһʲô˲õĶ


İٰʮһ 
ŵŵ㣬һֱ㵽ڶ賿ࡣ
ڼ䣬һֱڰ칫ûԡ
ΪһģǺòױץסоͻѸ
оֻһ칫ҵĵƻš
˸Ƿŵչһ壬˱ȡ
ȻһСںţһżȻеķֵġΰ
ڣŵһֲеĸоС
Ϊ֣۹ԳƵǡ̱ʽ塣
ұ֤һֹȥϵѧΪ֮
һУԴһɺϡ
磬ŵĪȺͬϽཻνбʾƵ
߽Ͷʱ򣬾ȥЩ̫鷳Ƿܹе߹һ棬ȥһͼ
ˣŵѰĶͼȫڲݸֽϻ󣬶ޱеһȤ
Щ㣬߶ȿߺĵ
ͬʱԸ㣬ȷλá
ŵûзżȻķ֡
һʱ䣬ŵ㣬ȷЩӳ㣬ÿnϹ㣬Щĸ߶ģʽȨ3/2ϵ
ŵ֮԰֮Ϊ̱ʽķ֣Ϊʡ
Ĺһֱѧڵļ֮һ
ֹڣѧδһͨõļ򵥷㷽Ѹٵλãб
ĳ֣Ժ׵ĸı״
⣬ͶӰ㻹ԱʾģʽȨصϵڸϵͳĹ
ǳŵ˵ѧңڿչǰʱҲޱȵ𺳡
⣬ϲ
û뵽ڹBSDʱ򣬻żȻ
ŵʱΪ㣬Ȼϵԣ̤ʵɫصԢ
Ϻƣ鼤ڴշתൽҹ˯š

գŵźȦо
̽磡
ţ硣
̽ڣҪעϢƴǺ£ҲƴʱȾһĲ˺ڶ
ܽڣллѣһעġ
һ·кŵ칫ҡ
ڡ㡱Ƶϸһ飬Ӧûʲô⣬绰ΰԼ칫һˡ
ΰڹҶϵ绰ʱҲơ
ոȥŵ칫һˣԼȥѵǡʲôشչ
ޱȺ飬ΰСŸϵѧо¥ĸ칫ҡ
ʦ֣ҪֱӸо߰һ칫ҰɡҪȥҲ̫鷳ˡ
ŵʾΰ£ƹȥһ裬Цſڡ
ΰҡҡͷʱˣԺ칫¥ҲԶӾܵ
ǻ̸°ɣٴνйѵʲôµķˣ
ûŵ˸ָӡõĹڡ㡱Ƶ̵ݸΰʾ⣬ʦ֣ȿ
ʮӺ󡭡
ΰͷ󺹵ųŵݺ˿ĭΪȾѾЩ㡭㷢ֵģ
ŵָָԼĺȦЦһʱ䣬ϰࡣ
һһ죿
ðɣΰѾŵĳ
ڳŵ֣ΰѾֲˡ
㣬ȷʵǸ˲÷֡
һųȥ֪𶯻ֻڶʮǰӼ뱻֤֮ʱ
ҪΰȻҪȻãŵһƽı飬ΰȻһ֣㣬ҲĴ
ΰľĿ죬ȥҲ졣
ô˵㣬BSDĵڶƴͼϾҪˣ
ŵ°Цô˵
չоΰǼҳڡ㡱֤̣ȥ
ͻȻΰʲôתͷʵڳķ֣費ҪһƪģͶ嵽ѧڿϣ
ŵ룬ҡҡͷʱҪôǰBSD볹֤ʱһѳƪĸȥ
㣬ȻѧֵҪߣɷϵһǣҲǶԸBSDһС
ҪǴʱƵĹñѧҸ֮ǰó㽫BSD֤
ǵʱ򣬳ŵ֪Ŀȥ
ԣʱ򲢲ǹ㡱ʱ
ʱֻ֪Ĵھͺá
ΰѣŵarxivϴһƪдģǰռӡ
Ȼʱڲ̫ѧҷ֡㡱ĴڣǰռӵĻΪ˷ֹķ


İٰʮ ˵Ĺ
ķ֣ΰǱߵĹȶȻӿ˺ü
һں֤BSDĵڶƴͼŵΰɡ
2/3
볹֤BSD룬ֻʣһƴͼأ
ҲƴͼѸ㶨һ顣
ǰƴͼҲԲߺĪȺֻƵ˼·Ƚѣ㸴ӡ
زͬѶĴ󣬶ҪļҲޱȵӡ
Ҫһˮĥ
ŵ֪򲻴ĵ˲û̫ż
ڵĽȣŵѾǱȽˡ
ŵԤƵоҪʱ䣬ڿһʱ䣬BSD֤
ŵٴλָյĹɡ
³һŵݽĲʿҵġ
оľǴη
֪ǲΪ˹ֺҵоĿ⣬ǳŵȥļСģ͸⡣
Сģ͸Դȥ걻ŵڶ̶һʱھͳʾ֮ơ
ǳںĿģĵǿԵģԴﵽʿҵĵҪ
ŵдһ޸ûȥСޡ
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⡭̽ںǿ²һְɣ
֮ǰҾͻǺģڿϢҸȷһ㡣
ţ#ŵ#ҲѰѸ
ǰŵμӡǿԡƵҲܵǰǳŵϡ
ʶǸڹϹâ꣬Ѿɳ˸߶ȡ

BSD뱻֤󣬲ڼ
һЩ˾BSD뱻֤±ҲˣĿ˳ŵϡ
Ĳãڵٹᡣ
ʵݺݵĴȺһơ
һʱŵʲô˲϶̫˳˳ˮ
ǣɹˡѧҶδ˵BSD룬ˣ
һѧĶˡ
ڣŵٲȻΪֻܹ
ʦڣΪͬһεѧңվڽˡ
ʱΪŵĴڣؽԣ

ǰʱ䣬ǷݷƽϢҲѸٷ仯
Ǻʵˡ
֪ŵ֤BSD룬ʮλĳŵˢºֱ޵е̬սаһλ
аϣÿλѧҺ涼һ񽱸ʵݡ
ʱŵβʱԤŵĻ񽱼ֻ0.87%
Σŵսһ󣬻񽱸һֱд100%
רҵʿǿһķƽѾǳŵ֮
Ҳʵ
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Ҳ˵ڵ81ŲµʱڣֻҪŵҵǷƶȽĸѾŵԤһ
Ҳֵһλƽ

廪ѧѧо
칫ǰµˮйͨ
ĶĽѧѧϵ廪ѧѧԺѧҲҪ׶һλֿȵġŽڡ
ˣ⼸ŵϰ࣬ǵȵȺɢȥŹ
ʱŵڶԺİ칫ѡ
ԺʿЦ˵Ϊ찡
ŵҡͷοЦ죬ҲҲա̫ˣ
ٴһ£ʱ䣬ǧҪ¡ѾеķƶȽͷɱΪһջϲİȫǵһҪ񣡡Ժɫ֣صĿ˵Ѿ룬Աİȫб
ŵɴ۾ԺûбҪɡҾһоģӦӦȺˣѵĹһѾ˼ң
δȻԺڰֻ֣Ǿܱķ


İٰʮ ѧ
ֱµףڳŵ֤BSDķ粨δˡ
û֮ǰַ񣬴󲿷ѧ߿ʼǵĿ¡
BSD뱻ɹ֤ȣѧ˵϶һǳĺõϢ
ΪζţBSD룬ŶӦ˵BSD
BSDоѾԿʼֽˡ
BSDֻһѧ
ӦѧӦ򣬹BSDӦãдȥ
һ൱ĵ⡣
ΪˣBSDӦоĿС飬ڸŵ֯£Ѿʼ齨
ѾδԾѧеһѧңҲ͸¶Ϣ뵽ԹҵǸСС
˵BSD뱻ɹ֤״ѧоBSDȳ
arxivϣƽÿ춼мʮƪйBSDԤӡϴ
ңһЩϸĵˣҲ˹ƪBSD֤һģΪˣ
ƪģֱԲȺ㡢Ͷ
ƽʱƪģóһƪѧҵĹע
ǡ㡱ǿһٸıԲļ״
BSDĹ£˶ʶƪġ
ⲻ֪ƪݣһ𣬶ѧӰ죬˿BSD֤
һЩ侲ˣ鱦أܶѡĿʼо
ֱѮŵƪĵҪԲű󲿷ѧҲʱϣѾ󽫽һ¡

µףѧоϵŵ
ǧߴ⣬ǿѧоһ
֮ԡߴѧ⡱緶ΧôߵⱾѶһ棬һԭ򣬾ǿѧо͡
֤ߴѧеһһԪĽ
һԪǧһ֣ڽ죬ڵһ׼ʮƽķӶ
ѧоǮŵ߸һ㶼care
̻Ҫһġ
ѧоǱϣŵܹһ׹н䷢
˳㣬һBSDרⱨᡣ
ѧоǴžž죬һ򣬵ŵĳѣǻ׬٣
鱻ŵϵľܾˡ
ԺԼŵ˵ڹѧҴٿ֮ǰŵϽ
ŵǹصע˲ţһ£Ԥϡ
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ҪʵڲͬĻһҲҪˡ
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տѧоǱ߻Эˡ
ͷʢʱΣѳŵ뵽Ǳ߿չһⱨ棬Ƕоǳһ¡
ŵԸ⣬ֻܾʹա
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ҪһǰͲŵˡ
ڣŵĵλͬ
Գŵѧĸ߶ȣѾǵһѧоǵĳ̶ˡ
ˣҪˣ
գѧо
ǱʾԳŵףأȻѾһ𷢷ŵŵСȻĺΣͨƪԳŵźۼԼͳŵϵ̸ǰڿѧоһٹ˹ɽ־ͳϸ£
˵ǿˣ

˻϶һ𣬳ŵ޲Ťͷ˵ˣԺղ˵ʲôţ
ѧУҪ㿪һBSD̵֤רⱨ棬һԺЦеʵ
ŵشĺˬ죬û⣬ǿŰžС
ʱ䡭
κʱζԡոôһ̣ҴϢһʱ䡣Խڲûʲôš
ԺʿȻĵͷһʱ̫ƴˣȷʵҪϢһʱ䡣ǺҾͲˣʱȷһ֪ͨġ
BSDרⱨʱܿȷ
ʱ415ţص廪ѧá
Ϣ廪ѧķųȥ
ǣѧ綼궯
BSD뱻֤ѧо䷢ͽ̣ȺڱݣǼǿС
¼λŵڣȴʼգδ¶档
ֱڣŵ˼ڹڳ¶Ϣ
ټϱǹBSD롣
ʹεѧѧļע
Ȼ廪ѧ棬ҲǱ˶αľӡ
ϾμӱģֻйڵһЩѧҡ
ϵһЩѧУ˵αҲѡ˽廪ѧ룬μεıᡣ
УͰλƶȽʮλ缶ѧ
Ժ֯ŵģô֪μӵĻѾһѧԺܹƿصסˡ
廪ѧУֱӽ֣һλУԶαһˡ


İٰʮ 濪ʼ
Уʾ廪ѧα㹻ӡ
ѧУһǼƵֱӱƴֵ廪ѧ£ڱڼѧߵд
ʱܽš
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⣬ǡBSD롱ĿĸȶȻ⡣
ˣ󲿷յ뺯ѧңû̫ҪĻѡ廪ѧ롣
587λѧңȫ60Һ͵
УһѧңǸѧѧҡ
ݣѾ˿κһ͵ѧ顣
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Ͼвѧ飬һһλƽѾ˵ʮֲס
Σμαķƽλ
˷ڻΪ˸ŵųǰʣµλȫǱųŵݶ
Ҳܺ棬һ꼶ŶʮͷСӣýʱ䣬֤BSDһģ

λѧĶѧңݰ廪ѧ
ֳ棬Ҫǰ׷ݵ08ǴڻٿĹѧҴϡ
꣬ǻѧܵĹңμӱѧ顣
֣ñĹҵѧߣƨƨߵĴԶֻܹΪһᡣ
ҶǸԹһѧߡ
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ѧ˵ʮΪ
ͬʱڵྩѧ廪ѧܹ˸߶˵ѧᣬĽĿˮˡ
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ҪǰܰѳŵѧУڣ϶һ

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뱨ỹвһʱ䡣
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ŵֻǸ𱨸ľݶѡ
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ŵЦЦ֪ԺĵʲôǳοԺİɣʲôĳụ̂һܹholdסġ

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ŵ˵һŵĶԺڣҲרΪԼųķڡ
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BSD֤ҽ򵥵ķλ֣ԲߡءĪȺ
棬ҽֱָԵԼƵ̡λ뿴Ļ
ȣԲߣǵһҪ񣬾ǡ
ŵһһ۵Ľš
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ŵƪ214ҳģĴ󲿷ѧҶ
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һˮŵɤӣЦſ˵BSD֤㽲ϣλʲôʣֱӾʡ
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Եѧһλڣǰ潲ĹBSD֤̣һʡڶųŵĿⲻƣʵ
ŵʼ磬ʾ⣬˵


İپʮ ʼ
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ѧ۾Ŀⶢųŵ̽ڣҷ֣ƪ֤BSDУµۣ
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һȻ
ǡȻͳŵˣ
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ʲôԭҾͲˣҽҲŵһ䣬λڣԲǼ¶ȷĽBSD֤ҽѧо䷢ҵİ򽱽תøΡҪǾòĻһټһ򡣡
ŵָЦĿλѧҡ
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в١
ŵΪʲôҪԼ춨ѧѾڵĶ֤BSD룿
Ϊеѧ޷㶨BSD룡
ҪˣBSDͱ֤ˣﻹֵõŵ
λѧңڳŵȺУֻһСѡ
š
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۾һ̽ڣ㵱棿
ŵͷЦЦѣҲں
ڵˡ
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ŵ˷絭˵ܡ
ǶѧĽڣƽʱеʱҲڴѧԵĻ˾ְϾֻһλѧң׬ǮȻȲЩӦ÷Ŀйߡ
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ңŵкܴɵĿܡ
˵ˮƽȻ޷֤BSDһⰡʦ֣ܻᣡ
Ͼλʦ֣ѧ磬ABC֤ߣһ
ȻʦABC֤ݲûеõѧĹϣҲûлùƶȽַ綥⽱ˮƽʦһκһλƽ
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ȫУνСʱġBSDרⱨᡱԲĻ
вĹڣԺŵߣĳŵļ򣬡ŵֲ
ŵЦЦԺ˵ˣС棬һHoldסġ
ˣ𡭡
ԺģҪĿһַ֤BSD룬ֵǮ룬Ӧû˻ɹҵǮɲôõģ


һɣŶҲλڱϺͳŵȻĵѧңڱĵһʱ䣬ûڻֱӸĺɻص
ѧ߹һӣСһһоǰ
Ҫڡ
¥칫ҡ
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һѾʮͷˣһ۾Цڰ칫ǰ
Ϊ񵺹ѧм֮һһѧˮƽȻƽƽڵȴ˵ӵء
ʦ֣鷳һ£һɵͷ
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һ߳칫ңܶࡣ
ǣ𣬳̽ڣϣʱ㲻ʳԡ
һ̧ͷ

ա
һԼĲϷһ֣BSD뷢𹥿ˣ
Ȼáˡʲ̫׼ȷΪBSDһǰͱŵˡ
һ˼Ǿŵ˵ǰ㣬׼еѧۣBSDȻ
ͺ˼ˣ
Ѹڹѧ˺ܴķ졣
ǾһС͸ѧҵĻ¹󣬿ܾͻᱻ˾ͻ𽥵ȻżȻʱµһ෹Ц̸
һļ룬ȫòͬ
󲿷ֶû뵽һɻһ֣һġ
ηһƪͿʼѾǼ򵥵Ԫ⡣
Сһ˵ǳŵһ˵ĸìܡ
һ˵Ǿѧ͵ѧĽ棡


İپʮһ ѧ
Ҫ˵һѧĿĳɾͣȻһƪ512ҳ֤ABCɣ
ͬҲһΪĳɾ͡
ͬǰᵽģƪ512ҳģǲõһЩȫµѧңоġ󡱣Ҳȫµģ
͵£ڵϣˣûκһܹȫƪݡ
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ˣABC룬ABC룬ʲôABC
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Σһϧ³˻ˮ

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Ѷ˵BSD뱾ͱABC֤ѶҪ
οŵɹ֤BSD룬ǵõѧϵġһأûеõѧĹϡ
䷽ڵĳŵķ棬һҪǿһء
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϶ԺĿ⣬һ䣬ԺҾãABC룬һȤĶ

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⣬ǳѧǷƶȽ
ѧȻΪ˷ƶȽֻǻȦһͷƶȽ缶ûȡ


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ˣ֮һʱ䣬Բϵõ༸λѧڲˢϢ
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ѪҺע룬ѧҵ𣬶ɲʾţѧ磬ѾɳΪһɲС
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ŵĳֲ֣һĲ㡣
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꣬ŵŲ24꣡

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ȷʵôһ˵Ҷûˣ
ɶͳ̽ڱҶԼǲǸˣ
Ѿ߽ƵĳŵȻȺԹȺڵ̸ۡ
߽žƵڲǸûʵװΣһȺֺЦԼĸѧңŵϸһĨȻ
ǰǽѧҴᣬҲμӹ
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ڳŵڲͬĻ᳡ѧڼ䣬÷ƽ飬Ѿýߴعڡ
ƶȽڻһ˲˽ѧȦƶȽǺŵͬȸ߶ȵĽ
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İپʮ ʱ
ABC룬˵һΪһɾ͡
ʱΪ׫дƪٶҳģķʱ䡣
ƪ֤ABCģһѪ
Ȼû˵۵ȷͬҲûҳдڵĴǡ
ңABC뷽棬ĿǰֻƪķУ;ȫ·
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ڣʲô
ŵѧݣABC֤
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һҡҡͷȥֲĺ
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ס˵ֻǹǡһ

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ŵؽΪʱĴ棬һᱻܡǣֻ֮һˡ


İپʮ ѧǿ
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˵󣬳ŵѸ뿪ãⱻ˳û֡

ѧҴᣬΪȫģѧ飬һֱܵĹ㷺ע
ֽѾǹѧҴٰĵ죬ýЩʧǣδᣬƺЩƽĹˣ
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ڱľݣ඼ǷˣѾоɹһ顣
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ңһ֤˵һμӳŵѧ档
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ǿôìܣһֱͲˣô˵ЦĸԷأ
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һ챨⣬ǽBSD롣
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BSD룬ǳŵĿǰĳɾͣABC룬ǡһΪĳɾ͡
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ʾģԼ֡һԼЩŵƵ˱㼱͵Լ߿
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