
                               


    ѧرȻѧҪĿ֮һ׷Ѱѧԭ 

Ի׷Ѱһƶͬʱѧ׷ֳΪ 

ᷢչһƶ 

    ѧѰֺ˽͹о¹ɣ 

ڲи׷ѧġϽġʵǵģͬʱѧ 

Ǵġѧ̬֮һʣѧ֮һ 

С 

    ȷѧرȻѧȽ 

ǲϽ浹˵ʱ򣬿ѧȴ 

ţʹǻѵĽȻѧа 

ء 

    ϣѧΪġһƶ 

    ѧرȻѧĽʵҪأ 

ִһġѧʹ˻͹֪ʶͼ 

ܣҪʹ˻ÿѧ˼롢ѧ񡢿ѧ̬Լѧ 

Ѭպʹ˻÷ﱾܵǻۣ÷ꡣ 

˵ûпѧġֻǽûܹ 

ѧˣֻܳΪܹѵܹ 

    ϣѧΪʹ˽Ϊִ˵ġһƶ 

    ʿʶǿй벻ѧ 

Ϊ֪˼׿ķܶйĿѧǴ 

ΪйĽڿѧ˶ͼɹ˵ǿ 

ΡȻӦ˵ĿԶδﵽյйҪµĿѧɣ 

Ҫִѧֻȫ˾߱ϸߵĿѧʣԿѧľ 

˼롢ѧ̬ȺͷΪֺ̽ͽĹͬͳ㣬 

ܸõǰչͽˣйĽ벻ѧӹ 

ɵġ 

    ϣƺ˵ѧѱйز 

ٵƶ 

    ȻⲢζţѧľҲͬرϺͽܡȻ 

ѧ͸ĸͲ棬ѧļֵ͵λҲˡǣ 

ӹԣһķΧڣĳЩضʱֻǳϡѧ 

õġֻͣڶԿѧĺĽܺͳϣǶԿѧԭ 

ѧľĽܺͳϡĴҲǲܺӵġ 

    ѧľ֮һġһƶҲ˵ 

ѧԭǲڷѧģڷѧģѧ 

ԭҲڷκѧѧǳԽڽ̲ģԽ 

ģԽɲģԽĻĵģѧʵġ 

ġס 

    Ͽѧ羫ѡһڿѧ˼Ϳѧ 

йѧĳ棬ĿľΪ˴ѧľ񣬿ѧ 

˼룬رȻѧľ˼룬Ӷ𵽳ѧƶƼ 

չȫµĿѧɺͿѧãΪйĽһ 

ƶ鶨ΪһƶȻ˵ÿһᶼǵһƶ 

ǿԿ϶̺ÿһеĿѧݡ۵㡢˼;񣬶 

ʹٵظӽһƶٵط֣γΪ 

ס 

                                        һƶί 

                              ǰ 


    ˹̹˵ǿġȷ 

ӳۺͰ˹̹Ĺۣѧȷ 

ͳɹܱͳһڵ𣿹⣬ 

λѧҡʷٷҡ𣨡ʱʷߣ޽ܡ 

˹ʵԡӰӣShadowsofMindߣ 

ͬⲿνݺ۵Уǲ˸Ե 

ЩڽŴѧˡţѧѧоеġ 

    ܹʹըĸʱԼڶԻ 

ôνأΪʲôǵһ飬 

˹̹ԤԵģЧӦӹʹڶ 

ûϢĶȥˣʱΪǰˣ 

    λڱдЩ⡣˹˹̹ 

ܾѧΪۡ뷨ͬ۶ϵ 

۲ܼ򵥵ؽĿˡֻޱ߽ϲ 

ǶĹ۲⡣ͻʵ֤ͬ˹ȡʵ 

ΪǿŵģԶ͡۶ϵչ׶ 

ΣʱյѹͱԼŤۣ档 

пԿ˹Ѱͳһѧ۵ 

βͬԼֲĶ棬еĲͬŬ 

                               


    죬ߵӦٸ̨ʡҹѧ 

һ壬ռڳʱ֮СⱾ 

µĽ 

    ̨λԶĸԶ𱤣һƬĻɽ 

Ƶɽ鲼ɭ֡԰ͱ˴֮ 

Ϊǽ̻Ĺڵء̨ԶĹ߲㣬 

߰칫ҵһ㼴ǽ̻ʵҡֵ̻ʹ 

κڽʤسصĽͽ 

    ˵ضڱһʷԨԴ1981 걾֮һӦ͢ 

ѧԺ֮ۻ״ηޱ߽˼롣֮󣬽 

ڸԶ𱤽ӼߡĴͳͽϱڽ̻ 

ǰй񡣵ǵ̻֮ǰʱʷһĻ 

ˣ̻뿪λ£ʹͻʹ 

ĽͽĿɿڴҲ˵Լޱ߽ 

ĳ֡ 

    ڽΪĻһ壬ѧ֮ĶԹԹܵ 

þġ³ŵ٤ܵȺ֪ġʵϣ1633  

ʱĽ̻ڶǩǴ٤Եļ1979  

11  10 ֵ˹̹굮̻Լ޶ĸ 

٤ȷģ֯׫й٤Եἰ 

˹̹ǰҫ٤ȴĥѡȷҲǣٶĽ죬 

٤ԻʲôأֵעǣûйϽ̻᷸ 

󡣵Ȼ̻ͿѧҲǶģڶԶĻ 

Ĺ׶ʷᣬ 12 ǰߵһν̸лǿ 

    Ӳ³ŵʻ㳡ܻ̣٤Եõƽ 

ǽˡǿԴݵشͿѧۣص 

ܵ٤һˡڿѧʷϣ٤һ˾ 

ԭڱбϽеʵ壬ֱ 

ɰ˹̹Ĺֲۡ 

ۺʱ۵ǰ֪ʶ˹ֱɵ 

Ʒ͡ǳǵϵʱͻǿһ 

̾컯档ȻЩۻ걸ģЩ⣬ʱͷ 

ȻԶδڳ磬ʹ֮ʣͬ 

    д˿̣ѽҹٺưɸѳţǿȻá 

ڴʱձԵġɷ硱Ž廳ͣпϵ֮ 

                                                   ҳ 

1996  8  15  

     ڸԶ 

                                ǰ 


    1994 ڽŴѧˡţѧѧоһΪ 

µļƻص޽ܡ˹ʷٷҡ֮еһ 

Ǹüƻĸ߳һй汾ԵĳЩĹ 

ۡ˵ǻδﾡͷ˲ȷԺ飬 

ɹġ 

    60 ǰѧĻ˹Ͱء 

˹̹֮һĿճ־õıۡ˹̹ܾѧ 

Ϊռ֣ۡѧǲģԲΪĸ 

ѧɵͳͷһҵս 

    ĳϣ˹ͻ֮ıۿǳļ 

˹ΰ˹̹ĽɫβĽɫ 

øΪӣҲΪ㷺ȥɵ֤ѧ 

۵໥޷ֿ 

    ۣĸ߼ʽӳۣѱ߶ȷչ 

ɷѾʮֳɹܻ޽ܡ˹ѧϳֻ 

̬ߡۣҲǰ˹̹ۣҲͬʱ 

飬ȡ˾ĿĳɹȻйԻߺڶ 

⡣ 

    𡪡˹۵ؼڰֳɹ۽ 

һ𣬲һ֡ۡǣ浽ĸͼ 

⣬Щֵ̽ķΧ 

    漰Ļ⣬硰ʱͷ浮ĳʼ 

ԼڶûϢķʽ˹йЩԼ 

϶ǳ΢زȡ˲ͬѧϻ 

ǶرԼĿ۵ʽʹ໥ 

ʵ֡ 

    ȻЩҪ߾֪߱ʶı֤ʹ 

߸ȤĸˮƽϽеġٶ۵Ĺ 

;΢ԼѰһְۺڵгͼ 

ΰսܻ֪š 

                                                 ˶ 

    һ¡ 

                              SW 


    ޽ܡ˹ҽЩзǹʱձԵصĵ 

൱ͬĹ۵㡣ǽ潲ݣÿ˽Σйǲͬ 

ۡӦڴǿЩ൱Եġٶ߾ 

ۺ۵Ļ֪ʶ 

    ¡дһƪģμӹۻľ顣 

 1962 ڻɳٿĻ顣ߵԼĲǳ 

Ʋ𡣴˺󲻾ù۵ҡϣ㷺ȤӦ 

ع鹦޽ܵоסڴ֮ǰ۱ڵ 

ϵͳµһѷƫ΢ַ̡ҵһֽ󼴻裬 

ںǷѧ塣Ȼ޽ȫַ 

ִָ׼ȷؽ̣ܷⷽһʡ 

ĵһԶȥоԽṹ̼йԺͺڶ 

оС 

    Ϊ޽ܺھ乤Ĺ۵൱һ¡Ȼ 

˵۱оϷֵȻΪ 

ɥʧĿԣѧ϶ΪΣյļߣ 

޽ȣ϶ֻߡҲȡʵ֤Ĺ۵㣬 

ֻһѧģͣѯǷʵӦǺġ 

ѰԤӦ۲һ¡Ϊ޽Ϊλ 

ͼߣҪԼϲ㡣 

    ȻʱտзṹҿκӦ 

ۣΪĳɹһƯۣ 

ей۲춼ϡҲʿ˳߶Ҫ 

ΪⲻӰԤԡҲֻĳָ 

ĵܽƣ˵ۣΪ۱ֶۡȣ 

ۺͳеֳʱǷܸ 

ۡڳı֮¡һ˶ 

ų޵ġһʱбֶ˵϶зɢ 

ȻûҵַɢҲ۵ĵڶԭǣ 

ûκοԼԤԡ˳ԱȵǣҽҪģ 

۹۵ֱӦѾԼԤԡе 

һԤǣڱڵС΢ŵķչƺΪ۲쵽΢ 

֤ʵһԤԣڶӦȷ䣬ԭǿԼġ 

Ҫһȥ̫ڶϧǣΧƺûкܶࡣ 

еĻǾ֪ӻ 

    ȻռۣôЩԤҲûһҪ 

ı䡣ۣĿǰķչ׶ϣƹ 

ΪĵЧ⣬ЩԤԡһνһ 

䣬ҲԶۻ߳Ԥԡ 

ˣǾͻɣǷΪһĿѧۡûر 

Ŀڹ۲ϼԤԣѧϵƯ걸ǷѾ㹻 

ˣңֽ׶ۼȲƯҲ걸 

    ЩԭҽЩ۹ۡҽ 

ƺȫͬص㡣һ 

ʹʱվһҲһյĹڶƺ 

ͬڴصķ֡ĳЩƣЩԤԲ 

뾭ƵΪĲ˵Ҳۣ 

ĨƽԲԺڶԣڴֻ 

ǽԵġιˣ൱Ȥġͺ 

ơǣţͬģΪԼγɹԼݵ 

̨ĳһֻڹ̶ʱձбݡҲΪ 

˲ŵʱп˵Ŀԡй۲ⲻ 

޷صĸ 

    νлع˾еЩĹڵ 

κ͵νݣº͵£нָۺ 

αı䱻ƹ㡣ҵĵڶνǹںڶģǹ 

ѧ 

    ޽ΪоԺͺڶ˹ؼļɣҲһ֮ 
ʱմ߶ԽṹѧʡIpΪʱ M ݵ p δ 
ָʱߵеļϣͼ 11ǿɰ IpΪ 

лᱻ p ֮¼Ӱ¼ļϡһƵĶǰѼӺ 

ɸţδɹȥҰֶΪġ 
    ڿһ S δı߽ IS൱׿ 

粻ʱġΪ£һǡڱ߽֮ĵ 

һǡĵ p δδı߽Ҳյģ˸ 

ڼ S ϵĳ⡣Ϊ£Ӹպڱ߽δÿһ 

ȥָ߶ᴩԽ߽粢뿪 S δͺ q  S δ 

еʵͻͼ 12 

     

    ͼ 11  p ʱ 

     

    ͼ 12ʱı߽ȲʱҲյ 

    ǿԵõۣ˼ S ֮δ߽Եġ 

ȷ˵ q ڸδı߽絫ǲ S ıհϣһͨ 

q ڱ߽ϵĹȥָԲ߶Σͼ 1.3Ҳܴڲ 

ֹһͨ q ڱ߽ϵԲ߶Σ£q  

߶εδ˵㡣仰˵S δı߽Բ 

ģԲڱ߽δ˵㣬ǺԪཻ 

ĻҪδڲһ棬òֻ S ϲйȥ˵㡣 

Ȼʱգһ S δı߽ԪԶ 

S ཻԪйȥ˵㡣 

      

     ͼ 13 ϣ q δ߽ϣڱ߽ͨ q һ 

߶Ρ£ڲֹһ߶Σ q ǵδ˵㡣 

     һ򵥵ɿɷ˹ռаһˮƽ߶ߣͼ 

14S ˮƽߵĹȥ߾ͻͶһӰҴ 

ڸպڸ߽ĵ㣬Щ㲻 S δ S δı߽һ 

ԪصˮƽߵĶ˵ϡȻΪˮƽߵĶ˵Ѵʱ 

ߣ߽Ԫûйȥյ㡣ʱǲģ 

ǰˮƽ߶˵㸽ĶȹһʵĹӣͿ 

ĿռǷǳΪģǣо 

ṹʱ棬ЩʮҪʵϣ޽ܡ˹ڵ 

ҵһλʿĿʱָһҸղĿռ䣬 

ĳЩԵķ 

      

     ͼ 14 ڴɿɷ˹ռһߣ S δı߽ 

һûйȥ˵Ԫ 

     ͼ 1.4 ڴɿɷ˹ռһߣ S δı߽ 

һûйȥ˵Ԫ 

     Ϊָδı߽Ԫڸüϵһȥ˵㣬Ǳ 

ԽṹϸĳȫֵǿҲҪ 

ȫ˫ԡһ U 㱻Ϊȫ˫ģ 

     1. U еκһԵ p  qp δ q ĹȥĽн 

ıհ֮һнĽʯ״ͼ 15 

      

     ͼ 15p ȥ q δнµıհ 

     2. U ǿԳҲ˵ U вպϵĻ߼ 

ϵʱߡ 

     Դʵȫ˫Ե壬 U һϣ 

tͼ 16U һϣǺ U еÿһʱཻһ 

һεյĻԵ档 

      

     ͼ 16U һϣ 

ӿϣϵݿԤ U Ҫ¼һȫ˫ 

ı¿ԱΪõӳۡһȫ˫ı 

ܷһӳۣһδȫ˫Ҳ 

ǱġǣҵĹ۵ǲӦô룬Ϊ 

ҲųҪǵĳֶԸϺ 

ƵʱյĳЩȫ˫ġ 

     ֤Ե֪ȫ˫ԶԶ塣 U ȫ 

˫ģp  q Ϊ U еĿɱʱ㡣ô p 

 q ֮һʱĻԵĲߣĳд p  q  

ʱȡֵͼ 17֤ķָд p  q 

ʱߵĿռһǽµġȻָ 

ߵĳ϶˰ĺԣ뵽伫ֵ 

伫󳤶ȵ߽һߣΪĻһС־ͻ 

ߡ 

     ǿԿǲߦóȵĵڶױָ֡ 

      

     ͼ 17ȫ˫ռУһߣĳ 

ʱȡֵ 

һڽĴ P Ĳߣ p  q ֮һ r  

ཻͦ r ͱ p ͼ 18ǿõ 

 p  q ܲʧһԵذѱ P 㡣Ϊ 

Ķȹ棬ȶȹ棬˴ڼСȵĲߣǼ 

󳤶ȵĲߡСǴӱܵ q һߡǴ 

p  q һߣӱڱܵϼٻص q 

߰ϼһΪ P Ĺ㣬дӱĲ߶ϼ 

ཻСֵ p  q Ĳ߶ǳȵȶ㡣 

ȹ£һйĲߵĶױܸ 

 p  q ĸ̵ߡڵУƵӺ 

ϼٷǸߣǴ p  q ̵ߡ 

ǷǳġȻʱյΣӦָĳּٶ£Ӧ 

һȫ˫ڸ֮ÿһӦ 

㡣͵һͻʱնĲ 

ԵļǴġ 

      

     ͼ 18 ڲϵ p  q ֮й rͲ 

м 

    СȵĲߡң p  q ķǼСϼй 

    㡣 

    ʱеõԭǣ 

ʽʹʱڽĲ໥۶뿪Ǵ 

·Ŧ˹̿Կһ㣬ͳһķʽⷽд 

 

    ǵ·Ŧ˹ 
               dp  = 2 + ijij + Rablalb 
                                    1 
               dv                    n 
    ˴ n2 Բߣ 

    n3 ʱߡ 

    һزߵķʸ laǳġ 
ǲƽʣбĲȡ RablalbʶԲ 

ֱЧӦ 

         ˹̹ 

                    Rab  gabR = 8Tab 
                          1 
                          2 
          
                        Tabab0 

    κʱʸa 

    հ˹̹̣ʷνκ 
ʸ laһǷǸġ˵ܶ T00κϵж 

ǷǸġκκʣ署ߵų߾к״̬ 

̵ľܶȻܶ 

ѧƽֲֵܾΥҵĵڶκ͵ν 

º͵£漰 

    Ҵӵ p Բ߿ʼٴ 
ЦǶֵ0ôŦ-˹ζţʦѻ 
                 1 
ڷ       ֮ڵһqԲչ 
                0 


    ôԶĻ 

    ڦ = 0 = 0ôѡ         1 
                                                        
                                            1 + v0  v 
    ڦ = 0 + 0 ֮ǰӦһ㡣 
                           1 


     P ڽĲ߽ q ཻǵ 

Բߵ q  p ๲ڱȵ q ԶĦϵĵ㣬ɦõı 

ɵõӦѳһʱߡڱȹ q Զò 

ѵδı߽ϡΪѵδı߽һԪýһδ 

Ķ˵㣨ͼ 19 

    ͼ 19 Բߵ q  p ๲ p  q Բ 

߽ q 뿪 p δı߽硣 

    ʱߵκƣǿҪģκʱ 
ʸ laRablalbǸ˼壬൱̡Ȼھ 

УƽϣȻǺġǿ 

ҴӦѳʱ߿ʼһ q  p  

 




    󣬴һ˵ǿΣÿһ 

ʱԲ߶ĳһ㣬ڸôĳʣͲ 

߹ض÷򡣺֪ܶ׼ȷⲻһ 

Ԥϣʵϵġһġһ 

ÿ߽۽һζ 

ÿ㹻ԶһԹ㡣 




    ͨʱԵʱ޴һȻ 

鷳ڣǿԳȥ㣬µʱ 

塣ԣʱնɶȹʵ⻬θáȻ 

ɴڲܱ쵽ֵķߵʵ֤ 

Եķ 




    巴ӳԵص㣬Ǵʷ޼ 

ھп˻սӡҵʱʱز 

ӡһؽŷʻᷢɢҪ 

ЧӦȥھе⣬һҪ 

ġ 

    ˹ 1965  1970 ļ֤һϵ 

Щǿһ 

ȻԽṹϵĳȫ署Ӧκαպʱ 

ߡ󣬻ĳǾĳһǿ 

ûκζݡ 

    Զ 

    1. 

    2.ȫֽṹ 

    3.ǿԲһ 

    ԲͬķʽһַĿռǱ 

ϵģûпݳȥһַǴνı 

ϲ档һպϵĶά棬ڵĻ䴹ֱ 

Բ߶ģͼ 110ͨ£ɿɷ˹ 

һεĶά棬ڵԲģǷɢ 

ġںǵ̮Уǿʹ׶бζ 

Ҳġ 

    ԶָĲͬϳʱձ 

ջԲ߲ġǿ 

ҽ-˹ʱһ㡣ҪһҲ 

ǿġȫ൱Ӧôڱպϵʱ 

ߡһģһ߱պϵά 

档 

     

    ͼ 1.10 պϣӸ߷ɢ 

ڱպϲϣڻ߶ 


    Ϊ˼ֻһպά S θ֤ 
ǿ԰δϣչ DSɵ p 򣬴 p ÿһ 

ȥָʱ߶ S ཻͼ 1.11ϣչܴ S ϵ 

ԤԵʱڼٶδչǽµġϣչ 
δ߽ HSϣӽ硣һδı 

֤Ե֪ϣӽûйȥ˵Բɵġ 

ȻڼٶϣչǽµģϣӽҲӦǽµġ 

Բ߽һ¼вϻơǽһ޵ 

ߦˣڿϣӽвйȥ߽Ķ˵㣨ͼ 112 

ǲģһ 

    ͼ 111  S δϣչԼδ߽磬ϣӽ HS 

Բߦ 

     

    ͼ 112 ڿϣӽϴһԲߦˣڿϣӽû 

йȥδ˵㡣 

ζһԹ p  qϵ p  q Զ 

     ӡᵼìܣΪϣӽϵκ 

㶼ʱָġԻߦ˲ǲģҲǶ 

֤ S δϣչǽµġ 

     ָںһ£һ S δָʱ 

ߦãԶ뿪 S δϣչ൱Ƶָ֤ 

ÿȥķӳԶ뿪ȥϣչ DSߣͼ 
                                                     - 

113ڿڦȥеһ xnԼе 
һ ynÿһ n xn ynʱ S ȫ˫ 

ϣչ֮ 

      

     ͼ 1.13 δȥϣչǽµģڴ S  

δȥָʱߣԶ뿪δȥϣչ 
Сˣڴ xn ynһ󳤶ȵʱߦnЦn 

Խµ Sζţڿϣչдһʱߦˣ 
ʱߦnļޣͼ 114ҪôǷģ 

֤ˣҪôһй㡣 
ΣֻҪ n 㹻󣬦nͰй㡣͵ìܣΪn 

Ϊм󳤶ȵߡǿԵóۣʱʱԲ 

߲ġ仰˵ԡ 

      

     ͼ 1.14 Ϊ y޵Ĳߦ˱ǷģΪĻ 

Ͱй㡣 

     ЩԤԡһںǺ 

̮δЩԱʱյ㣬ٶŸò 

˶ӶġԤԵһڹȥ 

͵ĿˡȥЩˣҪǶˣ۶˵ȥй 

࣬ԷԵʽͽ׶ΡڵڶԤԵԣ 

ʹЩ˷ǵĹ۵㡣ڼ˶ţԼʱ䱾 

ըһˡֱȷַָȶҪöˣ 

ûҪӮŵ 

     ԵԤζž۲һۡΪ 

ʱиǲǶ峡̣ҲԤϵ 

һðʲôڴڹȥһ㣬Ըһ 

Ψһ취ƺҪ 

     ҽڵνٻص£ǱԤδ 

ƺ˹֮Ϊලʡ˵Ǻ׵һ 

Щںڶж㿪۲ߵĵطЩ㴦ܷ 

κοԤԵʧЧӰ쵽ģٰվ 

˵ġ 

         ල 

                    Ȼ㡣 

     ȻҽһνҪָģдڲԤ 

ԡǺйأزɴġ 

ԼʱһˣҲиսᣬҽݵ⣬Ϊ 

ķʽ 

     һΪƵʵ״ڴ⾭ע 

ġ˹ල²⡣δ֤ģţ 

ʶһĳʼԼ״̬̣ȷġҪʹල 

ʽǰΧ̮ǵΧƳɽƽ̹ġô 
                                                       
˹ָģ԰ѸʱչεǶ뵽һб߽Mȥ 
ͼ 1.15߽M Ϊһ棬Ұ֣ I 

 I-δ͹ȥĻҾ˵ 

ȣٶ z-ԲԪһεĶȹġ 

ζţԶ̮Ĺ۲ܻ㹻ϣ̮Ƿ 

ݻ١Ǽ裬zĹȥȫ˫ġûдӴ 

ܿԡ˹ĸǿලмʱȫ˫ 

ģʽҵĿѾ㹻 

      

     ͼ 115 ̮ǱεǶ뵽һб߽С 

         ල 

                      1.I I-ġ 

                      2.I-Iȫ˫ġ 

     ලĻԤԵ̮зԾʹ 

Iζʱбһ IĹȥСΪ 

κζܴݵȥΪڶڶ 

ı߽类Ϊ¼ӽ硣ΪҲ IĹȥı߽磬¼ӽ 

Բ߶ɣ߶οйȥ˵㣬ǲκδ˵㡣 

ĻӽԪͲΪ 

Ļǽ޵ľཻ 

     ζ¼ӽĽԶʱСһؽ 

󡣴⣬ڶײҺϲһպڶԭ 

ڶ͸ͼ 1.16 

     ͼ 116 ǰڶڶϲʱ¼ӽ 

С 

ѧڶɵصΪǳơСϵͳرɲ 

ֵصܺ͸ 

        ڶѧڶ 

                    A0 

        ѧڶ 

                    S0 


    ڶѧһ 

      E =   k   A + J + Q 
            8 

    ѧһ 

              ETSPV 

    νĺڶѧһɺѧԡöɰѺڶ 

¼ӽĸı䣬Ƕ͵ɵĸı䣬ĸıϵ 

ǰЩѧһȽϣѧһɰϵͳصĸı 

Ĺܵĸı䡣ǿ¼ӽ 

أ¶ȵǺڶνı k¼ˮ 

ƽǿȵĲȡνĺڶѧ㶨ɣѧԸ 

ԣһʱ޹صĺڶ¼ˮƽıȡ 

    ڶѧ㶨 

    һʱ޹صĺڶӽϵ k ȡ 

    ѧ㶨 

    һƽϵͳ T ȡ 

     1972 ؿ˹̹ܵЩԵĹ¼ӽĳ 

ʵǺڶءƹĵڶɣڶغص 

ԶС 

       ƹĵڶ 

       ģScA0 

    Ȼ鲻Эġڶӽȵأ 

ҲӦȵķ¶ȡһڶ;бȺ 

µȷӴͼ 1.17Ϊݾκζ 

ӳڶԺڶһЩܷκζ 

ǾͷӵµȷµĺڶΪȷʧ 

ڶӸԾΥƹĵڶɡȻǽ 

´νпģǷֺڶȫԵķʱЭ 

ͱָˡʵ̫Ưˣһżϣ߽ 

һֽơڶĵȷȷءҼָģ 

ڶķƽءζһָˮƽĲ 

ԤԣԽͨ 

    ͼ 1.17 ڶںȷӴʱһЩ䣬ھˮƽ 

ܷκζ 

صĲȷ֮ϡ˹̹ϵ۲ӡʱ 

ˡԺڶ˼ʾϵ۲ӣʱ 

ǿĵطȥʹԻѣͼ 1.18 

     

                              ͼ 118 

                      ڶ¡ʱԽṹ 

                              R˹ 


    ʷٷҡڵһνԶЩҪ 

ǣںģȫֵģ£ԤϵԵĳ֡ǲû 

и֪йԵκԼںδ֡һ棬Щ 

ǳһģԣȻʣʱԵļΡͨٶ 

ԵʷɢȻⲢԶ׼ȷظ֪ 

ġ 

    ԷڴըڶʹѹɱΪڶĺϲ 

ҲԳ֡صνලҲǼٶ 

ЩԲᷢ 

    Ϊ˽ල˼룬ǻعһѧƵʷ˹ 

̹һڶĽĵһǰ±Ĭ˹ 

1939̮ơһԣ¼ӽΧ 

Դ翴ӽһڲ¼ܰźŷ 

Զı档̲סţͼһģҲ˵ 

һ̮Ȼ¡˹ģ;ĶԳƣҲԳƣ 

Ƿдδ 

    ڰ˹̹һؽѽ⣬ǾתѰȫʣ 

ԵĴڡ磬¡˹ģ;һ棬һ 

棬Ĺ߼Сͼ 2.1 

     

    ͼ 2.1 ±Ĭ˹̮ƣԽͲ档 

    ҲͼָĴζŴԣһں 

Լ裬ڲٶԳܹĵһԶ 

˹ 1965ڼٶһ׶ʱҲܵƵĽ 

˹ 1970һͬйںĳһʱ̿ʼ 

໥ʱͷ 

    ʷٷҡ1965۲쵽ѧĳ߶ϣ԰ 

ԭȵ֤ߵһ£ҲǰӦõʱ䷴ݵΡôһ 

ĲζŹȥԣʵԼ£˴ʱ 

䷴ݣĲǳ󣬾ѧĳ߶ȡ 

    Ҫһڶεķ֪ĳ 

ԣΪ˵õڶָһ¼ӽơල 

²ԵˣӸ˵ǲܴ濴Ա 

ǣĳһ򣬲ܴǶźŷ䵽Զ 

ı߽¼ӽ硣ǻʷٷϴνеһ 

߽ϣ¼ӽδĹȥı߽磬 

֪߽ 

  ⻬֮Ա棬Բɣ 

  д⻬ÿһûδ˵Բߣ 

Լ 

  ռԶʱС 

    ʵϣǻ֤ˣ˹׶ 1967 1971ޱѷ 1975 

 1972ʱյδǿ˶ʱաΪ˶ȹǰ 

˹̹շ̵ķǳ׼ȷ⣬һǳעĿĽ 

֤ͺڶصأҽ´νݣ£ص 

 

    Ӧģǵȷ˺Ͱ¡˹ģڶƵĳֶ 

һЩҲ˵սڿ˶ʷ⣬Щ 

ԴҪġҪͼ൱Ƶġ 

    Ȼ侫ȷ֤ǻල֮ϡʵϣල 

ǳҪģΪ۶ҪĻǻ 

ĶһڶǽҪѰ׵ǣǷȷ 

ҺܾǰһΪҲǴģǧټƵ跨 

ȥѰҷʷٷҡһලһǿ֤ 

ʵʵŬ޷֤ǴġΪ 

һǳ΢֤ 

    йʱյĳֹĿලЩ 

أ1971޺Ĭ˹1972ģ 

˼Ҫʵʵġ㡱ԼԶĵ㡱Ҳ 

ϲʱȥȽ IP ҲǲɷֽĹȥĸ 

ġȥǰȥһϣɷֽ⡱ 

Ĺȥϡһ֪ǣǻ԰ 

κ IP ĳһʱߵĹȥͼ 2.2 

     

    ͼ 2.2 ȥPIP Լ TIP 

    IP 룬Ҳ PIP  TIPһ PIP һ IPҲ 

һʱյĹȥһ TIP һն˵ IPʱеһʵ 

ʵĹȥTIP δ㡣⣬ǿԸǷ 

һޱȵɸ IP ʱ 

ߣǷΪԣÿʱ߶޵ı 

ȣ֣ǰ߳ΪޡTIP߳Ϊ TIPԣ 

ЩƵʺδǹȥ£ 

Ǿ˻ΪPIF  TIF  IFɷֽδTIF ֿٷΪ 

ޡTIF  TIF ֡һ£Ϊʹһеͨ 

ٶʵϲڱպʱߡʵ΢û 

ͬδͬĹȥ 

    Ժලأȣ 

費ӦųըĻѧҾ鷳֮У 

ǴӴըܳȥҲԶ 

һʱ߼ܽܳĳֶôըԶ 

ӦԵġǰһ TIP Ϊ 

һ PIP е TIPⱾһֲĶ壬Ҳ˵ǲ 

Ҫ۲ܵȥ֣˹ 1979ڶ壨ų 

ġTIFáδȡȥõʱų TIP 

ͬ TIPͬģTIFһʱвļ 

豻Ϊǿල衣ֱǣһԵ㣨㣩 

 TIP ʱյм䡰֡ʹĳһ޵ 

㣬 PIP ĶϱڸʱҲ 

֪ǷԹ۲߲Ҫġ⣬ 

ǿල豻Υˣǿ޵ʱ䣬۲쵽һ 

뵽һȥ㴦ɲЧߵҲһ 

⣩ǿͬල裺ֻҪá 

TIP ȡPIP ɡ 

    ǿලζţһһʱֻҪзӺ̬ 

գʣܱصԣԵ TIP 

ʱա֣˹ 1979ų TIP ȼȫ˫ԣ˵ʱ 

Ϊĳһϣ򣨸 1970ע⵽ǿල 

ıԵʱԳƵģǽ IP  IF ĻͿԽδ 

͹ȥ 

    һ˵Ҫӵȥųʾһ 

ԣдݻʱգ˹ 1978ͼ 7 

ҲΥලڸǿල汾Զ 

Σ˹ 1978 CC4 

    ǻصලǷȷҪᵽ 

вǣĺڶһ龰սᣬ 

ʱලƺȷʷٷҡԺͣ 

    ھУвͬĽдͼΪ֤ 

αලƵĳЩලȷĻĲʽ 

˹ 1973ʵϣ֤ȷģ˹ 1972Щ 

֧ලĳֶӦó˼룬෴ķ棬һ 

ЩȻΥһԼĳЩԵַܵ 

֤ݡ⣬һЩҸոյָ֪泣 

ģǰᵽĲʽеһЩͲʵϣǸ𡤻 

άҵġǣҲԵʺдڴ 

Ĺϵ泣ģյģΪԵġ 

Ӧأ泣ģʱʱģζģҲ 

Υල泣Ϊ㣬ҲԲԵ 

Ҳල 

    ΪԵʱʣҽ IP ֮Թϵ 



 B A  B ûһһߣ˵ A  B 

ģͼ 2.3 

     

    ͼ 2.3IP ֮ԹϵiA Ե BiiA ʱ 

 BiiiA  B  

    ǿල֮ɣһԶʱġգ 

ԣԿйȥδ͡ˣǿලĻ 

ԿɷΪ壺 

    PɡTIF Ĺȥͣ 

    F TIP δ͡ 

    ֿܰͳһһ֣һͬʱ 

TIP  TIFˣ໥ලۡ壨Fĵ 

ǺڶԼѹڵĻеԣըԼ 

İ׶ǴڵĻ壨PӡʵϲŴѹ 

ᷢڹԭҽһνʱ̸˵㣩׶ 

ˣΪΥѧڶɡ 

    ͵ҲȫͬĶɡǵ 

ɵȷӦȫͬġ 

    һϣʷٷҡҳֲͬۻǣݣ 

ҰΪ֤ݣ 

    1ѧڶɡ 

    2Ĺ۲⣨汳̽ߣȥ 

    ǳȵġ 

    3ڶĴڣʵϱ۲⵽ 

    ӵڣ1͵ڣ2۶ϵըǼ˾Ҵӣ1 

ɵóԱܰ׶Ľۣڰ׶صΥѧڶɣ 

ڶԱӷǳͬĶɣ3Ϊ˸ȷֲ 

һʱ Rabcd дκдϫ 

Σڵһ׵ľ±䣩͵Ч Rab϶ 

gcdʵذָһ£ǲ֮ͣСı 

ͼ 2.4 

     

    ͼ 2.4 ʱʵļЧӦiκʵĳϫα䣻ii 

ʵСЧӦ 

    ׼ģͣ鹦ڸأ޲ѷ߶ˣ 

ֵ 1977еĴըκһ⣬ 

R.P.A.C.Ŧ֤ģ˵һйιҲκ 

ΪĳʼԣҺʵ̬̳Ǹ棻 

Ŧ 1993һ棬ڣ׶ԣһ£зɢ 

κͰʾµģ 

    κʼ 

  ʼͣPԵκΪ㡣 

  սͣFԲơ 

    ʮһ¡Ǳպϵģսԣ 

ѹзɢκһ 

    ĺڶҲзɢκͼ 2.5 

     

    ͼ 2.5 κ裺ʼԣըκʱΪ㣬 

սԵκʻᷢɢ 

    ʵǶĽһ֧֣൱⻬Լûа 
ʹռټС1010123ǰհؿ 


˹˹̹ϼڶعʽ1080ӵĺڶƵռ 

ؿ˹̹ 1972 1975ʡ 

    ͱһɣǿһܵĽκ 

ʼṩֶɡ 

    ʴ 

    ʣΪų 

    Ҳ̫šĻը֮ǰ̮ 

ĽǾҪʣǰԾ˵͵ءͼ 

ǽ͵ڶɵûᡣң̮Աĳ 

ʽӵһ𣬵ƺзǳͬļΡһ 

ӦȡԴʱյĿǰһķ̸ 

ھгԵĶӦΪһԵʱգ 

ǼΪͬĳֶ 

                        ¡Ӻڶ 

                              SW 


    ׼ҵڶν̸ۺڶۡƺѧе 

һµˮƽϵĲԤԣֲԤԳԽںѧ 

صͨĲȷ֮ϡΪֺڶأ 

ϢǵʧӦ˵ЩǸģ 

оߣдתеˣܵؾܾ˼ 

룬йһϵͳ̬ϢɥʧȻʾϢ 

ܴӺڶȡͽ޹ţǽȽҵĽ飬 

Ϣɥʧˣǹȥͬڶһǵ 

ִ 

    ұйغڶľۡǴϴνݵ֪ 

ġ綯ѧʱ 
ʱų⣬ǾԶ쵽ΪԼȵ΢ 1040 

ͬţʹǺ͵е 

֮õܸоõ 

    ʵζţҪеʸϵһγ 

Ǻϵ塣һʱڣǿѹϵ 

תԼڲ˶֧ԼһȻȺͽǶջ 

ߣͿʼ̫һһСӻ 

ӵļѹֹͻֱ԰װǻ 

ΪޡȻ޻ûκΰ취֧ 

ֹһСĳһٽĳ߶ȣϵ 

ôǿ׶ۣͼ 3.1 ʾġΪ㻭 

һάͼȻѵʹŴѧֻṩάĻ 

ˣҰʱڴֱ򣬲͸ӷάռеά 

ԿĹҲ໥ڵˣ 

ĶǷɢˡһպϵĲ棬ǻ˹ 

ĵеһΡ 

    Ҫලȷģ򲶻ԤԵԲԶ 

ʱоһ򣬲ܴǶݵ 

Զȥϴνе֪ģ¼ӽĽԶС 

ھӦˡЩԼ̮΢ż㰵ʾ 

һȺ̬Ϊޡ˹׶ءޱѷԼԼͬ 

Ŭ֤ëָûʳʱ˶ǽеȺڶ 

 M ͽǶ Jޱѷëƹ㵽 

ųڵΡͼ˵ QҲǵɣ3.A 

׶˹ëδ֤ǽеƺҪ 

Ϊȶķָһ֤ʱ޹صİ 

˹̹׶˹ڶиɶȡ 

     

    ͼ 3.1 һ̮γɺڶʱͼͼϱ¼ӽͱպϲ 

档 

    ëָһ̮γɺڶʱϢɥʧˡ̮ 

ҪôʵԼֲĶ༫ء 

γɵĺڶȫ޹أҳȵ⣬ 

ж༫ѸɥʧرǣͶأҲǽǶ 

    ë̬ڶ MǶ JԼ Q  

    Ϣɥʧھûʲôϵǿ˵й̮ 

ȫϢȻںڶ֮СһλںڶĹ۲ȥȷǰ̮ 

ʲôǷǳѵġȻھԭȻǿ 

ġ۲ʵϽԶü̮塣ԵԽԽٻ 

¼ӽʱ÷ǳǹ۲ȻܿʲôɵԼ 

ηֲȻ۰һжıˡȣ̮ 

Խ¼ӽ֮ǰֻĿĹӡҪѹ̮Ϣ 

ЯϣʮֲġζţУ۲߸ 

̮״̬ҲΪ޹ؽҪΪܴ 

ϢȻںڶ֮Сڴ˴۶Ժڶ 

ڶЧӦˡҪָģʹڶ䲢ɥʧ 

ջȫʧһʧĻǵеϢҽ 

Ҫ۶ϣϢȷɥʧˣҲĳַʽõָ 

ҪָģϢɥʧѧˮƽĲȷԣֲȷ 

ǳԽںصͨĲȷ֮ϡϧǣͺɭ 

ȷԭֶͬˮƽĲȷںڶºѱʵ 

֤ʵҽڵνݣ£۶ϵģĳϣ 

Ѿڲ΢й۲쵽ЧӦ 

    ̮γɵĺڶıӳоʱ״η 

ڶʵͨ˹ͼĹڿ 

ġȻΪ˹˻ͬ⣬ǸӦóͼΪ 

ϵͳʹǡ̮УʱպͽǶȦȺͦ޹ء 

ļζ tr ƽϷΪκζά涼ƽռ๲Σ 

ǿһͼԽṹͼ rt ƽеǺʹֱ 

ɡ45ĽǶȡ 

    Ǵƽ̹ɿɷ˹ռ俪ʼ俨ء˹ͼһһ 

ϵΣͼ 3.2ұߵб߶Ӧڵһν 

ᵽĹȥδǴԶǵӽ 

ȥδʱо붼ɹСеÿһ 

㶼Ӧڰ뾶ΪrĶάߵĴֱ r0 Գģͼ 

ұ rޡ 

    ǴͼϿ׿ɿɷ˹ռеÿһ㶼δ 

 IĹȥСںڶ¼ӽ硣ȻԳ 

̮Ļͼ൱һˣͼ 3.3ڹȥͬģ 

εĶȥˣһˮƽı߽ȡǻ 

˹ԤԵԡǿԿˮƽ֮Щ 

㲻Ǵδ IĹȥ仰˵кڶ¼ӽ磬 

ҲǺڶ߽ǴϽбߣͶӦڶԳĵĴֱ 

 

     

    ͼ 32ɿɷ˹ռĿء˹ͼ 

     

    ͼ 33һź̮γɺڶĿء˹ͼ 

    ǿڴ˱пһʱʱ޹صģ 

 I-ֻƵʵĲ̵Ľ⣬ IҲƵʡͱû 

ӲԭûбӵĻ Iе 

ӡ 

    Ȼ̮֮ʶȹʱء͵ I-Ƶʵһ 

⵽ IʱֵرɸƵʵġǿȡһ Iʱ 

 e-iwuĲش I-ְ취ֻϡ 

ôʱǻᷢͨӽӽĲֲˡӡ 

̵ǣǷ֣ڵļޣ̮ϸ޹ءֻ 

ڱ kǺڶӽǿȵĲȡƵʵĻϵ 

Ӳ 

     1973 ״оЧӦʱԤϵ̮ᷢʱһ 

䱩֮Ӳٲµһڵĺڶʹ 

Ϊȵǣҷ̮ʱһη䱩ȻάӲͷ 
                                          k 
Ⱥʡ⣬ַ¶        ׼ȷԵġ 
                                         2 


ʹڶк¼ӽɱصĹЭؽĶ 

ѸñȷΪʿ˵λµķ֮һʿ˵λ Gc 
h1ʿ˵λ 10-66ƽף̫ĺڶ 
Ϊ 1078ءⷴӳ˿úڶļ޴ĿĲͬ 

ʽ 

         ڶȷ 

                       ¶ T =    k 
                                 2 

                        S = A 1 
                               4 


     ״ηֺڶʱ൱ҵļеȫԵķ 

䣬ƺһ׮漣ȻղķضԼ𡤼˹ĺ 

¶ԭΪ˽һ㣬Ҫʷȹ 

     ʷȹ 

     ds2 = (1     2M)dt2  + (1   2M)1dr2   + r2 (2 + sin2d2 
                  r             r 

     ˷תĺڶ޵ͨ r  t ϵУ 

ʷ뾶 r2M һԡȻֻΪѡȡö 

ġǿѡȡʹǶĶȹ 

     俨ء˹ͼͷƽĽʯ״ͼ 3.4 

r2M ָĸұߵͼбΪٵǽ 

ƽ̹Ŀռ䣬Ǿͼٶڴˡƽ 

     δ¼ӽȥ¼ӽ 

     ͼ 34 ʷڶĿء˹ͼ 
     ̹ʱյΣйȥδ I I-߻һ 

ƽֻ̹ۣͨһ涴ǵᡣȻ 

ǽῴģͨʱǵӡ¶˵ 

϶˵ǴǶݵұߵı߽硣 

δ¼ӽ磬δδʹ¶˵϶˵Ĺȥ 

ӽ 

     ǻصԭʼ rtеʷȹȡti 

õȹ棬ҰȹŷϵģҲġ 

ŷʷȹ r2M һԡȻǿԶһ 
                                  1 
µľx = 4M(1 2Mr1)2  

     ŷʷȹ 
           ds2 = x2(d4M)2 + (4M2 )2dx2 + r2(d2 + sin2 d2) 
                      r2 


ǰ 8M ͬ xƽϵĶȹͺͼ 

ԭơƵأŷϺڶȹǵӽҲбԣ 
                              k 
ֻҪʱ          ֱͬܰԣͼ 
                             2 

3.5 

     ʱĳڦͬʲôأΪ˿һ㣬 

 t1ϵĳæ1 t2ϵĳæ2ķȡ e-iHt2-t1 

ԪóȻǻһ·ȣ 
Ƕ t1 t2֮г͵óҪ󦵺ͳ 
1Լ2һ£ͼ 3.6 
    ڿ԰ʱt2-t1ѡȡģȦ 

    ͼ 35ŷʷ⣬Եصͬ 

    ͼ 36ڡʱ̬ʱ̬ķȡ 

    ڦ£ͼ 3.7ǻʹʼս᳡̬ͬ 

걸Ļ͡߾͵õ̬͵ƽֵ¶ȡ 

µѧֺ 
    ڷ̵ұһ·֡ʹ1ͦ2ͬԡ 

    z 

     

    ͼ 37 ʱ䷽ڡŷʱϵг͵· 

֣Եõ¶ T µֺ 
    еĳæn͡ʵڽ·֣Ƕ 

ʱ䷽ԦΪڵͬʱϵг͡¶ T £ 

ֺɶŷʱϵг͵·ָʱ 
ʱ䷽ڦ£T-1 

    Ƕʱ䷽ڦµͬƽ̹ʱϽ·֣ 

õֺͨȻǸտģŷ 
                                     2 
ʷʱ䷽Ҳ                 ڡζʷеĳ 
                                     k 
                           k 
Ϊͬھ              ¶ȵ״̬һ 
                         2 


    ʱԽΪƵʻϵķᵼ׼ȷԵ 

䡣ȻƵ˲ƵʻϷеļƵʵ⡣ 

ڱе໥óΡһԱн· 

ζţƩƽֵȵȣԵġƵʻ 

Ϸɷǳѵصõͬ 

    ǿ԰Щ໥ƹ㵽໥áǿ 
Դŷʷȹıȹ g0ֶȹǾ䳡̵ 
⡣Ȼ I Χ g0΢Ŧg ݴչ 
    IgݣIg0ݣI2g2I3g3 

ڱǳ̵Ľ⣬֡ƽΪ 

еӣԼ֮໥á 

ƽ·޵ġ˫Ȧˮƽɢģ 

ڳͷΪû㹻¸һµ 

й㣬Ի֪ȦȦˮƽǷɢ 

һЩʾҲ߽׶޵ġǣڸ 
߽׷ɢ˵ʿ˳ 10-33׵ĳ߶֮⣬ 

ЧӦ΢ġ 
    ȸ߽ȤҲǱȹ g0 
                     1       1              1 
    I =    1    R( g)2d4x +      k(   h)2 d3x 
         16               8 

۵ͨİ˹̹ϣʱ R ֡ 

սΪ㣬ǻΪŷʷΪ㡣Ȼ 

лһͱ߽ĵڶʽļ K Ļֳ 

ǰһȥȥƽռı߽ͻᷢŷ 
                      2 
ʷȹΪ       ʱڡ 
                      16 
                                        2 
ֺ·ֵҪe16  

                  Z = exp(  En) = exp(16) 
                                              2 


    ȡ lOgZ ڦµ΢֣͵õƽֵ 
                                                 
                        < E >=     d     (logZ) = 
                                 d            8 
                   
͵õ =      ֤ʵڣ¶ȵĹ 
                  8 

ϵѾ֪ġȻǿߵøԶձ׼ѧ 

ֺ֤Ķڸܳ¶ 

                             logZ =      F 
                                          T 
    ¶ȳԵ S 

                               FETS 
    һкϲܿڶ 4M2أ 

    S =  2  = 4M2 = A 
                       1 
        16            4 

պʹڶɺѧͬ 

    ΪʲôܵõأӳҲ 

ĶӦأԭʱξвͬˡǿǵ 
£ŷʷһΪ S2S1ı߽硣S2 
ľ޴նά򣬶 S1Ӧʱ䷽Եصͬͼ 

38ٿڴ˱ֲ߽ͬ˵Ķȹ䡣һ 
Ȼŷʷȹ档 R2S2ˣҲŷ϶άƽ 
άһ R3S1ŷƽռʱ䷽ڵͬˡ 

˾вͬŷܡ 

    ͼ 38ŷʷı߽硣 

    ڵͬƽռŷΪ㣬ŷʷŷΪ 

ڵͬƽռϣǿҵһʱ亯 

ӣݶȴΪ㣬ı߽ϵʱȻ 
1ͦ2֮ף 

һǶϰ˹̹ϣ֣һ 
Ǳʱ޹صģڦӣ1ıͺڦӣ2 

ı߽ǽеĶԱй֮õı 

ʱ˻һ롣Ϊ㣬ڲ 

ķʳ֤ϰ˹̹ϣ 

Ҳó M(2  1)  M2-1ͼ 
                   1 
                   2 
39ֺĹ״ѧʽͻᷢ 

ƽֵΪԤڵġȻصĹ㡣 

     
    ͼ 39ڵͬŷƽռM2-1 

    ȻŷʷͲͬˡΪŷΪ㣬 

ǾҲһݶȴΪʱ亯ӡǳֻѡȡ 

ʷʱꡣӱ֮û 

ʳԼʱΪ㣬Ϊ㡣ļ K ı 

c 

 M(2  1)Ȼӽ紦һӽc1 
   1 
   2 
ͦ2һ֮ǿԶԴ˱ֵֵ 
1M(2 
2         1)ͼ3.10)ڦ2ͦ1֮Ϊ 


M2-12-1£ͻᷢ 

Ϊ㡣ȻǴά 31 άĹ۵㿴ŷʷ 

ڶȹӽ紦ǹģûɰѸôı 

ȥųӽ紦ı൱Сӽķ֮һ 

պǺڶء 
乱׵M2-1 

    ų乱׵ = M(2  1) 
                                1 
                                2 
    ͼ 310 ûа r2M 䴦Ĺװŷʷ 

    Ϊ M(2  1) 
                   1 
                   2 
    ڶغ˲༴ŷһʵһ׮ǳǿ 

۶ϣǱۣ۶ȻЧڴ 

ѧҶԣһΪһ䣬һ˱ߣ 

ҪһжŪ-׶˹ۡ޳ɣڶʿ˳ȸ 

ڶķƺԵģγɵġ 

ҲƣźڶʧСʿ˳߶ȣӹ۾ 

ʧЧһжΪСȻҽһڶʵ飬Ϣ 

ڶпɥʧˣӽʱάźСʡ 

    һǿ糡ܲɵӶԣ֪ʵ 

ʱˡһֿİ취ע⵽һе q  

ӵƽ̹ľоȵ糡 E ŷϿռе˶һԲ 

ܡǿ԰˶ʱʵʱ t ͻõ 

һԴӣڵ糡໥ֿٷ루ͼ 311 

    ͼ 311 ŷϿռһڵ糡Բ˶Ͽռ 

УǵõһԴŵɵӣ໥ٷ롣 

    ԲĹ̿ɰͼ t0 ӣ0 жȻ 

ϿռͼһŷϿռͼһͼ 312ͼ 

пԿʹʵ 

     

ͼ 312 ðŷͼͰͼԲ 

ͬһӡһɿɷ˹߹ɵһͨŷÿռ 
͸ġԲʵĵһ׽ e-I˴ 

    ŷI =   2m2 
                          
                     qE 

Ѿʵй۲쵽ǿ糡ԲʺЩһ¡ 

    ںڶҲܴɣԤϣҲԳɶԵزȻ 
Ϊڶʺɱȴ 1020Բʺ͵һӶȾԵ 

ǳ΢СڲڶԵĸʴﵽɹ۵ֵ֮ǰһ 

ӶԲѰκε糡кˡȻһЩдźɵĺڶ⡣ 

ΪڴźɵĻӣڶ̮ 

ǿԤϣǿһǿųгɶԵزˣųǿ 

ʹźɵĺڶԲĸ൱ɹۡ 

    1976 ˹ҵһڴųеźɵ໥ 

ĺڶĽ⣨ͼ 3.13ڶŷϿռһԲ˶ 

ͬƽ̹ŷϿռһԲ˶һͼ 3.14Ϊ 

ʱ䲻ΧƺڶӽΧƺڶ˶ԲܵĶ 

Եģ˸ԡǱڶʺɱʹͬ 

ѧϣӦѡȡڶĲʹúڶ¶Ⱥ 

ٶֵ¶ȡŴźʿ˵λµڶ 

¶ȡ 

    ͼ 313 ڴųУһԴ෴źɵĺڶ໥ٷ롣 

    ͼ 314 ŷϿռһɵĺڶԲ˶ 

㡣ųУڵͼʱܿʹ 

ϡ 

    ڵӶԲΣǿŷϽʱ°벿 

Ͻʵʱϰ벿ڶԵĲͼ 3.15 

Ϊڶŷ͸ΪһԴŴźɵĺڶ֣ 

Ǳųٶ໥롣ڼٺڶھȵĴų 

Բǽƽ̹ġȻڴųľֲڶ 

ԵĲʡ 

    ͼ 315 ðŷͼͰͼһԺڶ 

͸Ĳ 

    ǿ󣬺ڶڴ֮໥Զ벢޴ųȻ 

԰ÿڶڽƽ̹ռ֮жֱǿ԰ 

ʺϢÿڶЩڶ䲢ɥʧȻ 

ڴźɵӣǲʧȥźɡվͻص 

ԭȵ״̬ȴźԴһЩѡȻǿ԰ڶŪ 

һʹ֮໥̿ΪǶԲʱ䷴ݡ 

ŷϽϰ벿Ͻ°벿ڶԲͶ֮ 

һκܳϽ׶Уڶ໥뿪ʣȻٷصһ 
顣ŷ϶˹ؽˡ S2S2ȥһ㣨ͼ 

3.16 

     

    ͼ 316 ڶЧӦЧӦ 

    ҲᵣǣںڶʱӽʧӶƹ 

ѧڶɻᱻΥȻǷڶ˹ؽеļӽ 

ûжԲʱеС¼ӽ 

޴һ൱΢ļ㡣ˣ൱ȷ 

˵޵ģҵںڶӽжԲԼû 

жԲĽ֮ô⣬Բܹ̣ 

ԲĹͲжԲĹͬҷǳлɡ˹ 

𡤻άΪνݼʱؼһСһ׮漣 

ָǵõĹ̡ʹŷڶѧ 

µĽơţʹǱĸۣ 

Ҳʧ 

    Ǵһʵ鿴ʱյ˺ƽ̹ɿɷ˹ռĲ 

ͬʱͻõԼϢɥʧԲĺڶʿ˳ 

ȴӽÿһʶʿ˳߶СҺ׻ 

߽׵΢ĽӦǿɿġںڶϢɥʧ 

Ӧǿŵġ 

    ںۺڶϢɥʧôҲӦȹֵ΢ 

۵ڶɥʧǿӺϢЩڶɥʧ 

Ҳǰ֮ڡ͵ĺ͹淶ϵ 

غģϢԼȫֵĺɻᱻɥʧ۶Ծ 

Զĺ塣 

    ͨٶһڴ̬ϵͳһôķʽͨ 

һϵд̬ݻǣͨڶĳֺʧϢ 

ɥʧ򲻴ôݻ෴أϢɥʧζţںڶʧ֮ 

̬ͱνĻ̬ɱΪǲ̬ͬһϵ 

ۣÿһ̬ԼĸʡǣΪκһ״̬ȷ 

úκ̬İ취̬ĸʼС㡣 

һˮƽĲȷԣֲȷԳԽͨ 

صĲȷ֮ϡҽһνݣ£ָǻ 

Ѿ۲⵽ֶĲȷԡʾѧ۵սᣬǲ 

ȷԤδϵһЩ޷׽Ĺơ 

     

    ͼ 317 

                        ¡ۺʱ 

                               R˹ 


    ۣQTۣSRۣGRԼӳ 

ۣQFT 20 ͵ΰۡЩ۲໥ģ 

ǻ۵ĻϽģӳۺ 

۽϶ɣͼ 41 

     

    ͼ 4120 ͵ΰۡԼǵĻ⡣ 
    ˵ӳȷۣԼ׼ȷ 10-11 

ȻԸָһȷϣڹ۱ 
׼ȷԵ 10-14Ȼǽڵϵʱӵľ 

ȣָɪ-̩˫ PSR191316һ໥ת 

ǣ֮һΪǡԤԣΪɥ 

ʧỺС̣ȷ۲⵽ 

һţٹм䷶Χǹ 

һ˹٣һкϲ͹Ұţ 

۹鲢ȥ 20 Ļ۵ʱﵽᵽ 

ӡ̵ľȷȡΪϵͳȻصõ 

ŵƣ۵׼ȷԣӦǸ 

ʺǵĿܣȴΪӳӦø 

Ŷԡ 

    Ȼ۶Ǽɹģǲû⡣ӳ۵ 

ǣֻҪһͨķͼ𰸱Ϊ޴Щ 

۵轫۳СԤʱ 

Ĵڡνġ⡱ҽҪ֮ǿ 

ΪЩ۵ĸĽһʵǸԶ 

걸ġ磬ԤӳҲĳַʽĨƽ 

۵ԡӳеķɢԲֵɹ۵ж 

Ƶģŵۺʵؽϳĳ 

֮ʱܽ⡣ 

    ̸̸ڶеϢɥʧҶǸйϵ 

ҼȫͬʷٷйЩ˵һСʷٷҰڶ 

ϢɥʧѧеĶⲻȷԣԽѧĲȷ֮ 

ϣȴһ֡ġȷԡҽһҵ뷨 

һкڶʱУʱտͼĹ죬ǿԿϢɥ 

ʧԷͼ 4.2 

     

     ͼ 42 ڶ̮Ŀͼ 
     Ϣڹȥ I-ϸϢδ 
 Iϸǻ˵Ϣڶӽʱɥʧˣ 

ԸΪʱɥʧڿһ̮ɺڶ֮ڶ 

ǿ϶Ҫ㹻ĲܵȴķҲ 

ҪͬʷٷҵĹ۵㣬һ̮ͼ 

ϢɥʧˡǻܻʱյĿͼͼ 4.3 

     ڶеյĲо޴κʣǰ潲ݵ 

ۣڶ£ںڶʱ̣ԲһӳһϢ 

ܵģԴδ۲ߵĹȥκʺ 

СΪ㣩ֻȡ΢СϢ̮ɥʧС̫ˣ 

ǿǺڶʧκκͼһʵ 

飬ϵͳһ֮УǿԿǺ֮ʵ 

ռݻռжӦڴһڶεݻġ 

     ͼ 43 ڶĿͼ 

ЩϢɥʧڶ 

ȥˡͨѧгΪάֱӳͻ 

˵ռֳһ䶨ϸؽǱ 

뿼ϣؿռеݻôάΥͶӦڷ 

ôݻڶʱΥغ㡣ȻҵͼУ 

ռɥʧɡԷӲƽ⣬ڲеõϢ 

ռΪΣҰɺڶϢɥʧĲȷ 

ΪеĲȷԵġһ棨 

ͼ 4.4 

     ǿԽȥЯϢδЯϢ 

ѧڶɵĸЩеķǶԳҲͲеķǶ 

һתеĲ 

     ˫۵ԭһ䵽 

 A  B һ͸ϡںĻϣģ 

ʽĹӻᵽĻķϣ 

      

     ͼ 44 ڶʱռɥʧɲ̮ R  

ռ»öõƽ⡣ 

ڸ棬ӴﲻĻϵһЩ㡣 P Ϊһ㡪 

ˣֻҪеһ϶סӾܵôͬĿʱ 

໥ʵѧԻǰ 

ѧĵԭԭ˵· A  B ǹ 

ͨģӦĹ̬ʾΪAͣBǼٶЩ 

ǹӵ P Ҫģͨһͨһ죬 

ô zAwBҲǿ̬ܵ˴ w  z Ǹ 

     w  z ǸκηʽΪǸʶǲʵġ 

ָ̬ӡϵͳôݻҽΪ Uά 
ӣ zA0wB0ʱ t һӣôʱ t ֮ 
 zA1wB1˴ At Btֱʱ t ̬ݻϵͳ 

вӵĲͬѡ񱻷Ŵ󣬸ֵ﷢˲ 

ͬ͵ġݻʸļ򡰲̮ҽΪ 

RֻеϵͳʱʲŽɫ¼Ի 
Ȼǣz2w2 

    U  R ǷǳͬḶ́U ǾԵģԵģÿռУ 

ԼʱԳƵġR ǷǾԵģ϶ǷԵģǶģ 

ԼʱǶԳƵġѧеݻ֮ĲǷǳ 

ģܰ R  U һֽƣȻǾͼô 

ǡ⡱ 

    رǣR ΪʱǶԳƵġٶԴ L һ䵽һ 

ľϣӺ´ 45ǣھӺһ Dͼ 

4.5 

     

    ͼ 45 򵥵ʵԴ R еӸʲʱ 

䷴ݷ 

    Ϊֻǰģ͸ͷ̬ĵȨȡ͵ 

κεһĸʼʵҵذա 50 

Ĵ𰸣 L ӣD յĸǶ٣ 

 R Ĵ𰸡Ȼǻ⣺ 

D յӣôǴ L ĸǶ٣ҲΪ 

ǿúǰͬķóʡU ʱԳƵģô R Ҳ 

ʵϣĴ൱ͬĿȷҲ 

ѧڶɡ˴ӦõǽϣǶԳԹΪ 

ʱϷǶԳġŵ򡢰ظвά棨1964 

ָΰѲʱԳƵĿȥֹ滮R  

ʱǶԳɽ͹ȥķǶԳƱ߽ġҲǸ׷˹ 

1984˹1992ԼǶ͹ض1990õһ 

ܡڵڶɵԴɻݵʱԽṹķǶԳԣֹϵ 

ʾѧĲ͹еصġعһ 

һνģʼԾзǳ΢СϢԼֵκ 

սԣЯдϢԼɢκ 

Ե£ 

     Ϊʹҿѧ͹۹ϵ֮ʱȷ 

һ˵ʵʲô̬ʸǡʵġ 

ܶȾǡʵġܶȾǶ̬Ĳʶ˰ 

ʡԼӸʡǿ԰ܶȾд 
          N 
     D = i >< i| 
         pi| 
         i=1 
     ˴ PiǸʣʵӡPi1ÿһi˹ 
һ̬ļȨʻϡiûҪģ N Աϣ 

ؿռάΪһӣһ˹̹һ 

˹-ѷ͵ʵ飬һΪӣʵģ˥ 

Ϊ֮һӡ෴벢ڡ˴ 

͡˴⵽˴Զ롰˴Ʃ署ϡ 

ǰ̬ʸдһʵĵ 
      = ϴˡ±ˡ  ´ˡϱˡ/4.1˴ / 2 


41˴ϴˡǴ˴һϵ̬ȵȡڼٶ 

ϽˡZ ǲ֪ô̬ 

˴ܶȾ 

      = ϴˡϴˣ + ´ˡ´ˣ4.2 
         1                   1 
         2                   2 
һֿǣҲ x ̬ʸ4.1 

д 
      = ˡұˡ  Ҵˡˡ 2ǵõ 


ʵܶȾΪ 

      = ˡˣ + ҴˡҴˣ 
         1                   1 
         2                   2 
ʵϺͣ4.2ȡȻ̬ʸʵڣôܶȾ 

ûʲôֻڼٶ㲻֪˴ʲô¸ 

˴Ľرǣҿյһ֪ͨй 

ǶʺͽšңԭϣܵõϢ 

ұһ̬ʸģϵͳ 

     һ㽲ڸܶȾ󣬴ڴİд̬ 

     ʵӵĲͬʽң˹٣Լɯ˹1993 

һַʽܶȾͬ˹̹ 

˹ѷϵͳġ˴֣Ϊ̬ϵκνͣ 

ڡ˴ܴһպø衰˴ܶ 

ļʻϽ͡ 

     һ棬Ҳ۶ϵܶȾʵڣҵ 

    ⣬ڶʱʷٷҵĹ۵ӽ 

    Լʱ̬ʸļ̵ı׼ FAPPǡΪ 

ʵĿġд׼裬ǿ԰̬ʸд 

    ܡwϴˡz´ˡ䡵 

    ˴дǲϢɥʧ 

ôֻܶȾ 
    Dw2ϴˡϴˣz2´ˡ´ˣ 

    ֻҪܴӻָϢǡҲԡFAPPΪ̬Ƿֱ 
иʣw2ͣz2ģϴˡ´ˡ 

    ȻܶȾûиЩ̬ɵģǻҪ 

ļ衣Ϊ˽һ㣬ǿѦèʵ顣д 

ںеè״̬һӱһľӣ 

ӲĴ͸һ⵽ӣԶ 

ǹèǹСûм⵽ӣèȻ֪ʷٷ 

׼Űèʵ֮УϵͳĲֲ 

ͬԵĵ 

    wèǹZèǹ 

˴ǹͣǹǱ״̬ 

    ѧĶ۵Ӧǣܻ 

    Wè֪èzè֪è4.3 

    ˴֪̬ʵߵͷ״̬ǣΪʲô 

ȥ֪ĺ۵ӣǺ۵Ŀԡè 
    èأ磬ڦ =  =1/ 2Σ̬ܰ 

    4.3дɵ 

    èè 

             ֪è֪è 

    è-è 
              ֪è  ֪è2 2 
ɰ磨֪è + ֪è 2  
    ġ֪̬ų⣬ǶĽûκνչͬ 
Ҳڻң磬w = z = 1 2£ܰ 
ܶȾдɵ 

    D = è + èè + è 
         1 
         4 
    + è  èè  è 
      1 
      4 
    ʹǵ֪۵㲢ûнΪèǻ 

    ڴҲһʶ⡣ҵ 

Ϊ۱漰ʱͬʱռεĵ 

ӳĳëҲͬεĵǲȶģ˥䵽 

еһ磬ּҲǻèèʱաҰһ 

һֿܵ˥Ϊ͹ۼϲΪһ 
дORʿ˳10-33׺кιϵأȻ 

Բͬоʿ˳߶йأͶ˼ܷͬ 

ʱ߶ȡ 

    ǿèúϢһ¡ٻصӵ 

ż⵽ӣʹһһ˶һͼ 4.6 

    ǰϸĵµıԵֻҪһӱܰ 

ȥǾͲصǼϵ̬⣡ƶ 

ʹֿԵĵӲȶأģṩ𰸣 

˹ 19931994ɲĵҰ 1989ϡ 

1990ṩķΪ˼˥ʱ䣬ǰһ״ 

һ״غ·ֿ˷һ״ֱ 

ڸĵΪֹķѵ Eӵ̬ʸ̮ 

ʱ߶Ⱦ 

     h   4.4 
        E 
    һӣʱ߶Ƚ 108꣬ڴڵʵпi 

 

    ii 

    ͼ 46 ޵èi˵İ汾ii 
ȶԡȻڳ߶Ϊ 10-5׵ˮΣ̮ҪԼ 2 С 
ʱˮ 10-4ף̮ҪԼʮ֮һ룬 10-3ף̮ 
ֻҪ 10-6ҡУǵһźͻ뿪Σ 

ڻе˶ٽ˥䡣һ۲ķ 

غͶԵ⡣ڹдڵĲ 

ȷԣǵǵЩԵ̬ι֮ʱе 

ǶģܷǶأԵأף 

ɴϵͳЯߣԵģǶһ£ƽ̹ 

ʱܶйסλĵ̬еȷԣ 

˴ǵģںɭȷԣ˥ʱ䣨4.4Э 

    ʴ 

    ʣᵽһЩ⡣Դк 

 

    ϶ġѧƵʷľ߷ζţٴ 

ѧ໥õԭʼ䷶ڷ 

ʵϺ໥ڱв졣ǽеӰ 

Ե໥ãǵڶϢɥʧԶĺ塣 

                        ¡ѧ 

                            S.W. 


    ҽڵνתѧѧڹȥΪαѧ 

һЩѧҵıأЩҲһЩõĹ 

״̬Ϣԭֿһǹȥ 

ûκοɿĹ۲⡣ȷֱ 20 ңеҪ 

ѧ۲ҹǺڵġǲûᵽ塣Ȼ 

۲ķΧżķչõ޴ĸơ˵ 

ѧûй۲Ϊѧ˵Ͳվסˡ 

    ȻڵڶֶҸصķԡѧǶԳʼ 

һЩ裬治κԤԡûּ裬˵ǣ 

֮ΪڸȽ׶ӡ 

ţѧֻӦԼʱݻĶĶɡǻã 

ȷʼ߽ζѧڽ̵⣬ǿѧ 

⡣ 

    ޽֤ܺĶ񻯡Щָݹ 

ۣǵĹȥӦԡԴ޷塣 

۵ʧЧԤԤ档 

    Ȼ˻ӭۣҶ֮ȴȲɿ 

ĿʧЧΪβκεطʧЧһԭ 

ֻҪǱԽﶼǻᷢġһ· 

ʷ룬ǾͻʱطԤԱʧ 

ԴѧʧЧôκεطʧЧ 

    ѧ۵Ψһ·ǣɱ봦ĿҲ 

⡣ǿɰЩΪԭʤΪĿ˿ 

ʺĶɵԼе㶼ƽȵģ;һЩ 

ƽЩ 

    ΪʵʩκεطЧĹӦ·ֻ 

ԷԶȹͨ͡·µ֪ȸڲ΢ 

·ĳЩʵУЩ·ǹ⻬·걸 

жõƵģǻԤϵ·Ӧ 

Թ⻬ȹ걸ռ͡·ֲܰԵĶȹ棬Ϊ 

ûж塣 

    ǿںڶУ·ӦŷҲȹ͡ 

ζʷĺڶŷ϶ȹв֣ŷ϶ȹ沢 

ûеӽȥ෴ģӽǼԭ㡣ŷ϶ȹ 

öġǿ԰ΪලӰ汾 

ṹƻӦӰκ 

    ˣ·ֿӦöԷŷ϶ȹ͡Ƕ 

ЩȹӦʲôı߽ҲֻȻѡ 

һǶȹڽ¼֮Ҫƽ̹ŷ϶ȹ档ڶֿ 

ºûб߽ϵĶȹ档 

    ·ֵȻѡȡ 

             1.ƽ̹ŷ϶ȹ档 

             2.ûб߽Ľ¶ȹ档 

    һཥŷ϶ȹɢȻʺϣͼ 5.1 

Щȹдӷ۲ܳʲôеĹ۲춼 

Уıȹƽ̹ģͨʽѳС 

ͳӡǲѯм໥ʲô 

Ϊ໥·ֶпʷͣҲǶ 

ŷ϶ȹ͡ 

     

    ͼ 5.1 ɢУͳӣҪ 

 

    ŷ϶ȹ档 

    ȻѧȤв 

Ǵ֮УǴ档Ϊ˿ֲ죬 

Ǽٶѧ·Ƕнŷ϶ȹ͡ô 

ĲĸʴֹסһͨĽŷ϶ȹ档 

ڶڷͨĶȹ棬һĽʱպһ 

֮Ľŷ϶ȹɣͼ 5.2ǲܰѷͨȹ· 

ųΪǿͨȹƣڴ˶ȹвͬĲֿ 

пԺԵϸܻ涴 

     

     

    ŷ϶ȹ 

    ¶ȹ 

    ͼ 5.2 УǱ뿼͵Ľ 

ŷ 

    ϶ȹ棺ͨģϣͷͨģ£ 

    ʱյķͨĽ򲻺ӣȴ 

ģԽӰɢ㡣ǻӰѧеĲ 

ΪеġȷַͨȹĹԶԶѹ 

ͨĽŷ϶ȹĹסǼѧ·ֶн 

ŷ϶ȹͣЧӦͶн¶ȹͼȫͬˣ 

ѧ·֣Ȼȡޱ߽Ľ¶ȹͣ 

ض 1983 ضͻ 1983 

     ޱ߽裨ضͻ 

     ·Ƕнŷ϶ȹ͡ 

ǿ԰Ϊı߽ûб߽硣 

     νݵ²Ҫָޱ߽ƺܽ 

е档һͬԵġȵġ΢С΢ŵ 

档ǿ΢й۲쵽Щ΢ŵ׺ͳơЩ 

ޱ߽һ¡΢Ĺ۲ⱻ쵽СĽǶȷΧ 

ʱֹ۲Ϊޱ߽ŷѧ˵Խʯ 

     Ϊʹޱ߽裬һʱ̵״ 

̬ĸ档ʱ M һǶάΡƵĸʣ 
άεĶȹ hijʾһ M ϵĶȹ gab· 
㣬ڴҪȹ gabڡϵĵȹΪ hij 

      ڡϵȹ   Mڦϵ         d[g]eI 
                                   hijĶȹ 

      M ǵͨģҪģƾͰ M ֳ֣ 
M M-ͼ 53£ƾжȹ hijĸǿʽֽ 

ġͦ-ĳ˻ǷֱǴӶ M M-ϵĶ 
͵·ֵóЩȹڡϵάȹ hij 
                hijĸ =  +(hij) (hij) 
      ˴ 
                 +(hij) = M +ڡϵhijĶȹ d[g]e1 



     ڴ£ȣҽϱ꣫-ȥ 

Ĳʳ򲨺ڡϵ 
ֵ0һպϵвһرԽʱ꣬ 

Բغʱйءޱ߽ĺǣĲ 
һڽ Mϵĳ͵·ָЩεĽб߽ 
Ǳƣͼ 54·Ƕ Mжȹʳͣ 
Щȹͳڡƺ hijԼʳ0һ¡ 

      
     ͼ 53 ưѽµġͨ M ָ M M-֡ 

      
     ͼ 54  Mϵһ·ָ 
     ǿ԰ѱƵλɡϵ xiĺӡ· 
ֶĲڦӻ xiѡȡ 

ĸ΢ַ̡̽Լ 

          Լ 
          ();j = 00 
           hij 

    Ǳʵ໥֮任õĲͬ 
ȹ hij䲨ͬĸ̳Ϊ-ط̡ 

    -ط 
                2 
     Gijkl             = 0 
             hijhkl 

    Ӧڲ޹ءǿ԰Ϊ޵̷̡ 

ǣΪʱ䣬ûʱ䵼 

    Ϊ˹ĲںڶΣ· 
İơ Mҵ㳡̵ŷ϶ȹ g0Ҫ g0 
ڱ߽ϵȹ h0ȻǿɰΧűȹ g0 

չ 

     I[g] = I[g0]+ gI2g+  
                  1 
                  2 
ǰһ΢ʧƽΪǱеӵĹף 

߽֮໥áʰ뾶ʿ˳߶ȱȽ 

ʱЩԲܣˣ 
               1 
      
                  1  e  I[g0] 
           (detI2)2 
    ǿɴһ򵥵ӿʲôӡһû 

Σֻһ泣ȡΪһά 
 hijΪ뾶 a ı׼άȹ档ȻԡΪ߽ MȡΪά 

㳡̵ĶȹǾа뾶 άһ֣˴H2 = 
                                  1                              
                                                                  
                                  H                             3 
                                    1        1          1 
ΪI =      1   (R   2)(g)2 d4x +    K( h)2 d3x 
                  16                      8 


ڰ뾶 СάƣܵŷϽ⣺+ԱȰ 
              1 
              H 


ٻ߶ࣨͼ 55Ȼ֤ӦȡӦڰ 

Ǹ⡣ 
    һͼͼ 56˶ȹ g0ԲĹסƵ 

     뾶 Сʱea2ʽָ 
              1 
              H 

     Ȼ ʱǿԶԸС뾶Ľ 
                    1 
                   H 

    õǳ񵴵Ĳ 
                 1              3                                3 
     =  {1 (1        
                           a2)2}      =  {1+ (1 
                                               1          a2)2}    
                A         3                      A           3 
    ͼ 55 б߽ 

      ƵܵŷϽ MԼǵͼ 56 Ϊ 

Ƶİ뾶ĺ 

    ǿɶԲ½͡ЦԳԵİ˹̹ʵʱ 

ǵؿռ䡣ԱΪһת˫汻Ƕάɿɷ˹ 

У 5Aǿ԰ǳһպ棬 

޳߶һС뾶Ȼֳָ͡ȹдɴ 

г߶Ϊ coshHt ĸеʽӣit  cosh  cos  

˾а뾶 άŷ϶ȹ棨5.ǵ֪ 
            1 
            H 


ȹ hijָʽ仯ʱͶӦʱŷ϶ȹ档 

һ棬񵴶Ӧʵʱ϶ȹ档 

    ںڶԲΣǿһָԷ 

ǰŷά°벿ת˫ͼ 57 

ͺڶԲβͬǣǲ˵ǴһԤȴ 

Ŀռеĳܴġ෴ģ൱׼ȷذ˵ 

޴ģ 

     5Aϵضȹ 

     

     5Bŷ϶ȹ 

     

     

     

    ͼ 57 ðŷϽͰϽЧ 

Ӧ 

ǴճǴӾԵгΪ֮û 

κζŷϷ룬ֻһպϵĿռ䣬 

ı棬ֻάѡ泣ʿֵСŷά 

ӦúС·ֵİǿɿģҲΪ 

ǺڷǳĶӰ沨ļ㡣 

    ǻԶԲάȹı߽ⳡ̡ά 
       1 
뾶 СΪʵŷ϶ȹ档;ͬά 
       H 


    ȽϣʵĶҲָʽ˥άİ뾶 

ٽ뾶⣬ hij΢С 

񵴡 

    κβ԰ղޱ߽ 

ʹѧΪѧΪǿԤκι۲ĽǸղſǵ 

ûʳֻ泣βӦе档 

ˣǸӣΪһ򵥵Ĳ൱ؽģ 

ͣǽҪӦڽ׶Ρ 

    ȻӲԣһͺڶ൱Ƶؾ 

ԡѵضȹдɺʷ൱Ƶľ̬ʽܿһ 

 5C 

    r = һԡȻʷΣ 
          1 
          H 


    任԰ųӦһ¼ӽ硣Դӿء 

˹ͼϿһΡߵĵ㴹ֱߴԳģ 

άİ뾶 r Ϊ㡣һԳұߵĵ㴹ֱߴڶ 

͵µˮƽߴȥͽյġ 

Ϸ·ĶԽֶԳĵĹ۲߹ȥı߽硣 

Գ¼ӽ硣ȻһλδطսĹ 

߾вͬ¼ӽ硣ڵؿռ¼ӽǸ˵ 

    ǻصضȹľ̬ʽӣit õŷ϶ 

档ӽһԡȻֻҪһµ 

     5Cضȹľ̬ʽ 

     
                             2 
겢ڦ        ͬ͵õһŷ϶ȹ棬 
                             H 


պάΪʱԵģԵؿռ֮ 
                                       H 
ӳΪͺǾ¶       ƵġǽҪģ 
                                       2 


΢пԹ۲쵽¶ȵĺǻ 
                                                                  
ڶŷϵؽ֤ᷢ       
                                                                 H2 


¼ӽķ֮һԭģά 

ŷΪŷϵؿռвȫʱꡣ 

԰һؽͳɹ۲߶¼ӽ֪֮ʶȱ 

ʧ 

    ؿռ䲻еĺģͣΪǿյĶ 

ڳָ͡ǹ۲쵽ʣǴ΢Ԫ 

ذƳڹȥȸܵöࡣǹ۲һµ򵥵ķ 

νġȴըģͣͼ 58Уڳ 

¶ȵķһʼͣȴ 

ܶȽ͡󣬷ܶȱȷʵܶȻͣͱ 

ռ 

    ˡȻȻ΢ıпĲ࣬ 

дԼȾȸ 3K ¶ȡ 

    ȴըģ͵鷳ѧ鷳ûгʼ 

ۣûԤΪԴʧЧӴըð 

κζΪڴΧ˵ؾȺ͸ͬԣȴ 

ϵͺľֲ޹أΪ˽ӽ̮ 

֮ķֽأΪʹ״ôӽڵʱ 
벻˼ؾȷѡڴըһС 10-10 
ڼ֮Ӧ̮ 10-10ͻڼ֮ 

ǿյġκ¶㹻ʱԷչ 

ҪôԭҪôѰѧĽͣ˵Ϊ 

ӵġ 

     

    ͼ 58 ȴըģ뾶¶Ϊʱĺ 


        ȴըģͲܽΪΣ 

        1漸ǾȺ͸ͬԵģȴ 

        С΢š 

        2Լպñ̮ٽ 

        ͡ 

    Щνıܹʹʼ۳Ϊࡣ˼ 

ڴըʱԴӼ״̬ʼокĲֻ 

ֽǵָʱڡʹ߶һ޴Ĵ 
 1030ıһʹȾָͬԣʹԸպ 

̮ٽ͡ǻֻڱǻŵ 

չˣǵ֮Լͬԣպٽ 

ͣӦеȡ 

    Ȼñǲܽ״Ҫһףֻ 

Ҫȡκ̬ʱĹȥݻٶ㹻ʣ 

Զڹȥԡǿڴըѡȡģ͵ 

ʼΪʼַָը 

ʼܵڵκ״̬ʼ 

ǽ۲쵽״̬ǵǲĳʼ 

Ȼȶ޵ġǲܶԺ߲ȸЩ 

    һ棬ǿھ泣ûʳΣޱ 

ᵼһۼڿɱԤԵ档ģͲ 

е棬ǵʶҾֵ 

ǳС泣Ȼǿ泣ʳԵõ 

һʵģ͡ƺҪһ Vգıա 

ٶVڦ = 0ʱһΪļСֵ򵥵ӱǾV = m22 
                                                            1 
                                                            2 
ʱͼ59 
                  . 


    ͼ 59 ʱ 


        ܶ 

        Tab =    gab   gabV() 
                         1            c 
                  a b     2        c 




ǴܶԿݶȺС Vһ 

Ч泣á 
    ڲڵȹ hijڦڡϵֵ0 
СάԲԼĦ0ֵǿԽⳡֱ̡߽ 

ƵΪάһ֣ԼΪĦΣ 
 V0泣áƵģάİ뾶ŷ 

άİ뾶󣬽һԸ⡣Щŷά 

ϵؽȥֳޱ߽費 

ڵζģУԤһָԷ 

    ǿԿģ͵ݻ͵βͬ 

޵سָȥ V ɽϹСֵ0 

Ȼĳʼֵʿֵµʾͱ͵ʱ 

߶ȸ͵һͿʼڦ0 񵴡 

ڴ V񵴱ʱ졣ͨٶЩ 

תӶԣȥȻһЩҪʱ 

ͷļһܿػصһ 

    ھ˾޴ָ֮;мǡõٽ 

ʡޱ߽ܽͣΪȻôӽٽ 

ʡΪоԺ͸ͬԵԤԣǱ뿼Ƕ 
άȹ΢ŵȹ hijǿ԰гչǹ 

ࣺгʸгԼгʸгֻӦ 
άϵ xiĸı䣬κζѧáгӦ 

егһֶӦɶȣһֶ 

Ӧܶ΢š 

        г 

        ʸг淶 

        гܶ΢ 

    ǿ԰Ѳɰ뾶ΪάĶȹĲϸ 

гϵĲĳ˻ 
    [hij,0]= (a,)a(an)b(bn)c(cn)d(dn) 
    ȻǰѲĻ  ط̰뾶ƽչ 


ףǰ΢ֻչһסǾ͵õһϵڱ 

ȹʱ΢ŸıʵĲҪѦ̷̡ 

        ޵̷ 
                      1     2 
        i  (dn) =      ( 
             t      2a3    d2n + n2d2na4)(dn) 

        ȵȡ 

    ǿޱ߽ȥЩ΢ŲĳʼǶ 

һСĵ΢εάⳡ̡͵õָʱڵ΢ 

ŲȻѦ̷ȥݻ֮ 

    ӦгΪ򵥡ǲκι淶 

ɶȶҺ΢Ųֱ໥áǿޱ߽ڱ΢ 
Ķȹȥгϵ dnĳʼ 

        ̬ 
                   2na2d2n 
                     1 
        (dn) e           = e 12x2  
                 1 
        ˴x = a2dnԼ =  n 
                             a 


    Ƿ֣һгƵµĻ̬Ƶ 

Ͷ½Ƶʱʦʱ޵̷ 

ȵɳڶģʽͣĻ̬ȻƵջС 

ʣָڼΪƵʱñʸСʱ޵ 

̷̲㹻ظı䲨ʹƵʸıʱȻάڻ 

̬෴ģԭȵĲ״̡ 

    ָʱ֮ʱģʽƵ½ø졣Ч˵ 

۲¼ӽ磬ҲʵĵģʽĲø졣 

ڱڼñӽ绹Һֻصӽ֮ڣͼ 

5.10һʱ̣ȻͲʱһȻƵ 

͵öˡ˲Ӧڸ߶ȼ̬ǲʱĻ̬ 

ģʽЩӼ΢ĽǶǲ 

ʱʿ˵λʡ汳̽΢Ϲ 
⵽ 10-5Ϊڲ֮ʱܶ˴Լ 10-10 

˵λޡֵ͵Ա֤ùĽʮ׼ȷ 

    ȻгֻΪʱܶޡԵǣ 
г΢ĸȹ hijгɶȣ 

ڱһȻеӦɶȡֻ 

һıɶȣӦܶ΢š 

    ͼ 510 ڱвӽ뾶ʱĺ 

    Ƕֱ֮ǰ֮ѡȡһ꣬ԶԱ 

гȡͶгǳƵķڴһһ 

ϵͳ任֮УȱŴʳԦյƽ仯ʡ 

ƵбʣǶںΪʮܶ΢Ų 

΢Ĵʮڲʱ̵ 
ܶȵֻʿܶȵ 10-12ͺܰȫشʹùĽ 

ЧΧ֮ڡĿҲҪۡ 

    ǶȴСףڵǰ۲ľںͼŽ޹صԤ 

ܶ΢ŵĴСպҪϵͺǵγɡ 

ޱ߽ܽнṹ΢СķǾ 

ԡ 




    ǿΪ΢΢ɱյġʱ 

ھʳ 2е¶ȣΪʱ䷽Ƶسԡ 

ĳϣǲҪѰ΢С̫ڶѾ۲⵽ 
Լ 1026ȵģ 10-6ʿ¶ȵ¶ȡ 

    ں¼ӽص˵Щʲôأܹ۲쵽 

ܣΪӦʵϵͺ 

Ǿ壬γɵġһձ 

ƿ棬ĳһʱ̺棬洦ɲ 

дĵ̬СȻԶȡƵһ࣬ 

Ƕǹȥ׶֮ʲôģȫ֪ζڼ 

۲ĸ֮ʱǱѡǲܹ۲⵽Ĳֵп 

ͣͼ 5.11͵ЧӦǰǹ۲Ĳִһ 

̬ıνĻ̬ͬԵͳϵͳһϵͳо 

ĶӵķʽΪνǱġͨ 

ȿĲϵͳ໥áв 

ϵͳ飬ǹ۲쵽ΪԭΪֻܿ 

Ĳ֡ҲΪԺʱܿȫ¼ 

ӽʧ鲢ˡޱ߽ڿռϱպϵġ 

һպ潫ڹ۲߿֮ǰ̮ 

    ͼ 511 һλ۲ֻܿκαƵĲ֡ 

֤һʱӦΪ¼ 

 14ͼ 5.12Ȼڴ˿ƺõ 316 ӣ 

 14ԣҪôŪˣҪôʲôˡ 

    Ҫ޽ܺǳһϽνݡʱ 

ͷǰڷǳֻ 

ҪӰƬصܿ𡣱ӲǴ²飬 

ƬԼƴòصϡʵͺˡ 

    ӵľֲʱԳƵģ߸ȷ˵ CPT  

ġڹȥͽ֮۲쵽ĲӦı߽ 

ǽڿռϱպϵģ͵߶Ȼ̮ 

޽ǿģʷǷǳͬġǽ 

˵ģƺǳ⻬ҹȻԤϵ̮ʱ 

ɷǳͼ 

    512ڹ۲֮ܿǰ̮ԡ 

޹棬Ϊڱö̫ãʼ 

˼ؾܵѡġ 

    ˣƺʱ˱вͬı߽޽ܵǣ 

ʱһ˶һκΪ㡣κʱв 

ͨ˹̶̹ǲ֡ڹ⻬ڽ׶ 

С̮кܴʱֿ 

˿Խʱļͷͼ 5.13 

    Ϊ޽ܵļеκڲֹһ㺬˵ġȣ 

 CPT ġ޽ܰ⵱ŵ㣬ȴóвѵ 

ȥԳƣӦ֮Ҫ֤ģҪ CPTΣ 

κһ 

    ͼ 513 κˡ 

׼ȷΪ㣬ʱӦȫҸͬԵĶһеʱ 

̱ˡ޽ܵκȲܽͱеҲܽͲ 

ϵԼ΢š 

    κ 

    1. CPT ġ 

    2.κһ׼ȷΪ㡣ܽС 

     

    һУΪ޽ץסʱ˵һҪ𡣵κ 

һ˺Сʵܱһرı߽Ӧһ 

ԭ򣬼ޱ߽ƳѾģζΧŰ 

ŷάͰϵؽӵı΢ŴǵĻ̬ 

˵ǺͲȷԭһµľС״̬޽ 

κκǾȷΪ㣬Ǿܵؽӽ㡣 

    ΪЩй΢Ŵǻ̬֤ѭ 

ˡӹ⻬ʼͱø޹档Ȼ 

ΪСʱֱصһֹ⻬״̬ζ 

ѧʱͷҪ򡣱ֻԼƴպò 

СԽԽᣬԽԽϡڵȴ̮ 

Ҫ̫ʱ䣬Եȵʱഺġʱ 

ʱͷôںڶ֮ҲӦ򡣿ǣҲᳫһ 

ڶΪһٵĺð취 

    дһƪƣʱʱͷᷴ򡣵֮ 

͵ԼɡɵһʹŷҷĴ 

󣬻ѧϵ治̮лص⻬״̬ 

ʱͷһָͬ 

    ʱ˵ôͬأΪһ΢űСһ 

ȴԭǣ̴΢Сά߽Ķܵĸ 

⡣һģǽƵðŷάϵ 

ؽһСӣͼ 5.14һֿܽͬİŷ 

άӵһϽϣϽ͵ǳİ뾶Ȼ 

߽С뾶ͼ 5.15ȻһӦʱһˣ 

һӦһˡ˵֮Ĳʵڵ 
һк̵ܶʱڵĽΣȹ hij΢˥ú 

ȻĽΣ΢ſԷǳ󲢲˥ 

޽ָʱ֮Ĳһ˷ǳ⻬κ 

ǳСȻ׼ȷΪ㣬ΪΥȷԭ 

෴ģںСЩɳΪϵԼ 

塣˳Աȵǣʱһ˵㣬ǳ޹һ磬 

κ޴ͽ˹۲쵽ʱͷԼΪαӴӻ 

ƴպ 

    ͼ 514ŷάӵһС 

    ͼ 515ŷάӵһС򣬸͵ 

뾶Ȼ 

    ʱͷ׼򡪡Ѿʱ䡪ý 

ݡǿʱолϤΪص㣺1 

ʱգʹһ˺һս᣻2Ϊȷ 

ϵεˣ͵ѧ֮һ̵Ĺ 

    ʱʲԣԴʧЧල 

ΪǷڶԣǴըԳر¶ǰ 

۲ԤοˡȻӹۺޱ߽ 

һԤǹ۲쵽棬ƺԤ΢й۲ 

סȻȻۻָ˾ɥʧ˵Ԥԣ 

ûȫΪںڶ¼ӽ磬ǲܿʱ 

գǹ۲̬ϵ۶һ̬˶ 

ˮƽĲԤԣҲʹ濴ǾԭҲ 

ܰ޵èڰ֮ȳ 

    ѧаѿԤȡȻһּٵĳ̶ְָ 

һ׮൱ɹĹ¡ҵĻˡ 

                         ʱյŤ۵ 

                               P˹ 


    ȶʷٷϻؽۡ 

    èľԡʷٷ֤ʱյһܴ 

ʹܶȾȻⲻԽ۲ľ 

ʡӦҵһֻèһֻèܶȾ 

ֵӵĻϵܶȾͬ 
        1 
           
         2 
        1 
            
         2 
    ܶȾ˵ǲǿèè 

ֵ֮һ֡ͼһνĩβ֤ģҪ 

ġ 

    κʼ裨WCHҶʷٷ⣬Ϊһ 

ǵ鲻̫󡣶ڳʼκʽΪ㣬սԾ 

дκʡʷٷ۵ڳʼ״̬С 

ָʼκ׼ȷΪļ費Ϊⲻ顣 

ڳʼԵκΪ˵ǾģڼľϿ϶ 

ȶءҵĹ۵㣬СǿԽܵģӷ϶ 

ġǻԤģ 
յͨ˹ȶγ 106̫ĺڶЩ 

ڽдκʣЩռ̬ǳʼ̬ 

ԣЩ WCH һ¡ 

    ͬʷٷ˵ģWCH ǡֲġҲΨĶǽ͵ġ 

Ҫһȥ֮ضͻġޱ߽衱NBPҲ 

ǳʼ̬ṹĺõĺѡߡȻҾҪĳַǳͬĶ 

ȥԸս̬رǣһԽṹ۱ȻΥ TPTCT 

Լ CPTܲĳЩ WCH ʵĶʱʧƿ൱΢ 

ģڳԽѧ۵Ĺ֮Сʷٷ۶ϣ 

ӳ۵ӦԤ CPT ġȻ֤ 

мٶ QFT ͨеͨұռƽ̹ġΪʷ 

ҺҶͬ⣬ڶһŵһʧܡ 

    һãʷٷޱ߽Ĺ۵㲢ų׶Ĵڡ 

ȷʷٷҵĹ۵㣬ôޱ߽ζŻϴ 

⣺⣨AдԳ΢Լ⣨B΢˥ʧA 

϶ӦڴըBдڶԺʹѹȷѧڶ 

ɵʱͷӽ⣨Aɵ⣨BȻҿޱ߽ 

ĽͺųB͵İ׶ҵĵһֿǡŷ 

û̡ʷٷҵ֤ʵǿ԰һŷϽһ 

ϽճһȻֻжԷǳĿռǲſô 

ΪǱ벻ŷϵĶϵĽ档һο϶˺Զ 


     ŤŤռ 


     ӳʹŷûԴںδأӳҪѳ 

۷ֽƵ͸Ƶ֡ǰʱǰ򴫲󴫲 

Ϊ˵õ۵ĴӣҪһְƵʣҲܣ 

İ취ŤַֽһͬĿܡʵϣ 

ֽŤһҪԭʼ˹ 1986 

     ΪϸؽͣȿΪۻĸǽ 

ָᷢṹҲʱսṹĻЩ zxiy ʽ x 
y Ϊʵ i  i2-1ļϱΪ Cǿһƽ 

ƽ棩ϰЩԶһ㣬һ 

棨ϱѧ 

УǷǳõĸѧҲˡɱͶӰһ 

ƽ棨Զһ㣩ϡȡһͨƽ棬 

ϵϼߺƽĽ E ƽϵĶӦ㡣 

ע⣺ӳ±ܵԭ㣬ϼܵԶʵᱻӳ䵽ͨ 

ϱһֱԲܡǿתʹʵӦڳ 

ڴ˿̱ϰߣͼ 61 

     ٶһʵ x ĸֵ fx֪ǿ 

 f Ϊһڳ϶ĺֹ۵һŵǣһ 

 f ΪƵǸƵȻоݣ fxڱϱأ 

һƵϰ 

      

     ͼ 61иԼޡ 

ϱأһƵһһ㺯ɷֽƵ֡Ť 

۵Ĺȫֵķʽõʱձȥɿɷ˹ 

ʱϸһҪƵطֽƵ֡ǽҪ 

Ťռ䣬Ϊֽ;˹ֵ 1986 Լݸ 

غе 1985ԶŤи˽⣩ 

     ϸ֮ǰѧеҪá 

1. ӵĲǡϡ͡¡һԵӣ 
            1 
            2 
w| > +z| >  

     һ״̬ɵ zw һӦĴ 

ĳཻᣨȹ鹦Լɣɲ˹ 

1994ǻϸӵĽṹߵͰ 

ѧĸȺʱսṹϵͼ 62 

    2λʱһĹ۲ߣ̫չǡٶһ滭 

ЩǵĽλáڣڶ۲ͬʱͬһ㣬͵ 

һ۲֮һٶȣôڹ 

     

    ͼ62  ӵĿռǱz/w򣬴˴wz 
        .       1 
               2 
    ֱϺķȡ 

ЧӦϰڲͬλû˾ȵǣ 

ϵĲͬλÿһΪĪ˹任任任 

ȷγάĸṹĽ⡣ͨһʱյĹ 

ռ䣬һȻ򡣴⣬ҷǳƯ 

ͬٶȹ۲ĻԳȺҲǣƵģȺ 

Ϊ򵥵һάģΣͬȺʵ֣ͼ 63  

˹ֵ 1984 

    Ť۵Ļͼѧʱսṹеϵ 

ʾġƹ㵽ʱաǽҪ 

ߵʱյĶǰʱΪǴ 

ĸŤռ䡪ԭǹ߿ռ䡪ΪǸռ䡣 

ֿռһֶӦʱеĹŤռõ 

ʱеĵͨĹ߼ʱеһŤռ 

бΪһӦðŤռ䵱Ŀռ 

ͼ 64 

     

    ͼ 63һ۲ߵȻسΪһ򡣡 

    ͼ 64ڻŤӦУɿɷ˹ʱеĹãͶӰ 

Ťռеĵʱյĵ 

    ֱܵŤռУʵģάڸռǣʵ 

ģżάŤռ䲻Ǹռ䡣ǰѹΪǹ 

ʷǻҪӵȣȿֻ֡ 

Ƚһ߸һЩŵտøͶӰ 
ռ䣨ʵάcp3ͶӰŤռ䣨PTάӿռ 

PNPN ѿռ PT ֲֽ֣ PT-ֲ PT 

    ڣʱеĵĸʵͶӰŤռĸı 
ΪꡣŤռɣZ1Z2Z3Z4һͨʱ 
еĵ㣨r0r1r2r3ôǱͶϵ 

    Z1  0          0 
          =            r3   1      2 
                                           (6.1) 
     Z        i rr1 +ir2 rr0 +irr3 Z23 
              2                     Z 
                                   

Ͷϵ61ṩŤӦĻ 

    ҪĳֶǺšͨǿʼ֮ 
Ϊ˼ϸڣּ¼κʸ ra rAA  
                                                            

ʽ 
             00'                 0          1   2 
    rAA' =  rr10'   r01'   =           r3 
                   r11'    1 rr1 +ir2 rr0 +ir3  
                           2                  r 

    raΪʵ rAA Ϊ׵ġŤռеһ· 
                           

 
    AԦ2 = 
            1      Z01        СԦ'1 = 
                                      '0 
                     Z                       Z23 
                                             Z 

Ͷϵ61ͱ 

                                  wirС 

Ӧᵽǣԭƶ֮ʱ༴ 
                                  rara-Qa 

 
                             AAiQAA A 
                                              
                                                 

˴A ֲ䣺 
        

                                   A A 
                                         

    ŤӶķ PaǶģԼǶ 

 MabĸЩǶģǿɱ 
    PAA' = iAAMAA'BB' = i(A A'B'  iAB(A'B') 
                                           B) 

    űʾԳƲ֣ABͦA бά-άšЩ 
                                            
                                           B 

ʽʵ PaԵĶָδ-³ 

˹ʸ s ĶЩŤAA  
                                                                   

ȷһŤӡȿɱΪ 

                                  S = ZaZa 
                                      1 
                                      2 
Ť = ئЦĸΪżŤZa = AA' ע 


⸴ѴֺźͲֺŵָ໥Ť 

Ķż໥s0 ӦӣҲǵŤ 
ϰ벿 PT s0 Ӧӣ°벿 PT- 

s0 
ǵõʵʵĹߣ˦ҲߵķΪa = 0Ҳ 
A Ц + A' = 0 
                 A' 

    ӵŤ 


    ϣõŤۣΪǱ趨ŤŤ 
ռϵĸֵ fZZ漰λñж 

ķһͬʱʹһЩ⺯ f 
ZΪһλúͶסŤռ 

׹ϵ 
    [Z ,Z ] = hĦ[Z,Z] = 0 [Z,Z ]= 0. 
                      

     ZΪеһ 


ĺ ZĽ򷴽 

    Ǳǰıʽ˳Ƿֶ 

ͽǶıʽʹ޹أȷġһ棬 

ıʽʹйأǱȷ塣ΪǱȡԳƵĻ 

Ҳ 

    S = (Za Za + ZaZa), 
        1 
        4 
     ZaռУ± 

    S = (2 Za 
        h            
                        ) 
        2           Za 

      = (2  Zaζ) 
        h 
        2 
ܰѲֽ s ı̬պȷԵĲ 

磬Ϊ-2 Ťһ 

 Ӿs =  Ť1 
  1                       h 
  2                       2 
ӵְ汾s =   3Ť2 
                            h 
                            2 


ֺŤӦΪ-6 ͣ2 

    ҲԵЩһбΪ۱ϾҶԳƵġ 

ȻҲԳƣҲô⣬ڹ 

еһǳǿĹߣʲؿġ±ҲҲԳ 

ġȤǣЩͬķʽᵼҲԳԡ 
     ҲΪֻҪı䦦ZaָܻԳԣߵ 


ıȻһæһZaȻͨ 


ѧУǲͬʱλúͶռƵģǲܻϺ 
ZaZaǱһһδ֪ 

    һҪõ fZʱΧʵ 
                                            
    A'G'(r)              A'G'      

                =   =ir               f(Za )E'dE' 
      AG(r)                              
                            A          
                                       G  
˴Ͷ䵽 r  Z ռΧУס Z Цغ֣ͦ 

лߦصĿԼһ̶ 

һʱճաrԶӵĳ̡Ť 

ƣٶƽ̹ռеԳ߰˹̹ܼ 

еӵķĳ̵롣 
    ʱе r ڼѧһŤռе CP1ߣһ 

򣩡߱봩 fZһ˵ fZǴ 

ģҾԵĵطΧЩΧ 

ֵѧϸܵؽһŤһͬԪΪ 

ǸȤŤռĿ塣ŤӦЩ 

ԵĽϱ塣ǵһͬһԪءҲϸ 

Щǡͬ˵ġ 

    ҪģǺӳƣҳһִӳȷ 

Ƶ͸Ƶķһ PN ϵŤΪһͬ 

ԪصŤռһ PT;Ƶصһ 

PT-ϣиƵŤռץסƵ͸Ƶĸ 

    ַֽŤռпչ³˹ 

198219851990Ťͼչһӳ۵ֶΣͼ 

ʱеķͼЩõĳַǳͬѰʹӳ 

滯ķһЩʱշǲõķŤ 

ǳȻһչǣԭԴˡһ¹۵ 

˹˹ 1989ҲܵγۣCFTĴ̼ʷٷ 

һνж۽һЩǳۣΪ 

CFTΪƬϵĳǷǳƯģȻȫģ 

ۡǱϣ򵥵ӣ 

аһάԲ͡Ť黨ΣŤ 

Ҫ CFT ƹ㵽άΣ߽ΪƬ PNҲʱ 

еĹ߿ռ䣩оڽ֮Уǻչò졣 


    ռŤ 


    һֻƽ̹ʱأ֪ʱ 

ģҪһŤۣʱգȻķʽ 

˹̡̹ 

    ʱǹƽ̹ģ߻仰˵κΪ 

㣩Ťдռûκ⣬ΪŤۻǹ 

βġһЩڸֹβƽ̹ʱյŤƩ׼ 

Ķ壨˹ 1982е 1990Լº˹-÷ɭ1988 

ɲμº˹ 1990̬ԳյĹ죨ǻ 

 1977 ƽ̹ʱϷԶż-׶˹Ĺ죻ɲֵ 

1983ӦڿɻϵͳķǳһŤһ֣ļ 

÷ɭº˹ 1996 

    ȻϣܹԸһʱաһзԶżκ 

ҲκԶżһΪ㣩ĸŷϻʱ M 

һ졪νķӹ졪ֵܳ 

˹ 1976ǿôеġȡһߵĹ״򣬻 

ƵĳЩһƵ PTɵŤռһ֣ 

ҰгɶС飬Ȼճһ飬ֻ֮ 

ƶһЩһ˵ԭȿռ P еֱ¿ռ p жϿȻ 

ѰµĽȥȡԭȣڶϵģֱߣٶЩ߹⻬ 

ؽһ𡣼ٶ P  p ıβְ̫취õĽ 

ԭȵߡͬ˵塪γһά塣Щ 

ߵĵĿռǷԶżģʱաMͼ 65 
ܰѰ˹̹շ̣ƽ̹ԣ p ͶӰ cp1 

һάԼһЩֻҪ p  P  

ɽͿԴﵽһУԭʱ M  

ϢЩ֮УȻ p ҵҪĽ߿Ǻ 

ѵģ 

     

    ͼ 65 ӹ 

    Ҫİ˹̹̣Ĺֻ˼ 

⣬κһΪ㣩Ȼѵģڹȥ 20 

ೢԶʧˡȻǰ곢һµķ 

˹ 1992Ȼһûн⣬ǿϣķ 

ǷŤͰ˹̹֮ȷ̵Ĺϵ 

۲пԿһ㣺 

    1.˹̹շRab = 0ҲǾs =   3 
                                                  ĺг 
                                                2 


óƸʱ 

    2.ƽ̹ʱs = ĺɵĿռպŤռ䡣Ͽ 
                     3 
                     2 


ʵ滮һƽ̹ʱգҲ Rab0Ǳȥ 

s = ĳĺɿռ䣨ⲻ׾ٵ飩Ǹ 
             3 
             2 


ƽ̹ʱյŤռ䡣ڶɽȥŤ 

䣬ÿ´ŤռؽԭȵʱΡ 

    ԤϵŤռ䲻ԵģΪؽʱʱ 

ģֹȻһ΢ķʽ߶ȵطǶġԤ 

ϵڽһνݣ£۵İ˹̹- 

˹-ѷʵķǶЩʵʱоңԶ 

ĳַʽ໥һ 


    Ťѧ 


    ѧŤһЩԽνݣȻ൱ 

Եġ˵ڹȥԴκΪ㣬ʱǶ 

뼸ǹƽ̹ġʼ̬Ťǳ򵥡ʱ 

ƽԽԽӣκʱԽŨܡ͵ 

Ϊ漸й۲쵽ʱǶԳһ¡ 

    Ť۵ĸһ k0 ĵ¿ 

ըʷٷҸһպϵ棩ԭֻһ k0 
УʼԵĶԳȺһȺҲǸպ cP1 

Ա任Ī˹ȺҲƵȺǿŤ 

۵ͬȺˣΪŤԭҿ϶ k0 

ֻǻڹ֮ϣʵǱպϵģҵȻ 

ջֿ 

    ʴ 


              3 
    ʣ ̬ʲô壿 
              2 
                       3 
     ûʵʵ˵Ϊ˶Ť 
                      2 


ĸΪֵܹӵĳһ棬ӳ 

ƵĹ۵㿴ӵĳ¡ 

    ʣŤ۵УϴνʱǶԳƵ R ںδ֣ 

    ʶŤһַǳصۣûд 

⡣ҷǳϣŤгʱǶԳƣڴ˿ 

Ҳ֪ӺζȻȫʵ滮϶֣ 

Ҳһֺң󷴶ԳƵģʽ֡У³ 

˹滯ķڼʱǶԳƣǹһ㳾 

δ䶨ʣַԵӳŤУ 

    Ť滮ĿУҪ˱׼ģ͡ʣ 

ԤӵסŤ۵ĺδ 

    Ҳ֪γ֣ȻһһЩ 

ΣҺܸ˻֪ۡԤסҵĹ۵ֱ 

Ť˹ۺǲܽ⣬Ϊ 

͹۹ϵܡǣĳϣҲ۵Ĺ۵㡣 

    ʣʲôŤ۹Ĺ۵㣿 

    Ť۵һڶۣ 

Ŭӷϵӹռ䡣ҲԴӷĶ 

ŤۡȻôѾϷƵ 

Ⲣ۵ӵȵġҲڷͽд 

ϵһ㻹ûκķʽ¶ 

                                ± 

                          SW R˹ 


    ʷٷҡ 


    Щݷǳʾ޽֮ܺĲǰͼ 

ߣʵ֤ߡѦèڰ̬С 

ⲻʵҶԴ޶ԡΪҲ֪ʵʲô 

ҲҪ֮ʵʲĳʯֽƷʡ 

ĵһӦԤԲһǷǳɹ 

ġԤԳ۲Ľè㲻ܻһ 

˼ˡ 

    ޽ʿҲЩߣѦèԭ 
            1                                                1 
ǣ       è+ è̬ƺǻġΪβ     è  
            2                                                  2 


èءһ˵èè֮ƺκθ档Ϊ 

ǿ԰ӺĻԵúܺãͨͬ϶ 

ܵõ档޷èôĶͨųЯķ 

֮뿪ǲȥѦè񾭵 

;ġ 

    Ҳû潨˵¼ӽѦèΪ䶯 

ϵԭ˵ģҪèණ 

ǷǳѵģǲȥңԶ档˵ȫǣ 

ǿԾ޴ľȹ۲쵽΢ԻԵþо 

ͳƷֲǼⲻκ̬ʣ粻ͬģʽ֮ĸ 

ԡ̸ʱûѦèµ 

绷Ϊǲܿ棬Ȼõ; 

Ϊ 

    ޽ܶʹŷϷʾʡ䷴Ұŷϼӵ 

ϼϵĻͼȷָģֻڷǳпܣ 

һһʱ临ûȹΪʵĻŷ 

Ľ档ȻڷҲǶŷ·ַ 

⡣-׶˹ӣѱˡ 
ɿɷ˹ռе-׶˹͵· ei 

ʼ񵴶ҲΪ˵õΪ·֣ 
ʱӣ-it άתɵŷϿռ䡣Ԫͱ e-ŷ 
 ȻŷϿռеʵ͵·֡һ 

˵ŷϿռΪʵɿɷ˹ռвʵģǲ 

Ҫ˼ǶŷϿռеʵ͵·ֺͶɿ 

˹ռʵ͵·ֵȼۡΣ 

ǿð㷨-׶˹·ֵİ-׶ 

˹˲ϢӣԴ޽ܺŤ滮˴зࡣ -׶˹˲Ϣ 

ŷϿռʵġɿɷ˹ռǸġⲻҪ 

ȻӲ̵ʡ 

    Ƶġ·ֶ 

ŷ϶ȹ϶ȹ͡вͬˣ 

ȷǱġֻھŷϲܸ϶ 

档ǣǿģȤЧӦǳ 

ھзŷ϶ȹʱϡŷ 

û½⣬ƺ·ֲȻǿڸΧϣ 

Թӻ֮ĵģΪΪ͹淶 

йأҵ֪ʵؽ·ʱᱻ 

ԭǣΪģǸġ 

ĳʽκг֡ߵôԶҲ 

֡ı൱ң̫ṹ 

˵ڶˡ 

    ڹһͨۺһصŷϷޱ߽ϡȻ· 

Ƕʵȹͣ䰰ȴǸȹ档еά 

ƴĳһǳС߶ʱͻᷢȻҰѶȹдɰŷ 

άӵ϶ȹϣֻһơʵʵİȹǸġ 

ʹ޽İͼ߲ãʵ֤ 

Խܵġǹ۲첻ȹ档ܹ۲쵽һǴ 

ĲӦʵ϶ȹ档Ҷ޽ܷʹŷϺ͸ʱ 

е㾪ȡŤ滮ʹøʱաʵ޽йƵ 

ǽҷչŷ滮Ը滮Ѿ 

ɱ۲ԤԡۻŤ滮˶Ԥԣ 

    ޽ܾͨ R ̽й۲̮ 

    CPT ΥѧΪΥã 

ѧͺڶͬ⣬ǿԲȡйع۲ͬķʽʱ 

Գơȫܾ˼룬ĳЩӦڲ̮ 

̣ʶкء˵ħ 

ǿѧ 

    ѾҵĽнˣΪΪޱ߽ûκΥ 

 CPT νй۲쵽ʱͷҪΪʲô 

޽ܲͬΪڶǣ浽κʱǶԳơھУ 

ڶȥûжܳǻʣ 

ڰ׶ҲܳûжȥҵĻ 

ǣȻھкڶͰ׶ǳͬȴ 

ͬġ۰ѺڶͰ׶֮Ĳųˣڶܷ䣬׶ 

աԸ飬ǳڶģǴľĶǷǴ 

һ棬һСӷĶԤϵİ 

Ϊ 

    ҽ޽ᵽʵͺڶͰ׶ͬġھ 

ȫڵķǳĺзһԸַʽֲ 

ںڿ״̬֮СֿܵζӦ̬ľǺ 

ӳȷһڶЩȷƽ⡣ξи 

΢̬ӳ߶ԼٶǿѡЩʹ 

ζӦڴͬĿ΢̬ǿԤϣú 

֮ǻѡúʱֻȷ䣬һʱ̷ 

ʹӴһСڣγɺڶͼ 71ٹһʱ䣬 

ΪӺڶķǻտ 

    ͼ 71̶ĺӻֻȷ䣬߰һȷ 

䴦ƽĺڶ 

úڶͻʧеϵͳ̬ռ 

ǻʱڶ֣ʱڶʧˣͼ 72 

    ޽ܺһͬ⣬ķʽΪ 

ϲһ¡ȣ޽ţڶĳֺʧѭռ 

ϢɥʧΣù̲ʱԳƵġڵһ㣬޽ 

ãڶëռɥʧΪ̮ӵ಻ 

ͬòͬĺڶ飬R ̣Ҳǲ̮ 

Ĳ档Ҳ R ̴Ӻζںûй۲ߣ 

Ҷ˵ԷĲͬ飬ķĻ 

ֻħβͬռɥʧ˵ڶ 
           1A 
еe4 Ŀ̬Ǿûռɥʧһ 
ϵͳûκ̬ϢûϢɥʧ 

    ͼ 72 ڶֲʧ 

    ǵڶ飬źڶĳֺʧʱԳƵġǾ 

ǣԺ¼ӰٵţԵͬġʱһ 

㿴ڶֲʧһ㿴׶ڶʱ 

ݡֲʧ׶ͺڶͬĻͼͬ 

ûбҪΪӵΪȥ CPT Υͼ 73 

    ޽ܻǵ涼ܾҵĽ飬ĺڶ 

ɺʱԳƵġȻѻתˡڴ޽Ҳ 

ô 

    ͼ 73 ׶ֲʧ 

    ޽ܡ˹ش 


    ˵֮һ֮֮ࡣȻ 

һЩģ۵ǲܴﵽʶ漯Щ 


    è 


    ۡʵڡʲôǶθ֪ġ 

ѧûһ㣬Ǳĳֶӵѧȥĳ 

ֲѧ׼ĶǣҾʷٷҲû 

йèۡⲻ 

    ϢɥʧζϵͳܶȾǱܶȾ 

       D =  
            1 
            4 
            +     71 
             1                                           . 
             4 
     
              1                 1 
         D  72   . 
              2 2 
    ȵġˣǱΪǸоèǻδ 

оһֵӡҾЩϣѧҪģûлش 

⡣ 

    ҾΪ˽ѧθ֪磬ǽҪ 

۵һ֣֣ 

    Aۡ 

    BΪۡ 

    ʵϣù۲߲ 71 £Ӧ̬ʸ 

Ծʽ 
    1۲߼è۲߼è 
    2 


    73ôһѡAͱųڶʽеĵӵĿ 

ԣΪ֪̬ǲġһ棬ҪBųһʽ 

ĵӡԼͼУЩ߶ȵǲȶģǱѸ 

أԷأ˥ɣ̬ͣеһʷٷһ 

һλ A-֧ߣۻ𣺷ݣΪһλ B-֧ߡŲ 

AǺΣյģᵼ޾鷳Ǽᶨ B-֧ߡ 

ǣһλ A-֧Ҫ񾭻ĳƶۡʷٷ 

ȷ A-֧ߣҲ B-֧ߣҶԴ˺ܾȣڵȴԴ˽ 

ۡ 


    άת 


    ӳõĹߡǰ t  it 滻ζʱ 

תͰɿɷ˹ռ䷭ŷϿռ䡣ôԴʵ 

ŷĳЩʽƩ·֣ɱõض塣ӳ 

άתһܺüĹǰӦƽ̹̬ 

ʱʱˡ 

    ʷٷҰѡάתõ϶ȹ棨Եõŷ϶ȹĿռ䣩 

˼϶ǷǳȤŵģͰάתӳ 

÷ǳͬڲͬˮƽϵһ֡άת 

    ޱ߽һǳõļ裬ҿ϶κʼ 

ءȻҵĹ۵㣬ޱ߽͹ȥԾСκʣ 

δԾдκʻңԶǵй۲쵽 

ģʷٷڹ۲췽ȡͬ 


    ռɥʧ 


    ΪʷٷҺҶͬںڶϢɥʧǹںڶ 

ɥʧз硣ʷٷ R ̽ħȻ 

һҲܹͬΪҵĵڶνѾˣΪʲôǺ 

ģҸ̬Ӧʵȷ룬Ҳʱ 

                           h       7.4 
                              E 
һΪĺڶͼǷǳ󵼵ġӦûͼȻԿ 

ʱԳƵġҶͬϢɥʧһռ 

С⣬ʱԳƵģӦа׶ 

ܳ򣬶ٺκʼ費һ£ѧڶ 

ɲһ£ҿܺ͹۲Ҳһ¡͡ 

ԵءΪ۱ʱǶԳơ 


    ʷٷҡ 


    ޽ΪѦ̿èǡڽʵ鲻ȷ 

ġ޽֮ԹΪèèȸʵܶȾҲè 

èè-èĵȸʡΪǹ۲쵽èǹ۲쵽è 

èè-èأʲôΪǹ۲˻ᣬ 

ǻͻ-أҪָǣֻеܶȾıֵǡ 

ʱǲ䱾̬ĺĸв𣬱 

̬Ͳκκ֮ΪܶȾı̬һԺ 

ĻֿôΪȻѡȡܶȾջԽǻ 

-Խǻأǣ̬è̬èڿ͹ˮƽϵĲͬ 

ӵλԼèϵ˿Ķһֱ׷ٵ㿴 

Ʃ˵ӵŶ̬è̬è֮κι۲ 

ԪƽΪ㡣Ϊǹ۲쵽èǶ 

ϡֻͨѧǲҪµĲۣ 

Ҫ 

    ǻص޽ƺޱ߽ܽ 

СκȻܷԤںڶ̮Լ 

̮гֵĴκʾʡΪΪޱ߽ 

ġ޽ܻͬ⣬ڴӼ⻬濪ʼģ̮ 

зչɸ߶޹Ͻ⡣ǿܰЩ϶ȹ 

İŷά͸̮и߶ȱάεĲ 

Ľư㣨ͼ 74Ȼ˵ģ׼ȷİ 

ǸģȲŷϵģҲϵġˣģ 

ںܺõĽ£ǿɰֳɼŷϺͼϵŷ 

ֻͰάвŷֻȰ 

άԴһЩ߶ӦھȵĸͬԵ档ϲֺ; 

ĸͬԵĽǳȻϲֵֻı䲨 

࣬ӰȡŷϲֵҼά 

α޹ءά̮жͬȿܣ 

     

    ͼ 74 ̮ά͸УŷϽȷάβ 

ķȣϽȷλ 

ǻ͵صõдκʵķǳ޹Ķȹ档ϣʹ޽ 

Լκ˶Դŷޱ߽ܽǹ⻬ģ 

̮ܽ޹ġ 

    ̸йغеĺڶʵ顣޽ƺȻҪ 

ƣΪ಻̮ͬγͬһڶԴռ 

ɥʧǺڶѧҪǱռɥʧǰһ 
ڶΪǿ eSγɡһʱԳƵķʽ 
ʱ eSʽ䡣ռɥʧҪ 

ȥ R ̸貹ô˵ҲУ̮ǲŲ 

̮ 

    Ҫ̸ڶͰ׶ĵͬ޽ܷԵ俨-˹ͼǳ 

ͬͼ 75ͬ⣬ǲͬģǻҪ˵ֻǾ 

ͼҪƣһλ۲߶ԣڶͰ׶ 

ͬġǣ޽Ҳᷴĳȥˣô 

ΪأΪ֤˼ٶʱھֻڵ 

ȹ塣 

    ڶ׶ 

     

    ͼ 75 ڶͰ׶Ŀ-˹ͼ 

һ棬УǱпܶȹ·֡Բ 

ͬ⽫вͬİȹ档ǣ۲ʵİ 

ȹ棬ͶһλĹ۲ߵİȹ治ͬǻڶ 

۲Сĵǿܵġһλ۲ߵİ 

ȹ潫Ӧڰ׶-˹ͼҹںڶͰ׶ȼ۵ 

Ǻгġǽеʹ CPT Ȼ 


    ޽ܡ˹ 


    һصʷٷйèۡʵϱֵ 

ءѱ֤˹ٵ 1993κܶȾȫ 

ͬıֵадɣģ̬ĸʻϣһ 

ֲԭϿԶԡ̬ʸδ֪֡иòܹ 

ѡ֪֡ܶȾͳɸضĸʻϡ⣬ͻЧ 

ӦԣָܷǶԽܺСǶԱ̬ЧӦҲ 

ܴʷٷһᵽӵȵȡⲢûлҪΪǶֻ 

èϵͳڵȻڡèӵϵͳΪ 

ءʵڡʷٷҺ֮ĸйء 

磬йذ׶ͺڶǷȣȵȡһʾˣ 

ˮƽֻ֪һʱյʵҾҪô֧ 

AҪô֧֣BҾʷٷû漰һ㡣 

    ڷǳСĶԣڶͰ׶ԷǳơһСڶᷢ 

䣬һ׶ơΪһС׶Ҳմ 

䡣Ҿֵͬںˮƽϲʣﻹȱһ 

ʲô 

    ѧŵ 75 ꡣǰţٵȽϣʱ 

Ƕݵġѧڷǳһ 

Ҳþȡ 

    ڱ۵Ŀͷʷٷ˵Ϊһʵ֤ߣһ 

ͼߡΪʵ֤ߣΪĹؼǣ 

ԸΪʵߡУ˰αۺͲ밮˹̹ 

֮ 70 ǰȽϣΪʷٷӦȡĽɫ 

ȡ˹̹ĽɫΪ˹̹۶ϵڲʾ 

ʵĳǿдһʵ΢ 

磬ֻǶԤõġ֪ʶѡ 

    ΪӮʵϣ˹1994İ 

˹̹ǣ˹̹ 1925 ֮ԵɹԿѧ 

ʧȷûлչϬзǳá 

ţ˹̹ûм๱ףѧȱʧ˹ 

Ĳ֡ȱʧĲ 50 ֮ʷٷҵķ֣ڶ䡣 

ֺͺڶصϢȱʧṩ¹ 


    ʴ 


    𡤻άģۣйӵۡ 

ӹеƺʾ൱Ҫġ 

һЩ󵼵ģЩȫȣ¹ 

ۣ˿ԵƳһСҲܸõ 

ԴģʵһЩܿƵķɢƺѱ 

ҵȻ˵Ѿ˷⣬Ȼ 

һǳǰ;; 

    ʣһŵ⣬ǹèġ 

    ޽ܡ˹½è⡣ 

    ʣ޽ܡ˹ܶʷķѾ֪ 

绷ķǳõȻǣδ⣬ 

δڲáҲҲʱʵйأ 

    ˹ʷ滮У R ЧĳֶǸÿ 

ܵһ֡ͨѧͬǾҲĳֺҵ 

ͬĶȻ˵Ҳʱսṹй˸Ȥġ 

ʱǶԳԣΪҵķͺгʷĲȺʷ 

ҷĲС 

    ʣеĺڶʵô£ʱ䷴ݵǷ 

Υѧڶɣ 

    𣨻𣩣Ӵ״̬ϵͳ̬п̬֮ 

ǻ˲Υ 

    ʣӲĻʵ 

    ˹ԭϣӦǿʵ⵽Ҳ 

볢ĳִ߶ȵ顣ʵ鷳ڣЧ 

ӦͨԸЧӦǾͱϵͳ÷ǳ 

á֪û˼ϸڣ϶ʮȤ 

ġ 


    ʣһıģУͺ֮ 

ƽ÷ǳáƽֻаٷ֮ʮ۲⵽Ѱ 

µʹͺͱ֮ԡ̫ѰҡԸԴ 

 

    ˹ҶԹȡǰֵķΧΪˣҿ 

ɰٷ֮ʮٽҴδرϲģ͡Ϊʷ 

ҪǱպϵģΪޱ߽һ֡ǣ 

    𣨻𣩣ܱСڹȥ 50  

10 ҿΪβټһ롣ͼҪѰҵʡ 


