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#7) ++
                          /CVJGOCVKECN 5EKGPEGU
                                  2CRGT ++
6KOG #NNQYGF   /KPWVGU?                         =/CZKOWO /CTMU  
0QVG  6JKU 2CRGT EQPVCKPU (KHV[  OWNVKRNG EJQKEG SWGUVKQPU 'CEJ SWGUVKQP
       ECTTKGU 6YQ  OCTMU #VVGORV #NN SWGUVKQPU

                                                 %QPUKFGT VJG VYQ UVCVGOGPVU HQT
   6JG UGIOGPV CГ D QH VJG Z CZKU QH
                                                     %
                                                       ^

     4 KU                                        C   G KU C QPG QPG HWPEVKQP

                                                   D   UKP  KU DQWPFGF GPVKTG HWPEVKQP
     # 0GKVJGT QRGP PQT ENQUGF
                                                   VJGP 
     $ 1RGP                                        #   DQVJ C CPF D CTG HCNUG

                                                   $   DQVJ C CPF D CTG VTWG
     % %NQUGF
                                                   %   QPN[ C KU VTWG
      $QVJ QRGP CPF ENQUGF                         QPN[ D KU VTWG

                                                 .GV H   GГ YJGTG   Z          K[Г
   #P QRGP UGV KP 4 KU 
                                                   VJGP 

     # CP KPVGTXCN                                 #   G      YJGP [ KU CP GXGP
                                                       OWNVKRNG QH SГ CPF G   YJGP
     $ HKPKVG WPKQP QH QRGP KPVGTXCNU                  [ KU CP QFF OWNVKRNG QH S

                                                   $   G      KH [ KU CP QFF OWNVKRNG
     % EQWPVCDNG WPKQP QH FKULQKPV QRGP
                                                       QH S

         KPVGTXCNU KP 4                            %   G   KH [ KU CP GXGP OWNVKRNG
                                                       QH S
      KPVGTUGEVKQP QH QRGP KPVGTXCNU
                                                    G        KH [ KU C OWNVKRNG QH S

                                                                                 =261
#7) ++

   H   VCP Г   % 
                      ^
                                                       9JKEJ QH VJG HQNNQYKPI HWPEVKQPU
     # CUUWOGU CNN EQORNGZ PWODGTU
                                                         6  4  o 4  KU PQV C NKPGCT
     $ CUUWOGU PQPG QH VJG EQORNGZ
                                                         VTCPUHQTOCVKQP !
         PWODGTU

     % CUUWOGU CNN EQORNGZ PWODGTU                       # 6 CГ D  C        DГ C  D
         GZEGRV K
                                                         $ 6 CГ D  C        DГ D
      CUUWOGU CNN EQORNGZ PWODGTU
         GZEGRV K CPF K                                 % 6 CГ D          CГ D

   .GV 8 ( DG C XGEVQT URCEG %QPUKFGT
                                                          6 CГ D  DГ C
     VJG HQNNQYKPI UVCVGOGPVU 

     +   +H   DГ    EГ     J   CTG   NKPGCTN[          .GV 8 DG C XGEVQT URCEG QXGT C HKGNF

         KPFGRGPFGPV XGEVQTU KP 8 ( Г
                                                         ( CPF 6  8 o 8 DG C NKPGCT
         VJGP D          EГ E Г JГ J Г D CTG
                                                         VTCPUHQTOCVKQP UWEJ VJCV 6 JCU  CU
         CNUQ NKPGCTN[ KPFGRGPFGPV

     ++ 6JG UGV QH XGEVQTU # Ž 8 (                       C EJCTCEVGTKUVKE TQQVГ VJGP 

         YJKEJ EQPVCKPU VJG GTQ XGEVQT
                                                         # 6 KU FKCIQPCNKCDNG QXGT (
         KU CNYC[U NKPGCTN[ KPFGRGPFGPV

     6JGP                                               $ /WNVKRNKEKV[         QH       GCEJ

     # $QVJ + CPF ++ CTG VTWG                                EJCTCEVGTKUVKE TQQV QH 6 KU 

     $ $QVJ + CPF ++ CTG HCNUG
                                                         % 6 KU KPXGTVKDNG
     % QPN[ + KU VTWG
                                                          6 KU PKNRQVGPV
      QPN[ ++ KU VTWG
#7) ++

   .GV H  7 o 8 DG C NKPGCT OCR CPF                +H 2 '   CPF 2 (  Г YJKEJ

     ]WГ WГ Г WP_ DG VJG UGV QH                QH VJG HQNNQYKPI KU PQV EQTTGEV !

     NKPGCTN[ KPFGRGPFGPV XGEVQTU KP 7                   #   2 ' ‰ (   CPF 2 ' ˆ (

     6JGP VJG UGV ]H W Г H W Г Г H WP _                 

     KU NKPGCTN[ KPFGRGPFGPV KHH                         $   2 '% ‰ (   CPF 2 ' ˆ (

     #    H KU QPG QPG CPF QPVQ                                


     $    H KU QPG QPG                                    %   2 ' ‰ (%   CPF 2 ' ˆ (%

                                                               
     %    H KU QPVQ

                                                           2 ' ‰ (   CPF 2 '% ˆ (
      7  8
                                                               
            §                       ·
 .GV #  ¨                        ¸ DG         .GV ' CPF ( DG VYQ KPFGRGPFGPV CPF
            ¨                            ¸
            ©                       ¹
                                                         OWVWCNN[ GZENWUKXG GXGPVU 9JKEJ QH
     C OCVTKZ QH VTCPUHQTOCVKQP 6JGP VJG
                                                         VJG HQNNQYKPI UVCVGOGPVU KU PQV
     TCPM QH # KU GSWCN VQ 
                                                         EQTTGEV !

     #                                                   #   'KVJGT 2 '   QT 2 (  

     $                                                   $   'KVJGT 2 '   QT 2 (  

     %                                                   %   2'  2' ‰ (  2(

                                                         2 '^(  2 '

                                                                                     =261
#7) ++

 .GV : CPF ; DG VYQ KPFGRGPFGPV                      6JG QRVKOCNKV[ QH C DCUKE HGCUKDNG
    2QKUUQP TXU YKVJ RCTCOGVGTU O CPF
                                                           UQNWVKQP QH C VTCPURQTVCVKQP RTQDNGO
    T TGURGEVKXGN[ 9JKEJ QH VJG
                                                           KU EJGEMGF D[ 
    HQNNQYKPI UVCVGOGPVU KU PQV EQTTGEV !
                                              
                                   O      T                 # )TCRJKECN OGVJQF
     # 2=:     ;  ?  G O T
                                        
                                                            $ 5VGRRKPI UVQPG OGVJQF
                                       O  T 
     $ 2=:  ;  ?  G OT           
                                                            % %WVVKPI RNCPG OGVJQF
                                  
                                              OM
     % 2=:  ^ ;  ?         ¦G
                                  M 
                                         O

                                              M
                                                             $TCPEJ CPF DQWPF OGVJQF

                                                        6JG QRVKOCN UQNWVKQP QH VJG NKPGCT
      2=:  ^:           ;  ? 
                                                           RTQITCOOKPI RTQDNGO 
          
             OT   


          TГ O      
                                                           /CZKOKG   Z       Z
 .GV : DG C PQTOCN TCPFQO XCTKCDNG
                                                           5WEJ VJCV Z       Z  
    YKVJ OGCP  CPF XCTKCPEG  GHKPG

    VJG GXGPVU '  ]  :  _Г                                      Z  Z        

    (  ]  :  _ CPF )  ]  :  _
                                                                      ZГ Z     
    9JKEJ QH VJG HQNNQYKPI UVCVGOGPVU

    KU EQTTGEV !                                            # KU WPDQWPFGF

     # 2'  2(  2)                                         $ KU KPHGCUKDNG
     $ 2(  2'  2)
                                                            % KU Z   Z  
     % 2'  2(  2)

      2)  2'  2(                                          KU Z   Z
#7) ++
                                                                   
                 f
                                                     H Z  GZ Г Z z Г Z  4
 6JG UGTKGU   ¦C 
                 P 
                        P
                            P
                                TGRTGUGPVU CP
                                                                    Г Z  
    GPVKTG HWPEVKQP KHH 
                                                        6JGP 
                   
     #   NKO ^ CP ^ P       
         Po f                                           #   H KU QPN[ C % HWPEVKQP
                   
     $   NKO ^ CP ^ P       
         Po f                                           $   H KU TGCN CPCN[VKE CV 
                   
     %   NKO ^ CP ^ P KU C HKPKVG RQUKVKXG              %   H KU PQYJGTG TGCN CPCN[VKE
         Po f


         TGCN PWODGT                                     H KU C %f HWPEVKQP
                   
        NKO ^ CP ^ P       f                                         1T
         Po f


                   1T                                .GV : DG C TCPFQO XCTKCDNG YKVJ

                                                        OGCP  CPF XCTKCPEG  9JKEJ QH
 .GV : DG C PQTOCN TCPFQO XCTKCDNG
                                                        VJG HQNNQYKPI KU PQV EQTTGEV !
    YKVJ OGCP  CPF XCTKCPEG 
                                                        #   : ECP PQV HQNNQY C $KPQOKCN

    6JGP                                                   FKUVTKDWVKQP

                                                        $   : ECP PQV HQNNQY C 2QKUUQP
     # '=EQU :?  G
                                                            FKUVTKDWVKQP
     $ '=EQU :?  
                                                        %   : ECP PQV HQNNQY CP GZRQPGPVKCN

     % '=EQU :?                                          FKUVTKDWVKQP

                                                         : ECP PQV HQNNQY C PQTOCN
      '=EQU :?  G
                                                            FKUVTKDWVKQP

                                                                                     =261
#7) ++
            ª º            f                                           
 +H #P  « Г » Г VJGP                         .GV CP   Г
            ¬P ¼            #
                            P 
                                  P
                                      KU 
                                                                       P
                                                                             Г P KU GXGP

                                                                        
     #   Г                                                              Г P KU QFF
                                                                       P

     $   Г ?                                       6JGP 

                                                     #   NKO CP ! NKO CP
     % =Г ?                                            Po f          Po f


      =Г                                          $   NKO CP        NKO CP     
                                                         Pof           Pof

                  1T
                                                     %   NKO CP CPF NKO CP DQVJ FQ PQV
                                                         Pof        Pof
 .GV : HQNNQYU C 2QKUUQP FKUVTKDWVKQP                 GZKUV

    YKVJ RCTCOGVGT O 6JG GUVKOCVQT                     NKO CP        NKO CP     

    6 KU FGHKPGF CU 6   KH :   CPF                                 1T
                                                  .GV :Г :Г  :P DG C TCPFQO
    6  Г QVJGTYKUG 9JKEJ QH VJG                   UCORNG HTQO QPG RCTCOGVGT
                                                                                           P
    HQNNQYKPI UVCVGOGPVU KU HCNUG !
                                                     GZRQPGPVKCN HCOKN[ .GV 6            ¦:   K

     # 6 KU WPDKCUGF HQT GO
                                                                                           K 

                                                     6GUV VJG J[RQVJGUKU *  T  T
                                                     CICKPUV *   T z T   6JGP VJG
     $ 8CTKCPEG QH 6 CVVCKPU %TCOOGT
                                                     WPKHQTON[ OQUV RQYGTHWN WPDKCUGF
         4CQ NQYGT DQWPF                             VGUV KU IKXGP D[ 
                                                     #   I:           KH    %  6  %
     % 6 KU PQV WPKHQTON[ OKPKOWO                                           QVJGTYKUG

         XCTKCPEG WPDKCUGF GUVKOCVQT QH              $   I:           KH    6       %
                                                                   KH       6  %
         GO
                                                     %   I:           KH    6  %
      8CTKCPEG QH 6 KU ITGCVGT VJCP                               KH       6       %
                                                      I:             KH    6  % QT 6        %
         %TCOOGT 4CQ NQYGT DQWPF
                                                                            QVJGTYKUG
#7) ++

 +H C CPF D CTG TGCN PWODGTUГ VJGP             %QPUKFGT VJG UGSWGPEG

     UWR ]CГ D_                                                  
                                                     CP   Г         KH P KU GXGP
                                                                  P
          C Г D  ^ C  D^                                        
     #                                                             KH P KU QFF
                                                                 P

          C Г D Г ^ C  D^                           6JGP 
     $
                                                         NKO      NKO CP    
                                                      #   Po f    Pof
          C  D Г ^ C Г D^
     %                                                $   NKO CP  NKO CP
                                                         Po f        Po f


          C  D  ^ C  D^                            %   NKO CP ! NKO CP
                                                          Po f        Po f
     
                 
                                                         NKO CP      NKO CP     
                                                          Po f        Po f

                     1T
                                                                      1T

 .GV :Г :Г  :P DG KKF IGQOGVTKE        6JG TX : JCU $GTPQWNNK FKUVTKDWVKQP

                                                     FGHKPGF D[ 2=:  ?    2=:  ?
     TXU YKVJ RCTCOGVGT R 6JGP VJG
                                                      TГ YJGTG   T   6JG ONG QH
     FKUVTKDWVKQP QH :   /KP : K KU 
                            K
                                                     T DCUGF QP : KU 
     # $KPQOKCN
                                                      #     :

                                                           :
     $ )GQOGVTKE                                      $
                                                              
                                                           :
     % 2QKUUQP                                        %
                                                              

                                                       :
      *[RGTIGQOGVTKE

                                                                                     =261
#7) ++

            ­                ½                                        UKP 
 +H +P  ® Z  4 ^   Z  ¾ Г VJGP                .GV H                Г  z   6JGP CV
            ¯                P¿                                          
         f                                                 Г H JCU 
                + P KU 
     P                                                   # C TGOQXCDNG UKPIWNCTKV[

     # ]_                                                $ C RQNG QH QTFGT 

                                                          % C RQNG QH QTFGT 
     $           I
                                                           C RQNG QH QTFGT 
     % ]Z  4^   Z  _
                                                                         1T

      4                                              .GV :Г :Г  :P DG KKF TCPFQO

                                                         UCORNG        HTQO       VJG   HQNNQYKPI
                             1T
                                                         RTQDCDKNKV[ OCUU HWPEVKQP
 9JKEJ QH VJG HQNNQYKPI FKUVTKDWVKQPU                                
                                                          2=:  Z ?          Z    Г Г 0
                                                                        0
    KU           PQV    CP    GZCEV   UCORNKPI
                                                         6JGP 2=: P  ?Г YJGTG : P 

    FKUVTKDWVKQP !                                       /CZ :K KU 
                                                              K

                                                                  0
     #           F FKUVTKDWVKQP                          #
                                                                  0P

     $ $GVC FKUVTKDWVKQP                                          0
                                                          $
                                                                  P0
     %           V FKUVTKDWVKQP                                   
                                                          %
                                                                  0
      ( FKUVTKDWVKQP                                             P
                                                          
                                                                  0P
#7) ++

                EQU                                                               
     ³
      ^^   
                     
                          F                              +H H 
                                                                          G  
                                                                                             Г  z PS K Г P  Г Г

                                                             Г Г VJGP 
       #        SK                                            #   H JCU TGOQXCDNG UKPIWNCTKVKGU CV
                                                                    PSKГ P  Г Г 
       $ SK                                                  $   H JCU GUUGPVKCN UKPIWNCTKVKGU CV
                                                                    PSKГ P  Г Г 
       % SK                                                  %   H JCU FQWDNG RQNGU CV VJG QOKVVGF
                                                                  RQKPVU CV YJKEJ VJG TGUKFWG KU
       SK                                                    GTQ
                                                               H JCU RQNGU CV   PSKГ P  Г
                               1T
                                                                  Г Г 

 .GV [  Г [  DG VYQ KPFGRGPFGPV                                                    1T
                                                          +P C VYQ YC[ ENCUUKHKECVKQP OQFGN
      QDUGTXCVKQPU JCXKPI GZRGEVCVKQPU
                                                             YKVJ GSWCN QDUGTXCVKQPU RGT EGNNГ
      ' [  T                TГ ' [  T  TГ           ' [KLM  z                JKL CPF 8 [KLM
                                                                                       DK          EL
                                                              V K  C L  Г D
      8 [  8 [  V T CPF T  CTG
                        Ž      Ž
                                                             M  E 9JKEJ RCTCOGVTKE HWPEVKQP
      NGCUV USWCTGU GUVKOCVQTU QH T CPF
                                                             KU GUVKOCDNG !
      T  TGURGEVKXGN[ 9JKEJ QH VJG                          #   ¦E DK
                                                                          K    K       YJGTG 6EK  

      HQNNQYKPI UVCVGOGPVU KU HCNUG !
                                                              $   ¦F EL
                                                                          L    L       YJGTG 6FL  
       #        Ž
                T        [ Г [ 
                                                              %   z       DK                EL
       $          Ž
                8 T          Ž
                            8 T        V

       %        Ž
                T        [  [ 
                                                                  ¦¦ H
                                                                      K   L
                                                                                       KL   J KL    YJGTG
                                                                                                             ¦H
                                                                                                              K
                                                                                                                  KL




                   Ž Ž
                %QX T Г T                                       ¦H L
                                                                          KL           


                                                                                                              =261
#7) ++


 .GV 0 DG C FGNGVGF PGKIJDQWTJQQF                               1T


    QH  6JGP EQTTGEV UVCVGOGPV HTQO
                                                 +P   QPG YC[     #018#      YKVJ    P

    VJG HQNNQYKPI KU 
                                                    QDUGTXCVKQPU CPF  VTGCVOGPVUГ VJG

    #    KU C TGOQXCDNG UKPIWNCTKV[ QH
                                                    GZRGTKOGPVGT YJKNG ECNEWNCVKPI VJG

        H KH H KU CPCN[VKE CPF WPDQWPFGF
                                                    ( TCVKQ HQTIQV VQ FKXKFG VJG UWO QH

        KP 0
                                                    USWCTGU D[ VJG EQTTGURQPFKPI


    $    KU C TGOQXCDNG UKPIWNCTKV[ QH            FGITGGU QH HTGGFQO *QYGXGT VJG


        H KH H KU CPCN[VKE CPF DQWPFGF              UVCVKUVKEKCP UCKF VJGTG KU PQ OKUVCMGГ


        KP 0                                        DGECWUG 


    %    KU C TGOQXCDNG UKPIWNCTKV[ QH
                                                    #    P  

        H KH  o     H  z 
             NKO
                                                    $    P  

      KU C TGOQXCDNG UKPIWNCTKV[ QH
                                                    %    P  
        H KH NKO    H     FQGU PQV
                 o 



        GZKUV                                        P
#7) ++

 6JG HWPEVKQP H   ^^Г   %
                                 ^
                                                       H        G  Г   % KU 
                                                                              ^


    KU 
                                                          #     CPCN[VKE KP %
                                                                            ^

    # EQPVKPWQWU CPF FKHHGTGPVKCDNG
                                                          $     CPCN[VKE QPN[ KP VJG WRRGT JCNH
           GXGT[YJGTG
                                                                RNCPG
    $ GXGT[YJGTG EQPVKPWQWU DWV
                                                          %     CPCN[VKE KP VJG HKTUV SWCFTCPV
           PQYJGTG FKHHGTGPVKCDNG

                                                           CPCN[VKE PQYJGTG KP %
                                                                                ^
    % EQPVKPWQWU GXGT[YJGTG DWV

           FKHHGTGPVKCDNG QPN[ CV VJG QTKIKP                               1T

     PGKVJGT           EQPVKPWQWU      PQT          .GV T FGPQVG VJG OKPKOWO PWODGT

           FKHHGTGPVKCDNG CP[YJGTG                        QH VKOGU CP[ VTGCVOGPV KU TGRNKECVGF

                     1T                                   KP EQORNGVGN[ TCPFQOKUGF FGUKIP

 +P C 4$ YKVJ  DNQEMU CPF                           YKVJ X VTGCVOGPVU CPF P RNQVU

    VTGCVOGPVUГ PWODGT QH RNQVU KP GCEJ                   9JKEJ QH VJG HQNNQYKPI UVCVGOGPVU

    DNQEM KU                                             KU CNYC[U VTWG !

    #                                                   #     T  X

    $                                                    $     T    KPVGIGT RCTV QH PX

    %                                                    %     T  KPVGIGT RCTV QH PX        

     
                                                           T  KPVGIGT RCTV QH PX

                                                                                         =261
#7) ++

                                                               9JKEJ QH VJG HQNNQYKPI UVCVGOGPVU
 +H               Г         K Г VJGP         KU 
                            
                                                                    KU VTWG !
                     K
    #                                                                # 'XGT[ ITQWR KU KUQOQTRJKE VQ C
                
                                                                          RGTOWVCVKQP ITQWR
           Г          K
    $
                                                                    $ # ITQWR ) KU KUQOQTRJKE VQ C

            Г         K                                                RGTOWVCVKQP ITQWR KHH KV KU HKPKVG
    %
                   
                                                                     % # ITQWR ) KU EQOOWVCVKXG KHH KV
                     K
                                                                         KU E[ENKE
                   
                                                                      # ITQWR ) KU PQP CDGNKCP KHH
                             1T
                                                                          QTFGT QH ) KU PQV RTKOG
 +P C 4$ YKVJ D DNQEMU CPF X
                                                                                      1T
    VTGCVOGPVU YJKEJ QH VJG HQNNQYKPI
                                                                 9JGP FGUKTGF KPHQTOCVKQP KU
    UVCVGOGPVU CNYC[U JQNFU !                                       CXCKNCDNG HQT CNN QDLGEVU KP VJG

                                                                    RQRWNCVKQPГ YG JCXG YJCV KU ECNNGF
    #      D       X
                                                                    C 
    $      D  X
                                                                     # %GPUWU
    %      D  X
                                                                     $ 2QRWNCVKQP

     D CPF X CTG CTDKVTCT[ RQUKVKXG                                 % 5CORNG

           KPVGIGTU                                                   5VGO CPF NGCH FKURNC[
#7) ++

 .GV ) DG C ITQWR QH QTFGT                    6JG TKPI QH ª OCVTKEGU QXGT  
    6JGP                                               #   KU EQOOWVCVKXG
     #   F^Q ) KORNKGU ) JCU C WPKSWG
                                                        $   KU CP KPVGITCN FQOCKP
         UWDITQWR QH QTFGT F
     $ )      JCU   QPN[   QPG      PQTOCN              %   JCU PQP GTQ GTQ FKXKUQTU
         UWDITQWR                                        KU C HKGNF
     % ) JCU VYQ UWDITQWRU QH QTFGT
                                                                       1T
          CPF QPG UWDITQWR QH QTFGT 
        G KU VJG QPN[ RTQRGT UWDITQWR              9JKEJ QH VJG HQNNQYKPI UVCVGOGPVU
         QH )                                          KPXQNXGU FGUETKRVKXG UVCVKUVKEU CU
                    1T                                 QRRQUGF VQ KPHGTGPVKCN UVCVKUVKEU !
 9JKEJ QH VJG HQNNQYKPI UVCVGOGPVU                   #   6JG (## UCORNGU  VTCHHKE
    KU HCNUG !                                              EQPVTQNNGTU KP QTFGT VQ GUVKOCVG
     # #NN EQORCPKGU NKUVGF QP VJG 0GY                      VJG RGTEGPV TGVKTKPI FWG VQ LQD
         ;QTM 5VQEM 'ZEJCPIG KU CP                          UVTGUU TGNCVGF KNNPGUU
         GZCORNG QH C UCORNG
                                                        $   $CUGF QP UCORNG QH 
     $ +P GPWOGTCVKXG UVWFKGUГ KPVGTGUV
                                                            RTQHGUUKQPCN VGPPKU RNC[GTUГ C
         KU   HQEWUUGF     QP   C   HKPKVGГ
                                                            VGPPKU OCICKPG TGRQTVGF VJCV
         KFGPVKHKCDNGГ      WPEJCPIKPI
                                                                 QH VJG RCTGPVU QH CNN
         EQNNGEVKQP QH KPFKXKFWCNU QT
                                                            RTQHGUUKQPCN VGPPKU RNC[GTU FKF
         QDLGEVU    VJCV   OCMG      WR   C
                                                            PQV RNC[ VGPPKU
         RQRWNCVKQP
     % # UCORNKPI HTCOG KU C NKUVKPI QH                 %   6JG #NEQJQNГ 6QDCEEQ CPF
         VJG KPFKXKFWCNU QT QDLGEVU VQ DG                   (KTGCTOU GRCTVOGPV TGRQTVGF
         UCORNGF                                            VJCV   *QWUVQP     JCF        Г
      #NN RQUUKDNG [KGNFU KP ITCOU                         TGIKUVGTGF IWP FGCNGTU KP 
         HTQO C EGTVCKP EJGOKECN TGCEVKQP                $CUGF        QP UWTXG[     QH    
         ECTTKGF QWV KP C NCDQTCVQT[ KU CP                  OCICKPG        TGCFGTUГ        VJG
         GZCORNG QH EQPEGRVWCN QT                           OCICKPG TGRQTVU VJCV        QH KVU
         J[RQVJGVKECN RQRWNCVKQP                            TGCFGTU RTGHGT FQWDNG EQNWOP
                                                            CTVKENGU

                                                                                     =261
#7) ++

 .GV ( DG C HKGNF YKVJ C HKPKVG PWODGT         .GV / DG C RTQRGT KFGCN QH C $QQNGCP

    QH GNGOGPVU 6JGP                               TKPI 4 %QPUKFGT VJG HQNNQYKPI

     # VJG QTFGT QH ( OC[ DG                        UVCVGOGPVU 

                                                           4
     $ VJG QTFGT QH ( OC[ DG                        +        KU C $QQNGCP TKPI
                                                           /
                                                           4        
     % VJG QTFGT QH ( KU RTKOG                        ++       #        KHH / KU C OCZKOCN
                                                           /        

      VJG EJCTCEVGTKUVKE QH ( KU GTQ                     KFGCN

                   1T                                6JGP 

                                                      # $QVJ + CPF ++ JQNF
 ;QW CUMGF VGP QH [QWT ENCUUOCVGU
                                                      $ 1PN[ + JQNFU
    CDQWV VJGKT YGKIJV 1P VJG DCUKU QH
                                                      % 1PN[ ++ JQNFU
    VJKU KPHQTOCVKQPГ [QW UVCVGF VJCV VJG
                                                       $QVJ + CPF ++ CTG HCNUG
    CXGTCIG YGKIJV QH CNN UVWFGPVU KP
                                                                        1T
    [QWT EQNNGIG KU  RQWPFU 6JKU KU

    CP GZCORNG QH                                6JG OGCUWTG OQUV WPCHHGEVGF D[

                                                     QWVNKGTU KU VJG 
     # KPHGTGPVKCN UVCVKUVKEU
                                                      # OGFKCP
     $ UCORNG
                                                      $ VTKOOGF OGCP
     % RQRWNCVKQP
                                                      % OGCP

      FGUETKRVKXG UVCVKUVKEU                          TCPIG
#7) ++
 .GV 4 DG CP KPVGITCN FQOCKP CPF                                   1T
    4=Z? DG VJG RQN[PQOKCN TKPI QXGT 4
    6JGP                                         #V C EGTVCKP ECT UGTXKEG UVCVKQP YKVJ

     # 4=Z? KU CP 'WENKFGCP FQOCKP                   UGTXKEG HCEKNKV[ HQT QPN[ QPG ECT CPF
                                                     PQ YCKVKPI URCEGГ ECTU CTTKXG HQT
     $ +H GXGT[ KFGCN QH 4 KU RTKPEKRCN
       VJGP UQ KU VTWG HQT 4=Z?                      UGTXKEG KP 2QKUUQP OCPPGT CV VJG
                                                     TCVG QH QPG RGT JQWT CPF UGTXKEG VKOG
     % 4=Z? KU CP KPVGITCN FQOCKP
                                                     KU CNUQ GZRQPGPVKCN YKVJ CP CXGTCIG
      4=Z? KU C HKGNF
                                                     QPG JQWTГ YKVJ KPFGRGPFGPEG QH
                   1T
                                                     UGTXKEG VKOGU CPF KPVGTCTTKXCN VKOGUГ
 6JG CXGTCIG UEQTG HQT C ENCUU QH               VJG RTQDCDKNKV[ VJCV CP KPEQOKPI
    UVWFGPVU YCU  +H VJG  HGOCNG
                                                     ECT HKPFU VJG UGTXKEG HCEKNKV[ CXCKNCDNG
    UVWFGPVU KP C ENCUU CXGTCIGF Г VJGP
    VJG OCNG UVWFGPVU KP VJG ENCUU                   KU 
    CXGTCIGF 
                                                            
     #                                            #
                                                            
     $ 
     %                                            $     G
      
                                                            
 %QPUKFGT VJG        HQNNQYKPI    VYQ              %
    UVCVGOGPVU                                             

     +   +H # KU C VTKCPIWNCT OCVTKZ CPF               0QPG QH VJG CDQXG
         PQ GPVT[ QP VJG OCKP FKCIQPCN
         KU GTQГ VJGP # KU UKPIWNCT             +H VJG VTCPUHQTOCVKQP 6  4P o 4
     ++ +H # KU VTKCPIWNCT OCVTKZ CPF CP             KU FGHKPGF D[ 6 :  : #:Г YJGTG #
        GPVT[ QP VJG OCKP FKCIQPCN KU                KU CP[ P ª P U[OOGVTKE OCVTKZГ VJGP
        GTQГ VJGP # KU KPXGTVKDNG                  6:         ; KU GSWCN VQ 
    6JGP 
                                                      #     6:      : #;    6;
     # QPN[ + KU VTWG
                                                      $     6:      6;
     $ QPN[ ++ KU VTWG
                                                      %     6:      : #;    6;
     % DQVJ + CPF ++ CTG VTWG
      DQVJ + CPF ++ CTG HCNUG                         6:          ; #:    6;

                                                                                    =261
#7) ++
                    1T
                                                   .GV 6 DG VJG NKPGCT VTCPUHQTOCVKQP
 6JG UVCHH TGRNCEGOGPV RQNKE[ KP
    TGRNCEGOGPV OQFGN 
                                                      QP 4 TGRTGUGPVGF D[ VJG OCVTKZ
     # CTKUGU FWG VQ TGUKIPCVKQPГ
       TGVKTGOGPVГ QT FGCVJ QH C UVCHH                §     ·
       OGODGT HTQO VKOG VQ VKOG                       ¨
                                                      ©        ¸ Г VJGP VJG EJCTCEVGTKUVKE
                                                              ¹
     $ KU NKMG TGRNCEGOGPV RQNKE[ HQT
       KVGOU YJQUG XCNWGU FGVGTKQTCVG                 XCNWGU QH 6 CTG 
       ITCFWCNN[
     % ECP DG GCUKN[ HQTOWNCVGF                        # Г 
       DGECWUG RGQRNG TGVKTG CV MPQYP
       VKOG
      FQGU PQV [KGNF VJG QRVKOWO                      $ Г 
       TGRNCEGOGPV KPVGTXCN

            §           ·                            % Г K
 .GV #  ¨             ¸ DG VJG OCVTKZГ
            ©          ¹
    VJGP VJG EQTTGURQPFKPI SWCFTCVKE                    KГ K
    HQTO KU 
     #   Z  [
                                                                   1T
     $   Z   Z[     [
     %   Z   [
                                                   # OKZGF UVTCVGI[ ICOG KP )COG
      Z     Z[        [
                    1T                                VJGQT[ ECP DG UQNXGF D[ 
 9JKEJ QH VJG HQNNQYKPI KU PQV CP
    CUUWORVKQP    WPFGTN[KPI     VJG
    HWPFCOGPVCN RTQDNGO QH '13 KP                      # /CVTKZ OGVJQF
    +PXGPVQT[ /QFGN !
     # GOCPF KU MPQYP CPF WPKHQTO                     $ )TCRJKECN OGVJQF
     $ *QNFKPI EQUV RGT WPKV RGT VKOG
       RGTKQF KU EQPUVCPV
                                                       % #NIGDTCKE OGVJQF
     % .GCF VKOG KU PQV GTQ
      5VQEM QWVU 5JQTVCIGU CTG PQV
       RGTOKVVGF                                        #NN QH VJG CDQXG
#7) ++

 .GV RГ SГ T   +H VJG XGEVQTU                        .GV D  Г  Г D  Г   4 CPF
                                                                  E  Г Г  Г E  Г Г   4
     § R·    § S·     §T·                                     .GV 6 DG C NKPGCT VTCPUHQTOCVKQP
     ¨ S¸Г   ¨ T ¸Г   ¨ R¸
     ¨ ¸     ¨ ¸      ¨ ¸       CTG     OWVWCNN[              HTQO 4 KPVQ 4 UWEJ VJCV 6DK  EK
     ©T¹     © R¹     © S¹
                                                                 K  Г  6JGP 

    QTVJQIQPCN KP 'WENKFGCP URCEG 4                                        §                                 ·
                                                               #   6 ZГ [  ¨ ZГ Z Г [Г  Z Г [ ¹
                                                                            ©                  ¸
                                                                                            
    VJGP 

     #   R           S     T                                           §                                   ·
                                                               $   6 ZГ [  ¨ Z Г [Г Z  [Г  Z Г [ ¹
                                                                            ©                      ¸
                                                                                        
     $   R           S     T z 
                                                                                §                           ·
     %   RS           ST     TR z                             %   6 ZГ [  ¨        [Г Z Г       [Г  Z        [¸
                                                                            ©                               ¹
      RS             ST     TR  
                                                                5WEJ C NKPGCT VTCPUHQTOCVKQP
                           1T                                      FQGU PQV GZKUV

 9JKEJ QH VJG HQNNQYKPI KU PQV QPG QH                                        1T
                                                           +P C OWNVK UVCIG UCORNKPI 
    VJG RTKPEKRNGU QH UCORNKPI !
                                                               #   VJG UCOG PWODGT QH RGQRNG CTG
     # 5CORNKPI                 WPKVU   OWUV   DG                  UVWFKGF OQTG VJCP QPEG
         KFGPVKHKCDNG CPF ENGCTN[ FGHKPGF                      $   FKHHGTGPV TGURQPFGPVU CTG
     $ 5CORNKPI                 WPKVU   CTG    PQV                 UVWFKGF OQTG VJCP QPEG
                                                               %   C UGSWGPEG QH UCORNGU CTG
         KPVGTEJCPIGCDNG
                                                                   FTCYP HTQO CNTGCF[ UGNGEVGF
     % 5CORNKPI                 WPKVU   OWUV   DG                  UCORNGU DWV QPN[ VJG NCUV
         KPFGRGPFGPV QH GCEJ QVJGT                                 UCORNG KU UVWFKGF
                                                                C UGSWGPEG QH UCORNGU CTG
      5CORNKPI                 WPKVU   OWUV   DG
                                                                   FTCYP HTQO CNTGCF[ UGNGEVGF
         TGRTGUGPVCVKXG CPF KPENWFG
                                                                   UCORNGU CPF GCEJ QPG QH VJGO
         OCNGU CPF HGOCNGU                                         KU UVWFKGF

                                                                                                     =261
#7) ++

 %QPUKFGT            VJG   HQNNQYKPI   VYQ                          1T
     UVCVGOGPVU                                      6JG VKOG TGSWKTGF VQ CUUGODNG CP
                                                         GNGEVTQPKE EQORQPGPV KU PQTOCNN[
     +     +H # KU C PKNRQVGPV OCVTKZ VJGP
                                                         FKUVTKDWVGF YKVJ C OGCP QH 
           +    # KU PQP UKPIWNCT
                                                         OKPWVGU CPF C UVCPFCTF FGXKCVKQP QH
     ++    # KU VTKCPIWNCT OCVTKZ YKVJ CNN                OKPWVGU (KPF VJG RTQDCDKNKV[
           FKCIQPCN GNGOGPVU CTG GTQГ                   VJCV VJG VKOG TGSWKTGF VQ CUUGODNG
           VJGP # KU PKNRQVGPV                          PKPG EQORQPGPVU KU ITGCVGT VJCP 
     6JGP                                               OKPWVGU 
     # 1PN[ + KU VTWG                                     # 
                                                          $ 
     $ 1PN[ ++ KU VTWG
                                                          % 
     % $QVJ + CPF ++ CTG VTWG                              
      $QVJ + CPF ++ CTG HCNUG                        .GV I  Г I DG VYQ NKPGCTN[
                    1T                                   KPFGRGPFGPV UQNWVKQPU QH VJG
 +P C UVWF[ QH CVVKVWFGU VQ 7PKXGTUKV[                EQPUVCPV EQGHHKEKGPV GSWCVKQP [
    RQNKEKGUГ C TGUGCTEJGT KPKVKCNN[ EJQUG               C[ C[   6JGP VJG 9TQPUMKCP
     HKTUV [GCT UVWFGPVUГ  UGEQPF                  QH IГ I KU EQPUVCPV KH CPF QPN[
    [GCT UVWFGPVU CPF  VJKTF [GCT                     KH 
    UVWFGPVU 6JGP VJG TGUGCTEJGT
                                                          # C  
    UGNGEVGF  OCNG CPF  HGOCNG
                                                          $ C  
    UVWFGPVU HTQO GCEJ [GCT ITQWRГ YJQ
    YGTG HKPCNN[ KPVGTXKGYGF 6JG                         % C  
    UCORNKPI RTQEGFWTG WUGF KP VJKU                        C      
    UVWF[ YCU                                                         1T
     # 2TQDCDKNKV[ UCORNKPI                           6JG EGPVTCN NKOKV VJGQTGO VGNNU WU
     $ 5VTCVKHKGF UCORNKPI                               VJCV VJG UCORNKPI FKUVTKDWVKQP QH VJG
     % /WNVK UVCIG UCORNKPI                              OGCP KU CRRTQZKOCVGN[ PQTOCN
      /WNVK RJCUG UCORNKPI                              9JKEJ QH VJG HQNNQYKPI EQPFKVKQPU KU
 6JG EQORNGVG UQNWVKQP QH VJG RCTVKCN                 PGEGUUCT[ HQT VJG VJGQTGO VQ DG
    FKHHGTGPVKCN GSWCVKQP                                XCNKF !
          w       w                                     # 6JG UCORNG UKG JCU VQ DG NCTIG
               Г  UKP Z    UKP [
        wZ  w[                                            $ 6JG RQRWNCVKQP XCTKCPEG JCU VQ
     KU                                                      DG UOCNN
      # C Z [       UKP Z  UKP [       D               % 9G OWUV DG UCORNKPI HTQO C
      $   C Z  [  EQU Z EQU [         D                   PQTOCN RQRWNCVKQP
      %   C Z [  UKP Z  EQU [         D                6JG RQRWNCVKQP JCU VQ DG
         C Z  [  EQU Z  UKP [       D                   U[OOGVTKE
#7) ++
 6JG EJCTCEVGTKUVKE EWTXG QH VJG VYQ                            1T
                                                9KUJCTV       FKUVTKDWVKQP      KU   C
    RCTCOGVGT HCOKN[ QH UWTHCEGU
                                                   OWNVKXCTKCVG IGPGTCNKCVKQP QH 
     Z  C    [  D         KU               # PQTOCN FKUVTKDWVKQP
                                                    $ DGVC FKUVTKDWVKQP
     # C EKTENG
                                                    % OCVTKZ DGVC FKUVTKDWVKQP
     $ C ITGCV EKTENG                                EJK USWCTG FKUVTKDWVKQP
                                                6JG KPKVKCN XCNWG RTQDNGO
     % JGNKZ                                       [  H ZГ [ Г [ Z  [Г YJGTG ZГ [
                                                   DGNQPIU VQ C FQOCKP Г JCU WPKSWG
      GNNKRUG                                     UQNWVKQP 
                  1T                                # KH H ZГ [ KU EQPVKPWQWU KP 
                                                    $ KH H ZГ [ KU EQPVKPWQWU CPF
 # ECPQPKECN EQTTGNCVKQP ECPPQV DG                   DQWPFGF QP 
    PGICVKXG DGECWUG                               % KH H ZГ [ KU EQPVKPWQWU CPF
                                                        UCVKUHKGU .KRUEJKV EQPFKVKQP HQT
     # YG VCMG QPN[ RQUKVKXG GKIGP                      CNN RQKPVU QP 
       XCNWGU                                        HQT CNN HWPEVKQPU H ZГ [ QP 
                                                                   1T
     $ KV KU IGPGTCNKCVKQP QH VJG              9JKEJ QH VJG HQNNQYKPI UVCVGOGPVU
       OWNVKRNG EQTTGNCVKQP                        CTG VTWG HQT VJG HQNNQYKPI FCVC XCNWGU
                                                   Г Г Г Г Г  CPF  !
     % YG VCMG QPN[ RQUKVKXG USWCTG                 # 6JG OGCP KU UOCNNGT VJCP VJG
       TQQV                                             OGFKCP
                                                    $ 6JG OGCP CPF VJG  VTKOOGF
      YG TGLGEV C PGICVKXG XCNWG                       OGCP CTG GSWCN
                                                    % 6JG OGCP CPF OGFKCP CTG GSWCN
 .GV IГ I DG VYQ FKHHGTGPVKCDNG                 6JG OGCP KU NCTIGT VJCP VJG
    HWPEVKQPU QP CP KPVGTXCN + VJGP                     OGFKCP
                                                +H VJG PWODGT QH EQPUVCPVU CTG VQ DG
     +   9 IГ I Z   Z  + Ÿ IГ                GNKOKPCVGF HTQO VJG IKXGP TGNCVKQP
         I CTG NKPGCTN[ FGRGPFGPV                 KU LWUV GSWCN VQ VJG PWODGT QH
                                                   KPFGRGPFGPV XCTKCDNGUГ VJGP VJG
     ++ 9 IГ I Z z  Z  + Ÿ IГ                 RCTVKCN FKHHGTGPVKCN GSWCVKQP
        I CTG NKPGCTN[ KPFGRGPFGPV                QDVCKPGF D[ GNKOKPCVKPI VJGUG
                                                   EQPUVCPVU 
    6JGP                                           # KU CNYC[U C NKPGCT GSWCVKQP QH
                                                        HKTUV QTFGT
     # 1PN[ + KU VTWG                               $ ECP DG C PQP NKPGCT GSWCVKQP QH
     $ 1PN[ ++ KU VTWG                                  HKTUV QTFGT
                                                    % KU C NKPGCT GSWCVKQP QH UGEQPF
     % $QVJ + CPF ++ CTG VTWG                           QTFGT
                                                     KU C PQP NKPGCT GSWCVKQP QH
      $QVJ + CPF ++ CTG HCNUG                          UGEQPF QTFGT

                                                                                =261
#7) ++

                                           1T                                 6JG UQNWVKQP QH C JQOQIGPGQWU

 .GV :Г :Г  DG C UGSWGPEG QH                                         KPKVKCN     XCNWG       RTQDNGO      YKVJ

    KPFGRGPFGPV                                 CPF       KFGPVKECNN[           EQPUVCPV EQGHHKEKGPV KU [  ZGZ

    FKUVTKDWVGF TXU YKVJ VJG EQOOQP                                           EQU Z 6JGP VJG NGCUV RQUUKDNG
                                                                                QTFGT QH VJG FKHHGTGPVKCN GSWCVKQP
    RFH IKXGP D[
                       ­                                                       KU 
                       ° Z Г
                       °
                                  Z  
    HZ                ®                                                         # 
                       °
                       ° Г
                       ¯      QVJGTYKUG
                                                                                 $ 
    %QPUKFGT VJG UVCVGOGPVU 
                                                                                 % 
               P
                                                      
     +     ¦ : P    CU P o f
           K
                   2
                   
                     o     K
                                                                                  

                                                                                                   1T
               P
                                  
     ++    ¦
           K       
                             2
                     : K  P   CU P o f
                                o
                                  
                                                                              6JG TCPFQO XCTKCDNGU : CPF ;
                                                                                CUUWOG QPN[  XCNWGU GCEJГ CPF
                                   P                                            EQX :Г ;   6JGP 
                                          §      ·
     +++
           P           
                               ¦
                               K       
                                            ©      
                                                     ¸
                                                       F
                                            ¨ : K  ¹ o
                                                                                 # :      CPF      ;    PGGF   PQV    DG
           0 Г  CU P o f                                                             KPFGRGPFGPV
    6JGP 
                                                                                 $ : CPF ; CTG KPFGRGPFGPV
     # #NN UVCVGOGPVU CTG VTWG
                                                                                 % : CPF ; CTG KPFGRGFGPV QPN[
     $ 1PN[ UVCVGOGPVU + CPF ++ CTG
                                                                                       KH HQWT XCNWGU CTG  CPF  HQT
       VTWG
                                                                                       DQVJ : CPF ;
     % 1PN[ UVCVGOGPVU + CPF +++ CTG
       VTWG                                                                       6JG NKPG KU RCTCNNGN VQ ; CZKU
      1PN[ UVCVGOGPV + KU VTWG                                                        QT : CZKU
#7) ++
528*+ :25.




                  =261
#7) ++
528*+ :25.

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Set paper 2

  • 1. #7) ++ /CVJGOCVKECN 5EKGPEGU 2CRGT ++ 6KOG #NNQYGF /KPWVGU? =/CZKOWO /CTMU 0QVG 6JKU 2CRGT EQPVCKPU (KHV[ OWNVKRNG EJQKEG SWGUVKQPU 'CEJ SWGUVKQP ECTTKGU 6YQ OCTMU #VVGORV #NN SWGUVKQPU %QPUKFGT VJG VYQ UVCVGOGPVU HQT 6JG UGIOGPV CГ D QH VJG Z CZKU QH  % ^ 4 KU C G KU C QPG QPG HWPEVKQP D UKP KU DQWPFGF GPVKTG HWPEVKQP # 0GKVJGT QRGP PQT ENQUGF VJGP $ 1RGP # DQVJ C CPF D CTG HCNUG $ DQVJ C CPF D CTG VTWG % %NQUGF % QPN[ C KU VTWG $QVJ QRGP CPF ENQUGF QPN[ D KU VTWG .GV H GГ YJGTG Z K[Г #P QRGP UGV KP 4 KU VJGP # CP KPVGTXCN # G YJGP [ KU CP GXGP OWNVKRNG QH SГ CPF G YJGP $ HKPKVG WPKQP QH QRGP KPVGTXCNU [ KU CP QFF OWNVKRNG QH S $ G KH [ KU CP QFF OWNVKRNG % EQWPVCDNG WPKQP QH FKULQKPV QRGP QH S KPVGTXCNU KP 4 % G KH [ KU CP GXGP OWNVKRNG QH S KPVGTUGEVKQP QH QRGP KPVGTXCNU G KH [ KU C OWNVKRNG QH S =261
  • 2. #7) ++ H VCP Г  % ^ 9JKEJ QH VJG HQNNQYKPI HWPEVKQPU # CUUWOGU CNN EQORNGZ PWODGTU 6 4 o 4 KU PQV C NKPGCT $ CUUWOGU PQPG QH VJG EQORNGZ VTCPUHQTOCVKQP ! PWODGTU % CUUWOGU CNN EQORNGZ PWODGTU # 6 CГ D C DГ C D GZEGRV K $ 6 CГ D C DГ D CUUWOGU CNN EQORNGZ PWODGTU GZEGRV K CPF K % 6 CГ D CГ D .GV 8 ( DG C XGEVQT URCEG %QPUKFGT 6 CГ D DГ C VJG HQNNQYKPI UVCVGOGPVU + +H DГ EГ J CTG NKPGCTN[ .GV 8 DG C XGEVQT URCEG QXGT C HKGNF KPFGRGPFGPV XGEVQTU KP 8 ( Г ( CPF 6 8 o 8 DG C NKPGCT VJGP D EГ E Г JГ J Г D CTG VTCPUHQTOCVKQP UWEJ VJCV 6 JCU CU CNUQ NKPGCTN[ KPFGRGPFGPV ++ 6JG UGV QH XGEVQTU # Ž 8 ( C EJCTCEVGTKUVKE TQQVГ VJGP YJKEJ EQPVCKPU VJG GTQ XGEVQT # 6 KU FKCIQPCNKCDNG QXGT ( KU CNYC[U NKPGCTN[ KPFGRGPFGPV 6JGP $ /WNVKRNKEKV[ QH GCEJ # $QVJ + CPF ++ CTG VTWG EJCTCEVGTKUVKE TQQV QH 6 KU $ $QVJ + CPF ++ CTG HCNUG % 6 KU KPXGTVKDNG % QPN[ + KU VTWG 6 KU PKNRQVGPV QPN[ ++ KU VTWG
  • 3. #7) ++ .GV H 7 o 8 DG C NKPGCT OCR CPF +H 2 ' CPF 2 ( Г YJKEJ ]WГ WГ Г WP_ DG VJG UGV QH QH VJG HQNNQYKPI KU PQV EQTTGEV ! NKPGCTN[ KPFGRGPFGPV XGEVQTU KP 7 # 2 ' ‰ ( CPF 2 ' ˆ ( 6JGP VJG UGV ]H W Г H W Г Г H WP _ KU NKPGCTN[ KPFGRGPFGPV KHH $ 2 '% ‰ ( CPF 2 ' ˆ ( # H KU QPG QPG CPF QPVQ $ H KU QPG QPG % 2 ' ‰ (% CPF 2 ' ˆ (% % H KU QPVQ 2 ' ‰ ( CPF 2 '% ˆ ( 7 8 § · .GV # ¨ ¸ DG .GV ' CPF ( DG VYQ KPFGRGPFGPV CPF ¨ ¸ © ¹ OWVWCNN[ GZENWUKXG GXGPVU 9JKEJ QH C OCVTKZ QH VTCPUHQTOCVKQP 6JGP VJG VJG HQNNQYKPI UVCVGOGPVU KU PQV TCPM QH # KU GSWCN VQ EQTTGEV ! # # 'KVJGT 2 ' QT 2 ( $ $ 'KVJGT 2 ' QT 2 ( % % 2' 2' ‰ ( 2( 2 '^( 2 ' =261
  • 4. #7) ++ .GV : CPF ; DG VYQ KPFGRGPFGPV 6JG QRVKOCNKV[ QH C DCUKE HGCUKDNG 2QKUUQP TXU YKVJ RCTCOGVGTU O CPF UQNWVKQP QH C VTCPURQTVCVKQP RTQDNGO T TGURGEVKXGN[ 9JKEJ QH VJG KU EJGEMGF D[ HQNNQYKPI UVCVGOGPVU KU PQV EQTTGEV ! O T # )TCRJKECN OGVJQF # 2=: ; ? G O T $ 5VGRRKPI UVQPG OGVJQF O T $ 2=: ; ? G OT % %WVVKPI RNCPG OGVJQF OM % 2=: ^ ; ? ¦G M O M $TCPEJ CPF DQWPF OGVJQF 6JG QRVKOCN UQNWVKQP QH VJG NKPGCT 2=: ^: ; ? RTQITCOOKPI RTQDNGO OT TГ O /CZKOKG Z Z .GV : DG C PQTOCN TCPFQO XCTKCDNG 5WEJ VJCV Z Z YKVJ OGCP CPF XCTKCPEG GHKPG VJG GXGPVU ' ] : _Г Z Z ( ] : _ CPF ) ] : _ ZГ Z 9JKEJ QH VJG HQNNQYKPI UVCVGOGPVU KU EQTTGEV ! # KU WPDQWPFGF # 2' 2( 2) $ KU KPHGCUKDNG $ 2( 2' 2) % KU Z Z % 2' 2( 2) 2) 2' 2( KU Z Z
  • 5. #7) ++ f H Z GZ Г Z z Г Z  4 6JG UGTKGU ¦C P P P TGRTGUGPVU CP Г Z GPVKTG HWPEVKQP KHH 6JGP # NKO ^ CP ^ P Po f # H KU QPN[ C % HWPEVKQP $ NKO ^ CP ^ P Po f $ H KU TGCN CPCN[VKE CV % NKO ^ CP ^ P KU C HKPKVG RQUKVKXG % H KU PQYJGTG TGCN CPCN[VKE Po f TGCN PWODGT H KU C %f HWPEVKQP NKO ^ CP ^ P f 1T Po f 1T .GV : DG C TCPFQO XCTKCDNG YKVJ OGCP CPF XCTKCPEG 9JKEJ QH .GV : DG C PQTOCN TCPFQO XCTKCDNG VJG HQNNQYKPI KU PQV EQTTGEV ! YKVJ OGCP CPF XCTKCPEG # : ECP PQV HQNNQY C $KPQOKCN 6JGP FKUVTKDWVKQP $ : ECP PQV HQNNQY C 2QKUUQP # '=EQU :? G FKUVTKDWVKQP $ '=EQU :? % : ECP PQV HQNNQY CP GZRQPGPVKCN % '=EQU :? FKUVTKDWVKQP : ECP PQV HQNNQY C PQTOCN '=EQU :? G FKUVTKDWVKQP =261
  • 6. #7) ++ ª º f +H #P « Г » Г VJGP .GV CP Г ¬P ¼ # P P KU P Г P KU GXGP # Г Г P KU QFF P $ Г ? 6JGP # NKO CP ! NKO CP % =Г ? Po f Po f =Г $ NKO CP NKO CP Pof Pof 1T % NKO CP CPF NKO CP DQVJ FQ PQV Pof Pof .GV : HQNNQYU C 2QKUUQP FKUVTKDWVKQP GZKUV YKVJ RCTCOGVGT O 6JG GUVKOCVQT NKO CP NKO CP 6 KU FGHKPGF CU 6 KH : CPF 1T .GV :Г :Г :P DG C TCPFQO 6 Г QVJGTYKUG 9JKEJ QH VJG UCORNG HTQO QPG RCTCOGVGT P HQNNQYKPI UVCVGOGPVU KU HCNUG ! GZRQPGPVKCN HCOKN[ .GV 6 ¦: K # 6 KU WPDKCUGF HQT GO K 6GUV VJG J[RQVJGUKU * T T CICKPUV * T z T 6JGP VJG $ 8CTKCPEG QH 6 CVVCKPU %TCOOGT WPKHQTON[ OQUV RQYGTHWN WPDKCUGF 4CQ NQYGT DQWPF VGUV KU IKXGP D[ # I: KH % 6 % % 6 KU PQV WPKHQTON[ OKPKOWO QVJGTYKUG XCTKCPEG WPDKCUGF GUVKOCVQT QH $ I: KH 6 % KH 6 % GO % I: KH 6 % 8CTKCPEG QH 6 KU ITGCVGT VJCP KH 6 % I: KH 6 % QT 6 % %TCOOGT 4CQ NQYGT DQWPF QVJGTYKUG
  • 7. #7) ++ +H C CPF D CTG TGCN PWODGTUГ VJGP %QPUKFGT VJG UGSWGPEG UWR ]CГ D_ CP Г KH P KU GXGP P C Г D ^ C D^ # KH P KU QFF P C Г D Г ^ C D^ 6JGP $ NKO NKO CP # Po f Pof C D Г ^ C Г D^ % $ NKO CP NKO CP Po f Po f C D ^ C D^ % NKO CP ! NKO CP Po f Po f NKO CP NKO CP Po f Po f 1T 1T .GV :Г :Г :P DG KKF IGQOGVTKE 6JG TX : JCU $GTPQWNNK FKUVTKDWVKQP FGHKPGF D[ 2=: ? 2=: ? TXU YKVJ RCTCOGVGT R 6JGP VJG TГ YJGTG T 6JG ONG QH FKUVTKDWVKQP QH : /KP : K KU K T DCUGF QP : KU # $KPQOKCN # : : $ )GQOGVTKE $ : % 2QKUUQP % : *[RGTIGQOGVTKE =261
  • 8. #7) ++ ­ ½ UKP +H +P ® Z  4 ^ Z ¾ Г VJGP .GV H Г z 6JGP CV ¯ P¿ f Г H JCU + P KU P # C TGOQXCDNG UKPIWNCTKV[ # ]_ $ C RQNG QH QTFGT % C RQNG QH QTFGT $ I C RQNG QH QTFGT % ]Z  4^ Z _ 1T 4 .GV :Г :Г :P DG KKF TCPFQO UCORNG HTQO VJG HQNNQYKPI 1T RTQDCDKNKV[ OCUU HWPEVKQP 9JKEJ QH VJG HQNNQYKPI FKUVTKDWVKQPU 2=: Z ? Z Г Г 0 0 KU PQV CP GZCEV UCORNKPI 6JGP 2=: P ?Г YJGTG : P FKUVTKDWVKQP ! /CZ :K KU K 0 # F FKUVTKDWVKQP # 0P $ $GVC FKUVTKDWVKQP 0 $ P0 % V FKUVTKDWVKQP % 0 ( FKUVTKDWVKQP P 0P
  • 9. #7) ++ EQU ³ ^^ F +H H G Г z PS K Г P Г Г Г Г VJGP # SK # H JCU TGOQXCDNG UKPIWNCTKVKGU CV PSKГ P Г Г $ SK $ H JCU GUUGPVKCN UKPIWNCTKVKGU CV PSKГ P Г Г % SK % H JCU FQWDNG RQNGU CV VJG QOKVVGF RQKPVU CV YJKEJ VJG TGUKFWG KU SK GTQ H JCU RQNGU CV PSKГ P Г 1T Г Г .GV [ Г [ DG VYQ KPFGRGPFGPV 1T +P C VYQ YC[ ENCUUKHKECVKQP OQFGN QDUGTXCVKQPU JCXKPI GZRGEVCVKQPU YKVJ GSWCN QDUGTXCVKQPU RGT EGNNГ ' [ T TГ ' [ T TГ ' [KLM z JKL CPF 8 [KLM DK EL V K C L Г D 8 [ 8 [ V T CPF T CTG Ž Ž M E 9JKEJ RCTCOGVTKE HWPEVKQP NGCUV USWCTGU GUVKOCVQTU QH T CPF KU GUVKOCDNG ! T TGURGEVKXGN[ 9JKEJ QH VJG # ¦E DK K K YJGTG 6EK HQNNQYKPI UVCVGOGPVU KU HCNUG ! $ ¦F EL L L YJGTG 6FL # Ž T [ Г [ % z DK EL $ Ž 8 T Ž 8 T V % Ž T [ [ ¦¦ H K L KL J KL YJGTG ¦H K KL Ž Ž %QX T Г T ¦H L KL =261
  • 10. #7) ++ .GV 0 DG C FGNGVGF PGKIJDQWTJQQF 1T QH 6JGP EQTTGEV UVCVGOGPV HTQO +P QPG YC[ #018# YKVJ P VJG HQNNQYKPI KU QDUGTXCVKQPU CPF VTGCVOGPVUГ VJG # KU C TGOQXCDNG UKPIWNCTKV[ QH GZRGTKOGPVGT YJKNG ECNEWNCVKPI VJG H KH H KU CPCN[VKE CPF WPDQWPFGF ( TCVKQ HQTIQV VQ FKXKFG VJG UWO QH KP 0 USWCTGU D[ VJG EQTTGURQPFKPI $ KU C TGOQXCDNG UKPIWNCTKV[ QH FGITGGU QH HTGGFQO *QYGXGT VJG H KH H KU CPCN[VKE CPF DQWPFGF UVCVKUVKEKCP UCKF VJGTG KU PQ OKUVCMGГ KP 0 DGECWUG % KU C TGOQXCDNG UKPIWNCTKV[ QH # P H KH o H z NKO $ P KU C TGOQXCDNG UKPIWNCTKV[ QH % P H KH NKO H FQGU PQV o GZKUV P
  • 11. #7) ++ 6JG HWPEVKQP H ^^Г  % ^ H G Г 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Г PWODGT QH RNQVU KP GCEJ 9JKEJ QH VJG HQNNQYKPI UVCVGOGPVU DNQEM KU KU CNYC[U VTWG ! # # T X $ $ T KPVGIGT RCTV QH PX % % T KPVGIGT RCTV QH PX T KPVGIGT RCTV QH PX =261
  • 12. #7) ++ 9JKEJ QH VJG HQNNQYKPI UVCVGOGPVU +H Г K Г VJGP KU KU VTWG ! K # # 'XGT[ ITQWR KU KUQOQTRJKE VQ C RGTOWVCVKQP ITQWR Г K $ $ # ITQWR ) KU KUQOQTRJKE VQ C Г K RGTOWVCVKQP ITQWR KHH KV KU HKPKVG % % # ITQWR ) KU EQOOWVCVKXG KHH KV K KU E[ENKE # ITQWR ) KU PQP CDGNKCP KHH 1T QTFGT QH ) KU PQV RTKOG +P C 4$ YKVJ D DNQEMU CPF X 1T VTGCVOGPVU YJKEJ QH VJG HQNNQYKPI 9JGP FGUKTGF KPHQTOCVKQP KU UVCVGOGPVU CNYC[U JQNFU ! CXCKNCDNG HQT CNN QDLGEVU KP VJG RQRWNCVKQPГ YG JCXG YJCV KU ECNNGF # D X C $ D X # %GPUWU % D X $ 2QRWNCVKQP D CPF X CTG CTDKVTCT[ RQUKVKXG % 5CORNG KPVGIGTU 5VGO CPF NGCH FKURNC[
  • 13. #7) ++ .GV ) DG C ITQWR QH QTFGT 6JG TKPI QH ª OCVTKEGU QXGT 6JGP # KU EQOOWVCVKXG # F^Q ) KORNKGU ) JCU C WPKSWG $ KU CP KPVGITCN FQOCKP UWDITQWR QH QTFGT F $ ) JCU QPN[ QPG PQTOCN % JCU PQP GTQ GTQ FKXKUQTU UWDITQWR KU C HKGNF % ) JCU VYQ UWDITQWRU QH QTFGT 1T CPF QPG UWDITQWR QH QTFGT G KU VJG QPN[ RTQRGT UWDITQWR 9JKEJ QH VJG HQNNQYKPI UVCVGOGPVU QH ) KPXQNXGU FGUETKRVKXG UVCVKUVKEU CU 1T QRRQUGF VQ KPHGTGPVKCN UVCVKUVKEU ! 9JKEJ QH VJG HQNNQYKPI UVCVGOGPVU # 6JG (## UCORNGU VTCHHKE KU HCNUG ! EQPVTQNNGTU KP QTFGT VQ GUVKOCVG # #NN EQORCPKGU NKUVGF QP VJG 0GY VJG RGTEGPV TGVKTKPI FWG VQ LQD ;QTM 5VQEM 'ZEJCPIG KU CP UVTGUU TGNCVGF KNNPGUU GZCORNG QH C UCORNG $ $CUGF QP UCORNG QH $ +P GPWOGTCVKXG UVWFKGUГ KPVGTGUV RTQHGUUKQPCN VGPPKU RNC[GTUГ C KU HQEWUUGF QP C HKPKVGГ VGPPKU OCICKPG TGRQTVGF VJCV KFGPVKHKCDNGГ WPEJCPIKPI QH VJG RCTGPVU QH CNN EQNNGEVKQP QH KPFKXKFWCNU QT RTQHGUUKQPCN VGPPKU RNC[GTU FKF QDLGEVU VJCV OCMG WR C PQV RNC[ VGPPKU RQRWNCVKQP % # UCORNKPI HTCOG KU C NKUVKPI QH % 6JG #NEQJQNГ 6QDCEEQ CPF VJG KPFKXKFWCNU QT QDLGEVU VQ DG (KTGCTOU GRCTVOGPV TGRQTVGF UCORNGF VJCV *QWUVQP JCF Г #NN RQUUKDNG [KGNFU KP ITCOU TGIKUVGTGF IWP FGCNGTU KP HTQO C EGTVCKP EJGOKECN TGCEVKQP $CUGF QP UWTXG[ QH ECTTKGF QWV KP C NCDQTCVQT[ KU CP OCICKPG TGCFGTUГ VJG GZCORNG QH EQPEGRVWCN QT OCICKPG TGRQTVU VJCV QH KVU J[RQVJGVKECN RQRWNCVKQP TGCFGTU RTGHGT FQWDNG EQNWOP CTVKENGU =261
  • 14. #7) ++ .GV ( DG C HKGNF YKVJ C HKPKVG PWODGT .GV / DG C RTQRGT KFGCN QH C $QQNGCP QH GNGOGPVU 6JGP TKPI 4 %QPUKFGT VJG HQNNQYKPI # VJG QTFGT QH ( OC[ DG UVCVGOGPVU 4 $ VJG QTFGT QH ( OC[ DG + KU C $QQNGCP TKPI / 4 % VJG QTFGT QH ( KU RTKOG ++ # KHH / KU C OCZKOCN / VJG EJCTCEVGTKUVKE QH ( KU GTQ KFGCN 1T 6JGP # $QVJ + CPF ++ JQNF ;QW CUMGF VGP QH [QWT ENCUUOCVGU $ 1PN[ + JQNFU CDQWV VJGKT YGKIJV 1P VJG DCUKU QH % 1PN[ ++ JQNFU VJKU KPHQTOCVKQPГ [QW UVCVGF VJCV VJG $QVJ + CPF ++ CTG HCNUG CXGTCIG YGKIJV QH CNN UVWFGPVU KP 1T [QWT EQNNGIG KU RQWPFU 6JKU KU CP GZCORNG QH 6JG OGCUWTG OQUV WPCHHGEVGF D[ QWVNKGTU KU VJG # KPHGTGPVKCN UVCVKUVKEU # OGFKCP $ UCORNG $ VTKOOGF OGCP % RQRWNCVKQP % OGCP FGUETKRVKXG UVCVKUVKEU TCPIG
  • 15. #7) ++ .GV 4 DG CP KPVGITCN FQOCKP CPF 1T 4=Z? DG VJG RQN[PQOKCN TKPI QXGT 4 6JGP #V C EGTVCKP ECT UGTXKEG UVCVKQP YKVJ # 4=Z? KU CP 'WENKFGCP FQOCKP UGTXKEG HCEKNKV[ HQT QPN[ QPG ECT CPF PQ YCKVKPI URCEGГ ECTU CTTKXG HQT $ +H GXGT[ KFGCN QH 4 KU RTKPEKRCN VJGP UQ KU VTWG HQT 4=Z? UGTXKEG KP 2QKUUQP OCPPGT CV VJG TCVG QH QPG RGT JQWT CPF UGTXKEG VKOG % 4=Z? KU CP KPVGITCN FQOCKP KU CNUQ GZRQPGPVKCN YKVJ CP CXGTCIG 4=Z? KU C HKGNF QPG JQWTГ YKVJ KPFGRGPFGPEG QH 1T UGTXKEG VKOGU CPF KPVGTCTTKXCN VKOGUГ 6JG CXGTCIG UEQTG HQT C ENCUU QH VJG RTQDCDKNKV[ VJCV CP KPEQOKPI UVWFGPVU YCU +H VJG HGOCNG ECT HKPFU VJG UGTXKEG HCEKNKV[ CXCKNCDNG UVWFGPVU KP C ENCUU CXGTCIGF Г VJGP VJG OCNG UVWFGPVU KP VJG ENCUU KU CXGTCIGF # # $ % $ G %QPUKFGT VJG HQNNQYKPI VYQ % UVCVGOGPVU + +H # KU C VTKCPIWNCT OCVTKZ CPF 0QPG QH VJG CDQXG PQ GPVT[ QP VJG OCKP FKCIQPCN KU GTQГ VJGP # KU UKPIWNCT +H VJG VTCPUHQTOCVKQP 6 4P o 4 ++ +H # KU VTKCPIWNCT OCVTKZ CPF CP KU FGHKPGF D[ 6 : : #:Г YJGTG # GPVT[ QP VJG OCKP FKCIQPCN KU KU CP[ P ª P U[OOGVTKE OCVTKZГ VJGP GTQГ VJGP # KU KPXGTVKDNG 6: ; KU GSWCN VQ 6JGP # 6: : #; 6; # QPN[ + KU VTWG $ 6: 6; $ QPN[ ++ KU VTWG % 6: : #; 6; % DQVJ + CPF ++ CTG VTWG DQVJ + CPF ++ CTG HCNUG 6: ; #: 6; =261
  • 16. #7) ++ 1T .GV 6 DG VJG NKPGCT VTCPUHQTOCVKQP 6JG UVCHH TGRNCEGOGPV RQNKE[ KP TGRNCEGOGPV OQFGN QP 4 TGRTGUGPVGF D[ VJG OCVTKZ # CTKUGU FWG VQ TGUKIPCVKQPГ TGVKTGOGPVГ QT FGCVJ QH C UVCHH § · OGODGT HTQO VKOG VQ VKOG ¨ © ¸ Г VJGP VJG EJCTCEVGTKUVKE ¹ $ KU NKMG TGRNCEGOGPV RQNKE[ HQT KVGOU YJQUG XCNWGU FGVGTKQTCVG XCNWGU QH 6 CTG ITCFWCNN[ % ECP DG GCUKN[ HQTOWNCVGF # Г DGECWUG RGQRNG TGVKTG CV MPQYP VKOG FQGU PQV [KGNF VJG QRVKOWO $ Г TGRNCEGOGPV KPVGTXCN § · % Г K .GV # ¨ ¸ DG VJG OCVTKZГ © ¹ VJGP VJG EQTTGURQPFKPI SWCFTCVKE KГ K HQTO KU # Z [ 1T $ Z Z[ [ % Z [ # OKZGF UVTCVGI[ ICOG KP )COG Z Z[ [ 1T VJGQT[ ECP DG UQNXGF D[ 9JKEJ QH VJG HQNNQYKPI KU PQV CP CUUWORVKQP WPFGTN[KPI VJG HWPFCOGPVCN RTQDNGO QH '13 KP # /CVTKZ OGVJQF +PXGPVQT[ /QFGN ! # GOCPF KU MPQYP CPF WPKHQTO $ )TCRJKECN OGVJQF $ *QNFKPI EQUV RGT WPKV RGT VKOG RGTKQF KU EQPUVCPV % #NIGDTCKE OGVJQF % .GCF VKOG KU PQV GTQ 5VQEM QWVU 5JQTVCIGU CTG PQV RGTOKVVGF #NN QH VJG CDQXG
  • 17. #7) ++ .GV RГ SГ T  +H VJG XGEVQTU .GV D Г Г D Г  4 CPF E Г Г Г E Г Г  4 § R· § S· §T· .GV 6 DG C NKPGCT VTCPUHQTOCVKQP ¨ S¸Г ¨ T ¸Г ¨ R¸ ¨ ¸ ¨ ¸ ¨ ¸ CTG OWVWCNN[ HTQO 4 KPVQ 4 UWEJ VJCV 6DK EK ©T¹ © R¹ © S¹ K Г 6JGP QTVJQIQPCN KP 'WENKFGCP URCEG 4 § · # 6 ZГ [ ¨ ZГ Z Г [Г Z Г [ ¹ © ¸ VJGP # R S T § · $ 6 ZГ [ ¨ Z Г [Г Z [Г Z Г [ ¹ © ¸ $ R S T z § · % RS ST TR z % 6 ZГ [ ¨ [Г Z Г [Г Z [¸ © ¹ RS ST TR 5WEJ C NKPGCT VTCPUHQTOCVKQP 1T FQGU PQV GZKUV 9JKEJ QH VJG HQNNQYKPI KU PQV QPG QH 1T +P C OWNVK UVCIG UCORNKPI VJG RTKPEKRNGU QH UCORNKPI ! # VJG UCOG PWODGT QH RGQRNG CTG # 5CORNKPI WPKVU OWUV DG UVWFKGF OQTG VJCP QPEG KFGPVKHKCDNG CPF ENGCTN[ FGHKPGF $ FKHHGTGPV TGURQPFGPVU CTG $ 5CORNKPI WPKVU CTG PQV UVWFKGF OQTG VJCP QPEG % C UGSWGPEG QH UCORNGU CTG KPVGTEJCPIGCDNG FTCYP HTQO CNTGCF[ UGNGEVGF % 5CORNKPI WPKVU OWUV DG UCORNGU DWV QPN[ VJG NCUV KPFGRGPFGPV QH GCEJ QVJGT UCORNG KU UVWFKGF C UGSWGPEG QH UCORNGU CTG 5CORNKPI WPKVU OWUV DG FTCYP HTQO CNTGCF[ UGNGEVGF TGRTGUGPVCVKXG CPF KPENWFG UCORNGU CPF GCEJ QPG QH VJGO OCNGU CPF HGOCNGU KU UVWFKGF =261
  • 18. #7) ++ %QPUKFGT VJG HQNNQYKPI VYQ 1T UVCVGOGPVU 6JG VKOG TGSWKTGF VQ CUUGODNG CP GNGEVTQPKE EQORQPGPV KU PQTOCNN[ + +H # KU C PKNRQVGPV OCVTKZ VJGP FKUVTKDWVGF YKVJ C OGCP QH + # KU PQP UKPIWNCT OKPWVGU CPF C UVCPFCTF FGXKCVKQP QH ++ # KU VTKCPIWNCT OCVTKZ YKVJ CNN OKPWVGU (KPF VJG RTQDCDKNKV[ FKCIQPCN GNGOGPVU CTG GTQГ VJCV VJG VKOG TGSWKTGF VQ CUUGODNG VJGP # KU PKNRQVGPV PKPG EQORQPGPVU KU ITGCVGT VJCP 6JGP OKPWVGU # 1PN[ + KU VTWG # $ $ 1PN[ ++ KU VTWG % % $QVJ + CPF ++ CTG VTWG $QVJ + CPF ++ CTG HCNUG .GV I Г I DG VYQ NKPGCTN[ 1T KPFGRGPFGPV UQNWVKQPU QH VJG +P C UVWF[ QH CVVKVWFGU VQ 7PKXGTUKV[ EQPUVCPV EQGHHKEKGPV GSWCVKQP [ RQNKEKGUГ C TGUGCTEJGT KPKVKCNN[ EJQUG C[ C[ 6JGP VJG 9TQPUMKCP HKTUV [GCT UVWFGPVUГ UGEQPF QH IГ I KU EQPUVCPV KH CPF QPN[ [GCT UVWFGPVU CPF VJKTF [GCT KH UVWFGPVU 6JGP VJG TGUGCTEJGT # C UGNGEVGF OCNG CPF HGOCNG $ C UVWFGPVU HTQO GCEJ [GCT ITQWRГ YJQ YGTG HKPCNN[ KPVGTXKGYGF 6JG % C UCORNKPI RTQEGFWTG WUGF KP VJKU C UVWF[ YCU 1T # 2TQDCDKNKV[ UCORNKPI 6JG EGPVTCN NKOKV VJGQTGO VGNNU WU $ 5VTCVKHKGF UCORNKPI VJCV VJG UCORNKPI FKUVTKDWVKQP QH VJG % /WNVK UVCIG UCORNKPI OGCP KU CRRTQZKOCVGN[ PQTOCN /WNVK RJCUG UCORNKPI 9JKEJ QH VJG HQNNQYKPI EQPFKVKQPU KU 6JG EQORNGVG UQNWVKQP QH VJG RCTVKCN PGEGUUCT[ HQT VJG VJGQTGO VQ DG FKHHGTGPVKCN GSWCVKQP XCNKF ! w w # 6JG UCORNG UKG JCU VQ DG NCTIG Г UKP Z UKP [ wZ w[ $ 6JG RQRWNCVKQP XCTKCPEG JCU VQ KU DG UOCNN # C Z [ UKP Z UKP [ D % 9G OWUV DG UCORNKPI HTQO C $ C Z [ EQU Z EQU [ D PQTOCN RQRWNCVKQP % C Z [ UKP Z EQU [ D 6JG RQRWNCVKQP JCU VQ DG C Z [ EQU Z UKP [ D U[OOGVTKE
  • 19. #7) ++ 6JG EJCTCEVGTKUVKE EWTXG QH VJG VYQ 1T 9KUJCTV FKUVTKDWVKQP KU C RCTCOGVGT HCOKN[ QH UWTHCEGU OWNVKXCTKCVG IGPGTCNKCVKQP QH Z C [ D KU # PQTOCN FKUVTKDWVKQP $ DGVC FKUVTKDWVKQP # C EKTENG % OCVTKZ DGVC FKUVTKDWVKQP $ C ITGCV EKTENG EJK USWCTG FKUVTKDWVKQP 6JG KPKVKCN XCNWG RTQDNGO % JGNKZ [ H ZГ [ Г [ Z [Г YJGTG ZГ [ DGNQPIU VQ C FQOCKP Г JCU WPKSWG GNNKRUG UQNWVKQP 1T # KH H ZГ [ KU EQPVKPWQWU KP $ KH H ZГ [ KU EQPVKPWQWU CPF # ECPQPKECN EQTTGNCVKQP ECPPQV DG DQWPFGF QP PGICVKXG DGECWUG % KH H ZГ [ KU EQPVKPWQWU CPF UCVKUHKGU .KRUEJKV EQPFKVKQP HQT # YG VCMG QPN[ RQUKVKXG GKIGP CNN RQKPVU QP XCNWGU HQT CNN HWPEVKQPU H ZГ [ QP 1T $ KV KU IGPGTCNKCVKQP QH VJG 9JKEJ QH VJG HQNNQYKPI UVCVGOGPVU OWNVKRNG EQTTGNCVKQP CTG VTWG HQT VJG HQNNQYKPI FCVC XCNWGU Г Г Г Г Г CPF ! % YG VCMG QPN[ RQUKVKXG USWCTG # 6JG OGCP KU UOCNNGT VJCP VJG TQQV OGFKCP $ 6JG OGCP CPF VJG VTKOOGF YG TGLGEV C PGICVKXG XCNWG OGCP CTG GSWCN % 6JG OGCP CPF OGFKCP CTG GSWCN .GV IГ I DG VYQ FKHHGTGPVKCDNG 6JG OGCP KU NCTIGT VJCP VJG HWPEVKQPU QP CP KPVGTXCN + VJGP OGFKCP +H VJG PWODGT QH EQPUVCPVU CTG VQ DG + 9 IГ I Z Z  + Ÿ IГ GNKOKPCVGF HTQO VJG IKXGP TGNCVKQP I CTG NKPGCTN[ FGRGPFGPV KU LWUV GSWCN VQ VJG PWODGT QH KPFGRGPFGPV XCTKCDNGUГ VJGP VJG ++ 9 IГ I Z z Z  + Ÿ IГ RCTVKCN FKHHGTGPVKCN GSWCVKQP I CTG NKPGCTN[ KPFGRGPFGPV QDVCKPGF D[ GNKOKPCVKPI VJGUG EQPUVCPVU 6JGP # KU CNYC[U C NKPGCT GSWCVKQP QH HKTUV QTFGT # 1PN[ + KU VTWG $ ECP DG C PQP NKPGCT GSWCVKQP QH $ 1PN[ ++ KU VTWG HKTUV QTFGT % KU C NKPGCT GSWCVKQP QH UGEQPF % $QVJ + CPF ++ CTG VTWG QTFGT KU C PQP NKPGCT GSWCVKQP QH $QVJ + CPF ++ CTG HCNUG UGEQPF QTFGT =261
  • 20. #7) ++ 1T 6JG UQNWVKQP QH C JQOQIGPGQWU .GV :Г :Г DG C UGSWGPEG QH KPKVKCN XCNWG RTQDNGO YKVJ KPFGRGPFGPV CPF KFGPVKECNN[ EQPUVCPV EQGHHKEKGPV KU [ ZGZ FKUVTKDWVGF TXU YKVJ VJG EQOOQP EQU Z 6JGP VJG NGCUV RQUUKDNG QTFGT QH VJG FKHHGTGPVKCN GSWCVKQP RFH IKXGP D[ ­ KU ° Z Г ° Z HZ ® # ° ° Г ¯ QVJGTYKUG $ %QPUKFGT VJG UVCVGOGPVU % P + ¦ : P   CU P o f K 2 o K 1T P ++ ¦ K 2 : K P   CU P o f o 6JG TCPFQO XCTKCDNGU : CPF ; CUUWOG QPN[ XCNWGU GCEJГ CPF P EQX :Г ; 6JGP § · +++ P ¦ K © ¸ F ¨ : K ¹ o # : CPF ; PGGF PQV DG 0 Г CU P o f KPFGRGPFGPV 6JGP $ : CPF ; CTG KPFGRGPFGPV # #NN UVCVGOGPVU CTG VTWG % : CPF ; CTG KPFGRGFGPV QPN[ $ 1PN[ UVCVGOGPVU + CPF ++ CTG KH HQWT XCNWGU CTG CPF HQT VTWG DQVJ : CPF ; % 1PN[ UVCVGOGPVU + CPF +++ CTG VTWG 6JG NKPG KU RCTCNNGN VQ ; CZKU 1PN[ UVCVGOGPV + KU VTWG QT : CZKU