906_Chapter1

906_Chapter1 - ‚ B QC.-  7b.-7e c7. < 7w.C ...

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G Ai [email protected]|L? |L |i ?Lh4@* uLhUi L? 6c @*tL Lu 4@}?|_i   *tL }h@|@|L?@* uLhUi @?_ ih|U@* uLhUi uhL4 |i }hL?_c U i }?Lhi Ai t|_i?| tL*_ _h@ uhiiML_) _@[email protected] ‚ B QC.-  7b.-7e c7. < 7w.C  2 Ai 6 ' 6@ i^@|L?t 6Lh 6c E% |L |i h}|c + _L?@h_  t? w ' 6@% c 6}   ULt w ' 6@+ ( 6Lh  EL?*) |i % UL4TL?i?|G  t? w '  Ahii i^@|L?tc uLh ?!?L?t Ec @% c @+ c  +i*@|i i*LU|) i^@|L?G 6* n V *C ' 6*C ( 4i@??}G 6* 4i@?t |i i*LU|) Lu 6 | hitTiU| |L  ( @*tL C t|@?_t uLh |i }hL?_ A@!i % @?_ + UL4TL?i?|t `h|i 6*  c V *C  Vc 6*C   6Lh i*LU|itc i|U |@!i + TLt|i T@h_ Ai? % n T ' % c + ' +   _@[email protected] ** tL |@| m+ *% m ' |@? w #L tL4i @*}iMh@ @?_ |@!i _ih@|it h| | |L @hhi @| @+ UL| w n  ' @%  A@|<t |i uLh| i^@|L? Ai tL*|L? t @% ' }  t? w ULt w c 6 t?2 w n  E6 n   t?2 w c @+ ' } 6 t?2 w n  6 t? w ULt w  ' }  6 t?2 w n  Aihi @hi L|ih @)t |L _L |t Oihi t |i w@}h@?}@?G   u '  6 m^m2 n   '2 n 6}^+ c 2 2 ihi ^ t |i TLt|L? Lu 6 E+ TLt|i _L?@h_ @?_ ' t |i Lh3L?|@* TLt|L? 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Lu |i Lu t  ' 8 *  ,?ih}) t !?i|UG A '  6T 2 '   E|2 ' E  |2  ' 2 2 2 8 f ' 8 _M c ihi _M t |i _t|@?Ui |i @?_ 4Lit EAi @?_ @?_ |i U)*?_ih @i |i [email protected] @UUi*ih@|L?c i?Ui _M ' f  EM  ' 8 *  k?i|U i?ih}) t A '  T 2 n  U/2 ' 8 f n  U/2  ALh^it @ML| 2 2 2 |i L )i*_ EUL?t|@?| @?}[email protected] @UUi*ih@|L? k ' 8 -*Uc tL  U/2 '  U Ek|2 ' 2 2 UkE  k|2  ' 8 -w , A ' 8 Ef n -w c ihi w t |i @?}*i |hL} U |i 2 ‚ B QC.-  7b.-7e c7. < 7w.C  U)*?_ih @t |h?i_ A@|  @|2 t|g ** Mi *iu| L| Lu |i L|ih [email protected]|t O@?_<t 2 @UUi*ih@|L? t  n -k , @?_ 4Lit @ _t|@?Ui _M ' f n -w , A ' 8 _M ' Lh! _L?i d6Lh [email protected]tL? | [email protected]| E_ ?L|i |@| |i ML||L4 Lu |i U)*?_ih @UUi*ih@|it @|   k- '   -2 *U ' E  -2 *U o EU 8  s ' c ihi s t |i uhU|L?@* uLhUi @tt4i_ |L |i *iu| ALh^it @ML| 2 L , k ' s -*U +L**?} , k ' *- , s ' U*-2 ,  ' 8* E n U*-  @*tL 2 2 }it s ' 8 EU*- *E n U*-  ,?ih}) A '  T 2 n  U/2 '    ' E8  s f n 2 2 s -w ' 8 f  s f n s f ' 8 f ' 8 _ c t?Ui @?_ @?_ U)*?_ih 4Li |i [email protected] _t|@?Ui L|Ui |@|  t *itt |@? ? 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Ei 8  s '  ALh^it @ML| L , s -  8 o ' Ukc hL**?} , k ' 2 2 2 *- , ' 8 E  o*-*E n U *- c s ' 8 Eo*- n U *- *E n U *-  [email protected] |i *4|t o ' f @?_ o ' - | |i @TThLTh@|i [email protected] @MLi hLM*i4 e tL*|L? E@ L?tih@|L? Lu 4L4i?|4G 6  ' 6  n 62 2 ,  62  2 62 2 '   n 2  2  ULt w  2  62 L?tih@|L? Lu i?ih}) E!?i|UG  6 2 2  '  6 2 n  62 2 ,  2 2 2 2  6 2 2 6  ' 6 2 n   n 2  2  ULt w    62  '  6 ULt w  s 62  62 t?2 w 2  c  5L*i uLh  G ‚ B QC.-  7b.-7e c7. < 7w.C  e ihi  ' 6 n 62 t |i |L|@* [email protected] Ai ?i}@|i t}? Lu |i t^@hi hLL| U@? Mi uL?_ uhL4 |i tTiU@* [email protected] ? U 6 ' 62 @?_ w ' f  EM wi| |i L EUi?|ih Lu [email protected] i*LU|) Mi V Ai?  '   Vc 2 ' V Ai? 6   6  n 62 2 ' f , V '    EU 62 6    '  c 2 '      LLti @ it @*L?} @?_ TihTi?_U[email protected] |L   Ai?  '  V , % ' %  UL| w ' At 6  c + ' +   % 6  ' UL| w   +   t? w UL| w ' UL| w  6 q r s t? w 6 ULt w  62  62 t?2 w 2  6?@**)c M) UL?tih@|L? 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W? |ih4t Lu % @?_ %2 ? |i _@[email protected] _i€?i % ' %2 % @?_ + ' E6 % n 62 %2  *c ihi  ' 6 n 62  >% n &% ' fc + ' } , % '  ULt E/| n  c + '  }|2 n f | n +f    2 Oihi > ' 6 62 *c / 2 ' & *> | | ' f G % Ef ' fc %2 Ef '  n 62 }*&c % Ef ' %2 Ef ' f ,   ‚ B QC.-  7b.-7e c7. < 7w.C  D  '  n 62 }*&c  ' fc f ' fc +f ' 62 E n 62 }*& * , % '  }|2 n 2 62 E n 62 }*& E  ULt /|  E n 62 }*& %2 '  }|2 n E62 n 6 ULt /| 2  hLM*i4 S tL*|L? `h|i  ' 6i n 64 c > ' 6i 64 * +iU@**G j ' E6i hi n 64 h4  * 6hL4 _ @[email protected] ' h4  hi  ,^@|L?t Lu 4L|L?G C6t C64 hi n c oi % C6t C6i 4 '  h4   h o4 % i '  h Ai?   4  i ' C6t h h @?_  h4 hi  o4 oi    C %   6ii n 644 h h C6t  j '   6i hi 64 h4 n oi o4 , T@?_ |i _i?L4?@|Lht   6 % 2 26  j 3 *2    i i ' n n ' o4 f f f 2 mj n 6i * m      6i  j 62 E  j2 i 2 '  % D n    f f 2 2 2 f 2 f2  t4[email protected] U@*U*@|L? )i*_t      E  j2  64  j 62 4 2 ' n % D n    oi f f 2 2 2 f 2 f2 ‚ B QC.-  7b.-7e c7. < 7w.C  S  W?tih| |iti ?|L |i i ThittL?t uLh j @?_  u|ih tL4i @[email protected]    E  j2 C6tj E  j 6i  64 2  n % D f f2 2f 2 f2    C6t E6i  64   j E62  6i 64 n 62  E  j2 i 4 2  % D   f f 2 2 2 f 2 f2 C  c %    E  j2 2    C6t j   > % D j f 2f 2 f2    C6t > E6i  64   E  j2 2 n % D   jn  f f 2 2 f2 AL *Lit| Lh_ih ? %*fc C c % C6t  j   j f  hLM*i4 . tL*|L? Ai TihL_ t E|i TL|i?|@* t t)44i|hU ' s ] 26 3 _% s c .  T E% ihi . ' T E 8 ' &%2?n , T ' g%2E?n c ihi g ' &*2E? n  | . @?_ T ?|L |i ?|i}h@*G ] s _% ss  ' 26 2E?n  %2E?n g 3 `h|i % ' 5 G ' u 26 g  s 3 _5 s 2E?n   5 2E?n s _5    5 2E?n u ' 26 3?  g  3 ‚ B QC.-  7b.-7e c7. < 7w.C  . Ai ?|i}h@* t @ UL?t|@?| ,  2 3?  Ai ? ' f [email protected] t |i @h4L?U LtU**@|LhG ?L ThLM*i4 | ? '  , T ' & *? m%*Km c ihi K t @ UL?t|@?| Ai? tMt|||?} @t @MLic ' s ] 26 3 _5 s & *?E*K  & *? m5*Km ] u ] _5 26 _5 s s '  &  *? 5  *? m5 m f u ' 26  & 3 Ai ?|i}h@* i t|t Eh|i *? 5 ' + 2  ,  2   3E3  |ih ?i}@|i ? Thiti?| ?L ThLM*i4 hLM*i4 H tL*|L? wi| >  6 n 2 Mi |i |L|@* [email protected] @?_ U   6o2 n -2 Mi |i 4L4i?| Lu ?ih|@ 2 @ML| |i Ui?|ih E@ L?tih@|L? Lu i?ih})G  > 2 2 n  U/2  >} ' f 2 A4i _ih@|iG BiL4i|h)G , >@ n U/k  >} ' f  ' /oc @ ' ko @'} > > n U*o2 EM Wu |i Lu t t|@|[email protected])c |i t|h?}|i?tL? A i^@*t |i uLhUi Lu }h@|) >} Ai? 4L4i?|t @ML| |i Lu }i k ' >}o*U Ai uhii i?_ Lu |i t|h?} 4t| Mi T**i_ T | @? @UUi*ih@|L? @ ' ko  >}o2 *U [email protected] | E@G 4Li |L @ t)t|i4 @UUi*ih@|?} @| @ W? |@| t)t|i4 |i i^@*i?|Th?UT*i }h@|@|L?@* €i*_ t }  ' } n @ @?_ |i @UUi*ih@|L? Lu |i )L)Lc [email protected]*) @ ' } >* E> n U *o2  tL*_ |h? L| |L Mi @ iU! | L| EU 8 t |i |L|@* uLhUi L? |i )L)L W|t Lu |ihiuLhi @t @? @UUi*ih@|it @ ' 8 *> ALh^it @ML| |i Lu )i*_ k ' 8 o*U Ai uhii i?_ Lu |i t|h?} @UUi*ih@|it @|    o2 n   ' @ n ko ' 8 > U At U@? @*tL Mi UiU!i_ M) i^@*i?Ui ‚ B QC.-  7b.-7e c7. < 7w.C  H hLM*i4 b tL*|L? ?tih ? t| L?i _4i?tL? Ai i^@|L? Lu 4L|L?G % ' }  k%   }  E| '  n e3k| , k }  % E| '  |  e3k| n  k k L|i |@|  9' %f  W? [email protected]| %f '   *k @?_ f '   }*k ,  ' f n }*kc  '   } %f n n f , kk  }  } n f Ee3k|   n %f c % E| '  |  k k} k  }   E| '  n n f e3k|  k k } Ai? *4  E| '   EL|itG  #L |i [email protected] uLh @ Lh3L?|@* _4i?tL? M) ti||?} |<" k } ' f 2 iU! |@| )L }i| |i t@* u@**?}ML_) hit*| ? |i *4| k $ f  hLM*i4 f tL*|L? `h|i j ' jErc jf ' jErf c j ' jEr  E?ih|M*i ,     ] r  ] j  _% _% 2 _% _j _% _j 2 _r ,Erf c r  ' _r ' _j _r _r _j _r _j _r _j rf jf   ] j  ] j  _% _% 2 _j _r _% _% 2 _j ' _j ' _j _j _r _j _j _j jf jf hLM*i4  tL*|L? E@ wi|  Mi @ € i_ ?| iU|Lhc  Mi ?| |@?}i?| iU|Lh @*L?} |i Uhic w Mi |i @?}*i Mi|ii?  @?_ c @?_ , Mi *i?}| @*L?} |i Uhi Ai?   _  _ _ E   '  '   ULt   _,  _, _, _ _w ' ULt w '  t? w c _, _, ihi  t |i @?}*i Mi|ii? _ *_, @?_  | _ _ E    ' f ' 2  _, _, AL tL*ic ti| % '      ‚ B QC.-  7b.-7e c7. < 7w.C  b , w  '  Z ,EUL?t_ih t| |i n t}?( |i  t}? t t4[email protected] t? w ' ULt  @?_ 2 _w*_, n _*_, ' f ,   _  _w V '   _,  _, 6Lh @ UhU*ic , ' -w , _w*_, ' *- EM  '  a ? @?_  ' V ?  V,? ,  _   ' a?'  , ' w,? , _, w,  w, E a ? '  a E? a   ' ? m m2   E?        2 | m m ' c @?_ ?   ' f , ?   ' ?   ' V, tL   w, ' ? n V, c  ",# hLM*i4 2 tL*|L? Ai [email protected]? |t ThLM*i4 U@? Mi tL*i_ [email protected]*) t |@| |i t)t|i4 @t t| |L uhii_L4tc i |@| |i ?_Uit c c & c i|U Ei ti L?*) *Lih ?_Uit |@!i L? L?*) |i @*it  @?_ 2 Ai i^@|L?t @hi @ % % ' c @ % %   E%% ' fc   @ E% % n % %  ' fc   %& %& ' T 2 c  %& %& ' f  E E2 E  Ee ED ,^@|L? ED , @UUi*ih@|L? t Lh|L}L?@* |L |i i*LU|) u ULhti- Ai tTii_ t UL?t|@?| , |@?}i?|@* @UUi*ih@|L? t 3ihL , @UUi*ih@|L? t Ui?|hu}@*c Lh|L}L?@* |L |i i*LU|)c @?_ ThLTLh|L?@* |L T 2  ,^@|L? E2 _i€?it |i  @?_ tLt |@| |i  E% uLh4 @ iU|Lh |@| t Lh|L}L?@* |L |i i*LU|)c tL %& ' 4E%T 2 & E%  ES  Ai ThLM*i4 ?L t |L €?_ 4E% hLUi_hi G E  tL*i E2 @?_ Ee uLh |i %& @t u?U|L?t Lu |i % @?_ E  ?tih| ES ?|L E  @?_ tL*i uLh 4 E  +ih|i E2G  % n 2 %2 ' f , 2 %2  2 %2 ' f     2 2 ‚ B QC.-  7b.-7e c7. < 7w.C  f ,^@|L? Ee t Ai tL*|L?t @hi %2 ' 2  2 %2 n %2 ' T 2   2 T2 T2 c %2 ' 2 2 c      @?_ |@!?} t^@hi hLL|t E@||i?|L? |L t}?tc T T % ' 2 s  c %2 '  s       E  ,^@|L? E  U@? Mi h||i? 4T 2   ' @ % % ' T 2  tL 4' [email protected] 2  [email protected]  2 n @22 2  2  c  T 2 & & & &  E& & 2 | - U@? Mi h||i? ? |ih4t Lu |i @& @?_ |i %&  @ 2  [email protected]  2 n @22 2 ' @ @2 % @2& %&  [email protected] @ % @2& %& n @22 @ % @& %& 2  ' [email protected]& [email protected] @2  @2 @   @ [email protected] @2&  @22 @& o % %&  Ai |L |ih4t | [email protected]?|i|U@* i ThittL?t U@? Mi i@*@|i_ Eh|i { ' _i| i@& j 6ht| @2& E    G & ' c 2c  '  $ fc & ' c 2c  ' 2 $ @2& { L  @ E    G & ' c  ' c 2 $ @ {c & ' 2c  ' c 2 $ f Oi?Ui 4' [email protected]& %2 %& n @ % %  {@& % %& { ' ' c 2 2 E, ,  E, ,  E, , 2 {@& %&  E@,6 @,? %6 %? 2 ihi i ti ,^Ec [email protected]*) @& % %& ' c tL €?@**)c % ' 4T 2  ' T 2   t}}it|L?G iU! |t M) tTiU@*3?} |L @ UhU*i ‚ B QC.-  7b.-7e c7. < 7w.C   hLM*i4  tL*|L? >2 >2 >  '  , ?L?i Lu |i >& @?tc tL U@? __i uhii*) M) |i4 `h|i >   *6 ,6  n  ' 6  L >2 >2 ' 6  `h|i >2 ' 6 *>2  62 , n 62 2 ' k Ai? 2 n >2  ' 2 n E6 *62   ' w , 62 2 n 6  ' 62 w Ai |hii ML i_ i^@|L?t @hi Lu |i _ithi_ uLh4 | 6 '  @? [email protected] |i 6 M) S6 c ihi S t @?) UL?t|@?| hLM*i4 e tL*|L? 6ht| ? iU|Lh ?L|@|L?G   ) ' + , ) ' + n +  , ) ' + n 2+  n +c   ihi +'  ULt /|  t? /| t? /| ULt /|     , ) U@? Mi ?L?3ihL ii? u  ' f ? 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This note was uploaded on 04/22/2010 for the course PH 531 taught by Professor Clavelli,l during the Fall '08 term at Alabama.

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