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jki= : kg kto lclmletr kr kebkdlet tf jed fxkletld jqj{ gxfm tol ito h|r%
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fg [ H|r Mjtxk h{ Rkea|cjx Txjergfxmjtkfe Mltofd ef fg h|rlr 0 < ef fg ckelr 0 7 rtjxtkea h|r 0 : ledkea h|r 0 8 km~ldjebl wjc|l0 >%8<` rtjxtkea h|r 0 8 ledkea h|r 0 2 km~ldjebl wjc|l0 >%4` rtjxtkea h|r 0 2 ledkea h|r 0 4 km~ldjebl wjc|l0 >%8` rtjxtkea h|r 0 4 ledkea h|r 0 8 km~ldjebl wjc|l0 >%:8<` rtjxtkea h|r 0 : ledkea h|r 0 < km~ldjebl wjc|l0 :%8<` rtjxtkea h|r 0 2 ledkea h|r 0 < km~ldjebl wjc|l0 :%8<`
8:
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:% Rtjxt 8% Alt tol ef% fg h|rlr# e|mhlx fg lclmletr 2% Alt tol rtjxtkea jed ledkea h|rlr fg ljbo lclmlet 4% Gfxm tol h|r kebkdlebl mjtxk J fg rkpl l*e <% Gfxm tol txjer~frl fg h|r kebkdlebl mjtxk JT 7% Gfxm tol ~xkmktkwl jdmkttjebl mjtxk [ fg rkpl l*l 1% Gfxm [-h|r |rkea lz|jtkfe JT*[*J ?% Dkr~cj{ [-h|r mjtxk ;% Rtf~%
H|r Kebkdlebl Mjtxk YJ]0 : -: > > > : -: > > > : -: > -: > : : > > > > > : >
> > > > -: -:
Txjer~frl fg H|r Kebkdlebl Mjtxk YJt]0 : > > > : > -: : > -: > > > -: : > > : > > -: : > > > > > > -: -: ^xkmktkwl Jdmkttjebl Mjtxk0 Y{] > - 4%>>k > > > > >
> > - 8%<>k > > > >
> > > - <%>>k > > >
> > > > - ?%>>k > >
> > > > > - >%?>k >
> > > > > > - >%?>k
[-H\R = YJt] Y{] YJ] > - 4%?>k > ) 4%>>k > > > ) >%?>k 55
> > > > >
) 4%>>k -:4%<>k ) 8%<>k ) ?%>>k
> > > > >
) ) )
8%<>k ?%2>k <%>>k >%?>k
> > ) ?%>>k > ) <%>>k > -:2%>>k >
> ) >%?>k > > ) >%?>k > > - :%7>k
82
MJTCJH ^XFAXJM0 ,Gfxmjtkfe fg [ H|r Mjtxk h{ Rkea|cjx Txjergfxmjtkfe Mltofd bcljx jcc jcc9 9 bcfrl jcc jcc9 9 bcb9 dkr~/ !Gfxmjtkfe fg [ H|r Mjtxk h{ Rkea|cjx Txjergfxmjtkfe Mltofd !+ !+ eh = ke~|t / !Letlx tol ef fg h|rlr0! +9 ec = ke~|t / !Letlx tol ef fg ckelr0! +9 gfx `= :0ec rh/`+=ke~|t /!Letlx /!Letlx tol rtjxtkea h|r0!+9 h|r0!+9 lh/`+=ke~|t /!Letlx /!Letlx tol ledkea h|r0 !+9 p/`+ =ke~|t /!Letlx /!Letlx tol h|r km~ldjebl wjc|l0!+9 wjc|l0!+9 h/`+ =ke~|t /!Letlx /!Letlx tol ojcg ckel bojxakea jdmkttjebl wjc|l0!+9 wjc|l0! +9 led ,Gfxmjtkfe fg H|r Kebkdlebl Mjtxk {=plxfr/ec#eh+9 gfx k=:0ec i=rh/k+9 m=lh/k+9 {/k#i+=:9 {/k#m+=-:9 led dkr~/!H|r dkr~/!H|r Kebkdlebl MjtxkYJ]0!+ MjtxkYJ]0!+ dkr~/{+ t={!9, t={!9, Txjer~frl fg H|r Kebkdlebl Mjtxk dkr~/!Txjer~frl dkr~/!Txjer~frl fg H|r Kebkdlebl MjtxkYJt]0!+ MjtxkYJt]0!+ dkr~/t+ ,Gfxmjtkfe fg ^xkmktkwl Jdmkttjebl Mjtxk |=plxfr/ec#ec+9 gfx k=:0ec |/k#k+=:&p/k+)h/k+&89 led dkr~/!^xkmktkwl dkr~/!^xkmktkwl Jdmkttjebl Mjtxk0Y{]!+ Mjtxk0Y{]!+ dkr~/|+ jerq=t*|*{9 dkr~/![-H\R dkr~/![-H\R = YJt]Y{]YJ]!+ YJt]Y{]YJ]!+ dkr~/jerq+
XLR\CT0 To|r# tol ―MJTCJH‖ ~xfaxjm ojr hlle qxkttle tf gfxm tol H|r jdmkttjebl mjtxk –[” fg j akwle ~fqlx eltqfxi h{ |rkea Rkea|cjx Txjergfxmjtkfe
Mltofd%
Gcfq bojxt0
8<
L%Ef0<
R[MMLTXKBJC GJ\CT JEJC[RKR H[ P H\R
8;&>1&::
JKM0 Tf dlwlcf~ j ―MJTCJH‖ ~xfaxjm tf jejc{pl tol R{mmltxkbjc Gj|ct fg
j akwle ~fqlx eltqfxi h{ |rkea H|r Km~ldjebl Mjtxk% R{mmltxkbjc gj|ct mj{ hl j rfckd toxll ~ojrl rofxt bkxb|kt kr mj{ kewfcwl je{ km~ldjebl% R|bo bfedktkfer jxl bj|rld ke tol r{rtlm jbbkdletc{ toxf|ao ker|cjtkfe gjkc|xl fg lz|k~mlet fx Gcjrofwlx fg ckelr kektkjtld h{ j ckaotlekea rtxfil fx toxf|ao gjb|ct{ f~lxjtkfe% Tol r{rtlm m|rt hl ~xftlbtld jajkert gcfq fg oljw{ rofxt bkxb|kt hxljilxr jed ~xftlbtkea xlcj{kea# ql m|rt lrtkmjtl tol mjaekt|dl fg b|xxlet tojt qf|cd gcfq |edlx rofxt bkxb|kt bfedktkfer% TOLFX[0
GFXM\CJL0
Clt j toxll ~ojrl gj|ct fbb|x ke h|r‒i% Clt j ^xl-gj|ct wfctjal jt h|r-i hl W~g% Clt tol Gj|ct Km~ldjebl jt tol Gj|ctld ckel hl Pg% Tole# Gj|ct B|xxlet ke h|r ‒ i# K g
W ~g P ii P g
Ke alelxjc tol bojeal ke Wfctjal ke h|r-z d|l tf toxll ~ojrl gj|ct ke h|r-i kr akwle h{% W z K g P zi
Tol Wfctjal jt j h|r d|xkea j gj|ct ke h|r-i kr akwle h{ tol r|m fg ~xl-gj|ct h|r wfctjal jed bojeal ke h|r wfctjal% Rkebl tol r{rtlm kr |ecfjdld r{rtlm tol ~xl-gj|ct wfctjal jt jcc h|rlr hl W~g = :~%|%#/rjml jr h|r-I wfctjal+%
W: = W~g ‒ KgP:i = : W8 = W~g ‒ KgP8i = :
> -
KgP:i KgP8i
> -
KgPei
> -
% %
Wi = W~g ‒ W~g = > % % We = W~g ‒ KgPei = :
81
JCAFXKTOM0
:% Rtjxt 8% Alt tol hjrl MWJ jed hjrl IW 2% Bjcb|cjtl tol hjrl b|xxlet Kh=Y/MWJ*:>>>+&/rzxt/2+*IW+] 4% Alt h|r djtj <% Gfxm P-h|r mjtxk 7% Xljd tol gj|ct h|r e|mhlx jed gj|ct km~ldjebl 1% Bjcb|cjtl gj|ct b|xxlet
K g
W ~g P ii P g
?% Bjcb|cjtl Wfctjal jt tol h|rlr d|xkea gj|ct
We = W~g ‒ KgPei = : ;% Rtf~%
> -
KgPei
8;
MJTCJH ^XFAXJM0 ,R{mmltxkbjc Gj|ct Jejc{rkr |rkea P H|r Mjtxk g|ebtkfe ph|rr{mgj|ct/pdjtj+ ec=pdjtj/0#:+9 ex=pdjtj/0#8+9 X=pdjtj/0#2+9 _=pdjtj/0#4+9 ehx=cleato/pdjtj/0#:++9 , Cleato fg tol Wlbtfx = Ef fg Lclmlet eh|r=mj/mj/ec+#mj/ex++9 , Cjxalrt Lclmletr ke j Jxxj{ = Ef fg H|rlr P=X)`*_9 , Hxjebo Km~ldjebl ke j Bfm~cl Bfc|me Wlbtfx {=felr/ehx#:+%&P9 , Hxjebo Jdmkttjebl ke j Bfm~cl Bfc|me Wlbtfx [=plxfr/eh|r#eh|r+9 , Kektkjckpl [ tf plxflr gfx i=:0ehx9 , Gfxmjtkfe fg tol fgg dkjaefc lclmletr kg ec/i+ 5 > '' ex/i+ 5 > [/ec/i+#ex/i++ = [/ec/i+#ex/i++ - {/i+9 [/ex/i+#ec/i++ = [/ec/i+#ex/i++9 , [ H|r Mjtxk kr R{mmltxkbjc led led gfx e= :0 eh|r , Gfxmjtkfe fg dkjafejc Lclmletr gfx i = :0ehx kg ec/i+ == e ss ex/i+== e [/e#e+=[/e#e+) {/i+9 lcrl# lcrl # led led led iw=ke~|t/!Letlx iw=ke~|t/!Letlx hjrl IW0!+9 IW0!+9 mwj=ke~|t/!Letlx mwj=ke~|t/!Letlx hjrl MWJ0!+9 MWJ0!+9 hb=/mwj*:>>>+&/rzxt/2+*iw+9 Ph|r = kew/[+9 dkr~/!H\R dkr~/!H\R KM^LDJEBL MJTXK_0!+9 MJTXK_0!+9 dkr~/Ph|r+9 ghe=ke~|t/!Letlx ghe=ke~|t/!Letlx tol Gj|ct h|r ef---5!+9 ef---5!+9 Pg=ke~|t/!Letlx Pg=ke~|t/!Letlx tol Gj|ct km~ldjebl /Pg = X ) `*_+0!+9 `*_+0!+9 W> = felr/eh|r# :+ ) `*plxfr/eh|r# :+9 Kg = W>/ghe+&/Pg ) Ph|r/ghe# ghe++9 Kgm = jhr/Kg+9 Kgj = Kgm*hb9 ,Kgmjea=jeacl/Kg+*:?>&~k9 g~xketg/!Tftjc g~xketg/!Tftjc Gj|ct b|xxlet = ,?%4g ~lx |ekt SeSe!# SeSe!# Kgm+ g~xketg/!SeTftjc g~xketg/!SeTftjc Gj|ct b|xxlet = ,g Jm~lxlrSeSe!#Kgj+ Jm~lxlrSeSe!#Kgj+ g~xketg/!SeH|r g~xketg/!SeH|r Wfctjalr d|xkea gj|ct ke ~lx |ekt SeSe!+ SeSe!+ g~xketg/! g~xketg/! H|r Wfctjal JeaclSe!+ JeaclSe! + g~xketg/! g~xketg/! Ef% Mjaekt|dl dlaxllrSe!+ dlaxllrSe!+ gfx e = :0eh|r kg e==ghe Wg/ghe+ = W>/ghe+*Pg&/Pg ) Ph|r/ghe#ghe++9 Wgm = jhr/Wg/ghe++9 jeaw=jeacl/Wg/ghe++*:?>&~k9 lcrl Wg/e+ = W>/e+ - W>/e+*Ph|r/e#ghe+&/Pg ) Ph|r/ghe#ghe++9 Wgm = jhr/Wg/e++9 jeaw=jeacl/Wg/e++*:?>&~k9 led g~xketg/! g~xketg/! ,4a!# e+# g~xketg/!,:2%4g! ,4a!# g~xketg/!,:2%4g!# # Wgm+#g~xketg/!,:2%4gSe! Wgm+#g~xketg/!,:2%4gSe!# # jeaw+ led
F\T^\T0
55 pdjtj = Y > > : : 8
: 8 8 2 2
> > > > >
>%89 >%49 >%?9 >%49 >%4]9
55 ph|rr{mgj|ct/pdj ph|rr{mgj|ct/pdjtj+ tj+ Letlx hjrl IW02> Letlx hjrl MWJ0:>> H\R KM^LDJEBL MJTXK_0 > ) >%:7>>k > ) >%>?>>k > ) >%:8>>k Letlx Letlx Tftjc Tftjc
> ) >%>?>>k > ) >%84>>k > ) >%:7>>k
> ) >%:8>>k > ) >%:7>>k > ) >%24>>k
tol Gj|ct h|r ef---52 tol Gj|ct km~ldjebl /Pg = X ) `*_+0> ) `* >%:7 Gj|ct b|xxlet = 8%>>>> ~lx |ekt Gj|ct b|xxlet = 2?4;%>>:1;< Jm~lxlr
H|r Wfctjalr d|xkea gj|ct ke ~lx |ekt H|r Wfctjal Jeacl Ef% Mjaekt|dl dlaxllr : >%17>> >%>>>> 8 >%7?>> >%>>>> 2 >%28>> >%>>>> 55
2:
XLR\CT0 To|r# tol ―MJTCJH‖ ~xfaxjm ojr hlle qxkttle gfx R{mmltxkbjc gj|ct
jejc{rkr fg akwle ~fqlx eltqfxi h{ |rkea H|r Km~ldjebl Mjtxk%
Rtjxt
Xljd ckel djtj# gj|ct h|r# gj|ct km~ldjebl# ^frktkwl# elajtkwl# plxf rlz|lebl xljbtjebl fg ljbo lclmlet
Jrr|ml ~xl-gj|ct wfctjal kr : ~%|%
Dxjq tol ~frktkwl# elajtkwl jed plxf rlz|lebl eltqfxir |rkea rlz|lebl km~ldjeblr fg tol ~fqlx r{rtlm% Bfm~|tl ~frktkwl# :
elajtkwl# plxf rlz|lebl h|r km~ldjebl mjtxkblr Y p
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Bolbi Bjrl
C-A
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R{mmltxkbjc Bfm~feletr fg B|xxlet
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= >#
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fg
= -
=
Gj|ct ~ojrl b|xxlet
= Kg = Kj = 2
Gj|ct ~ojrl b|xxlet
= Kj = ># Kh = -Kb
Kh = Kb = > R{mmltxkbjc Wfctjalr
= ^frt gj|ct wfctjal
=
Gj|ct ~ojrl b|xxlet
= > R{mmltxkbjc Wfctjalr R{mmltxkbjc Wfctjalr
=
= ^frt gj|ct wfctjal Bfm~|tl ^frt gj|ct wftjal wftjal |rkea txjergfxmjtkfe txjergfxmjtkfe mjtxk
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22
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\ER[MMLTXKBJC ROFXT BKXB\KT GJ\CT JEJC[RKR H[ P H\R MJTXK_
JKM0 Tf dlwlcf~ j ―MJTCJH‖ ~xfaxjm tf jejc{pl tol R{mmltxkbjc Gj|ct fg
j akwle ~fqlx eltqfxi h{ |rkea H|r Km~ldjebl Mjtxk% TOLFX[0
Tol Gj|ct qokbo akwlr xkrl tf |er{mmltxkbjc gj|ct b|xxlet kr bjccld je |er{mmltxkbjc gj|ct% Wjxkf|r t{~lr fg |er{mmltxkbjc Gj|ct fbb|x ke ~fqlx r{rtlm% Tol{ jxl:% Ro|et t{~l Gj|ct /fx+ Rofxt Bkxb|kt Gj|ct j+ Rkeacl ckel tf Axf|ed /C-A+ Gj|ct h+ Ckel tf Ckel /C-C+ gj|ct b+ Df|hcl Ckel tf Axf|ed /C-C-A+ Gj|ct /fx+ 8% Rlxklr t{~l gj|ct /fx+ F~le Bkxb|kt Gj|ct j+ F~le Bfed|btfx gj|ct /Fel fx Tqf bfed|btfx+ Mfrt fg tol gj|ctr tojt fbb|x fe ~fqlx r{rtlmr jxl |er{mmltxkbjc gj|ctr# qokbo mj{ bferkrt fg |er{mmltxkbjc rofxt bkxb|ktr# |er{mmltxkbjc gj|ctr toxf|ao km~ldjebl# fx f~le bfed|btfxr% Je{ |er{mmltxkbjc gj|ct bj|rlr |ehjcjebld b|xxletr tf gcfq ke tol r{rtlm# rf tol mltofd fg r{mmltxkbjc bfm~feletr kr wlx{ |rlg|c ke je jejc{rkr tf dltlxmkel tol b|xxletr jed wfctjalr ke jcc ~jxtr fg tol r{rtlm jgtlx tol gj|ct fbb|xxlebl fg tol gj|ct% Rlz|lebl Km~ldjebl0
Rlz|lebl Km~ldjebl kr tol km~ldjebl fg je lz|k~mlet fx bfm~felet tf tol b|xxlet fg dkgglxlet rlz|leblr% Tol km~ldjebl fgglxld tf gcfq fg ~frktkwl rlz|lebl b|xxletr kr iefqe jr tol ~frktkwl rlz|lebl km~ldjebl jed dleftld h{ p:% Tol km~ldjebl fgglxld tf tol gcfq fg plxf rlz|lebl b|xxletr kr iefqe jr tol elajtkwl rlz|lebl km~ldjebl jed dleftld h{ p8% Qole plxf rlz|lebl b|xxlet gcfq# tol km~ldjebl iefqe jr plxf rlz|lebl km~ldjebl jed dleftld h{ p>%
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tf
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|ecfjdld alelxjtfx% Tol bkxb|kt dkjaxjm gfx Rkeacl Ckel tf Axf|ed Gj|ct fe je |ecfjdld [- bfeelbtld alelxjtfx qkto ktr el|txjc axf|edld toxf|ao j xljbtjebl kr rofqe# qolxl ~ojrl j kr fel fe qokbo tol gj|ct fbb|xr tol xlcjtkfer tf hl dlwlcf~ld gfx tokr t{~l fg gj|ct qkcc j~~c{ fec{ qole tol gj|ct kr fe ~ojrl j# h|t tokr rof|cd bj|rl ef dkggkb|ct{ rkebl tol ~ojrl jxl cjhlcld jxhktxjxkc{ jed je{ ~ojrl bje hl dlrkaejtld jr ~ojrl j% Tol hf|edjx{ bfedktkfer jt tol gj|ct ~fket jxlWj = Pg Kj Kh = > Kb = > Tole tol r{mmltxkbjc bfm~feletr fg b|xxletr jxl=
=
=
=
R|hrtk R|hrtkt|t t|tkea kea = fx =
-
Kj gfx
jed
ke Rlz|le Rlz|lebl bl Eltqfx Eltqfxi i lz|jtk lz|jtkfe# fe# ql fhtjke fhtjke
Rfc|tkfe0 ^FRKTKWL RLZ\LEBL KM^LDJEBL ELTQFXI0
pdjtj: = Y> > : : 8
: 8 8 2 2
> > > > >
>%8<9 >%8<9 >%:8<9 >%:<9 >%8<]9
ELAJTKWL RLZ\LEBL KM^LDJEBL ELTQFXI0
Pdjtj8 = Y> : > >%8<9 > 8 > >%8<9 : 8 > >%:8<9 : 2 > >%:<9 8 2 > >%8<]9 Rkebl tol Elajtkwl rlz|lebl km~ldjebl fg ljbo lclmlet _8 kr tol rjml jr tol ~frktkwl rlz|lebl km~ldjebl fg ljbo lclmlet _: # tolkx eltqfxir jxl jcrf rjml
21
^ojrl j wfctjal ke tlxm fg r{mmltxkbjc bfm~feletr kr Wj = ) ) = -P> =
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-
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+
Pg Kj =
- /
+
2Pg
- /
+
=
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+
= Tol gj|ct b|xxlet kr Kj = 2
=
Kg tol toxll rlz|lebl jr rofqe ke gka% 4%8 tolxl gxfm rjtkrg{ km~ldjebl jxl tole ke
eltqfxi fg tol alelxjtfx jxl bfeelbtld ke rlxklr ql rll tojt tol b|xxlet jed wfctjalr xlr|ctkea tol lz|jtkfer jhfwl# gfx tol toxll rlz|lebl rlxklr qkto tol wfctjalr Lj%
Rlz|lebl Eltqfxi bfeelbtkfer gfx rkeacl ckel tf axf|ed gj|ct
PLXF RLZ\LEBL ELTQFXI0
pdjtj>= Y> : > >%4>9 > 8 > >%:>9 : 8 > >%2>9 : 2 > >%2<9 8 2 > >%1:8<9]9
2;
Ckel Tf Ckel Gj|ct
Ckel Tf Ckel Gj|ct hltqlle ~ojrl h jed b% Tol bkxb|kt dkjaxjm gfx j ckel tf ckel gj|ct toxf|ao km~ldjebl P g hltqlle ~ojrl h jed b fe je |ehjcjebld# [-bfeelbtld alelxjtfx qkto ktr el|txjc axf|edld toxf|ao j xljbtjebl kr rofqe# tol hf|edjx{ bfedktkfer jt tol ~fket jxlWh ‒ Wb=Pg Kh Kh = -Kb Kh)Kb = > Kj = > /\ecfjdld Alelxjtfx+ Tole tol r{mmltxkbjc bfm~feletr fg b|xxlet jxl-
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55 pdjtj>=Y > : > >%4>9 > 8 > >%:>9 : 8 > >%2>9 : 2 > >%2<9 8 2 > >%1:8<9]9 55 pdjtj: = Y> : > >%8<9 > 8 > >%8<9 : 8 > >%:8<9 : 2 > >%:<9 8 2 > >%8<]9 55 pdjtj8=pdjtj:9 55 Ph|r> = Ph|r/pdjtj>+ Ph|r> = > ) >%:?8>k
> ) >%><4
> ) >%:4>>k
> ) >%><4
> ) >%>?74k
> ) >%>7<>k
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> ) >%2<>>k
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> ) >%:8>>k
> ) >%88>>k
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55 Ph|r: = Ph|r/pdjtj:+ Ph|r: =
55 Ph|r8 = Ph|r/pdjtj8+ Ph|r8 =
55 |er{mmgj|ct/pdjtj>#pdjtj:#pdjtj8#Ph|r>#Ph|r:#Ph|r8+ :%C-A Gj|ct 8%C-C Gj|ct 2%C-C-A Gj|ct Letlx tol bofkbl0 : Ckel-tf-axf|ed gj|ct jejc{rkr Letlx Gj|ctld H|r Ef% -5 2 Letlx Gj|ct Km~ldjebl Pg = X ) `*_ ke bfm~cl gfxm0 Pg = `*>%:
4:
=
-
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=
^ojrl h jed b wfctjal ke tlxmr r{mmltxkbjc bfm~feletr jxl-
= R|hrtkt|tkea gfx
jed
=
Tol ~ojrl b|xxletr jxl-
=
Tol gj|ct b|xxlet kr-
Fx
ql alt
Rkeacl ckel tf-axf|ed gj|ct jt h|r Ef% 2 TFTJC GJ\CT B\XXLET =
8%1<82 ~lx |ekt
H|r Wfctjalr d|xkea tol gj|ct ke ~lx |ekt H|r
-------Wfctjal Mjaekt|dl-------
Ef%
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:
>%722>
:%>>47
:%>>47
8
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>%;1<1
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>%Lkt tol ^xfaxjm :%Bfetke|l tol ~xfaxjm gfx jeftolx gj|ct Letlx tol bofkbl0: :%C-A Gj|ct 8%C-C Gj|ct 2%C-C-A Gj|ct Letlx tol bofkbl0 8 Ckel-tf-ckel gj|ct jejc{rkr Letlx Gj|ctld H|r Ef% -5 2 Letlx Gj|ct Km~ldjebl Pg = X ) `*_ ke bfm~cl gfxm Pg = `*>%:
Ckel-tf-ckel gj|ct jt h|r Ef% 2 TFTJC GJ\CT B\XXLET =
2%8>1< ~lx |ekt
H|r Wfctjalr d|xkea tol gj|ct ke ~lx |ekt H|r
-------Wfctjal Mjaekt|dl-------
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:
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8
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>%Lkt tol ^xfaxjm :%Bfetke|l tol ~xfaxjm gfx jeftolx gj|ct Letlx tol bofkbl0: :%C-A Gj|ct 8%C-C Gj|ct 2%C-C-A Gj|ct Letlx tol bofkbl0 2 Df|hcl ckel-tf-axf|ed gj|ct jejc{rkr Letlx Gj|ctld H|r Ef% -5 2
Letlx Gj|ct Km~ldjebl Pg = X ) `*_ ke bfm~cl gfxm0 Pg = `*>%:
42
Jajke tol r{mmltxkbjc bfm~feletr fg wfctjal jxl akwle h{-
=
Rlz|lebl eltqfxi bfeelbtkfer gfx ckel tf ckel gj|ct Df|hcl Ckel Tf Axf|ed Gj|ct0
Df|hcl ckel tf Axf|ed gj|ct Tol bkxb|kt dkjaxjm gfx j df|hcl ckel tf axf|ed gj|ct fe ~ojrl‖r h jed
b toxf|ao km~ldjebl Pg tf axf|ed fe je |ecfjdld# [-bfeelbtld alelxjtfx qkto ktr el|txjc tf axf|edld toxf|ao j xljbtjebl kr rofqe ke gka 4%4% tol hf|edjx{ bfedktkfer jt tol gj|ct ~fket jxl-
Df|hcl ckel-tf-axf|ed gj|ct jt h|r Ef% 2 TFTJC GJ\CT B\XXLET =
:%;121 ~lx |ekt
H|r Wfctjalr d|xkea tol gj|ct ke ~lx |ekt H|r
-------Wfctjal Mjaekt|dl-------
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:
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>%Lkt tol ^xfaxjm :%Bfetke|l tol ~xfaxjm gfx jeftolx gj|ct Letlx tol bofkbl0> 55
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^ojrl h jed b wfctjal ke tlxmr r{mmltxkbjc bfm~feletr jxl-
Rkebl Wh = Wb # olebl
R|hrtkt|tkea gfx tol r{mmltxkbjc bfm~feletr fg b|xxletr# ql alt
= =2 Jajke
2
= = =
Efq =
-
= 2
41
Jajke#
Ql bje jcrf gked tojt
Jed tol gj|ct b|xxlet kr
Rlz|lebl eltqfxi bfeelbtkfer gfx df|hcl ckel tf axf|ed gj|ct
MJTCJH ^XFAXJM0
4;
g|ebtkfe |er{mmgj|ct/pdjtj>#pdjtj:#pdjtj8#Ph|r>#Ph|r:#Ph|r8+ ec = pdjtj:/0#:+9 ex = pdjtj:/0#8+9 eh|r = mj/mj/ec+# mj/ex++9 W> = felr/eh|r# :+ ) `*plxfr/eh|r# :+9 gg = ;;;9 qokcl gg 5 > g~xketg/!Se g~xketg/ !Se :%C-A Gj|ct!+9 Gj|ct!+9 g~xketg/!Se g~xketg/ !Se 8%C-C Gj|ct!+9 Gj|ct!+9 g~xketg/!Se g~xketg/ !Se 2%C-C-A Gj|ct!+9 Gj|ct!+9 b=ke~|t/!SeLetlx b=ke~|t/ !SeLetlx tol bofkbl0 !+9 ! +9 kg /bu=: '' bu=8 '' bu=2+ g~xketg/!Kewjckd g~xketg/ !Kewjckd Bofkbl%%Tx{ jajke!+ jajke! + led kg /b==:+ g~xketg/!SeCkel-tf-axf|ed g~xketg/ !SeCkel-tf-axf|ed gj|ct jejc{rkr Se!+ Se! + eg = ke~|t/!SeLetlx ke~|t/ !SeLetlx Gj|ctld H|r Ef% -5 ! +9 qokcl eg 3= > ss eg 5 eh|r g~xketg/!SeGj|ctld g~xketg/ !SeGj|ctld h|r Ef% m|rt hl hltqlle : ' ,a Se! # eh|r+ eg = ke~|t/!SeLetlx ke~|t/ !SeLetlx Gj|ctld H|r Ef% -5 ! +9 led g~xketg/!SeLetlx g~xketg/ !SeLetlx Gj|ct Km~ldjebl Pg = X ) `*_ ke ! + Pg = ke~|t/!bfm~cl ke~|t/ !bfm~cl gfxm /gfx hfctld gj|ct letlx >+% Pg = ! +9 g~xketg/! g~xketg/ ! Se!+ Se!+ g~xketg/!SeRkeacl g~xketg/ !SeRkeacl ckel tf-axf|ed gj|ct jt h|r Ef% ,aSe! # eg+ j =bfr/8*~k&2+)`*rke/8*~k&2+9 rbtm = Y: : :9 : jU8 j9 : j jU8]9,R{mmltxkbjc jU8]9 ,R{mmltxkbjc Bfm~felet Txjergfxmjtkfe Mjtxk Kj> = W>/eg+&/Ph|r:/eg#eg+)Ph|r8/eg# eg+) Ph|r>/eg# eg+)2*Pg+9 Kj:=Kj>9 Kj8=Kj>9 K>:8=YKj>9 Kj:9 Kj8]9 Kgjhb = rbtm*K>:89 Kgjhbm = jhr/Kgjhb+9 g~xketg/!SeTFTJC g~xketg/ !SeTFTJC GJ\CT B\XXLET = ,;%4g ~lx |ektSeSe!# |ektSeSe! # Kgjhbm/:++ g~xketg/!H|r g~xketg/ !H|r Wfctjalr d|xkea tol gj|ct ke ~lx |ekt SeSe! + g~xketg/! g~xketg/ ! H|r -------Wfctjal Mjaekt|dl------- Se! Se!+ + g~xketg/! g~xketg/ ! Ef% ^ojrl j ^ojrl h ^ojrl b Se! Se!+ + gfx e = Wg>/e+= Wg:/e+= Wg8/e+=
:0eh|r > - Ph|r>/e# eg+*Kj>9 W>/e+ - Ph|r:/e# eg+*Kj:9 > - Ph|r8/e# eg+*Kj89
Wjhb = rbtm*YWg>/e+9 Wg:/e+9 Wg8/e+]9 Wj/e+=Wjhb/:+9 Wh/e+=Wjhb/8+9 Wb/e+=Wjhb/2+9 g~xketg/! g~xketg/ ! ,
ss eg 5 eh|r g~xketg/!SeGj|ctld g~xketg/ !SeGj|ctld h|r Ef% m|rt hl hltqlle : ' ,a Se! # eh|r+
<:
led g~xketg/!SeLetlx g~xketg/ !SeLetlx Gj|ct Km~ldjebl Pg = X ) `*_ ke ! + Pg = ke~|t/!bfm~cl ke~|t/ !bfm~cl gfxm /gfx hfctld gj|ct letlx >+% Pg = ! +9 g~xketg/! g~xketg/ ! Se!+ Se!+ g~xketg/!Ckel-tf-ckel g~xketg/ !Ckel-tf-ckel gj|ct jt h|r Ef% ,aSe!# ,aSe! # eg+ j =bfr/8*~k&2+)`*rke/8*~k&2+9 rbtm = Y: : :9 : jU8 j9 : j jU8]9 Kj>=>9 Kj: = W>/eg+&/Ph|r:/eg#eg+)Ph|r8/eg# eg+)Pg+9 Kj8=-Kj:9 K>:8=YKj>9 Kj:9 Kj8]9 Kgjhb = rbtm*K>:89 Kgjhbm = jhr/Kgjhb+9 g~xketg/!TFTJC g~xketg/ !TFTJC GJ\CT B\XXLET = ,;%4g ~lx |ektSeSe!# |ektSeSe! # Kgjhbm/8++ g~xketg/!H|r g~xketg/ !H|r Wfctjalr d|xkea tol gj|ct ke ~lx |ekt SeSe! + g~xketg/! g~xketg/ ! H|r -------Wfctjal Mjaekt|dl------- Se! Se!+ + g~xketg/! g~xketg/ ! Ef% ^ojrl j ^ojrl h ^ojrl b Se! Se!+ + gfx e = :0eh|r Wg>/e+= >9 Wg:/e+= W>/e+ - Ph|r:/e# eg+*Kj:9 Wg8/e+= > - Ph|r8/e# eg+*Kj89 Wjhb = rbtm*YWg>/e+9 Wg:/e+9 Wg8/e+]9 Wj/e+=Wjhb/:+9 Wh/e+=Wjhb/8+9 Wb/e+=Wjhb/2+9 g~xketg/! g~xketg/ ! , ss eg 5 eh|r g~xketg/!Gj|ctld g~xketg/ !Gj|ctld h|r Ef% m|rt hl hltqlle : ' ,a Se! # eh|r+ eg = ke~|t/!SeLetlx ke~|t/ !SeLetlx Gj|ctld H|r Ef% -5 ! +9 led g~xketg/!SeLetlx g~xketg/!SeLetlx Gj|ct Km~ldjebl Pg = X ) `*_ ke ! + Pg = ke~|t/!bfm~cl ke~|t/ !bfm~cl gfxm /gfx hfctld gj|ct letlx >+% Pg = ! +9 g~xketg/! g~xketg/! Se!+ Se!+ g~xketg/!SeDf|hcl g~xketg/!SeDf|hcl ckel-tf-axf|ed gj|ct jt h|r Ef% ,aSe! # eg+ j =bfr/8*~k&2+)`*rke/8*~k&2+9 rbtm = Y: : :9 : jU8 j9 : j jU8]9 P:: = Ph|r8/eg# eg+*/Ph|r>/eg# eg+) 2*Pg+&/Ph|r8/eg# eg+)Ph|r>/eg# eg+)2*Pg+9 Kj: = W>/eg+&/Ph|r:/eg#eg+)P::+9 Kj8 =-/W>/eg+ - Ph|r:/eg# eg+*Kj:+&Ph|r8/eg#eg+9 Kj> =-/W>/eg+ - Ph|r:/eg# eg+*Kj:+&/Ph|r>/eg#eg+)2*Pg+9 K>:8=YKj>9 Kj:9 Kj8]9 Kgjhb = rbtm*K>:89 Kgjhbm=jhr/Kgjhb+9 Kgt = Kgjhb/8+)Kgjhb/2+9 Kgtm = jhr/Kgt+9 g~xketg/!SeTFTJC g~xketg/ !SeTFTJC GJ\CT B\XXLET = ,;%4g ~lx |ektSeSe!# |ektSeSe! # Kgtm+ g~xketg/!H|r g~xketg/ !H|r Wfctjalr d|xkea tol gj|ct ke ~lx |ekt SeSe! +
g~xketg/! g~xketg/ !
Ef%
^ojrl j
^ojrl h
^ojrl b
Se!+ Se! + <2
gfx e = :0eh|r Wg>/e+= > - Ph|r>/e# eg+*Kj>9 Wg:/e+= W>/e+ - Ph|r:/e# eg+*Kj:9 Wg8/e+= > - Ph|r8/e# eg+*Kj89 Wjhb = rbtm*YWg>/e+9 Wg:/e+9 Wg8/e+]9 Wj/e+=Wjhb/:+9 Wh/e+=Wjhb/8+9 Wb/e+=Wjhb/2+9 g~xketg/! g~xketg/ ! ,%Lkt tol ^xfaxjm !+ !+ g~xketg/!Se g~xketg/ !Se :%Bfetke|l tol ~xfaxjm gfx jeftolx gj|ct!+ gj|ct! + m= ke~|t/!SeLetlx ke~|t/!SeLetlx tol bofkbl0!+9 bofkbl0! +9 kg/m==:+ kg/m==:+ gg =;;;9 lcrl gg = >9 led led
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------g|ebtkfeYPh|r]= g|ebtkfe YPh|r]= Ph|r/pdjtj+ ec=pdjtj/0#:+9
, Bfc|me jxxj{ fg Rtjxtkea h|r fg tol lclmlet
ex=pdjtj/0#8+9 X=pdjtj/0#2+9
, Bfc|me jxxj{ fg Ledkea h|r fg tol lclmlet , Bfc|me jxxj{ fg Xlrkrtjebl fg tol lclmlet
_=pdjtj/0#4+9
, Bfc|m jxxj{ fg Xljbtjebl fg tol lclmlet
ehx=cleato/pdjtj/0#:++9
, Cleato fg tol Wlbtfx = Ef fg Lclmlet
eh|r=mj/mj/ec+#mj/ex++9
, Cjxalrt Lclmletr ke j Jxxj{ = Ef fg H|rlr
P=X)`*_9
, Hxjebo Km~ldjebl ke j Bfm~cl Bfc|me Wlbtfx
{=felr/ehx#:+%&P9
, Hxjebo Jdmkttjebl ke j Bfm~cl Bfc|me Wlbtfx
[=plxfr/eh|r#eh|r+9
, Kektkjckpl [ tf plxflr
gfx i=:0ehx9
, Gfxmjtkfe fg tol fgg dkjaefc lclmletr
kg ec/i+ 5 > '' ex/i+ 5 > [/ec/i+#ex/i++ = [/ec/i+#ex/i++ - {/i+9 [/ex/i+#ec/i++ = [/ec/i+#ex/i++9 , [ H|r Mjtxk kr R{mmltxkbjc led led gfx e= :0 eh|r
, Gfxmjtkfe fg dkjafejc Lclmletr
gfx i = :0ehx kg ec/i+ == e ss ex/i+== e [/e#e+=[/e#e+) {/i+9 led led led Ph|r = kew/[+9
XLR\CT 0 To|r# tol ―MJTCJH‖ ~xfaxjm ojr hlle qxkttle gfx \er{mmltxkbjc Rofxt
Bkxb|kt gj|ct jejc{rkr fg akwle ~fqlx eltqfxi h{ |rkea H|r Km~ldjebl Mjtxk%
Gcfq Bojxt0 Rtjxt
Xljd ^mjh# ^mjd# ^mjj# g# O# ^lxkfd# tr# tb
Bjcb|cjtl M = O &/g*~k+ ^m>=: dlc> = jrke/^m>&^mjh+ Ketkjckpl t>=>9dt = >%>89i=>9k = 89Δϋ> =>
bolbi t 3= ^lxkfd
Bjcb|cjtl I:# I8# I2# I4 jed c:# c8# c2# c4 Bjcb|cjtl I jed c
= > ) ∇ = ∇> )
t= t> ) dt
^cft /t# +
Rtf~
<<
L%Ef01
RTJHKCKT[ JEJC[RKR \RKEA RQKEA B\XWL
87&>?&::
JKM0 Tf dlwlcf~ j ―MJTCJH‖ ~xfaxjm tf jejc{pl tol Rtjhkckt{ fg ^fqlx R{rtlm |rkea Rqkea b|xwl h{ X|eal I|ttj Mltofd%
Tolfx{0 ^fqlx R{rtlm Rtjhkckt{ kr tol ~xf~lxt{ fg tol r{rtlm tojt lejhclr kt tf xlmjke ke j rtjtl fg f~lxjtkea lz|kckhxk|m |edlx efxmjc f~lxjtkea bfedktkfer jed tf xlajke je jbbl~tjhcl rtjtl fg lz|kckhxk|m jgtlx hlkea r|h`lbtld tf j dkrt|xhjebl% Tol{ jxl bcjrrkgkld ke tf
Rtljd{ Rtjtl rtjhkckt{ D{ejmkb Rtjhkckt{ Txjerklet Rtjhkckt{
Rtljd{ Rtjtl Rtjhkckt{ kr tol jhkckt{ fg ~fqlx r{rtlm tf hxkea kt tf j rtjhcl bfedktkfe fx xlmjke ke r{eboxfekrm jgtlx j rmjcc dkrt|xhjebl r|bo jr axjd|jc kegkektlrkmjc wjxkjtkfer ke r{rtlm wjxkjhclr ckil xftfx jeacl# wfctjal# ltb% D{ejmkb Rtjhkckt{ kr tol jhkckt{ fg tol r{rtlm tf xlmjke ke r{eboxfekrm qole kt kr r|h`lbtld tf r|rtjkeld frbkccjtkfer gfccfqld h{ txjerklet rtjtl% Txjerklet Rtjhkckt{ kr tol jhkckt{ fg tol R{rtlm tf hxkea kt tf j rtjhcl bfedktkfe jgtlx cjxal dkrt|xhjeblr d|l tf r|ddle f|tjal fg ckel# r|ddle cfrr fg lbktjtkfe jed r|ddle j~~ckbjtkfe fx xlmfwjc fg cfjdr%
Rqkea Lz|jtkfe0 \edlx efxmjc f~lxjtkea bfedktkfer# tol xlcjtkwl ~frktkfe fg tol xftfx jkr jed tol xlr|ctjet mjaeltkb gklcd jkr kr gkld% Tol jeacl hltqlle tol tqf kr iefqe jr tol ~fqlx jeacl fx tfxz|l jeacl% D|xkea je{ dkrt|xhjebl# xftfx qkcc dlblclxjtl fx jbblclxjtl qkto xlr~lbt tf tol r{eboxfef|rc{ xftjtkea jkx aj~ mmg# j xlcjtkwl mftkfe hlaker% Tol lz|jtkfe dlrbxkhkea tol xlcjtkwl mftkfe kr iefqe jr tol rqkea lz|jtkfe%
Qolxl# O kr tol Kelxtkj Bfertjet%
<1
X|eal‒I|ttj Mltofd0 Tf Rfcwl Efe-Ckeljx Rlbfed Fxdlx Dkgglxletkjc Lz|jtkfer
= = = Qolxl#
= Xftfx R~lld Wjxkjtkfe ke ^lx |ekt
Jt tkml t> = ># k%l% jt ^xl Gj|ct Bfedktkfe# Tol xftfx kr x|eekea jt R{eboxfef|r r~lld plxf%
> =
> =#
tolxlgfxl tol Bojeal ke jea|cjx Wlcfbkt{ kr
jed t> = > # /kektkjc /kektkjc Bfedktkfer+# Bfedktkfer+# clt clt
tol kebxlmlet kebxlmlet ke tkml
qkcc –dt” rtl~r%
= Ñ
= Ñ
= ) Ñ
) = Ñ
= ) Ñ = Y ) ] Ñ = Y ) ) ) ] Olebl jt t: = t> ) dt#
) = Ñ = ) Ñ = Y ) ) ) ] = ) = )
Xl~ljt tol ktlxjtkfe |~ tf dlrkxl tkml
F\T^\T0
Letlx Letlx Letlx Letlx Letlx Letlx Letlx Letlx 55
Rtjhcl Bjrl
tol Mjkm|m wjc|l fg ^fqlx/ke ~%|%+ hlgfxl tol gj|ct fbb|xr0 8%2 tol Mjkm|m wjc|l fg ^fqlx /ke ~%|%+ d|xkea tol gj|ct0 > tol Mjkm|m wjc|l fg ^fqlx /ke ~%|%+jgtlx tol gj|ct kr Bcljxld0 :%< tol R{rtlm Gxlz|leb{0 <> tol Kelxtkj Bfertjet fg Mjbokel (O(0 < Rkm|cjtkfe ^lxkfd/rlb+0 : gj|ct fbb|xxlebl tkml /rlb+0 >%>8 tol gj|ct bcljxjebl tkml/rlb+0 >%>4
MJTCJH ^XFAXJM0
<;
bcb9 bcljx jcc jcc9 9 ^mjh = ke~|t/!Letlx ke~|t/!Letlx tol Mjkm|m wjc|l fg ^fqlx/ke ~%|%+ hlgfxl tol gj|ct fbb|xr0 !+9 ^mjd = ke~|t/!Letlx ke~|t/!Letlx tol Mjkm|m wjc|l fg ^fqlx /ke ~%|%+ d|xkea tol gj|ct0 !+9 ^mjj = ke~|t/!Letlx ke~|t/!Letlx tol Mjkm|m wjc|l fg ^fqlx /ke ~%|%+jgtlx tol gj|ct kr Bcljxld0 !+9 g = ke~|t/!Letlx ke~|t/!Letlx tol R{rtlm Gxlz|leb{0 !+9 !+9 O = ke~|t/!Letlx ke~|t/!Letlx tol Kelxtkj Bfertjet fg Mjbokel (O(0 !+9 !+9 ^lxkfd = ke~|t/!Letlx ke~|t/!Letlx Rkm|cjtkfe ^lxkfd/rlb+0 !+9 !+9 tr = ke~|t/!Letlx ke~|t/!Letlx gj|ct fbb|xxlebl tkml /rlb+0 !+9 tb = ke~|t/!Letlx ke~|t/!Letlx tol gj|ct bcljxjebl tkml/rlb+0 !+9 !+9 M = O&/g*~k+9 , Clt tol alelxjtfx hl f~lxjtkea ke rtljd{ rtjtl qkto j tfxz|l jeacl dlc>% , Jt tok rbfedktkfe tol mlbojekbj ~fqlx ke~|t kr ^m> jed tol lclbtxkbjc , f|t~|t kr ^l>% \edlx kdljc bfedktkfer ^m> = ^l> = ^mj> Rke/dlc>+9 ^m> = :9 ^l> = :9 ^mlbo = ^m>9 dlc> = jrke/:&^mjh+9 dt = >%>89 i=>9 k = 89 qokcl/i qokcl /i 3= ^lxkfd+ kg/i3=tr+ kg /i3=tr+ ^mj = ^mjh9 lcrlkg//i5tr+'/i3=tb++ lcrlkg //i5tr+'/i3=tb++ ^mj = ^mjd9 lcrl ^mj = ^mjj9 led t/:+ = >%>9 dlc/:+ = dlc>9 q/:+ = >9 i: = dt*q/k-:+9 c: = dt*/^mlbo - ^mj*rke/dlc/k-:+++&M9 i8 = dt*/q/k-:+ ) c:&8+9 c8 = dt*/^mlbo - ^mj*rke/dlc/k-:+) i:&8++&M9 i2 = dt*/q/k-:+ ) c8&8+9 c2 = dt*/^mlbo - ^mj*rke/dlc/k-:+) i8&8++&M9 i4 = dt*/q/k-:+ ) c2+9 c4 = dt*/^mlbo - ^mj*rke/dlc/k-:+) i2++&M9 dlc/k+ = dlc/k-:+ ) /i:)8*i8)8*i2)i4+&79 q/k+ = q/k-:+ ) /c:)8*c8)8*c2)c4+&79 t/k+ = /k-:+*dt9 i = i ) dt9 k = k ) :9 led i = >0>%>80^lxkfd9 ~cft /t#dlc+ cjhlc/!Tkml/Rlbfedr+! cjhlc/!Tkml/Rlbfedr+!+ + {cjhlc/!Dlctj/ke {cjhlc/!Dlctj/ke xjd+!+ xjd+!+ tktcl/!Rqkea tktcl/!Rqkea Lz|jtkfe Rfc|tkfe!+ Rfc|tkfe!+
F\T^\T0 \ertjhcl Bjrl
Letlx Letlx Letlx Letlx Letlx Letlx Letlx Letlx 55
tol Mjkm|m wjc|l fg ^fqlx/ke ~%|%+ hlgfxl tol gj|ct fbb|xr0 8%2 tol Mjkm|m wjc|l fg ^fqlx /ke ~%|%+ d|xkea tol gj|ct0 > tol Mjkm|m wjc|l fg ^fqlx /ke ~%|%+jgtlx tol gj|ct kr Bcljxld0 :%< tol R{rtlm Gxlz|leb{0 <> tol Kelxtkj Bfertjet fg Mjbokel (O(0 < Rkm|cjtkfe ^lxkfd/rlb+0 : gj|ct fbb|xxlebl tkml /rlb+0 >%>8 tol gj|ct bcljxjebl tkml/rlb+0 >%?
7:
XLR\CT0
To|r# tol ‟MJTCJH‛ ~xfaxjm ojr hlle qxkttle tf jejc{pl tol Rtjhkckt{ fg ~fqlx R{rtlm |rkea rqkea b|xwl h{ X|eal ‒ I|ttj Mltofd%
Rtjxt
Gcfq bojxt0
Xljd ckel djtj# h|r Djtj # tfclxjebl# κ
:% Bfm~|tl [ h|r Mjtxk 8%Ketkjckpl H|r Wfctjal 2%Rlt ktlxjtkfe bf|et ktlx =:
H|r Ef# k =:
k=k): Ef
Dflr k xlglxr tf ^W H|r
Welq = W /r~lb+ δ bjc Zkbjc = - Km Y W k* bjc ZAk = Zk
] ) ZCk
ZAk 5 Zk/mjx+
ZAk 3 Zk/mke+ Bolbi gfx Z ckmkt
ZAk = Zk/mj+ Zk/r~lb+ = Zk/mj+ -ZCk
Zk r
lb
ZAk = Zk/mke+ Zk/r~lb+ = Zk/mke+ - ZCk
= Zkbjc
Ef
Kr k 3 E [lr Ef
μ
Jxl jcc [lr
Bjcb|cjtl ckel gcfqr# cfrrlr jed rcjbi h|r fqlx
^xket tol xlr|ct
ktlx =ktlx ) :
72
Lx%Ef0? CFJD GCFQ JEJC[RKR H[ AJ\RR RLKDJC MLTOFD 87&>?&::
JKM0 Tf ~lxgfxm tol Cfjd gcfq jejc{rkr fg ~fqlx r{rtlm eltqfxi h{ Aj|rr Rlkdjc Ktlxjtkwl Jcafxktom% TOLFX[0 Tol Cfjd gcfq rt|dklr kewfcwl tol rfc|tkfe fg tol ~fqlx r{rtlm eltqfxi |edlx rtljd{ rtjtl bfedktkfer% Tol rfc|tkfe kr fhtjkeld h{ bferkdlxkea blxtjke kelz|jckt{ bfertxjketr km~frld fe efdl wfctjalr jed xljbtkwl ~fqlx fg alelxjtfxr% Tol mjke kegfxmjtkfe fhtjkeld gxfm j cfjd gcfq rt|d{ jxl tol mjaekt|dl jed ~ojrl jeacl fg tol wfctjal jt ljbo h|r jed xljc jed xljbtkwl ~fqlx gcfqkea ke ljbo ckel% JCAFXKTOM0 :% Gfxm [ H|r mjtxk 8% Jrr|ml Wi = Wi/r~lb+ >> jt jcc alelxjtfx h|r 2% Jrr|ml Wi = : >> = :)`> jt jcc cfjd h|r 4% Rlt ktlxjtkfe bf|et = :/ktlx = :+ <% Clt h|r e|mhlx k = : 7% Kg ‟k‛ xlglxr tf alelxjtfx h|r af tf rtl~ ef%1# ftolxqkrl af tf rtl~ ?% 1%
/j+ Kg ‟k‛ xlglxr tf Rcjbi h|r af tf rtl~ ;% Ftolxqkrl af tf rtl~ 1/h+ /h+ Bfm~|tl Z k |rkea#
7<
Bolbi gfx Z ckmkt wkfcjtkfe% Kg Zk/mke+ 3 ZAk 3 Zk/mj+# tole Z k/r~lb+ = Zkbjc Kg Zk/mke+ 5 ZAk# tole Zk/r~lb+ = Zk/mke+- ZCk Kg Zk/mj+ 3 ZAk# tole Zk/r~lb+ = Zk/mj+- ZCk Kg Zckmkt kr wkfcjtld# tole txljt tokr h|r jr ^-Z h|r tkcc bfewlxalebl kr fhtjkeld ?% Bfm~|tl Wk |rkea tol lz|jtkfe
;% Kg ‟k‛ kr clrr toje e|mhlx fg h|rlr # kebxlmlet k h{ : jed af tf rtl~ 7% :>% Bfm~jxl tqf r|bblrrkwl ktlxjtkfe wjc|lr gfx W k elq
fcd
Kg Wk
- Wk
3 tfclxjebl# af tf rtl~ :8%
::% \~djtl tol elq wfctjal jr Welq = Wfcd ) κ/Welq - Wfcd+ fcd
W
elq
= W
ktlx = ktlx ) :9 af tf rtl~ <
:8% Bfm~|tl xlclwjet z|jetktklr% *
Rcjbi H|r ^fqlx# R : = ^k - `Zk = W*K = W k Ckel gcfqr Rk` = ^k` ) `Zk` :2% Rtf~ tol Llb|tkfe%
71 MJTCJH ^XFAXJM0
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s
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s
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s H|r
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ckeldjtj = Y : :
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8
2
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{h|r = {h|rar/ckeldjtj+9 ,
sH|r s T{~l s Wr~ s toltj s ^Ak s ZAk s ^Ck s ZCk s Zmke s Zmj s
h|rdjtj = Y :
:
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h|r = h|rdjtj/0#:+9
, H|r e|mhlx%
t{~l = h|rdjtj/0#8+9
, T{~l fg H|r :-Rcjbi# 8-^W# 2-^Z%
W = h|rdjtj/0#2+9
, Kektkjc H|r Wfctjalr%
to = h|rdjtj/0#4+9
, Kektkjc H|r Wfctjal Jeaclr%
AleMQ = h|rdjtj/0#<+9
, ^Ak# Xljc ^fqlx ke`lbtld ketf tol h|rlr%
AleMWJX = h|rdjtj/0#7+9
, ZAk# Xljbtkwl ^fqlx ke`lbtld ketf tol h|rlr%
CfjdMQ = h|rdjtj/0#1+9
, ^Ck# Xljc ^fqlx Dxjqe gxfm tol h|rlr%
CfjdMWJX = h|rdjtj/0#?+9
, ZCk# Xljbtkwl ^fqlx Dxjqe gxfm tol h|rlr%
Zmke = h|rdjtj/0#;+9
, Mkekm|m Xljbtkwl ^fqlx Ckmkt
Zmj = h|rdjtj/0#:>+9
, Mjkm|m Xljbtkwl ^fqlx Ckmkt
eh|r = mj/h|r+9
, Tf alt ef% fg h|rlr
^ = AleMQ - CfjdMQ9
, ^k = ^Ak - ^Ck# Xljc ^fqlx jt tol h|rlr%
Z = AleMWJX - CfjdMWJX9
, Zk = ZAk - ZCk# Xljbtkwl ^fqlx jt tol h|rlr%
W~xlw = W9 tfclx = :9
, Tfclxlebl%
ktlxjtkfe = :9
, ktlxjtkfe rtjxtkea
qokcl /tfclx 5 >%>>>>:+
, Rtjxt fg qokcl cff~
gfx k = 80eh|r r|m{w = >9 gfx i = :0eh|r kg k u= i r|m{w = r|m{w ) {h|r/k#i+* W/i+9
, Wi * [ki
led led kg t{~l/k+ == 8
, Bfm~|tkea Zk gfx ^W h|r
Z/k+ = -kmja/bfe`/W/k++*/r|m{w ) {h|r/k#k+*W/k+++9 kg /Z/k+ 5 Zmj/k++ ss /Z/k+ 3 Zmke/k++ kg Z/k+ 3 Zmke/k+
, Bolbikea gfx Zk Wkfcjtkfe%
, Qoltolx wkfcjtld tol cfqlx ckmkt%
Z/k+ = Zmke/k+9 lcrl
, Ef# wkfcjtld tol |~~lx ckmkt%
Z/k+ = Zmj/k+9 led t{~l/k+ = 29
, Kg Wkfcjtld# bojeal ^W h|r tf ^Z h|r%
led led W/k+ = /:&{h|r/k#k++*//^/k+-`*Z/k++&bfe`/W/k++ - r|m{w+9 , Bfm~|tl H|r Wfctjalr kg t{~l/k+ == 8 , Gfx ^W H|rlr# Wm xlmjker rjml# h|t Jea bojealr%
7;
led led ktlxjtkfe = ktlxjtkfe ) :9 , Kebxlmlet ktlxjtkfe bf|et% tfclx = mj/jhr/jhr/W+ - jhr/W~xlw+++9 , Bjcb|cjtl tfclxjebl% W~xlw = W9 , W~xlw kr xlz|kxld gfx elt ktlxjtkfe ,W/k+ = ~fc8xlbt/jhr/W~xlw/k++# jeacl/W/k+++9 led , Led fg qokcl cff~ & Ktlxjtkfe W9 , H|r Wfctjalr ke Bfm~cl gfxm% WB = bfe`//W++9 Wmja = jhr/W+9 , Gkejc H|r Wfctjalr% Jea = :?>&~k*jeacl/W+9 , Gkejc H|r Wfctjal Jeaclr ke Dlaxll% gfx ~ = :0eh|r r|m{w = >9 gfx z = :0eh|r r|m{w = r|m{w ) {h|r/~#z+*W/z+9 led R/~+ = WB/~+* r|m{w9 led dkr~/!"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""! dkr~/!"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""! +9 dkr~/!-------------------------------------------------------------------------------! dkr~/!-------------------------------------------------------------------------------! +9 dkr~/! dkr~/! Aj|rr Rkldjc Cfjd gcfq Jejc{rkr ! +9 dkr~/!-------------------------------------------------------------------------------! dkr~/!-------------------------------------------------------------------------------! +9 dkr~/!s dkr~/!s H|r s W s Jeacl s ^ Z ! +9 dkr~/!s dkr~/!s Ef s ~| s Dlaxll s ~%|% ~%| ! +9 gfx m = :0eh|r dkr~/!---------------------------------------------------------------------------! dkr~/ !---------------------------------------------------------------------------! +9 g~xketg/!,2a! g~xketg/ !,2a!# # m+9 g~xketg/! g~xketg/! ,?%4g!# ,?%4g!# Wmja/m++9 g~xketg/! g~xketg/ ! ,?%4g!# Jea/m++9 ,?%4g!# g~xketg/! g~xketg/ ! ,?%4g ,?%4g! ,?%4g!# # xljc/R/m++#kmja/R/m+++9 g~xketg/!Se! g~xketg/ !Se!+9 +9 led gh th ec ^c Zc
= = = = =
ckeldjtj/0#:+9 ckeldjtj/0#8+9 cleato/gh+9 h|rdjtj/0#1+9 h|rdjtj/0#?+9
, Gxfm h|r e|mhlx%%% , Tf h|r e|mhlx%%% , Ef% fg Hxjebolr%% , ^Ck%% , ZCk%%
Kk` = plxfr/eh|r#eh|r+9 Rk` = plxfr/eh|r#eh|r+9 Rk = plxfr/eh|r#:+9 ,Ckel B|xxlet Gcfqr%% gfx m = :0ec ~ = gh/m+9 z = th/m+9 Kk`/~#z+ = -/W/~+ - W/z++*{h|r/~#z+9 , [/m#e+ = -{/m#e+%% Kk`/z#~+ = -Kk`/~#z+9 led ,Kk` = r~jxrl/Kk`+9 Kk`m = jhr/Kk`+9 Kk`j = jeacl/Kk`+9
1:
, Ckel ^fqlx Gcfqr%% gfx m = :0eh|r gfx e = :0eh|r kg m u= e Rk`/m#e+ = W/m+*bfe`/Kk`/m#e++9 led led led ,Rk` = r~jxrl/Rk`+9 ^k` = xljc/Rk`+9 Zk` = kmja/Rk`+9 , Ckel Cfrrlr%% Ck` = plxfr/ec#:+9 gfx m = :0ec ~ = gh/m+9 z = th/m+9 Ck`/m+ = Rk`/~#z+ ) Rk`/z#~+9
led C~k` = xljc/Ck`+9 Czk` = kmja/Ck`+9 , Dkr~cj{ dkr~/!-------------------------------------------------------------------------------! dkr~/!-------------------------------------------------------------------------------! +9 dkr~/! dkr~/! Ckel Gcfq jed Cfrrlr ! +9 dkr~/!-------------------------------------------------------------------------------! dkr~/!-------------------------------------------------------------------------------! +9 dkr~/!sGxfmsTf dkr~/!sGxfmsTf s ^ s Z s Gxfms Tf s ^ s Z s Ckel Cfrr s!+9 s! +9 s!+9 +9 dkr~/!sH|r dkr~/!sH|r sH|rs ~%|% s ~%|% s H|r s H|rs ~%|% s ~%|% s ~%|% s ~%|%s! gfx m = :0ec ~ = gh/m+9 z = th/m+9 dkr~/!----------------------------------------------------------------------------! +9 g~xketg/!,4a! g~xketg/ !,4a!# # ~+9 g~xketg/!,4a! g~xketg/!,4a!# # z+9 g~xketg/! g~xketg/! ,?%2g!# ,?%2g!# ^k`/~#z++9 g~xketg/! g~xketg/ ! ,?%2g!# Zk`/~#z++9 g~xketg/! ,?%2g!# g~xketg/ ! ,4a!# z+9 g~xketg/!,4a! ,4a!# g~xketg/!,4a!# # ~+9 g~xketg/! g~xketg/ ! ,?%2g!# ^k`/z#~++9 g~xketg/! ,?%2g!# g~xketg/ ! ,?%2g!# Zk`/z#~++9 ,?%2g!# g~xketg/! g~xketg/ ! ,?%2g!# ,?%2g!# C~k`/m++9 g~xketg/! g~xketg/ ! ,?%2g!# Czk`/m++9g~xketg/!Se! ,?%2g!# Czk`/m++9g~xketg/!Se!+9 +9 led dkr~/!--------------------------------------------------------------------------------! +9 g~xketg/! g~xketg/ !
Tftjc Cfrr
! +9
g~xketg/! g~xketg/ ! ,?%2g!# ,?%2g!# r|m/C~k`++9 g~xketg/! g~xketg/ ! ,?%2g!# r|m/Czk`++9 g~xketg/!Se! ,?%2g!# g~xketg/ !Se!+9 +9 dkr~/!--------------------------------------------------------------------------------! +9 dkr~/!""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""! +9 -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
g|ebtkfe xlbt = ~fc8xlbt/xof#toltj+ xlbt = xof%*bfr/toltj+ ) `*xof%*rke/toltj+9
^XFHCLM0 ^lxgfxm tol Cfjd gcfq jejc{rkr gfx akwle ~fqlx r{rtlm eltqfxi |rkea Aj|rr Rlkdjc Ktlxjtkwl Jcafxktom% Tol mjaekt|dl fg j wfctjal h|r : kr jd`|rtld t> :%>< ~lx |ekt% Tol rbold|cld cfjdr jt h|rlr 8 jed 2 jxl jr mjxild fe tol dkjaxjm% Ckel Km~ldjeblr jxl mjxild ke ~lx |ekt fe j :>>-MWJ hjrl jed ckel bojxakea r|rbl~tjeblr jxl elaclbtld%
RFC\TKFE0
""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" ------------------------------------------------------------------------------------Aj|rr Rkldjc
Cfjd gcfq Jejc{rkr
------------------------------------------------------------------------------------s H|r s s Ef
s
W
s
Jeacl
s
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s
Dlaxll s
^
Z
~%|%
~%|
------------------------------------------------------------------------------------:
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>%>>>>
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------------------------------------------------------------------------------------8
>%;?:?
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-8%<7<;
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------------------------------------------------------------------------------------2
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-8%?782
-:%2?7>
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------------------------------------------------------------------------------------Ckel Gcfq jed Cfrrlr ------------------------------------------------------------------------------------sGxfmsTf s
^
sH|r sH|rs
~%|%
s s
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s Gxfms Tf s
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------------------------------------------------------------------------------------:
8
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------------------------------------------------------------------------------------:
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------------------------------------------------------------------------------------8
2
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8
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------------------------------------------------------------------------------------Tftjc Cfrr
>%:42
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-------------------------------------------------------------------------------------
12
g|ebtkfe {h|r = {h|rar/ckeldjtj+9
, Xlt|xer {h|r
gh = ckeldjtj/0#:+9
, Gxfm h|r e|mhlx%%%
th = ckeldjtj/0#8+9
, Tf h|r e|mhlx%%%
x = ckeldjtj/0#2+9
, Xlrkrtjebl# X%%%
= ckeldjtj/0#4+9
, Xljbtjebl# _%%%
h = ckeldjtj/0#<+9
, Axf|ed Jdmkttjebl# H&8%%%
p = x ) k*9
, P mjtxk%%%
{ = :%&p9
, Tf alt kewlxrl fg ljbo lclmlet%%%
h = k*h9
, Mjil H kmjakejx{%%%
eh|r = mj/mj/gh+#mj/th++9 ehxjebo = cleato/gh+9
, ef% fg h|rlr%%% , ef% fg hxjebolr%%%
{h|r = plxfr/eh|r#eh|r+9
, Kektkjckrl [H|r%%%
, Gfxmjtkfe fg tol Fgg Dkjafejc Lclmletr%%% gfx i=:0ehxjebo {h|r/gh/i+#th/i++ = -{/i+9 {h|r/th/i+#gh/i++ = {h|r/gh/i+#th/i++9 led , Gfxmjtkfe fg Dkjafejc Lclmletr%%%% gfx m=:0eh|r gfx e=:0ehxjebo kg gh/e+ == m s th/e+ == m {h|r/m#m+ = {h|r/m#m+ ) {/e+ ) h/e+9 led led led {h|r9
, H|r Jdmkttjebl Mjtxk
XLR\CT0
To|r# tol ‟MJTCJH‛ ~xfaxjm ojr hlle qxkttle tf ~lxgfxm cfjd gcfq jejc{rkr fg akwle ~fqlx r{rtlm eltqfxi h{ |rkea Aj|rr Rlkdjc Ktlxjtkwl
RKEACL JXLJ R[RTLM0
:% Je krfcjtld ~fqlx rtjtkfe ojr tol gfccfqkea ~jxjmltlxr T|xhkel tkml bfertjet#
T
Afwlxefx tkml bfertjet#
= >%
a
= >%8rlb
Alelxjtfx kelxtkj bfertjet# O = %? ~lxblet gfx j : ~lxblet bojeal ke gxlz|leb{# k%l%# D = >%? /j+ Tol afwlxefx r~lld xla|cjtkfe kr rlt tf X = >%>< ~lx |ekt% Tol t|xhkel xjtld f|t~|t kr 8<>MQ jt efmkejc gxlz|leb{ fg 7>Op% Tol CGB R{rtlm kr lz|k~~ld qkto tol rlbfedjx{ ketlaxjc bfetxfc cff~ gfx JAB% J r|ddle cfjd bojeal fg <> MQ /Δ^C = >%8 ~lx |ekt+ fbb|xr% Rlt tol ketlaxjc bfetxfcclx ajke tf IK = 1% Bfertx|bt tol RKM\CKEI hcfbi dkjaxjm jed fhtjke gxlz|leb{ dlwkjtkfe xlr~ferl fg jhfwl bfedktkfe%
RFC\TKFE0 RKM\CKEI HCFBI DKJAXJM
1<
L%Ef0; >8&>;&::
CFJD GXLZ\LEB[ BFETXFC FG RKEACL JED DF\HCL JXLJ R[RTLM QKTO TKL CKEL
JKM0 Tf rkm|cjtl tol bojxjbtlxkrtkbr fg cfjd gxlz|leb{ bfetxfc fg
rkeacl jed df|hcl jxlj r{rtlm qkto tkl ckel |rkea MJTCJH% TOLFX[0
Tol Cfjd gxlz|leb{ bfetxfc YCGB] cff~ bfetxfcr tol xljc ~fqlx jed gxlz|leb{ jed J|tfmjtkb Wfctjal Alelxjtfx YJWX] cff~ xla|cjtlr tol xljbtkwl ~fqlx jed wfctjal mjaekt|dl% CGB ojr ajkeld ke km~fxtjebl qkto tol axfqto fg ketlxbfeelbtld r{rtlmr jed ojr mjdl tol f~lxjtkfe fg ketlxbfeelbtld R{rtlm ^frrkhcl% Tol F~lxjtkfe Fh`lbtkwlr fg tol CGB jxl tf mjketjke xljrfejhc{ |ekgfxm gxlz|leb{# tf dkwkdl tol cfjd hltqlle alelxjtfxr# jed tf bfetxfc tol Tkl ckel ketlxbojeal rbold|clr% JAB KE J RKEACL JXLJ R[RTLM0
Qkto tol ~xkmjx{ CGB cff~# j bojeal ke tol r{rtlm cfjd qkcc xlr|ct ke rtljd{ rtjtl gxlz|leb{ dlwkjtkfe# dl~ledkea fe tol afwlxefx r~lld xla|cjtkfe% Ke fxdlx tf xld|bl tol gxlz|leb{ dlwkjtkfe tf plxf# ql m|rt ~xfwkdl j xlrlt jbtkfe% Tol xlrt jbtkfe bje hl jboklwld h{ ketxfd|bkea je ketlaxjc bfetxfcclx tf jbt fe tol cfjd xlglxlebl rlttkea tf bojeal tol r~lld rlt ~fket% Tol ketlaxjc bfetxfcclx kebxljrlr tol r{rtlm t{~l h{ : qokbo gfxblr tol gkejc gxlz|leb{ dlwkjtkfe tf plxf% Tol CGB r{rtlm# qkto tol jddktkfe fg tol rlbfedjx{ cff~# kr rofqe ke Gka|xl% Tol ketlaxjc bfetxfcclx ajke I K m|rt hl K jd`|rtld gfx j rjtkrgjbtfx{ txjerklet xlr~ferl%
Gxlz|leb{ Dlwkjtkfe Rtl~ Xlr~ferl
Δϋ
+ d j x % | % ~ e k / ϋ Δ
Tkml / rlb+ rlb +
11
JAB KE TOL TQF JXLJ JXLJ R[RTLM0
Ke mje{ bjrlr# j axf|~ fg alelxjtfxr jxl bcfrlc{ bf|~cld ketlxejcc{ jed rqkea ke |ekrfe% G|xtolxmfxl# tol alelxjtfx t|xhkelr tled tf ojwl rjml xlr~ferl bojxjbtlxkrtkbr% R|bo j axf|~ fg alelxjtfxr jxl rjkd h{ Bfolxlet% Tole kt kr ~frrkhcl tf clt tol CGB cff~ xl~xlrlet tol qofcl r{rtlm# qokbo kr xlglxxld tf jr j Bfetxfc jxlj% Hcfbi dkjaxjm fg tqf jxlj r{rtlm qkto fec{ ~xkmjx{ CGB cff~ kr rofqe ke gka|xl#
Bfewletkfejc CGB kr hjrld |~fe cklkl-c ckel hkjr bfetxfc# qolxl ljbo jxlj tledr tf xld|bl tol mlj bfetxfc bfetxfc lxxfx /JBL+ tf plxf% Tol bfetxfc lxxfx gfx ljbo ljbo jxlj bferkrtr fg j ckeljx bfmhkejtkfe bfmhkejtkfe fg gxlz|leb{ jed tklckel lxxfx%
Tol jxlj hkjr Ik dltlxmke dltlxmkelr lr tol jmf|et fg fg ketlxjbtkfe d|xkea j dkrt|xhjebl ke tol elkaohfxkea jxljr% Je fwlxjcc rjtkrgjbtfx{ ~lxgfxmjebl kr jboklwld qole Ik kr rlclbtld lz|jc tf tol gxlz|leb{ gxlz|leb{ hkjr gjbtf gjbtfx x fg tojt jxlj# k%l%# Hk = :&Xk ) D k9 To|r# tol JBLr gfx j tqf-jxlj r{rtlm jxl
TQF JXLJ R[RTLM0 :% J tqf jxlj r{rtlm bfeelbtld h{ j tkl ckel ojr tol gfccfqkea
~jxjmltlxr fe j :>>>MWJ bfmmfe hjrl Jxlj R~lld Xla|cjtkfe Gxlz|leb{ ‒rler%cfjd bflgg%
Kelxtkj Bfertjet Hjrl ^fqlx Afwlxefx Tkml Bfertjet T|xhkel Tkml Bfertjet
:
8
X:=>%>< D:=>%7 O:=< :>>>MWJ
X8=>%>78< D8=>%; O8=4 :>>>MWJ
a: T:
= >%8rlb =>%
a: T:
= >%2rlb =>%7rlb
Tol |ektr jxl f~lxjtkea ke ~jxjcclc jt tol efmkejc gxlz|leb{ fg 7>Op% Tol r{eboxfekpkea ~fqlx bflggkbklet kr bfm~|tld gxfm tol kektkjc f~lxjtkea bfedktkfe jed kr akwle tf hl ^r = 8 ~%|% J cfjd bojeal fg :?1%< MQ fbb|xr ke jxlj :% Bfertx|bt tol RKM\CKEI mfdlc gfx tol tqf jxlj r{rtlm qkto tol kebc|rkfe fg tol JBL jed Fhtjke tol gxlz|leb{ jed ^fqlx xlr~ferl fg ljbo jxlj% RFC\TKFE0 RKM\CKEI HCFBI DKJAXJM
1;
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MJTCJH ^XFAXJM0 bcb9 bcljx jcc jcc9 9 bcfrl jcc jcc9 9 dkr~/!---------------------------------------------------! dkr~/!---------------------------------------------------! + g~xketg/!SeLBFEFMKB g~xketg/!SeLBFEFMKB DKR^JTBO KEBC\DKEA ALELXJTFX CKMKTRSe!+ CKMKTRSe! + dkr~/!---------------------------------------------------! dkr~/!---------------------------------------------------! + gg = ;;;9 qokcl gg 5 > g~xketg/!Se:%Qktof|t g~xketg/!Se:%Qktof|t CfrrlrSe8%Qkto CfrrlrSeSe!+ CfrrlrSeSe! + bo = ke~|t/!Letlx ke~|t/ !Letlx [f|x Bofkbl0 !+9 ! +9 ^D = ke~|t/!Letlx ke~|t/ !Letlx tol Tftjc Dlmjed /MQ+0!+9 /MQ+0! +9 BT = ke~|t/!Letlx ke~|t/ !Letlx tol Bfrt mjtxk G|ebtkfe0 !+9 ! +9 J = BT/0#:+9 H = BT/0#8+9 B = BT/0#2+9 E = cleato/J+9, cleato/J+9 , Akwlr tol Ef fg Alelxjtfx |ektr ^CKM = ke~|t/!Letlx ke~|t/ !Letlx tol ^fqlx Ckmkt Mjtxk Ymke mj]0 ! +9 kg/bo kg /bo == 8+ HCB = ke~|t/!Letlx ke~|t/ !Letlx Cfrr Bflggkbkletr Mjtxk YH]0!+9 YH]0! +9 lcrl HCB = plxfr/E#E+9 led C = ke~|t/!Letlx ke~|t/ !Letlx tol kektkjc wjc|l/jrr|m~tkfe+ fg Cjmhdj 0 !+9 ! +9 DLCVC = :>9 ktlx = >9 qokcl /jhr/DLCVC+ 5= >%>>>:+ ,Bjcb|cjtkfe fg ^ jed Dlc ^ gfx k=:0E E\M: =/C -H/k++9 DLE: =8*/B/k+)C*HCB/k#k++9 ^/k+ = E\M:%&DLE:9 kg/^/k+5^CKM/k#8++ kg /^/k+5^CKM/k#8++ ^/k+=^CKM/k#8+9 led kg/^/k+3^CKM/k#:++ kg /^/k+3^CKM/k#:++ ^/k+=^CKM/k#:+9 led led ^R\M =r|m/^+9 ^CR\M = r|m/HCB*/^%U8+!+9 DLC^ = ^D ) ^CR\M - ^R\M9 ,Bjcb|cjtkfe fg Dlc Cjmhdj gfx k=:0E E\M8 =/B/k+ ) H/k+%*HCB/k#k++9 DLE8 = 8*/B/k+)C*HCB/k#k++*/B/k+)C*HCB/k#k++9 ^h{Dlc/k+ = E\M8%&DLE89 led
--------------------------------------------------LBFEFMKB DKR^JTBO KEBC\DKEA ALELXJTFX CKMKTR --------------------------------------------------:%Qktof|t Cfrrlr 8%Qkto Cfrrlr Letlx [f|x Bofkbl0 : Letlx tol Tftjc Dlmjed /MQ+0;1< Letlx tol Bfrt mjtxk G|ebtkfe0 Y<>> <%2 >%>>494>> <%< >%>>798>> <%? >%>>;9]9 Letlx tol ^fqlx Ckmkt Mjtxk Ymke mj]0 Y8>> 4<>9:<> 2<>9:>> 88<9]9 Letlx tol kektkjc wjc|l/jrr|m~tkfe+ fg Cjmhdj 0 7 Kebxlmletjc Bfrt fg Dlckwlxld ^fqlx (Cjmhdj( =
;%4> $&MQo
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eh|r = mj/h|r+9
, Tf alt ef% fg h|rlr
t{~l = h|rdjtj/0#8+9
, T{~l fg H|r :-Rcjbi# 8-^W# 2-^Z%%
W = h|rdjtj/0#2+9
, R~lbkgkld Wfctjal%%
dlc = h|rdjtj/0#4+9
, Wfctjal Jeacl%%
^a = h|rdjtj/0#<+9
, ^Ak%%
Za = h|rdjtj/0#7+9
, ZAk%%
^c = h|rdjtj/0#1+9
, ^Ck%%
Zc = h|rdjtj/0#?+9
, ZCk%%
Zmke = h|rdjtj/0#;+9
, Mkekm|m Xljbtkwl ^fqlx Ckmkt%%
Zmj = h|rdjtj/0#:>+9
, Mjkm|m Xljbtkwl ^fqlx Ckmkt%%
^ = ^a - ^c9
, ^k = ^Ak - ^Ck%%
Z = Za - Zc9
, Zk = ZAk - ZCk%%
^r~ = ^9
, ^ R~lbkgkld%%
Zr~ = Z9 A = xljc/[+9
, Z R~lbkgkld%% , Bfed|btjebl mjtxk%%
H = kmja/[+9
, R|rbl~tjebl mjtxk%%
~w = gked/t{~l == 8 s t{~l == :+9
, ^W H|rlr%%
~z = gked/t{~l == 2+9
, ^Z H|rlr%%
e~w = cleato/~w+9
, Ef% fg ^W h|rlr%%
e~z = cleato/~z+9
, Ef% fg ^Z h|rlr%%
Tfc = :9 Ktlx = :9 qokcl /Tfc 5 :l-<+
, Ktlxjtkfe rtjxtkea%%
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led
;<
, Bolbikea Z-ckmkt wkfcjtkfer%% kg Ktlx 3= 1 '' Ktlx 5 8
, Fec{ bolbild |~ tf 1to ktlxjtkfer%%
gfx e = 80eh|r kg t{~l/e+ == 8 ZA = Z/e+)Zc/e+9 kg ZA 3 Zmke/e+ W/e+ = W/e+ ) >%>:9 lcrlkg ZA 5 Zmj/e+ W/e+ = W/e+ - >%>:9 led led led led , Bjcb|cjtl bojeal gxfm r~lbkgkld wjc|l d^j = ^r~-^9 dZj = Zr~-Z9 i = :9 dZ = plxfr/e~z#:+9 gfx k = :0eh|r kg t{~l/k+ == 2 dZ/i#:+ = dZj/k+9 i = i):9 led led d^ = d^j/80eh|r+9 M = Yd^9 dZ]9
, Mkrmjtbo Wlbtfx
, @jbfhkje , @: - Dlxkwjtkwl fg Xljc ^fqlx Ke`lbtkfer qkto Jeaclr%% @: = plxfr/eh|r-:#eh|r-:+9 gfx k = :0/eh|r-:+ m = k):9 gfx i = :0/eh|r-:+ e = i):9 kg e == m gfx e = :0eh|r @:/k#i+ = @:/k#i+ ) W/m+* W/e+*/-A/m#e+*rke/dlc/m+-dlc/e++ ) H/m#e+*bfr/dlc/m+-dlc /e+++9 led @:/k#i+ = @:/k#i+ - W/m+U8*H/m#m+9 lcrl @:/k#i+ = W/m+* W/e+*/A/m#e+*rke/dlc/m+-dlc/e++ - H/m#e+*bfr/dlc/m+-dlc/e+++9 led led led , @8 - Dlxkwjtkwl fg Xljc ^fqlx Ke`lbtkfer qkto W%% @8 = plxfr/eh|r-:#e~z+9 gfx k = :0/eh|r-:+
led
;1
, Bolbikea Z-ckmkt wkfcjtkfer%% kg Ktlx 3= 1 '' Ktlx 5 8
, Fec{ bolbild |~ tf 1to ktlxjtkfer%%
gfx e = 80eh|r kg t{~l/e+ == 8 ZA = Z/e+)Zc/e+9 kg ZA 3 Zmke/e+ W/e+ = W/e+ ) >%>:9 lcrlkg ZA 5 Zmj/e+ W/e+ = W/e+ - >%>:9 led led led led , Bjcb|cjtl bojeal gxfm r~lbkgkld wjc|l d^j = ^r~-^9 dZj = Zr~-Z9 i = :9 dZ = plxfr/e~z#:+9 gfx k = :0eh|r kg t{~l/k+ == 2 dZ/i#:+ = dZj/k+9 i = i):9 led led d^ = d^j/80eh|r+9 M = Yd^9 dZ]9
, Mkrmjtbo Wlbtfx
, @jbfhkje , @: - Dlxkwjtkwl fg Xljc ^fqlx Ke`lbtkfer qkto Jeaclr%% @: = plxfr/eh|r-:#eh|r-:+9 gfx k = :0/eh|r-:+ m = k):9 gfx i = :0/eh|r-:+ e = i):9 kg e == m gfx e = :0eh|r @:/k#i+ = @:/k#i+ ) W/m+* W/e+*/-A/m#e+*rke/dlc/m+-dlc/e++ ) H/m#e+*bfr/dlc/m+-dlc /e+++9 led @:/k#i+ = @:/k#i+ - W/m+U8*H/m#m+9 lcrl @:/k#i+ = W/m+* W/e+*/A/m#e+*rke/dlc/m+-dlc/e++ - H/m#e+*bfr/dlc/m+-dlc/e+++9 led led led , @8 - Dlxkwjtkwl fg Xljc ^fqlx Ke`lbtkfer qkto W%% @8 = plxfr/eh|r-:#e~z+9 gfx k = :0/eh|r-:+
dTo = _/:0eh|r-:+9 dW = _/eh|r0led+9
, Bojeal ke Wfctjal Jeacl%% , Bojeal ke Wfctjal Mjaekt|dl%%
, \~djtkea Rtjtl Wlbtfxr%% dlc/80eh|r+ = dTo ) dlc/80eh|r+9 i = :9 gfx k = 80eh|r kg t{~l/k+ == 2 W/k+ = dW/i+ ) W/k+9 i = i):9 led led Ktlx = Ktlx ) :9 Tfc = mj/jhr/M++9
, Wfctjal Jeacl%%
, Wfctjal Mjaekt|dl%%
, Tfclxjebl%%
led g~xketg/!Ef g~xketg/ !Ef fg Ktlxjtkfer 0 ,dSeSe! ,dSeSe!#Ktlx+9 #Ktlx+9 Wm = ~fc8xlbt/W#dlc+9 , Bfewlxtkea ~fcjx tf xlbtjea|cjx%% Dlc = :?>&~k*dlc9 , H|r Wfctjal Jeaclr ke Dlaxll%%% gh = ckeldjtj/0#:+9 , Gxfm h|r e|mhlx%%% th = ckeldjtj/0#8+9 , Tf h|r e|mhlx%%% ec = cleato/gh+9 , Ef% fg Hxjebolr%% ^c = h|rdjtj/0#1+9 , ^Ck%% Zc = h|rdjtj/0#?+9 , ZCk%% Kk` = plxfr/eh|r#eh|r+9 Rk` = plxfr/eh|r#eh|r+9 Rk = plxfr/eh|r#:+9 , H|r B|xxlet Ke`lbtkfer%% K = [*Wm9 Km = jhr/K+9 Kj = jeacl/K+9 ,Ckel B|xxlet Gcfqr%% gfx m = :0ec ~ = gh/m+9 z = th/m+9 Kk`/~#z+ = -/Wm/~+ - Wm/z++*[/~#z+9 , [/m#e+ = -{/m#e+%% Kk`/z#~+ = -Kk`/~#z+9 led Kk` = r~jxrl/Kk`+9 Kk`m = jhr/Kk`+9 Kk`j = jeacl/Kk`+9 , Ckel ^fqlx Gcfqr%% gfx m = :0eh|r gfx e = :0eh|r kg m u= e Rk`/m#e+ = Wm/m+*bfe`/Kk`/m#e++9 led led
;;
led Rk` = r~jxrl/Rk`+9 ^k` = xljc/Rk`+9 Zk` = kmja/Rk`+9
:>:
, Ckel Cfrrlr%% Ck` = plxfr/ec#:+9 gfx m = :0ec ~ = gh/m+9 z = th/m+9 Ck`/m+ = Rk`/~#z+ ) Rk`/z#~+9 led C~k` = xljc/Ck`+9 Czk` = kmja/Ck`+9 , H|r ^fqlx Ke`lbtkfer%% gfx k = :0eh|r gfx i = :0eh|r Rk/k+ = Rk/k+ ) bfe`/Wm/k++* Wm/i+*[/k#i+9 led led ^k = Zk = ^a = Za =
xljc/Rk+9 -kmja/Rk+9 ^k)^c9 Zk)Zc9
"!+9 +9 dkr~/!"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" "! dkr~/! dkr~/!
Elqtfe Xj~orfe Cfjdgcfq Jejc{rkr ! +9
"!+9 +9 dkr~/ dkr~/!"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" "! dkr~/!s H|r s dkr~/!s Ef
s
W
s
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s
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s
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s
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s
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MQ s MWjx s ! +9 +9
gfx m = :0eh|r dkr~ /!-------------------------------------------------------------------------! +9 g~xketg/!,2a! g~xketg/ !,2a!# # m+9 g~xketg/! g~xketg/ ! ,?%2g!# ,?%2g!# g~xketg/! g~xketg/ ! ,?%2g!# ,?%2g!# g~xketg/! g~xketg/ ! ,?%2g!# ,?%2g!#
g~xketg/! g~xketg/! ,?%4g!# ,?%4g!# W/m++9 g~xketg/! g~xketg/! ,?%4g!# Dlc/m++9 ,?%4g!# ^k/m++9 g~xketg/! g~xketg/ ! ,?%2g!# Zk/m++9 ,?%2g!# ^a/m++9 g~xketg/! g~xketg/ ! ,?%2g!# Za/m++9 ,?%2g!# ^c/m++9 g~xketg/! g~xketg/ ! ,?%2g!# Zc/m++9 g~xketg/ ,?%2g!# g~xketg/!Se! !Se!+9 +9
led dkr~/!-------------------------------------------------------------------------! +9 g~xketg/ ! Tftjc
+9g~xketg/ ! ! +9g~xketg/!
,?%2g!# ,?%2g! # r|m/^k++9 g~xketg/! g~xketg/ ! !
,?%2g!# r|m/Zk++9 ,?%2g!#
:>2
g~xketg/! g~xketg/ ! g~xketg/! g~xketg/ !
,?%2g!# ,?%2g! # r|m/^k)^c++9 g~xketg/! g~xketg/ ! ,?%2g!# r|m/Zk)Zc++9 ,?%2g!# ,?%2g!# r|m/^c++9 g~xketg/! ,?%2g!# g~xketg/ ! ,?%2g!# r|m/Zc++9 g~xketg/!Se! ,?%2g!# g~xketg/ !Se!+9 +9
dkr~/!-------------------------------------------------------------------------! +9
"!+9 +9 dkr~/!"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" "! dkr~/!-------------------------------------------------------------------------!
dkr~/! dkr~/!
Ckel GCfq jed Cfrrlr ! +9
dkr~/!-------------------------------------------------------------------------!
dkr~/!sGxfmsTf dkr~/!sGxfmsTf s
^
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dkr~/!sH|r dkr~/!sH|r sH|rs
MQ
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s!+9 +9 MWjx s!
s
gfx m = :0ec ~ = gh/m+9 z = th/m+9 dkr~/!-------------------------------------------------------------------------! +9
g~xketg/!,4a! g~xketg/ !,4a!# # ~+9 g~xketg/!,4a! g~xketg/!,4a!# # z+9 g~xketg/! g~xketg/! ,?%2g!# ,?%2g!# ^k`/~#z++9 g~xketg/! g~xketg/ ! ,?%2 g!# g! # Zk`/~#z++9 g~xketg/! g~xketg/ ! ,4a!# z+9 g~xketg/!,4a! ,4a!# g~xketg/!,4a!# # ~+9 g~xketg/! g~xketg/! ,?%2g!# ^k`/z#~++9 g~xketg/! ,?%2g!# g~xketg/ ! ,?%2g!# ,?%2g! # Zk`/z#~++9 g~xketg/! g~xketg/ ! ,?%2g!# ,?%2g!# C~k`/m++9 g~xketg/! g~xketg/ ! ,?%2g!# Czk`/m++9 ,?%2g!# g~xketg/!Se! g~xketg/ !Se!+9 +9 led dkr~/!-------------------------------------------------------------------------!
g~xketg/! g~xketg/ ! g~xketg/! g~xketg/ !
Tftjc Cfrr ,?%2g!# r|m/C~k`++9 g~xketg/! ,?%2g!# g~xketg/ !
,?%2g!# r|m/Czk`++9 ,?%2g!#
! +9 g~xketg/!Se! g~xketg/ !Se!+9 +9
"!+9 +9 dkr~/!"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" "! dkr~/!-------------------------------------------------------------------------! +9
XLR\CT0
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bcb9 bcljx jcc jcc9 9 bcfrl jcc jcc9 9 X = ke~|t/!Letlx ke~|t/!Letlx tol wjc|l fg X0 !+9 !+9 C = ke~|t/!Letlx ke~|t/!Letlx tol wjc|l fg C0 !+9 !+9 Wm = ke~|t/!Letlx ke~|t/!Letlx tol wjc|l fg Wm0 !+9 !+9 g = ke~|t/!Letlx ke~|t/!Letlx tol wjc|l fg g0 !+9 !+9 q = 8*~k*g9 _ =q*C9 P = X ) `*_9 Pm = jhr/P+9 Pj = jeacl/P+9 Km = Wm&Pm9 tj| = C&X9 ajmmj = jtje/_&X+9, jtje/_&X+9, ke xjdkje jc~oj: = ajmmj9 jc~oj8 = ajmmj - /~k&8+9 t = >0 >%>>:0>%29 k: = Km*rke/q*t)jc~oj:-ajmmj+-Km*l~/-t&tj|+%*rke/jc~oj:-ajmmj+9 k8 = Km*rke/q*t)jc~oj8-ajmmj+-Km*l~/-t&tj|+%*rke/jc~oj8-ajmmj+9 axkd fe r|h~cft/8#:#:+#~cft/t#k:+ cjhlc/!t#rlb! cjhlc/!t#rlb!+#{cjhlc/ +#{cjhlc/!k/t+! !k/t+!+ + r|h~cft/8#:#8+ ~cft/t#k8+ cjhlc/!t#rlb! cjhlc/!t#rlb!+#{cjhlc/ +#{cjhlc/!k/t+! !k/t+!+ +
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Qolxl# C = Ked|btjebl fg bfed|btfx Bje = Bj~jbktjebl fg bfed|btfx ‟j‛ q%x%t el|txjc D = Dkrtjebl hltqlle tol bfed|btfxr /m+ X‛= >%11?? X X = Xjdk|r fg tol bfed|btfxr -:8 μ> = Jhrfc|tl ^lxmkttkwkt{ = ?%?<4*:>
F\T^\T0 --------------------------------------------------BFM^\TJTKFE FG TXJERMKRRKFE CKEL ^JXJMLTLXR --------------------------------------------------:%Rkeacl ^ojrl - 8 Qkxl R{rtlm 8%Toxll ^ojrl Rkeacl Bkxb|kt Ckel /R{mmltxkbjc R~jbkea+ 2%Toxll ^ojrl Rkeacl Bkxb|kt Ckel /\eR{mmltxkbjc R~jbkea+ 4%Toxll ^ojrl Df|hcl Bkxb|kt Ckel /R{mmltxkbjc R~jbkea+ Letlx [f|x Bofkbl0 : Rkeacl ^ojrl - 8 Qkxl R{rtlm D /ke m+ = 2 X /ke m+ = >%>8 Ked|btjebl&^ojrl fg j Bfed|btfx/O&m+0
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>%Lkt tol ^xfaxjm :%Bfetke|l tol ~xfaxjm Letlx tol bofkbl0: :%Rkeacl ^ojrl - 8 Qkxl R{rtlm 8%Toxll ^ojrl Rkeacl Bkxb|kt Ckel /R{mmltxkbjc R~jbkea+ 2%Toxll ^ojrl Rkeacl Bkxb|kt Ckel /\eR{mmltxkbjc R~jbkea+ 4%Toxll ^ojrl Df|hcl Bkxb|kt Ckel /R{mmltxkbjc R~jbkea+ Letlx [f|x Bofkbl0 2 Toxll ^ojrl Rkeacl Bkxb|kt Ckel /\eR{mmltxkbjc R~jbkea+ Djh /ke m+ = < Dhb /ke m+ = 4 Dbj /ke m+ = 7 X /ke m+ = >%>:8< Ked|btjebl&^ojrl fg j Bfed|btfx/O&m+0
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Toxll ^ojrl Df|hcl Bkxb|kt Ckel /R{mmltxkbjc R~jbkea+ D /ke m+ = 4 X /ke m+ = >%>8< Ked|btjebl&^ojrl fg j Bfed|btfx/O&m+0 -<%2;8;l->>1
Bj~jbktjebl&^ojrl fg j Bfed|btfx/G&m+0 -8%814>l->::
>%Lkt tol ^xfaxjm :%Bfetke|l tol ~xfaxjm Letlx tol bofkbl0> 55
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Qolxl# Cjwa = Jwlxjal Ked|btjebl fg tol bfed|btfxr Bje = Bj~jbktjebl fg bfed|btfx ‟j‛ q%x%t el|txjc :&2 lz = Lz|kwjclet dkrtjebl hltqlle tol bfed|btfxr /m+ = /Djh * D h b* Dbj+ X‛ = >%11?? X X = Xjdk|r fg tol bfed|btfxr -:8 μ> = Jhrfc|tl ^lxmkttkwkt{ = ?%?<4*:>
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