On rotation distance between binary coupling trees and applications

!"#$%'&!("')*+, -.&/&/("
"0124365789:;< =
@> ?BADCEDFHGBI:?KJ'LNMOM P=QRC2P2S*T?>!C2PUS=MVWTMX=Y=Z[
\^]`_ a+bdcdef]ghcji
kBlm__ npoq]rsta+cdu]eva+cdopw`xma
grzy!iev_ {c|]`bm}w`oq]g w9]
~
^goq€
]`bxdopc"‚ƒi
k'„…u]g,c`~D†…bo ‡|ˆxdnpa
a
g@‰
Š‹ŒŽ}6~Œ+‘
‘
‘@„^]ghc`~D!]nqˆop{ e
”’ “.•–˜—`™š–
›!œ˜œž1Ÿ ¢¡¢£œ˜¤mžŽœ˜¥d¦¨§© ¢¡ª,«H¥¦+œd¬”¥d¡¢œ®­Ž¯.¦¨ž°±,²³´¥d¦+œd¬”¥¡ªœ˜¨­1¯Dµp¦žŸH¶¡¢œ'Ÿ ¢«œ˜·ž1Ÿm¸N¹B¡º­Ž»”¯"§ ¸½¼¾d¿
­Ž»œÀ¶ ¡ªœ”Ÿ ª«¨œ·ž1Ÿ”µp¦¨ž­»,œ”Á¨§hŸ®­§Âí»œ˜¦žŽÄv¦µBŸ,«§ şžÂÆ¦ÂÆœ˜¨­Ž§ÂÇ¿Ÿ¨¯H«œ˜œžŽ¡¢¥^œÈ
ŸÂÆ© ªœ9¾
¥˜Ÿ4Ÿ ¢¹KŸ9Ä
¯^·6œfœdÈ
©žŽœ˜¯Ž¯"œ¤zŸ¨¯mÂm§ ª­¡¢© ªœÉ¯"§Â…¯Æ¦`ʨœžÆ©žŽ¦+¤§,¥|­1¯Æ¦µË'Ÿ¥˜Ÿ»z¥¦+œd¬”¥d¡¢œ®­Ž¯Ì¸p¡½Í œ¨Í
Î ²³Ï¥¦®œ¬”¥d¡¢œ®­Ž¯1¾|Ívдz«œ˜œž1Ÿ ­Ž»œžŽœÀœÈ
¡¢¯"­m…Ÿ+į"§h¥1»ÑœdÈ
©žŽœ˜¯Ž¯"¡¢¦h¯Ò¹KœÓ¯ŽŸ9Äv­Ž»,Ÿ`­…¯"§h¥1»ÑŸ
œÈ
©žœ¯¯¡¢¦4¡¢¯Ó¦©­¡¢ÂƟ ¡ªµ­»œÉ+§ÂÔ·6œžR¦µjË'Ÿ¨¥Ÿ»Õ¥¦+œd¬”¥d¡¢œ®­Ž¯À¡ªÖ¯"§,¥1»ÕŸÑ©ž¦
¤
§h¥|­ƒ¸×Ÿ,¤¿
¥¦žŽžœ˜ ¢Ÿ­œ¤¿­»,œf®§,ÂÔ·6œž…¦µH¯"§,Â^…Ÿ­¡¢¦t¡ª,¤¡¢¥œ˜¯1¾^¡¢¯ÆÂÆ¡¢¡ªÂ…Ÿ ×ÍÙØ:»œÇ©žŽ¦· ¢œÂÚ¦µÛh,¤
¡¢«
Ÿ¦¨©
­¡¢Â…Ÿ KœdÈ
©žŽœ˜¯Ž¯"¡¢¦@µp¦¨ž^ŸÌ«¡¢Êœ˜°±,²³´¥d¦+œd¬”¥d¡¢œ®­^¡¢¯mœ˜Á®§¡¢Ê`Ÿ ¢œ®­m­Ž¦ÌÛh,¤
¡¢«ƒŸÉ¯"»,¦ž­œ˜¯"­
©hŸ`­»ƒ¡¢ƒŸÓ«ž1Ÿ©»ÉÜÝÍmØ:»œ^ʜ˜ž"­Ž¡¢¥œ˜¯!¦µ­»¡Å¯H«ž1Ÿ©»ÉÜÝÌ¥d¦¨,¯¡¢¯"­!¦µ=·¡¢,ŸžÄv¥¦§© ¢¡¢«À­Žžœ˜œ˜¯˜¿
žŽœ©,žœ¯"œ˜¨­Ž¡ª,«Æ­»œÔ¥¦§©, ª¡¢«”¯Ž¥1»œÂƜ˜¯¡ªÇ­Ž»œj·ž1Ÿ®Þ`ߜ­Ž¯:¦µ.­Ž»œm°±,²³´¥d¦+œ¬…¥¡ªœ˜®­Ž¯˜Í=Ø:»¡Å¯'¡Å¯B­Ž»œ
«¨žŽŸ©»^¦µž¦+¦­Žœ˜¤Ç¸p§,¦ž1¤
œžŽœ˜¤h¾ ·,¡ª,ŸžÄÔ­žŽœœ¯.¹B¡º­Ž»… ¢Ÿ·hœ˜ ª ¢œ˜¤^ ¢œ˜Ÿ9ʜ¯¿¨Ÿ,¤^»,Ÿ¨¯.¦ž1¤
œž'¸½¼`±HàÇ፾|â¢â¢Í
ã ¯­»œB¦¨žŽ¤œž¡ª,¥žœŸ¯œ˜¯.¯¦/ž1Ÿ©¡Å¤
¢Ä¿`Ûh,¤
¡¢«Ÿ!¯»¦¨ž"­Žœ˜¯"­©,Ÿ­»^¡¢¯¥¦ÂÆ©§
­1Ÿ`­Ž¡ª¦¨,Ÿ ¢ ªÄjŸ¨¥1»¡¢œÊ`Ÿ· ¢œ
¦¨ ¢Äɵp¦¨žÔ±Uä-á¨áÍv僜À©žŽœ˜¯œ®­m¯¦ÂƜ”Â…Ÿ­»œ˜ÂƟ­¡Å¥Ÿ ­Ž¦®¦¨ ¢¯j­¦ƒ¥d¦ÂÆ©§­œÀ¦¨žÔœ¯­Ž¡ªÂ…Ÿ`­Žœ”­Ž»œ
¢œ,«­»ƒ¦µ:¯"§h¥1»É¯»¦ž­œ¯­H©,Ÿ`­Ž»,¯H·6œd­¹KœœÉ·¡¢,ŸžŽÄv¥d¦¨§© ¢¡ª«R­Žžœ˜œ˜¯˜ÍÔØ:»œ…¤
¡ÅŸÂƜd­ŽœžH¦µ:Ü Ý ¡Å¯
¤œd­œ˜žÂÆ¡¢œ˜¤vœdÈ
© ¢¡¢¥¡º­Ž ªÄǧ©
­Ž¦À±Ñäæáá¿6Ÿ,¤v¡º­!¡¢¯!¯"»,¦`¹BÓ­Ž¦À«¨ž¦`¹ ª¡¢ßœÔ±! ¢¦«6¸p± ¾dÍ/Ø:»+§,¯Bµp¦¨ž±
şžŽ«œœ¦¨§«»¿¨­»,œ/+§Âm·hœ˜ž=¦µDË'Ÿ¥˜Ÿ»”¥¦®œ¬”¥d¡¢œ®­Ž¯=¡ªÀ­»œ/œdÈ
©,Ÿ,¯"¡¢¦À¦µ ŸÔ°±,²³Ï¥¦®œ¬”¥d¡¢œ®­¡Å¯
¦µ
¦ž1¤
œž±H ¢¦«6¸p± ¾|Í僜Ÿ ů"¦'¯»¦`¹É­»,Ÿ­ ­Ž»¡¢¯ ©žŽ¦· ¢œÂ¡ªj˟¥Ÿ»
³ÏåÙ¡ª«¨œž­Ž»œ¦¨žÄ/¡¢¯ œ˜Á®§¡¢Ê`Ÿ ¢œ®­
­Ž¦RŸÀ©žŽ¦· ¢œÂ-¡¢Ì…Ÿ`­Ž»œÂ…Ÿ­¡Å¥Ÿ ·¡¢¦ ¢¦«¨Ä¿6¹B»œžŽœm¦¨œÔ¡Å¯H¥d¦¨,¥dœ˜žœ¤Ç¹B¡º­Ž»Ì­Ž»œÆÁ¨§hŸ®­¡ª­ŽŸ­¡¢Êœ
¥¦ÂÆ©,Ÿž¡Å¯"¦¨”¦µ.¥d ş¯Ž¯"¡ªÛh¥˜Ÿ`­¡¢¦h¯¦¨ž:¤œ,¤
žŽ¦«¨žŽŸÂ…¯Í瞎¦Â<­Ž»¡¢¯B¥¦®­œÈ+­˜¿
¯"¦¨ÂƜ!Ÿ ª«¨¦žŽ¡º­Ž»Â…¯µp¦¨ž
Ÿ©©žŽ¦9È
¡ªÂ…Ÿ`­Ž¡ª,«Ô­Ž»œj¯"»,¦ž­œ˜¯"­B©,Ÿ`­Ž»R¥˜ŸÇ·6œj¤
œ˜¤
§h¥dœ˜¤Í
è ã é:êëì ¼Í ¼ ì ¸×›!žŽ¦§,©ÌØ:»œ¦¨žÄ¾dÒ ì ¼
Íîí ì ¸ é ¦ÂÆ©§
­1Ÿ`­Ž¡ª¦¨,Ÿ D­œ¥1»¡ÅÁ¨§,œ˜¯1¾|Ò ì °Í Î¨ï çÖ¸ ã ª «¨œ·ž1Ÿ¡Å¥jÂÆœd­Ž»¦
¤¯!¡ª
ð/§,Ÿ¨­Ž§ÂñØ:»œ˜¦žŽÄ¾|Í
é ¦žŽžŽœ˜¯©h¦¨,¤
¡¢«ƒŸ§
­»,¦ž ëfò Í=ç,Ÿ¥1ß¿K󜘩,Ÿž­ÂƜ®­”¦µ ã ©© ¢¡ªœ¤tô̟`­»,œÂ…Ÿ`­Ž¡¢¥˜¯…Ÿ,¤ é ¦ ÂÆ©§­œž ê ¥d¡¢œ,¥œ¿
õ ,¡ªÊ¨œž1¯"¡ª­Ä”¦µ›!»œ®­¿,öHž¡ ÷«¨¯ şŸÇ¼ø,ád³ ê
ù ¿+ú=³ ù¨ììì ›!œ®­¿,úKœ ¢«¡¢§ÂÇÍ
ØDœ ½Í6ûûU°®¼ ù ¼ Îüü ø ì ø,Ò®çhŸ`ÈÇûûý°¨¼ ù ¼ Îüü ù¨ù ï Ò¨þ³Ï…Ÿ¡¢ ò œœ˜ž ¢œÍ ç,Ÿ¨¥1ßÿ/žŽ§«hÍ Ÿ¨¥Í ·hœ¨Í
"!#$%&''()*,+-/."! 10324.'56'7-8
‹
u]Æxd{ ‡1]w9c!i
k2cdu]…w9i{_ nNopgˆ”i
k U‹Æa
gˆ{npa+bHefief]ghcda~a
grƒcdu]^bd]npa+c|]r
Œ"w9ih]!Éw`op]g,cdx`~oNx
Ìa r o"Éw`{nqcig]
~Da
grcdu]Ónpopc|]`ba+cd{bd]ÀoNx]!#6c|]g xdoq€
]%$^yHnNa
xdxdopw`a
n2evigi
ˆ
ba+_ ux'&ŋ+~‰(Kr]a
n_ bopeva+boNnq‚
) oqcduÓc|]wu go+*6{]xk½i
bBopef_ np]ef]g,cdoNgˆjˆ
ba+_ u opw`a
nhev]`cdui6r x-,/.gi ) gÇa
x10{cdxdopx=ˆ
ba+_ ux322k½i
b:w`a+bbd‚6oNgˆ
i{c@xd{eÌeva+cdoqigxƒi€
]`b_bdi®‡|]w9cdoqig4*h{ a
g,cd{e g6{e]`b˜xÉopg _bi6r{ w9cdxÉi
k5 opˆg]`b@w9ih]!Éw`op]g,cdx6$
718
g &9~ i
_DopwNj:‰ (~bd]w9i{_ nNopgˆRcdu]`i
bd‚opxHw9igxdopr]`b]rk×bdie cdu]…_ioNg,c!i
k=€oq] ) i
k<;!=/>@?BADCFEHG%IKJLM=/>ON
l oNga+bd‚Ùw9i{_ npoNgˆxdw˜u]ef]@opxÓcdu]Ébihi
c|]rW oNga+bd‚4c|bd]`]bd]`_bd]xd]g,cdopgˆcdu]ƒi
br]`bÇi
k
P E6QSR!TUR P $ÙV
w9i{_ nNopgˆÌi
kHax|cda+c|]v€
]w9c|i
bRopgcdu]fc|]gx|i
b…_bdir{w9c^i
Xk ñ‹fa
gˆ{npa+b…efief]ghcd{e eR{nqcdoq_Dnq]`cdx`~
npBa .]npnq]r bd]x|_.]w9cdoq€
]nqY
‚ h‚Õcdu]a
gˆ{npa+bÇefief]ghcda [[Z [\ Z6]6]6]KZ 6^%_ [ $ u]nq]a€
]xfi
kÔcdu`] opga+bd‚
c|bd]`]Àa+b]ÀnpBa .]npnq]ar 6‚ƒcdu]x|]Àa
gˆ{nNa+bÔefief]ghcda ![ Z K\ Z6]6]6][Z [^B_ [ ~ a
g r@cdu]”bd]eÌa
opgopgˆÇ€
]`bdcdoNw9]xji
k
cdu]mc|bd]`]^w`a
Fg .]mnpBa .]npnp]br h‚Çcdu]Æopghc|]`bef]roNa+c|]ma
gˆ{nNa+b/efief]ghcdSa $Xci
b!!] #a
ef_ nq]
~opgvcdu]Ôc|]gx|i
b
_bdir{w9c d f[ ehg6g6gie dj®~ ) u]`bd]Ç]a
wk
u dlHw`a+bdboq]x…abd]`_ bd]x|]ghcda+cdoqigÙi
k!cdu]va
gˆ{npa+b…efiev]g,cd{e
a
nqˆ
6] b˜afnpBa .]npnq]ar h‚ l ~cdu]…k×inpnpi ) opgˆR€
]w9c|i
bÆw`a
g .]”w9igxopr]`bd]n
r m
o ,p,q [\K2r \ ,q[s ,q6t j 2r6t j 2r[sut j 2Hv
:[ Z
[ Z Z Z
Zwyx{z
ƒ † ƒ ‹Œ‡Šˆ
|
ƒ …„ ƒu† „ ƒ †
 p„  † „  †
ƒ…‡ „ ƒuˆ „ ƒ‰‡Šˆ
 ‡ „  ˆ „  ‡Šˆ
ƒ…‹ „ ƒ…‡Šˆ „ ƒ‰‹Œ‡Šˆ
 ‹ „  ‡Šˆ „  ‹Œ‡Šˆ
„ „
 † „  ‹Œ‡Šˆ „ Ž
}u~9~€‚
‚
‚
‚
 o  3x e o [\  \ x e o [s  s x e o [t  t x e o j  j x3]
,1K‹ 2
[ 4[
‘m]`bd]opg~ ƒ „ ƒ’ „ ƒH’ ’ opxÔà
]w9c|i
b|Œ"w9i{_ nNopgˆ“,/5 oqˆg]`bmi
b”yHnq]6 xwuŒŽ„^i
b˜ra
g@2Hw9i6]!Éw`oq]ghc&9~”%(Š$ u]
’ ’’
opg a+bd‚Rw9‚i{ _ „  npopg„ ˆÓxdwu]ev]mbd]`_ bd]x|]ghcdopgˆ”cdu]ÆaB.i€
]^€
]w9c|i
bjopx'ˆop€
]gÉopgFc:oqˆ{bd]R‹B$ u]Ô_ bdi®‡1]w9cdopig
:oqˆ{b]v‹BmHopga+bd‚ƒw9i{_ npopgˆÇxwu]ef]Àbd]`_bd]x|]ghcdopgˆ•,1‹K2
c
J
j345
j12
j1
j45
j2
j3
j4
j5
6{a
g,cd{ e g6{e]`b w opxRgi
cRbd]`_bd]x|]ghc|]ropg cdu opx oNga+bd‚Ùw9i{_ npoNgˆxdw˜u]ef]ƒk×i
bÇbd]a
x|ig xÓcdu a+c
) opnNnxdihig–.]w9ief]Óa+__ a+bd]ghc6$
u]`bd]Ôa+bd]m%i h€oqi{xdnp‚Çxd]`€
]`ba
n ) a‚x!opg ) u opwub֋ja
gˆ{nNa+b/efief]ghcdaRw`a
gU.]Ôw9i{_Dnq]r~ha
g r
cdu] *h{ a
g,cdoqcdop]xcdua+c!c"‚6_ opw`a
nNnq‚va+__.]a+b!oNgÌa+c|ievopw^a
grƒgh{ w`nq]a+b!xdc|b{w9cd{bd]Æw9ief_ {cda+cdoqigx!a+bd]mcdu]
bd]npa+c|]rш
]g]`ba
n2b]w9i{_ npopgˆÇw9i6!] Éw`oq]ghcdxji
b+Œ"w9i6]!Éw`oq]ghcdx6$/lˆ
]g]`b˜a
n2bd]w9i{_DnpopgˆÇw9ih]!ƒw`oq]g,c
,½i
bÓaш
]g]`ba
npqo —`]˜
r +Œ"w9i6!] Éw`oq]gh3c 2”opxÀr!] ™Dg]r4c|i .]fcdu]Ìc|ba
gx|k½i
beva+cdoqig w9ih!] Éw`op]g,c ]`c ) ]`]g
a
gh‚x{wu@c ) iÉw9i{_ npopgˆÇxwu]ef]x~%] $ ˆ $
š ,p,p,q [t:2r t ,qK\ [s:2rK\psK2r t\ps j 2Hv o ,p,q K\K2r \ ,qKs ,q6t j 2r6t j 2rKsut j 2Hv
,´›‰ 2
K[ Z
[ Z Z
[ Z
K[ Z
[ Z Z Z
x3]
] 5 oqˆg]`bdŒ
u] w Œ"r]`_]g r]gw9]Hopx=rbdi
__.]r”xdopg w9]!xd{ wuRw9ih!] Éw`op]g,cdxBa+bd]Hopgr]`_]g r]g,ci
k w 6‚…cdu{
œHw .®a+bc!cdu]`i
bd]
e & ”%(Š$ž7Žc!opx!aRk½{ gra
ef]ghcda
n cdu]`i
bd]e i
k2bd]w9i{_DnpopgˆÓcdu]`i
bdŸ
‚ &9~ _ $O”i¡%¡:(2cdua+cH]a
wu
xd{w˜u@c|ba
gxdk×i
beÌa+cdoqig@w9ih!] ƒw`oq]g,'c ,όo $ %] $]`€
]`bd‚ˆ
]g]`ba
np+o —`]r +Œ"w9i6!] Éw`oq]gh3c 2jw`a
–g .]Æ!] #_bd]xdx|]ropg
*
‰
|c ]`bevxÔi
k'xd{evxji€
]`b^_bdir{w9cdxi
kma
w`a
uzw9i6]!Éw`oq]ghcdx',6
Œ"w9ih]!ƒw`oq]g,cdxD23$Ôlk½a
efi{ xj_bdi
ˆ
b˜a
e i
k
H{b.
]F&9¡B(~
.~opxja
nqb]a
r‚@r]a
npopgˆ ) opcdu@cduopx_ bdi% nq]e–$/!{b.
]îxÔa+__ bdia
wuzopx][*6{oq€+a
nq]g,cc|i
™Dgr opgˆÆa…w9]`bdcda
opgf_ a+cdu.]`c ) ]`]gÌcdu]c ) i opg a+bd‚Ów9i{_DnpopgˆÆxdwu]ef]x ,½bd]`_b]x|]g,cdoNgˆ…cdu] ba®Œa
g r
.
]`c1Œ_ a+bdc!i
k.cdu]jˆ
]g]`b˜a
n bd]w9i{_ npopgˆ…w9i6!] Éw`oq]gh3c 2ž6‚fxd{w`w9]xdxoq€
]j]nq]ef]ghcda+bd‚fc|ba
g x|k×i
b˜eva+cdoqigxBig
cdu]jc|b]`]6x $Blmx ) ]Ôxua
npn!] #_ npa
opgÇnpa+c|]`b~hcdu]Ôxdui
bdc|]`b'cduopx'_ a+cdu~cdu] ]`c|c|]`bcdu]jbd]xd{ nqcdopgˆÆk½i
beÓ{ npSa $
r 6‚ Éopx!ˆ
]g]`ba
npnp‚Ìba+cdu]`bjnpigˆ~cduh{xH‚oq]npr opgˆÀ!] #_bd]xxdoqigx ) uoNwua+bd]Æk½a+b
u]Æ_ a+cduk½i{ga
k½bdieÚi
_ cdopeva
Œn $ 71gi
b˜r]`bmc|iopef_ bdi€
] .~ Ha+b|ŒŽ}ua
nqie a
grt†”npa+_ oNxdwY
u &B(Kr]`€
]nqi
_.]rtaÉg] )
_bdi
ˆ
b˜a
e “h‚ oNef_ nq]ef]ghcdopgˆzˆ
ba+_ uoNw`a
n!ev]`cdui6r xRr {]Éc|n
i 0{cdxdop–x &ÅD‹ (Š$Ô]w9]g,cdnq‚
{~ .i
cdu
ef]`cduirx ) ]`bd]”b]9Œ!] #a
evoNg]r@a
grÑba .]`c|c|]`bÔoNef_ nq]ef]ghcda+cdoqig ) a
xjˆoq€
]˜
g &6~DŠ6~D: (Š$
71gcdu]À_bd]xd]g,c^_ a+_.]`b ) ]Rw9ig xdopr]`b^cdu]Óev]`cdui6rzi
f
k oNga+bd‚w9i{_ npopgˆvc|bd]`]Rc|ba
gx|k½i
beva+cdoqig x
a
xÔ{ x|]rÑopg n&9¡(Ka
gr !"$#$Ÿ&:(~Da
gr@bd]npa+c|]Roqcc|iÌ_ bd%i nq]evxoNg@ˆ
ba+_ u@cdu]`i
bd‚
~Deva+cduŒ
]eva+cdopw`a
<n oqinqi
ˆ
‚
~Ha
grýw9ief_D{c|]`bÌxdw`oq]g w9%] $ ci
b ™#]W
r B~ ) ]Ñw9igxopr]`bvcdu]Ñxd]`cvi
k^a
nN-n opga+bd‚
w9i{_ nNopgˆÇc|bd]`]x ) oqcd–u F ‹”np]a€
]bx ,όo $ %] $F ‹ a
xdopw”a
gˆ{npa+bÔefiev]g,cdia 23$ uopxxd]`cÔopxjxdui ) g@c|i
ua€
]fcdu]Rg a+cd{ba
n:x|c|b{w9cd{bd]Ói
k!ä
b˜a+_ u&~ %^D~ ) oqcdut]a
wu4€
]`bdc|!] #4i
'k % ^ƒb]`_bd]x|]ghcdopgˆaa opga+bd‚
w9i{_ nNopgˆÇc|bd]`%] $ ) iv€
]`bdcdopw9]xmop(
g %^ƒa+bd]Ów9ig g]w9c|]•
r 6‚@a
g@]rˆ
]Roqk=cdu]`bd]”!] #opx|cdxÔa
g]nq]ef]ghcda+bd‚
c|ba
gxdk×i
beÌa+cdoqi˜
g ,½c|Fi ]Ór!] ™Dg]rznpa+c|]`Db 2.]`c ) ]`]gtcdu]Àw9i
bdb]x|_.igropgbˆ Dopga+bd‚w9i{_ npoNgˆÇc|bd]`]6x $ 71g
i
br]`b…c|ai ™Dg rta
g4i
_ cdopeva
nK!] #6_ bd]xdxdoqigtk½i
b”aƒˆ
]g]`ba
n:bd]w9i{_Dnpopgˆƒw9ih!] Éw`op]g,Uc ,½ˆ
]g]`b˜a
npqo —`]8
r +Œ
w9i6!] Éw`oq]gh3c 2˜~'oqcÀopx…cdu]g xdS{ ƒw`oq]g,cÀc|itw9igxopr]`b”cdu]Éc ) iz€
]`bcdopw9]xÓoN
g %^4w9i
bdbd]x|_.igr opgˆ@c|icdu]
ba®Œ^a
gY
r .
]`c1Œ€
]w9c|i
b~a
grÕc|Ÿ
i ™Dgr axdui
bc|]x|cÀ_ a+cdY
u .]`c ) ]`]gÖcdu]e op)
g % ^ $Ñl^nqcdui{ˆu cduopx”oNx
axdopef_Dnq]”bd]r{ w9cdoqigi
kcdu]Çi
boqˆopga
n_bd%i np]e@~Dcdu]Rg] ) ˆ
ba+_Duzcdu]`i
bd]`cdopw`a
nK_bd%i np]eÚcd{b˜gxÔi{c
c|Ui .]”a
xmua+brÑa
xÔcdu]”i
boqˆoNga
n._bd%i np]–e $+*Æg]”a
r€®a
ghcda+ˆ
]Ói
k:cdu]À[] *h{op€®a
nq]ghcjˆ
ba+_Du@cdu]`i
bd]`cdopw`a
n
_bd%i Dnq]e$oNx=cdu a+c:opc:u a
xKa+_ _]a+b]rRoNgRaÆg6{e ]`b:i
kr-o ,.]`bd]g,c:w9ighc|!] #6cdx`~6xd{w˜uRa
xBw9iev_ {c|]`b'xdw`oq]g w9]
a
greva+cdu]eva+cdoNw`a
{n Doqinqi
ˆ
‚
~'a
grÖcduh{ xRxdief]É_ bdi
_.]`bdcdoq]x”i
kÔcdu]Ɉ
b˜a+_ u.x %^Õw`a
k
g .]Ìk½i{gropg
cdu]fnpoqc|]`b˜a+cd{bd%] $ 71gt_ {bd]Rˆ
ba+_ u4cdu]`i
bd‚
~2cdu]Ç_bd%i Dnq]e ) a
x ™Dbx|cÆw9igxdopr]`b]Ÿ
r 6(
‚ Ôi% opgxdiW
g &ŋ`%‘ (Š$
71gýw9ief_ {c|]`bƒxdw`oq]gw9]
~cdu]Ñ[] *h{ oq€®a
np]g,cf_b%i nq]e op
x .6gi ) gæa
x ™DgroNgˆ4cdu]Ñbdi
cda+cdoqig ropxdcda
gw9]
.]`c ) ]`]g@{gi
br]`bd]rvbdi6i
c|]a
r opga+b‚Rc|b]`]x ) oqcduƒnpBa .]npnq]rvnq]a€
]x &ŋ
6‹ (Š$ž71gÉeÌa+cdu]eva+cdopw`a
n oqinpi
ˆ
‚
~
cdu]@_b%i nq]e opx .gi ) gýa
xÌw9ief_D{cdopgˆ4cdu]g]a+bd]x|cvg]oqˆOu .i{bvopghc|]`bwu a
gˆ
]ef]`c|boN`w ]`c ) ]`]g
r]grbdi
ˆ
ba
evx &ŋ‰~2[‹ ~!‹ ”~2[‹ ¡(Š$
}oNgw9]i{bveva
opgW_b%i nq]e opxfgi ) bd]r{w9]rWc|n
i ™gropgˆ4xdui
bc|]x|cf_ a+cduxfopgcdu]@ˆ
b˜a+_ /
u %^ ~
]) vxdua
npnBx|cd{ r‚zx|iev]f_bdi
_.]`bdcdoq]x^i
0k %^cdu a+c”a+bd]vbd]npa+c|]r4c|izropx|cda
gw9•
] &Å1‹ B(Š$'71gÙ_ a+bcdopw`{npa+b ) ]
xdua
nNXn .]w9igw9]`bg]r ) opcduÖw`a
npw`{ npa+cdopgˆti
bf]x|cdopeva+cdoNgˆzcdu]r opa
ef]`c|]`.b 2@,3% ^S2Ài
4k % ^~xdopg w9]ÉcduoNx
ˆoq€
]x”a
g {__.]`b .i{g rzk½i
b…cdu]vg6{e ]`b…i
+k Ôa
w`a
uÖw9ih!] Éw`op]g,cdx”a+_ _]a+b˜opgˆopg4cdu]f!] #_bd]xdxdopigx
i
k:i{bjˆ
]g]`b˜a
npqo —`]•
r Œ"w9ih!] Éw`op]g,cd6x $ ci
b 65$‹
‹+~ 2,3%^2Hopxw9ief_D{c|]rÑ!] #_ npopw`opcdnq‚ 6‚ev]a
gxi
k
aƒw9ief_ {c|]`b^_bdi
ˆ
ba
e $Æ}opg w9]”cdu]Çgh{e .]`bÔi
k'€
]`bcdopw9]x^i
+k %^ƒˆ
bdi ) xmb˜a+_ oprnq“
‚ ,½cdu]Ri
br]`b^i
+k %^
opx ,´‰ 87<K‹ 2:9;9M2˜<~ 2,3%^2^w`a
gÕgiÑnqigˆ
]`b ]fw9ief_D{c|]rÙk½i
b >= ‹
B‹ $ u]g2~ ) ]v{ x|]va@gh{ e .]`b…i
k
c|]wu g+o *6{]x”k½bdie w9iev_ {c|]`bÇxdw`oq]gw9]Éc|iˆoq€
]ƒ{__.]`bÀa
grÖnqi ) ]`b .i{g rxÆk×i
?b 2@,3% ^S23$–5Ù]ƒxdui )
cdua+@c 2,3% ^ 2^ˆ
bdi ) xÀnp+o .
b] ”nqi
@ˆ ,/23$Ñ}6ief]v_bi
_]`bcdoq]xÆi
Ak % ^ cdu a+cÓa+bd] .gi ) gÕopgÙcdu]Ìnpoqc|]`ba+cd{bd]
a+bd]mcdu]gÌxd{ eveva+bqo —`]rfa
g rÌw9igh€
]`bdc|]rƒc|iÀi{b!w9ig,c|!] #c/i
k Œ"w9ih!] Éw`op]g,cd6x ${cKoNga
npnq‚
~ ) ]Ô_ bdi
_.ix|]
x|ief]Óopr]a
xigÑui ) c|iÌw9iev_ {c|]Àa+__ bd[i #opeva+cdoqig xHk×i
bjcdu]Àxdui
bdc|]xdcj_ a+cdu@_b%i nq]e op(
g % ^$
Ÿ<[  bH ž H3
a Œ"w9ih!] Éw`op]g,n
c ,όo $ %] $Bcdu–] ba®ŒÀa
g r
u]c ) iÖ_ a+bdcdxÇi
kÆaو
]g]`ba
nb]w9i{_ npopgˆtw9i6!] Éw`oq]ghcvi
bÌ8
]`c1Œ€
]w9c|i
bD2mw9igxdoNx|ci
kDopga+bd‚ƒw9i{_ npopgˆÇxwu]ef]x[$lmxÔxdui ) gÑopgcdu]”]!#a
ef_ np]”opg–c:oqˆ{bd]v‹+~cdu]
€
]`bdcdopw9]x^i
kaF opg a+bd‚@w9i{_ npopgˆÌxdwu]ef]fa+bd]RnNaB]nNnq]r–6‚Ñcdu]Ça
gˆ{npa+bÆefief]ghcd{e €®a
nN{]x6$ u]
nq]a€
]xBi
k cdu]- oNga+bd‚”w9i{_ nNopgˆÆxdwu]ev]Ha+b]jnpaB.]npnq]r6‚ Da
xdopw!a
gˆ{npa+bBefief]ghcd{e-npaB.]npx l cdu]
i
cdu]`b^€
]`bdcdopw9]x ,½cdu]Ów9i{_ nq]rр
]`bcdopw9]3x 2a+b]ÓnpBa .]npnq]`r 6‚@cdu]ÀoNg,c|]`bev]ropa+c|]Óa
gˆ{npa+bÔefiev]g,cd{e
€+a
np{]x a
grÑcdu]…bdi6i
cji
bjc|i
_€
]`bc|!] #@oNxjnpBa .]npnq]ar 6‚Écdu] ™Dga
na
gˆ{nNa+bjefief]ghcd{e €+a
np{] vž$
l^xÇ%i x|]`bd€
]W
r 6‚֐H{Hb .
“
] &9¡B(a
g r{ x|]rUopg &:(~c|i ™DgrWa
g!] #_bd]xdxdopigÖi
k^a4ˆ
]g]`ba
nHbd]w9i{Œ
_ npoNgˆRw9i6!] Éw`oq]ghcma
xԕ
a ,ÏeÓ{ nqcdoq_ nq:] 2/xd{ e i€
]`b^_bdir{w9cdxHi
k Ôa
w`a
uzw9ih!] Éw`op]g,cdx`~Doqcjopxjxd{ Éw`oq]ghc!c|i
™Dgrzax|[] *h{]gw9]Ói
k]nq]ef]ghcda+bd‚Ñi
_.]`ba+cdoqigx ) uoNwuzc|ba
gx|k½i
be cdu
] Dopga+bd‚@w9i{_ nNopgˆÌxdw˜u]ef]Çi
k
cdu'] ba®Œ€
]w9c|i
bÀoNg,c|iƒcdu'] opga+bd‚Ñw9i{_ npopgˆÉxdwu]ev]Ri
kcdu] .
]`c1Œ€
]w9c|i
[b $ u]`bd]Óa+bd]Çc ) i]nq]ef]gŒ
cda+bd‚ti
_.]`ba+cdoqigx`~ .i
cduÙw9i
bdb]x|_.igropgˆÉc|iÑxdopef_Dnq]Ób]w9i{_ npopgˆƒw9i6!] Éw`oq]ghcdx”a
gr4cdu6{xÆc|iÑxdopev_ nq]
w9ighc|bqo {cdopigxopgcdu]”xd{ eveva+cdoqig@k½i
beR{npaRk½i
bjcdu] Œ"w9ih!] Éw`op]g,6c $
5Ù]ƒbd]`k½]`bÀc|˜
i &:(!k×i
bRaÑr]`cda
opnp]r r]xdw9b˜oq_cdoqig4i
kHcdu]Éc ) i]nq]ef]ghcda+bd‚Ùi
_.]`ba+cdoqig x`~=a
gr@‡|{ x|c
bd]w`a
npn!cdu]opbÇeÌa
opg_bdi
_.]`bdcdoq]xÇu]`bd%] $ ua] ™ bx|cR]nq]ef]ghcda+bd‚Öi
_]`b˜a+cdoqigUopxÇw`a
npnq]rWa
h
g ROE!Q ?%>ONOR
,½c|]`bevoNginqi
ˆ
‚ýi
`
k &:(/2Ìi
bÑ
a ž= P b,Ïw9ief_D{c|]`bÑxdw`oq]gw9]4c|]`beÌopginqi
ˆ
‚ 23$ 7cw9i
bdbd]xd_ig rxƒc|icdu]
c|ba
gxdk×i
beÌa+cdoqigi
kmatx|cda+c|]@€
]w9c|i
bvi
kÔcdu]ƒk½i
be o , Z 2"! x c|i o , :Z 2"! x $˜7cdxÇ] ,.]w9cfigWa opga+bd‚
w9i{_ nNopgˆÀxdw˜u]ef]Æopx!xdui ) gÉopFg c:oqˆ{bd]Ɖ6~ ) u]`bd#] Ìa
gr w`a
ag ]^nq]a€
]xHi
bHw9i{_ np]r̀
]`bdcdoNw9]6x $ž7cdx
.
:oqˆ{bd]À‰ m
c
opx|cHi
_.]`ba+cdoqig
)
c
a
c
b
b
a
€+a
np{]”opxr]`c|]`b˜evopg]r`6‚cdu]…bd]w9i{_ nNopgˆfw9ih]!ƒw`oq]g,c
_%"&('
š , 2"! o , 2"!
Z
: Z
xXz , 7 K2"$
Z
À‹
,Œ›2
k½inpnqi ) opgˆÇk×bie cdu]ÓyHnq]6DxdwuŒŽ„Æi
bra
gÑw9i6]!Éw`oq]ghcj_bdi
_.]`bdc‚
$ „ % „ ' z , 7ÀK‹ 2 $ _%"&(' % „ $ „ ' ]
,/”O2
) „ *O„ +
*i„ ) „ +
‚
a , G3Jk,½c|‚ ]`bevoNginqi
ˆ
‚@i
k&:(/2ji
bÆa•ApG.Š?.r=ŒGB>˜,Ïw9ienj
u]Rx|]w9igrt]nq]ef]ghcda+bd‚Ñi
_.]`ba+cdopigopx^w`a
npnq]rt_ {c|]`bjxw`oq]gw9]…c|]`bevoNginqi
ˆ
‚ÉoNgÉcdu]”w9ig,c|!] #cji
k opga+bd‚Éx|]a+bwuÑc|bd]`]3x 23$ u opxHopxaÇc|ba
gx|k½i
beva+cdopig
i
kaÑx|cda+c|]ɀ
]w9c|i
bÓi
kHcdu]vk½i
be o ,p, Z 2 2 Z ![2/ x c|i o , Z , KZ ![202/ x i
bӀ6opw9]f€
]`b˜xdSa $F7Žcdx…] ,.]w9cÀigÖa
opg a+bd‚Rw9i{_ npopgˆ”xwu]ef]Æopx'xui ) gÉopU
g c:oqˆ{bd] u]`bd]Ôa+ˆa
oNg1~ D~ i
2b !jw`a
Fg .]mnq]a€
]x!i
b/w9i{_ np]r
€
]`bdcdopw9]x[$f7cdxԀ®a
nN{]”opxr]`c|]`beÌopg]`r 6‚Écdu]Àbd]w9i{_ npoNgˆRw9i6!] Éw`oq]ghc
š ,p, 2 2 ![2/ o , , !6202/
š
o
Z Z
Z : Z
x{z , Z , :Z [! 20:2/ p, , Z 2 2 Z !62/ x
2
_%Š_' _
$ „% „5
698 , 2 K2!, .0- K2;:
z 3 ' „ 6!„ 7 z , 7 K2 $
4
! / 0< ]
À‹
”
´‰ <‹ ´‰ <‹
,Œ¡›2
:oqˆ{bd]
c
m
Ôi
cda+cdoqigzig– opga+b‚Ìw9i{_ npoNgˆfxdwu]ev]
f
f
d
e
a
b
c
a
b
c
m]`bd]opg~ 3 oNx”a ma
w`a
uÖw9i6]!Éw`oq]ghc`~Ba
grÕcdu]ƒnpa
x|cÀxd‚6e.in'opx”a 6+Œ"w9i6]!Éw`oq]ghc–& ”›(Š$ u ]Ôa
w`a
u
w9i6]!Éw`oq]ghcÔw`a
g.]”r]!™Dg]r@a
x
‘
%
3 ' $ „ „6!„ „ 7 5 z
%
|
 p„ „  ˆ ‚
$ „ „5
 p„  † „  ‹
'
% '
5!„ „ 6
 ‹ „ ‡ „
‚
‚
„ „7
 † „ ‡ „ ˆ
‚
,›2
$ „ 7H„ 6
 p„  ˆ „  ]
71gvi
br]`b/c|iR%i cda
opgÉa
gÌ!] #_bd]xdxoqigÌopgvc|]`bevx/i
k Ôa
w`a
uw9ih]!ƒw`oq]g,cdx!k½i
b!aÀˆ
]g]`ba
nDbd]w9i{_ nNopgˆ
w9i6]!Éw`oq]ghc,½i
b<+Œ"w9i6]!Éw`oq]ghc32˜~ ) ]^xdcda+bdc/k½bdie cdu] opga+bd‚Çw9i{_ nNopgˆÀxdw˜u]ef]^i
k2cdu] ba®Œ€
]w9c|i
b
a
grtc|bd‚Ñc|ic|ba
g x|k×i
b˜e oqcÆopghc|iÉcdu]'Dopga+bd‚@w9i{_ nNopgˆÉxwu]ef]Çi
k'cdu].
]`c1Œ€
]w9c|i
b~6‚a+__ nq‚opgˆÉa
x|[] *6{]gw9]Æi
k2]nq]ev]g,cda+bd‚Éi
_.]`ba+cdoqigx/igxd{c|bd]`]x!i
k2cdu]Æw9i{_ npopgˆÓxdwu]ev]b&(Š$fœa
wui
_.]`ba+cdopig
w9ighc|bqo {c|]xÌaÙ_ a+bdcvopgWcdu`] ™Dga
nH!] #_bd]xdxdopig $ ci
bÉa4c ) opx|c`~!cdu]Ñig nq‚Öw9igh% c|bqo {cdoqigUopxvaÙxdopˆg
kÏa
w9c|i
bÔi
k:cdu]”k½i
be ,Œ›23$ci
bmafbi
cda+cdoqig~cdu]Ów9ig,c|b+o {cdoqig@opxavk½a
w9c|i
b 3 ' $ „ „66„ „ 7 5 efi
bd]`i¨€
]`b , ) u]g
ˆ
iopgˆ4k½bdie nq]`k½cÇc|iÙboqˆuhcÇoNk
g c:oqˆ{bd] 6~k½i
bv!] #a
ev_ nq:] 2Óoq#k 0rih]xfgi
cf‚
]`cva+__.]a+bva
xfa4€
]`bdc|!] #
opgÙcdu] opga+b‚tw9i{_DnpopgˆÑxdw˜u]ef]Éi
k!cduU] .
]`c1Œ€
]w9c|i
b~'cdu]gÕcduopx”i
_]`b˜a+cdoqig a
npxdiшoq€
]x”b˜opx|]vc|ita
g] ) x{eveva+cdoqigՀ®a+boNBa nq] 7 $U7ŽgÙcdu opx”w`a
x|]vcdu]vbdi
cda+cdoqigÖopx”xda
opr4c|itw9bd]a+c|]Éag] ) €
]`bdc|!] # 0›$
] ™ga
n.!] #6_ bd]xdxdoqigÑk×i
bjcdu]”ˆ
]g]`ba
nb]w9i{_ npopgˆÇw9i6!] Éw`oq]ghcmoNxHcdu]gѕ
a ,ÏeR{nqcdoq_Dnq:] 2/xd{eveva+cdopig
u
k½i
beÓ{ npa^i€
]`bcdu]_bdir{w9cdxKi
ka
nNn6w9ighc|bqo D{cdoqigx:w9i
bdbd]xd_ig ropgˆ^c|i…cdu]jx|[] *6{]gw9]i
k]nq]ef]ghcda+bd‚
i
_.]`ba+cdoqig[x $fci
bma
g@!] #a
ef_ np]
~ x|]`F] &h~}]w9cdoqig:‰ (Š$ uopxHnq]a
rxc|iÌcdu]”k½inpnqi ) opgaˆ m
%G > P = iR!A–?–NOR6>R!Ap?BLApRHEHGBI:J@L =/>ON˜E3GKR E[=ŒR6>(GBA pEHGKR E6=ŠR!>( š o x ž=/Q
?B>
XGE3GBI:J@L = >ON P G <` ;? P =rEb?B> N%ISL"?%ATGBTUR!>9Š? R ?B> / ;HR /QSRb;6= >?BA3C–EHG%IKJLM=/>ON
EP 6QSR!TUR P E3GBADApR P JSGB> B= > N ŠG ?B>
AR P JRE r= %R!L C
= P ? P R 6IR!>E3R G R!L+R!TUR6>(Š?BADC'G3JR6Au? r=rGB> P
EHG%> P = P r=/>ONUG
ž= P P ?%>
Ap.G Š.? r=ŒGB> P rAu?B> P 6GBA3T=/>ON ŠG / /QSR6> /QSR!AR R %= P P ?B>nRDJApR PHP =ŒGB>
6GBA /QSR pEHGKR E6=ŠR!(
> ? P ? T'ISL r= JLqR P IST ž= /QUR?›E6
Q R6A3T EHGB> P = P r= > NbG <?-J@ApG BIE G
?›E3?Q
EHG:R E6=ŠR!9
> P ?B> ?'JQS? P R 6?›E ŠGBA
8GBARG %R!A /QSR>ISTU;HR!AG P IST'T.? r=ŒGB> ?BAD=Œ?i;!L+R P = P R 6I?BL
ŠG /QSR>ISTU;HR6AG Ap.G Š.? r=ŒGB> P = >
/Q .? E6AR.? R?U> R BR!A R ‹
%
-/.10
"!
'&
2.13
)('+*
4#
:9
8
<;=?>
=&
B&
Ù]”xdu a
npnbd]`k×]`bc|ivx{wu@a
g]!#_bd]xdxoqigÉa
x?B>“R DJS?%>
5
?›E3?Q E3GKR
5
A*
E[=ŒR6>( P $
7
$#
,
@&
-6.5387
,
C
P =ŒGB>8G -/QSR pEHG:R
E6=ŠR!>9f=/> R6A3T P G
71g i
b˜r]`bÓc|iÙr]`c|]`b˜evopg]ƒa
g i
_cdoNeva
n]!#_bd]xxdoqigÖk×i
bÇa Œ"w9ih]!ƒw`oq]g,c`~/ig]xdui{npr8™DgrÖa
|x ][*6{]gw9]ƒi
kÔ]nq]ev]g,cda+bd‚ i
_]`b˜a+cdoqigxÇw9igxdopxdcdopgˆi
kÔcdu]ƒeÌopgopeR{e g6{e.]`bÀi
kÔbi
cda+cdoqigx6$n71gŒ
r]`]r~aƒc ) opx|c…opx^opg]!#_]g xdoq€
]Óxopgw9]Çoqc^w9ighc|boqD{c|]x^ignq‚axdoqˆg ,Ïa
gr4g]`€
]`b”a
gt]!#c|ba@xd{eÌeva®Œ
cdoqig€+a+bopaB nq]:23$Ùl bi
cda+cdoqigUui ) ]`€
]`bÌopxÓ]!#_]g xdoq€
]xdopgw9]oqcÇw9ig,c|bo+ {c|]xÇa(ma
w`a
uUw9ih]!ƒw`oq]g,c
,Ïw9ief_ {cda+cdoqiga
npnq‚É!] #6_.]gxoq€
]…xdopgw9]…cduoNxopg,€
inp€
]xcdu]…]`€+a
np{a+cdoqig@i
k:afxdopgˆnq]…xd{e ]!#_bd]xdxdopig@2˜~
¡
a
grÖxdopgw9]ƒoqcÓw`a
gֈoq€
]Ìb˜opx|]Ìc|ita
g ]!#c|batxd{eveÌa+cdoqigՀ+a+bopaB np]%$–7Žg cdu]Ìc|]`beÌopginqi
ˆ
‚Ùi
kja
gˆ{Œ
npa+bjefiev]g,cd{eÑ~aÇc ) opx|copxHoqbbd]nq]`€+a
g,cxdopg w9]^cdu]Æw9i
bbd]x|_.igropgˆÓx|cda+c|]”€
]w9c|i
b˜xÔa+bd]Æbd]npa+c|]rh‚ƒa
_ ua
xd]k½a
w9c|i
b~ ) u]`bd]a
xaÆbdi
cda+cdoqigÌoNxBw9b{w`opa
nxdopg w9]cdu]jw9i
bdbd]x|_.igr opgˆÆx|cda+c|]j€
]w9c|i
bx!a+bd]bd]npa+c|]r
cdubdi{ˆu r-o ,.]`bd]ghc”opghc|]`bef]ropa+c|]Éa
gˆ{npa+bRefief]ghcdSa $ uh{x~ ) ]Éxdua
nNnBxda‚Ùcdua+cRa
gÕ!] #_ a
gxdopig
i
kÔa +Œ"w9i6!] Éw`oq]ghcvopx”i
_cdoNeva
n/opk!cdu]ƒg6{e ]`bÓi
Ak Ôa
w`a
uWw9i6!] Éw`oq]ghcdxÇa+__.]a+bopgˆoNg xd{w˜uÖa
g
]!#_ a
gxdoqig@oNxjevopgoNeva
Œn $
5 oqcduRcduopxKopgRevopgr ) ]Hw`a
gÇbd]r!] ™Dg]i{b:_bd%i Dnq]eña
grRcdu
] a
xdoNwx|c|b{ w9cd{bd]!cdua+cBoqc=opxKr]a
npoNgˆ
o) qcd u $:V
l ;6= >@?%A3C`EHGBI:J@L = > N rApR3Rig F ‹”nq]a€
]xÔopxjaÇbihi
c|]•
r opga+bd‚Éc|bd]`]Àxd{ wu@cdua+c
cdu] F ‹…nq]a€
]xma+bd]ÓnpBa .]npnq]r4‹ Z ‰ Z6]6]6]KZ a<‹ cdu]Àopghc|]`bga
n.€
]`bdcdopw9]xma+bd]Àgi
cjnNBa ]nNnq]r k½i
b]a
wuzopghc|]`bga
n€
]`bdc|!] #.~ig]”w`a
g!] #w˜ua
gˆ
]”cdu]Ænp]`k×ca
grbopˆu,cwu opnprbd]gÉi
kcdu a+c€
]`bdc|!] #$
x IS>@GBA iR!AR AuG[G R n;!=/>@?BADC rARHR P ž=/QL"?O;HR!L/L+R –L+R? BR P $Ôl^g
u]xd]Óa+bd]Rx|ief]`cdopef]xmbd]`k½]`bdbd]rc|iƒa
]!#a
ef_ nq]@opxӈoq€
]gUopW
g c:oqˆ{bda] ”$mi
c|]@cdua+cvopgÖcduopx ™ ˆ{bd]
~ ,Ïia 2Ra
g4
r ,/2Àbd]`_b]x|]g,cÇcdu]@xda
ev]
-
&
:oqˆ{bd] ”mHopga+bd‚w9i{_ nNopgˆRc|bd]`]x
c
0
1
2
3
(a)
4
5
2
1
4
(b)
5
1
3
2
3
(c)
4
5
po g a+bd‚vw9i{_ npoNgˆ”c|bd]`]
~xdoNgw9]mig]^w`a
gk½bd]`]nq‚v]!#wu a
gˆ
]Æcdu]…nq]`k×cHa
grƒboqˆuhcHwuopnNrbd]g$'}6ief]`cdopev]x
oqc ) opnpn-.]w9igh€
]goq]ghcc|iÖa+c|cda
wu<a
g*]!#c|ba €
]`bc|]!# ) oqcdu*npaB.]nԑÕc|icdu]zbdihi
cƒi
k…cdu]Ÿ opga+bd‚
w9i{_ nNopgˆÀc|b]`]
~xd{wu@a
xoNg ,ÏwK23$ u]Æignq‚v]nq]ev]g,cda+bd‚Éi
_.]`ba+cdoqigƒcdua+cjgi ) b]eva
opgxHopx!bdi
cda+cdoqig
iŸ
g opga+bd‚ƒw9i{_ npoNgˆfc|bd]`]bx ,Ïxdopgw9] h‚@r!] ™Dg oqcdoqigÑaÌc ) opxdcÔri6]xmgi
cmwua
gˆ
]Rcdu] opga+bd‚w9i{_ nNopgˆ
c|bd]`:] 23$ u opx”opxÓopnpnp{xdc|ba+c|]rÙop8
g c:oqˆ{bF] ¡6~ ) u]`bd] Ó~ a
gr bd]`_bd]xd]g,cRxd{c|bd]`]xÀa
gr opxÓa
_ a+bdci
k:cdu] Dopga+bd‚ƒw9i{_ npopgˆRc|b]`]Àw9ig,cda
oNgopgˆfcdu]…bihi
c ,½i
b~‚ [] *h{ oq€®a
np]g,cdnq‚
~cdu]”npBa .]ni‘ 23$
u opga+bd‚zw9i{_ npopgˆƒxdw˜u]ef]xÓopxÆ%i h€oqi{[x $ u]vnq]a+k/nNBa ]nNxf‹ ‰
$‹
u]fbd]npa+cdoqig ) opcdn
bd]`k½]`bvc|iÙcdu]Ña
gˆ{ npa+bvefief]ghcd{e €+a
np{]x [[ Z [\ Z6]6]6][Z [^B_ [ $Ul^gýopghc|]`bga
n!€
]`bdc|!] #ýZ opxfZ6g]6]6iÕ]:Z nqigˆ
]`b
]!#_ npopw`oqcdnp‚znpBa .]npnq]r2 ~ {c”oqcÓopxÀopev_ npopw`oqcdnp‚ÑnpBa .]npnq]n
r 6‚tcdu]Éw9inpnq]w9cdopigÕi
kjnq]a€
]xÓ{g r]`bg]a+cduÕop6c $
ci
b”aƒˆoq€
]“
g +Œ"w9i6!] Éw`oq]ghc ) oqcdŸ
u opg a+bd‚Ñw9i{_ npoNgˆÌxdw˜u]ef]x ja
gr / a
g rzk½i
bÆ]`€
]`bd‚zxd[] *h{]g w9]
<w9ig xdopx|cdopgˆÑi
k c ) opx|cdxÓa
gr bdi
cda+cdoqigxÓc|ba
gx|k½i
bevoNgˆ ^oNg,c|i /K~=cdu]`bd]É!] #opxdcdxÀaxd[] *h{]g w9]
i
k Æbdi
cda+cdoqigx^c|ba
gxdk×i
beÌopgˆvcdu]Çw9i
bdbd]xd_ig ropgbˆ oNga+bd‚@w9i{_ npoNgˆfc|bd]`]xÆopghc|iÉ]a
w˜uzi
cdu]`bÆa
g r
€opw9]…€
]`bxdSa $!ynq]a+bnq‚
~k½bdie cdu]”x|[] *6{]gw9]…i
kKbdi
cda+cdoqig x .]`c ) ]`]gÑcdu] oNga+bd‚Ìw9i{_DnpopgˆRc|bd]`]x`~cdu]
x|[] *6{]gw9]!i
kc ) opx|cdx:a
grÓbdi
cda+cdoqigx .]`c ) ]`]gÇcdu] opga+bd‚…w9i{_DnpopgˆÔxwu]ef]xBw`a
'g .]b]w9igx|c|b{w9c|]r
a
gr u]gw9]4giÖoNgk×i
b˜eva+cdoqigæoNxÌnqix|cƒk½i
bƒr]`c|]`b˜evopgopgˆÕcdu]zx{eveva+cdoqig*k½i
beÓ{ npaÙk½i
bƒcdu] +Œ
w9i6!] Éw`oq]gh6c $4*Æ{b a
xdopw”_bd%i nq]e opxÔgi ) bd]r{w9]rzc|i ™Dg ropgˆvaƒxdui
bdc|]xdcmx|[] *6{]gw9]Ri
kBbdi
cda+cdoqigx
c|ba
gxdk×i
beÌopgˆÇig] oNga+bd‚Ìw9i{_DnpopgˆÇc|bd]`]ÀoNg,c|iva
gi
cdu]`[b $
#
*
.
0
.
3
+.13
:#
:oqˆ{bd] ¡ m/!oNga+bd‚w9i{_ npopgˆÓc|bd]`]xÔbd]npa+c|]r•h‚afbdi
cda+cdoqig
c
X
A
B
X
C
A
B
C
X
A
C
B
l oNga+bd‚Éw9i{_ npopgˆfc|b]`]Ów`a
Ÿ
y
g ]Àˆoq€
]gÑ]oqcdu]`bÔ]!#_ npopw`oqcdnp‚Éa
x^avˆ
ba+_ u2~ x|]`]c:oqˆ{bd]”~i
bma
x^a
ba
wH.
]`cdopgˆi
k'cdu]Çnq]a+knNaB]nNx6$ci
b…]!#a
ef_ np]
~cdu] oNga+bd‚@w9i{_ npoNgˆÌc|bd]`]Ri
k{c:oqˆ{bd] ”@w9i{nprŸ.]
bd]`_b]x|]g,c|]ra
x
,p,1‹ Z ›‰ 2 Z ,Œ Z ,/” Z ¡›2p2p2
i
b ,p,´‰ Z ‹K2 Z ,p,/” Z ¡›2 Z ›22 ]
,3%2
‘m]gw9]`k×i
bcdu ) ]…xdua
nNnD{xd]mcduoNx/gi
cda+cdopigk×i
b'
a opga+b‚Çw9i{_ npopgˆÓc|bd]`]%$!}6iev]`cdopef]x ) ]…xdu a
npn ]`€
]g
{x|]…oqc!c|ifbd]`k½]`bc|ifcdu]…{gr]`b˜nq‚6oNgˆ opg a+bd‚vw9i{_ npoNgˆRxwu]ef]”opcdx|]nqkŽ~6oqkcdu]…opg,c|]`b˜ef]ropa+c|]…a
gˆ{nNa+b
efief]ghcd{e €+a
np{]xj_ npa‚gif!] #_ npopw`opc!binq%] $
71gÇcdu]k½inpnqi ) opgˆÆx|]w9cdoqig ) ]jxdua
npnxdui ) cdua+c ™Dgr opgˆÆa^xd[] *h{]g w9]i
kDbdi
cda+cdopigxBc|ba
gxdk×i
beÌopgˆ
ig] opg a+bd‚Ñw9i{_ npoNgˆÌc|bd]`]fopghc|i@a
gi
cdu]`bÆig]fopx^[] *6{oq€+a
nq]g,c^c|`i ™Dgr opgˆÌaƒ_ a+cdu4opg4aƒˆ
ba+_ u %^$
c:oqbx|c`~cdu]`bd]Àa+bd]…c ) iƒopef_.i
bdcda
ghc%i x|]`bd€+a+cdoqig6x $
5Ù] ) opxdutc|iÑrb˜a ) a+c|c|]ghcdoqigÕc|i@cdu]fkÏa
w9c…cdua+c…cduoNx…ef]`cduir4i
Xk opg a+bd‚w9i{_ nNopgˆ
c|bd]`]xHopx!efi
bd]^ˆ
]g]`ba
npnp‚va+__ npopw`Ba Dnq]jcdua
gƒcdu]Æw`a
x|]^i
k2cdu]Æa
gˆ{npa+bHefief]ghcd{e a
nqˆ
6] baRw9igxdoNrŒ
]`bd]rÖu]`bd%] $ u]Ìa
gˆ{nNa+bÀefief]ghcd{e a
npˆ
6] baÑopx”cdu] =oq]va
nqˆ
6] ba ,´›‰ 2˜~:a
g rÙcdu]ÌeR{nqcdoq_Dnq]`cdx
w9i
bdbd]xd_ig rWc|“
i ™Dgoqc|]9Œ"r opef]gxdopiga
n/opbdbd]r{w`+o nq]Ìb]`_bd]x|]ghcda+cdoqigxfi
k ,´›‰ 23$æl^npx|iÙk½i
bÌa
gýa+b DoŌ
c|ba+bd'‚ ™Dg oqc|]9Œ"ropef]g xdoqiga
nx|]evoqŒ"xdopef_ np] =oq]Ôa
nqˆ
6] b˜a ~6ig]Ôw`a
gƒw9igxdopr]`bcdu] ,/ K‹ 2"Œk½inprfc|]gx|i
b
_bdir{w9c d [ eyg6g6ge d^B_ [ ${xdcÇa
xÌop4
g ,1K‹ 2˜~/ig]Ñw`a
gær!] ™Dg]€
]w9c|i
bxÉopgcduopxÇc|]gx|i
bf_ bdi6r {w9c
{xdoNgˆfcdu]RyHnp6] xdwuŒŽ„^i
bra
gzw9ih!] Éw`op]g,cdxmi
k cdu]ag 6l'x|cda
g rxjk½i
bÔcdu]Àbd]`_bd]x|]ghcda+cdoqigtnpBa .]npxHi
k
d l a
gr
l k×i
b^cdu]Çopghc|]`bga
nKnpBa .]npxji
k'cdu]Ӏ
]w9c|i
[b $À}oNgw9]Àcdu]Rc|]gx|i
bÆ_bi6r{ w9cÔopx^opgˆ
]g]`ba
n=gi
nqigˆ
]`b”eR {nqcdop_ npopw`oqc‚,Œk½bd]`]
~.cdu]fw9i{_ np]r4€
]w9c|i
bxÀa+bd]vnNBa ]nNnq]•
r 6‚tbd]`_bd]x|]ghcda+cdoqigÕnNBa ]nNxma
grÙa
g
a
rropcdoqiga
nBnpBa .]n ,Ïx|]`]
~:%] $ ˆ $&ŋ 6~B}6]w9cdoqigý‹ $ :(~:i
`b &ŋŠ (k½i
b”cdu]v!] #a
ef_ nq]fi
k ,“2p23$ɐH{c”cdu]
k½i
beva
n_bd%i np]e i
k ) boqcdopgˆÓaӈ
]g]`ba
nbd]w9i{_ npoNgˆÓw9i6!] Éw`oq]ghcHi
k •&ŋ ~ }6]w9cdoqig4‹ $p‹
D‹ (opgÉc|]`bevx
i
k Ôa
w`a
u4w9i6!] Éw`oq]ghcdx^i
k b]eva
opgxÔ!] #a
w9cdnq‚cdu]Óxda
ev]Ra
xmk×i
b ,´›‰ 2˜~a
grÑcdu6{xmcdu]Óev]`cdui6rzi
k
opg a+bd‚Ìw9i{_ nNopgˆRc|bd]`]xjuinpr x!u]`bd]…a
x ) ]nNŒn $ uh{ x`~a
npn.cdu]Æk×inNnqi ) oNgˆÓb]xd{nqcdxHopgcduoNx/_Da+_]`bjuinpr
k½i
b/cdu]^!] #_ a
gxdoqigÉi
ka +Œ"w9i6!] Éw`oq]ghci
k2a
ga+b oqc|ba+b‚vx|]evoŌ"xdoNef_ nq] =oq]ma
nqˆ
6] ba vopgÌc|]`bevx!i
k
Ôa
w`a
uw9i6!] Éw`oq]ghcdxi
k @$ *Æg]mw`a
gÉ]`€
]gƒ!] #6c|]g rÌcdu]^a+__ npoNw`Ba opnpoqc‚Àc|iRgigŒ"w9ief_ a
w9c op]Ԉ
bdi{_Dx`~
i
bjc|ivopg ™Dgoqc|]9Œ"roNef]gxdoqig a
nbd]`_bd]xd]g,cda+cdoqig 6x $fci
bj!] #a
ef_ nq]
~cdu]”ef]`cduir@a
npx|i ) i
Hb .6xk½i
bc|]gx|i
b
_bdir{w9cdx/i
k2_.ixdoqcdop€
]mropxw9bd]`c|]^xd]`boq]x!bd]`_bd]xd]g,cda+cdoqig x/i
k ,1‹ Z K‹ 2˜~xdopgw9]Æxd{w˜uaÀc|]gxdi
b!_ bdi6r {w9c
opxRw9ief_ nq]`c|]np‚ r]w9ief_.ixdBa np]ƒopghc|iÙazr oqbd]w9cÇxd{e i
kj_.ixdoqcdoq€
]ropxw9bd]`c|]ƒxd]`boq]xÓbd]`_bd]x|]ghcda+cdoqigx
.
.
.
.
.
,½]`€
]g ) opcdui{cÓeR{nqcdop_ npopw`oqc‚ÙnpaB.]npx323$nœ'€
]gWcdui{ˆu ) ]@w9ig,cdopg6{]c|iÙ{x|]ƒcdu]c|]`bevopginqi
ˆ
‚Õi
k
a gˆ{nNa+b!efiev]g,cd{e w9i{_ nNopgˆÀopgÉcdu]^k×inNnqi ) oNgˆÀx|]w9cdoqig x`~ ) ] ) opxduÌc|iÓ]ef_Dua
xdoq—`]^cdua+c ) ]Æua€
]
cduopxH]!#c|]gr]rzw9i{_ npoNgˆÓ_ bdi% nq]e opg@eÌopgr$
ci
b'cdu]jw`a
x|]i
k ,´‰›2˜~cdu]_.i ) ]`bdkÏ{nef]`cduirÇi
k0{cdxdopx:ˆ
ba+_ u x ) a
x'r]`€
]npi
_]r&ŋ6(Š$
uoNx=ˆ
b˜a+_ uopw`a
nef]`cdui6rvoNx:!] #6c|bd]ev]nq‚R{ x|]`k½{ nc|i™Dgr,½i
_cdopeÌa
n 2=]!#6_Da
gxdoqigx:k½i
b{
Œ"w9ih]!Éw`op]g,cdx
i
k ,´›‰ 2 &6~h (~,i
bc|iÀw`npa
xxdoqk½‚Àcdu]e–$ž‘mi ) ]`€
]`b~opghc|bopgxdoNw`a
npnq‚…cduopxBev]`cdui6rÌ{x|]xB€+a+boqi{xBxd‚6evev]9Œ
c|bd‚É_bdi
_.]`bdcdoq]x/i
kKyHnq6] DxdwuŒŽ„Æi
bra
gƒi
0b Ôa
w`a
u@w9i6!] Éw`oq]ghcdxHcdua+cja+bd]ƀ+a
npoprÉk×i
bHcdu]…w`a
x|]…i
k ,´›‰ 2
ignq%‚ $ u6{xÆoqc…opx…gi@nqigˆ
]`bÀ€®a
npoNrk½i
b”cdu]f!] #c|]gr]rÙw`a
x|]Ér]xdw9bqo .]rtopgtcdu]f_bd]`€oqi{4x Ô]eva+b .
a
grÙw9igxopr]`bd]r4opgzcdu]fbd]x|cÆi
k/cduopxÆ_ a+_.]`[b $ ci
b”cdu]Ç!] #6c|]g r]rÙw`a
x|]
~2ignp‚c ) i@_bdi
_.]`bdcdop]x^a+b]
g]`]r]r m•,/”O2a,½i
bfa
g [] *6{oq€+a
nq]ghcÀig]
~'x|]`“
] &ŋŠ~ ,Œ¡ $p‹ %2 (/2Ra
gr ,›2˜~ ) u opwuÖopxÀa
n ) a‚xR€®a
nNopr ,Ïx|]`]
][*@$,1‹ $9”,› 2i
<k &ŋ :(/23$
.
.
.
±
2]`c ‹U.]b™#]r~Ka
g Ör w9igxopr]`bÀcdu]Éx|]`cÓi
kja
npnf oNga+bd‚4w9i{_ npopgˆ@c|bd]`]x ) oqcdu“•‹ƒnq]a€
]x6$
}opg w9]Ài{bÆignq‚–Da
xdopw”i
_.]`ba+cdopigtoNxÔbdi
cda+cdopig~ ) ]fxdua
nNnw9igxdoNr]`bmcdu]FApG.Š?.r=ŒGB>8N%Ap?3JQÌi
kX opga+bd‚
w9i{_ nNopgˆvc|bd]`]x[$ uopxԈ
ba+_ u %^@ua
xÆa
x^€
]`bdc|!] #txd]`c^cdu]Rx|]`cÆi
ka
nNn1 oNga+bd‚Ñw9i{_ nNopgˆvc|bd]`]x ) oqcdu
ñ‹fnp]a€
]x`~:a
gr4cdu]`bd]voNx…a
gÙ]rˆ
] .]`c ) ]`]gÕc ) i€
]`bdcdopw9]xÀopk/a
gr4ignp‚zoqk/cdu]vw9i
bdbd]x|_.igr opgˆ
opg a+bd‚ w9i{_ nNopgˆtc|bd]`]xva+bd]Ñb]npa+c|]rWcdubdi{ˆuUa xdopgˆnq]ƒbdi
cda+cdoqi g $k7Žcfk½inpnqi ) xÇcdua+cÌa
gWi
_cdopeÌa
n
]!#_bd]xdxdopig@k×i
bÆFa Œ"w9ih!] ƒw`oq]g,cÆw9i
bdbd]xd_ig rxc|i ™gropgˆvaÉxdui
bdc|]xdcj_ a+cdutop(
g %^a.]`c ) ]`]gcdu]
c ) iUDopga+bd‚Ìw9i{_ npopgˆÇc|bd]`]xÔbd]npa+c|]r@c|iÌcdu] ba®Œa
g –r .
]`c1Œ€
]w9c|i
bÆi
kKcdu] +Œ"w9i6!] Éw`oq]gh6c $
5Ù]”xdu a
npn gi ) w9igxdopr]`b!x|iev]^!] #a
ef_ np]x`~6a
g rƒr]r{w9]Æx|ief]ƈ
]g]`ba
n_bdi
_.]`bdcdop]xi
<
k % ^$žci
b
z ‰fcduopxHˆ
ba+_ uopxjxdopev_ nq‚Ìafc|b˜opa
gˆnq%] $ž71
g c:oqˆ{bd@] ) ]”ˆop€
?] % \¨~ a
gr{x|]”cdu]”w9igh€
]ghcdoqik
g ,3%2
c|iÌnpBa .]ncdu]”w9i
bdb]x|_.igropg'ˆ opg a+bd‚Ìw9i{_ nNopgˆRc|bd]`]6x $ u]”g!] #6cˆ
b˜a+_ u~ % s ~ ua
xHi
b˜r]`bÀ[‹ ¡ $ u opx
:oqˆ{bd]@ m u ]…ˆ
ba+_ u
c
((1,2),3)
% \
(1,(2,3))
((1,3),2)
ˆ
ba+_ uÙoNx^xui ) g4opgnc:oqˆ{b] h~2{ xdopgˆƒcdu]ba
wH.
]`c”bd]`_bd]xd]g,cda+cdoqig ,3%2mk½i
b…cdu]b oNga+bd‚Ñw9i{_ nNopgˆ
c|bd]`]x6$ u]][*h{ oq€®a
np]gw9]-]`c ) ]`]gÌi
_cdopeva
n]!#6_b]xdxdoqigx:k½i
b{
Œ"w9ih]!Éw`op]g,cdx!a
grvxdui
bdc|]x|c'_ a+cdu x
op)
g % ^ w`a
gY.]ƒopnpnp{xdc|ba+c|]rÕopg˜cKopˆ{bd] Ñk½i
bÓcdu]ƒw`npa
xdxdoNw`a
n!6
Œ"w9ih]!Éw`op]g,c6$“ci
bÇcduopxÓw9ih]!ƒw`oq]g,c`~
cdu]Æw9i
bdbd]x|_.igr opgˆ oNga+bd‚vw9i{_ nNopgˆ”c|bd]`]xa+b],p,1‹ Z ‰›2 Z ,Œ Z ”O2p2ma
grn,p,1‹ Z ›2 Z ,´‰ Z ”O2p23$ u]Æxdui
bdc|]xdc
_ a+cduUop>
g % s oNxÇi
k^nq]gˆ
cdu 6~!a
grWcdu6{xÇcduoNxfopef_ npop]xÀcdua+cfcdu opxv6+Œ"w9i6]!Éw`oq]ghcÉw`a
g .] ) bopc|c|]g
a
x^aÌxdopgˆnq]”xd{eÚ!] #6_b]xdxdoqigi€
]`bÆcdu]À_ bdi6r {w9ci
kBcdubd]`?] 6+Œ"w9i6!] Éw`oq]ghcdx , ) uopw˜uopx`~Da+cmnq]a
x|cmk×i
b
,´›‰ 2˜~a ) ]npnŊŒ .gi ) gvk½a
w93c 23$ mi
c|]mcdu a+c/opgfi{b'c|]`bevopginqi
ˆ
‚
~ ) ]jbd]`k½]`bc|iÓi
cdu]`bHw9ih!] Éw`op]g,cdx!xd{w˜u
a
xcdu]Æig]xÔw9i
bdbd]x|_.igroNgˆÀc|i š ,1‹ Z ,´‰ Z ,Œ Z ”O2p2p2 o ,Œ Z ,´‰ Z ,|‹ Z ” 2p2 x ~ š ,1‹ Z ,´‰ Z ,Œ Z ”O2p2p2 o ,´‰ Z ,Œ Z ,1‹ Z ” 2p2p2 x i
b
š ,1‹ ,´‰ ,Œ ”O2p2p2 o ,p,1‹ i‰ 2 ,Œ ”O22 a
npx|iÙa
xÌ6 Œ"w9ih!] ƒw`oq]g,cdx~/]`€
]gUcdui{ˆuWcdua
] ™ bx|cRc ) iÕbd]r {w9]Éc|i
cdu]jZ _ bdi6Z r {Z w9cBi
kc ) i Z 6
Z Œ"w9ihZ !] Éw`x op]g,cdxHa
grÌcdu]Ônpa
x|cig]Ôc|iRa”xdopgˆnpA] 6+Œ"w9i6!] Éw`oq]ghc ,Ïa
x!w`a
Ug .]jx|]`]g
op–g c:oqˆ{b] Rk×bie cdu]”w9i
bdbd]xd_ig ropgˆÇropx|cda
g w9]xjopg % s[23$
.
Š
:oqˆ{bd]Om u ]…ˆ
ba+_ u
c
% s
(3,(4,(1,2)))
(3,(1,(2,4)))
((1,2),(3,4))
(4,(3,(1,2)))
((1,3),(2,4))
(1,(3,(2,4)))
(1,(2,(3,4)))
(3,(2,(1,4)))
(4,(2,(1,3)))
(2,(1,(3,4)))
(2,(4,(3,1)))
(1,(4,(2,3)))
(4,(1,(2,3)))
(2,(3,(4,1)))
((1,4),(2,3))
]`c”{x”gi ) w9igxdopr]`b”xdief]fˆ
]g]`ba
nB_ bdi
_.]`bdcdoq]x^i
k/cdu]fˆ
ba+_ u % ^ $flmgÙa+bDoqc|ba+bd‚z]nq]ef]ghc
i
k@%^~HoŒ$ ]%$'a“Dopga+bd‚w9i{_ npopgˆzc|bd]`]zig ËÑnq]a€
]x`~ua
xb 7‹Ñopghc|]`bga
nH]rˆ
]x ,ÏoŒ$ ]%$']rˆ
]x
w9ighcda
opgopgˆginq]a+3k 23$ ) iÉbdi
cda+cdopigx…w`a
g ]R_.]`bdk½i
bef]r ) oqcdub]x|_.]w9cmc|i]a
wuÙoNg,c|]`bg a
n]rˆ
]
~
cdu6{x!]`€
]`bdF‚ Dopga+bd‚vw9i{_DnpopgˆÓc|bd]`]…opxHw9igg]w9c|]r–6‚Éa
gƒ]rˆ
]…c|iv‰,/ 7֋K2/i
cdu]`b oNga+bd‚vw9i{_ nNopgˆ
c|bd]`]6x $ž71gvi
cdu]`b ) i
brx`~ %^Çopx/a”bd]`ˆ{nNa+bˆ
ba+_ uÌi
k2r]`ˆ
bd]`]…‰ ,/7ÙK‹ 23$fci
bH]!#a
ef_ nq]
~% sjoNx'bd]`ˆ{nNa+b
i
kBr]`ˆ
bd]`] ”$
e .]`bi
k oNga+bd‚Çw9i{_ npopgˆ”c|bd]`]x!iUg ‹^nq]a€
]x ,½i
b!cdu]^i
br]`b o %^ o i
k
iRr]`c|]`bevopg]mcdu]mg6{
%^S2˜~w9igxdopr]`b ™Dbx|cHa opga+bd‚vw9i{_ npopgˆRc|bd]`] i`g Ùnq]a€
]x , ) oqcdunpBa .]npx^‹ Z6]6]6]KZ 2˜~a
g r!] #6c|]gr
cdu]@bdi6i
cvi
k ) opcduUa
gU!] #6c|b˜aÙ]rˆ
]Ñ]gr opgˆÙopgWcdu]Ñnq]a+kƑ ,Ïa
xÉopg c:oqˆ{bd–] ”O23$ uopxRc|bd]`]ua
x
‰ 7 ‹”]rˆ
]xÆopg@c|i
cda
Šn $ u]`bd]`k½i
bd]
~Dcdu]`bd]Óa+b]lj 7 ‹Àr;o ,]`bd]ghc ) a‚x^i
k'a
rropgˆva
gz!] #c|baÌ]rˆ
]
]groNgˆ ) opcdunq]a+knNBa ]n añ‹Rc|iÉcduoNxÔc|bd]`]
~2g a
ef]nq–‚ 6‚a+c|cda
wuoNgˆÑoqcÔc|i]a
w˜uÙw9igxdopx|cdoNgˆÌ]rˆ
]
~
x|]`]”%] $ ˆ $c:oqˆ{bd]ÀŠ $ uh{x ) ]Àua€
] o %^ o z ,´‰ 7æK‹ 2 o % ^ & [ o ~a
g `r ™Dg8
r ,Ïx|]`]Óa
npx|Ÿ
i &ŋ`B‘ (/2
o % ^ o ,´‰ 7æK‹ 2:9;9 ,´‰ 7æK‹ 2!,´‰ (7˜›2
,´›Š 2
g6g6g g ‹ ]
z
z
k %^@ˆ
bdi ) x^!] #6_.ig]ghcdopa
npnq%‚ $ Ba nq]‹Óˆop€
]xmcdu]Çr]`ˆ
bd]`]Ra
g rzcdu]
uoNxÔopef_Dnpoq]xjcdu a+c^cdu]Ói
br]`b^i
'
i
br]`bÔi
k % ^ k½i
<b 65ñ‹
B‹ $
7Žcmopxma
npx|iÉ]a
x|‚@c|iƒxui ) cdua+4
c % ^ oNxÔaÌw9ig g]w9c|]rtˆ
ba+_ u~Œo $ %] $ k½i
b^a
gh‚@c ) ai opga+bd‚w9i{_ nNopgˆ
c|bd]`]x [ a
g r \¨~Kcdu]`bd]Ì!] #opxdcdxÀa+cÀnq]a
xdcÀig]v_Da+cd8
u .]`c ) ]`]
g [ a
g
r \•&ŋ`B‘ (Š$a71gÕax|]g x|]
~cduoNx
x|cda+c|]ef]ghc”opxÔ[] *h{op€®a
nq]ghc^c|iÉcdu]RkÏ{gra
ef]ghcda
n=cdu]`i
bd]e i
k'bd]w9i{_Dnpopgˆvcdu]`i
bd˜
‚ &96~. _ $”i¡%¡:('cdu a+c

:oqˆ{bd]NJ m c:oq€
] ) a ‚6xÆi
k'a+c|cda
w˜uopgˆ@a
gt]!#6c|b˜aÉnq]a+k/npaB.]n ”ƒc|iƒaɈoq€
]g po ga+b‚w9i{_ npopgˆÌc|bd]`]Óig
npBa .]npx…‹+~º‰6~ c
0
1
4 4
2
4
4
3
4
a nq]v‹Bm/\m]`ˆ
b]`]Óa
gr@i
b˜r]`bji
k%^
¡
Š
Š
‹`‘
‹‰
!‹ ”
”i¡ ‹`›‘ % ¡ [‹ %¡[‹ %¡ ‰+‘‰ ®‘%‰ ¡
B
r]`ˆ
‰
,3%^ 2
o% ^ o
‰
”
[¡
‹
”
‹`‘›¡

 ,‰
‹1
”%”i¡ ” %¡
‹`‘
‹ Š
%¡”+‰
+‘B¡
]a
wuƒˆ
]g]`b˜a
npoq—`]r`+Œ"w9i6]!Éw`oq]ghcHw`a
ga.]j]!#_bd]xdxd]rÉopgvc|]`bevx!i
k2xd{evxi€
]`bH_bdir{w9cdxi
k&Ôa
w`a
u
w9i6!] Éw`oq]ghcdx ,6+Œ"w9i6!] Éw`oq]ghcd3x 23$
yHnp]a+bnq‚
~k½i
b 6=ñ‹
‹Àcdu]”i
br]`bÔi
k % ^U.]w9ief]xÔc|ihiÌnNa+bdˆ
]”c|ivbd]`_ bd]x|]ghc %^ƒopgcdu@] mlms i
k
aw9ief_ {c|]`b~ ) uopwutopx^g]w9]xdxda+b‚k½i
b^cdu]Rw9ief_D{cda+cdoqig4i
kxdui
bdc|]x|cÆ_ a+cduxmi
b…i
k'cdu]fropa
ev]`c|]`b
i
k %^$ 7Žgcdu]”k½inpnqi ) opgˆÌx|]w9cdopig ) ]Óxdua
nNn2r]xdw9b+o ]”xdief]Ài
kBcdu]Óbd]xd{npcdxji
k:i{bmw9iev_ {cda+cdoqigx
k½i
–b 5 ‹
B‹ $ lÔk½c|]`bÑcdua+c`~ ) ]Õxdua
npnÆw9igw9]ghc|ba+c|]Õig<cdu]4r opa
ef]`c|]`b@i
k %^~Æa
gr ˆoq€
]Õx|iev]
a+__b[i #opeva+cdoqig[x $
±
}6iÑkÏa+b~ ) ]ƒua€
]Ébd]r{w9]rÙi{bÀ_bdi%Dnq]e c|icdu]Ìk×inpnpi ) opgˆ“mÀˆoq€
]g c ) i• opg a+bd‚zw9i{_Dnpopgˆ@c|bd]`]x
raÉxdui
bdc|]xdcÔ_ a+cdu•]`c ) ]`]g [ a
gr \®~.a
gropgÑ_ a+bdcdopw`{nNa+bÔr]`c|]`bevoNg]
[cdu]ta
nqg]r gˆ
\cd”uýk½bdi
ik…e cdu %opxf^_ ~ a+™Dcdgy
u ,Ïxdopgw9]cduopxvr]`c|]`b˜evopg]xÌcdu]zg6{e]`bÌi
k Ôa
w`a
u w9ih]!Éw`op]g,cdxopgUcdu]
]!#_ a
gxdoqig23$ u]Ìnq]gˆ
cdu i
kjaxdui
bc|]x|cÀ_ a+cdY
u .]`c ) ]`]g [ a
gr \voNx.gi ) gÖa
xÀcdu]Éropxdcda
gw9]
2@, [[Z \K2.]`c ) ]`]g [ a
gr \+~Dxdopgw9]ÆcduopxÔopgr{w9]xHavr opx|cda
gw9]…kÏ{gw9cdoqigi
b^ef]`c|bopw&ŋ‰~2‹[¡(Š$
]`c!{x/w9igxdopr]`b/a+ˆa
opgÉcdu]Ô!] #a
ef_ np] z 6~ ) oqcdu %sˆoq€
]gƒopUg c:oqˆ{bd] O$/}6cda+bdcdoNgˆÀk½bdie cdu]
opg a+bd‚Éw9i{_DnpopgˆRc|bd]`F
] ,p,1‹ Z ›‰ 2 Z ,Œ Z ”O2p2˜~2ig] ™Dgrx!cdua+c
cdu]`bd]Àa+bd] ”f]np]ef]g,cdxÔi
k % s a+cÔropxdcda
gw9]v‹+~ ga
ef]np‚
,/” Z ,Œ Z ,1‹ Z ›‰ 2p2p2˜
~ ,Œ Z ,/” Z ,1‹ Z ›‰ 2p2p2˜{~ ,´‰ Z ,1‹ Z ,Œ Z ”O2p2p2^a
gY
r ,1‹ Z ,´‰ Z ,Œ Z ”O2p2p2 cdu]`bd]Àa+bd]ӊR€
]`bcdopw9]xji
k % sÆa+cÔr opx|cda
gw9]À‰6~ g a
ef]nq‚
,Œ Z ,1‹ Z ,´‰ Z ”O2p2p2˜
~ ,Œ Z ,´‰ Z ,1‹ Z ”O2p2p2˜{~ ,/” Z ,1‹ Z ,´‰ Z ›2p2p2˜X~ ,1‹ Z ,Œ Z ,´‰ Z ”O2p2p2˜{~ ,1‹ Z ,/” Z ,´‰ Z ›2p2p2˜~
,/” Z ,´‰ Z ,1‹ Z ›2p2p2˜
~ ,´‰ Z ,Œ Z ,/” Z K‹ 2p2p2^a
gY
r ,´‰ Z ,/” Z ,Œ Z K‹ 2p2p2 ‹`‘
< H
cdu]`bd]Àa+bd]ӉR€
]`bcdopw9]xÔa+c^ropx|cda
gw9] 6~Dga
ef]nq‚n,p,1‹ Z ›2 Z ,´‰ Z ”O2p2Æa
gr8,p,1‹ Z ”O2 Z ,´‰ Z ›2p23$
u]/x|][*h{]gw9]ˆoq€opgˆÔcdu]g6{e .]`b=i
k]nq]ef]ghcdxa+c:ropx|cda
gw9]U, z ‘ Z ‹ Z6]6]6] 2.k½bdieñaԈoq€
]gӀ
]`bdc|]!#
æopx:w`a
npnq]rÇcdu] B= P Š?B>@EDR iRŠN›ApR3R P R [IR!>@EDR ,Ï\Æ\…} 2Kk×i
bBcdu a+cB€
]`bdc|]!# $ uh{x~+oNg.%s®~cdu]jropxdcda
gw9]
r]`ˆ
bd]`]”xd[] *h{]g w9]^i
-k ,p,1‹ Z ›‰ 2 Z ,Œ Z ”O2p2mopx ,1‹ Z ” Z Š Z ›‰ 23$ u]^c ) if]np]ef]g,cdxa+cjeÌa#opeR{e ropx|cda
g w9]
~opg
w`a
xdn
{ ,p,1‹ Z ›2 Z ,´‰ Z ”O2p2Ha
gr ,p,1‹ Z ”O2 Z ,´‰ Z ›2p2˜~ ˆoq€
]mbopx|]jc|i +Œ"w9i6!] Éw`oq]ghcdx ) oqcdufcdu]^eva #opeÓ{ e gh{ enj
.]`bi
k ma
w`a
uRw9i6!] Éw`oq]ghcdxKopgÀa
gÓi
_cdopeva
n,!] #6_ bd]xdxdoqig oNg…cduopx=w`a
x|] š ,p,1‹ Z ›‰ 2 Z ,Œ Z ”O2p2 o ,p,d‹ Z i2 Z ,´‰ Z ”O22 x
a
gr š ,p,1‹ Z ›‰ 2 Z ,Œ Z ”O2p2 o ,p,|‹ Z ” 2 Z ,´‰ Z ›2H2 x ˆoq€
]Óbopx|]Àc|iɈ
]g6{opg]R6 +Œ"w9i6!] Éw`oq]ghcdxÆcdua+cmua€
]Ra
xmi
_cdopeÌa
n
!] #_ a
gxdoqig@aÌxdopgˆnq]…xd{ e i€
]`b^_bdir{w9cdxHi
k:cdubd]`@
] 6
Œ"w9ih!] Éw`op]g,cd6x $
7ŽcjopxHgi
cxd{bd_ bopxdopgˆ”cdua+ccdu]…ropxdcda
gw9]…r]`ˆ
bd]`]”x|[] *6{]gw9]…i
k ,p,1‹ Z ›2 Z ,´‰ Z ”O2p2Ôi
b ,p,1‹ Z ”O2 Z ,´‰ Z ›2p2
opxÆa
npx|8
i ,1‹ ” Š ›‰ 23$vlmk×c|]`bÓa
npn´~aƒ_]`b˜eÓ{cda+cdopigzi
k/cdu]vnq]a+k!npBa .]npxÔi
k/cdu] opga+b‚Ñw9i{_ npopgˆÉc|bd]`]x
op)
g %^4rihZ]xRZ gi
Z cRwua
gˆ
]ƒcdu]x|c|b{w9cd{bd]vi
k %^@$ *Æg cdu]Ìi
cdu]`bÇua
gr2~KoqcRopxÀa+c ™ bxdcÀxdoqˆuhcÓxd{b|Œ
_boNxdopgˆ”cdu a+c!a
npxdiÓcdu]Æi
cdu]`bH€
]`bdcdoNw9]xHi
k % s i
k2cdu]^k×i
b˜e , Z , :Z ,! Z 2 2p2p2u a€
]…cdu]Æxda
ef]…ropxdcda
gw9]
r]`ˆ
bd]`]ƒx|[] *6{]gw9]Éa
`x ,p,1‹ Z ›‰ 2 Z ,Œ Z ”O2p23$n7Žg r]`]r~cduU] opg a+bd‚tw9i{_ npopgˆc|bd]`]xÓk½i
`b ,1‹ Z ,´‰ Z ,Œ Z ”O2p2p2Ri
b
,p,1‹ Z ›‰ 2 Z ,Œ Z ”O2p2fnpih%i .Õr;o ,]`bd]ghc`~Bx|]``
] cKopˆ{bd]ƒ ,Ïia 23$ u6{?x % svua
xÓc ) iÙr-o ,.]`bd]ghc rC3JR P i
k opga+bd‚
4
:oqˆ{bd]À m
c
)
,
iÉro-,.]`bd]g,cc‚h_.]xi
k No ga+bd‚Ìw9i{_DnpopgˆÇc|bd]`]x ) oqcducdu]”xda
ev]Àxp.
]nq]`c|ig
(a)
1
2
3
4
1
2
0
3
4
0
(b)
0
1
3
2
4
1
4
1
3
2
2
3
=
2
=
1
0
4
4
3
(c)
w9i{_ nNopgˆ…c|bd]`]x`~6cdu] ™Dbx|c'i
kcdu]Ôk×i
be , Z , :Z ,! Z 2 2p2p2a
grvcdu]mx|]w9igrÉi
kcdu]Ôk½i
be ,p, Z 2 Z ,! Z 2S2p23$
uoNxropxdcdopgw9cdoqigvw˜ua
gˆ
]xHui ) ]`€
]`b ) u]gvig]Æa+c|cda
wu]xÔa
gÌ]!#c|baRnq]a+k2npaB.]n ‘Óc|iÓcdu]mbdi6i
c ,rcKopˆ+Œ
{bd]f,/2p23$ u]ÀkÏ{npn1 opga+bd‚@c|b]`]x ) oqcdutnpaB.]npnq]rnp]a€
]xU,ÏnpaB.]npxmk½bdie ‘ Z ‹ Z6]6]6]Z ”O2^a+bd]fgi ) cdu]
xda
ef]
~{_c|iÓa…_.]`beÓ{cda+cdoqigvi
k.cdu]^npaB.]npx6$:}opgw9]jropxdcda
gw9]Ôopxˆ
i€
]`bg]rF6‚Rbi
cda+cdoqigx/i€
]`bHopg,c|]`bdŒ
ga
n6]rˆ
]x`~opcKk½inpnqi ) x=cdua+c:cdu]w9i
bdbd]x|_.igroNgˆ oNga+bd‚…w9i{_ npoNgˆÔc|bd]`]x ) opnpn,oNgr]`]rRua€
]cdu]xda
ev]
ropxdcda
gw9]vr]`ˆ
bd]`]vx|[] *6{]gw9%] $ mi
c|]Ìcdu a+c…cdu]`bd]vopx…a
gi
cdu]`b ) a‚4i
kHxa‚opgˆcduopx`1~ h‚4opghc|bdi6r {w`opgˆ
‹
‹
cdu]Rxp.
]nq]`c|ig &ŋ[(Š$^„^]g]`ba
npnq‚
~Dcdu] P R!L+R ŠG%>ƒi
k'aU opga+b‚w9i{_ npopgˆfc|b]`]i
k+%^ ) oqcduznpaB.]npnq]r
nq]a€
]Ÿ
x ,ÏnpBa .]npxRk½bdie ‘ Z ‹ Z6]6]6]:Z n ‹K2RopxÇi% cda
opg]rW6‚Ör]nq]`cdoNgˆÙa
npnHnq]a€
]xÉa
grUw9i
bdbd]x|_.igr opgˆ
]rˆ
]xÀk×bdie $ u]fbd]xd{npc”opx…cdu6{xÀa
gÖ{gnpaB.]npnq]rzc|bd]`]n,½i
kHeÌa#opeR{e r]`ˆ
bd]`]F›2 ) oqcdu“ 7 ‹
]rˆ
]x`~Dx|]`] c:oqˆ{bd]À ,ÏKw 2k×i
b z $
]`cÓ{x”w9ig xdopr]`b”cdu]Ìg!] #cÀw`a
x|U] ”W,Ïw9i
bdbd]x|_.igr opgˆc|i֋6‰ Œ"w9ih!] Éw`op]g,cd3x 23$(% tvua
x̋`‘›¡
€
]`bdcdopw9][x $a7ŽcÀopxÀ]a
x|‚Ùc|i€
]`b˜oqkׂtcdua+cÓcduz]`bd]Éa+b]Ìgi ) cdubd]`]Ér-o ,.]`bd]g,cÀc"‚6_]xÀi
-k opga+bd‚4w9i{_ nNopgˆ
c|bd]`]x`~6ˆoq€
]gƒopg c:oqˆ{b]À‹`‘ ,Ïia 23$X5 u]gvig]mw9igxdoNr]`bxBcdu]opb/w9i
bdbd]xd_ig ropgˆ…px .
]nq]`c|ig x`~cdu]`bd]jcd{b˜g
:oqˆ{bd]v‹`‘Sm/!oNga+bd‚w9i{_ npopgˆÓc|bd]`]xÔk×i
b
c
1
1
1
2
3
2
3
2
3
4
Ìa
gr@cdu]oqbjxp.
]nq]`c|igx
z ”
5
4
5
4
5
(a)
(b)
i{cjc|iU]À‰vro-,.]`bd]g,cig]x`~ˆoq€
]gÑoNg–cKopˆ{bd]v‹`‘,/23$ uh{ x`~c|iÌua€
]Óavw9ief_Dnq]`c|]”_ opw9cd{bd]Æi
kKcdu]
ropxdcda
gw9]Óopg %t+~Dig]Óxdui{ nprÑr]`c|]`beÌopg]”cdu]Çropxdcda
gw9]Àr]`ˆ
bd]`]Çx|][*6{]gw9]xmignq‚k½i
bmc ) i€
]`bdcdopw9]x
opg % t ~%] $ ˆ $ k×i
b [ z ,1‹ Z ,´‰ Z ,Œ Z ,/” Z ¡›2p2p2p2Æa
grÑk×i
b \ z ,1‹ Z ,p,´‰ Z ›2 Z ,/” Z ¡›2p2p2D$<5Ù]Óua€
]”k½i{grcdu a+c
\Æ\”} , 2 ,1‹ ‰+‘ ”‘ ” ” 2Éa
grÖ\Æ\”} , \K2 ,1‹ ‰ ” +‘ ”%”O23$ u6{xÀk½i
b cdu]`bd]a+bd]a”
€
]`bdcdopw9]x…[ a+c…z roNx|cdZ a
gZ w9b] Z ¡6~ ) Z u]`Z bd]a
x^k½i
b \ cdu]`bd]fa+z bd]ÇgiZ €
Z ]`bdcdopZ w9]x…Z a+c…ropx|cda
g w9] ¡6~ {[ c ”%”@€
]`bdcdopw9]x
a+cÔroNx|cda
gw9] ”$ u]…€
]`bdcdopw9]xÔa+cmeva #oNeÓ{eÚropx|cda
gw9]…i
k [ z ,1‹ Z ,´‰ Z ,Œ Z ,/” Z ¡›2p2p2p2…a+bd]Àˆoq€
]–g 6‚
,Œ¡ Z ,´‰ Z ,Œ Z ,1‹ Z ”O2p2p2H2 Z
,Œ¡ Z ,Œ Z ,´‰ Z ,1‹ Z ”O2p2p22 Z
,/” Z ,´‰ Z ,Œ Z ,1‹ Z ¡›2p2p22 Z
,/” Z ,Œ Z ,´‰ Z ,1‹ Z ¡›2p2p2p2 ]
l^xjavw9igx|[] *6{]gw9]
~ k×i
bmcdu]v‹6‰ +Œ"w9i6!] Éw`oq]ghc^w9i
bbd]x|_.igropgˆRc|i
š ,1‹ ,´‰ ,Œ ,/” ¡›2p22p2 o ,Œ¡ ,´‰ ,Œ ,|‹ ”O2p22p2
Z Z Z Z
Z Z Z Z
x!Z
cdu]fi
_cdoNeva
nB!] #_ a
gxdoqigÙoNx…aÑri{ np]Çx{e i€
]`bR_bdir{w9cdxÆi
k ¡Ôa
w`a
uÖw9ih!] ƒw`oq]g,cd[x $ uopx…eÌa‚
x|]`]e$c|i^w9ighc|ba
roNw9c=cdu]/k½a
w9c:cdua+c=cdu]Hw`npa
xdxdopw`a
nD‹6‰ +Œ"w9i6!] Éw`oq]ghcdxBk½i
b ,´›‰ 2ua€
]a
gÓ!] #6_b]xdxdoqigÓopg
$.
‹‰
c|]`bevxi
k2aÀxdoNgˆnq]jxd{e i€
]`bH_bdir{w9cdxBi
kig nq‚” Ôa
w`a
uƒw9ih]!ƒw`oq]g,cdx~ ) u opwuvw`a
gF.]jk½i{grv{xopgˆ
cdu]mc|]wugo *h{]Ôi
k 0{cdxdopx6$ 71gfcduopx/w9ig,c|]!#c`~ui ) ]`€
]`b~bd]w`a
npn cdu]Ôi%Dx|]`bd€+a+cdoqigÌopgj]eva+b.U $ u]
kÏa
w9cjcdua+cjcdu]Ài
_cdopeva
n.]!#_ a
gxdopigxHk×i
bӋ‰6+Œ"w9i6]!Éw`oq]ghcdxmi
k ,´‰›2Hw`a
gÑ]`€
]gÑkÏ{bdcdu]`b .]…bd]r{ w9]r
opx^bd]npa+c|]r4c|iÑxd‚6evev]`c|bd‚_bi
_]`bcdoq]xÔcdu a+c”uinprzignq‚k½i
b ,´‰›2^w9i{_ npoNgˆƒw9i6]!Éw`oq]ghcdx`~a
g rtgi
c
k½i
bjcdu]”ˆ
]g]`b˜a
n oq]”a
npˆ
6] bafw`a
x|]Rw9igxdopr]`b]r@u]`bd%] $
cbie cdu]É_bd]`€oqi{x…!] #a
ef_ np]
x z a
g8
r z ”toqcÀopxÓw`nq]a+bÀcdu a+cRopgÕi
br]`bÀc|itr]`c|]`bevoNg]
ropxdcda
gw9]”_bdi
_.]`bdcdop]xjk½i
bԈoq€
]6
g % ^ oqcÔopxmxdS{ Éw`op]g,c ,Ïia 2jc|iÉr]`c|]`bevopg]Àcdu]Óg6{e ]`bmi
k'px .
]nq]`c|igx ,/2!c|iƒr]`c|]`bevoNg]…cdu]Ór opx|cda
gw9]”r]`ˆ
b]`]Óx|[] *6{]gw9]Ók×i
bj]a
w˜u4px .
]nq]`c|i
g $0*^kBw9i{bx|]
~ cduopxjri6]xÔgi
c
‚
]`cLjoq€
]ƒcdu]ƒxui
bdc|]x|cR_ a+cd˜
u ]`c ) ]`]gWa
gh‚Õc ) i4ˆoq€
]g]nq]ef]ghcdxRi
k %^$tH{cRopcÓri6]xÇa+cRnq]a
xdc
‚oq]nprteva
g,‚zi
cdu]`b”ropxdcda
gw9]fw9igw9]`_cdUx ,½]w`w9]ghc|bopw`oqc‚
~2ba
roN{x`~w9]g,c|]`b~2_.]`boq_ u]`b‚
~ ]6]6] &Å1‹ (/2˜~a
g r
oqc^a
npx|ir]`c|]`bevopg]xjig]Ri
k'cdu]Refix|cÆopef_.i
bdcda
ghcmropxdcda
gw9]Ów˜ua+ba
w9c|]`bopxdcdopw`x^i
+k %^~oqcdx^ropa
ev]`c|]`b
2@,3% ^ 23$ u] B=Œ?BTUR R!Ai
k % ^ opxr!] ™Dg]r@a
xjk½inpnqi ) x m
2@,3%^2 z eva # 2@, [KZ \K2 o [[Z \ % ^ ]
,´› 2
xm
u6{xKoqc=opx=cdu]Heva #opeÓ{ eñ€+a
np{]/i€
]`b'a
npnh_.ixdxdqo np]'xdui
bdc|]x|cK_ a+cduÇnq]gˆ
cdu xi
k % ^ opgÓi
cdu]`b ) i
br{
oqcjopxHcdu]Ànq]gˆ
cdu@i
kKcdu]Ànpigˆ
]x|cjropxdcda
gw9]”r]`ˆ
bd]`]Àxd[] *h{]g w9%] $
e .]`bBi
k.x .
]nq]`c|igx …^ÓoNx'a
gf]a
x|‚fcda
px .~hxopgw9]k½i
b'ˆoq€
]g @cdu]Ôpx .
]nq]`c|igx
iÀr]`c|]`beÌopg]cdu]Ôg6{
a+bd]ƒcdu]É{ gnpBa .]npnq]r4c|bd]`]xÓi
kÔeva #opeR{e r]`ˆ
bd]`a] k,½cdu]x|i+Œ"w`a
npnq]rÖc|boq€+a
nq]ghc”c|bd]`]3x 2 ) oqcdY
u 7$‹
]rˆ
]x ,½i
b~[] *6{oq€+a
nq]ghcdnq‚
~ ) oqcdFu t€
]`bcdopw9]3x 23$ u opx/g6{e .]`b!opx .gi ) g~6xd]`]…%] $ ˆ $x|[] *h{]gw9]…gh{e .]`b
l^‘
‘
‘ +‰Çi
Xk &ŋB (~6i
b & ‰+B‘ (Š$ u] ™ bx|c/k×] ) €+a
np{]x!a+bd]mˆop€
]gƒoNg Ba nq]…‰ $ž7Žag c:oqˆ{bd]R‹
‹ ) ]…npopx|c'cdu]
.
2.
a nq]À‰ m m{ e .]`bi
kKc|boq€+a
nq]g,cc|b]`]x ) qo cdu`ـ
]`bcdopw9]x
‰ ” ¡ Š  ‹`‘ ‹
‹ ‹‰
…^ ‹ ‹ ‰ ‰ ” ‹
‹ ‹Š ‹[%¡
B
c|boq€+a
nq]ghcc|bd]`]x ) oqcdu`ـ
]`bdcdopw9]x',Ïxp.
]nq]`c|igx32{_c|ib z –,Ïxd]`]Àa
npx|iŸ& ‰‹6(/23$
u]v_ {bd_.ix|]voNx”cdu]g c|izw`a
npw`{nNa+c|]Ìcdu]ƒropx|cda
gw9]Ér]`ˆ
bd]`]x|][*h{]gw9]Ìk½i
bÓa• opga+bd‚4w9i{_ nNopgˆ
c|bd]`]Rw9i
bdbd]x|_.igroNgˆÇc|iÉaÌx.
]nq]`c|ig$A*Æ{bÔev]`cdui6rÑk×i
b^riopgˆvcdu opxjopxjr]xdw9boq.]r@opg@cdu]Àk½inpnqi ) opgˆ
x|]w9cdoqi g $
± 2]`c .]ƒaшoq€
]g˜ opga+b‚4w9i{_ npopgˆ@c|b]`]Éi
k % ^ $5Ù] ) opxduÕc|itw9ief_D{c|]Ìcdu]ropxdcda
gw9]Ér]`ˆ
b]`]
x|][*6{]gw9]…\Æ\”}, 23$ 2]`c l ]^cdu]Æx|]`cHi
k2]nq]ef]ghcdxHi
k<% ^va+cHr opx|cda
gw9] :k×bdie $ u]`bd]Æopxig]
]nq]ef]ghc”a+c”ropxdcda
gw9]f‘~ga
ef]nq‚ Ãoqcdx|]nqk cdu6{x ) ]vu a€
] z ›$ * x|]`b€
]Rcdu a+c”oqc…opxÆ]a
x|‚
c|ivr]`c|]`beÌopg]^cdu]”g]oqˆOu .i{bx/i
k ñopg %^•mBcdu]x|]”a+bd]Æcdu]…]nq]ev]g,cdxHi
k%^va+cjroNx|cda
gw9]f‹Æk×bie
À~'oŒ$ ]%$Kcdu]`‚ a+b]ƒcduF] oNga+bd‚Ùw9i{_ npoNgˆÑc|bd]`]xÇ%i cda
oNg]r k½bdie h‚Ù_.]`bdk½i
bevoNgˆÑig]bdi
cda+cdoqig $
}{w˜ufbdi
cda+cdoqig xa+bd]m]a
x|‚Çc|iÀ_.]`bdk½i
be a
x ) ]^ua€
]^a
nqbd]a
r‚R%i x|]`bd€
]rÉopgÉ}6]w9cdopiFg 6~,]`€
]`bb‚ opga+bd‚
w9i{_ nNopgˆ@c|bd]`]ua
xlj 67æ‰g]opˆiu .i{b[x $ uh{x [ ua
xlj 67æ‰]nq]ef]ghcd6x $ m!] #6c ) ]w9ief_ {c|]
cdu]fx|]`c…i
kHg]oqˆOu .i{bxmi
kcdu]f]nq]ev]g,cdxÆi
k [ ~2a
grÙr]nq]`c|]fk½bdie cduopxÆx|]`c…cdu]fig]xÆcdua+c ) ]`b]
‹[
f
"#
:oqˆ{bd]f‹
‹Bm} .
]nq]`c|igx ½, c|b˜oq€®a
np]g,cjc|b]`]x32 ) oqcdu`ـ
]`bcdopw9]xjk½i
b<
c
n=3
(a)
n=4
(a)
z Z6]6]6]:Z (b)
n=5
(a)
(b)
n=6
(a)
(b)
(c)
(d)
n=7
(a)
(b)
(c)
(d)
(e)
(f)
a
nqbd]a
r‚Õopg i
b ~B‚oq]npr opgˆ \ $Õy!ig,cdoNgh{oNgˆÑcduopx ) a‚
~'ig]w`a
gWr]`c|]`bevopg]Éa
npnl~'a
g r
cdu]oqbi
b˜r]`bxˆoq€
]Ó\^\”[ }, 23$
}{ wutaÌw9ief_ {cda+cdoqigb][*h{opbd]xm,Ïai2ÔaÌxdopev_ nq]”ra+cdaƒx|c|b{w9cd{bd]”k½i
b^aF opga+b‚ƒw9i{_Dnpopgˆfc|bd]`]
~
cdua+c^a
npnqi ) xÔa
gÑ]a
xd‚Ñr]`c|]`bevopg a+cdoqig@i
k'oqcdxjg]oqˆui.i{b˜x ,ÏoŒ$ ]%$ _.]`bdk½i
be bi
cda+cdoqigx32 ,/2aÌ_bdi
_.]`b
) a‚ i
k .
]`]`_ opgˆtc|ba
w .Öi
kjcdu]]nq]ef]ghcdxRi
k %^Ùcdu a+cRua€
]@a
nqbd]a
r‚8.]`]gÖ]gw9i{ghc|]`bd]rUopg +~
~
~ l ) uopnp] l _ opx .]opgˆr]`c|]`bevopg] r $'5Ù]ƒua€
] ) boqc|c|]gÙaty_bdi
ˆ
ba
e c|iw`a
npw`{nNa+c|]
cdu[ ]Ìr ]6op]6x|] cda
gw9]Ìr]`ˆ
bd]`]Éx|[] [*6{]gw9]Éop
g %^zk×i
bRa
g,‚Ùˆop€
]8
g opg a+bd‚zw9i{_Dnpopgˆc|bd]`%] $ *Æ{b…_ bdi
ˆ
ba
e oNx
opgxd_ oqbd]Ÿ
r h‚Ùx|iev]vc|]wug +o *h{]x…i
k & ‰
%‰ (,½i
b~K[] *h{op€®a
nq]ghcdnq‚
{~ & %‰ B(/2˜~Ka
gr ) ]Ìxua
npn:gi
c”ˆ
itopg,c|i@cdu]
r]`cda
opnNxi
k=cduopx/_bdi
ˆ
ba
e u]`bd%] $ mi
c|]…cdua+-c 6‚vcdu]Æx|]w9igrbd[] *6{oqbd]ev]g,c!oqc!oNx/g]w9]xxda+bd‚Ìcdu a+c!cdu]
]nq]ef]ghcdxÓi
k %^4w`a
k
g ]Éx|c|i
bd]ropgÕcdu] Ôl^s i
kcdu]ƒw9ief_ {c|]`[b $z†”gi ) opgˆÑcdu]ƒi
br]`bÓi
k %^ ~
x|]`] ,´›Š 2Bi
b Ba nq]”‹+~hopc'opx'w`nq]a+b'cdu a+c'igva
gh‚R_ bd]x|]ghc1Œ"ra‚fw9ief_ {c|]`bcdu]jw9ief_D{cda+cdoqigÌw`a
g gi
fc .]
_.]`bdk½i
bef]Fr ]`‚
ig `r z ‹`S‘ $f5Ù]Àua€
]”w`a
npw`{npa+c|]r@a
npnropxdcda
gw9]…r]`ˆ
bd]`]”x|[] *6{]gw9]x{_ c|i z ‹`S‘ $
] tˆoq€
]xfcdu]@b]xd{nqcdxÇ{_c|“
i z O$Wci
bÌcdu]@w9ief_ np]`c|]@bd]xd{nqcdxf{_c|n
i z ‹`‘Ùx|]`]Ñ Ba nq
!#"$"%&' $
‹!”
a nq] W\Æopxdcda
gw9]Ùr]`ˆ
bd]`]Õx|][*6{]gw9]x@opg
:oqˆ{bd]v‹
‹B$
B “ m
c
0368
0368
0368
0 8
0 8
03!"8
0368
0 8
0368
0 8
u]4xp.
]nq]`c|ig c"‚6_]x8,Ïai2˜~b,/2˜~^]`cdwB$bd]`k½]`bƒc|i
% ^ $ 0 8
0 8
03!"8
0 8
0$8
cbieÃcdu]mw`a
npw`{npa+cdoqigÌi
k.cdu]Ôropxdcda
gw9]Ôr]`ˆ
bd]`]^x|][*6{]gw9]x`~6ig]j]a
xdoNnq‚Rr]r{w9]x'cdu]mropa
ev]`c|]`b
i
k %^@$ aB nq]”̈oq€
]xÔcdu]Àropa
ef]`c|]`b^{_Ñc|iF z ‹`‘~ ) uopw˜uÑopxja
xÔk½a+b^a
xjig]Rw`a
gw9ief_D{c|]Àigza
_ bd]xd]g,c1Œ"ra‚@w9ief_ {c|]`b~Da
gr ) uopw˜u@ˆ
i6]x<.]`‚
igr_bd]`€oqi{xnq‚Ìw`a
npw`{nNa+c|]rropa
ev]`c|]`bx&ŋ[~ ‰
‰(Š$
a nq] ”m\Æopa
ev]`c|]`bÔi
k
%^
B
2,3% ^ 2
‰
‹
”
¡
¡
‹`‘ ‹‰ ‹[¡
Š
 `‹ ‘
‹Š ‰‹
u ]Óropa
ev]`c|]`b^opxmopef_.i
bdcda
ghcÔa
xÆoqcjˆoq€
]xÆa
gt{__.]`b<.i{grÑk×i
b^cdu]Óg6{e.]`bÔi
k ma
w`a
uzw9i6]`kNŒ
™Dw`oq]ghcdx…a+__.]a+bopgˆÉopg4a
g4i
_cdopeÌa
n=]!#_ a
gxoqigti
k/a+Œ"w9i6]!Éw`oq]ghc`~=xd]`]v}]w9cdoqigՉ $f}opgw9]Çoqc^oNx
x|iro"Éw`{ nqcjc|i@w`a
npw`{npa+c|]Çcdu]Çropa
ev]`c|]`b^]!#_ npoNw`oqcdnq‚`.]`‚
igr• z ‹`‘~ig]Reva‚ ) igr]`b ) u]`cdu]`b
a4_bdi
_.]`bfa+__b[i #opeva+cdoqigWi
4k 2@,3% ^S2Rw`a
g .]@r]`c|]`bevoNg]r $ uopxÇopxfopgr]`]rÖcdu]Ñw`a
x|%] $W7ŽgWcduoNx
_ a+_.]`b ) ]…xdua
nNnˆoq€
]…aÇg] ) nqi ) ]`ba
gr{__.]`Xb .i{g rvk½i
'b 2,3%^23$ u]^r]`cda
opnpx!i
k2cdu]^_bdi6i
kÏx!a+b]
ievoqc|c|]ru]`bd]
~a
gr ) oNnpn ]ƈoq€
]gopgavx|]`_ a+ba+c|]Ów9ief_bd]u]g xdoq€
]…x|cd{r‚Éi
kKr opa
ef]`c|]`bj_bi
_]`bcdoq]x
i
k %^Ÿ& ‰ ”›(Š$
=/Qi= > B= P Š?B>E3R
QSR >IST;3R!A G R6LqR6TUR!>( P ž
^%_ \ l
=/> % ^Ÿ= P +L R HP P /QS?B>YGBA'R 6I?BL ŠG l! ” l
@
,
DApGBT
#
?B>CN%= BR6>n;!=/>@?BADCFE3GBI:J@LM=/>ON rARHR
&
uoNxw`a
g–.]”xdui ) gÑ{xdopgˆÇxdi+Œ"w`a
npnq]rÑxdui
bdc]gw9iropgˆx& ‰%¡( k×i
bÔaÌr]`cda
opnq]r_bihi
k:x|]`]F& ‰”%(Š$
‹[¡
QR B=r?%TR R!AG
-
%^ P ? r= P R P
2@,3%^2
” ‹ nqi
ˆ,/ 9M2 ” ‹ ” nqi
ˆ@,/ 02 ]
1‹`‘
, i2
‘m]`bd]opg˜,Ïa
g rzopg ) ua+cmk×inpnpi ) x32˜~nqi
ˆ z nqi
ˆ \ oNxÔcdu]Rnqi
ˆa+boqcdu eÚopg• a
xdopx^‰6~a
gr 0Çopxjcdu] a
xdoNxji
k
cdu]Àg a+cd{ba
nnqi
ˆa+bopcdue–$
iv_bdi¨€
]”cdu]”cdu]`i
b]e@~ nq]`c z 2,3%^S2˜~ cdu]g–6‚Écdu]ÓaBi¨€
]Ónq]eÌevaÇa
grY,´Š›2 ) ]Àua€
]”cdua+c
FW‰ ”A= ,´‰ 7æ‹K2:9;9 z ,´‰^ 2:9 ]
,1‹
‹K2
‰ 9
k ,1‹
K‹ 2jw`a
g .]…]gnpa+bˆ
]–r h‚
u]”nNuxHi
‰ ^%_ \ FU‰ ‰
Z
a
npnBopghc|]`ˆ
]`bx ‘Ña
g
r ‹+~Kxd]`Ÿ
] & ‰ ”%(Š$ u]fbux…i
k ,1‹
K‹ 2…w`a
g8]b.i{g r]r
) uoNwuÙu\u^inpr xÆk×i
\ubR
{xdoNgˆ ^ =*‰ ^ S,´‰ 23$ u6{x ,1‹
K‹ 2H‚oq]npr x m
‰ t 9Z
k½bdie ) uoNwucdu]”cdu]`i
bd]e k½inpnqi ) 6x $
l^gÑ{__.]`-b .i{grk½inpnqi ) xHk×bie
QR B=r?%TR R!AG % ^ P ? r= P R P ñ‹
2@,3% ^2 5 ½nqi
ˆ ,/27lj ~ ^ ̉ ,/ 7½npi
@ˆ ,/-K‹ 2:2K‹ 5 ½nqi
ˆ ,/2SA7f‰ ½nqi
@ˆ ,/2S‹ ] ,1‹›‰ 2
!'R!AR!=/> #"$`= P /QR P T?BL/LqR P = >9 RŠNOR6ALq?BArN R!A /Q ?B>8GBAR 6I?BL ŠG%" æ‘
a opga+bd‚
u]@_ bdihi
k^i
kÆcduopxfcdu]`i
bd]e k½inpnqi ) xfcdu]nNopg]xfopgr opw`a+c|]rUopg & ‰
‰ (Š$ 2]`cÉa P J@=/>R]Ñ8
w9i{_ nNopgˆÇc|bd]`]”i
kKcdu]”k½i
be
,1‹ Z ,´‰ Z ,Œ Z , ]6]6] ,/ Z F K‹ 2p2 g6g6g 2 ,1[‹ ›2
x|]`] c:oqˆ{b]R‹‰Rk½i
bjoqcdx!ˆ
]g]`ba
nxdu a+_%] $fc:oqb˜x|c`~hig]”r]`c|]`bevopg]x!a
g@{__.]`{b .i{grÉk½i
b!cdu]”gh{e .]`b
i
kKbdi
cda+cdoqigxg]`]r]r@c|ifc|ba
gx|k½i
be xd{ wu@afx|_ oNg] ) oqcdua+b oqc|ba+b‚vi
br]`bd]r@nNBa ]^nNx! oNg,c|iÇcdu]”x|_Dopg]
x ,1[‹ ›23$ u opxH{__.]`b .i{gr@opxHˆoq€
]•
g h`‚ ½nqi
ˆ ,/207։ ~ <‹+~ x|]`a] & ‰ ”›(Š$
) oqcdui
b˜r]`bd]rÑnpBa .]np
m!] #6c`~oqcopxjgi
cÔr "o Éw`{nqc!c|iÌx|]`]Àcdua+cjcdu]`bd]Óa+bd]Àa+cÔefixd<c 7&½nqi
ˆ ,/F<K‹ 2Àbdi
cda+cdoqig xjg]`]r]r@c|i
c|ba
gxdk×i
be a
g a+b oqc|ba+b‚ opga+b‚w9i{_ npoNgˆÉc|b]`]Ìopghc|iÑa@x|_ opg%] $ u6{xÆc|iÑc|ba
gxdk×i
be c ) •
i opga+bd‚
w9i{_ nNopgˆÀc|b]`]x a
gr \Æopg,c|iÇ]a
w˜uÑi
cdu]`bS~ ™Dbx|c!c|ba
gx|k½i
be .i
cdu [ a
gr \^oNg,c|ifafx|_ oNg]
~6a
g r
cdu]g@c|b˜a
gx|k½i
be i[ g]”x|_Dopg]…opghc|ivcdu]”x|]w9igrig%] $ u opxHnq]a
rxc|Ÿ
i ,1‹›‰ 23$
ˆ ,/2˜~
i
ˆ
]`cdu]`b~cdu]ÀBa .i€
]Óc ) iÉcdu]`i
bd]evxÔoNef_ nq‚Écdua+cjcdu]Rropa
ef]`c|]`bji
k % ^ƒopxji
kKi
b˜r]`b ”nqi
Œo $ %] $
2@,3%^2 z(' ,/”npi
@ˆ ,/2p2 ]
mi
c|]^cdu a+c!a ) ]Ba .
]`bj{__.]`bnpopevopcua
{x ]`]gɈoq€
]gÉ]a+bnpoq]`bHopg &ŋ
!‹ (~a
gr ) ]Ba .
]`bj{__.]`ba
g rÉnqi ) ]`b
npopeÌoqcdx ) ]`bd]Ór]`c|]`bevopg]r@op8
g & ‰
‰ (Š$
x m
u]…k×i
bÔ{ xjopef_.i
bdcda
ghcw9igx|[] *6{]gw9]Àop
-
;
?9
,
‹1
:oqˆ{bd]v‹‰ m/Hopga+b‚Éw9i{_ nNopgˆÇc|bd]`] ) u opwu@opxÔafx|_ opg]
c
0
1
2
n
n+1
GB> P = iR6A'?B>YG3Jr= T?BLfR!JS?B> P r= GB>kG ?b pEHG:R E6=ŠR!>9{=/> R!ADT P G
i? EH?Q 3E GKR
E[=ŒR6>( P SQ R6> /QSR >IST;3R!A G
?iEH?QEHGKR 6E =ŠR!>( P ?3J›JR?BAD= > Na= >Ÿ? R!ADT G /QSRR DJS%? > P =ŒGB> = P
G G%A iR6A ”nqi
ˆ,/2XTGBApRURDJLM=ŒE6=rLMC ={= P ;G%I > iR ;6C
.13
87
‹ ” nqi
ˆ@,/ 02+5
”
b X <
½nqi
ˆ,/2{k7‰ ½nqi
ˆ,/2<‹ ]
f
7
%
.13
5 1gWcduopxR_ a+_.]`b~ ) ]Ñua€
]bd]r{w9]rcdu]@_bi% nq]e i
k ™gropgˆta
gWi
_cdopeva
nH]!#_ a
gxoqigi
kma8+Œ
w9i6]!Éw`oq]ghcÉc|icdu]tˆ
ba+_ u*cdu]`i
bd]`cdopw`a
n^_bdi%Dnq]e i
k™Dg ropgˆÕaxdui
bdc|]xdcÉ_ a+cdu .]`c ) ]`]g opga+bd‚
w9i{_ nNopgˆ”c|bd]`]x!opg %^$ u opxnpa
xdc_bdi%Dnq]eÃua
x{.]`]gv]gw9i{ g,c|]`bd]ra.]`k½i
bd]mopgÉro-,.]`bd]ghcw9ig,c|]!#cdx6$
*Æg]Ìi
kcdub
] ™ bxdc”_ a+_.]`bx ) u]`bd]vcduopxÀ_bdi% np]e opxÀx|cda+c|]r2~ ) oqcduÕa+__ nNopw`a+cdoqigx”oNgÕevopgr2~opxF&ŋ‰B(Š$
71g@cdua+cÔw9ighc|!] #6c`~i{<
b Dopga+bd‚ƒw9i{_ npopgˆÓc|bd]`]x^a+bd]”w`a
npnp]r iR!> BAuGHN%Ap?BT P ~2a
gr@cdu]”_ {bd_.ix|]Æopxcdu]
w9ief_ {cda+cdoqig4i
k!axdoNevopnpa+bopc"‚Ñef]a
xd{bd]Çi
b”ropx|cda
gw9] ,Ïw9iopg w`opropgˆ ) oqcduti{b…roNx|cda
gw9].2@, [KZ \K2p2
.]`c ) ]`]gr]g rbdi
ˆ
ba
ev[x $
\^]grbi
ˆ
ba
evx:w`a
'g ]!r!] ™Dg]rRa
xKbdi6i
c|]rÓc|b]`]x ) u]`bd]!]a
wuÇi
kcdu]!c|]`bevopg a
n,€
]`bdcdoNw9]-x ,Ïnp]a€
]3x 2
bd]`_b]x|]g,cÓa
gÙ%i ‡|]w9cÓa
gr ) u]`bd]fcdu]vbihi
c”€
]`bc|!] #Õbd]`_bd]x|]ghcdx…cdu]Ì]g,cdoqb]v%i ‡|]w9c1Œ"x|]`ac & ‰ %(Š$ÌlmwŒ
w9i
broNgˆc|i & ‰ (ž~ oNga+bd‚Ùr]grbi
ˆ
ba
evxRw`a
gu a€
]@npBa .]npnq]r i
bÇ{ gnpBa .]npnq]rÙnq]a€
]x`~a
grWw`a
k
g .]
ba
g .
]ræi
bÉgigŒba
g .
]r ,½i
b˜r]`bd]rUi
b{gi
br]`bd]r~/oNgUi{bvc|]`beÌopginqi
ˆ
‚ 23$ l^gU]g6{ef]`ba+cdopigýi
k
k½i{bÓc‚h_.]xRi
<k oNga+bd‚Ùr]grbi
ˆ
ba
evx ) a
xRˆoq€
]gWopg & ‰ (Š$ u]Ìig]xRi
kÔoNg,c|]`bd]xdcÀc|iÙ{xRa+bd]Écdu]
gigŒb˜a
g .
]4
r ,Ï{gi
br]`b]@r 2”r]grbdi
ˆ
ba
eÌx ) opcduÖnpBa .]npnp]r nq]a€
]x`~/xdoNgw9]Écdu]`‚Öw9iopgw`oNr] ) oqcdu i{b
opg a+bd‚@w9i{_ npopgˆfc|bd]`]6x $ u]x|]Óa+b]Ra
npxdiÌcdu]Çr]grbi
ˆ
ba
evxÔa+_ _]a+b˜opgˆÌopgcdu]R_ a+_.]`bÔi
ž
k 5Õa+c|]`b|Œ
eva
gWa
grU}evoqcdu &ŋ‰ (~'a
grWa+bd]ƒi
kÔopev_i
bcda
gw9]ƒoNg eva+cdu]eÌa+cdopw`a
-n oqinqi
ˆ
%‚ $ uF] ™ bxdcÓa+bd]ati
k
a+__ nNopw`a+cdoqigopxHcda #igieÀ%‚ $‘Ô]`b]
~€®a+b˜oqi{xHuoq]`ba+b˜wuopw`a
n.w`np{ x|c|]`bjef]`cduirxa+bd]À{ x|]rƒc|iÌw9igx|c|b{ w9c
cda #igievopwÑr]grbdi
ˆ
ba
eÌ6x $Ul w`np{ x|c|]`bÌa
nqˆ
i
bopcdue w`a
gUbd]xd{ nqcfopgUr]grbi
ˆ
ba
evx ) oqcduUr -o ,]`b˜opgˆ
opgopcdopa
n6i
br]`bopgˆ~
cduh{xa”ef]`cduirfi
k.ef]a
xd{boNgˆÆcdu]Ôr]`ˆ
bd]`]Ôi
kxdoNevopnpa+bopc"‚ .]`c ) ]`]gÌr]grbdi
ˆ
ba
eÌx
opxÔi
k:oNef_.i
bdcda
gw9F] &ŋ‰ (Š$ u]ÀxdopeÌopnpa+boqc‚Éopxmw9ief_ {c|]•
r h‚Ñev]a
gxji
kBcdu]Rropx|cda
g w9] .]`c ) ]`]gtr]gŒ
rbdi
ˆ
b˜a
evx`~.w9iopgw`oproNgˆ ) oqcduzropx|cda
gw9]Çop8
g %^$^l x|]w9igrta+bd]aƒi
žk oqinqi
ˆoNw`a
nbd]xd]a+bwu4opgh€
inq€opgˆ
r]grbdi
ˆ
ba
evxÓopxÀopgÖefi
bd_ ui
ˆ
]g]xdopxÓa
gr ¨i
bÇw9]npn/r -o ,]`b]g,cdopa+cdopigÕx|cd{rop]x`~ ) u]`bd]Ìcdu]Ér]`€
]nqi
_Œ
ef]ghcji
kBx|‚x|c|]evxjopxjbd]`_bd]x|]ghc|]r 6‚afc|bd]`F] ,Ïr]w`oNxdoqig@c|bd]`] [] *h{ oq€®a
np]g,cc|ivi{<b opga+b‚Éw9i{_ nNopgˆ
c|bd]`:] 23$X‘m]`bd]Æa+ˆa
opg~aÓc|bd]`]…xdopevopnNa+boqc"‚Çef]a
xd{bd]^oNxi
koNef_.i
bdcda
gw9'] &ŋ%‰ (~a
grÉoNxˆoq€
]ag 6‚Ìropxdcda
gw9]
7
‹
%
opg
% ^$
}6iev] ) a‚xÆi
k/w9ief_D{cdopgˆÉi
b^]xdcdopeva+cdopgˆƒcdu]ÇxdopevoNnpa+boqc‚Éi
k!r]grbdi
ˆ
b˜a
evxmu a€
].]`]gtw9igŒ
xdopr]`bd]r4opgcdu]vnpoqc|]`ba+cd{b]%$5Õa+c|]`beva
gÕa
g r }evoqcdu &ŋ‰(~ ) uioNg,c|bdir{w9]rtxdopeÌopnpa+boqc‚Ñef]a
xd{b]
~
a
npx|iÑ{ x|]Çcdu]fc|]`be >RH?BAR P >R6="N%QS;GBISA=/>( R6AuE6Q ?B>ON RFTR rA3=ŒE…c|i@b]`k×]`b”c|icdu]vropx|cda
g w9]?2zopg %^$
j]a
nNqo —opgˆÙcdua+c 2ÖopxÌr"o Éw`{npcRc|iÖw9ief_ {c|]oNgUˆ
]g]`ba
n´~!cdu]`‚Uopghc|bdir{w9]rUa
gi
cdu]`bƒef]a
xd{b] !
‚ &Å[‹ ~ !‹ ”~ [‹ ¡(Š$B!bdi ) gÌa
grÌ\^a‚
) uoNwufa+k½c|]`b ) a+b˜rx'cd{b˜g]rfi{c'c|iÀ€6oqinNa+c|]jcdu]jc|boNa
gˆnq]jopg[] *6{a
npopc"a
xdui ) ]rzcdua+c i
cdu 2ƒa
g r !…a+bd]Rr"o Éw`{npc!c|iƒw9ief_ {c|`] & ‰ :(Š$ u]`‚@r]xdopˆg]rÑa
ga+_ _bd[i #opeva+cdopig
c|.i 2~a
gra
ga
np‚6x|]rƒcdu]…a
nqˆ
i
b˜oqcdue k×i
bcdu]…w9ief_D{cda+cdoqigƒi
kcduoNx/a+__ bd[i #opeva+cdoqi g $:l^gi
cdu]`bja+_Œ
_bdKi #oNeva+cdoqig ) a
x!w9igxdopr]`b]rÌop•
g & ‰
%Š (~hb[] *h{opbopgˆÆignq‚ U,/2:cdopef]Ôc|iRw9ief_D{c|%] $ ua+c!opgfˆ
]g]`ba
n
2oNx…r"o Éw`{npcmc|iw`a
nNw`{npa+c|] ) a
xÀopgr opw`a+c|]r h‚4
† b oq€ a
g6] . & ‰
 (~ ) uixui ) ]rÙcdua+cÀw9iev_ {cdopgˆ 2
opxÓa
g BŒ"w9iev_ nq]`c|]ƒ_bd%i nq]e $7cRxdui{nN8
r .]Ìef]ghcdoqig]rÖcdua+c o R ?BL{& ‰
‰ (Hk½i{gr atevopxdcdBa .
]
opgن b op€ a
g6] . îx…_bihi
kŽ~x|i@cduF] *h{]xdcdoqig4i
k 'Œ"w9ief_ nq]`c|]g]xx…bd]eva
opg xÆi
_] g $É}6cdopnpn´~a+c”_ bd]x|]ghc
cdu]`bd]”oNxgifxdopef_ np]^a
nqˆ
i
b˜oqcdue c|iÌw9ief_ {c|]…cdu]…ropx|cda
gw9] 2, [[Z \K2{.]`c ) ]`]g@ˆoq€
]–g Dopga+bd‚Ìw9i{Œ
_ npoNgˆÀc|bd]`]xmopg %^$ u]`bd]`k½i
bd]
~ ) ]…_Dnpa
gc|ifbd]w9igxdoNr]`bHcdu]”ef]`cduirxHi
k & ‰ :(2i
b & ‰
Š (opgƒi
br]`bc|i
r]`€
]nqi
_z_bdi
ˆ
ba
eÌxcdua+cÔ_ bdi6r {w9]”w`nqix|]Àa+_ _bd[i #opeva+cdopigxk½i
bÔcdu]Àr opx|cda
gw9] 2, \K2 ,Ïa
grcduh{ x
_bdi
ˆ
b˜a
evxcdua+cj_ bdi6r {w9]Æ!] #6_ a
g xdoqigxHi
fk +Œ"w9i6!] Éw`oq]ghcdx ) uopw˜u@a+bd]Àg]a+bnp‚Ìi
_cd[KopZ eÌa
n 23$
u]z_b%i nq]e i
kÓw9ief_ {cdopgˆ cdu]4ropx|cda
g w9] 2Uopg %^ ) a
xa
npx|iWw9igxdopr]`b]r 6‚ýw9ief_ {c|]`b
xdw`oq]ghcdopx|cd–x &ŋ
‹
~'%‰ (Š$*Æk×c|]g~'ui ) ]`€
]`b~/w9ief_D{c|]`bfxdw`oq]ghcdopx|cdxÇa+bd]@efi
bd]opghc|]`bd]x|c|]rUopga4w`nqix|]nq‚
bd]npa+c|]rƒ_b%i nq]e m:w`a
nNw`{npa+cdopgˆRcdu]^bdi
cda+cdoqig@roNx|cda
gw94] 2vopgÉcdu]mˆ
b˜a+_ u b^fw9igxdopx|cdoNgˆÓi
1k opga+bd‚
x|]a+bw˜uc|bd]`]x ,½bdi6i
c|]r@i
br]`b]Fr Dopga+bd‚Çc|bd]`]x`~ ) oqcduÉ{ gnpBa .]npnq]rvnp]a€
]3x 2 ) oqcdUu 4opghc|]`bga
nD€
]`bdcdopw9]6x $
71n
g &ŋ
[‹ (~oqc ) a
xja
npbd]a
r‚Ìxdui ) gcdua+ccdu]Ær opa
ef]`c|]`0b 2@,
^S2*‰ 7Õa‰ ,ÏxdivaRnNopg]a+b{__.]`b i{ gr~
opgxdc|]a
rfi
ka ”nqi
@ˆ ,/2:{__.]`žb i{ grÇk×i
b 2@,3%^2p23$Bl r]`cda
opnq]rvxdcd{r–‚ &9+B‘ ( bd]`€
]a
nq]rÌcdua+c 2,
b^S2
‰ 7)6~nNa+c|]`bÀw9iSg ™ bev]Ÿ
r 6‚4efi
bd]Ç]nq]ef]ghcda+bd‚4ef]`cduirx &9‹
~ ‰ (Š$Çlmnqcdui{ˆu4cdu]fropa
ef]`c|]`b”oNx
]a
xdoq]`bÓc|i]x|cdoNeva+c|]Éopg4cdu opx”w`a
x|]
~Bw9ief_ {cdopgˆ@cdu]ƒa
w9cd{a
nroNx|cda
gw9] 2top
g b^tigw9]Ìa+ˆa
oNgÕcd{bg x
i{cjc|Ui ]…rqo Éw`{nqc &9%(Š$
*Æg]Ài
k'cdu]Ó_bdi
_.]`bdcdoq]xÔi
k'cdu]Rropx|cda
gw9]Ók½{ gw9cdoqig 2Ék½i
b % ^ ~ ) uoNwuu a
xÔbd]w9]op€
]rta+c|c|]ghcdoqig
opg cdu]ÕeÌa+cdu]eva+cdopw`a
n Doqinqi
ˆ
‚ npoqc|]`ba+cd{b]
~^opxcdu a+cÑi
kRgigŒ"r]w9ief_.ixdBa oNnpoqc"%‚ $ uoNxÉ_.]w`{nNopa+b
_bdi
_.]`bdc‚ýopxƒa
npx|ii
k”opg,c|]`b]x|cƒoNgæi{bw9ighc|!] #6c@i
k Œ"w9ih!] Éw`op]g,cd6x $ ]`c Z %^W.]c ) i
opg a+bd‚tw9i{_ npopgˆc|bd]`]x ) oqcdu nq]a€
]xÇnpBa .]npnq]rU‹ Z ‰ Z6]6]6]Z •B‹ $}{__.ix|]fcdua+c`~:opgÙcdu]Égi
cda+cdoqig
i
bk ,3%2˜~ z , [6Z u\K2Ra
gr z , [ Z \ 2˜~ ) u]`bd] [[Z [ %a+bd–] Dopga+bd‚ w9i{_ npopgˆzc|bd]`]x ) oqcdu
nq]a€
]xnpBa .]npnq]r 6‚Ñ‹ Z ‰ Z6]6]6]Z W‹+~a
gr \ Z \ (% ^ & & [ a+bd] opga+b‚Çw9i{_ npopgˆÀc|bd]`]x ) oqcduƒnq]a€
]x
npBa .]npnq]ar 6‚ U‰ Z6]6]6]KZ F<B‹ $ u]”ropx|cda
gw9] 2ƒopxjxa
opr@c|iÌxda+cdoNx|kׂcdu]Ór]w9ief_.ixdoqcdoqig_ bdi
_.]`bdc"‚
oqk=k×i
bÔa
nNn2xd{w˜u $a
gr m
2, Z 2 z 2@, [[ Z [ 2)2@, u\ Z \ 2 Z
] ,/6‚Ba {x|]…i
k:gi
cda+cdoqi@g 2/cdu] ™ bx|c 2ÌoNgcdu]…buxHopxHcdu]”r opx|cda
gw9]…kÏ{gw9cdoqigopg %~a
grcdu]
) u]`bb
x|]w9ig.r 2Àop?g % ^ & & [ $ *Æcdu]`b ) opxd]
~ 2Àopx:gigŒ"r]w9ief_.ixdBa Dnq%] $7Žc ) a
xBopg ropw`a+c|]rRop–g &Å!‹ ”%(a
grÇxdui ) g
opg & ‰
‰ (/cdua+c”cdu]Ìr opx|cda
gw9]fkÏ{gw9cdoqi6
g 2zk½i
b %^trih]xÀgi
cÀxda+cdopxdkׂzcdu]Ìr]w9ief_.ixdopcdoqig4_bdi
_.]`bdc%‚ $
x &ŋ
i~ c:oqˆ{bd]Æ!‹ ”$º:‰ (‰&›(
uoNx=opev_ npoq]x=cdua+cBk½i
bBˆ
]g]`ba
n +Œ"w9i6!] Éw`oq]ghcdx`~6a…x|i+Œ"w`a
npnq]rfw`{c:igÇc ) iÀnNopg]opgcdu]Ów9i
bdb]x|_.igropgˆ 0{cdxdopxmˆ
ba+_ urih]x^gi
cmg]w9]xdxda+bopnp‚ƒ‚oq]nprcdu]Óevix|cÔi
_cdoNeva
n2!] #_ a
gxdopig
opg ma
w`a
uw9i6!] Éw`oq]ghcdx ,Ïa
nqcdui{ˆuÑoqc ) opnNnrivx|ivk½i
<b %23$
‹Š
3H
Ù]/u a€
]/w9ig xdopr]`bd]rÆcdu]'_bdi% np]e i
kO™gropgˆHa
g”i
_ cdopeva
n+]!#_ a
gxdoqig”i
kajˆ
]g]`ba
ni
Œ"w9ih]!Éw`op]g,c
,½k½i
b™Dgoqc|]9Œ"roNef]gxdoqig a
nbd]`_bd]xd]g,cda+cdoqig xÆi
k/ax|]evoŌ"xopef_ nq] oq]Ça
nqˆ
]6baS2^oNgc|]`beÌxÆi
k Ôa
w`a
u
w9i6!] Éw`oq]ghcdxÇi
k $ uoNx”_bdi%Dnq]e ) a
xRbd]r{w9]rc|itcdu]@xdui
bdc|]xdcÓ_ a+cdu_bi% nq]e opgÕcdu]ˆ
ba+_Du
%^ ~i
k ) uopw˜uÌcdu]^€
]`bcdopw9]xa+bd]ƈoq€
]g`6‚ opga+b‚vw9i{_ npopgˆÀc|bd]`]xHiga'ý‹^np]a€
]xja
grƒcdu]Æ]rˆ
]x
w9i
bdbd]xd_ig rÑc|iƒbdi
cda+cdoqig6x $ c:opgropgˆvxdui
bdc|]x|c^_ a+cdux^opgcdu]Àbdi
cda+cdopigzˆ
b˜a+_ ui
kžDopga+bd‚@w9i{_ nNopgˆ
c|bd]`]xfcd{bgxRi{cÇc|“
i .]a4rqo Éw`{nqcR_bd%i np]–e $ÕÔ_ c|“
i ‹`‘~/cdu]@roNx|cda
gw9]@r]`ˆ
bd]`]Ñx|[] *6{]gw9]x
i
k %^Wua€
Ÿ
] .]`]gæw`a
nNw`{npa+c|]r*!] #6_ nNopw`oqcdnq‚
~!‚6op]npropgˆÙeva
ghz ‚ýropxdcda
gw9]Ñ_bdi
_.]`bdcdop]xfi
k %^Wa
gr opg
_ a+bdcdoNw`{npa+b/oNef_ nq‚opgˆ…cdu]Æropa
ev]`c|]`+b 2,3%^S23$ uopx/ropa
ef]`c|]`bHopx!a
gÉ{_ _]`{b .i{grvk½i
bHcdu]Ægh{e .]`b
i
0k Ôa
w`a
uWw9i6!] Éw`oq]ghcdxÓa+_ _]a+b˜opgˆopg a
g i
_cdoNeva
n'!] #_bd]xdxoqigÕk½i
bÓn
a +Œ"w9i6!] Éw`oq]gh6c $•5Ù]ua€
]
xdui ) gÙcdua+c 2@,3% ^S2^ˆ
bdi ) xRnpqo .
b] ”nqi
@ˆ ,/2h‚4ˆoq€opgˆÑ{_ _]`b”a
g rÕnqi ) ]`b .i{g rxÆk×i
bRoq6c $Fc:opg a
npnq‚
~
) ]Éua€
]ƒxdui ) g cdua+cÀi{bÇxdui
bc|]x|cÀ_ a+cdu _bd%i np]e ua
xRa
nqbd]a
r‚Ùa+__.]a+bd]rÖopgÙi
cdu]`bÇw9ig,c|!] #cdx`~
xd{w˜u@a
xeva+cdu]eva+cdoNw`a
n oqinqi
ˆ
‚Ìa
g r@w9ief_ {c|]`bxdw`oq]g w9]
~ ) u]`bd]…oqcHua
xopef_.i
bdcda
ghcHa+__ npopw`a+cdopig6x $
sz]`cdui6r xÇc|Ÿ
i ™grÖa+_ _bd[i #opeva+cdopigxRi
kÔcdu]@xdui
bc|]x|cÇ_ a+cdu~'r]`€
]nqi
_.]rWopgcdu]x|]@a+bd]a
x~/w`a
W
g .]
{x|]`kÏ{nopgi{bÔw9ig,c|!] #cÔi
žk +Œ"w9i6!] Éw`oq]ghcdx^a
gr ) opnN@n .]”x|cd{ roq]ropgcdu]”kÏ{cd{b%] $
5
XX ŋ Rl {cdxdoNx`~%73$î $ ]`€6oNgx|igfa
gr'$$'a
ga+ˆa
x`~sza+cdu]eÌa+cdopw`a
n lm__ a+ba+cd{ x:i
kcdu] u]`i
bd‚
i
k:l^gˆ{npa+bÔszief]ghcd{e ,/71x|ba+]n 'bdi
ˆ
ba
e k×i
b^}w`oq]g,cdoq™Dw b˜a
gxdnpa+cdoqig2~ ]`b{xda
np]e@~‹
‰›23$
& :‰ ('œ $iœnHBa —^a
grv $yHa
xdc|]n´~6„^ba+_Duopw`a
nsz]`cduirxBi
k}6_ opgfl^nqˆ
]6b˜a…opgvlHc|ievopw+~ m{ w`nq]a+b~ha
g r
:a+bdcdoNw`nq] uh‚6xopw`x ,Ïsta+bw9]n\^6] . .
]`b~ m] ) 0'i
b .~‹ +›‰ 23$
&9:( X$ªy $Hoq]r]g ua+bgÙa
gr $î'
\ $ 2i{ w .~ u] Ôa
w`a
uŠŒ 5 oqˆg]`bRlmnpˆ
6] baÑop
g Æ{a
ghcd{e u]`i
b‚
~
œ/gw9‚w`nqi
_.]ropaÓi
k:sta+cdu]eva+cdoNw`xÔa
grÑopcdxlÔ__Dnpopw`a+cdoqigx~ BiŒn $6~]
r $D'„ $ ŒŽy $ji
cd•
a ,Ïl^rropxdigŒ
5Ù]xnq]`‚
~ Ô]a
ropgˆ~stlÀ~=‹
ŠK‹ 23$
& ”B(R
l $$œrevigrx`~l^gˆ{npa+bƒsief]ghcd{e op
g …{a
g,cd{ e uh‚xdopw`Ÿ
x ,bopgw9]`c|ig*mg oq@€ $'bd]xdx~
bopgw9]`c|ig2~2‹% ¡%23$
&9¡:( $ª'
„ $H{b .
]
~l-_ bdi
ˆ
ba
e c|iƒw`a
nNw`{npa+c|]fä
]g]`ba
nKbd]w9i{_ npoNgˆÌw9i6!] Éw`oq]ghc`~=y!ief_ {6c $ uh‚6[x $
yHieveÓ{ g $2‹ ,1‹ ®i‘ 2ԉ ”‹Œ%‰ ¡+S‘ $
&:(R
l $Ha+b|ŒŽ}u a
nqie a
gr*Y
s $†Ànpa+_ opxdw˜u~ h„ Ôl clmgæ!] Éw`oq]ghcv_bdi
ˆ
b˜a
e k×i
bƒw`a
npw`{npa+cdopig
i
kRˆ
]g]`ba
nÀbd]w9i{_ nNopgˆWw9ih!] Éw`op]g,cd•x h‚ ˆ
ba+_ u opw`a
n…a
ga
nq‚xdopx`~Æw9ief_ a+cd+o nq] ) oqcdu hO} 0…˜
s $
yHief_ {6c $ /u,‚6x $Dy!ieveR{g $¡+Ÿ
‘ ,1‹
Š
›Š 2 B¡¨‰Œ % $
&K('$Oc a
w .~D
} $ $ opc|bd]Ôa
gr $'a
gÉr]`b ]{ˆ
c`~ m] ) !] Éw`oq]ghc_bdi
ˆ
b˜a
evxc|iÇw`a
npw`{nNa+c|]Ԉ
]g]`ba
n
b]w9i{_ npopgˆw9i6!] Éw`oq]ghcd6x $ :a+bdc 7DmK„^]g]`b˜a+cdoqigÕi
kjaÑx{eveva+cdoqigÕk×i
beR{npa~'y!ief_D{6c $ uh‚6[x $
yHieveÓ{ g $ %Š ,1‹
 ”O2m‰ B¡¨Œ‰

‰ $
& :Š ('$Oc a
w .~D
} $ $ opc|bd]Ôa
gr $'a
gÉr]`b ]{ˆ
c`~ m] ) !] Éw`oq]ghc_bdi
ˆ
b˜a
evxc|iÇw`a
npw`{nNa+c|]Ԉ
]g]`ba
n
b]w9i{_ npopgˆÉw9i6!] Éw`oq]ghcd6x $ :a+bdc 77Dmœ€®a
np{ a+cdoqigti
k/a@xd{eÌeva+cdoqigtk×i
b˜eÓ{nNa~2yHief_ {6c $ uh‚6[x $
yHieveÓ{ g $ Š ,1‹
% ¡›2À‹`›‘ ¡¨Œ‹‰
‰ $
& D( $ $%0
‹
a
w ~} $ $ /oqc|bd]/a
g r $ 'a
gRr]`b]{ˆ
c`~hyHa
npw`{ npa+cdoqig…i
kˆ
]g]`ba
n,b]w9i{_ npopgˆÔw9ih]!ƒw`oq]g,cdx
{ xdopgˆÇˆ
ba+_ u opw`a
nef]`cduirx`~Dy!iev_ {c6$ uh‚x6$Dy!ieveR{g$2‹`‘‹U,1‹
%2À‹[¡%¡¨Œ‹ ®‘S$
&ŋ`‘(R\'$ c$'ji% opg x|ig~Ôy!ief_ a+b˜opx|igýi
k”nNaB]np]rUc|bd]`]x ) oqcdu怮a
nq]g w9‚Ucdubd]`]
~ $Hy!ie opga+c|i
b˜opa
n
‹ ,1‹ 6K‹ 2À‹`›‘ ¡¨Œ‹
‹ $
u]`i
bd‚Ñ}6]`[b $-‹
U
&ŋ
D‹ (R
† $DyH{npqo .b7H7/a
gr@'\ $5Ùi6i6r2~l$gi
c|]ÀigÑx|ief]…c|bd]`]ÓxdopevopnNa+boqc"‚vev]a
xd{bd]x`~ 71gk½i
b–e $ 'bi6w9]xdx[$
]`c|6c $[‹ ¡•,1‹
Š
›‰ 2 ¨ŠŒ ”,‰ $
&ŋ:‰ (R˜
s $ª} $5Õa+c|]`beÌa
g a
gr $ c{$=}evoqcdu~ *Æg4cdu]vxdopevopnNa+boqc"‚i
k!r]g rbdi
ˆ
ba
evx~ $ u]`i
Kb $2!opiŒn $
B•,1‹ +›Š 2 +Š
¨ŒŠ+‘
S‘ $
&Å[‹ :( $ $,a+bd€6oNx`
~ $îb† ${]r]eÌa
gta
g rz'\ $$}u oq]`b~2y!ievef]ghcdx^igtw9iev_ {cdopgˆÉcdu]fxdopevoNnpa+boqc‚
i
k opg a+bd‚Ìc|bd]`]x~ $ u]`i
[b $ HoqiŒn $2‹`‘
•
‘ ,1‹
%Š ›2<”,‰ ŠŒ ”i% $
&Å!‹ ”B(5 $ ‘$ œ<$ \Æa‚
~ 'bdi
_.]`bdcdop]xHi
k=cdu]”g]a+bd]x|cjg]oqˆOu .i
bjopghc|]`bwua
gˆ
]Àef]`c|bopw^k½i
bjc|bd]`]xÔi
kKxdeÌa
npn
xqo —`]
~ $ u]`i
[b $HoqiŒn $2‹`‘U‹ ,1‹
%Š ›2m‰ B¡¨Œ‰
Š
Š $
&Å[‹ ¡:( $ $®!inpa
gr2B~ œ $îb
† $¨!bdi ) gÇa
gr 5 $ ‘$ œ<$+\Æa‚
~,lm__bdKi #oNeva+cdopgˆÔeÌopgopeR{enj"nq]gˆ
cduŒ"x|[] *6{]gw9]
ev]`c|bopw`6x m'avw`a
{cdoqiga+bd‚gi
c|]
~ sta+cdu $.}i6Bw $D}w`Šo $”Ÿ,1‹
%Š ›2j‰ ‹Œ‰ ®S‘ $
&Å1‹ :('c$6!{ w .nq]`‚va
gU
r c$ ‘ma+ba+b‚
~6\Æopx|cda
g w9]^opgƒ„^ba+_ ux ,Ïlmr ropx|igŠŒ 5Ù]xnq]`‚
~ Ô]a
ropgˆRszlÓ~D‹
+i‘ 23$
&ŋ K(R $ª'
„ $5 O‚ .i{bg]
~jynpa
xdxdopw`a
n^„^bdi{_ xÌk×i
b uh‚xdopw`opx|cdŸ
x , iug 5 opnp]`‚ }6igx~ m] ) 0'i
b .D~
‹:”O23$
&ŋ:Š ( $ Œ '$Hyu]g
~ $ Œ $5Õa
gˆ~ $ Œ"˜
s $ {æ
a
g
r $ Œ" $X5Õ{2~ Ba np]xvi
k…cdu]ÙyHnq6] xdw˜uŒŽ„^i
br a
g~
ma
w`a
u-a
grxd{ r{w9cdoqig$w9ih!] ƒw`oq]g,cdx4i
k}' ,/2ш
bdi{_Dk
x ,/5Ùi
bnNrÃ}w`oq]ghcd"o ™Dw+~R}oNgˆa+_.i
bd]
~
‹
Š %23$
&ŋ: ( $ $î
l $}npia
g]
~ *ÆgŒ =opg] œgw9‚w`nqi
_.]ropaRi
k 7Žghc|]`ˆ
]`b”}6[] *h{]gw9]x
,Ï m !" 23$
& ‰+‘ (R
l $!yHa‚6np]`‚
~ *Ægýcdu]Ña
ga
nq‚6cdopw`a
nk½i
bevxvw`a
nNnq]rWc|bd]`]x`~ ) oqcduUa+_ _ npopw`a+cdoqigWc|i cdu]@cdu]`i
bd‚Wi
k
w˜u]evopw`a
nw9ie oNga+cdoqigx`~ Ô]`_.i
bdcdxj!boqcdopxuƒl^xdx|iBw $ l^r€+a
gw9%] $}w`Œo $”i¡•,1‹Š B¡›2˜~.%‰ ¡‰Œ +›‘ ¡ $
& ‰D‹ ('c$‘^a+ba+bd‚
~.„^ba+_ u u]`i
bd“
‚ ,Ïlmrr opx|igŠŒ 5Ù]xdnp]`‚
~ j]a
ropgˆvszlÓ~‹ › 23$
& ‰
:‰ (R˜
s $ =o´~ $ bdief_Àa
gr f$ua
gˆ~ *…g”cdu]g]a+bd]x|c=g]oqˆiu .i{b2oNg,c|]`bw˜ua
gˆ
]!ropx|cda
gw9X] ]`c ) ]`]g
]`€
inN{cdoqiga+bd‚ƒc|bd]`]x`~ $ u]`i
Kb $!opiŒn $2‹Š
•
‰ ,1‹
 ›2<”%¨ŠŒ ”O$
& %‰ :(R˜
s $ =o´~ $ bdiev_ýa
gr f$ua
gˆ~j}6ief]Ñgi
c|]xÌigUcdu]Ñg]a+bd]xdcÌg]oqˆOu .i{bvopghc|]`bwua
gˆ
]
r opx|cda
gw9]
~ ]w96c $ mi
c|]x^y!ief_D{c|]`b^}w`oq]g w9]v‹`‘+Ÿ
‘ ,1‹
 ›2˜~ ”i¨‰Œ %¡B‹ $
& ‰ ”B('$ ca
w .~K
} $ oq]`€
]gx^a
gr $ 'a
g4r]`b ]{ˆ
c`&~ *Ægzcdu]Ór opa
ef]`c|]`bÆi
k'cdu]Rbdi
cda+cdoqigtˆ
ba+_ uzi
k
Dopga+bd‚Ìw9i{_ npopgˆÇc|bd]`]x~ mg oq€
]`bxdoqc‚Éi
k'„Æu]ghcj_b]`_bopgh
c ,1‹

› 23$
& %‰ ¡:(R'
\ $î'\ $h}nq]a+c|i
b~ $ œ<$ a+bχda
gRa
g r 5 $ $ u6{bx|c|ig~,}ui
bdc]gw9iropgˆx=i
k ]`€
inq€6oNgˆ…x|c|b{w9cd{b]x`~
S} 7Žl^s $\ÆopxdBw $ sta+cd
u $@¡,1‹

›‰ 2<”,‰
Š¨ŠŒ ”i¡+S‘ $

& :('$:c .
‰+‘
‰
2st{bdcda+ˆu~:y!i{ghcdopgˆ@r]grbi
ˆ
ba
evxm…a@xd{bd€
]`‚
~=\^oNxdw9bd]`c|]Ìlm__ nŒ$.sta+cdu$ “,1‹
Š”O2f‹‹Œ
‹
 $
& ‰K('œ $îb
† $,!bdi ) gÌa
grU5 $ ‘$ œ<$6\Æa‚
~l w9ief_ {cda+cdoqig a
npnq‚R]!Éw`oq]ghc/a+__bi[#opeva+cdopgˆ…c|iÓcdu]Ôg]a+bdŒ
]xdcÔg]oqˆOu .i
bjopg,c|]`b˜wua
gˆ
]Óef]`c|bopw+~ $DyHnpa
xd6x $2F‹ ,1‹
Š ”O2Ô% ¨Œ‹‰ ”$
& ‰
:Š (5 $ ‘$ œ<$ \Æa‚
~ *^_cdopeÌa
na
npˆ
i
boqcduevx!k½i
bÔw9ief_ a+b˜opgˆÇc|bd]`]x ) opcdu@npBa .]nq]rnq]a€
]x`~ $DyHnpa
x6x $‰
,1‹
%Š ¡›2 Œ‰
Š $
& ‰
: (R˜
s $† b op€ a
g6] .~y!ief_ {cdoNgˆHcdu]g]a+bd]xdcg]oqˆOu .i
b2opg,c|]`b˜wua
gˆ
]/ef]`c|bopwBk½i
b{g npBa .]nq]r opga+bd‚
c|b]`]xÔopx BŒ"w9ief_Dnq]`c|]
~ $DyHnpa
xd6x $–,1‹
Š ›2¡%¡¨Œ +S‘ $
&9+‘ (R'
\ $î'\ $D}nq]a+c|i
b$~ $ œ<$ a+bχ|a
g@a
g Fr 5 $ $ u6{bx|c|ig$~ ji
cda+cdopigÑropx|cda
g w9]
~6c|b˜opa
gˆ{npa+cdopigx/a
g r
uh‚6_]`Hb inNopwԈ
]`iev]`c|bd‚
~ $lmef]`Kb $ sza+cd u $}6iBw $2U‹ ,1‹
Š
›Š 2A”Œ ŠB‹ $
&9D‹ ('œ $s Ba .opg]g&
~ *Æg4cdu]Rcdu]Rbi
cda+cdoqigÙropx|cda
g w9]Ri
{k opga+b‚@c|bd]`]x` ~ 71gk½i
b–e $ 'bdiw9]xd6x $ 2]`c|6c $‰ ,1‹
Š %2m‰ 6‹Œ‰ +‰ $
&9
:‰ ('c$ { w`w`oqiRa
g r X$ :a+ˆnpo~ *…gÌcdu]…{_ _]`{
b .i{grÉigÉcdu]mbdi
cda+cdopig@ropx|cda
gw9]^i
1k Dopga+bd‚Çc|bd]`]x`~
71gk½i
b–
e $ 'bi6w9]xd[x $ 2]`c|6c $@a‹ ,1‹
Š
› 2<¡Œ +S‘ $
&9%:( $ *'$ji
ˆ
]`b˜xva
gr $î'
\ $\Æ{c|c|ig2~ *ÆgUr opx|cda
gw9]@opgWcdu]@bi
cda+cdoqigUˆ
ba+_ uWi
k opg a+bd‚Õc|bd]`]x`~
yHigˆ
[b $ ^{ef]`[b $2‹‰+‘ ,1‹
 ›2”‹`›‘ ¨Œ‹
[‹ $
& :('c$
‰‹