$ =44>
?A@CBEDGFHI@KJL@CMEN'DG@CO'PRQDTS'MEUWV'V%UYXZ@CDTBEU
[]\_^a`cb`cde`f%ghGfi+j<kml
nonon7p h+qode`cr#serE^<i%tcr`crE^.lvu<wx'wLy poz l
{o|opo{7}Z~ j<x%G[a[axj<[ ~ i,f% <f!lvvt7\_r
f7bT,E7tcbTwoqo_Wo^vbTloobd_^r.vCrow.7btcr77r.dvtcrEqowt
2' .¡.¢¤£v¥7¡
¦Yr<qo\_^b§ser.t%#q¤¨]qoZvr©eb`a!^b\vor].7tctcbr.t^_or
`cbZrªqeseb\v^cvr.ZrAqot«tcrE¬Wdvr.\_W]^r.rE`cb®orR_7\e
\vr.§^A_o^rEs9qo\9`cvrqo\_.¤`cr.\_¤`cbqo\9q7`ctcr.b§^a]qeserEs
Zqesedv§¤`cbqo\¯°i,k²±¨+b`c`cbZrtcr.®or.t^c72qot`cvqooqo\_7
^_orT`cbZrvqe#qeseb\v!¯°+h ~ +uGi±w¤vr%+h ~ +uGi
`cdvtc\_^9`cvr³tcrE¬Wdvr.\_W]^r.rE`cb®or´!dv`cbb\vvde`µ!dv`cb
qode`cvde`_7\v\vr.,b\W`cq¶²^a`7\_sv7ts^b\vorb\vvde`Z^b\vor
qode`cvde`_7\v\vr.e¤·rE`crEs!K#b\W`cr.t]^K!CqoKb\W`cr.tr.tcr.\_row
vr+serEqeser.t¸b§^¸_o^rEs=qo\!tcrEsed_rEsK]^a`¤`cr¹aqob\W`'rE¬Wd_7bºE¤
`cbqo\¶7\_s²serEqeseb\v_lL¨+vr.tcr»Zb\vb!dv¼ZrE7\e]^c¬Wd_7tcr
r.tctcqot+serEb§^bqo\eTr.rEse_orE¬Wd_7bº.r.tb§^+qo!vb\vrEs*¨+b`c
½b`cr.tcvb+serEqeser.tqoCr.t¤`cb\v3qo\`cvr*i,k¾`ctcr.b§^.l7\_s
¨+vr.tcr<`cr.\W`¤`cb®or#serEb§^bqo\_^+7tcrqodv\_s*qo\»`cvr#^dvtc®Kb®oqot^
¯Cr.t]^dvtc®Kb®oqot#vtcqerE^c^b\vK±w*[]\¶`cvb§^!¨ol`cvr*serEqeser.t
qoZvr©eb`a¿b§^*b\_ser.Cr.\_ser.\W`q7=`cvr¶_7\v\vr.ÀZr.Zqotc
7\_sÁq7!`cvrmqo\_^a`cr.§¤`cbqo\A^bº.rowÂGr.®or.t`cvr.rE^c^.lÀ^b!de
§¤`cbqo\_^^vq¤¨Ã`c_¤``cvrvtcqoCqW^rEsÄ^cvr.ZrKbr.§sv^^b
b§7tŤ^dvCr.tcbqotZCr.tqotc7\_r¨+b`c«tcrE^CrE``cq¶`cvr3CrE^a`
vtcr.®Kbqod_^<vtcqoCqW^rEs=^cvr.ZrE^¸¤`¸!d_=q¤¨,r.t¸qoZvr©K
b`aow ÆCÇÈÉ
¡.¢¤Ê˸̸¥7¡EÍ°Ê
É
vrserE^bo\Yq7^_orT`cbZrZqeserE^¯
~
i,^±Gqot=^b\vor
.7tctcbr.t!`ct7\_^Zb§^c^bqo\q¤®or.t=tcrE¬Wdvr.\_^r.rE`cb®or*!dv`cb
b\vvde`»!dv`cbqode`cvde`Y¯°k[akYjÀ±Z_7\v\vr.§^Z_o^Cr.r.\«b\e
®orE^a`cbW¤`crEsÎb\¿¶\Kdv!Cr.t2q7#tcrEr.\W`2qo\W`ctcbvde`cbqo\_^3ÏyÐ
}7Ñ
wYk3¤©eb!dv]bor.bvqKqes¿¯°k3¸±=serEqeseb\v²b\Äk[akYj
tcrE¬Wdvr.\_W]^r.rE`cb®or_7\v\vr.§^¸b§^'or.\vr.t7<`cqKq#qoZvr©
qotvto`cb§.7,_7\v\vr.%Zr.Zqotc¶7\_smZqesedv§¤`cbqo\Äqo\e
^a`cr.§¤`cbqo\Y^bº.rowGr.\_roltcrE^rE7t_o^qed_^rEs²qo\Y^dve
qoe`cb7!q¤¨ÒqoZvr©eb`aR^cvr.ZrE^.w´¦YrÄÁotcqodv
`cvrE^r¿7vvtcqWovrE^3b\W`cqÁ`a¨,qR§o^c^rE^.wvrÄÓ_t^a`7e
vtcqWob§^<_o^rEsqo\²Zb`cbW¤`cb\v»b\W`cr.t]^K!CqoÔb\W`cr.tr.t
r.\_r«¯[ ~ [±2K¿^qoZrYk[akYjrE¬Wd_7bºE¤`cbqo\«`crEv\vb§¬Wdvrol
7\_s¿`cvr.\RserE^bo\vb\v«Î^_orT`cbZr¶qeser¤Å¤serEqeser.t»qot
`cvr»tcrE^dv`cb\vÕC¤`=°oseb\v²_7\v\vr.Twvqot!r©v7ZvrolÔ`cvr
d_^r+q7Àb\vrE7tZb\vb!dvZrE7\e]^c¬Wd_7tcrr.tctcqot,¯°k3k ~ f,±
k[akYjrE¬Wd_7bº.r.t*qo!vb\vrEs¿¨+b`cÁG§7Zqode`cbTÖ^*^_or
`cbZrZvqe3qeseb\v¶¯~ +uGi±_o^<Cr.r.\Yb\K®orE^a`cbW¤`crEsb\
Ï}7Ñ wGq¤¨,r.®or.tEl`cvb§^!^cvr.Zr»seqKrE^=\vq7`ovbr.®orZb\or.\e
r.t7Z`cvrפ©eb!dvØseb®or.t^b`aªqotser.tmq7·r.tcrEsÙKª`cvr
_7\v\vr.Twvr^rEqo\_s7vvtcqWomb§^_o^rEsmqo\ÎserE^bo\e
b\v2`cvr ~ iÁK»`7Kb\v2b\W`cq»o.qodv\W`G`cvr![ ~ [G_7\v\vr.
7\_s`cvr.\«Cr.tqotcZb\v*¹aqob\W`rE¬Wd_7bºE¤`cbqo\Î7\_sÎserEqesK
qeserEsZqesedv§¤`cbqo\A¯°u,[ci,k²±=¨+b`c`cdvtcCqYrE¬Wd_7bºE¤`cbqo\
_®or3Cr.r.\ÁvtcqoCqW^rEs«b\ÚÏz lEÛel |¤ÑwbZr²tcr.®or.t^c7Gqot
`cvqooqo\_7 ~ +uGi¯°+h ~ +uGi±3Ïy Ñ ¯°^r.r²7§^qÁÏnѱqo\e
®or.t`^!`cvrk[akYjÜtcrE¬Wdvr.\_W]^r.rE`cb®or»_7\v\vr.b\W`cqm
^a`7\_sv7ts^b\vorb\vvde`^b\vorqode`cvde`¯
~ [~
j˱_7\v\vr.
¨+b`c[ ~ [lE`cq<¨+vb§qo\K®or.\W`cbqo\_7o`crEv\vb§¬WdvrE^'ser.®or.qoCrEs
qot#[ ~ [À_7\v\vr.§^#.7\YCr»7vvbrEsLw2vrZvtcqovr.¨+b`c
`cvrE^r^cvr.ZrE^b§^Ô`c_¤`Ô`cdvtcCq7rE¬Wd_7bºE¤`cbqo\#\vr.rEsv^¸^q7Ý`
b\3^q7Ý`qode`<k3x¿serEqeser.tGqot+`cvr=[~ [+_7\v\vr.Tl_¨+vqW^r
qoZvr©eb`a*b§^Gr©eCqo\vr.\W`cb§7b\`cvr_7\v\vr.r.\v7`c37\_s
b\Z`cvrGqo\_^a`cr.§¤`cbqo\Z^bº.row'vqotr©v7ZvrolWk3xm^K!Cqo
KW]^K!Cqo%ser`crE`cbqo\mbZvr.Zr.\W`crEsmK²`cvr»uGi,ÞWh7
oqotcb`cv´tcdv\_^=qo\Ä`ctcr.b§^!¨+b`cÎßRàáâ^a`¤`crE^.l¨+vr.tcr
ßser.\vq7`crE^G`cvrqo\_^a`cr.§¤`cbqo\²^bº.r7\_s²ãÁser.\vq7`crE^`cvr
_7\v\vr.Lr.\v7`cr©evtcrE^c^rEs2b\^K!CqoTw
[]\`cvb§^¨,qotcÙ¨,rÁqo\_^b§ser.tm`cvrAqo\_.¤`cr.\_¤`cbqo\q7
+h ~ +uGi¨+b`cR7\Aqode`cr.t*`ctcr.b§^qeserEsÁZqesedv§¤`cbqo\
¯°i,k²±^cvr.Zr=Ïä Ñw¸¦YrG^_7vvtcq¤®Kb§ser+7\Zb\eqotc¤`cbqo\e
`cvr.qotcr`cb§3¹ad_^a`cbÓC.¤`cbqo\ªqotY`cvr«vtcqoCqW^rEsª^cvr.ZrÎb\
`cr.tc^2q7=ovbr.®¤7vrt¤`cr²7\_s«seb®or.t^b`aowR,`2`cvr3tcr
r.b®or.tEl»¨,rA7vvtcrEsed_rEsK]^a`¤`crÁ^rE¬Wdvr.\_rÁser`crE
`cbqo\å_o^rEsÃqo\åk3k ~ fæserEb§^bqo\eTr.rEse_oÚrE¬Wd_7bº.r.t
¯°k3k ~ f] <'f,±37\_sACr.t]^dvtc®Kb®oqotvtcqerE^c^b\v¯°x ~ x,±w
~ b\_r»`cvr*x ~ xªser`crE`cqotŤserEqeser.t!¨,qotce^#qo\m`cvr»`ctcr.
b§^q7`cvr*dv\_ser.tcKb\v¶i,kqeserol`cvr*tcrEr.b®or.tZqo
vr©eb`a²b§^Àb\_ser.Cr.\_ser.\W`!q7%`cvr2_7\v\vr.r.\v7`cm7\_s²q7
`cvr3qo\_^a`cr.§¤`cbqo\Î^bº.row«vb§^7orE^qodvt^cvr.Zr7e
vb§.7vr»b\vto`cb§rol'¨+vbr2`cvr*^cvr.ZrE^=vtcqoCqW^rEs¶b\
Ïn l z l |¤Ñ 7tcr3\vq7`EwG\vq7`cvr.tose®¤7\W`7orb§^»`c_¤`i,k
.7\»rEo^bbZvr.Zr.\W`Gosv7e`cb®or<Zqesedv§¤`cbqo\Y¯b`Gb§^^deÝ
ÓCbr.\W`%`cq=r©e_7\_s`cvrqo\_^a`cr.§¤`cbqo\lWosvsZdv\_qeserEsvb`^
7\_s!b\_tcrEo^r%`cvr\Kdv!Cr.tq7C_7t7r.o`ct7\_^b`cbqo\_^¸b\`cvr
i,k`ctcr.b§^.lKqoq¤¨+b\vÏä ѱw
ç Ê_¡E£e¡EÍ°Ê
É
oè bݱé´êæë*ì¯é%ícî*±ZrE7\_^`c_¤`3`cvr
t7\_seqo¾®orE`cqot*éb§^qoZvr©AïÀ7d_^c^b§7\Á¨+b`cRbtde
§7t!^KZZr`ctcol'¨+b`cmZrE7\ð2Ïé
ÑGñ
é×7\_smq¤®¤7tcb§7\_r
ð2ÏéLéÔò Ñ+ó é é ò ñ î3w/bbݱ
Èô
ser.\vq7`crE^²`cvr«õªö¿õ
b§ser.\W`cb`a¶¤`ctcb©Lwbbbݱ ~ dvCr.t^ctcbe`^!÷Á7\_smòÃb\_seb§.¤`cr
`ct7\_^CqW^r7\_s2Gr.tcZb`cb§7\Z`ct7\_^CqW^rolWtcrE^CrE`cb®or.ow¸b®v±
øù
ñ
¯úLû
ü
áâ íúLû
ü
áý í.þ.þ.þ.íúLû
ÿ
±a÷«b\_seb§.¤`crE^<`cbZrtcr.®or.t^c7
qoZvr©*qo\¤¹advW¤`crÀq7®orE`cqot
ù w
Ç
£
ɸÉ
ÊË
¦YrÒqo\_^b§ser.t³tcrE¬Wdvr.\_W]^r.rE`cb®or¼!dv`cbb\vvde`
\vr.b§^À^a`ct7boW`qotc¨7tsLwÀvr!dv`cb_¤`c¶_7\v\vr.Ôtcqo
`cvrTT`c`ct7\_^Zb`%7\W`cr.\v\_<`cqÀ`cvrGtcrEr.b®Kb\v#7\W`cr.\v\_Àb§^
o^c^dvZrEs`cq!Crt7\_seqoÙvde`,`cbZrb\K®¤7tcb§7\W`qot,=^dZ
br.\W`c*§7tcor#\Kdv!Cr.tGq7^K!Cqo§^=¯°¬Wd_o^b]^a`¤`cb§<°oseb\v
o^c^dvZe`cbqo\C±wÁvrq¤®or.t7TT`c¿_7\v\vr.GbZvdv§^rtcr
^Cqo\_^r3b§^2ob®or.\«KÄ`cvr²qo\K®oqode`cbqo\«q7À`cvr3vKe^b§.7
_7\v\vr.¨+b`c*`cvr<`ct7\_^Zb`+^_7vb\v!Ó_`cr.tEw+Ý`cr.tG^c7
vb\vm¤``cvr^K!Cqo+t¤`crYy .l,¨,rqoe`7b\«seb§^ctcr`cr
`cbZr#q¤®or.t7bZvdv§^r#tcrE^Cqo\_^r'q7'r.\v7`c
ã ñ ¯ay±
¨+vr.tcr Gtcr.vtcrE^r.\W`^Z^K!Cqosedvt¤`cbqo\l b§^,`cvr=ser
§Y^vtcrEos¶7\_s¶b§^#`cvr2r.\v7`cmq7`cvr»^_7vb\vÓ_`cr.t
bZvdv§^r!tcrE^Cqo\_^r=r©evtcrE^c^rEs*b\²^K!CqoÔb\W`cr.tc®¤7§^.w+¦Yr
o^c^dvZr`c_¤`,#vqe
Lq7 9^K!Cqo§^b§^%^r.\W`tcqoÙ`cvr
TT`c27\W`cr.\v\_vl7qoq¤¨,rEsKã ó y+º.r.tcqW^+¯º.r.tcq7_osvseb\vK±l
b\Zqotser.t¸`cqÀr.bZb\_¤`cr+b\W`cr.tvqe#b\W`cr.tr.tcr.\_row'r`
ser.\vq7`cr`cvr=¯ ó y2ã,±Cö `7vÔqKr.vbº+¤`ctcb©!¨+vqW^r
T`cqodvZ\b§^ob®or.\*K
¯{ í.þ.þ.þí {
! "
#
í$
÷ í { í.þ.þ.þí {
! "
ü
áâá
# ± ÷
vr.\l'`cvr»seb§^ctcr`crT`cbZr2tcrEr.b®orEsm^bo\_7qot`ct7\_^a
Zb``crEsvqe2q7¸r.\v7`c µb§^ob®or.\*K
¢ ñ ü&%
'( â
*) ¯n ±
¨+vr.tcr)åêmë*ì3¯,+í ÿ È ü
áâ-à
±,b§^GÔ¦¿ïÀ=w
. Ç Ê É
¥o£e¡
KÉ
£e¡
Ë0/ / î2143 /65
.
Ç°ÆCÇ
/=Í7
î é
¢¤ E£
3
/65
+h ~ +uGiåÏy Ñ b§^#`cvr»\_¤`cdvt7r©K`cr.\_^bqo\mq7Gqot`cvqo7
qo\_7 ~ +uGi/_o^rEsÜqo\Âor.\vr.t7bº.rEsåqot`cvqooqo\_7ser
^bo\_^Z¯Tï=j< À±G`cq*`cvrtcrE¬Wdvr.\_W]^r.rE`cb®or_7\v\vr.§^.lLb\
`cvr¿^r.\_^rÄ`c_¤`¶`cvr«qoe`cb7ZtcrEr.b®or.tYb§^²qotcZrEsªK
¤`vrEsÚÓ_`cr.tcb\vª7\_sqo!vb\vb\vª7\_sÚ`c_¤`Îser`crE
`cbqo\ªq7Z`cvrÎsv¤`×^a`ctcrE7^3^r.\W`²KÁ`cvrÎ7\W`cr.\v\_o^b§^
Cr.trE`cserEqodvvrEsLwÒGq¤¨,r.®or.tElÀ¨+vbrqot3qot`cvqooq7
\_7
~
+uGiÂb\AtcrE¬Wdvr.\_WTÕC¤`*°oseb\v«CqW^a`]qo!vb\vb\v
^K!CqoKW]^K!Cqomser`crE`cbqo\´b§^qoe`cb7TlÎqotª+h
~ +uGi¾b\ÂtcrE¬Wdvr.\_W]^r.rE`cb®orÁ°oseb\v`cvrªtcrE^dv`cb\v
_7\v\vr.¤Ý`cr.tGqo!vb\vb\vZb§^+7\*[ ~ [,_7\v\vr.TlKqot+¨+vb§
^rE¬Wdvr.\_r#ser`crE`cbqo\qot+rE¬Wd_7bºE¤`cbqo\»b§^+tcrE¬WdvbtcrEsLw
µÏGící98 Ñ ï=j< åb§^serÓ_\vrEsK¶:ö À¤`ctcb©
3¯
ù
±¨+vqW^r*r.\W`ctcbrE^7tcr*r.r.Zr.\W`^q7
ù
qot!`cvr.bt2qo\e
¹advW¤`crE^.l¨+vr.tcr
ù
b§^Ä®orE`cqot*q7;8×^K!Cqo§^»tcqo/
qoZvr©¶qo\_^a`cr.§¤`cbqo\l'7\_s¶^d_¶`c_¤`;3¯
ù
±aò63¯
ù ± ñ
<ù <ý È>=
Ï? Ñ
wÁï<b®or.\¿«ÏGí í98
Ñ
ï=j< ¼¨+b`cÎ`cvrvtcqoe
r.t`a¶`c_¤`7\K¶tcq¤¨Ãqo\W`7b\_^!r.b`cvr.tZr.r.Zr.\W`^q7
ù
qot
r.r.Zr.\W`^+q7
ù
û7lv¨,r=qo\_^a`ctcd_`+`cvr=qotctcrE^Cqo\_seb\vZ+h
~ +uGi«Ktcr.v§ob\v!rEo*^K!Cqoú¸K»!®orE`cqot,q7
^K!Cqo§^ qoq¤¨,rEsZKã ó yGº.r.tcqW^.lW7\_sZrEo»^K!Cqo
øù
ã ó yÀº.r.tcqW^.w
vrtcrEr.b®orEsÄ^bo\_7+b§^Z_o^c^rEs`cvtcqodvo«Y_7\vq7
Ó_`cr.t^¸¤`vrEs=`cq
â
í.þ.þ.þ.í$
ü&%
w'vr¤`vrEs#Ó_`cr.t
qode`cvde`^#7tcrqo!vb\vrEsb\²qotser.t`cq*qoe`7b\@83^r._7t¤`cr
~ [ ~ jª_7\v\vr.§^¨+b`c[ ~ [%b\*`cvrÀqotc
A
CB ô ñ
àáâ
'
D(
áFEàáâG>H
D
úCB ô á D
ICB
ô ¯z ±
¨+vr.tcr
H D ñKJ
ü&%
(
âL6M
¯CN±
M û
¯CN óO ±PQNÀb§^#`cvr»^dvµq7
`cvr*_7\v\vr.,7de`cqeqotctcr.§¤`cbqo\_^<q7G7 <`ct7\_^Zb`7\e
`cr.\v\_o^.l77\_s=¨+vr.tcrGICB
ô
,b§^'qoZvr©ïÀ7d_^c^b§7\=\vqob§^r
^rE¬Wdvr.\_rÀ¨+b`c7de`cqeqotctcr.§¤`cbqo\2dv\_`cbqo\ ÿ H Dw
. Ç Ç Ê É
¥o£e¡
KÉ
£e¡EÍ°Ê
É
− 1 L
N D
) 1 ( N + L − T
3 2 1 x x x
x 1 − x 2 − x 3
x 1
x 2
x 3 x 1 − x 3
x 2
− 1 L
!
!
y z j
RTSUVWYX[Z\>]_^`Sa9U!b_a9c\9de\!fbg,]_hicijd\!b&kmlnpo
Gr©K`Ele¨,rÀqo\_^b§ser.t,`cvr#qo\_.¤`cr.\_¤`cbqo\2q7¸+h ~ +uGi
¨+b`cm7\Yqode`cr.t#i,kæ^cvr.ZrowZ7Zr.olL`cvrvqee^<q7
^K!Cqo§^
ù
,7tcr#vtcqesed_rEsK*b\W`cr.tcrE®Kb\vZ`cvr!qode`cvde`
q7Ci,kÃr.\_qeser.tEw¸¸b_wyW¯°W±Ô^vq¤¨G^L`cvr,vqe=seb§7ot7
q7#`cvr²vtcqoCqW^rEs¿qo\_.¤`cr.\_¤`crEs¿^cvr.Zrqot
ñÒz
l
_o^rEs=qo\=`cvrt¤`crz Å }<~ +uGiY¨+b`cvqe#r.\v7`cq ñ¿}
7\_s»`cvrÀqoq¤¨+b\v!`ct7\_^Zb`7tct
3¯ú
â
íú
ý
íúr± ñ sttu ú â ú ý úr
ó ú û
ý ú ûâ {
ó úLû
r { úLû
â
{ ó úrú
ý vww
x
vr¼^rE¬Wdvr.\_r9or.\vr.t¤`crEs KÒ`cvri,k r.\_qeser.tEl
qotcZrEs3q7%^K!Cqo§^tcqo97\YßÁ]7tcqoZvr©²qo\_^a`cr.
§¤`cbqo\ܯrow_wlx
~y
qotz<k²±l#b§^¶7tct7\vorEsKtcq¤¨G^
b\W`cqm 0ö{ tcq¤¨]qodvZ\b\W`cr.tcrE®or.tEwvrtcrE^dv`
b\v|{)®orE`cqot^3q7»r.\v7`c 7tcrÄ7vCrEsªqo\W`cq×`cvr
!¯}¿ã ó y±ö +h ~ +uGiR`ct7\_^Zb`=7tct¯Ý`cvb§^
b§^+^vq¤¨+\`ct7\_^CqW^rEs2b\¸b_wyW¯°W±¨+vr.tcr`cvr#^_oseq¤¨,rEs
7tcrEo^qotctcrE^Cqo\_sY`cqYº.r.tcqW^±wmvr^CrE`ct7,r42br.\_
q7»`cvr«tcrE^dv`cb\vqo\_.¤`cr.\_¤`crEsÙ^cvr.ZrÎb§^¶ob®or.\ÙK
~ ñ ü
ü
-àáâ 9
l_¨+vr.tcr
b§^+`cvr=t¤`cr2Ï^K
CqoŤ_7\v\vr.Ld_^r Ñ q7¸`cvr#dv\_ser.tcKb\v ~ +uGil_7\_s
b§^`cvr#t¤`crÏvb`Ť^K!CqoÑ q7Ô`cvr#qode`cr.tGi,k´qeserow
ÊCÍ ¡ ̸£ Ío£e¡EÍ°Ê £ Ë¿Ë ¥oÊ˸Í
k3»ser`crE`cbqo\=q7e`cvr%q¤®or.t7oqo\_.¤`cr.\_¤`crEs#^cvr.Zrb§^
`cqKq#qoZvr©Ll7^b\_rb`¨,qodv§s=tcrE¬Wdvbtcr%tcdv\v\vb\v#½b`cr.tcvb
Goqotcb`cv¯½'<±Zqo\«7\Îr©e_7\_serEs`ctcr.b§^.l,¨+vr.tcr*`cvr
\Kdv!Cr.tq7^a`¤`crE^Gser.Cr.\_sv^qo\*`cvr_7\v\vr.r.\v7`cl_qo\
`cvr¶qo\_^a`cr.§¤`cbqo\Á^bº.rY7\_s¿qo\¿`cvr¶osvseb`cbqo\_7<Zr.
qotc»b\W`ctcqesed_rEsK»`cvr=b\W`cr.tcrE®or.tEw,Ôq2q¤®or.tqoZr<`cvb§^
vtcqovr.l¨,r!vtcqoCqW^r!2tcrEsed_rEsK]^a`¤`crG¹aqob\W`<rE¬Wd_7bºE¤
`cbqo\Y7\_s²serEqeseb\v*7vvtcqWo®Kb§*x ~ x'wvrvqeseb
7ot7 q7À`cvr²tcrEr.b®or.t2b§^»^vq¤¨+\¿b\׸b_wyW¯C±w ~ b\_r
`cvrx ~ x×serE7§^¨+b`c`cvr.7d_^c7Ô[~ [+K*d_^b\v2`cvr^dvt
®Kb®oqot^!q7`cvr*`ctcr.b§^Zq7<½'=l²vtcrTÓ_`cr.tZb§^Z\vrErE^c^c7tc
`cqr.bZb\_¤`cr`cvr²7\W`cb].7d_^c7[
~
[Zb\ª¯
z
±wRvr.tcrqotcrol
¨,r*b\W`ctcqesed_r2`cvr»qotc¨7ts¶Ó_`cr.tq7G`cvrk3k ~ f] <'f
vtcbqot#`cq3½'=wj\_r`cvr2[ ~ [=_7\v\vr.CrEqoZrE^!.7d_^c7Tl
serEqeseb\vq7%`cvr2i,kæqeserb§^#seqo\vr<¹aqob\W`c3¨+b`cY`cvr
r.rEse_o»Ó_`cr.tq7'`cvr!k3k
~
f] <'f¿K*d_^b\v`cvr#`cr.\e
`¤`cb®orÀserEb§^bqo\_^qodv\_s2qo\2`cvrÀ^dvtc®Kb®oqot^q7`cvr<½'=wK[]\
`cvb§^G¨olW`cvr=½'RqoCr.t¤`crE^qo\*`cvrÀ`ctcr.b§^+q7¸`cvr=i,k
^cvr.ZrolbtctcrE^CrE`cb®or.²q7+`cvr*_7\v\vr.,r.\v7`c7\_smq7
`cvr=qo\_^a`cr.§¤`cbqo\^bº.row
Ç°ÆCÇ
31 Ê_¢
)
£e¢¤Ë ¡ ¢
[]\=qotser.tL`cq<qoZvde`cr`cvr,k3k ~ f] <'fqotc¨7tsÓ_`cr.t
¨+b`c¶b\vrE7t#qoZvr©eb`ab\²`cvr_7\v\vr.r.\v7`c¶ãA7\_s
b\²`cvr2+h
~
+uGiAvqe²^bº.r ml¨,rZde`cbbº.r`cvrvqe
qotc!dv§¤`cbqo\Ä_o^rEsqo\¿i%vqorE^KY°o`cqotcbºE¤`cbqo\q7Ïp¤Ñ w
vqotZ7\K¶q7G`cvrTT`cÄvqee^.l¨,r»tcr.¨+tcb`crY¯z ±=b\Ävqe
qotcÜo^
ñ
ù
¯} ±
¨+vr.tcr
ù ñ ¯ú
ü
áâ í.þ.þ.þ.íú
ÿ
±a÷%l
ñ ¯A ü
áâ í.þ.þ.þ.í
A ÿ
±a÷%l
êÄë
ì
¯,+í ÿ ±+7\_s b§^ ´ö ´^c¬Wd_7tcr=ÔqKr.vb`cº
¤`ctcb©¨+vr.tcr»Ï
Ñ
# B# - D ñ H D
wGvri%vqorE^K2°o`cqotcbºE¤
`cbqo\ob®orE^
ÿ È Äñ 5
ò
5 ¯TÛo±
¨+vr.tcr 5 b§^7\dvvCr.t`ctcb§7\vodv§7t=¨+b`cÄdv\vb`seb§7oqo\_7
¯°.7d_^c7C7\_sZqo\vb§E±7\_s
ñ seb§7C¯
ü
áâ í.þ.þ.þ.í
ÿ
±b§^,
seb§7oqo\_7W¤`ctcb©=¨+b`cCqW^b`cb®or,tcrE7Kseb§7oqo\_7Wr.r.Zr.\W`^.w
vrGr.rEse_o=Ó_`cr.t,¤`ctcb©b§^%rE¬Wd_7e`cq 5 ó È
lW¨+vb§b§^
^a`ctcb§`c¶.7d_^c7Tw
~
Kdvt!7oqotcb`cvµqoZvde`crE^#`cvb§^=°o
`cqotcbºE¤`cbqo\¨+b`cZb\vrE7tqoZvr©eb`a=b\ã¶7\_s åKqo\e
^b§ser.tcb\v¶`cvr3_7\_serEs«ÔqKr.vb`cº²^a`ctcd_`cdvtcrq7 ¨+vr.tcr
rEoÎtcq¤¨q7Àqo\W`7b\_^¤`ZZqW^a` n ã ó y\vqo\eº.r.tcq²r.r
Zr.\W`^.wvr=k3k
~
f] <'fÄqotc¨7tsÓ_`cr.tGb§^ob®or.\*K
ñ áâ
5
áò
¯| ±
vrqode`cvde`=q7%`cvb§^ÀÓ_`cr.t!.7\YCrqoe`7b\vrEs²r42br.\W`c
KÄ7vvKb\v¶_oW]^dv_^a`cb`cde`cbqo\Ä`cq
lKbr.§seb\v¶b\vrE7t
qoZvr©eb`a2b\ã«7\_smw
Ç Ç ¢ 143 ÌÔ¢ é Íé Ê_¢
¢¤Ê¥
E EÍ É
r`
#
CrG`cvrÀ^rE¬Wdvr.\_rq7Ô^K!Cqot¤`cr^c7ZvrE^%qoe
`7b\vrEs#¤Ý`cr.tLqotc¨7tsGÓ_`cr.tcb\v7\_sÀser.b\W`cr.tcrE®Kb\v_wÔ dvr
`cvr#serEb§^bqo\eTr.rEse_o^rE`cbqo\*q7`cvrÀrE¬Wd_7bº.r.t.7\*Cr
qodv\_sZqo\`cvr^dvtc®Kb®oqot^¸q7LÀ½'×o`cb\v#qo\`cvrGqotcbob\_7
i,k´`ctcr.b§^¯bTwrowlC¨+b`cvqode`#^a`¤`cr=r©e_7\_^bqo\±wGr.\_rol
`cvrvt7\_²Zr`ctcb§Z¤`À`cvr T`c²`ctcr.b§^#^a`cr.Yr©K`cr.\_seb\v
tcqoÜ^a`¤`cr #b§^ob®or.\*b\*`cvrÀqotc
! #
¯"oíú± ñ ###### #
ó$ y ó y
ô&%
ú ó à('
') (
â+*
ô B ),
ú # á ).-
¯"±
######ý
¯ä7±
¨+vr.tcrGõ ñ {;olKã0/ ñ Zb\Ô¯°ãGíõÔ±lWú»b§^`cvr<qo\_^a`cr.§¤
`cbqo\»^K!Cqo_§7Cr.b\v=`cvrG`ctcr.b§^%vt7\_l
,
ú ô á ).-
¯"±7tcr
`cvrZ`cr.\W`¤`cb®orserEb§^bqo\_^<qodv\_sYqo\²`cvr2^dvtc®Kb®Kb\v*_¤`c
`cr.tcZb\_¤`cb\vmb\¿^a`¤`cr1ol+7\_sR¯
* ô Bâ í.þ.þ.þí
* ô Bà
±7tcr*`cvr
qKr42br.\W`^q7Ô`cvr=k3k ~ f] <'fÄr.rEse_oZÓ_`cr.tG¨+vr.tcr
* ô B) ñ Ï5 Ñü áâá
ô Bü
áâá ô - D w
vr%vtcqoCqW^rEsÀ^cvr.Zr%b§^Zq7`cb®¤¤`crEs#K`cvrqoq¤¨+b\v
tcrE^dv`E
¢¤Ê32%ÊC EÍ¡EÍ°Ê É²ÆCÇ
gG\_ser.t'ïÀ7d_^c^b§7\<t7\_seqoAqeseb\vG7\_s
b\2`cvr<bZb`qot{5476¯b\eÓ_\vb`crÀb\W`cr.tcrE®Kb\v!ser.e`cC±l
qotob®or.\×_7\v\vr.<tcrE7bºE¤`cbqo\A
H )
Wl+`cvr²vtcqoCqW^rEs
¹aqob\W`GrE¬Wd_7bºE¤`cbqo\7\_sserEqeseb\v2^cvr.Zr#ovbr.®orE^,`cvr
b\eqotc¤`cbqo\*t¤`cr
8 ñ:9 â<;cý
áâ<;cý
qo
ý $ y>=
ÿ@?
¯"AL±
%
P.A ¯?W±
¨+vr.tcr
?
¯"AL±CBñ J ) H )D
á # ýE
)GF
w H
vr%b\eqotc¤`cbqo\#t¤`cr08b\»¯?W±Lb§^`cvr%¤©eb!dvRovbr.®W
7vr+t¤`crqot`cvrG[
~
[_7\v\vr.¯
z
±'dv\_ser.t`cvrqo\_^a`ct7b\W`
`c_¤``cvrmb\vvde`3^bo\_7À_o^qo\_^a`7\W`Cq¤¨,r.t^CrE`ct7
ser.\_^b`a»rE¬Wd_7`cq
= w
^,°7to^%`cvrÀovbr.®¤7vrÀseb®or.t^b`aZb§^qo\_r.tc\vrEsLlW¨,r
_®or<`cvrÀqoq¤¨+b\vtcrE^dv`E
¢¤Ê32%ÊC EÍ¡EÍ°Ê
É Ç
gG\_ser.t'ïÀ7d_^c^b§7\<t7\_seqoAqeseb\vG7\_s
b\`cvrGbZb`%qot {54I6¿l7`cvr<qo\_.¤`cr.\_¤`crEsZi,k9+h
~ +uGi´^cvr.Zr«ovbr.®orE^²¤©eb!dv&seb®or.t^b`a ]ãKJel
¨+vr.tcr²ãKJ¶b§^Z`cvr²\Kdv!Cr.t»q7#^r._7t7vr_¤`c_^2q7À`cvr
dv\_ser.tcKb\vZvKe^b§.7_7\v\vr.Tw H
¦Yr_o^a`cr.\Ä`cqm^cm`c_¤`2xtcqoCqW^b`cbqo\
n
seqKrE^Z\vq7`b
vÁb\Ror.\vr.t7<`c_¤``cvrmvtcqoCqW^rEsA^cvr.ZrYqot3ÄÓv
\vb`cr2vto`cb§.7'®¤7dvrq7{´7\_sYob®or.\¶i,k0^cvr.Zr
q¤®or.t^qoZrseb§^ctcr`cr*7v_7Cr`ovbr.®orE^=¤©eb!dv³seb
®or.t^b`aow»gG\eqot`cdv\_¤`cr.olÔ`cvr27\_7e^b§^Àq7,`cvr»x
~
xRser
qeseb\v!`crEv\vb§¬Wdvrqot,Ó_\vb`cr {Ãb§^,®or.tcZ_7tsLlKb¸\vq7`b
CqW^c^bvrow'Gr.®or.t`cvr.rE^c^.loqodvt\KdvZr.tcb§.7etcrE^dv`^ser.Zqo\e
^a`ct¤`cr=`c_¤`El^qoZr.¨+_¤`À^dvtcvtcb§^b\voolCb\Y7'.o^rE^<qo\e
^b§ser.tcrEs²b`=b§^=^d2br.\W`À`cq3vqKqW^r;{µrE¬Wd_7'`cq^7
b\W`cr.or.t<b\Yqotser.t`cq»qoe`7b\Y2t7Zrr.tctcqotGt¤`cr¯°'f%h±
dvtc®or3¨+b`c×vboe~ hÂCr._®KbqotLZ¯ ~ h
á
ü&%
àM
±lGbTwrowl
¨+b`c¤©eb!dvÜseb®or.t^b`aow
N Ç ¢¤£T7
¢¢¤Ê_¢ î £e¡
É £
EÍ°
[]\`cvb§^^rE`cbqo\lv¨,r#vtcq¤®Kb§ser<`a¨,q27vvtcq©eb¤`cbqo\_^%`cq
'f%hÙq7`cvrvtcqoCqW^rEs3+h~ +uGii,k ^cvr.ZrZ¨+b`c
vr._^Ô`cvrx ~ x3serEqeser.t¸KÀtcr.Zq¤®Kb\v^qoZr%[ ~ [w¤r`¸`cvr
serEqeser.tGb\vvde`¤Ý`cr.tGor.\vbr]7b§serEs»b\W`cr.tr.tcr.\_rÀtcr.Zq¤®¤7
Cr#Zqeser.rEs*K
#
ñ ú #
# ¯p ±
¨+vr.tcr*ð2Ï
< # <ý Ñ<ñ yolð2Ï
<ú # <ý Ñ<ñ
=
7\_sm¨+vr.tcr = b§^
`cvr+^bo\_7o`cq<b\W`cr.tr.tcr.\_r,vd_^¸\vqob§^r,t¤`cbq¯~ [ah±w7¦Yr
7or,<ïÀ7d_^c^b§7\=7vvtcq©eb¤`cbqo\#q7e`cvr,tcrE^b§sed_7Wb\W`cr.t
r.tcr.\_rvd_^%\vqob§^r
#
7\_s¨,rd_^r+`cvr<dv\vbqo\2Cqodv\_sZ`cq
`cvr='f%hAq7Ô`cvr=i,k´^cvr.Zrow'¦YrÀÓ_\_s¶Ïy {¤Ñ
«fZb\yoí
'
= P ý
n
¯ay { ±
¨+vr.tcr!Üser.\vq7`crE^Ô`cvr,t7Zr,r.\v7`cb\!`ctcr.b§^'^a`cr._^'7\_s
b§^À`cvr»®or.t7or\Kdv!Cr.t=q7#"%$'&)(+*,=r.tctcqotÀr.®or.\W`^=¤`
^c¬Wd_7tcrEs*fd_b§serE7\seb§^a`7\_r P_w
£e¡E¥
Ë Í¡ ¢ 5ÊCÌ
É
Ë- 5.
[¨,r+o^c^dvZr%`c_¤``cvror.\vbrtcr.Zq¤®orE^¸7e[~ [l`cvr.\ ²ñ
H ÿ
l7\_s»`cvrïÀ7d_^c^b§7\7vvtcq©eb¤`cbqo\*qo\/
#
b§^Gr©vo`Ew
vb§^b§^G`cvr^q7].7rEs*¤`vrEsKTÓ_`cr.tCqodv\_sLw[`<b§^\vq7`
7\*r©vo`+q¤¨,r.t,Cqodv\_s^b\_rÀb\¶¯ay
{
±%¨,rÀd_^r<`cvrÀdv\vbqo\
Cqodv\_sY¯°7\»dvvCr.tCqodv\_s2q7¸!q¤¨,r.t%Cqodv\_s»Kbr.§sv^Ô¹ad_^a`
7\¿7vvtcq©eb¤`cbqo\C±w¿Gq¤¨,r.®or.tElr©K`cr.\_^b®or3^b!dv§¤`cbqo\
tcrE^dv`^Gb\_seb§.¤`cr=`c_¤`G`cvrk3'uAKbr.§sv^7¨e^Gq¤¨,r.t
Cqodv\_s»`cqZ`cvr='f%h#w
KÉ
Í 1 »Í°Ë
Ë 31 5ÊCÌ
É
Ë- 5.
['¨,r#o^c^dvZr`c_¤``cvr#or.\vbrÀvtcq¤®Kb§serE^%r©vo`GserEb§^bqo\_^
qo\rEo^dvtc®Kb®oqot#¯bTwrowl_`cvr=k3k ~ f] <'f«¨,qotce^dv\_ser.t
`cvr#b§serE7Lr.rEse_o»o^c^dvZe`cbqo\C±lK`cvr.\
²ñ r©e0 9
â<;cý
áâ<;cý
\ $ y>=
ÿ@?
¯"AL±
%
P.A
ó yoþ ¯ayoy±
¨+vr.tcr
?
¯"AL±¨o^¸serÓ_\vrEs=CrqotcrowÔ[]\=`cvb§^.o^rol¤^b\_r%`cvr
`cr.tc1
# b\Á¯p ±=qo\W`7b\_^=Cq7`c\vqob§^r»7\_s7\W`cb].7d_^c7
[ ~ [l7`cvr<ïÀ7d_^c^b§7\ZGvvtcq©eb¤`cbqo\b§^\vq7`r©vo`EwYzdvb`cr
^dvtcvtcb§^b\voolÔ^b!dv§¤`cbqo\_^#^vq¤¨ª`c_¤`#`cvb§^=7vvtcq©eb¤
`cbqo\«b§^Z®or.tcm`cboW`27\_sÎvtcrEseb§`^Z®or.tcÄo.dvt¤`cr.¶`cvr
'f%h¼Cr.tqotc7\_r3q7!qodvt^cvr.Zr²¨+b`cAo`cd_7Àx ~ x
¯bTwrowlv¨+b`cvqode`Gb§serE7ÔserEb§^bqo\»r.rEse_ov±w
2 Ç ç Ì&7
¢¤Í°¥o£
î
EÌ
¡E
[]\qotser.t#`cq3r.®¤7d_¤`cr2`cvr2Cr.tqotc7\_r2q7`cvr»vtcq7
CqW^rEs^e^a`cr.lW^b!dv§¤`cbqo\_^¨,r.tcr+Cr.tqotcZrEsb\Z`cvr+qo
q¤¨+b\v2qo\_seb`cbqo\_^.w%¨,q[~ [_7\v\vr.Zqeser.§^G7tcr=qo\e
^b§ser.tcrEsL*Y^K!Cqo]^_orEs<_¤`cÎ_7\v\vr.¨+b`cÄ`cvr
rE¬Wd_7,^a`ctcr.\v7`cm_¤`c_^!7\_sY`cvr»CrEserE^a`ctcb§7\m_7\v\vr.,u
Ïyoy Ñ qot²`cvr¿+ G ~ i, <k3 z ï¾^a`7\_sv7tsÃÏy nÑw0vr
gG\vor.tcCqKrEi,k qeserE^7tcr=d_^rEsqotÀseb·r.tcr.\W`<ZqesK
dv§¤`cbqo\»^q!o^'`cq!bZvr.Zr.\W`osv7e`cb®orGZqesedv§¤`cbqo\rEo^a
bow<u,*bo\vqotcb\v`cvr!qW^c^sedvr=`cq2º.r.tcq7_osvseb\v_l+3
b§^serÓ_\vrEs3o^43 Bñ
ü&%65
ü7 ñ
68:9<;>=
ü7
¨+vr.tcr=¨,r=d_^rEs
ð8
~ ñ
68:9
=
w!¸b_wn qoZ_7tcrE^qodvt<vtcqoCqW^rEs3^e^a
`cr.³¨+b`cÄq7`cvr.tZ^cvr.ZrE^=qot ñ9n Ïvb`Ťwd_^r Ñw¶¦Yr
^Cqo\_seb\v«qode`7orYvtcqo_7vbb`a¿b§^^vq¤¨+\×qot3qoZ_7t
b§^qo\w ~ bZb§7t»Cr.tqotc7\_rb§^»qoe`7b\vrEs«KÄ`cvr ~ ,
u,[ci,k¾^cvr.ZrE^Àq7#Ïn l |¤Ñ 7\_s²`cvr`ctcr.b§^ ~ iÙ^cvr.Zr
q7ZÏÛ Ñ ¨+b`cÎvbovr.tqoZvr©eb`aowÎu,q7`c`cvrE^r^cvr.ZrE^
d_^r*7\mb`cr.t¤`cb®or»^_orT`cbZr`cdvtcCq3rE¬Wd_7bº.r.tqo\_^b§^a`
b\vGq7K`a¨,qG^q7Ý`b\vvde`¸^q7Ý`qode`cvde`¸k3x3serEqeser.t^.w'j\vr
qot=`cvr»[ ~ [#_7\v\vr.%¨+b`c?¤ly | <^a`¤`crE^Àqot*ÏnÑl,ÏÛel |¤Ñ
7\_s¿7\vq7`cvr.tZqot`cvr`ctcr.b§^»qeser¯ay | l zWn ]^a`¤`crE^qot
Ïn lÛ
Ñ
lÔÏ
|¤Ñ
tcrE^CrE`cb®or.v±w+vr!qoZvr©eb`a»q7uGi,ÞWh7
oqotcb`cvªb§^tcqodvovÀ`a¨+b§r+o^'vboo^<½b`cr.tcvb_serEqeser.t
7\_sÛ`cdvtcCq#b`cr.t¤`cbqo\_^7tcrCr.tqotcZrEsLw'vr.tcrqotcrol7qodvt
^cvr.ZrG¨+b`cZ`cvr |7} ]^a`¤`cr+i,kÂqode`cCr.tqotc^'`cvrb`cr.t
¤`cb®or#^cvr.ZrE^¨+b`c*°7t+rE^c^+qoZvr©eb`aow
¸b_wz ^vq¤¨G^#`cvr*Cr.tqotc7\_r2q7Gqodvtx ~ xÙ^cvr.Zr
qoZ_7tcrEs`cqÚ`cvrqode`7orAvtcqo_7vbb`aqot×seb·r.tcr.\W`
Zqesedv§¤`cbqo\!^cvr.ZrE^q¤®or.t } _¤`c#[~ [_7\v\vr.7qot ñ
n w }
]^a`¤`crZgG\vor.tcCqKrEi,k b§^Àd_^rEsLw¨,q7vvtcq©eb
¤`cr+Cqodv\_sv^o^'¨,r.vo^'`cvrG^b!dv§¤`cbqo\tcrE^dv`^'q7Lx ~ x
7\_s×or.\vbr]7b§serEsK]ser`crE`cqot2¨+b`cÁCr.trE`*r.rEse_o¿o^a
^dvZe`cbqo\Á7tcr3vtcq¤®Kb§serEsLwvrYx ~ xvq7`^»7tcrqodv\_s
Cr`a¨,r.r.\¶`cvr*k3'uÚ7\_sY`cvrïÀuÚ7\_sY`cvr.¶qob\_b§ser
¨+b`c`cvror.\vbr]7b§serEsK]ser`crE`cqot¸vq7`^.w'vb§^¸ZrE7\_^¸`c_¤`
¨+b`cÄ7\mb\W`cr.tcrE®or.t=ser.e`c{ ñÃ} `cvr*serEb§^bqo\Ytcqo
^dvtc®Kb®oqot^Zb§^*^d2br.\W`cÎtcr.b§7vr²^qm`c_¤`x ~ xqodv§s
r.bZb\_¤`crCr.trE`c`cvr[~ [wW¦Yr<.7\qo_^r.tc®orG7§^q#`c_¤`
qot'7\K<Zqesedv§¤`cbqo\#`cvr,W7#Cr`a¨,r.r.\#`cvr,qode`7orvtcqoe
7vbb`a7\_s¶`cvrx ~ xªvq7`^!tcr.7b\_^qo\_^a`7\W`El¨+vb§
^vq¤¨G^`cvr<qoe`cb7b`aZq7qodvt,+h ~ +uGiÎi,k^cvr.Zr
¨+b`cZ`a¨,qÀ`ct7\_^Zb`%7\W`cr.\v\_o^'b\Z`cvr^r.\_^rq7<`ctoser.q7·
Cr`a¨,r.r.\seb®or.t^b`a27\_s*!dv`cbvr©eb\vÏy
z¤Ñ
w
¸b\_7olK¸b_w} ^vq¤¨G^ ñ¿} 7\W`cr.\v\_#^e^a`cr.Ùq¤®or.t
`cvr#CrEserE^a`ctcb§7\_7\v\vr.u<w_Ôqqo\_^a`ctcd_`GZ+h ~ +uGi
7tctol+¨,r²qo\_.¤`cr.\_¤`crEsy
|
]^a`¤`cr²gG\vor.tcCqKrE«i,k
7\_sm`cvr*t¤`crz Å } ï=j< ´Ï?ví } í |¤Ñ Ïy }7Ñ w¶f®or.\qo\Î3tcr
7b§^a`cb§*_7\v\vr.Zqeser.+¨+vr.tcr»`cvr\Kdv!Cr.tZq7<^r._7t¤
vr_¤`cmãKJ»b§^=^7r.t<`c_7\Y`cvr\Kdv!Cr.t#q7vKe^b§.7
_¤`c_^.l¤`cvr+x ~ x²_o^'7ZqW^a`Ô`cvr+^c7Zr^qoCr+o^`cvrqode`
7or=vtcqo_7vbb`a*¤`vbo?3
lC¨+vb§3^vq¤¨G^`c_¤``cvr
¤©eb!dv seb®or.t^b`a¶q7 ãKJ²b§^Zovbr.®orEsLwÄGq¤¨,r.®or.tEl
dv\vbor!`cvrtcrE^dv`<b\Y¸b_wz lC`cvrZW73Cr`a¨,r.r.\`cvrqode`
7or<vtcqo_7vbb`a27\_s»x ~ xÄb\_tcrEo^rE^o^qo\_^a`cr.§¤`cbqo\
CrEqoZrE^§7tcor.tEw¸vb§^°o`b§^¨,r.K\vq¤¨+\Z7\_sb`%b§^%sedvr
`cqZ`cvr#\vqo\eqoe`cb7b`aq7ï=j< <^qot NA@
n Ïy z¤Ñ
w
B Ç Ê É ¥ ̸ EÍ°Ê
É
[]\¿`cvb§^»_7Cr.tElG¨,r3vtcqoCqW^rEs¿qo\_.¤`cr.\_¤`crEs¿+h
~ +uGiªi,k¾^cvr.ZrZqot=^b\vor].7tctcbr.t<tcrE¬Wdvr.\_Y^r
rE`cb®or°oseb\v_7\v\vr.Tw¸_7\ve^L`cq'¹aqob\W`ÔrE¬Wd_7bºE¤`cbqo\
7\_sÄserEqeseb\v¶7vvtcqWol'qodvtZ^cvr.Zrovbr.®orE^=!d_
q¤¨,r.tqoZvr©eb`a»¨+b`c²^bZb§7tŤ^dvCr.tcbqotCr.tqotc7\_r
`c_7\»q7`cvr.t%vtcqoCqW^rEs2^cvr.ZrE^¨+b`c2`cvrÀ^c7Zr<^CrE`ct7
r42br.\_ow^G7\7vvb§.¤`cbqo\*q7'qodvtG+h~ +uGi¿i,k
^cvr.Zrole¨,rÀ.7\»r.\K®Kb§^c7or<k[~ jseq¤¨+\»b\v»^cr.\_7tcbq
^d_¶o^#+ G~ i, <k3=w¸vb§^#^e^a`cr.¼b§^#_o^rEs²qo\¶^q7`
`crEs׬Wd_o^b]^K\_vtcqo\vqod_^2i, <k3¤`²yown ?mk3vbŤ^3¯ê
6 7 8 9 10 11 12 13 14 15 16 10 −4
10 −3 10 −2 10 −1 10 0
SNR[dB]
FER
Outage probability TR−STBC with 16−state TCM
2[bit/Hz/sec]
Zhou−Giannakis, Liu−Fitz−Takeshita
TR−STBC with 64−state TCM
block size = 256[info.bits]
2Tx antenna systems over 2−path ISI channel
16 state, # iter = 5
RTSUV[\!ca9b,Sg,\FS,h c\!b,ij]\!cZi g,]_hicig
0 4 8 12 16 20 24
10 −5 10 −4 10 −3 10 −2 10 −1 10 0
FER
SNR[dB]
128[symbol/block]
2Tx antenna TR−STBC over 4−path ISI channel
Macthed Filter Bound Genie−aided−detector PSP(D=4)
QPSK 8PSK
analysis
simulation 32cross
Outage Probablity
16QAM
4state−Ungerboeck TCM
Genie−Aided Bound
RTSUVo[\!ca9b,Sg,\FS,h \!f_a9U!ib,\aSZS
n k3Gº_7\_se¨+b§sK`cC±w!Ú^q7`#^a`ctcd_`cdvtcr¯| ä7Û^±b§^Gqo
q¤¨+b\v_Ô`a¨,q=vqee^q7 z Û n vb_^,7tcr^r._7t¤`crEsZK*y }o}
vb_^ÀZb§sv7!vrqot#_7\v\vr.rE^a`cb¤`cbqo\w,`#`cvrZr.\_s
q7`cvr^rEqo\_svqel'y
|
vb_^<q7%od_7tsb\W`cr.tc®¤7¯Tï<[±
7tcrosvserEs=qot^q7`^r._7t¤`cbqo\w¦¿b`cy n ?vb_^'vd_^y |
vb_^<q7,ï<[!¯Ý`cq7`7y }o} vb_^±+¨,rZ.7\3rE^a`cb¤`crrEo^b
} _7\v\vr.§^q7<r.\v7`cAy | vb_^b\Î`cvr*tcrE¬Wdvr.\_Äseq7
7b\l_d_^b\v7\''Aq7'r.\v7`c¶y n ?vwvqotGr©v7Zvrole¨,r
.7\×7vvÄt¤`crz Å } +h ~ +uGiqot } 7\W`cr.\v\_o^¨+b`c
?¤]x ~y i,kqeserowg^b\v ñ ä | l%ã ó y ñ y | l
7\_s
69 ñ³n l,`cvr²tcrE^dv`cb\v^CrE`ct7r42br.\_Îb§^.
~ ñ r
69 ñ yoþ{ Û | Ïvb`Ťvb Ñw<vb§^Kbr.§sv^!yoþn ?
kŤ^Gqo\32^b\vor!.7tctcbr.tEw+j\`cvtcr.r!.7tctcbr.t^#¯rE¬Wdvb®¤¤
r.\W`%`cq=`cvr#Û#k3GºÀfdvtcqoCrE7\gk3 ~ ±lK¨,rqoe`7b\ z þ? }
kŤ^.l7¨,r.vCr.oqo\_s=`cvr`7tcor`'q7 n kŤ^.wÔ¦YrG.7\Zqo\e
d_ser`c_¤`¸qodvtÔ+h ~ +uGi²i,kÃ^cvr.Zr%.7\#Cr,+oqKqes
0 4 8 12 16 20
10 −5 10 −4 10 −3 10 −2 10 −1 10 0
FER
SNR[dB]
114 [symbol/block]
4Tx antennaTR−STBC over Pedestrian channel
PSP(D=6)
QPSK 8PSK
32cross
Outage Probability
16QAM
16state−Ungerboeck TCM
3.8dB 4.2dB 5dB 5.4dB
RTSUV,b_ag,cSFa,i !ag" g",ic \$#4ib&%Ti`ig",b,Sa ]_ha!iZ
î ¢ KÉ
¥
'
W(*)FV+ V,a9b,g,g,\.-/%TV0,\!S] a-1)FV, S`g,^!\!U!-ma`32V, S4-6507a9]i8
,Sci9Z\>]_^ ]\>`SUmd\!bTdb,i :>fi ]78g,iZi],S#4iF]_ha!iZg$-;=<?>@ A
BDCE4EFGEHI"JKJKJMLN"OPQ RSHPUTVCN"F$WF$QQXYHBDBDP
>
PZR -Z[F\$#4ic8
ib&\\ V
'
(]0 V^ h\!fpa`3+ VX&V+&Sa!a9^>Sg$-_50>SU!Zi8] a9b,b,Sibg`a9]i84,Sci
Z\>]_^]\>`i`a,b_ag,cSg,g,S\g\$#4ibFdb,i :>fi ]78g,Zi],S#4iYda9`SU
]_ha!iZg$-;
I"JKJKJbLN"OPQ RYHPaIPcHNBR/LedFHNf
-#4\!ZV!g-! V
W$hi Wjg-Z24a>fa9b"V\\!o V
'
o(lkYV)Zm+ja9ca9Z4-on VpmVk&a9cc\g$-UqV, Sf.-orqV%TVRTS`s- a`
t VqVuFa9^!ig,hS_a-&5 t v,him`ig,SU\9dg`a9]i84,Scija`g`a9]i8
db,i :>fi ]d\!b[cSc\&db,i :>fi ]g,iZi],S#4i&da9`SUY]_ha!iZg$-;
<?>@
BDCE4EFGEHI"JKJKJMLN"OPQ ReIPcH7R&LedFHNf
-n/b,SZ.\\ W!V
'
(xw V[h\!S&a`y2VrqV[S\za-{5rfZ,SZi S!f|$cfZ,SZi\!f"8
f$}cSc\7~Ti :>fa9ZSs a,S\ d\!b g`a9]i84,Sci/Z\>]_^]\>`SU!-; CP
N"H$RI"JKJKJ
O$CKCB XYHPc RXYHBDB
>
PZRXYHB/
>
EF$NQ
OP?G
< C7R
N"H$R
-! V oWi o!-W$ggg V
'
(xqV, Sf.-rqV%TVRTS`s- a`
t VqVuFa9^!ig,hS_a-507a9]i84,SciY]\>`ig
ibd\!b,ca]i ]b,S,ib,Sa a``ig,SU d\!bdb,i :>fi ] g,iZi],S#4i
da9`SUm]_ha!iZg$-;
IXX1
N"H$FFGCP
-#4\!ZV7g-! V\\$i
\!-?\\ W!V
'
h(*n Vt VX[ib",hi$-pmVjSg,\s-a`b2V2VX[\!f,b,\!g$-507a9]i84,Sci
X"9r]#4ib,g,fg6g`a9]i84,Sci,b,iZZSg ]\>`i;d\!brar t Z\>]_^
da9`SU cfZ,Sa,hnewy+[]_ha!iZ4-;
N"H$RCPIL/TV
-
r a9b,]_hV\\!o V
'
j$(]+ VS&U!ib` \>i]_^?-y5`ub,iZZSg"8]\>`i`qc\>`fZa,S\FS,hqb,i`f!8
`aYg,SUa9ZTg,i,g V.,b,\>`f],S\.-;
I"JKJKJXYHBDB
>
PZRO7R
-
#4\!ZV
-\V-! V i W!W- W$gj>V
'
(xVuTa9b,\!^>h.-!kYV24a$da9b,^>haS4-a`n VpmV a9Z`ib`a^?-/507a9]i8
,Sci9Z\>]_^]\>`ig[db,\!c@\!b",h\!U!\a9Z `ig,SUg$-;
I"JKJKJLN"OPQ R
HPIPcHNBRDLedFHNf -S#4\!ZV
-Y\V
-Y! V[W
h$i W hj7-92!fZ
W$ggg V
'
g(]+ V V ma9Zih.-5[ha!iZi :>fa9ZSs a,S\ d\!bSZ\>]_^1,b_ag,cSg,g,S\
g" g",icg$-;
I"JKJKJo¡!R
<
F$WF$ER¢/N"FOQVXYHBDB
>
PZR
-?#4\!ZVTW o-Z\V
W-!! V W!W$\$i W$ W-.24a>fa9b"6W$gg
V
'
W$\(=+ V a9Sb,i a`£+ V[\!Za #4\!Z i-¤5 t g`a9]i84,Sci6]\>`SU d\!b
:>fa9g,S8g"_a,S][cfZ,SZi8Ca,i !a&]_ha!iZg$-;
I"JKJKJ£LN"OPQ RZHP
IPcHNBRKLedFHNf
-#4\!ZVg-\Vh-! VW \\$i W W$h-!2!f!i\\!o V
'
W!W(Vu&-35pi]!Vu&8p&r}W$
-&+&fS`iZSigd\!bi#!a9Zfa,S\ \9d
b_a9`S\,b_ag,cSg,g,S\,i]_h!\!Z\!U!SigFd\!brau98\\\-; W$ggj>V
'
W$(=Kwyu/0?-M5`%h g,S] a9Zj]_ha!iZg a`ca!SUq\9d1,b_ag` \!b"
]_ha!iZgj\,\vh g,S] a9Z]_ha!iZg$-;¥#4\!ZVu/0a&W$\mo V\ V\ V-
W$ggg V
'W o(V,V^ hi U2a`U¦ V[YV&Vug,i-§5¦&S#4ib,g,S a`cfZ,SZi SU!
n df!`a9ci _a9Z/,b_a9`i\¨ S cfZ,SZi8Ca,i !aq]_ha!iZg$-;
I"JKJKJ£LN"OPQ RZHPIPcHNBRKLedFHNf
-#4\!ZVg-\V
-! V W$\j9o$i
W$\gh-?r a V\\!o V
'
W (V©&fi8CX[S§, SaU!-ª5 t b",h\!U!\a9Z `ig,SUgyFS,h ca Sca9Z
b_a,ig$-; Q
>@
BDCE4EFGvEHI"JKJKJbLN"OPQ RYHPaIPcHNBR/LedFHNf
V