HAL Id: inria-00072697
https://hal.inria.fr/inria-00072697
Submitted on 24 May 2006
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub-
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non,
Continuous Management of Modes and Resources in Detection of a Moving Target
Frédéric Dambreville, Jean-Pierre Le Cadre
To cite this version:
Frédéric Dambreville, Jean-Pierre Le Cadre. Continuous Management of Modes and Resources in Detection of a Moving Target. [Research Report] RR-3952, INRIA. 2000. �inria-00072697�
ISRN INRIA/RR--3952--FR+ENG
a p p o r t
d e r e c h e r c h e
INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE
Continuous Management of Modes and Resources in Detection of a Moving Target
Frédéric Dambreville, Jean-Pierre Le Cadre
N˚3952
Juin 2000
THÈME 3
( &!$)!*,+-."%&
/103254%26087:9<;>=@?-A%03B6CD7FE:EFBHGJI@BK=HL!MN.7FB60803B<OBQP=@408B
RTSVUXW<Y#Z[]\_^a`YXbdcKeX`gfihK^jSVhKWkW<Y8lmWncKedSofp^VYrq
fpWnc5stYvuwqDxohK^o^VyvYvuwqVevhK^o^Dc5fiuudc5^VevYvu
zbh5{gYX`|}fiug`dc
~}c5ohKbg`xoYbYvedSVYXbeSVY^aZrrr [tofp^rrr[Zr>Dc5stYvu
Q&vw6otr
RTSofiukDc5YXb<xoYwc5iu<.fp`gShKo`gfpWkfpc5`gfihK^h5}xfp@fiugfpoiY-bYvuhKobevYvuQc5fpW<Yvx`h
`gSVY}xoYX`YveX`gfihK^-h5cW<hHfp^os`dc5bgstYX` ¡hKpih.fp^os>c¢£c5bg¤thHf¥c5^¦W<hwtYXW<YX^H`hKbTc#evhK^Vxfp`gfihK^Dc5pp§
xoYX`YXbgWkfp^ofiu`gfie>W<hK`gfihK^1¨©ªob«hKbg¤£Y8¬@`YX^Vxou bhw.^1®¯uuDc5`gf¥c5°hKo`gfpWkfpc5`gfihK^±W<YX`gSVhHxJ¨ §
VudYh5cstYX^VYXbdc5pfpwYvx¦pfp^VYwc5b«¡hKbgWnc5pfiuW qH YªxoYXtYXihK²cW<YX`gSVh@xn¡hKb hKo`gfpWkfpvfp^os`gSVY}uYwc5bedS
Y8³JhKbg`uªhK`gS£ugDc5`gf¥c5pp§´c5^Vx´`YXWkhKbdc5pp§¶µFW<h@xoYXpfp^os¦bYvuhKobevY#bYX^VYXª·8q.fp`gS£Wnc5^Dc5stYXW<YX^a`
h5W#op`gfpoiY¸bYvudhKobevY`¹§@Yvu-hKb²W#op`gfºlmW<h@xoYvu²bYvuhKobevYvu¨¼»HVedS'hKo`gfpWkfpc5`gfihK^'fp^athKptYvu
c5iudh´`gSVYQ¡VugfihK^h5ªuYXtYXbdc5xoYX`YveX`gfihK^xoYX@fievYvuwqfp^hKbxoYXbk`h£Wnc5¤tY¦`gSVYXW½«hKbg¤±`hKstYX`gSVYXb
Y8¾neXfiYX^H`gp§t¨
¿ ÀtÁ%ÂÃÄ 6Å&r »@Ywc5bedS±`gSVYvhKbg§tq&ÆYX`YveX`gfihK^1q&©ªo`gfpWkfpc5`gfihK^1q&bYvuhKobevYnc5pih@ewc5`gfihK^1q°»@YX^VudhKb
Wnc5^Dc5stYXW<YX^H`
ǺÈ)É_ÊmËwÌÉ«Í)ÎpÊmÏÑÐvÒ
Unité de recherche INRIA Rennes
&!$)! ¼$& *«
Ybdc5o%hKbg``gbdc5fp`YkxoYm®¯hKo`gfpWkfiudc5`gfihK^±xoY>bYvuudhKobevYvuuyvewc5oiYvuc5oopfaVyvYvu
¥cxoyX`YveX`gfihK^xJ®o^VY eXfpoiY uhKoWkfiuY
o^W<hKotYXW<YX^a`Q¢c5bg¤thw@fiYX^hKevhK^Vxfp`gfihK^o^VYXpiY8l
W<YX^H`²xoyX`YXbgWkfp^ofiug`Yr¨ªhK`gbY´bYveSVYXbedSVY¸yX`YX^Vx ¥c W<yX`gSVh@xoYxJ®¯hKo`gfpWkfiudc5`gfihK^'ugDc5`gf¥c5iY£xoY
bh.^1¨^o`gfppfiudc5^H`no^ÑhKbgWnc5pfiugW<Y²pfp^Vywc5fpbY styX^VyXbdc5pfiuyrq ^VhKVuQcvthK^VuQxoyXtYXihKoy o^VY
W<yX`gSVh@xoYxJ®¯hKo`gfpWkfiudc5`gfihK^ `dc5^H`ugDc5`gf¥c5iYaVYª`YXWk%hKbYXpiY<µFW<hHxoyXpfiudc5`gfihK^ xoY}bYvuudhKobevYvuTbY8l
^VhKotYX¥c5oiYvu8·#xoYQm®¯Y8³JhKbg`xoYnbYveSVYXbeSVYrq cvtYve¦stYvug`gfihK^ xoYnopVufiYXobu`_§H%YvuxoYnbYvuudhKobevYvu
hK²xoYopVugfiYXobuTW<h@xoYvuxoYªÑhK^VeX`gfihK^o^VYXW<YX^a`w¨fp^VugfJuY}`gbhKotYX^H`fpWkopfaVyvuxoYª^VhKWobYX¬
xfiuhrugfp`gfºÑu.xoYxoyX`YveX`gfihK^H1®fp)Yvug`.^VyvevYvududc5fpbYxoY}mc5fpbYevhHhK%yXbYXbY8¾newcKevYXW<YX^H`w¨
Ä w  RTSVyvhKbgfiY xoY¥c'bYveSVYXbeSVYrq-ÆyX`YveX`gfihK^1q²©ªo`gfpWkfiudc5`gfihK^1q²c5pihHewc5`gfihK^ xoY
bYvuduhKobevYvuwq! Yvug`gfihK^´xoYewc5o`YXobu
Z
& '
ªD"% $)!
RTSofiuDc5YXbxoYwc5iu.fp`gSk`gSVYTWnc5^Dc5stYXW<YX^H`«h5%W<hHxoYvuc5^Vx<bYvuhKobevY ¡hKbxoYX`YveX`gfp^osc}W<hw@fp^os
`dc5bgstYX`w¨ RTSofiu<W<Ywc5^Vun`gSDc5`<`gSVYjudYwc5beSVYXbnSDcKu<W#op`gfpoiY£xoYX`YveX`gfihK^xoYX@fievYvu´µ¡Yr¨sV¨bdcKxVc5bwq
\ ~#qDuhK^Dc5b3·c5`ªfp`uxfiug%hrudc5m¨ cKedS£YXiYXW<YX^H`dc5bg§jxoYXHfievYewc5^£c5iudhk«hKbg¤jhK^´Kc5bgfihKVuªW<h@xoYvuw¨
RTSVYvudYªW<[email protected]^-Y}bYX¥c5`Yvx-`h@fiugfpofppfp`¹§QÑcKeX`hKbuµ¡Yr¨sV¨°bdcKxVc5b.bdc5^ostYrqoudYveX`hKbugfpwYª¡hKb.\ ~#q
YX`er¨·<c5^Vx(5hKb`hkbYvuhKobevYevhK^Vu`gbdc5fp^a`uµ¡Yr¨sV¨bYvuhKobevYbYX^VYXqVxfiueXbYX`gfihK^£evhK^Vug`gbdc5fp^a`u8·8¨
»Hfp^VevY`gSVYobhKoiYXW evhK^Vugfiug`u±fp^hKo`gfpWkfpvfp^os xoYX`YveX`gfihK^ bYvuhKobevYvuwqQiYX`±Vu¶obgfiY)V§ bY8l
ewc5p`gSVY}Wnc6{ hKb.ug`dc5`YXW<YX^H`h5)uYwc5beS²`gSVYvhKbg§t¨ »@Ywc5bedS²`gSVYvhKbg§nfiu `gSVY}xfiueXfpopfp^VY`gSDc5`«`gbYwc5`u
`gSVYQobhKoiYXW h5SVhw¼Yvu`#`hjudYwc5beS ¡hKb>c5^ hK{gYveX`²µF`gSVYn`dc5bgstYX`3·.SVYX^¶`gSVY-c5W<hKo^a`kh5
udYwc5beSofp^osY8³%hKbg`¦fiu¦pfpWkfp`Yvx c5^Vx hK^op§obhKDc5ofppfp`gfiYvu h5`gSVY£hK{gYveX`w®¯uQ%hruugfpoiY´ih@ewc5`gfihK^
c5bYsrfptYX^1¨^fpWk%hKbg`dc5^a`pfp`YXbdc5`gobY<SDcKuYvYX^¸xoYXthK`Yvx`h-`gSVY>ugo{gYveX`*1`gSVYfp^a`YXbYvug`Yvx
bYwcKxoYXb¸Wncw§ evhK^Vugop`¸rc5bgfihKVu¸Y8¬`YX^VugfptYugobgtYX§u,+.-w0/1+Z2/¹q#fp^H`gbhHxVeX`hKbg§ `Y8¬`u,+3/nc5^Vx
uYveXf¥c5pfpwYvx²%h@hK¤@uw¨
\_^ `gSofiu±udYX` lmoc xoYX`YveX`gfihK^ µ¡hKb±udYwc5beS!·obhKoiYXW fiu eSDc5bdcKeX`YXbgfpwYvxa§ `gSobYvYofiYvevYvu
h5£xVc5`dc4 µFf:·¶`gSVY obhKDc5ofppfp`gfiYvuh5£`gSVY udYwc5beSVYvx¼`dc5bgstYX`%YXfp^os fp^¼rc5bgfihKVu hrudugfpoiY
%hrugfp`gfihK^VuwqµFfpf:·&`gSVYih@ewc5DxoYX`YveX`gfihK^¦obhKDc5ofppfp`¹§k`gSDc5`TcDc5bg`gfieXo¥c5bTc5W<hKo^H` h5Jih@ewc5DuYwc5bedS
Y8³JhKbg`nevhKoixxoYX`YveX`<`gSVY `dc5bgstYX`wqµFfpfpf:·>`gSVY `hK`dc5}c5W<hKo^a`¦h5uYwc5beSofp^os Y8³%hKbg`QcwKc5fp¥c5oiYr¨
RTSVYobhKoiYXW fiu`h65V^Vx `gSVYhKo`gfpWnc5&xfiug`gbgfpoo`gfihK^´h5`gSVYxoYX`YveX`gfihK^µ¡uYwc5beS!·Y8³%hKbg``gSDc5`
Wnc6¬fpWkfpwYvu`gSVYobhKDc5ofppfp`_§ h5°xoYX`YveX`gfihK^1¨
RTSVYbdc5ofix srbhw.`gS h5¦`gSVYudYwc5beS `gSVYvhKbg§ pfp`YXbdc5`gobYfiu¶eSobhK^ofieXiYvx fp^ bY8¡YXbYX^VevY7+Z2/¹¨
8DhKb«W<hHfp^os>`dc5bgstYX`u obhKoiYXW<uwqxoYveXfiugfptYªobhKsrbYvuu SDcvtY}YvYX^QWncKxoY}fp^¦xoYXtYXihKofp^oskuYwc5bedS
u`gbdc5`YXsrfiYvu.ÑhKbªc>W<hw@fp^os£µ¡¢c5bg¤thw@f¥c5^!·`dc5bgstYX`w¨«\_^ Dc5bg`gfieXo¥c5bwq«bh.^9+;:0/°c5^Vx=<±cKugSaoobg^
+?>0/kSDcwtY obhKhruYvx c5^ fp`YXbdc5`gfptYc5psthKbgfp`gSoW µ8 }c5psthKbgfp`gSoWQ·£fp^ .SofiedS `gSVY W<hK`gfihK^
uDcKevYc5^Vx´`gSVY`gfpW<Y#Fbdc5W<YSDcvtYYvYX^£xfiueXbYX`gfpwYvxJ¨\_^j`gSofiuc5oobhtcKeS1q%`gSVYuYwc5beSY8³JhKbg`
cwKc5fp¥c5oiYQfp^¶YwcKedS¶%YXbgfih@x fiuhKo^VxoYvx c5htYnH§±c evhK^Vug`dc5^H``gSDc5`>xoh@Yvu^VhK`>xoYXYX^Vx¶hK^
`gSVYc5pih@ewc5`gfihK^VuWncKxoYxobgfp^osQc5^a§²hK`gSVYXb%YXbgfih@xou@w¨
A}YXbYrq'c5p`gSVhKosrS`gSVY stYX^VYXbdc5ÑhKbgWnc5pfiugW h5'uYwc5bedS`gSVYvhKbg§ .fpp%Y VuYvx uoVuY8l
HVYX^a`gp§tq°hKobobhKoiYXW ug`gbhK^osrp§ xoYXDc5bg`u#¡bhKW `gSVYnhKbgfpsrfp^Dc5TuYX`go1¨B8VhKbkc-W#op`gfºlm%YXbgfihHx
udYwc5beS1q`gSVY5V^Dc5bYvugop`}fiu}`gfpsrSa`gp§´bYX¥c5`Yvxj`h¦`gSVYKc5bgfihKVuxoYX`YveX`hKbuc5^Vx´W<hHxoYvuw¨}RTSaVuq
hKo`gfpWkfpvfp^osQ`gSofiuuY HVYX^VevYfiu Hofp`YeSDc5piYX^osrfp^osV¨TRTSofiuhKo`gfpWkfpc5`gfihK^£W#Vu`Y%YXb ÑhKbgW<Yvx
C1DFE1GHJILK?H!G"M;MONQPRILS2K?TUHWVX0TIYE1GK?XQIZTIYELVX2[MONEL\!]0^0HW\WT_ILS2\`K?XQIL\JEL\WTIZV"abILS2\dcegfhGM?[VELKOILS2ijGX]M;K?i`KOILTUK?ILT
Gk2k0M?K;HWG"ILK?VXlILVmTYK;i`k0M?\_]0\JIL\WHnILK;VXlTNoTIL\Wi`T
3
%hK`gS²`YXWk%hKbdc5pp§²c5^VxjugDc5`gf¥c5pp§t¨
A}YXbY YugSDc5pjxoYXtYXihKc tYXbudc5`gfpiY'¡hKbgWnc5pfiugW ewc5Dc5oiYh5¸SDc5^Vxpfp^os `gSVYWnc5^Dc5stY8l
W<YX^H`.h5&ctYXbg§<stYX^VYXbdc5JxoYX`YveX`gfihK^ ug§@u`YXW ¨&RTSofiuTfiu `gSVYc5fpW h5)`gSVYª¡hKbgWnc5pfiugW¼h5)c5`YXbdc5
»Hopfp`g`gfp^os µ¨»¨·.SofieS1qH{ghKfp^a`gp§ .fp`gS£`gSVYbYvuhKobevYhK%YXbdc5`hKbxoY5V^ofp`gfihK^Vuwq%evhK^Vug`gfp`go`Y`gSVY
DcKed¤H%hK^VYh5°`gSofiu.Dc5%YXbw¨ªugfp^oskfp`wqVfp`.fiuThruufpoiY`hkWnc5^Dc5stY#c.fixoYrc5bgfiYX`¹§-h5&bYvudhKobevY
c5pih@ewc5`gfihK^kobhKoiYXW<upfp¤tYTWop`gfºlmW<hHxoYrqHW#op`gfºlmbYvudhKobevYuedSVYvxopfp^osVqtbYvuhKobevYxoYX%YX^VxoYX^VeX§
c5^Vx `hjxoYwc5.fp`gS c5^a§ evhKW#ofp^Dc5`gfihK^ h5.`gSVYXW ¨-RTSVYkbYvuhKobevY<W<h@xoYXpfp^ostu>c5bYkobYvuYX^a`Yvx
fp^²uYveX`gfihK^j>cKu. YXp)cKuT`gSVYKc5bgfihKVuTTcv§u.`h>evhKW#ofp^VY#`gSVYXW ¨RTSVYYXiYXW<YX^a`dc5bg§²hKYXbdc5`hKbu
µkq>quewc5¥c5b}obhHxVeX`wq·c5bY`gSVYX^£obYvudYX^a`Yvx£fp^´`gSVY¥c5`YXbdc5ugopfp`g`gfp^os¦Fbdc5W<YX hKbg¤¨\_^
`gSofiu<c5bYwcq«`gSVY²hK%YXbdc5`hKb xoYvuYXbgtYvuncug%YveXf¥c5TW<YX^a`gfihK^ ugfp^VevY-fp`u<c5fpW½fiu>`hbYXobYvuYX^a`
evhK^Vxfp`gfihK^Dc5xoYXYX^VxoYX^VeX§-%YX`¹«YvYX^j`¹«h»@uw¨RTSVYstYX^VYXbdc51obhK%YXbg`gfiYvuh5&`gSVYvuYhKYXbdc5`hKbu
c5bYª`gSVYX^²ug`dc5`YvxJ¨}ugfp^os`gSVY!»Qc5^Vx-hKYXbdc5`hKb ÑhKbgWnc5pfiugW q@«Yc5bY}fp^Q%hrugfp`gfihK^¦`h>xoYXtYXihK
`gSVY¶stYX^VYXbdc5¡hKbgW h5Qc5^ c5psthKbgfp`gSoWhKo`gfpWkfpvfp^os `gSVY uYwc5beS Y8³JhKbg`u"µ¡uYvY¶uYveX`gfihK^ Zt·8¨
8&fp^Dc5pp§tq%`gSVY>o`gfppfp`_§´h5«`gSVYstYX^VYXbdc5°ÑhKbgWnc5pfiugW c5^Vx£`gSVY>bYX¥c5`Yvx£hKo`gfpWkfpwYvx¶c5psthKbgfp`gSoW fiu
fpppVu`gbdc5`Yvx hK^juYXtYXbdc5)Y8¬Vc5WkoiYvu.fp^HthKpHfp^os¦evhKWkoiY8¬²xoYX`YveX`gfihK^£ug§ug`YXW<uµ¡uYvYuYveX`gfihK^=3H·8¨
#²À$%'& &FÄ(% r `dc5bgstYX`«W<hw@fp^os#fp^Qc#uYwc5beS¦ugDcKevY*) fiu`h%YxoYX`YveX`YvxJ¨RTSVYxoYX`YveX`gfihK^
fiucKeSofiYXtYvx#xobgfp^os*+¶%YXbgfihHxouwq6YwcKeS%YXbgfih@xYXfp^os.obgfiY8VYX^VhKosrS`hudc5`gfiu ¡§`gSVYug`dc5`gfihK^Dc5bgfp`_§
SH§H%hK`gSVYvugfiuTh5)`gSVYª`dc5bgstYX` ¡hKb `gSVY}YXbgfih@xJ¨°RTSVYª`gbdc6{gYveX`hKbg§-,
.0/21.436587878795:.<;=?>
) ; h51`gSVY
`dc5bgstYX`ªfiuxoYvueXbgfp%Yvx H§²ckobhKDc5ofppfiug`gfieobgfihKbc5hKo`@,
.
qosrfptYX^jH§ c>obhKDc5ofppfiug`gfie#xoYX^Vufp`¹§
AB1
,
.4=
¨ ¢c5bg¤thw@f¥c5^¸cKudugoWko`gfihK^.fpp%YWncKxoY#¡hKbc5psthKbgfp`gSoWkfiebYwcKuhK^Vu*
A
fiu}`dc5¤tYX^¸cKu
cobh@xVeX`h5YXiYXW<YX^a`dc5bg§ xoYX^Vugfp`gfiYvuo4
AB1
,
.=C/DA 3:EF 1. 3 5:. F =BGIH8H8H(G A ;4JK3:E; 1. ;LJK3 5:. ; =M7
µW-·
srfptYX^±c5W<hKo^a`h5TuYwc5beS Y8³JhKbg`NPO<fiucvrc5fp¥c5oiY<c5`YwcKeS¸%YXbgfih@xIQ%¨RTSVhruY>Y8³JhKbg`uc5bY
evhK^Vu`dc5^a`uh5`gSVY#obhKoiYXW ¨ T`YwcKeS£%YXbgfihHxRQ%qV`gSVYY8³%hKbg`!N(OWncw§ Yxfiug`gbgfpoo`Yvxc5ihK^os
) `hncKevevhKWkopfiuS´`gSVYuYwc5beS1¨RTSVY#ihHewc5&uYwc5beS£Y8³%hKbg`wq%c5oopfiYvx´`hk`gSVY#%hKfp^a`
. O > ) c5`
`gfpW<YSQ%qfiuxoYX^VhK`YvxUT'O
1.
O = ¨ hK^Vug`gbdc5fp^a`u>µÑt·.c5bYevhK^VugfixoYXbYvxb4
V Q
>XWYZ587878795 +[
5
T'O\^]nc5^VxU_a`bT'O
1.K=acd.Re NPO
7
µÑt·
fhg S2\ G"K;i Va ILS0K;TGM?[VELKOILS2i K?TILVHWViji2K?X0\ ILS2\ TYK?i`k2M?K?HWKOINmGX]Z\lk`HWK?\WX2HnNZVa ILS0\qceqf%G"M?[VELKOILS0inm KOILS
ILS2\o\nELTLG"ILK?M?K?I NlV"aILS2\CpaqaVELiGM?K?TYi
hKbY Hofprc5iYX^a`gp§ 4 V Q
>XWYZ587878795 +[
5
T'O\^]nc5^Vx _a` T'O
1.K=acd. / NPO
7
µÑZt·
RTSVY ih@ewc5<Y8³JhKbg`u TxfpbYveX`gp§ evhKWkWnc5^Vx `gSVY ihHewc5QxoYX`YveX`gfihK^ obhKDc5ofppfp`¹§t¨ < Yewc5ºl
O E 1 T'O
1.
O
=:=
`gSVY«obhKDc5ofppfp`¹§#^VhK`&`hxoYX`YveX`&.fp`gSofp^>`gSVY%YXbgfihHx Q%q5.SVYX^`dc5bgstYX`&ih@ewc5`gfihK^
fiu
.
Oa¨kRTSVY<¥cv h5TxfpWkfp^ofiugSofp^osjbYX`gobg^ fiucKuugoW<YvxJ¨kRTSaVu¡hKb
.
O65o¬oYvxJq
O E
] c5^Vx
O E
]o¨RTSVYobhKoiYXW fiuª`h65V^VxITuhncKuª`h<Wkfp^ofpWkfpwY`gSVYsrihKDc5&obhKDc5ofppfp`¹§£h5^VhK^
xoYX`YveX`gfihK^
1T =
o^VxoYXbª`gSVY#evhK^Vug`gbdc5fp^H`>µÑZt·8¨T\_^VxoYXYX^VxoYX^VevYSa§@hK`gSVYvufiuhK^´YXiYXW<YX^H`dc5bg§
xoYX`YveX`gfihK^Vu§HfiYXixouo4
1T
=/
_ `
AB1
,
.4=
O
;
O
3 O E 1 TO
1.
O
=:=
O
;
O
3
c.
O 7 µ3H·
Ä@Ã% À Ä Å« bh.^QhKo`dc5fp^VYvxQcevhK^HtYXbgstYX^VevY`h c5bxn`gSVYhKo`gfpWnc5DuhKpo`gfihK^1qaa§
uVevevYvuugfptYXp§QhKo`gfpWkfpvfp^os-c5ihK^VYYwcKeS %YXbgfih@xQ.fp`gSj`gSVYhK`gSVYXbZ5o¬YvxJ¨¢£hKbY}obYveXfiuYXp§tqÑhKbc
Dc5bg`gfieXo¥c5bªYXbgfih@x1q
1 T =
ewc5^jc5iuhk%Y.bgfp`g`YX^ 4
1 T
=?/
_ `
!
1.
!
="
! E#a1 T !
1.
!
=:=ac.
! 5
.SVYXbY4
!
1.
!
=/
_ `
%$%&
AB1
,
.=
O('
!
3*)
O ) ; + O E 1 T'O
1.
O
=:=acd.
O,
7
µÑt·
RTSofiu ugSVhu«`gSDc5`wqH.SVYX^-`gSVYuYwc5bedS²Y8³%hKbg`uTc5bY5o¬oYvxkÑhKb c5p%YXbgfihHxouwqHY8¬evYXo`«ÑhKb c#YXbgfih@x
)q`gSVYhKo`gfpWkfpc5`gfihK^jobhKoiYXW YvevhKW<Yvu`gSVY}¡hKpih.fp^os
Y
lm%YXbgfihHx obhKoiYXW 4
¢jfp^ofpWkfpwY-
1 T !
=/
_ `
!
1.K="
! E 1T !
1.=:=ac.R5
ugo{gYveX`.`h _a` T !
1.=acd. / N !
c5^Vx T
! \ ] 7
µ/.t·
RTSVY¡hKpih.fp^os¦hKo`gfpWnc5pfp`_§´evhK^Vxfp`gfihK^Vuuewc5iYvxja§²Dc5bdc5W<YX`YXb0±µ¡Y aDc5`gfihK^Vu}h5 xoY VYX^ofp^
+1.0/F·c5bYhKo`dc5fp^VYvxb432
!
1.K=" ! E 1T ! 1.=:=C/
0 ! 5 fº4
!
1.=
0
!65 ! E 1] =
T !
1.=C/
] 5 YXiuY
7
µL:r·
»Hfp^VevY
! E
fiuug`gbgfieX`gp§ W<hK^VhK`hK^ofierq`gSVYQc5%hwtY-Y aDc5`gfihK^Vu>c5bYQfp^atYXbg`gfpoiYrq.SofpiY70¸fiu^VhK`
uYveXf5DYvxJ¨ ^ o^ofºÑhKbgWkp§fp^VeXbYwcKugfp^os Fo^VeX`gfihK^ T 8
!
fiu¦hKo`dc5fp^VYvxJ¨ RTSVY£fp^VeXbYwcKuYX^VYvuu-h5
.
T 8
!
Wnc5¤tYvu
`
T 8
!
1.=ac.
fp^VeXbYwcKugfp^osV¨ RTSVYsth@hHx rc5pVY£ÑhKb70
!
fiu-`gSVYX^ hKo`dc5fp^VYvxa§c
x§eSVhK`hKWkfieobhHevYvuuThK^ T 8
!
¨RTSVY}.SVhKiYobhHevYvudu«bY HofpbYvuhK^op§-cÑYX fp`YXbdc5`gfihK^Vuw¨\_`«VudYvu
DcKufiewc5pp§ `gSVY²¢c5bg¤thw@f¥c5^ cKudugoWko`gfihK^bYX¥c5`gfptY `h
A
qTuh cKuk`h xbdcKu`gfiewc5pp§ bYvxVevY `gSVY
evhKWkoo`dc5`gfihK^¸bY HofpbYXW<YX^a`u}ÑhKb}`gSVYfp^H`YXsrbdc5µÑt·8qµThKbg c5bx
^Vx kcKed¤HTc5bxc5psthKbgfp`gSoW
+;:o/1+?>/F·8¨RTSofiufixoYwc.fpp1%Yfp^Vug`gbgoW<YX^a`dc5c5sac5fp^ fp^ hKobªc5psthKbgfp`gSoW ¨
°"% &
bh.^1®¯u>c5psthKbgfp`gSoW cKuuoW<Yvu N`hj%Y<¤@^Vhw.^c5^Vx¶xoYwc5iu>hK^op§±c5%hKo`bYvudhKobevYvuuDc5`gf¥c5
uSDc5bgfp^osV¨°©ªo`gfpWkfpc5`gfihK^nhK^ NPO.fiuSVhw«YXtYXb c hKbg`gSa.SofpiY.fiuuVYr¨)RTfpW<YTugopfp`g`gfp^osh5csrihKDc5
c5W<hKo^H`h5T^VhK^ bYX^VYX c5oiYnbYvuhKobevYvuwq&hKb#c5pihHewc5`gfihK^¶obhKoiYXW<u#hK^ bYX^VYXTc5oiY<bYvuhKobevYvu
c5bY¦Y8¬Vc5WkoiYvuw¨ W<hKbYQstYX^VYXbdc5.obhKoiYXW qewc5piYvx ¥c5`YXbdc5Tuopfp`g`gfp^osVq.fpp YQobYvuYX^a`YvxJ¨
RTSofiuobhKoiYXW fp^H`YX^Vxou`hkfp^HthKptY#Wop`gfºlmbYvuhKobevY>c5^Vx²W#op`gfºlmW<h@xoYudeSVYvxopfp^osn`hKstYX`gSVYXb
.fp`gS£ugDc5`gfih5lm`YXWk%hKbdc5°hKo`gfpWkfpc5`gfihK^h5bYvuhKobevYvuw¨.RhQxohn`gSDc5`wqDfp`}evhKW#ofp^VYvuugDc5`gf¥c5&hKl
`gfpWkfpc5`gfihK^VuµÑcKu«VugDc5pp§V·c5^VxQsrihKDc5hKo`gfpWkfpc5`gfihK^Vuwq.SofiedS-cKeX`Tc5`«`gSVYfp^VxoY8¬niYXtYX&µ¡udhKW<Y
fp^VxoY8¬oYvu¦Wncv§^VhK`¦%Yj`YXWk%hKbdc5:·8¨ Y8ÑhKbY£xoY5V^ofp^osc ÑhKbgWnc5pfiugWÑhKb¦¥c5`YXbdc5uopfp`g`gfp^osVq
udhKW<YªY8¬Vc5WkoiYvuc5bY}srfptYX^1¨RTSVYX§QugSVhKoix¦YX^opfpsrSa`YX^jhK^¦SVhw¥c5`YXbdc5Jugopfp`g`gfp^oskevhK^Vug`gfp`go`Yvu
cevhKWkW<hK^²ewc5^arcKu ¡hKb W<h@xoYXpfp^os%hK`gS¦`gSVY^Dc5`gobYh5)Dc5bg`gfieXo¥c5b.bYvuhKobevYvu.c5^Vx¦`gSVY}evhKW>l
ofp^Dc5`gfihK^Vukh5}xfº³%YXbYX^H`kbYvuhKobevYvuw¨ 8VhKbkhKobkY8¬oc5WkoiYvuq«Y¦.fppTbYvug`gbgfieX`>`h¸cjuYwc5bedShK^
+
/
YXbgfih@xouw¨
Ä Å À &% À Ä 5 À r bYvuhKobevYnfiu#evYXbg`dc5fp^op§±edSDc5bdcKeX`YXbgfpwYvx¶H§fp`u^VhK^¶xoYX`YveX`gfihK^
¡o^VeX`gfihK^Vu
qVoo`}fp`}fiu^VhK`ug¾neXfiYX^a`w¨}RTSVYbYX¥c5`gfihK^Vuª%YX`¹ YvYX^srihKDc5&bYvudhKobevYvu NPOkSDcwtY
`h>%YuYX`w¨\_^ bhw.^1®¯u.ÑhKbgWnc5pfiugW q`gSofiuudYX`g`gfp^os<fiu.srfptYX^ hK^op§-a§¦`gSVYevhK^Vug`dc5^a`ªtYveX`hKb N&¨
\_`fiucQh@hKb}¡hKbgWnc5pfiugW q)ugfp^VevY>evhK^Vug`dc5^a`g^VYvuu¡hKbgofixoufp^H`YXbdcKeX`gfihK^ %YX`¹«YvYX^±YXbgfih@xouw¨ 8DhKb
Y8¬Vc5WkoiYrqrfº%«YTTc5^a` `hxoY5V^VYc}^VhK^kbYX^VYXTc5oiYbYvuhKobevYrqa.SofieS<`hK`dc5Dc5W<hKo^H`wqHu3cv§
Y ] ]oq
SDcKu `hY}ugSDc5bYvx¦%YX`¹«YvYX^²`gSVY
YXbgfih@xouwqHfp`«fiu ^VYvevYvuu3c5bg§<`hSDc5^VxiY!N´cKu.crc5bgf¥c5oiYc5^Vx
^VhK`}cKuckevhK^Vug`dc5^H`w¨U< fp`gSjugVedSj^VhK^ bYX^VYXTc5oiY#bYvuhKobevYrqVbYvuhKobevYDc5¥c5^VevYxoYveXbYwcKuYvuh5
NPOnc5`YwcKedS¸YXbgfih@xIQ%¨»Hfp^VevYDc5¥c5^VevYkSDcKu}`h-Y%hrugfp`gfptYkc5^VxbYvuhKobevYvuc5bYpfpWkfp`Yvxa§
Y ] ]oqVKc5bgf¥c5oiYvu N´hK%YX§¦`hk`gSVY
evhK^Vug`gbdc5fp^H`u4
N 3 e Y ] ] 5
N
3
N F e Y ] ] 5
N
3
N
F N
e Y ] ] 5
N
3
N
F N
N
e Y ] ] 5
:
.SofiedS bYwcKxoufp^jckWnc5`gbgfº¬¦ÑhKbgWnc5pfiugW 4
N
e
.fp`gS
/ Y ]] ]
YY ] ]
YYY
]
YYY Y
c5^Vx
/ Y ] ] Y ] ]
Y ] ]
Y ] ]
\_` fiu ^VhK`YX«hKbg`gSa§ `gSDc5`wq²ufp^VevY N \^]Vq N fiuu¾neXfiYX^a`gp§¼eSDc5bdcKeX`YXbgfpwYvx H§ `gSVYhK^op§
evhK^Vu`gbdc5fp^a` N
3
N
F N
N
e Y ] ]V¨ }YXtYXbg`gSVYXiYvuuwqfp^ uVeS ¡hKbgW `gSVY¶fp^¡hKbgWnc5`gfihK^
hK^ NfiuQSofixoxoYX^1¨ < Yudcw§`gSVYX^1qª`gSDc5`¦`gSVY£evhK^Vug`gbdc5fp^H`²fiu Q$6 Z $P.1 ¨
»HVedS ÑhKbgW .fpp)^VhK`YevhKWkDc5`gfpoiY-µ:ÑhKbgWnc5pp§jc5^Vx uYXWnc5^a`gfiewc5pp§V·.fp`gS´hKobW<h@xoYXpfp^osQh5
Wop`gfºlmW<hHxoYueSVYvxopfp^osV¨T»@hoqofp`.fiu.^VhK`VudYvx-fp^ `gSVYuY HVYXm¨
\_`Tfiu°{ Vug`cKuYwcKug§¦`hkxoY5V^VYbYvuhKobevYbYX^VYX c5oiYc6F`YXbYXbgfih@xouw¨ }uugoW<Y}`hK`dc5c5W<hKo^a`
%YZ]o¨»Hfp^VevYjbYvuhKobevYjbYX^VYXc6F`YXb¸%YXbgfihHxJq bYvuhKobevY´Dc5¥c5^VevYjxoYveXbYwcKudY´h5NPO¸c5^Vx
%hruugfpop§Qfp^VeXbYwcKuYh5CNPO
JF
c5`YwcKedS %YXbgfihHx Q%¨RTSHVuwqorc5bgf¥c5oiYvu N£hK%YX§Q`h<evhK^Vu`gbdc5fp^a`u4
N 3 e Z]
5
N 3 N F e Z]
5
N F N
e
Z]
5
N
N
e
Z]
5
§@fiYXixfp^osQc5sac5fp^ fp^jckWnc5`gbgfº¬QÑhKbgWnc5pfiugW 4
N
e
.fp`gS
/ Y ] ]]
YY ]]
] Y Y ]
]]
YY
c5^Vx
-/
Z]
Z]
Z]
Z]
Ä £ &%'&% À Ä 5 À r RTSVY¦`¹ h£obYvevYvxfp^os Y8¬oc5WkoiYvu>.fppT%Yn^Vh fp^VxoY8¬oYvx uhcKu
`h²xfiu`gfp^osrofiugS¸`gSVYXW ¨kRTSVY>^VhK^ bYX^VYX c5oiYnbYvuhKobevY>fiufp^VxoY8¬oYvx µFfm¨¯Yr¨bN-q ²q
¨v¨v¨d·¶c5^Vx`gSVYkhK`gSVYXbµFfm¨¯Yr¨ N F q F
q¨v¨v¨d·8¨k»Hoo%hruY>^VhwqJ`gSDc5``gSVYvudY>`¹«h ¤Hfp^Vxouh5
bYvudhKobevYvuªc5bYVuYvx ufpW#op`dc5^VYvhKVugp§t¨«RTSVYobhKDc5ofppfp`¹§
1 T =
%YvevhKW<Yvu4
/
_!
#"
`
AB1
,
.=
O
;
O
3
O E
1T
O
1.
O
=:=
F
O E
1 T F
O
1.
O
=:= cd.
O 7
¢£hKbYvhwtYXbwq&ugfp^VevYkbYvudhKobevYvuc5bYkDc5bdc5piYXpfpwYvxJq°evhK^Vug`gbdc5fp^H`uhK^nN c5^Vx N
F
c5bY<ugfpWkop§
¤tYvYXo^VedSDc5^ostYvxc5^Vx oo`k`hKstYX`gSVYXbw¨RTSofiu<hK%YXbdc5`gfihK^1q«stYX^VYXbdc5pfpwYvxfp^^VY8¬@`<udYveX`gfihK^cKu
>
hK%YXbdc5`hKb >q§@fiYXixou.`gSVYÑhKpihw.fp^osQevhK^Vug`gbdc5fp^a`4
]
]
F
N
N F
e
F
}hwq«cKuugoW<Y¦`gSDc5`>bYvuhKobevYvu>«hKbg¤¶fp^ `_«hW<h@xoYvuwq°fm¨¯Yr¨ Y8¬VcKeX`gp§ pfp¤tY¦bYvuhKobevY fp^
W<h@xoY
Y
c5^Vx¦Y8¬ocKeX`gp§kpfp¤tYªbYvuhKobevYfp^¦W<hHxoY¨zbhKDc5ofppfp`¹§ bYXWnc5fp^Vu o^VeSDc5^ostYvx
c5p`gSVhKosrS´fp^ `gSofiu^VYX evhK^a`Y8¬`w¨ }uugoW<Y#c5iudhk`gSDc5`bgo^o^ofp^osnW<h@xoYewc5^ %YedSDc5^ostYvx´hK^op§
.SVYX^bYvuhKobevYvunc5bY²o^HVuYvxhKb<bYX^VYX YvxJqTc5^Vx`gSDc5`
Y ] ]¸bYvuhKobevYvu fp^W<hHxoY
Y
fiu
Y Hofprc5iYX^a`T`h Z]bYvuhKobevYvu #fp^QW<h@xoY ¨RTSVYX^1q`gSVYDc5¥c5^VevYh5)bYvuhKobevYvuTevhKW<Yvu ¡bhKW
`gSVYevhK^Vewc5`YX^Dc5`gfihK^-h5J`gSVY«YXfpsrSa`YvxQDc5¥c5^VevY}h5%`gSVY`¹«hoobYbYvudhKobevYvuw¨°RTSaVuwqHKc5bgf¥c5oiYvu
N c5^Vx N
F
hK%YX§¦`hk^VYXevhK^Vug`gbdc5fp^H`u4
2 N
3 N F
3 e Y ] ] 5
!
O
3
N
O N
F
!
JK3
N
F
! e Y ] ]kÑhKb / 5a5 7
RTSofiuhK%YXbdc5`gfihK^1q%stYX^VYXbdc5pfpwYvxfp^´^VY8¬`uYveX`gfihK^ cKu}hK%YXbdc5`hKb>q!§HfiYXixou}`gSVY¡hKpih.fp^os²evhK^l
u`gbdc5fp^a`4
Y
]]] ]] ]
Y Y
]] ] ]
Y YY
] ]!]
Y YYY
]]
N
N F
e Y ] ] Y ] ]
Y ] ]
Y ] ]
ªp°`gSVYvuY>Y8¬oc5WkoiYvubYXp§´hK^ ugfpWkfp¥c5bÑhKbgWnc5pfiugW qJ.SofiedS .fpp°Yo^of5DYvx¸fp^H`h-`gSVY>¥c5`YXbdc5
uopfp`g`gfp^osVqY8¬@o¥c5fp^VYvxfp^^VY8¬@` uYveX`gfihK^1¨ RTSVY ug`gbgVeX`gobY YXWkoih§tYvxÑhKb Y8¬@o¥c5fp^ofp^os`gSofiu
ÑhKbgWnc5pfiugW Wncw§jc5oYwc5b}c>ofp`ªc5Vug`gbdcKeX`w¨ \¹^ ÑcKeX`wqofp`ªugfpWkop§-bYXpfiYvuhK^´ckxoY5V^ofp`gfihK^h5°^VhK^
hKbxoYXbYvx Wnc5`gbgfº¬JqcKuuh@eXf¥c5`Yvx±.fp`gScj¥c5YXpfp^osh5ªYwcKeS rc5bgf¥c5oiY£µ¡evhKpoWk^Vu8·c5^Vx h5ªYwcKedS
evhK^Vu`gbdc5fp^a`u#µFbhu3· a§¦c`YXWk%hKbdc5µ¡hKb ^VhK^²`YXWk%hKbdc5:· fp^VxoY8¬%¨ RTSVYª¥c5%YXpfp^os>fiu VuY8FoÑhKb
udYXWnc5^a`gfiebYwcKuhK^1¨8DhKbY8¬oc5WkoiYfp`TsrfptYvu.Vuc>eXbgfp`YXbgfihK^-ÑhKbevhK^Vewc5`YX^Dc5`gfp^os<`_«hkbYvuhKobevYvu
fp^#W#op`gfpW<h@xoY4evhK^Vug`gbdc5fp^H`uhK^ 5Vbug`1bYvuhKobevY¡hKb)YXbgfih@xQfiuevhK^Vewc5`YX^VYvx#.fp`gSevhK^Vug`gbdc5fp^a`u
hK^²uYvevhK^Vx¦bYvuhKobevY}ÑhKbTudc5W<Y}YXbgfih@xJ¨R)hfpppVug`gbdc5`Y`gSofiu ÑhKbgWnc5pfiugW qougoo%hruYc#bYvudhKobevY
bgo^o^ofp^osn.fp`gS `gSVY`¹ hkÑhKpihw.fp^os<W<h@xoYvu4
c>evhKWkoiY8¬²W<hHxoYrqoDc5bdc5piYXpfpvfp^os c5^Vx q
coobYW<h@xoYrqo.SVYXbYbYvuhKobevYvubYX^VYX c6F`YXb
YXbgfih@xouwq ¨
»HVedS-bYvuhKobevY}.fppbgo^-fp^ 5Vbug`TW<hHxoYªpfp¤tY}`¹ h>Dc5bdc5piYXpfpwYvx-bYvuhKobevYvuwquhKW<Y}^VhK^-bYX^VYXTl
c5oiYrq qac5^Vx<udhKW<Y.bYX^VYX c5oiY}c6F`YXb YXbgfih@xouwq ¨°\_^<uYvevhK^VxkW<h@xoYrqtfp`.fppVbgo^npfp¤tYc
bYvudhKobevYbYX^VYX c5oiY#c6¡`YXb
YXbgfih@xouwq
¨8VhKbudc5¤tYh5eX¥c5bgfp`¹§tqo Y.fppJoo`T^Vh>«YXfpsrSa`ªhK^
W<h@xoYvuw¨ ^Vx-ÑhKb`gSofiuªY8¬oc5WkoiYrq!`gSVY`hK`dc5&c5W<hKo^H`ªh5bYvuhKobevYvuªfiuZ5o¬oYvx²`h #¨ \¹^´hK`gSVYXb
hKbxJq&«Y<evhK^VugfixoYXb>c-obhKoiYXW h5 `gSVY<¡hKbgW
1
=
µFbY8ÑYXb`hj^VY8¬@`#udYveX`gfihK^!·8¨
RTSVYX^1q
Y
bYvuhKobevY bgo^o^ofp^os}fp^#W<h@xoY
ewc5^1qrc6F`YXbbYX^VYXq6%Y edSDc5^ostYvx#fp^H`h
Y Y
bYvuhKobevYvu
fp^%5Vbug` W<hHxoYrq@udcv§
Y
bgo^o^ofp^os>fp^nW<h@xoY c5^Vx
Y
fp^nW<h@xoY ¨°~YXtYXbuYXp§tqHfº
Y
bYvudhKobevY
fp^¸W<h@xoY -c5^Vx
Y
bYvuhKobevYkfp^¸W<h@xoY c5bY>bYX^VYX«Yvxµ¡udYvevhK^Vx ewcKuY^VYXtYXbSDc5o%YX^!·8q
`gSVYX§<evhKoix¦%YWkfº¬oYvxQudhcKu `hbgo^¦fp^¦udYvevhK^VxnW<h@xoYpfp¤tY
Y
bYvuhKobevYfp^¦W<h@xoY ¨ }hK`gfievY
`gSDc5``gSVY`¹ hkbYvuhKobevYvuh5g5Vbug`W<h@xoYSDcwtY`gSVYX^ `hk%YbYXiYwcKuYvxJ¨UA}YXbYfiu.srfptYX^ `gSVY`¹«h
Wnc5`gbgfievYvu}ÑhKbYwcKeS¸W<h@xoYr¨RTSVYevhKbgbYvuhK^Vxfp^os²%YXbgfihHxouqhKb`YXWk%hKbdc5°fp^VxfievYvuwq1c5bYsrfptYX^
ÑhKbYwcKeS´evhK^Vug`gbdc5fp^a`wq!hKbbhwqVh5°`gSVYWnc5`gbgfievYvu4
]
] F / Y ] ]] ] ]]]
YY
]] ] ]]]
YY Y ] ] ]]]
YY YY
] ]]]
]] ]] !]]]
]] ]] ]]
]] ]] ] ]
]] ]] ] ]
Y
Y
c5^Vx
/ Y
]] ]
YY ] ]
YYY
]
]
YY Y
Y
RTSVYvudYWnc5`gbgfievYvujhK%YXbdc5`Y hwtYXb´Kc5bgf¥c5oiYvu
+ N
5 N F ,
c5^Vx N
bYvugYveX`gfptYXp§t¨ RTSVY
evhK^Vewc5`YX^VYvx evhK^Vug`gbdc5fp^H`u c5bYj`gSVYX^ bYXobYvuYX^H`Yvx a§`gSVYj¡hKpih.fp^os Wnc5`gbgfº¬%q..SVYXbYYwcKedS
evhK^Vu`gbdc5fp^a`u&h5ou3c5W<Yfp^VxoY8¬c5bYevhKW#ofp^VYvxJ¨RTSofiu)Wnc5`gbgfº¬#hKYXbdc5`YvuhwtYXb`gSVY.SVhKiYbYvudhKobevY
tYveX`hKb + N
5 N F 5 N ,
qVc5^Vx²`dc5¤tYvu.`gSVYÑhKpihw.fp^osn¡hKbgW 4
Y ] ]] ] ]]]
Y
]] ]
YY
]] ] ]]]
YY ] ]
YY Y ] ] ]]]
YYY
]
YY YY
] ]]] ]
YY Y
]] ]]
Y
]]]
Y
]] ]
]] ]]
Y Y ]]
YY ] ]
]] ]] ]
YY
]
YYY
]
]] ]] ] ]
YY
]
YY Y
Y
Y
N
N F
N
e
#
#
#
#
#
#
#
#
}hK^hKbxoYXbYvxWnc5`gbgfº¬£ug`gbgVeX`gobY>fiu}VuY8¡o`h¦bYXobYvuYX^H`hKobhKYXbdc5`hKbuwqJufp^VevYfp`}fiufp^¸cKe8l
evhKbxVc5^VevY.fp`gS<`gSVYXfpb hKHHfihKVu obhKYXbg`gfiYvu}µ¡evhKWkW#o`dc5`gfp@fp`¹§tqoxfiug`gbgfpoo`gfp@fp`¹§t¨v¨v¨d·8¨¢£hKbYvhwtYXbwq
`gSofiu«ug`gbgVeX`gobYcvthKfixou«VuYXiYvuufp^)!c5`gfihK^-h5J`gSVYevhK^Vug`gbdc5fp^H`«bYXobYvudYX^a`dc5`gfihK^-fp^VxVevYvxnH§>`gSVY
hK%YXbdc5`hKbuw¨8VhKbfp^Vug`dc5^VevYrq)fp`fiuYwcKug§j`h-tYXbgfº¡§j`gSDc5`
1
=
srfptYvuevhK^Vxfp`gfihK^Vu
Y Hofprc5iYX^a``h
1
d=
1
d=
¨ o`.bgfp`g`YX^fp^£`gSVYkeX¥cKudugfiewc5°Wnc5`gbgfº¬jÑhKbgWnc5ºl
fiuW q)`gSVYXbYnfiuc5iuhjfp^)!c5`gfihK^ hK^¶`gSVY<rc5bgf¥c5oiYvuc5^Vx hK^ `gSVY<^HoW#%YXbh5evhKpoWk^Vu#¡hKb#`gSVY
-w
udYvevhK^Vx-.bgfp`g`gfp^osV¨RTSVYevhKbgbYvug%hK^Vxfp^oskWnc5`gbgfº¬-hK%YXbdc5`Yvu.hwtYXb
+
N 5
N 5
N F 5
N , ¨
\_`fiu hKHHfihKVu«`gSDc5``gSVY}cKuuh@eXf¥c5`Yvx<evhK^Vug`gbdc5fp^a`«fiu Y HofpKc5iYX^H` `h`gSVYobYXHfihKVu«ewcKuYrqaxoYvuofp`Y
fp`uxfº³%YXbYX^H`.¡hKbgWo¥c5`gfihK^ 4
Y
]]]
Y
]]] ]] ]] ] ]]]
Y Y ]]
YY
]] ]] ]] ] ]]]
Y YY
]
YYY
] ]] ]] ] ]]]
Y YYY
]
YYY
]] ]] ] ]]]
] ]]] ]]]]
Y ] ]]
Y
]]]
] ]]] ]]]]
YY ]]
Y Y ]]
] ]]] ]]]] ] Y Y ] Y YY
]
] ]]] ]]]] ]]
YY
]
YYY
Y
Y
N
N
N
F
N
e #
#
#
#
#
#
#
#
!"$#
)YX`%
/ WYZ5878787 5
+[%Y#c<uYX`}h5`YXWkhKbdc5&fp^VxfievYvuwq%c5^Vx'&
5
> % ckstYX^VYXbgfie^VhK^j`YXWk%hKbdc5
fp^VxoY8¬J¨ )c5`YXbdc5°»Hopfp`g`gfp^osVq(*)qfiuc aofp^H`gooiYX`+
/21-,j5/. 5L510 512U=
q.SVYXbY4
3,
fiu«cuYX` h5Jrc5bgf¥c5oiYvufp^VxfievYvu«^VhK`fp^VeXpVxfp^os
Y
¨°\_^VxoY8¬
Y
.fppV%Y.VuYvx>ÑhKbfp^VxoY8¬fp^os
evhK^Vug`dc5^a`}xVc5`dcq
4.657,98:<;
%>=
W & [#fiucWnc5oofp^osVqV¡hKb.`gfpW<Y¥c5YXpfp^osnh5°`gSVYrc5bgf¥c5oiYvuwq
@/21?=
? "@ $ &1ACBED
c5bY#^VhK^¸xoYX`YveX`gfihK^£Fo^VeX`gfihK^VutYXbgfº¡§@fp^os
? E ]²c5^Vx
? E ]
µ¡xfpWkfp^ofiugSofp^osnbYX`gobg^!·8q
F0HGJIKL<MON 3QP
fiuªc<uYX`h5«YXfpsrSa`gfp^osQÑhKbKc5bgf¥c5oiYvuc5^Vx evhK^Vug`dc5^H`/Rt¨ hK^Vu`gbdc5fp^a`uc5bY
xoY5V^VYvx²a§-`gSofiuhK{gYveX`w¨ }hK`Y`gSDc5`
0
fiuc¤Hfp^Vxjh5&^VhK^jhKbxoYXbYvx Wnc5`gbgfº¬%q
F2S50T;VU1
%
=XW WZY
[fiu cWnc5oofp^osFbhKW
0
qa.SofiedS xoY5V^VYvu«`gSVY}`YXWk%hKbdc5JevhK^a`Y8¬`
h5°YwcKedSjevhK^Vug`gbdc5fp^H`w¨
8VhKb)Y8¬Vc5WkoiYrqKevhK^VugfixoYXb
rc5bgf¥c5oiYvuN[aqZN\Xq N]1c5^VxN tqbYXobYvuYX^a`gfp^os}bYvuhKobevYvu
evhK^VugoW<Yvxc5`k%YXbgfihHx
Y
ÑhKb_^
5a` 5/b
c5^Vxc5`k%YXbgfih@x ´ÑhKb
c
¨»Hoo%hruY-`gSVYvuY
Kc5bgf¥c5oiYvuQugo{gYveX`Yvx `h evhK^Vug`gbdc5fp^a`u¦cKuuh@eXf¥c5`Yvx.fp`gS`YXWk%hKbdc5evhK^a`Y8¬`¦cKu
¡hKpihu4
YY ]]
]
YY ]]
YY
N[
Nc\
N]
N
e
Z]
Y ]
Z]
5
µY>t·
dqNoi?iVMfe EL\Wk0EL\WTY\JXILT G ggK;TihVK?XQIXjgX2K?VXfk
--
.SVYXbYk`gSVYjµF%YXbgfihHxD·¥c5YXhK^±YwcKedS±evhK^Vug`gbdc5fp^H`#fiusrfptYX^¶a§£`gSVYkiY8F`#c5bgbhuw¨
RTSVY»²cKuduhHeXf¥c5`Yvx-`h<`gSofiuY8¬oc5WkoiYfiu.`gSVYX^ srfptYX^ H§ 4
% / WYZ5 [ 5
, / W ^ 5a` 5/b 5c
[ 5
.41
^
=C/9.41!` =/>.41b6=C/ Y c5^Vx
.41c =C/
5
02/ W9A?5 [
5
.SVYXbY
2
Aj1
^
=/DAB1!`8=C/ YZ5AB1 b6=?/DAB1ca=?/
]
5Aj1hY9=j/ : Z]
5
1^
=?/
] 5
1!`8=?/
1b8=?/
1c =C/
5
1hY9=j/ :Y ] 5
2 1A=C/ WYZ5 [kc5^Vx
2 1
=C/ WY [ 7
µÑt·
Rh<evhKWkoiYX`Y`gSVY#xoY5V^ofp`gfihK^´h5»qDc5bYxoY5V^VYvxRN
/ 1 N
?C=
? " L
qDcÑc5Wkfpp§²h5°srihKDc5)Y8³JhKbg`
rc5bgf¥c5oiYvuc5^VxnT
/21
T ? = ? "Z@$%&1AiBXD
q&c¦mc5Wkfpp§h5.ugDc5`gf¥c5 ugSDc5bgfp^os²¡o^VeX`gfihK^Vuw¨ hK^VeXbYX`YXp§tq
obhK%YXbg`¹§
.41
=/
Q >
%W<Ywc5^Vu<`gSDc5`<bYvuhKobevYvu N ?
c5bY VuYvx ¡hKb<udYwc5beS c5`k%YXbgfih@x Q%¨
©ª`gSVYXbg.fiudYrq.SVYX^
.41
=C/
&Vq)bYvudhKobevYvu N ?
c5bY<^VhK`VuYvxJ¨ hK^Vug`gbdc5fp^a`u-µW-wt·evhK^Vxfp`gfihK^
`gSVYobhKoiYXW h5°uDc5`gf¥c51bYvuhKobevYxfiug`gbgfpoo`gfihK^ 4
V > ,?5
N ? \ ] c5^Vx V > . JK3
1%
=M5
T ? \ ] 5
V > . JK3
1%
=M5
_ ` T ? 1.K=acd. /
N
?n5
µW-wt·
}hwqfp^jcKxoxfp`gfihK^j`h>`gSVYvuY}DcKugfieevhK^Vug`gbdc5fp^a`uµW-wt·8qVhK`gSVYXbY HDc5`gfihK^VuhK^²srihKDc5JKc5bgf¥c5oiYvu
N ?
c5bYYXthKptYvx-¡bhKW
0 4 V ^ > 0 5
? " L ^ 1 = N ? ^ 1hY9=Be
] 7
µW--·
RTSVYobYvevYvxfp^osnY aDc5`gfihK^´SDcKuh5evhKobuYc>Wnc5`gbgfº¬-¡hKbgW 4
N e ^5
µW-wt·
.SVYXbY "F!*! QL
/21Q:
^
1hY9=:=
[
"
c5^Vx FW $6
/21
^ 1
=:=? " L E[
"
c5bY«evhK^Vug`dc5^a`u°h5o`gSVYobhKoiYXW ¨°\_^#ugVedS#W<h@xoYXmq6fp`°c5oYwc5bu`gSDc5`)`gSVY«ugfpsr^h5^
1 = µ¡hKbE^
1hY9=
·
xoYX`YXbgWkfp^VYvun.SVYX`gSVYXbnbYvuhKobevYvuQc5bY evhK^VugoW<YvxJq hrufp`gfptY ewcKuYrq hKbkstYX^VYXbdc5`YvxJq«^VYXsac5`gfptY
ewcKudYr¨±RTSVY¦obhKoiYXW evhK^Vug`gbdc5fp^a`unYXfp^os¸xoY5V^VYvxJq `gSVY²hK{ YveX`gfptY¦¡o^VeX`gfihK^Dc5.fiu>`gSVY¦^VhK^l
xoYX`YveX`gfihK^´obhKDc5ofppfp`¹§
1T =
srfptYX^ %YXihw 4
1 T
=d/
_ `
AB1
,
.K=
O
;
O
3
? "Z@ $ & AO D
? E 1T
?j1.
O
=:=
cd.
O µW-wZt·
&»almobhKoiYXW .fp`gS¦fp^VY HDc5pfp`¹§nevhK^Vug`gbdc5fp^H`uwq (*)qaevhK^Vugfiug`u fp^¦Ä & & &% Ä N % Å
T Ä
ok
Ä
&%'&
&tÀ
1T = % Å À
<
Ä(%
vw5
&%
w#
%
Å
 ¨