IV Escola de Primavera de Transição e Turbulência
Universidade Federal do Rio Grande do Sul
Pontifícia Universidade Católica do Rio Grande do Sul
Porto Alegre, RS, 27 de setembro a 1o de outubro de 2004
!#"%$'&(*),+.-0/1-%2%34(6587 "0)95:+;/<2%/>=*58?A@B/
CEDGF1H.IKJLH.MNDPO,JRQNSTDVUWOBXYDGOBZ1H.IR[\H]^DP_a`YOT[b_aHdcegfihkjmln[bQ
opo.q,rYs jmtpupuvln[bQvSTDdwpH.OBDG[xIRQBy1lzw
{%H.|}QpIRH.J~QY[bIRDESBDVhQpM|BBJ~[xQpODPJ
SBDCEPJRQpOB[xTD
hDGOJ~IKDdzH.J~[xQpO1HYSTDbHvl
DP_LZBDGIK_LZBDv_G[bDPOJ~[xBTD
p t T TJRBIRQpK_GQpF DVhZ1HYKRDGOTDGB[x l
Ei
bB[xK:DGI~iMNDP_YFBB_jIR[xQB|TI
8 1¢¡ -}£¤+;3*2%"¦¥p§B3
¨ FBIRQ_GDPRKQNSBD©_PQpM|BTKJLª.QDPKJ~«¬FTIRDGKDGOJ~DDPM®SB[x¯YDGIKRQp6MQpMDGOJ~QpSBD©OBQpKRQSB[\H°j±H°j±ST[\HTy,SBQp6MNHY[x
_GQpIKIR[b,BDP[bIKQpGygJLHY_GQpMQ²QHY_PDGOBSTDGI¬SBQ²:QpXpQ²F1HYIRH²DPR,BDPO,J~HYIH²«YXY1H³SBQ´_GH.:S1H³MµH.OBZ1ªTy#HYQpv,BD
DGO¯pQp¶¯pDPM·MNHY[xQpIEKQY1KJR[b_GHY¸aªYQJ~P_GOB[x_aHTy0_PQpMNQF QpI©D¹9DPMNFBxQBy0HTDG[bMNH,BDQ9_PQpIRIKDOTQpMNQYJRQpIRDP©SBD
HYTJ~QYMNº¤¯pDP[bP[bMF QpIKJ~`YOB_G[bH»SBH²_PQpM|BTKJLª.Q<FBHYI~H¼Q³ZBQYMNDPM½JLH.,BDSB[x¯YDGIKRQp¬M[xJ~QYdD¢bDPOBS1HYPy
FBIRDPRDGOJRDG¢DGMJRQ9S1H.N_PBxJRBI~HYPy6_GQpxQ9_GHYM¾Q<:QpXpQ_PQpMQ´DPbDGMDGOJRQ_GDPOJ~I~H.zSBQ[bMNHYXp[bOB«YIR[xQB¿EbXYBOB
ZB[bJ~QpIK[\HYSBQYIRDG#_LZBDGXpHYMÀHVS1H.JLH.IQ[xOBÁb_P[bQS1Hd_GTxJ~TI~Hd_PQpMNQVRDPOBSBQvQMQpMDGOJ~QVDGMTDHdZ,BMµH.OB[bS1H.SBD
_GQpMDG¸GHÂH^_PQpÃG[xOBZ1HYIRDPBH.b[bMDGOJRQpGy0QÂ,BDNFBIRDPRKBF}ÄDH^HYOJ~DPIR[bQYIR[bSBHYSBDvOBQ^SBQpMÁbOB[xQ»STQ^:QpXpQT¢UWM
SB[x¯YDGIRKQpnHY_GHYMNFBHYMNDPOJ~QpÅFTIRjZB[bJ~ºpIK[b_PQpDPOB_GQpOJRI~HYMvj±KD©HYIKJRDP8H.JRQpÅSBDPKJR[bO1HYSTQp6HRDPIRDPM®TJ~[xb[xÃaHYSBQY#DPM
_GDGIK[bMQpOB[bHY[bgDGKF}DP_G[¶1_aHYMDGOJRD©IRDGbHY_G[xQpO1HYSTQpÅHYQV:QpXpQBy,JLHY _GQYMNQQV¯YH.R[bxZ1HYMDzMQpJ~I~H.SBQO1H [bXBÆÈÇ9 ;É y
TD»:Qp[FBIRDPRBM[bS1H.MNDPO,JRD¢TJ~[xb[xÃaHYSBQÂF1HYI~H³Q³J~IRHYOBKF}QpIJ~DSBQ³:QpXpQÊÆ8l
[xXpXpPy tpt opÉ >e¦QpIKGM»y#OBªYQ²~ªYQ
_GQpOBZTDG_G[xSBQpn_GQYMÀFBIKDG_G[x~ªYQ¬OBDPMÀQ¬MQpMNDPOJ~QOBDPMHvMµH.OBDG[xI~HdF DGbHBHYQ¬ZBQpMDGMSBQpM[bOBQYQv:QpXpQB
[xXpBI~H¬Ç pËÍÌ H.RQ¬FBIRÎj±ZB[xKJRºpIR[x_GQvFBIKDGRTMN[xS1HYMDGOJ~DTJR[bb[xÃaHYSTQdF1HYIRH¬JRI~HYOTRF QpIKJRD©SBQ:QYXpQB
WU M| QpI~H¢H._GQpMF1HYOBZTD¬HZ,BMNHYOB[xS1HYSBDvSTDGRSTDNHHYTIRQpIRHSBH_P[x¯[bx[bÃGHY¸aªYQTyH¢_GQpMd|BBKJ~ªYQF}DPIRMNHYOBDP_GD
BMÏ:DGOBÐYMNDPOBQn_G°ÑRHnSBDGK_GIK[b¸aª.QzkHY| DGIJLHTy°O1ªYQnQp|BJLHYOJRD#FBIKQpXpIKDGRKQp%_GQpOBK[bSBDPI~«a¯pDP[b%IRDGHYb[xÃaHYSBQYOBQ
ÒBxJR[bMQ
RG_PBbQT©UWKJ~DP©FBIRQYXpIRDPRRQYiF}DPIRM[xJR[bI~H.M^yBF QpIzD¹9DGMFBbQTy}QFTIRQ°ÑKDJ~QSBDdMNQYJRQpIRDPE_GHYF1HYÃPDGiSBDdFBIRQpFTBbRHYI
_aHYIKIRQpPyO1Ha¯[bQpPyHa¯[bÄDGEDdO1Ha¯pDG©[xOJ~DGIKFB\H.OBDPJ~«YIR[bHYGzÓÔHYMd|}PMÕ:QY[ÔHYx_aHYOT¸aHYS1HNBMµHMNDPbZBQYIz_PQpMNFTIRDGDPO9j
~ªYQ²SBQ³SBDPRDPO,¯YQpx¯[xMNDPO,JRQ²D¢S1H¼FBIRQYF1HYXHY¸GªYQ¼SBD¢[xOB_GÖPOBSB[xQpGyWKDmÑRHYMDGbDP×1QpIKDGKJ~HY[bdQp>BIR|BHYOBQpPCE[Øj
¯pDGIKRQpDG,B[xF1HYMDGOJ~QYv[bOBSBTKJ~IK[\HY[xd,BD¢TJR[bx[bÃaH.MÙH²_PQpM|BTKJLª.Q³_GQpMQ¼:QpOJ~D¢SBD¢DPOBDGIKXp[\H9yÍJLHY[x_GQpMQ
:QpIROBQYGyÍ_GHYbSBDP[bIRHYDµ[bOT_G[bOTDGI~H.SBQpIRDPGy%J~[x¯YDGIRHYMÙR1HÂD1_G[xÖGOB_P[\H»XpI~HYOTSBDGMDGOJ~DHYBMDGOJLHYSBH^F DG\H»MNDPbZBQYI
_GQpMFBIRDPDGOBRªYQÂSTQp©:BOBS1HYMDGOJRQpS1H»_PQpM|BTKJLª.QBe¦QpIKGM»y¦Ú¢KDGMFBIRDFBIRDPRDPO,JRDNSTDGMNHYOBS1HSBD¬MNDPbZBQ°j
IR[\H³O1H<DP1_P[bÖPOB_G[bH<DPOBDGIKXpPJR[b_aH²SBQpFBIKQ9_PDGRKQpSBD^_PQpM|BTKJLª.QBy#¯[bDPI~HYM½RDÑKBKJ~HYF}QYIGyOTQpNÒTxJ~[xMNQY o u
HYOBQpPyWRQpx[b_G[¶JLHY¸PÄ9DPVSTD|1HY[عTQÂ[bMF1HY_PJRQ¼HYMd|B[bDPO,J~HYgDSBD9J~[bx[bÃGHY¸aªYQ»SBD_PQpM|BTKJ~Á¶¯pDP[b,BD¢F DGIKMN[¶JLHYM
BMÀSBDPRDPO,¯YQpx¯[xMNDPO,JRQNKBKJRDGOJL«a¯YDGÈ#UWKJ~HY6FBIRDPQ9_PBF1HY¸PÄ9DPn_GQpM|T[bO1HYSBHYÅ_GQYOBKJR[xJ~TDGMÀSTDG~H°1Qp6,BD©J~ÖPM
OBQpIKJRDaHYSTQNQ¬SBDPRDGO¯YQpx¯[bMDGOJRQNSBDDPKJ~TSBQp
DF DGK,B[bRHYG
e¦HYI~HYxDGbHYMNDPOJ~DWHYQY*FBIRQp|TbDGMNHY_PQpbQ_aH.SBQp*F DGbQYR[xKJ~DPMµH.*FBI~«.JR[b_PQp*D¹9[bJ~DPO,JRDGPyYQnSBDGKDGO¯pQYx¯[bMDGOJ~Q
SBDvOBQ¤¯.HYiJ~DP_GOBQpxQpXp[bHYzSTDv_GQpM|TBKJ~ªYQ¢FBIRDPRKBF}ÄD¬HD¹9[xKJ~ÖPOB_G[bHSBQ¢_GQYOBZBDG_P[bMDGOJ~QSBDJLHYxZ1HYSBQµS1HYi[xO9j
J~DGIRHY¸GÄDG:BOBSBHYMNDPOJLHY[x©DNKDGBMNDP_aHYOT[bRMQp©SBD¬_PQpOJ~IRQYbDYCEDPOJ~IRDNDGJLHY[bOJ~DPI~HY¸PÄ9DP©:BOBS1HYMDGOJ~HY[bPy
SB[x¯YDGIRKQpnFBIRQY|BbDPMµHY#O1ªYQ¬IRDPRQp¶¯[bSBQpSB[bÃPDGMIRDGKF}DP[xJRQNÚ.TDG\H,BD©DPO¯pQp¶¯pDQ¬FBIRQ_GDPRRQ¬SBD©_PQpM|BTKJLª.QBy
DGMXHYKDGnQpDGM8HYRDPzSB[xRF DGIK~HYPy1DVHJRBIR|BTbÖGOT_G[\H9
¨ FTIRQ_GDGKRQNSBDV_PQpM|BTKJLª.QNDPO,¯YQpx¯YDVJRI~HYOB:QpIRMNHY¸PÄ9DP
,BÁxMN[x_aHY6STQpzIKDaHYXYDGOJ~DPGy SBBI~H.O,JRDdH.
,1H.[b
BMµH¬XpIRHYOBSBD,1HYOJ~[xS1HYSBDSBD_aH.bQpI6b[x|}DPI~HYSBHBHYOBSBQNS1HYnIRDP_GQpM|T[bO1HY¸PÄ9DPnDGOJ~IKDVQp
«.JRQpMQp6_GQpOTKJ~[Øj
J~B[xO,JRDGzSBQµK[bKJRDGMNHTnEH[bMDGOBRHMNHY[xQpIR[bHSBQpEK[bJ~DGMNHY
IRDGH.J~[¶¯pQpPy}H¬JLH°¹THSBDdIKDaHY¸GªYQµ,BÁxMN[x_aHvdBMNH
:BOB¸aª.Qi_GIKDGR_PDGOJ~DnS1HnJ~DPMNF DGIRH.J~BIRHTÍUWJLHY¦SB1HYÍ_GHYI~H._PJ~DPIRÁxKJ~[x_aHY%IRDPBOB[xS1HYÔ[xMNFTb[b_GHYM ,BDQpÔFBIKQ9_PDGKRQp
SBD¬_GQpM|TBKJ~ªYQ¢~ªYQFBIKQ9_PDGKRQp,BD¬RD¬HY9J~Q.j±HY_GDPbDGIRHYM»yBMNHµ¯pDPÃ[xOB_G[bHYSBQpvÆ DG STQ;¯[x_LZ³DPJHY'xy t rpÉ
EbPMST[bKJRQByW_GQYMNQ¼IKDGKBxJ~HYSBQ¼SBDPKJ~HY¬_aHYIRHY_PJRDGIRÁxKJR[b_aH.GyWHÂJRI~HYOB:QpIRMNHY¸GªYQ¼,BÁbM[b_GH^D¢H¼x[b| DGIRHY¸aªYQ^SBD
_aHYxQpI©H¢DGbH¢HYRKQ9_P[\HYS1HQ_GQYIRIRDPM DPM DGK_aHYbHY©SBDvJ~DPMNF Q¢DvSBDv_PQpMNFTIR[bMDGOJRQF}DP,BDGO1H.V,1HYOTSBQ_GQpMvj
F1HYI~H.S1HYÚY©DPR_aH.\HYi_GHYI~H._PJ~DPIRÁxKJ~[x_aHYESBQDGR_PQHYMDGOJ~QTUWKJ~HY©DGK_aHYbHY©_aHYIRHY_PJRDGIKÁbKJR[b_GHYiRDPI~ªYQSBDPR_PIR[xJ~HY
|BIRD¯pDGMDGOJRDOTDGKJRDEJ~DιJ~QByTHY|}QYIRS1HYXYDGOBÅMNHY[x#DιBH.BKJR[x¯.HYF QSBDGMRDPIÅDGOB_PQpOJ~IRHYS1HYÅDPMx[x¯IRQY#_P\«YKR[b_PQp
Æ'{*D n[xÅHYOBSN¯pQpO¢UWx|}D.y t T bHYRKMµHYOy tpt [bxb[\H.MNPy t pr BÃPOBDPJRRQ¤¯µHYOBSTH.|}DP OB[ .Q;¯ y tptpu QpIRXYZB[0HYOBS^hZ1HYMFB[xQpOy o uYupu e%DPJ~DPIRPy o upupu HYIKO1H.JRÃDJzHYȶy tYtpt É
hQpMQ4:Qp[E¯[xKJ~Q¿OBQY¢_aHYFBÁ¶J~BxQp¢HYOJRDGIR[xQpIRDPGyEH>JRBIR|TBbÖPOB_G[bH¿F QSBD³RDPI»_GHYI~H._PJ~DPIR[xÃaHYS1H4_PQpMQÊTM
MNQ¤¯[bMDGOJ~Q³×1T[bSBQ³J~IK[¶jSB[bMDGOBK[bQpOBHYgDÂHYxDaH.JRºpIR[xQ¼,BDF}QYRRT[
TM¾DGKF}DP_PJ~IKQ_PQpOJ~ÁbO,BQ²SBD»DGK_aHYbHY¬SBD
_GQpMFBIR[xMNDPOJ~QdQYµSBDEJRDGMF}QTyDPO¯pQp¶¯pDGOTSBQ¬BMµH_G[xOBDGMN«.J~[x_aHIRQYJ~HY_G[xQpO1HY1DEBMµHSB[bOB`YMN[x_aH©O1ªYQdb[bOTDaHYIgD
SB[bKR[bFBH.J~[¶¯YHNÆÈhZBHYRRHY[bXpOy o uYupu É Ô [xO,JRDGIRHY¸aªYQVDGOJ~IKD©HYkDGK_aHYbHY_GHYI~HY_J~DPIRÁbJ~[x_aHYkSBDE_PQpMFBIR[xMNDPO,JRQVDzSBD
J~DGMF QNQpIK[bBOTS1HYnSBQMNQ¤¯[bMDGOJ~QvJRBIR|BTbDGOJRQNDVHY,BDGbHYnIRDPFBIRDPRDGOJ~H.J~[¶¯YH.zSBQFBIKQ9_PDGRKQµSBD_GQYM|BBJLªYQ
bDP¯.H¬HvIRDGHYb[xÃaHY¸GªYQvSBDSB[x¯YDGIKRQp
IRDPXp[bMDGÅF QpKRÁx¯YDG[x
FBHYI~H¬H¬_GQpM|TBKJ~ªYQ¬DGM®DPR_GQpHYMNDPOJ~Q¬J~BIK|BBbDPOJ~QB
zF}ºpg[xO,JRIRQSBBÃP[bIW_GQYOB_GDP[xJ~QYk:BOTS1HYMDGOJLHY[xgSBDz_LZBHYMµH.kDPMMNDP[bQpgXH.RQpKQpGy,DGJ~D
J~D¹JRQdSBDPR_GIKDP¯YDiQp
IRDGKBxJ~HYSBQpzF}QYRRÁ¶¯pDP[b
S1HN[xO,JRDGIRHY¸aªYQDGOJRIRDd_PQpM|BTKJLª.QµDJ~BIK|BBbÖPOB_G[bHND.y F QpIn1M»y}H.FBIRDPRDGOJ~HHYbXYBMµH.
MNQSBDGbHYXpDPOB6F}QYRRÁ¶¯pDP[bnF1HYIRH¬DPKJ~H[xO,JRDGIRHY¸aªYQT
/ /1&?8/ 5'-0/B+;)&
zE_LZ1HYMNHYz\HYM[bO1H.IRDG6RªYQ¢HY,BDP\HYzDGMÕ,BDQNFBIRQ_GDPRRQ¢STDVJ~IRHYOB:QpIRMNHY¸aª.Qµ,BÁbM[b_GHQ_GQYIRIRDRDPM
TDQ¢DPR_PQHYMDGOJ~QRDvJRQpIROBDJRBIR|TBbDPO,JRQBVUgMd|}QpIRHDGJLHY_LZ1HYMNHYiFBHYIRDP¸aHYM_PQpOBJ~[xJRB[bI !#"$%#"
TM
_aHYKQ´F1H.IKJ~[x_GBbHYIdSTD¢F}QpT_aH²HYFBx[b_aH.¸aªYQ¼FTI~«.JR[b_aH9ygHYbXpTOBR[xKJRDGMNHYvBRBHY[bvQpF DGIRHYM½_PQpM½DPKJRDJR[bF Q³SBD
IRDGXY[bMD
STDz_PQpM|BBJLªYQTgCEDGOJ~IKDEDPKJ~DPGy9_aHY| DE_P[xJLH.IgHY#¯YDG\H.#F1H.I~HHV[bxBM[bO1HY¸GªYQ©SBQpMGJ~[x_aHDzIKDGb[xXp[bQY~HTy
Qpi,BDG[xMµH.SBQpIRDPESBDV:QpXpÄDGESTQpMNPKJR[b_GQYiDdSBDd_GQpÃP[bOBZ1H.i[bOBSTBKJRIR[\H.[bGy Dd,BDP[bMNHYSBQpIKDGiIRHYSB[bHYOJ~DGz_GQpMQ
QpEDPOB_GQpOJRI~HYSBQYiDG&
M '$%(")*),+-#"+*)dDdF1H.S1HYIR[bHYG6zbPMSB[bJ~QBy MB[¶JLHY6¯pDPÃGDPHN[bOT[b_G[bHY¸aª.QSTQµFBIKQ9_PDGRKQ¢SBD
_GQpM|TBKJ~ªYQQ_GQpIKIRDDGMÕIRDPXp[bMD\HYM[bO1H.I6QpÂ_P°ÑRHNJ~TIR|BBxÖGOB_P[\H:IRHY_aHTy _GQYMNQNVQ_GHYRQµSBDVMQYJRQpIRDPEH
[bXpOB[x¸aªYQ6F QpI*_PDGOJ~DPbZ1HTÔeÔHYIRH6DGKJRDG¦R[bJ~DPMµHYPy;BM HYSBDP,1HYSBQ
_GQpOTZBDG_P[bMDGOJ~Q
SBQ
FBIRQ_GDPRRQ
SBDg_GQYM|BBJLªYQ
DGM IRDGXY[bMDbHYM[bO1HYI6VDGKRDGOT_G[\H.ÍHNTMFBIKQ°ÑKDPJRQµ| DGM RB_PDGSB[xSBQBze¦QpIzQpTJRIRQbHYSBQBy HN_PQpMFBIRDPDGOBRªYQS1H
:DGOBQpMDGOTQpbQpXY[\H¼S1HY_LZ1HYMNHY¬\H.MN[xO1HYIRDP_GQYOBKJR[xJ~T[nH<|1H.RD»OBDG_PDGRR«YIR[bH´F1H.I~H²Q´DPKJ~TSBQ4S1H²[bOJ~DPI~HY¸GªYQ
DGOJ~IKDV_LZ1H.MµHvD©J~BIK|BBxÖGOB_P[\HT
) 15'4- 3£;55 1p7
/ 6"¦5$ 455 1p/
8 1/
. 3*¥ 0)&¬202
zEIRDGHY¸GÄDGz,BÁbM[b_GHYnQ9_PQpIRIKDGMÕRDPXpBOBSBQµBMÕ_GQpO°ÑKTO,JRQSBDVDPJLH.F1HYEDPbDPMNDPO,J~HYIRDPEDPO,¯YQpx¯YDGOBSTQ¢_LZBQ.j
TDGµDPOJ~IRDÂHYMNQpxG_PB\HYvFTIRDGKDGOJ~DPG hÅHYS1H²BMNH<STDGKJ~HYµDJLHYFBHYNDPbDPMNDPO,J~HYIRDP¬F}QpKRB[
RDP FBIKºpFBIK[bQ
J~DGMF Q´_GHYI~HY_J~DPIRÁbJ~[x_GQ²SBDDP¯YQpbB¸GªYQByk:BOB¸aª.Q´S1H³J~DPMNF DGIRH.J~TI~H³DS1H<FTIRDGK~ªYQT ]^DPRMQHY¬M[bJ~BIRHY
_GQpM|TBKJRÁx¯pDP[bVMµHY[xVK[bMFBbDPVDPO¯pQp¶¯pDGM·BMÙXpIRHYOBSBDNOÒTMNDPIRQ¼SBDµDPJLH.F1HYdDPbDPMNDPO,J~HYIRDPdDNSB[x¯YDGIRRHYDPj
F}P_G[bDPTÁbM[b_aH.GeÔHYIRH1OBSBDv[bxBKJRI~HY¸GªYQBy}O1H¢ÓÔHY|gÆÈÇ9 ;É vSBHYSBQBM MDG_GHYOB[xRMQF1HYIRH»H_P[bOBJ~[x_aH
TÁbM[b_aH³SBD^MN[xKJRBI~HYvDPO¯pQp¶¯pDGOTSBQ>ZB[bSTIRQpXpÖPOB[bQ²D^HYI^Æ ÅH.\8H ,IR[xRZBOBHYO H.OBS [xbb[bHYMGy tpt q,É zDGJLH
JLHY| DGbH~ªYQS1HYSTQp©Q_GQDP1_P[bDGOJRDFTIRjD¹9F QpOBDGOT_G[\H.È:y 9dy*QDιTF QDGOJ~D¬S1HJ~DPMNF DGIRH.J~TI~HT<y ;gy*D¬H¢DGOTDGIRXY[\H
SBDH.J~[¶¯YH.¸aªYQB
y =NyBFTIRDGKDGOJ~DPEO1HvxDG[STDzIRIKZBDGOB[xBGyTF1HYI~H¬HY6ST[x:DGIKDGOJ~DPnIRDaH.¸GÄDGn,BÁbM[b_GHYÅDGxDGMDGOJLH.IRDGP
DιTFTIRDGK~ªYQvXYDGI~H. FBHYI~HBMNHVIRDGHY¸aª.QV,BÁxMN[x_aHDGO¯pQp¶¯pDPOBSBQ >vIKDaHY¸PÄ9DPDGxDGMDGOJLH.IRDGkO1HBHY [bOJ~DPIK¯pPM
DGKF}P_G[xDG
Æ'Ç9 ;É
> QpOBSBD vQRÁbMd|}QpxQµ,BÁxMN[x_GQ¢S1H"!,jGÃG[xMµHNDGRF G_P[bD¬D $ RªYQQp©_GQDP1_P[bDPO,JRDGDGJ~DPT[bQpMPJRIR[b_PQp
SBDGJLHNDPRF G_P[bDO1H jGÃG[xMµHvDJLHYF1HvDPbDGMDGOJ~HYIGyB_P°ÑRHvJLH°¹THvSB# D IRDG
HY¸aªYQ©S1HYSBHF QpI
!('
% &
)
,.
/
*+ #
)
Æ'Ç9 opÉ
,. 2*+ # #
!10
zDGJLHD¹9FBIKDGRRªYQBy ¬H_PQpOB_PDGOJ~IRHY¸aªYQMQp\H.IzS1H¢DPRF G_G[xD3!¼D3!(4 ¬HµJLH°¹TH¢SBD¬Ha¯.HYOB¸PQ5.IRDJ~QpIKOBQ¢S1H
IRDaH.¸aªYQ gÏJLH;¹BH¬SB* DIRDGHY¸aª.QSTD_GHYS1H¬BMNHS1HYnDPJ~HYF1HYnDGxDGMDGOJLH.IR DGnKDGXpBDBMNHbDP[SBDEIRIKZBDGOT[bB
!(' 9 687 -:9<;(=?> = A@2B6C<
Æ'Ç9 sÉ
/
RDGOTSBQ,BDiH.#_PQpOBKJ~HYOJ~DPÅSBDiHa¯.HYOB¸PQ 5.IKDPJ~QYIROBQ~ªYQVIRDP\HY_P[bQpO1H.S1HYgF}DP\H_GQpOTKJLH.O,JRDESBDzDG,B[xbÁb|TIR[bQTy ED - !(' @ !F0 y1TDVi:BOT¸aªYQS1HJ~DPMNF DGIRH.J~BIRHTy 6 y1D©S1HYnFBIKQpFBIK[bDGSBHYSBDG6JRDGIRMQSB[bO1`.MN[x_aHY
ED
- ,YXZ ,.-
HG
-JIKMLONQP
B6SRUTWV
+
HG
- 9[;\=^]`_3aU b
/
B
_3cd b
B6fe
Æ'Ç9 q,É
QpOBSBD
H¼FBIKDGK~ªYQ<H.JRMNQp:GIK[b_aH9y B H¼_GQpOBJLHYOJRD¢BOB[x¯YDGIK~HY6SBQYXHYKDGGy $h
ygDQ
RÁbMd|}QpK1xQ LgNQP _ D¹9FBIK[bMDH^¯.HYIK[\HY¸GªYQÂ_PQpIRIKDGKF}QpOTSBDGOJ~DÚ»J~I~H.OBK:QpIKMµH.¸aªYQ^SBDµIKDaHYXpDPOJ~ DGvDPM FT
IRQ/ SBT J~
QYdO1H
j±PÃG[xMµHvIRDGHY¸aª.Q
_3a b B
a b B
_ic b B6
c b B6
Æ'Ç9 rpÉ
EEDPOJLHYxFB[\HY
SBD:QpIRMNHY¸aª.QBy cj b y DHY
DGOJRIRQpFB[bHYEOTQµDGJLHYSTQF1HYSBIRªYQBy aU b y ~ªYQDι9FBIRDPRRÄDG©_PQpOBZBDP_G[xS1HY
S1H¬JRDGMF}DPI~H.JRBI~HvF1H.I~Hv_aHYSBH¬DPRF G_P[bDTÁbM[b_aHÆ DGDDPJzHY'xy tpt q,É
zF}DP~HYISTQ¼MNDP_aHYOT[bRMQÂSTDIRDGHY¸aªYQ³FBHYI~HÂM[bJ~BIRHYdSTDZB[bSTIRQpXpÖPOB[bQ^DSBD¢H.IdS1HYSTQ¼O1H¼Ó¦HY|6Æ'Ç9 ;É
O1ªYQd_PQpOJ~DPMNFBbHYIkHST[bRKQ9_P[\HY¸GªYQSBQdOT[xJ~IKQpXpÖPOB[bQByptVDGKF}P_G[xDG,BÁxMN[x_aHYWDPKJ~ªYQdDPO,¯YQpx¯[xS1HYkDGM o9 IRDaH.¸GÄDG
DGbDPMNDPOJLHYIKDGGg
Qv_aHYKQS1H_PQpM|BBJLªYQdSBDiZB[xSBIRQ_aHYIK|}QYOBDPJRQp#DPKJRDG6O,ÒBMDGIRQYÅ~ªYQdXpI~HYOTSBDGMDGOJ~DiHYMNFTb[¶j
HYSBQpP]»DG_aH.OB[bKMNQpSBD©IRDGHY¸aªYQv¯[bRHYOBSBQvSTDGR_PIRD¯pDGIzH_GQYM|BBJLªYQ¬SBD©MDPJ~HYOBQ_PQpM®HYIDGO¯pQp¶¯pDPM®_GDPIR_aH
SBDÇYudDPRF G_G[xDG6,BÁxMN[x_aHYkDGMMµH.[bkSBD sr uIRDaH.¸GÄDG6DGxDGMDGOJLH.IRDG©Æ ÅHYTb_LZDJnHYȶy tpt o HYIRSB[xOBDGIÅwYIG¶y
o upupu ÓÔH.O»DJ
HYȶy tpt q \k BXYZBDGnDPJ
H.ȶy o uYu H (k BXpZTDGnDPJnH.ȶy o upu | É ÍeÔHYIRH¬ZT[bSBIKQ9_GHYIR| QpOBDJ~QpÅMNHY[x
_GQpMFBbDι9QpQ¼XpIRHY>SBD[xOB_GDPIKJRDGÃaH¼STQpMDG_aH.OB[bKMNQpVSBDIKDaHY¸GªYQ³SBDPJ~HYbZBHYSBQpdHYBMDGOJLHTyWTMµH^¯YDGâ,BD
Q¢OÒTMNDPIRQ¢SBDv_GHYMN[xOBZBQpz,BD¬HµIRDP¸aªYQ,BÁxMN[x_aHNF QSBDF DGIR_PQpIRIKDGI©H.BMNDPOJLH_GQYM H_PQpMNFTbD¹9[xS1HYSBDVS1HY
MNQpxG_PB\HYIRDaH.XpDGOJ~DPzDPO¯pQp¶¯9[xS1HYÆ'hÅH.J~ZBQYOBOBDPJ
DJEH.ȶy t 9 DGKJR|BIRQQ µHYOBS^CE$I lYDGIGy t Yq HYIKO1H.J~Ã.y
t Yq,É WzDPKJRDGÅ_GHYRQpPyBQdSTDGRDPO¯pQp¶¯9[xMNDPOJ~QvSBDzMNDP_aHYOB[xRMQpkSBDPJ~HYbZ1H.SBQpk©HYRKBOJ~QvSBDzF}DPR,B[x~HH.JR1HY'
hQpMQ³¢SBD¢KD¢DGRF DGIRHYIGy#H¼IRDGHY¸aª.Q<,BÁxMN[x_aHÂF QSBDQ_GQpIKIRDGIHYF}DPO1HYvKD»ZTQpT¯pDPI¬_GQpOJLH°J~Q³DGOJRIRDQp
IRDaH.XpDGOJ~DPµH¼OTÁx¯pDPÅMQpbDP_GBbHYIG<zQ²DPKJ~TSBQ²S1HYv_LZ1HYMNHYvbHYMN[xO1HYIKDGGyÔ¢BR1H.ÅIRDGHYb[xÃaHYIVBMµH¼_P\HYKR[¶Tj
_aHY¸GªYQµ|1H.RDaH.S1HµOBQNXpI~HY»SBDVFBIRÎj±M[bKJRBI~HvDPO,JRIRDV_GQpM|TBKJRÁx¯pDP¦DQa¹9[bS1HYOJRDYneÔH.I~HBOBESBDdHYO1«Yx[bKDYy1SBQp[x
_aHYKQpD¹J~IKDGMQp©F}QSBDPM RDPI©[bSBDPOJ~[xB_aHYSBQYGy*OBQFBIK[bMDG[bIKQµQp©IKDaHYXYDGOJ~DPDPOB_GQYO,JRI~HYMvj±KDvF}DPIK:DP[xJLH.MNDPO,JRD
FBIRÎj±M[bKJRBI~H.SBQpGy}_GQpOTKJ~[¶J~B[xOBSBQNBMµHNMN[xKJ~TI~HNZTQpMNQYXpÖGOBDGHTy DGOB,1HYOJRQ¢TDvOBQRDPXpBOBSTQ¢QpiIRDGHYXpDPO,JRDG
DGOB_PQpOJ~I~H.M¬jRDJ~QYJ~HYbMDGOJ~DKDGXpIKDGXHYSTQpG
Q´_GHYRQ´SBD»IRDaH.XpDGOJ~DPµFBIKjMN[xKJ~TI~HYSBQYGy#H´_LZ1HYMNH²RDGFBHYI~H
XHYRDP¢:IRDGK_GQpSBQY¢FBIRQSBTJRQp¢SBD²_GQpMd|BBKJ~ªYQBfzMNH4_LZ1HYMNH¿ST[xJLH4STD³SB[x:BRªYQ>RDPF1HYIRH¿Qa¹9[bSBHYOJ~D²SBD
_GQpM|TBKJRÁx¯pDPWOBQRDPXpBOBSBQ_GHYRQBv9[xJR1HY¸GÄDG©DPM ,BD¬Q_GQpIKIRDvBMNHFBIRÎj±M[bJ~BIRHµF1HYIK_G[\H.ÔF Q9SBDPM Q_GQpImj
IRDGIPy#_PQpMQ¼OBQ²_aHYKQ²S1H³[bXpOB[x¸aªYQ^F}QYI_GQpMFBIKDGRRªYQ²,BDQ9_PQpIRIKDOBQpvMQYJ~QYIRDG¬Cz[bDGKDG'yWMµHYvOBªYQ³RDPI~ªYQ
HY|}QYIRS1HYSBHY
HY,B[È
ÓÔHY| DGbHÇ pË ]^DG_GHYOB[xRMQ SBDIRDGHY¸aª.Q,BÁbM[b_GH F1HYI~HM[bKJRBI~H.ÊSTD ZB[xSBIRQYXpÖGOB[xQD SBD HYIPy^! 9
DGM Æ:_GM»yEMQpÈy6 É y =¾DPM Æ:_aHY5.MNQY É UÍ1_P[bÖGOT_G[\H.¢SBD³J~DGIK_GDP[bIRQ>_PQpIRF Q Ë c
6 7 > / = @2B6C y 9
K ;o ¶y o r y u c r y xy uT q c ;r ¶y o r y !" u9
lzUW
$ # ¨
9
;
=
¨ & ¨ k'% ¨
k% s rpo U ¤ jmuT Ç Ç.uÇYuT
¨ k'% k
k & % ¨ r u U q o Ç po tpuT
¨ k% ¨ k k &¨ % ¨
r9 Ugt aq tptT
k & % ¨ k k &Ψ % k
ÇYUgt
s sYoY
¨ & % ] k ¨ & % ]
k% Ç U t L j q,o uT
¨
&
¨
¨
uTu Ç q
k% k
k%
k
ÇYupU aq
¨ & k & % ¨ &
uTu GqBp
k% k q oY U ¤s
¨ k% k ¨ & k &Ψ % ¨ &
uTu j q tÇ
o tpU ¤s
&
]
p
u
U
j
uT
k% k% ]
k
%
¤
(
u
uT
k% ¨ k% ]
k &¨ % ]
o o upU opo L j o u
¨ & % k ¨ & k &¨ & % ¨ & s u o U ;o D uTu as tpuT
k ¨ & % ] ¨ k% ¨ k% ] o uYU Ç
uTu q,rYr upuT
k &Î
¨ & % ¨ k k &Ψ % k ¨ & Ç9u U ;o
uTu Gqs uT
k &Î
¨ % k ¨ & ¨ k% ¨ &
uTu
uT
o upupU ¤s
¨ & ¨ % k &Ψ
uTu Ç o uT
k% k s upU ¤s
¨ k'% ]
uT
k% ¨ % ]
o upU ¤ L jmuT
¨ % ¨ % ] ¨ & % ]
uT
ÇYU ;r L jmuT r
¨ & % k k &¨ % ¨ k
uTu spr tpuT
k &Î
upupU ¤s
Î
&
¨
&
¨
&
&
Y
Ç
p
t
U
uTu Ç.t r uT
k
% k k
% k
q ¤s
¨ % ¨ k'% ] k ¨ & % ]
uTu
uT
upupU ¤
¨ & ¨ k'% ¨ k
uTu q ÇYÇ uT
k & % ÇYupU ¤s
//B&N?:/458-%/T+°)&*)%+ 3+'458&P£;"0+;/12%/B&
f
MµHM[bJ~BIRHZBQpMQpXpÖGOTDaHvSBD_GQpMd|BBKJRÁx¯YDG*DSBDQa¹T[xS1HYOJ~D.y1,1HYOBSBQ[bXYOB[xJ~HYS1HTy_GQpOBKBM[bS1HvFBIKQ.j
XpIRDPRR[¶¯.HYMNDPOJ~D
F}QpIgBMNH_LZ1HYMNH,BD
RDzFBIRQpFBHYXHSBQpgXHYKDG,BDP[bMNHYSBQpgF1H.I~HQp#XpHYRDPk:IKDG_GQYGWÓ¦HYx¯YDGÃ
QvD¹9DGMFBbQvMNHY[x_GQYOBZBDG_P[bSBQvSTD©_LZ1HYMNH\HYM[bO1H.Ik,BDKD©FBIRQpFBHYXHdDPMÀDGK_GQH.MNDPO,JRQ¬FBIRÎj±M[bKJRBI~H.SBQ©H
_LZ1HYMNHiDGKJ~HY|B[xb[bÃGHYS1HnRQp|TIRD6BM |B[b_PQiSBD #BOBRDPOÍ [bXB9ÆÈÇ opÉ MNQYKJ~IRHEBMNHE[bMNHYXpDPM SB[bIKDPJ~HES1Hi_LZ1HYMNH
\HYM[bO1H.I¦ÑKBOJLHYMDGOJ~DV_GQpMÕF1H.IKJ~Áx_GBbHYnRºpx[bS1H.
9J~[bx[bÃGHYS1HYnF1HYIRHNMNHYIR_GHYInQµDPR_GQpHYMNDPOJ~Q²Æ8Ug_LZTD ,[WHYOBS
]^BOBXH.Èy tptpu É E
Q_aHYKQ¢SBDO1ª.QµQ_GQpIKIRDGIKDGM [bOBJLHY|T[bb[xS1HYSBDP
HYDGIKQ9SB[xO1`YM[b_GHYGy _GQYMNQµHµ[bOBJLHY|T[bb[xS1HYSBD
SBDi{0HYOBSBHY²Æ DP SBQ¤¯[b_LZµDJ6HY'xy t rpÉ y,F QpIkD¹9DGMFBbQTy9OBDPM Qp|BKJ~«Y_GTbQp#DGM RDP_aHYM[bOTZBQBy,BMNHV_LZ1HYMNH
FBIRÎj±M[bKJRBI~H.S1Hµ\H.MN[xO1HYInRDvFBIKQpF1HYXpHYI~«x[x¯IRDPMNDPO,JRDdDPM IRDPXp[bMDdF DGIKMµH.OBDGOJ~DvDd_GQpM ¯pDGxQ9_P[bS1H.SBDd_PQpO9j
KJLH.O,JRDY<®D¹9F DGIK[bÖGOT_G[\H¼MQpJ~I~H^TD¢DGKJ~H¯pDPbQ_G[bSBHYSBDSBDPF}DPOBSBDHYF DGOBHYSBQ³DPKJLH.SBQ³J~DGIKMNQSB[xO1`YM[b_GQ
S1HMN[xKJRBI~H¬DSBDK1Hµ_PQpMNF QpK[b¸aª.Qµ[bOT[b_G[bHYÈnf
MµH¬¯pDPÃvTDQI~H.[bQµSTDd_GTIK¯.H.J~TI~HS1HN:IKDGOJ~DdSBD_LZ1HYMNH
J~QpIKO1H°j±KD¬XpI~HYOTSBDNST[\HYOJ~DvSBH»DPRF DGRKBI~H^SBDGJLHTy¦H^H.FBIRQa¹9[bMNHY¸aª.Q»STDDPR_PQHYMDGOJ~Q^MNQpOTQ9SB[xMNDPOBR[xQpO1HY%
HYSBDG,1H.S1HTdziDG,1H.¸GÄDG,BDvSBDGK_GIKDP¯pDPMÙHFBIRQYF1HYXHY¸GªYQ¢SBDPKJLHµ:IKDGOJ~DvSTDv_LZ1HYMNHOTMµHM[bJ~BIRHµSBD
XHYRDPzF DGI:DG[¶J~Qp6RªYQ
,.-/
Æ'Ç9 É
10(
,
-/
,32 , /
,54 7 6 8
, 9;< : >= !
[
Æ'Ç9 Ç É
-/ G
, 6
, ,
, ]
, 6
,
G 6 4 76 8 6
/
, e
, /
Æ'Ç9 É
< > = M
% :
9
DGKJ~HYÅDPBHY¸GÄDG 4 6 8 y G 6 D M RªYQByIRDGKF}DP_PJR[x¯.HYMDGOJ~D.yTQd×1¹TQdSBDESB[¶:B~ª.QdMQpbDP_GBbHYIgO1HdSB[xIRDG¸GªYQ
> / -52 176 8:C y#Q<_aHYxQpIDPRF DG_GÁ¶1_GQH³FBIRDPR~ª.Q_GQYOBKJ~HYOJ~DD»H<DPO,J~HYbFT[\H¼DGKF}DP_GÁ¶1_aH²S1H²DGRF G_P[bDd!}¿
¯pDGxQ9_P[bS1H.SBDYyJ~DPMNF DGIRH.J~TI~HDzSBDPOBR[xS1HYSBD
SBQDGK_GQHYMDGOJRQd~ª.Q / y 6 D - ¨ ×19¹9QdSTDz_GHYbQpIgF QpIgI~HYST[\HY¸GªYQ
% y GiD ~ª.QdQd_GHYbQYIkDPRF DG_PÁx1_PQHVFTIRDGK~ªYQV_GQpOTKJLH.O,JRDEDEH_PQpOBSBTJR[x¯[bSBHYSBDnJ~GIKMN[x_aH©S1HMN[xKJ~TI~HT¦E
DG,1HY¸PÄ9DPz_PQpMNFTbDPJ~HY6,BDSBDGK_GIRD¯pDPM Q¬FBIKQ9_PDGKRQµSTD_PQpM|BTKJLª.QDPM®XHYKDG
~ªYQ¬S1H.S1HYnOBQNHYF}ÖPOBSB[x_GDY
QVx[bM[xJ~DSBDz|BHY[¶¹9QpgO,ÒBMDGIRQY#SBDi]ÂHY_LZyD
SBDGKFBIRDPÃaHYOBSTQ.j±KDiQVD:DG[¶J~QSBQdDPMNFB¹TQVSBD
EIR,B[xMNDPSBDGPy
HDG,1HY¸GªYQ¢SBD|1H.\HYOB¸PQSBD,1H.O,JR[bS1H.SBDSBDvMQ¤¯9[xMNDPOJ~QµIKDGSBTÃj±KD¬H _PQpOBKJ~HYOJ~D.VUWJLHY©DPBHY¸GÄDG
F}QSBDGM½RDGIIRDPRQp¶¯[bS1HYJRDGOBSTQ´_PQpMNQ²_PQpOBSB[x¸GÄDGvSBD»_GQpOJRQpIROBQ²XH.RDG¬K :IRDPR_PQpNDPM /
DXHYKDG
TDG[bMNHYSBQYÅDGM ÍÏ[bOJRDGXpIRHY¸aªYQdS1HDG,1HY¸GªYQ¬SBDi_PQpOJ~[bO,B[xS1HYSBDEF}DPIRM[xJ~D
¯pDPIR[xB_aHYIÅ,BDH¯YH.ÃaªYQ
Mµ«YKR[x_aH´^_GQpOTKJLH.O,JRD³H.JRI~Ha¯pPS1H´_LZBHYMµH<DÂ,BD.y
F QpI_GQpOTRDGXYB[bOJ~D.ynR1HFTIRQpFBIRHYXHY¸GªYQ<Q9_PQpIRIKDÂ_GQYM
¯pDGxQ9_P[bS1H.SBDv_GQpOTKJLH.O,JRDYy / y*DPM IKDG\H.¸aªYQHYQY©XHYRDPi:IRDPR_GQYGvD¹9[xKJ~ÖPOB_G[bHSBDGJLH¢¯pDPbQ_G[bSBHYSBDFBIKºpFBIK[\H
S1H»_LZBHYMµH[xMNFTb[b_GHµO1H¢D¹9[xKJ~ÖPOB_G[bH¢SBD¬BMµHDPR_GHY\H¢_aH.I~HY_J~DGIKÁbJ~[b_GH¢SBDv_GQpMFBIK[bMDGOJ~QByHDPRF DGKRBIRH^S1H
_LZ1HYMNHTy y
- / G
/ / Æ'Ç9t É
QpOBSBDQ¢ÁxOBSB[x_GDb uVSBDPOBQYJLHµHYi_GQYOBSB[b¸PÄ9DPiDGM /
zDGJLHDPBHY¸aªYQTy,BDTJR[bb[xÃaHHµZB[xF}ºYJRDGKDSBD
OÒTMNDPIRQdSTDi{*D n[x > @ - G C DE9_LZBM[bS9J > a @ C BOT[xJL«.IR[bQYGy zH¯[bK_GQpK[bS1H.SBDz_P[bOBDPMµ«°J~[b_GH
DÕQ¬_GQDP1_P[bDPO,JRDSBDSB[x:BRªYQ¬MNQYbDG_PB\H.IG
]^DPSB[\H.O,JRD¬ZB[bF ºYJ~DPRDP©SBD^Æ8[ É HYBRÖPOB_G[bH»STD¬JRI~HYOTRF QpIKJRDvSBD¬_aHYxQpIiF QpI©I~HYST[\HY¸GªYQBygÆ:[b[ É J~IRHYOBRF QpIJ~D¬SBD
MµHYK~HF QpINSB[x:BRªYQ4SBD^DGKF}P_G[bDP¢RDPXpBOBSBQ¿H{0DP[zSTD [b_* yÆ:[b[b[ É FBIRQpFTIR[bDPS1HYSBDPµSBD^J~I~H.OBRF QpIKJRDÂ_PQpO9j
KJLH.O,JRDGPygÆ8[¶¯ É O,ÒBMDGIRQµSBD{*D n[xzTOB[xJ~«YIR[xQNDÆ8[x¯ É ,BDdBMÕIKDaHYXpDPOJ~DM[bOBQYIR[xJ~«YIR[xQ_GQYO,JRIRQpbHNQNFBIRQ_GDPRRQ
SBD_GQpM|TBKJ~ªYQBy1DGJLHY
DG,1H.¸GÄDGnF}QSBDPM®RDPI
K[bMFBb[¶1_aH.S1HY
&
/
& -
9
> /
C 9<;\=j]
;
9
:@ e
6
6
6
/
L!
/
6
b
2 2 6 Æ'Ç9 u É
pQ OBSBD 6 ´H¿JRDGMF}DPI~H.JRBI~H¿SBD<_LZ1HYMNH HYST[\HY|1«°J~[b_GHTyEQY|TJ~[xS1H>DGM # b
DGKb J~H DPBHY¸aªYQ
H¯YH.ÃaªYQ>L" MN«YRK[b_GH,BD<H.J~IRH¤¯YDGK~H¿H4_LZ1HYMNHTy ³H¯.HYIK[\«a¯pDPESBD²Ha¯.HYOB¸PQ>S1H4IRDGHY¸aªYQTy ; D RªYQ>Qp
¯YH.bQpIKDGHYSB[xMNDPOBR[xQpO1HY[xvS1H<DPOBDGIKXp[\H²SBD^H.J~[¶¯.HY¸aªYQTy ; = @2B6 yD»SBQ_GHYbQpIvx[b| DGIRHYSBQ²F}DP\H³IRDGHY¸aª.QBy
b
[xXpBIRH¬Ç9 oË hZ1HYMNH¬bHYM[bO1HYIkDGJLHY|T[bb[xÃaHYSBHRQp|BIKDBM®|B[x_GQ¬SBD BOBKDGO
IRDaH.XpDGOJ~D<b[xMN[¶JLHYOJRD¼F1HYIRH¿QÊFBIKQ9_PDGRKQ SBD<_GQYM|BBJLªYQ
>6
6 C$@ 6 yiIRDPRF DG_J~[x¯.HYMDGOJRDY ¨
}F QpKRB[}:I~L"HY¸GªY/ QvSBb D©MNHYb RRH 2 gUWKJLHvDPBHY¸aªYQvF QpKRB[KQpbT¸aªYQvKDGM[¶jmH.O1HYbÁ¶J~[x_aH©,BD©F}DPIRM[xJRDE_GQYOBZBDG_PDGInH
¯pDGxQ9_P[bS1H.SBDSBD#FBIRQYF1HYXHY¸GªYQE_PQpMQz:BOB¸GªYQiS1H.ÔFBIKQpFBIR[xDGS1H.SBDG%:ÁbR[x_GQ.j,BÁbM[b_GHYS1HEM[bJ~BIRHT¦hÅHY| DÅOBQYJ~HYI
TDYyÍF1H.I~H»H»XpIRHYOBSBDMNHY[bQpIK[\HµSBHYVIKDaHY¸PÄ9DPVSTDµ_GQYM|BBJLªYQBy ; y%Q^,BDN[bMFBb[x_aHµ,BDNQ^_PQpOBRTMNQ
SBDNIKDaHYXYDGOJ~DPdRº^¬[bMF}QpIJLHYOJRDvO1H¯[xÃG[bOTZ1HYOB¸GH»SBD µEKR[xM^y%H_LZ1HYMNH»F Q9STDKDGISB[x¯[xSB[bS1H¢DPM
SB1HYzIRDGXY[bÄDG
SB[bK[xJ~[xOJLHYP6EHµFTIR[bMDG[xI~HTyT_GQpOBZTDG_G[xS1HN_PQpMQµIRDPXp[\ª.QNSBDVFBIRÎjmHY,BDP_G[xMNDPO,JRQBy SBDdDPRF DGKRBIRH
UW 6ÆÈÇ t É yÔQ9_PQpIRIKDDG,B[xbÁb|TIR[bQDPO,JRIRDQYFBIRQ_GDPRKRQpvSBDµ_GQpO¯pDP_G¸GªYQ²DSB[x:T~ªYQ¼STDµMNHYRRH¼Dµ_aH.bQpIPy
_GQpMIKDaHY¸GªYQµ,BÁxMN[x_aHOBDPXpb[xXpDGOB_P[\«a¯pDPÈk KDGXpTOBS1HN_aH.I~HY_J~DGIK[bÃGHYS1H¬F}QpInBMDP,B[bxÁb|BIK[bQDPO,JRIRDVSB[x:BRªYQ
DIKDaHY¸GªYQTÁbM[b_aH9yTD©F QpRKB[0DGRF DGKRBIRH y1S1HYSBH¬F QpI
Æ'Ç9 Y;É
; UgJLHRDPF1HYI~H.¸aªYQDGMSB1HY©IKDGXp[xÄ9DPiSB[xKJ~[xOJLHYPy_GQpOTRDG BÖPOB_G[bH»SBHZT[bF ºYJ~DPRDvSBDvXpIRHYOBSBDvDPOBDGIKXp[\HSTD¬H.J~[Øj
¯YH.¸aªYQ F1HYI~HÊH IKDaHY¸GªYQ ,BÁxMN[x_aHTyzF}QYRR[x|B[bx[xJ~H4H SBDJ~DPIRM[bO1HY¸GªYQÊS1HÊDPKJRIRTJRBI~H SBHY^_LZBHYMµH.Gy©MDGRMQ
BHYOBSBQ²RDxDP¯.HÂDGM_GQpOJ~H²TM½MDG_aH.OB[bKMNQ¼STDPJLH.bZ1HYSTQ³F1HYI~H¼STDGR_PIR[x¸aªYQ³SBQ²FBIKQ9_PDGKRQ²,BÁbM[b_PQ¿Æ'e%Dj
J~DGIKEH.OBS [bbx[\HYMGy t Ç 9DPRZ1H.SBIR[0HYOTSÂe%DPJ~DPIRPy tptpu É
Q>DGOJLHYOJRQByEH4KQpbT¸aªYQ4O,BMGIK[b_GHSBQ>R[xKJRDGMNH4SBD¼DG,1H.¸GÄDG´ÆÈÇ9 cTÇ É O1ªYQ>H.FBIRDPRDGOJ~HTyiH.JR1HYØj
MNDPO,JRDYyBST[x1_PBbS1H.SBDGÅMNHY[xQpIRDPGyBMµH¯pDGé,BDEDGKJ~ªYQvSB[xRF QpOBÁx¯YDG[xÅFBIRQYXpI~HYMNHYk_GQpMFBTJ~HY_G[xQpO1HY[x#_GHYF1HYÃPDG
SBDJ~IRH.JLHYIzBMNHµMN[xKJRBI~HIRDaH°J~[x¯.Hµ,1H.b,BDGIPy_GQYMNQF QpIiDι9DGMFBbQQµFBIRQpXYI~HYMNHeWIRDPMN[ع>Æ IK_aHYIzDPJH.ȶy
t p
< DPDDPJH.ȶy t rpÉ ©DGKJRIRTJRBI~HSTDBMNHµ_LZ1HYMNHSBDFBIKjMN[xKJ~TI~HµFBIKQpF1HYXpHYOBSBQ.jRDVOTMµHM[bmj
J~BIRHNDGJ~DPT[bQpMPJRIR[b_GHvSBDVMDPJ~HYOBQDVSTDdHYIPy1_aHYx_GBbHYS1HvTJR[bb[xÃaHYOTSBQ.j±KDiDGJ~DVFBIRQpXYI~HYMNHTyBMNQYKJ~IRHYS1HvO1H
[bXBTÆÈÇ sÉ Ô
DGJLHE1XpTI~HiÅF QpRKÁx¯YDGT_PQpOBJLH.J~HYIÍ,BD6HiDPRF DGRKBI~H©SBDPKJ~H_LZBHYMµHzÅS1HEQpIKSBDGM SBD6u9y ÇEMM^
2500
0.1
2000
0.08
1500
0.06
0.2
0.01
0.18
0.16
0.008
0.04
0.006
OH
0.12
CO, H2O
T
CH4
CO2
1000
CH4, CO2
T (K)
0.14
0.1
0.08
0.06
500
0.02
0.004
CO
OH
H2O
0.04
0.002
0.02
0
-1
-0.5
0
0.5
x (cm)
1
1.5
2
0
0
-1
-0.5
0
0.5
1
1.5
2
0
x (cm)
[bXpTI~HÊÇ9 sTË UWJ~IR9J~BIRH S1H¿_LZ1HYMNHÊbHYM[bO1HYINFBIRQYF1HYXHYOTSBQ.j±KD´O,BMNH¿MN[xKJ~TI~H>SBD²MNDJLHYOTQ D<SBD<HYI
DGKJRDG,B[xQpMNJ~IK[b_aH9
DGKJRDv_aHYKQBy0Hµ¯pDPbQ_G[xS1HYSBDSTDvFBIRQpFBHYXHY¸GªYQ¢S1H_LZ1HYMNH\H.MN[xO1HYI
SBD qB _PM 5.PV¯YDGxQ9_P[bS1HYSTDSBD
FBIRQpFBHYXHY¸GªYQvMµ«°¹9[xMµHµFBHYI~HM[bJ~BIRHYi_G;ÑRH_PQpMF}QpK[b¸GªYQ¢vFBIRºa¹9[bMNHS1H¢DGJ~DPT[bQpMPJRIR[b_GHTyDvF QpRKB[
b[bM[xJRDG0SB[xKJ~[xOJ~QpÔHEF1HYIJ~[bI¦SBQpÍ,1H.[bÍHiFTIRQpF1H.XHY¸aª.QEDGJLHY_P[bQpOB«YIR[bHzO1ªYQEÅF}QYRRÁ¶¯pDPÈÔ [bXB9Æ'Ç9 qÉ MQpKJRI~H
H¢¯.HYIK[\HY¸GªYQµ_GHYb_PB\H.S1HµS1Hµ¯YDGbQ_G[xS1HYSBDdSBDvFBIRQYF1HYXHY¸GªYQ¢S1H_LZ1H.MµHDPM BMNHµM[bKJRBI~HNSBDvMNDJLHYOTQ¢DvHYI
_GQpMQ:TOB¸aªYQS1H_GQpMF QpR[x¸aªYQ©S1HM[bKJRBI~H9Ô
DGKJ~H1XYBI~HTyHIR[xTDGÃaHnSBDPBOB[bS1H_GQYMNQHI~HYÃGªYQDGOJ~IKDzQ
OÒTMNDPIRQSBDzMQpxDGÍSBQ_GQYM|BBJ~Áx¯YDG FBIKDGRDPOJ~DEOTQpgXHYRDPk:IKDGK_GQpkDnQVO,ÒBMDGIKQSTDzMQpbDPWSBQ_GQpMd|BBKJRÁx¯YDG
O1H©MN[xKJ~TI~HiDGJ~DPT[bQpMPJRIR[b_GHT¦UgJ~Dn_GQYMNF QpIKJ~HYMDGOJ~Q©O1ª.Q©MNQpOTQYJ~ÐpOT[b_GQES1Hi¯pDGxQ9_P[bS1H.SBDÅSBD6_LZ1H.MµH©_GQYM
HIK[b,BDGÃGHvSBDP¯YDVKDGI
bDP¯.HYSTQvDGM_GQYOBR[xSBDGIRHY¸aªYQ¬,1HYOTSBQNSBHMQ9STDG\H.XpDGMS1HY6_LZ1H.MµHY6JRBIR|BTbDGOJ~HYG
50
45
velocidade (cm/s)
40
35
30
25
20
15
10
5
0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
riqueza
[bXpTI~HNÇ9 qTËkÌ DPbQ_G[bSBHYSBDSBDFBIRQpFBHYXHY¸GªYQNSBHN_LZ1HYMNH¬\HYM[bO1H.IÅO,BMµHMN[xKJRBI~HvSBDVMNDJLHYOBQDSBDdH.IzDPM
:BOB¸aª.QNS1HvIK[b,BDGÃGHSBHM[bJ~BIRHTy 6 00 y H.JRM^
K
//B&N?:/458-%/T+°)&v-0§B3 )%+ 3+'458&P£;"0+;/12%/B&
¨ TJRI~H²R[xJR1HY¸GªYQ²b[bM[xJRDµ,BD^HYF1HYIKDG_PD^,1HYOTSBQSBQ<DGJ~BSTQS1HY_LZ1HYMNHY¬\H.MN[xO1HYIRDP^HY,BDGbH<DPM
TDÂQa¹9[bS1HYOJRDÂD»_GQpM|TBKJRÁx¯pDPzDPOB_GQYO,JRI~HYMvj±KD^KDGXpIKDGXH.SBQpµF DGbH<KBF DGIK:Áx_G[xD^S1H²_LZ1HYMNHT
±J~QQ_GQYIRIRD.y
F}QpIvDι9DGMFBbQByg,1HYOTSBQ´SBH²_PQpM|BTKJLª.Q<STD»XYQYJLHYvSTD¢_GQpM|TBKJRÁx¯pDP6_GDPIR_aH.S1HYSBD¢_GQpMd|BBIRDPOJ~DYy#_GQpMQ
MNQpJ~IRHYSBQµOBH [xXB%ÆÈÇ9 r H É Æ'9Z1H DPJEHYȶy t ppÉ y QpÂ,1H.OBSBQS1H,BDG[xMµHSBDVTMµH¬¯pDGbH [bXT%ÆÈÇ9 r | É Æ8EOTQpO l9MQpBPy o upu q,É EzDGJ~D_GHYRQTySBQF1Ha¯[bQµDGMNHYO1HNFBHYI~H.BO1HµDGM DGJLHYSTQ¢XHYRQYRQ,BD.yF}QYIESB[¶:B~ªYQTy
MN[xXpI~HvH.JRH¬KBF DGIK:Áx_G[xD©S1H_LZBHYMµH9 ¨ HYI6©J~IRHYÃG[xSBQH.J~HvÃGQpOBHSBDIKDaHY¸GªYQ¬F}QpIn_PQpO¯pDG_P¸aªYQNO1H.JRBI~HY'yBD
QpWFBIRQSBTJRQpÍSBD6_PQpM|BTKJLª.Q©~ªYQ©IKDPJ~[xI~HYSTQpÔS1HiFTIRQa¹9[bM[bS1HYSTDSBQ©F1Ha¯[bQESBDP¯[bSTQHYQ©DP:DP[xJ~QESBQ©DGMFB9¹9QSBD
EIR,B[xMNDPSBDG#D¹9DGIK_G[xSBQvRQp|TIRDEQYXHYKDG#TDGOJ~DPG#fzMNH¯YDGé,BDiH_LZ1HYMNHdDGOT_GQpOJ~IRH°j±KDEF QpR[x_G[xQpO1HYS1HO1H
[bOJ~DPIK8HY_PDDGOJRIRDQYÔIRDGHYXpDPO,JRDGPyp_GQpOJRI~HYIK[\HYMDGOJ~D#HYQz_aHYKQiS1Hz_LZBHYMµH
FBIRÎj±M[bKBI~HYSBHTy.DPKJRD#J~[xF}QzSBDk_LZ1HYMNHTy
TDµ_GQpOBZTDG_G[xS1H^_PQpMQ»_LZBHYMµHSBDNSB[x:BRªYQQp_LZBHYMµHO1ªYQ»FBIKj±M[bJ~BIRHYS1HTy0O1ª.Q^F QpRKB[g¯pDGxQ9_P[bS1H.SBD
FBIRºpFTIR[\H9
CED¢MNHYOBDP[bIRH¼HYO1«YxQpXH¼Ú.v_LZ1HYMNHYvFBIRÎj±M[bJ~BIRHYS1HYPyWQ<K[bJ~DGMNH¼SBD¢DPBHY¸GÄDG^ÆÈÇ c9Ç9 pÉ SBDPR_GIKDP¯YD
QpdFBIKQ9_PDGKRQ³SBDN_GQpM|TBKJ~ªYQ¼DGMÙ_LZ1H.MµHYVSBDµST[x:BRªYQBEV_GQpOBST[b¸GÄDGVSBDµ_PQpOJ~QpIKOBQ³HYFTIRQpFBIK[\HYSBHY~ªYQ
Q¤¹9[xS1HYOJ~DzDGM /
Dz_GQpM|TBKJRÁx¯pDPDPM f
MµHSBDGK_GIK[b¸aª.QdR[xMNFTb[xB_aHYS1HEF QpKRÁx¯YDG _GQpOTR[bSTDj
I~HYOBSTQ.j±KDzH.WRDGXYB[bOJ~DPgZB[bF ºYJ~DPRDP Ë Æ:[ É HYTRÖGOT_G[\H©SBDÅJRI~HYOTRF QpIKJRD
STD6_aHYxQpIÍF QpIWI~HYST[\HY¸GªYQBy Æ:[b[ É J~IRHYOBRF QpIJ~D
SBDvMµH.R~HNF}QpIESB[x:BRªYQSBDdDGRF G_P[bDP©RDGXYBOBSBQ»H¢{*DG[¦SBD [x*_ yWÆ8[b[x[ É FBIKQpFBIR[xDGS1H.SBDGiSTDdJ~IRHYOBRF QpIJ~D_PQpO9j
KJLH.O,JRDGPy Æ8[x¯ É O,ÒBMDGIRQzSBDÅ{*-D n[b%BOB[xJ~«YIR[xQnD©Æ:¯ É HzIKDaHY¸GªYQE,BÁxMN[x_aH6O1Hz_LZBHYMµH
F}QSBDkRDPIÔSBDPR_GIK[xJ~HzF QpI¦TM
FBIRQ_GDPRRQvXYbQp|1H. OTQ_GQpMd|BBKJRÁx¯YDG > C DiQa¹9[bS1H.O,JRD >
C RDEJRI~HYOB:QpIRMNHYMDPMFTIRQSBTJ~QY > C KDGXpTOBSBQvH
IRDaH.¸aªYQ
Æ'Ç9 ¤opÉ
9 E%ZB[bF ºYJ~DPRDPÆ:[¶j[x¯ É ~ª.Q
_PQpOBZBDP_G[xS1HY%_GQpMQ
HYFBIRQa¹9[bMNHY¸GªYQ6SBD#9_LZ¯.HY|9j DPbSBQ¤¯[b_LZÍe¦QSBDÎj±RDgDPO,J~ªYQ
SBDP1OT[bI
BMµH¯.HYIK[\«a¯pDP*_GQpOBZTDG_G[xS1Hv_GQpMQv:I~HY¸GªYQ¬SBDMN[xKJRBI~HTy Vy
QpOBSBD
=
+
/
/
/
/
+
NH¢MµHYK~HMNQY+ \HYIiD
2
9 / /
+
+
/
/
Æ'Ç9 asÉ
H¢:I~HY¸GªYQ+ SBDNMNHYK~HSBQp_GQpOTKJ~[¶J~B[xOJ~DGPy¦QÁxOBSB[b_PDuIRDPFBIRDPRDGOJ~HÂQp
)(*+*
,'-
,$./"0
'4.5
/67
8
"!# %$&"'
1%$&32
"!# 1%$&9'
[bXpBIRH¬Ç9 r9Ë 9[xJR1HY¸PÄ9DP
DPM®,BDQpnIRDGHYXpDGOJRDG
DGOB_PQpOJ~I~H.M¬jRDRDPXpIRDPXHYSBQpnF DGbH¬KBF DGIK:Áx_G[xD©SBD_LZ1HYMNHT
¯YH.bQpIKDGÔSTDGKJ~HYÍFBIKQpFBIK[bDGSBHYSBDG¦OBQi_PQpM|BBJ~Á¶¯pDGQpOTQiQa¹T[xS1HYOJ~D.ÔÊ:I~HY¸GªYQESBD#MN[xKJRBI~H
BMNHzXpIRHYOBSBDPÃaH
OBQpIRMNHYx[bÃaH.S1HTy 0 yBDRBHDPBHY¸aªYQSBD©J~IRHYOBKF}QpIJ~D
;:
-/
:
- ]
Æ'Ç9 Gq,É
e
F}QSBDdKDGIiQY|TJ~[xS1HF QpIzBMµHRQpMNHNF QSBDGIRHYS1HNSBHYEDPBHY¸GÄDGiXYQ;¯YDGIKO1HYOJ~DP©S1HYEDPRF G_P[bDGETÁbM[b_aH.G
zQ
_aHYKQ S1HY»_GQYOBSB[b¸PÄ9DPSBD´_PQpOJ~QpIKOBQÊF1HYI~HÊHY»DGKF}P_G[bDP^,BÁxMN[x_aHY¢D´H¿DGOJLHYxFB[\H>KDGIRDPM ZBQpMQpXpÖPOBDaHYPy
H²¯.HYIK[\«a¯pDP »H<ÒTOB[b_GH²¯.HYIK[\«a¯pDP6OBDG_PDGRR«YIR[bH´F1H.I~H<H<SBDPR_PIR[b¸GªYQ<SBQ´FTIRQ_GDGKRQ4STD»IKDaHY¸GªYQBy#SBDP¯[bSTQÚ
HYBRÖPOB_G[bHNSBDJ~DPIRMQ:QYO,JRDY6
QYJ~DÎj±KDV,BDVHY
SB[x1_PBb[xS1HYSBDP
HYRKQ9_P[\HYS1H.zÚ¬IRDPRQpxB¸aª.QNS1HNUW ¦Æ'Ç9 Gq,É ~ªYQ
MNDPOBQpIRDPnTDdHY,BDP\HY6IKDP:DPIRDGOJRDGiÚ.
DP,1HY¸GÄDGnSBD©JRI~HYOBKF}QYIKJ~DQpIK[bXp[xO1HY[xGy9Ug,PÔÆ'Ç9 cTÇ9 É
Q^_GHYRQ»DGM ,BDQ¢J~DGMF Q^_GHYI~HY_J~DPIRÁbJ~[x_GQS1HIRDaH.¸aªYQ»,BÁbM[b_GH DzMdB[xJRQ»MDGOTQpI©,BDNQJ~DPMNF Q
_aHYIRHY_PJRDGIRÁxKJR[b_GQESBQp¦JRI~HYOTRF QpIKJRDGÍMDG_G`YOB[b_PQpGy ypHzDGRF DGKRBIRH©S1HEÃGQYO1HEIRDGH.J~[¶¯.HzMdB[xJRQE[bO9:DGIR[xQpI0SBQi,BD
HY,BDGbHzS1HY¦ÃGQpOBHYÔSBD#SB[x:T~ªYQB%ÊDGKJRIRTJRBI~HzS1HzP _LZ1H.MµH
\HYM[bO1H.I*SBDSB[¶:B~ª.QzIKDGRTxJLH.O,JRDSBDPKJ~HEZB[bF ºYJRDGRD.y
_GQpOBZTDG_G[xS1H´_PQpMQHYFTIRQa¹9[bMNHY¸aªYQ²SBD BI YDÎj9_LZ,BMNHYOBOyn»MNQYKJ~IRHYS1H³O1H [bXB6ÆÈÇ9 É zDGJ~D^_aHYKQByÅH
IRDaH.¸aªYQ¼DPOJ~IRDµ_GQpM|TBKJRÁx¯pDPDQa¹9[bSBHYOJ~DµQ_GQYIRIRDµHYF DGO1HYV,1HYOBSBQ³DPKJRDGKDDGOB_PQpOJ~IRHYMDPMFTIRQpF QpIR¸GªYQ
DGKJRDG,B[xQpMNJ~IK[b_aH9yB[ÈDY¶y g
QYJ~DÎj±KD©TDOBªYQvZ1«v_GQD¹9[bJ~ÖPOB_G[bHDGOJ~IKD_PQpM|BTKJ~Á¶¯pDPD©Qa¹T[xS1HYOJ~D.yBD
=<
<
?>
N
YO,0
YC,0
YO
TC
T
TO
TC
0
Z st
Z
1
b[ XpTI~H¿Ç9 TË UWKJRIRTJRBI~HÊS1H>_LZ1HYMNH¿bHYM[bO1HYINO1ªYQ¿FBIKj±M[bJ~BIRHYS1H4KDGXpBOTSBQ H>ZB[xF}ºYJRDGKD³SBD BI .Dj
9_LZ,BMµH.OBO
1
3000
2500
Temperatura (K)
0.8
H2
H2, O2
0.6
0.4
0.2
2000
1500
1000
N aumenta
500
O2
N aumenta
0
0
0.2
0.4
0.6
0.8
0
1
Z
0.2
0.4
0.6
0.8
1
Z
1&'4
5
.
0
)( 7
*751
?
[bXpTI~HÇ9 Ç Ë UWKJRIRTJRBI~HS1H¢_LZ1HYMNHO1ªYQFBIKjMN[xKJ~TI~HYS1HDPKJR[bI~H.S1HTUͯYQpbB¸GªYQS1HJ~DPMNF DGIRH.J~BIRHD¬S1HY
:I~HY¸PÄ9DPkSTD6MµHYK~H©SBDnZB[xSBIRQpXYÖGOB[xQiDnSBDnQ¤¹9[xXpÖGOB[xQiDGMBMµH©_LZ1H.MµHiSBDnZB[xSBIRQYXpÖGOB[xQiDnSBD
HYIÍF1H.I~H©SB[x¯YDGIKRQp
¯YH.bQpIKDG6S1HvJLH°¹THvSBDDGJ~[xI~HYMDGOJ~
Q <
TD¬HIRDGXY[\ªYQNSBDvIRDGHY¸aªYQµ\HYSTDaHYS1HNF}QpIESB1HYiIKDGXp[xÄ9DPEO1H.©BHY[bzQJ~I~H.OBRF QpIKJRDSBD_GHYbQYIEDSBDdMµHYK~H
Q9_PQpIRIKDF QpI6SB[¶:B~ª.QNH.F}DPO1HYG
1HYOTSBQ^QO,ÒBMDGIKQ^SBDCiH.M pbDPIGy @ DE¬FBIKºa¹T[xMNQSBD¬BM»y%H^H.FBIRQa¹9[bMNHY¸aª.Q¢SBD BI .Dj
9_LZ,BMµH.OBOSBDG[عBHVSBD©RDPI¯.«Yb[xS1HTÍ
DGJ~D©_aH.RQBy9BMµP HVSBDGK_GIR[x¸aªYQvK[bMFBb[¶1_aH.S1HSBH_GQpM|TBKJ~ªYQiF QpRKÁx¯YDG
DGR_PIRD¯pDGOTSBQ.j±KD¼HY¬UW,G
Æ'Ç9 cTÇ9 É O,BMIRD:DGIRDPOB_G[bHYÅOBQYIRMNHYÚ³KBF}DPIK:Áx_G[bDµSBD¢_LZ1HYMNHTyWDJ~QYMµHYOTSBQ.j±KD
_GQpMQv_GQQpIRSTDGO1HYSBHOBQpIRMNHY}HDGJLHvHd:I~H.¸aªYQvSBDEMN[xKJ~TI~HTy VWCED1OB[bOTSBQ.j±KDHdJLH°¹THSBD©DPKJR[bI~H.MNDPO,JRQS1H
_LZ1HYMNHTy <
]
&
Æ'Ç9 ¤rpÉ
e
<
QpOBSBD IRDGFTIRDGKDGOJLHV* HOTQpIRMNHYBÚRTF}DPIK:Áb_P[bD6S1H_LZ1HYMNHTy,HYkUW,G}ÆÈÇ Ç¤c9Ç9 pÉ F}QSBDGMRDGIgIKDj±DPR_PIR[xJ~HYg_GQpMQ
*
&
2 & < : > =
&
0 & (
2
!
2[
Æ'Ç9 aÉ
Æ'Ç9 Ç É
z QYJRDj±KD³,BD³HJLH;¹BH4STD¼DGJ~[bIRHYMDGOJ~Q4ÂDG,B[x¯.HYxDGOJ~D¼HYQ4[bO¯YDGIRKQ¿SBD¼BM J~DPMNF Q4_aH.I~HY_J~DGIKÁbJ~[b_PQ4S1H
IRDaH.¸aªYQzTÁbM[b_aH9y¤IRDGFTIRDGKDGOJLH.SBQ©HYKR[bM BM O,ÒBMNDPIRQ
SBD#CiHYM pxDGIG¦eÔH.IKJ~[xOBSBQ.jRDgSBQ
DG,B[xbÁb|TIR[bQ6,BÁxMN[x_GQBy
R[xJR1HY¸GªYQiS1HE_LZBHYMµHzSBD BI YDÎj9_LZ,BMNHYOBOy,BM HYTMNDPO,JRQ©SBQiDPKJ~[xI~HYMDGOJRQEMQ9SB[¶1_aH
FBIRQYXpIRDPRR[¶¯.HYMNDPOJ~D
H»DPKJ~IKTJ~TI~HS1H»_LZBHYMµH9¬UgJLHMNQSB[¶1_aHY¸GªYQ¢F Q9SBDvKDGIQp|BKDGI¯YH.S1H»OBH [xXBWÆ'Ç9 Ç É y0HYQYOBSBD¬¬MNQpJ~IRHYS1H
H»D¯pQpxB¸aªYQS1H¢J~DPMNF DGIRH.J~TI~H¢DvSBD¬:I~HY¸PÄ9DP©SBD¬MµHYK~HSBD¬BMNH_LZ1HYMNHSTDNZB[xSBIRQYXpÖGOB[xQ > :C D¬SBD
HYI > ;0C F1HYIRH²ST[x:DGIKDGOJ~DP¯.HYxQpIRDP¬S1H²J~H°¹TH<STD»DPKJR[bI~H.MNDPO,JR
Q Æ'THY| DG OB[ YQ¤¯>DPJNHY'xy tpt É ¿
MNDPSB[bS1HvDPM®,BDQDPKJR[bI~H.MNDPO,JRQHYBMDGOJLHTyTQ9_PQpIRIKD©BMµHvFBIKQpXpIKDGRK[x¯.Hv[bOJ~DPIRF DGOBDJ~IRHY¸aªYQ¬SBQY
IKDaHYXYDGOJ~DPG
UgJLHÂ[xOJ~DGIKF}DPOBDPJRI~HY¸GªYQÂIKDGKBxJ~H»O1H»FBIRDPRDPOB¸aHÂSTDµ_GQYM|BBKÁx¯pDPgO1ªYQÂ,BDP[bMNHYSBQ»O1H^IKDGXp[bªYQQa¹T[xS1HYOJ~DS1H
_LZ1HYMNHTyDd¯[b_PDjȯpDGIK~HT ±KJRQ¢bDP¯.HHTMµHµST[bM[bO,B[b¸GªYQµFTIRQpXpIKDGKR[x¯.HµSBHµJ~DGMF DGI~H°J~BIRHO1H_LZ1HYMNHTyH°J~Q
F}QpOJRQ¼DGM·,BDO1ªYQµMNHY[bF}QYRRÁ¶¯pDPMNHYOJ~DGI_GQYM|BBJLªYQ¼DPKJ~HY_G[xQpO1«YIK[\HT^fzM·HYBMDGOJRQ¼S1H^J~H°¹THÂSBD
gases queimados
oxidante
uL
lt
lt
v’
v’
δL
δL
frente de
chama
gases frescos
.
2 5.
chama
combustivel
(*
2 .
[bXpTI~H^Ç9 9Ë eWIRQ_GDGKRQ¼STDµ[bOJRDGI~H.¸aªYQ»DGxDGMDGOJLHYIDGOJRIRDµTMÙJRBIR|T[bbZBªYQDµBMNH:IKDGOJ~DNSBDµ_PQpM|BTKJLª.QB
b[xOBZ1HRºpx[bS1H¬IRDPFBIRDPRDGOJ~HQNMµ«;¹T[xMNQS1HNJ~H°¹THµSBDVIRDaH.¸aªYQDdHµF QpOJ~[bxZ1HYS1H¬SBDPb[bM[xJ~H¬HNDGKF}DPRKBI~H¢S1H
IRDGXY[\ªYQ¬SBDFBIKjmH.TDG_G[xMNDPOJ~QB
DGKJR[bIRHYMNDPOJ~QdxDP¯.HDGOJLªYQÚVD¹JR[bOB¸GªYQHY|TIRBFTJ~HVSBQVFBIRQ_GDPRKQSBDE_PQpM|BTKJLª.QBy9_PQpMQVF Q9STDzKDGIQY|BRDPIK¯.HYSBQ
O1H [bXB Æ'Ç9 Ç©| É Í D¹9[xKJ~ÖPOB_G[bH©SBDzTM¯.HYbQpIÔ_GIRÁ¶J~[x_GQS1HiJLH°¹THSBDnDGJ~[bIRHYMDGOJ~Q,BDzHY_aHYIKIRDJLHHDιJ~[bOT¸aªYQ
S1H³_LZ1HYMNH²¢[xOJ~[bMNHYMDGOJ~DNb[xXHYS1H¼H³SBDPR_PIR[b¸GªYQ²S1H¼JLH°¹TH³SBD¢IKDaHY¸GªYQ²F}QpIvTMµH¼xDG[STD»zIRIKZBDGOB[xBvO1H
BHYÔHDGOBDPIRXp[bHNSBDdH.J~[¶¯.HY¸aªYQXpI~HYOTSBDY
eÔH.I~HN¯.HYxQpIRDPzS1H¬JLH°¹THSBDdDPKJ~[xI~HYMDGOJRQµMNHY[bQpIKDGnSBQNTDdDGJ~D
¯YH.bQpI_GIKÁxJ~[x_GQBy0Q_GQpIKIRDµHYF}DPO1HYVMN[xKJ~TI~HDGOJ~IKDµQpVIRDaH.XpDGOJ~DPGyWKDGM·IRDaH.¸aªYQ^TÁbM[b_aH9EH [bXBkÆ'Ç9 Ç»H É
DGKJ~H^K[xJ~BHY¸aªYQ»¬MµH°J~DGIK[\HYx[bÃGHYS1HµF DGbHYIRDPJ~HYTD¯.ªYQ»SBD 0 H HYQp¯YH.bQpIKDG©MN«°¹9[bMQp©SBD
_GQpOB_PDGOJ~IRHY¸aª.QµSBQpnIKDaHYXpDPOJ~DGP
),7 5 ´)9*& )W3 &a&G$:@ )5'&v20/ 1p!3 ¦"¦&P£a§B3) )& 1p3 / )-}£¤3<£;"%+ ¦"¦?:)-}£¤3
CiH.M pZBbDPIz:Qp[¦Q¢FBIR[xMNDP[bIKQHFBIKQpF}QYIEBMNHµSBDPR_GIK[b¸GªYQF1HYI~HµHDGKJRIRTJRBI~H¢[xO,JRDGIKO1HSBDBMNH_LZ1HYMNH
J~BIK|BBbDPOJLHVFTIRjMN[xKJRBI~HYSBHTyp_GQYMNQRDPOBSBQd_PQpOBJ~[xJRBÁbSBHSTDzBMNH_LZ1HYMNHbHYMN[xO1HYI¦_GQpMDPRF DGRKBI~HVMB[xJRQ
1O1HTy_PQpOJ~[xOBHYMNDPOJ~DSBQY|BI~HYSBHµDSBDPRbQ_aH.S1HµF DGbQµDGR_PQHYMDGOJ~QJRBIR|TBbDPO,JRQ²Æ #QpIRXpZT[ÍHYOBS³hZ1HYMFB[bQpOy
o upupu É UgJLH¯[bRªYQ>,1HYKDj±DPKJ~«.J~[x_aH>_GQpIKIRDPRF QpOBSBD²HYQ>FTIRQ_GDGKRQ¿DGxDGMDGOJLH.IµSBD³[xO,JRDGIRHY¸aªYQ>DPOJ~IRD³TM
J~BIK|B[bxZ1ªYQSBD[bOJ~DPOBR[xS1HYSBDD¬SB[bMDGOBRªYQ»_GQpOBZTDG_G[xS1HYDN_LZBHYMµH.bHYM[bO1HYIKDGPyJLHYg_GQYMNQQ»[bbTKJ~IRHYSBQO1H
[bXB Æ'Ç9 É ÔzDGJLH[bOJ~DPIRFBIKDPJLH.¸aªYQBy9H©:IRDGOJRDzSBD
_LZ1HYMNH©J~BIK|BBbDPOJLHV
BMNH_PQpbDP¸aªYQTyOBQdKDGOJ~[xSBQdDPKJLH°J~Ábmj
J~[b_PQBySBDdSB[x¯YDGIRRHY©IRDGHYb[xÃaHY¸PÄ9DPiSBDPKJ~DvFTIRQ_GDGKRQDGxDGMDGOJLH.IGE©Qp|TRDGI¯.HY¸GÄDG©DιTF DGIK[bMDGOJLH.[bE_PQpIRIKQp| Q.j
I~HYMDGKJ~HSTDGR_PIR[x¸aªYQBy9JLHYOJ~Q¬OBQ¬_GHYRQSBD©_LZ1HYMNHY6FBIKjMN[xKJ~TI~HYS1H.Å,1HYOBSBQOBQ¬S1HY6_LZBHYMµH.6SBDSB[x:BRªYQ
J~BIK|BBbDPOJLHYPÏUWOJ~IRDJLHYOJRQBy6_GQpMQKD¯pDPI~«4H<RDPXpB[bIPy6D¹9[bJ~DPM SB[¶¯pDPIRRQYµIRDPRB¶JLHYSTQpµF QpRKÁx¯YDG[bNSBDGJ~D
FBIRQ_GDPRRQ»SBD[xOJ~DGIRHY¸aª.Q¢DGbDPMNDPOJLHYIiDPOJ~IRDv_PQpM|BTKJLª.Q¢DJ~BIK|BBbÖPOB_G[bHµDGM_LZ1HYMNHYGyDGKJRD¬vHYF DGO1HY©TM
SBDGxDGGgUWM F1HYIKJR[b_PB\HYIPyH©DGJ~IR9J~BIRH[xO,JRDGIKO1H©S1HYW_LZ1HYMNHYg\H.MN[xO1HYIRDPÔF Q9STDů9[xIWH©RDPIkKB|BJLHYOB_P[\HYxMNDPOJ~D
MNQSB[xB_aHYS1HF DGbHJ~BIK|BBbÖPOB_G[bHT
8 1¢¡ -}£a)+;/1¥ 0)9& )W3 &a&a$A@ )5'&v)-}£¤+;)^£¤"%+ ¦"¦
? - 15:/²) 1p!3 Ô"%&P£¤§B3 )¦+ 3+'45'&£;"%+;/120/
¨ EJR[bF QpESBDd_LZ1HYMNHF}QSBDGM RDPIi_GbHYRK[x1_GHYSBQpiHF1HYIKJR[bIzSBDBMNHN¯[bRªYQ,1HYKDj±DPKJ~«.J~[x_aH¢S1HYi[xOJ~DGImj
HY¸GÄDGvF QpRKÁx¯YDG[bdDGOJ~IKDHÂJ~BIK|BBbÖPOB_G[bHÂDHÂ_PQpM|BBJLªYQTy#H^BHYÅFBIKDGRKBF Ä9D¢,BDH¼_LZ1H.MµH¼bHYMN[xO1HYI
_aHYIRHY_PJRDGIR[xÃaHYSBH¼F}QpIdR1H³DGKF}DPRKBI~HTy UW nÆÈÇ9t É ygDF QpIK1H¼¯pDGxQ9_P[bS1H.SBDµ:BOBSBHYMNDPOJLHYÅSTD¢FBIRQpFBH°j
XHY¸aª.QBy / wp«»HJ~BIK|BBbÖPOB_G[bH¢v_GQpOBJ~[¶J~BÁxS1H¢F}QpI©TMµH_GHYR_GH.JLH¢J~BIK|B[bxZBQpO1H.Ii_aHYIRHY_PJRDGIK[bÃaH.S1H¢F}QpI©TM
¯YH.bQpI6SBDDGOTDGIRXY[\Hv_G[xOBPJR[b_aH9y !}y1DVTMµHvDGK_aHYbHSTDV_PQpMNFTIR[bMDGOJRQ[xOJ~DGXYI~HY'y ÆÈhZ1HYK~HY[xXpOy o upuYu É kfzMNH
IRDGFTIRDGKDGOJLH.¸aªYQDGK,BDGMN«.J~[x_aHS1HN[bOJ~DPI~HY¸GªYQDGOJRIRDBMÕJ~TIR|B[xbZ1ªYQDvHµ_LZBHYMµN HNdS1HYSBHµO1H [xXB¦ÆÈÇ9 H É
[bXpTI~H
Ç9t Ë hZ1HYMNHnJRBIR|TBbDPO,J~H
FTIRjMN[xKJRBI~HYSBHÅDGKJ~HY|B[xb[bÃGHYS1HÅDPM XpDGQpMDPJRIR[bHÅSBD#F QpOJ~QnSBDkDGJLHYXYO1HY¸aª.QB
EH [xXBÍÆ'Ç9t É MQpKJRI~HYSBHµBMNH[bMNHYXpDGM[xOBKJ~HYOJL`YOTDaHSBDvBMNHµ_LZ1H.MµHµJRBIR|BTbDGOJ~HDGM DPR_PQHYMDGOJ~Q
SBDXHYRDPzFTIRjMN[xKJRBI~HYSTQpÅ,BD[bOJ~DPI~HYXpD©_PQpM®BM®HYOJ~DGFBHYIRQ¬RºYb[bSTQ»Æ QH.JnDJEH.ȶy o upu ;É
¨ JR[bF QNSBDV_LZ1HYMNHJRBIR|BTbDGOJ~HµFBIRDPRDP& O,JRDO,BM DGR_PQHYMDGOJ~QµSBDGF DGOBSTDS1HYzIRDGbHY¸GÄDG
DGOJRIRDHN[bOJ~DPO9j
R[bSBHYSBDS1H»J~BIK|BBbÖPOB_G[bHTy > ! @ C yÔD¢H^¯pDPbQ_G[xS1HYSBD:BOBS1HYMDGOJ~HYSBDµFBIRQpFBHYXHY¸GªYQÂSBDµ_LZ1HYMNHTy
/ y%DSBH»DPR_aH.\H¢[bOJ~DPXpI~H.WSB
D¬_GQpMFBIR[xMNDPOJ~Q DµH¢DGKF}DPRKBI~HÂSTDN_LZ1H.MµH¢\H.MN[xO1HYIEFT\HYO1H9y y0,BDRD
FBIRQpFBHYXHYIK[\H¢OBQ»MNDP[bQ_GQpOTR[bSTDGI~H.SBQ>5Æ QpIRXYZB[gHYN OBS4hZ1HYMFB[bQpOy o upupu 0Ì D lO1HYOJRDHYOBS Ì DGI¯9[xR_LZy o upu o e¦DPJRDGIKGy o upuYu É zhQpMÕDGJLHYEDGR_GHY\H.ESBDV_GQpMFBIR[xMNDPOJ~QµDVSBDV¯YDGxQ9_P[bS1HYSTDddF QpKRÁx¯YDG%DGK_GIRD¯pDPIO,ÒBMDGIKQp
SBDl
[D l9OTQpbSB6JRBIR|BTbDGOJRQNDSBDCiHYM YbDGI
B
/
/ N Æ'Ç9 aÉ
N N
Æ'Ç9 t É
DzJLH.M|}PMQdO,ÒB
MDGIKQSBD .H IRbQ¤¯[xJRÃYy,,BDEIKDGbHY_G[xQpO1HHVDGKF}DPRKBI~HSBDz_LZ1HYMNHdHDGR_GHY\HSBDE_PQpMFBIR[xMNDPO,JRQ
SBD QpxMNQpXYQpIRQ¤¯ y y
]
&
e
B 0
N
UgJ~DPzJ~IKÖGnO,ÒBMDGIRQYzH.SB[bMDGOBK[bQpOBHY[b#DGKJ~ªYQIRDGbHY_G[xQpO1HYSTQpÅ_GQYMNQ
Æ'Ç9 o u É
'Æ Ç9 o;É
[xXBgÆ'Ç9 u É J~IRHYÃYy0O,BM FBbHYOBQ > @ @ / C y%QYST[x:DGIKDGOJ~DPIRDGXY[bMDG©SBD¬_GQYM|BBJLªYQ»F}QYRRÁ¶¯pDP[b
BHYOBSBQVS1H[xOJ~DGIRHY¸aª.QVDPO,JRIRD
BMNH©:IKDGOJ~D
N SBDn_LZ1
HYMNHD
TMµHFBIRÎj±M[bJ~BIRHEJ~BIK|BBbDPOJLHTW
DGJLHVIKDGFBIKDGKDGO9j
JLHY¸GªYQ / Ty}H.Eb[xOBZ1HYnSBD B _GQYOBKJ~HYOJ~DdF QpKRBDPMSBDP_Gx[x¯[bS1H.SBD / y}HNIRDJLH_GQpMSBDP_Gx[x¯[bS1H.SBD
,BD#F1HYK~HEF DGbHzQpIK[bXpDPMÏ_GQpIKIRDPRF QpOBSBD6H yYDHzIRDJLH
F1HYI~H
,1HY\ JLHYMd|}PM MQpKJRI~HYS1H9
zQRDGM[¶jFB\H.OBQDGMÀTD B y HYF DGOBHY6_LZ1HYMNHYn\HYM[bOBHYIRDPQ_GQpIKIRDGM»
1HYOTSBQ³HYDPR_GHY\HYdSBD_GQYMNFBIK[bMDGOJ~Q^S1H^JRBIR|BTbÖGOT_G[\H^~ªYQÂJRQ9SBHYMNHY[bQpIKDG,BDHÂDGKF}DPRKBI~H³S1H
_LZ1HYMNH´\H.MN[xO1HYIGykQp RDmÑRH9y yÅD¼H<[bOJ~DPOBR[xS1HYSBD ^S1H´QpIKSBDGM SBD^XpI~H.OBSBDGÃGH´S1H<¯pDGxQ9_P[bS1H.SBD
SBD¬_LZ1HYMNH\HYM[bO1H.I / y*[ÈDY¶y y0H_LZ1HYMNHµJ~BIK|BBxDG
OJLH¢v_GQYOBKJR[xJ~TÁbS1HSBDvDPbDPMNDPO,JRQp©SBD¬_LZ1HYMNH
\HYM[bO1H.IRDGdÆ"! $# +%+-( ) É ,BDvRªYQ¢_GQYO,JR[bO,1HYMDGOJRDSBQp|BIRHYSBQpEDDGJ~[bIRHYSBQpEF}DP\HJRBIR|TBbÖPOB_G[bHT©_LZ1HYMNH
J~BIK|BBbDPOJLH>³Q>_GQpO;ÑKBOJ~QByzOBQ>RDPO,JR[bSBQ¿DPKJLH°J~ÁbJ~[x_GQBynSBD³SB[¶¯pDPIR~H.¢IRDaH.b[bÃGHY¸GÄDGµSBDGJ~DGDPbDGMDGOJRQp¢SBD
_LZ1HYMNHTÏe%QpKJRQ4,BD ynHDGJ~IR9J~BIRH[bOJ~DPIRO1H´SBDÂ_GHYS1HDPbDGMDGOJRQ4SBDÂ_LZBHYMµH´O1ªYQ¼H.:DPJ~HYS1H
B
&
&
log(v’/u L)
Da=1
chamas
espessas
chamas
espessas
chamas
dobradas−espessas
Ka=1
chamas
dobradas
1
chamas
1
laminares
log(l t /δL)
ReT=1
chamas
dobradas
[bXpBIRH¬Ç9 u Ë CE[¶:DGIRDPOJ~DGnJ~[xF}QYÅSBD_LZ1HYMNHJ~BIK|BBbDPOJLH¬SBDFBIRÎj±M[bKJRBI~H9
F}DP\H¢J~BIK|BBbÖPOB_G[bHTUWKJ~DIRDPXp[bMDvSBD¬_GQYM|BBJLªYQBy%_GQYOBZBDG_P[bSBQ»_GQYMNQIRDPXp[bMDvSBDDGxDGMDGOJ~QpSBD_LZ1HYMNH
SBQp|BIRHYSBQpPybDP¯.H©HiBMNHE[xMNF QpIKJ~HYOJ~D#[bOJ~DPOBR[¶1_aHY¸GªYQ©S1HEJ~H°¹THiSBD6_GQpO¯YDGIRRªYQDGOJ~IKD6IRDaH.XpDGOJ~DPgDÅFBIRQSBTJRQp
SBD_GQYM|BBJLªYQF QpIzBOB[bSBHYSBDdSTDdJ~DPMNF QµDSTDV¯pQYbBMDY ¨ FTIRQ_GDGKRQ¢SBDd_GQpO¯pDPIRRªYQ¢_GQYO,JRIRQpbHYSBQNF}DP\H
J~BIK|BBbÖPOB_G[bHTyDdHµD¹9F DGIK[bÖGOT_G[\HNMNQpJ~IRHN,BDBMNHµ_PQpIRIKDG\H.¸aªYQND¹9[bJ~DDPO,JRIRDvH¯pDGxQ9_P[bS1H.SBDdS1H:IRDGOJRDSBD
_LZ1HYMNH¬JRBIR|BTbDGOJ~H / DH¬[xOJ~DGOTR[bSBHYSBDS1H¬HYXp[¶JLHY¸GªYQJ~BIK|BBxDGOJLH»Æ #QpIRXpZT[0HYOBS^hZ1HYMFB[bQYOy o upuYu É
/
/ 9
]
& &
/ e
Æ'Ç9 oYopÉ
QpOBSBD
BMNH_PQpOBJLHYOJ~DEDGMFBÁbIK[b_aH9ÔUWKJRDEIKDGXp[xMNDnzHY,BDGxDzOBQV,1HY QpF}DPI~HYMQY#MQYJ~QYIRDGkHY¶J~DPIRO1H.JR[x¯YQp
H|1H.RDSBQ¬_G[x_GbQ ¨ JRJRQB
Q<_GHYRQ²DPM¾,BD yk[ÈDY¶ygBHYOBSBQ´H¼[bOJ~DPOBR[xS1HYSBD¢D»H³SB[xMNDPOB~ªYQ³_GHYI~H._PJ~DPIRÁxKJ~[x_aH¼S1H.×19j
J~1HY¸PÄ9DPJRBIR|TBbDPO,J~HY¬J~HYW ,BDNH»DPKJ~IKTJ~TI~H[bOJ~DPIRO1HS1H¢:IRDGOJRDNSBD_LZ1HYMNH¢JRQYJLH.bMDGOJ~DvF DGIKMNDGHYS1H
F}DP\HJRBIR|TBbÖPOB_G[bHTy QµIRDPXp[bMDSBDd_LZ1H.MµHDGRF DGK~HVQp|TJ~[xSBQBn
DGKJRDIRDPXp[bMDHYn×1TJ~BHY¸GÄDGEJRBIR|TBbDPO,J~HY
FBIRQ¤¯pQ_aH.MOTMNDPIRQpRHYn[bOJ~DPI~HY¸PÄ9DP
DPOJ~IRDQpnDPbDGMDGOJRQpnSBD_LZ1HYMNHTW [bOJ~DPOBR[xS1HYSBDSBQ¬MQ¤¯9[xMNDPOJ~Q¬SBD
HYXp[xJ~HY¸aª.QJ~BIK|BBbDPOJLH¬J~ªYQMµH.[bQpIiSTQ^,BDH¢¯pDGxQ9_P[bS1H.SBDvSBD¬_LZ1HYMNH»bHYM[bO1HYIz,BDYy%SBD¬BMF QpOJ~Q»SBD
¯9[xKJ~H¼MµHY_PIRQpK_GºpFT[bQBy¦Q9_PQpIRIKDµ[bOJRDGOBRH¼MN[xKJ~TI~H^DPOJ~IRD¢IKDaHYXYDGOJ~DPvDFBIRQSBTJRQpSBDµ_GQpM|TBKJ~ªYQB³CED¢TM
F}QpOJRQVSBD6¯[bJLHMN[x_GIKQpR_PºpFB[bQTyH©ÃGQpO1HSBD6J~IRHYOB:QpIRMNHY¸aª.Q,BÁxMN[x_aHiF Q9STD6RDGIg:QpIJ~DGMDGOJRDzH.xJ~DPI~HYSBHiF}DP\H
J~BIK|BBbÖPOB_G[bHTy_GQpM RTIRXp[xMNDPO,JRQdSBDED¹J~[xOB¸GÄDG#bQ_aHY[x#Dz_GQpOBKDG BDPO,JRD©F}DPIRS1HVSBDi_GQYO,JR[bO,B[xS1HYSBDzS1H:IKDGOJ~D
SBDv_LZ1HYMNHTUWKJ~D¬IKDGXp[xMNDV_GQpOJRIRQpbHYSBQ¢F DGbQNJ~DGMF Q_aHYIRHY_PJRDGIKÁbKJR[b_PQ¢S1HIRDGHY¸aªYQ¢,BÁxMN[x_aHTyHµ:IRDPO,JRDvSBD
_LZ1HYMNH^_GQYMNF QpIKJ~H°j±KDv_GQpMQ»BMµH¢:IRDPOJ~DSBDN_LZBHYMµH\H.MN[xO1HYIGy}J~QpIKO1HYS1H»DGRF DGK~HÂF DGbH¢SB[x:BRªYQJ~BIK|B9j
bDGOJ~HTUWKJ~H¢R[xJR1HY¸GªYQ¢vFBIRºa¹9[bMNH¢HSBQIRDGH.J~QYIiZBQpMQpXpÖPOBDGQByR[bJ~DPMµHMT[xJ~QµTJ~[xb[bÃGHYSBQNDGMFBIKQ9_PDGKRQp
SBDDGOBXpDPOBZ1HYIK[\HT
1HYOTSBQ
D y9[bOJ~DPI~HY¸PÄ9DPDPO,JRIRDiQYDGxDGMDGOJ~QYÅSBDE_LZBHYMµHVMµHY[x#FTIRºa¹9[bMQp#_PQpMDG¸aH.M
H HY_PQpOJ~DP_GDGI_PQpM XpIRHYOBSBD³:IRDP BÖGOB_P[\HT ±J~QÊHY_GQYO,JRDG_PD´SBD¯[bSBQ HYQ¿SBQp|BIRHYMDGOJ~Q¿[bOJRDGOBKQ H¿,BD²Qp
DGbDPMNDPOJ~QpSTD_LZ1HYMNH¼~ªYQÂRB|BMDPJR[bSBQYG ¨ I~HY[xQÂSBD¢_PBIK¯.H.JRBI~H^SBDGJ~DG¬SBQY|BI~HYMDGOJRQpGyWOBDPKJRDIRDPXp[bMD
SBD´DPR_PQHYMDGOJ~QBy©<S1H¿QpIRSTDGM SBD<XpI~H.OBSBDGÃGH SBD ®UWM _PQpOBRDP BÖGOB_P[\H STD<J~HY[bSBQp|TI~HYMDGOJ~QYGy©H
DGRF DGKRBIRHÊSBH>:IKDGOJ~D³STD¼_LZ1HYMNHJ~QpIKO1H°jRD¼DPM HYxXpBOBF QpOJ~QYRBF DGIK[bQpIH UWM QYTJ~IKQpbQ_aH.[bGy
SBDP¯[bSTQÂH»HYxJ~HYEJ~H°¹THYSBDN_P[bRHYbZ1H.MNDPO,JRQ¢[bMF}QYKJLH.iF}DP\HJ~TIR|BBxÖGOB_P[\HÚ¢_LZ1HYMNHTy0BMNHDιJ~[bOT¸aªYQbQ_aH.
[xXpBI~H¬Ç pYË hZ1HYMNHvJRBIR|TBbDPO,J~HvO1ªYQFBIRÎj±M[bKJRBI~H.S1HT
S1H³_LZ1HYMNH²F QSBD¢Q9_PQpIRIKDGIP4UWKJ~HY¬[bOJ~DPI~HY¸PÄ9DPvDGOJ~IKD»DPbDPMNDPO,JRQpvSBD_LZ1HYMNH¼D¢DGJLHY¬Dι9JR[bOB¸PÄ9DP¬bQ_aHY[x
FBIRQ¤¯pQ_aH.MÀSBDPR_GQYO,JR[bO,B[xS1HYSBDP6O1HRBF DGI:Áb_P[bDESBH_LZ1HYMNHTyTDiQv_PQpOBKDGRBDPOJ~DRBIKXp[bMDGOJ~QdSBDi| QpbKÄ9DPÅSBD
XHYRDPE:IRDPR_PQpE_PQpMNFTbDPJ~HYMDGOJ~DDGO¯YQpxJRQpEF QpI
FBIRQSBTJRQpzSTDd_GQYM|BKJ~ªYQBnUWKJRDIRDPXp[bMDSBDd_PQpM|BTKJLª.Qµ
_GQpOBZTDG_G[xSBQ_GQpMQIKDGXp[xMNDVSBD_LZ1HYMNHSBQp|TI~HYS1H¤cDGKF}DPR~H9VFBIKDGKDGOB¸GHSTDGKJRDG| QpbKÄ9DPGy*HYx[\HYSBHNHYQ8H°J~Q
SBDv,BD ySB[¶1_GTxJLHRB|TKJLH.OB_G[bHYbMDGOJ~DHHYO1«Yx[bKDdSBDPKJ~DvIKDGXp[xMNDµÆ #QpIRXpZT[ÔHYOTS<hZ1HYMFB[bQpOy
o upupu É
N
zªYQVKDESBD¯pDiF DGIKSBDGIkSBD
¯9[xKJ~HQ8H.J~QSBDE,BDEH:IKQpOJ~DP[bI~HD¹TH.J~HdS1HDGOJ~IKDzQp#SB[x:DPIRDPO,JRDG#IRDGXY[bMDGgSBD
_GQpM|TBKJ~ªYQzJRBIR|BTbDGOJ~H
k[bMFBIRDP_G[x~HTy;BMNHn¯YDGÃ#TDHY%DGK_aHYbHY%SBDkJRDGMF}Q
DgSBDk_GQpMFBIR[xMNDPOJ~QnTJ~[xb[xÃaHYS1H.
~ªYQn,1HYOJ~[xS1HYSBDP0MNPSB[\HYP0EbPM SB[xKJRQBy¤F1HYIRHnXYI~HYOBSTDG¯.HYbQYIRDG*STQ6OÒTMNDPIRQnSBD HYIRxQ;¯[¶J~ÃYyGBMµHÅDιJ~[bOT¸aªYQ
_GQpMFBbDJLHSBQÂFTIRQ_GDGKRQ¼STDN_PQpM|BBJLªYQ^F}QSBDQ9_PQpIRIKDGIP ¨ VMDG_GHYOB[bKMNQYDPO¯pQp¶¯9[xSBQpVOBDGJLH^DιJ~[bOT¸aªYQ
HY[bOBSBHO1ª.Q:QpIRHYM®_PQpMNFTbDPJ~HYMDGOJ~D©[xSBDGOJ~[¶1_aH.SBQpGy1ZB«[xOBSB[b_GHY¸GÄDGnSBD,BDDGKJ~H:IKQpOJ~DG[xI~HvRDPIR[bH¬:BOT¸aªYQ
SBQNO,ÒBMDGIKQ¬SBD{0-D n[bnSBQIRDGHYXpDGOJRDx[bM[xJ~HYOJ~DEFBHYI~HvQ¬FBIRQ_GDPRKQNSBD_PQpM|BBJLªYQT
¢¡ -}£a)+;/1¥ 0)9& )W3 &a&a$A@ )5'&v)-}£¤+;)^£¤"%+ ¦"¦
? - 15:/²) 1p!3 Ô"%&P£¤§B3-%§T3 )¦+ 3+'45'&£;"%+;/120/
Q_aHYKQ¢SBDDPR_GQpHYMNDPOJ~QpEJRBIR|TBbDPO,JRQpiKDGM FBIRÎj±M[bKJRBI~H9y}DSTDMµH.OBDG[xI~HµH.O1«YbQYXHNH.Q,BDQ_GQpIKIRD
F1HYI~HÂHYd_LZ1H.MµHYVSBDFBIKjMN[xKJ~TI~HTy¦HYd[xOJ~DGIRHY¸GÄDGVDGOJ~IKD¢H^JRBIR|BTbÖGOT_G[\H»DµQ¼FTIRQ_GDGKRQ³,BÁxMN[x_GQ^HY_aHYImj
IRDPJ~HYMÕSBQp|BIRHYMDGOJ~QpPy}DPKJR[bI~H.MNDPO,JRQp
DdD¹JR[bOB¸PÄ9DPES1HYz_LZ1HYMNHYEDPbDPMNDPO,J~HYIRDPGy [bOT×BBDGOB_P[\HYOTSBQµK[bXpOB[¶1_aH;j
J~[x¯.HYMDGOJRDnHJ~H°¹THSTD
IKDaHY¸GªYQBW
DGJ~D
_aHYKQBy,F}QpIKGM»yH©:IRDGOJRD
STD
_LZBHYMµH©O1ª.QVF QpRKB[1SB[xO1`YM[b_aHzFBIRºpFTIR[\H9
[xXBzÆÈÇ9 p;É MNQYKJ~IRH<TMµH²:QYJ~QpXYI~H. H<SBDÂTMµH<_LZ1HYMNH<J~TIR|BBxDGOJLH´O1H,1HY
BM ÑRH.J~Q´_GDPO,JRI~HYzSBD
_GQpM|TBKJRÁx¯pDP},BDP[bMNHVDPM_PQpOJLH.JRQd_PQpM BM ÑRH.J~QVD¹J~DPIR[xQpI#Dz_GQpOT_GÖGOJRIR[b_PQSBDzHYIEÆ'e¦DPDPJRDGIR6DJÅH.ȶy tpt q,É
e¦HYI~H¢_GbHYRK[x1_GHYIiQpiJR[bF QpESTD_LZBHYMµHSTDvSB[x:BRªYQByQYFTJ~Qpj±RDvF QpI©H.SBQYJLH.I©H¢SBDGK_GIR[x¸aªYQ»H.JRI~Ha¯pPSBQp
OÒTMNDPIRQpSBD¬CiH.M pZBbDPI DSTD¬l
[D l9OTQpbSBiJRBIR|TBbDPO,JRQ B ykÆ QpIKXpZB[WH.OBS´hZ1HYMFB[bQpOy o upupu É ¨
OÒTMNDPIRQSBDCiHYM pZBxDGIzdSBD1OB[bSTQF}DP\HI~HYÃGªYQDGOJRIRDvHDGR_GHY\HNSBDdJ~DPMNF QµSBHNJ~BIK|BBxÖGOB_P[\H yHNBHY
F}QSBD»RDGINDGJ~[bMNHYS1H<H´FBHYIKJR[bI¬S1H<×BTJ~1H.¸aªYQ´S1H<¯YDGbQ_G[xS1HYSBD _PQpMQ´KDGOBSBQ @ D»Q´
N J~DPMNF Q
;<
<
N
N
chamas em equilibrio
quimico
log(Da)
τc ∝ τη
chamas dobradas
τc ∝ τt
chamas com
extinçoes
1
1
ReT*
log(ReT)
chamas pseudo−
laminares
[bXpBIRH¬Ç9 ;o9Ë h\H.RR[¶1_aH.¸aªYQ¬SBQpnSB[¶:DGIKDGOJ~DPnJR[bF Qp6SBDP_LZ1HYMNHSBDSB[¶:B~ª.QB
_aHYIRHY_PJRDGIRÁxKJR[b_GQ¬SBQ¬FBIKQ9_PDGKRQµ,BÁxMN[x_GQBy LD y
<
Æ'Ç9 o.sÉ
<
<
DN ¨ O,ÒBMNDPIRQ¬SBDlnD lOBQpxSB6J~BIK|BBbDPOJ~Q¬:Qp[SBD1OB[bSTQOBHNUW %ÆÈÇ9 ¤É
z<_LZBHYMµH.²JRBIR|TBbDPO,J~HY²F}QSBDPM RDPI´_P\HYKR[xB_aHYSBQY<DPM SBQp|TI~HYS1H.Gyv_GQYM D¹J~[xOB¸GÄDG<D¿_LZ1HYMNHY
BF RDPBSBQ.j\HYM[bO1H.IRDGDDPM®DG,B[xbÁx|BIR[xQBÍUWKJ~H_P\HYKR[¶1_aHY¸GªYQ¬DGOB_PQpOJ~IRH°j±KDV[xbBJ~I~H.S1HO1H [bXT*ÆÈÇ ;oYÉ
zHIKDGXp[bªYQVSTDz_LZ1H.MµHYkFBKDGBSBQ°j±\H.MN[xO1HYIRDPWQJRDGMF}Q_aH.I~HY_J~DGIKÁbJ~[b_PQVSBHIKDaHY¸GªYQd,BÁxMN[x_aH©zMNHY[xQpIÍSBQ
TDNH.©DGR_GHY\HSBHYi×1TJR1HY¸GÄDGiJRB|BBxDGOJLH.G
DGJ~DvIRDPXp[bMDYyHµJ~BIK|BBbÖPOB_G[bHµF DGIRMDG[bH¢HµJ~QYJ~HYb[xS1HYSBDSBQ
FBIRQ_GDPRRQSBDVIRDGHY¸aªYQTyDH.E×1TJR1HY¸GÄDGESBDV¯YDGbQ_G[xS1HYSBDV~ªYQµSB[bKR[bFBHYS1HYz_GQpM¯pDPbQ_G[xS1HYSBDVMµHY[xQpInSBQ,BD
HY,BDGbHDPM ,BDHµJ~IRHYOB:QpIRMNHY¸aª.Q¢TÁbM[b_aHNQ9_PQpIRIKDYUWJLH¢_LZ1HYMNHSB[x:TR[x¯.H,1HYKD¬O1ªYQ×1TJR1HTy*KDGOBSBQ
\HYSBDGHYS1HvF QpI6ÃGQpOBHYnSBDSB[x:BRªYQBy1H.
,1H.[b6~ª.QN_PQpOJ~IRQY\HYS1H.6F}DP\HdJ~TIR|BBxÖGOB_P[\HT
1HYOTSBQ y9H_LZ1HYMNHJ~TIR|BBxDGOJLHz_PQpMF}QpJLHF}QYIkTM_GQpO°ÑKTO,JRQSBD
_LZ1HYMNHYkDGbDPMNDPOJLHYIKDG
O1HYi,1HY[xiHµIKDaHY¸G ªYQµ
,BÁxMN[x_aHdMB[¶J~QMµH.[b
I~«YFB[xS1HNSTQ,BDQµMNHY[xzIR«YFB[bSTQµMQ;¯[xMNDPO,JRQµSBDdHYXp[¶JLHY¸GªYQ
J~BIK|BBbDPOJLHT ¨ FBIKQ9_PDGRKQ^,BÁxMN[x_GQDPOB_GQYO,JRI~H°jRD¬DGMDG,B[xbÁb|TIR[bQTy}D¬H:IRDPOJ~D¬SBDv_LZ1HYMNHvSB[xKJ~QYIR_G[xS1HD
J~I~H.OBRF QpIKJ~HYS1HvF DG\HJRBIR|BTbÖGOT_G[\H9
f
MµHÂx[bOBZBH D @ _GQpOBJLHYOJRD¢RDGFBHYI~H³HYd_LZ1HYMNHYdJ~TIR|BBxDGOJLH._GQpOTKJ~[¶J~BÁxS1HYVSBDDGxDGMDGOJ~QYSBD
_LZ1HYMNHYWSBQp|BIRHYSBQpWSBHYW_LZ1HYMNHYWO1HYW,1H.[bWQ_GQpIKIRDGM D¹JR[bOB¸PÄ9DPkxQ9_GHY[bPyYQpOTSBD Å_GQpIKIRDGKF}QYOBSBD
HYQiJ~DPMNF Q
J~BIK|BBbDPOJ~QÊS1H>DGR_GHY\H>SBD QpbMQpXpQpIKQ¤¯}ynIKDGFBIKDGRDPOJLH.JR[x¯pQ SBQpMDGOBQpIKDG¯YºpIKJR[b_GDPGUWKJ~HY^DιJ~[bOT¸GÄDG
F}QSBDGMÀQ9_PQpIRIKDGI6,1HYOBSTQµHvJ~BIK|BBxÖGOB_P[\HvH.:DJLH:QpIKJRDGMDGOJ~DQ¬SBDPRDGOTIRQpbHYInS1Hv_GQpO¯pDPIRRªYQµ,BÁxMN[x_aHT
zHEIRDPXp[\ªYQE_GQpIKIRDGKF}QYOBSBDGOJRDnHiDGbDPMNDPOJ~QpÍSTDÅ_LZ1HYMNHYÍ_PQpM DιJ~[bOT¸GÄDGÍxQ9_GHY[bPy°:DPOBÐpMDGOBQpÔ[bOJ~IK[bOBK[b_aH;j
MNDPO,JRDkJRI~HYOTR[bDPOJ~DG0F Q9STDGM Q_GQpIKIRDGI*,1H.OBSBQEQY%DPbDPMNDPO,JRQp0SBDg_LZ1HYMNH
RªYQnDGJ~[bIRHYSBQpPÍf
MµH6FBIKj±M[bJ~BIRH
F1HYIR_P[\HY%Q_GQpIKIRDDPO,JRIRD_PQpM|BTKJ~Á¶¯pDPÍD_GQYM|BBIKDGOJ~DSTBI~HYOJRDvQµJ~DPMNF QDGM ,BDvQDPbDGMDGOJRQSBDv_LZ1HYMNH
DGOB_PQpOJ~I~H;j±RDdHYF1HYXpHYSBQB 1HYOBSTQNQDGxDGMDGOJ~QSBD_LZ1HYMNH¬¯YQpxJ~H¬HNHY_PDGOBSTDGIGy BMNHv_LZ1HYMNHF1H.IR_G[bHYbMDGOJRD
FBIRÎj±M[bKJRBI~H.S1H©:QpIRMNHYS1HTy9QN,BD_PQpMNFTb[b_GHvHvMNQSBDGbHYXpDPMS1Hv_LZ1H.MµHJ~TIR|BBxDGOJLH9
DGKJ~HBXpBI~H©JLH.M|}PM :Qp[BJRI~HY¸GHYSBQQOÒTMNDPIRQSBDzl
[D l9OTQpbSBg_PIRÁxJR[b_PQ B ,BD
b[bM[xJ~HEH©IRDPXp[\ª.QQYOBSBD
DGbDPMNDPOJ~QpSTD¢_LZ1HYMN
H ! $# +%+-( )F}QSBDPMKDGIvDGOT_GQpOJ~IRHYSBQpPUWJ~D¢O,ÒBMDGIRQ³STD¢l
[D lOBQpbSTvF}QSBDµKDGI
D¹9FBIRDPRKQµDGMJ~DPIRMQp6S1Hd¯.HYIR[bHYOB¸GHS1HYÅ×1TJR1HY¸PÄ9DP6SBQ¬DGR_GHY\H.IÅF1HYKR[x¯YQB
y & y9D©S1HvDGRF DGKRBIRHNS1HÃPQpO1H
IRDaH°J~[x¯.HTy > _ C y
##
<
<
B
<
& &
>
_
##
C Æ'Ç9 o°q,É
BHYOBSBQ B
B yQ¢FBIRQ_GDPRKQ»STD_GQpMd|BBKJ~ªYQ¢dJRQYJLHYxMNDPOJ~DH°:DPJLH.SBQF DG\HJ~BIK|BBbÖPOB_G[bHTyDdO1ªYQ¢
F}QpKRÁ¶¯pDG0SB[xKJR [bOBXpT[bIDP bDPMNDPO,JRQpnSBD_LZ1HYMNHv[bOBSB[¶¯[bSB1H.[bG
zF}ºpDPKJLH»|BIRD¯pDNSB[bK_GBK~ªYQ^S1HY[bOJ~DPI~HY¸PÄ9DPVF QpKRÁx¯YDG[xDPOJ~IRDµHYDGK_aHYbHYVSBHJRBIR|BTbÖGOT_G[\H¢_PQpMÙHY
_LZ1HYMNHYEOBQµ_aHYKQµSBDDPR_PQHYMDGOJ~QpzFBIRÎj±M[bJ~BIRHYSBQp
QpÂOBªYQBy FBIRDJ~DGOTSBDjRD[xO,JRIRQSBBÃP[bInRDPF1HYI~H.S1HYMDGOJ~D
HY
HY|}QYIRS1HYXYDGOBnTJR[bb[xÃaHYSBHYF1H.I~HvMNQSBDP\HYXpDPMSBH_PQpM|BBJLªYQ¬DS1HvJ~BIK|BBxÖGOB_P[\HT
0 3*20)9?:/B7 ) 2%/ Å"0+ ¦"%? - 158/
hQpMQ^:QY[k¯[bJ~Q³OBQYd_aH.FBÁxJRBbQpdHYOJ~DPIR[bQYIRDGPyWH^JRBIR|BTbÖGOT_G[\H^µBMÙ:DGOBÐYMNDPOBQ¼_GQYMNFBxD¹9Q¼_PQpMTM
XpI~HYOTSBDnOÒTMNDPIRQ©SBDnXpIRHYBWSBD6x[b| DGIRSBHYSBDY¦ IRDPRQpxB¸aªYQ©ST[bIRDJLH©S1HYWDP,1HY¸GÄDGg,BDnIRDPXpDGM JLHY:DGOBÐpMDGOTQBy
HYÔDPBHY¸GÄDG¦SBDPJRDGIRM[bOTÁbKJR[b_GHY0_G\«.RR[x_aHY%SBDEHa¯[bDGImjJRQ YDPGy.bDP¯.HYMH
_GQpMF QpIKJ~HYMNDPOJ~QzHYbDGH.J~ºpIK[bQ6SBD¯[bSBQ
HK1HOBH.J~BIKDGÃGHO1ª.Qx[bOBDGHYIÍD6JLH.M|}PMH©[bMF QpRK[b|B[xb[bSBHYSBDkSBDnRDGIKDGMSTDP1OB[xS1HYg_GQYOBSB[b¸PÄ9DPgSBDn_GQpOJ~QYIROBQ
H_GHYS1H©[bOTKJLH.O,JRD6SBDÅJ~DPMNF Q©DnHi_aH.S1H©F}QpOJRQ©S1Hi:IRQpOJ~DP[bIRHTypF DGbQ©MDGOTQpWF1HYIRHiDGR_PQHYMDGOJ~QYkSTD6[bOJ~DPIRDGKRD
FBI~«.JR[b_PQÂÆ k [xOBÃGD.y t r t É
DGx[bÃPMNDPO,JRDYy%F1HYIRHÂHÂMNHY[bQYI©F1HYIKJRDµS1H.HYFBx[b_GHY¸GÄDGSBDNDGOBXpDPOBZ1HYIK[\HTy¦DµMDGKMNQ^F1HYI~H^H^_PQpMNFTIRDGDPO9j
~ªYQ¼:DPOBQpMDGOBQpxºpXp[x_aH¢SBQpDPR_PQHYMDGOJ~QpPygHÂFBIKDP¯[bRªYQ³D¹TH.J~HÂSBQpd¯.HYxQpIRDPV[xOBKJ~HYOJL`YOTDGQpSBHYd¯.HYIR[b«a¯pDG[x
_aHYIRHY_PJRDGIRÁxKJR[b_aH.VSBQ»DGK_GQH.MNDPO,JRQ¼O1ªYQ»[bOBSB[xRF DGOBR«a¯pDG'¢fzMNH|}QH»FBIRDPSB[b¸GªYQ»SBQpFBIR[xMNDP[bIRQY©MNQpMDGOj
J~QpNDGKJ~H.J~ÁxKJR[b_GQYSTQR[xKJRDGMNH<DPKJ~TS1HYSBQ4»MB[¶JLHYv¯YDGÃGDPR91_G[xDGOJ~D. UWJLHYN_GQpOBK[bSBDPI~HY¸PÄ9DPµxDP¯.HYMH
TJ~[xb[bÃGHY¸aª.QSBD©:DGIKI~HYMDGOJLH.
DPKJ~H.J~ÁxKJ~[x_aHY6OBH¬MQSBDGbHYXpDGMS1HvJ~BIK|BBxÖGOB_P[\H»Æ'e%QpF}D.y o upupu É
¨ ÅFBIK[bMDG[xIRQpkMNQSBDPbQpkF1HYIRHHSBDGK_GIK[b¸aª.QvS1HdJ~IRHYOBK:DPIRÖPOB_G[bHSBDi,1HYOJ~[xS1HYSBDESBDiMQ;¯[xMNDPO,JRQb[xOBDaH.I
DzSBD
DGOTDGIRXY[\H©DGMDPR_GQpHYMNDPOJ~QpgJ~BIK|BBxDGOJ~QpkF1HYIJ~DPM^y,DGKRDPOB_G[bHYbMDGOJ~D.y,S1H[xSBDGOJR[x1_GHY¸aªYQSBDnXpIRHYOBSBDPÃaHY
HYSB[bMDGOTR[bQYO1HY[bWFBHYI~HH_GHYI~H._PJ~DPIR[xÃaHY¸GªYQVSTQVDPR_GQpHYMNDPOJ~Q¢Æ ±OB_GIKQpF DGI~HVHYOBSNCED [¶JRJGy tYt É ¨ #MQ9STDGbQY
HYRK[bMSBDPRDGO¯YQpx¯[bSTQp#IKDGbHY_G[xQpO1HYM ,1HYOJ~[xS1HYSBDP#_PQpMNQO,ÒBMDGIRQSBDzzTRRDPxJ#DGM:TOB¸aªYQSBD
F1HYIR`YMNDJ~IKQp
JLHY[x*_GQpMQnOÒTMNDPIRQp*SBDklnD lOBQpxSB0DkegIRHYOBSTJRÈ%UWM| QpI~H6ÒTJRDG[b*DPM HYxXpBMNHYR[¶J~1H.¸GÄDGGy;DPR~H.¦_PQpIRIKDG\H.¸GÄDG
~ªYQBy.¯9[bHESBD#IRDGXYI~HTypx[bM[xJ~HYS1HY0ÚEXYDGQpMDPJRIR[\H.%DPRF DG_PÁx1_GHYWDÅÚY¦8HY[¶¹THY%SBDÅO,ÒBMDGIKQiSBD6lnD lOBQpxSBÔDÅegIRHYOBSTJR
ÚY#,1H.[bÍ:QpIRHYMH;ÑKBJLHYSBHYGy9HYbPMSBDnO1ª.QVF DGIKMN[¶J~[bI¦BMNH_GHYI~H._PJ~DPIR[xÃaHY¸GªYQVSTDPJLH.bZ1HYSBHSTQpgDGR_PQHYMDGOJ~QYG
hQpM Q>HYS9¯pDGOJRQÊSTQp¢_GQpMFBTJ~HYSBQpIKDGNDGbDJ~IKÐpOB[b_PQpµST[bXp[¶JLHY[xGyJRQpIROBQY9j±KD¼F}QYRRÁ¶¯pDPiH>HYFBx[b_GHY¸aªYQ´SBD
J~G_POB[b_GHYOTMNPIR[b_GHY©F1HYIRHH»KQpbB¸GªYQS1HYDG,1H.¸GÄDGXpQ¤¯pDGIKO1HYOJ~DPdSBQDPR_GQpHYMNDPOJ~QB¬6Q»bQpOBXYQ¢SBDGJ~DG
ÒBxJR[bMQpkHYOBQp#HYbXYBMµH.gJRG_POB[b_GHY#JRDGM RDzSBDGJLHY_GHYSBQBy9RDGOTSBQvHYMFB\H.MNDPO,JRDnDGMFBIRDPXHYS1HYkDGM FBIKQp|BxDGMNHY
SBD¢J~BIK|BBbÖPOB_G[bHTygF}QSBDPOBSBQ²RDPI_P[xJ~HYS1HY¬HY]»GSB[bHYvSBD»l
[D lOBQpbSTvF1HYI~H³DPBHY¸GÄDGSBDEHa¯[bDPIjmJ~Q .DG
Æ + $% %) 8+- + ,"+- ( $ +*)y¦l
Ei É y¦9[bMT\HY¸GªYQ»zBMGIK[b_aHS1HY IRHYOBSBDPdUWK_aHYbHY¢Æ :8 +
" #
% 8(5"$ 1y°{%Uk É D9[bMT\HY¸GªYQnzBMGIK[b_GH
Cz[bIRDJLHVÆ " '+ -( # +-#" $% " # % 8(5"$ 1y.CEi É _GQpMQ
HY6J~G_POB[b_GHYnMµH.[bÅBK1HY[xG
9[xMB\H.¸aªYQ¬
BMNPIR[x_aH¬CE[bIKDPJ~HÂÆ']^Qp[bO»HYOTS³]ÂHYZTDGRZy tpt TH.I °HYInDPJzHY'xy tpt TH .H.IzH.OBS¼QBy
tptÇ É BMNH¢JRG_POB[b_GH^O,BMGIR[x_aH¢RQ.1KJR[b_aH.S1HTy0J~DGOTSBQÂF QpIQp|ÑKDJ~[x¯YQÂH»RQpxB¸aª.Q»STDJRQ9SBQYVQpXpIRHYBSBD
b[b| DGIKS1HYSBDVSBQK[bKJRDGMNHµDGM ,BDGJLªYQTyQp¼KDmÑRHTyJRQ9STQQDGKF}DP_PJRIRQ¢SBDd:IKDG BÖPOB_G[bHS1HNJ~TIR|BBxÖGOB_P[\HTiUgJLH
J~G_POB[b_GHvx[bM[xJ~HYS1HHRQpxB¸aªYQ¬SBD©K[bJ~DGMNHY6_PQpMÀ|1H.[¶¹9Qp6O,ÒBMDGIRQY6SBDl
[D lOBQpbSTGy.ÑR«,BDQ¬OÒTMNDPIRQ¬SBD
XpI~HYTESBDb[x|}DPIRS1HYSTDSTQµR[xKJRDGMNHNHRDGIzIRDPRQp¶¯9[xSBQVBMNH:TOB¸aªYQN_GIKDGR_PDGOJ~DdSBQµO,ÒBMDGIKQµSBDdl
[D l9OTQpbSBP
UgOJRIRDPJ~HYOJ~QBy}HNJRG_POB[b_GHN,BDF QpRKB[%MNDPbZBQpInF QYJ~DPOB_G[bHY0SBDdIKDGFBIKDGKDGOJLHYIPyDGMJRDGIRMQp
DGJLH.JRÁbKJR[b_PQpGy Qp
DGR_PQHYMDGOJ~QYNJ~TIR|BBxDGOJ~QYGyD¢JRDGMRDPIK¯[bSTQ_GQYMNQ³:DGIKI~HYMDGOJ~H<F1H.I~H²BMµH³MDGxZBQpIv_GQYMNFBIKDGDPOB~ªYQ<S1H
:DGOBQpMDGOTQpbQpXY[\HdDPO,¯YQpx¯[xS1HÂÆ8e¦QpF DYy o upupu É
OTDG_GDPRK[bS1HYSTDvSBDRQYbB¸PÄ9DPiSBDDPR_GQpHYMNDPOJ~Qp©_PQpMMNHY[xQpIRDPzO,ÒBMDGIKQp©SBDvlnD lOBQpxSBGyOBQpi,1HY[xiH
J~G_POB[b_GHµSBDdCii»JRQpIROBH°j±KDVFBIKQp[b|T[xJ~[¶¯.HTyBbD¯.HYMÕHNTJR[bx[bÃaH.¸aªYQ¬S1Hµ9[bMT\HY¸GªYQµ
BMGIR[x_aH¬SBDdSTD I~HYOBSTDG
UgK_aHYbHYÆ'{*DPR[bDPBIGy tptÇ THYXHY9Jay o upu eW[xQpMNDPbx[Èy tptYt 9F DGÃP[\HYxDYy tpt É iJ~P_GOB[x_aH¢{0Uk¼_GQpOBK[bJ~D
DGMÙ1xJRI~HYIdHYdDPBHY¸GÄDGvXpQ¤¯YDGIROBHYOJ~DYygKDmÑRHÂOBQ³DPRF DG_J~IRQ³STDµ:IRDPTÖGOB_P[\HYPyWRDmÑRH¼OTQ¼DGKF1HY¸GQ¼:ÁxR[x_GQB^E
DGKJRIRTJRBI~H.EJ~BIK|BBxDGOJLHYzIRDPRF QpOB~«a¯YDG[b©F DGxQNJRI~HYOBKF}QYIKJ~DVSBDdDPOBDGIKXp[\HDdSBDV,1HYOJ~[xS1HYSBDVSBDMQ;¯[xMNDPO,JRQ
~ªYQNIRDGKQpx¯[xS1HY6SB[xIRDPJ~HYMDGOJ~D.y1DGOB,1HYOJRQ,BDdH.F}DPO1HYzHYnMNDPOBQpIRDPnDGKJRIRTJRBI~H.E~ª.QNMQ9STDG\H.S1HYG#hQpMQ
HYMNDPOBQpIRDPDGKJRIRTJRBI~H.JRDGOBSBDPMÙH¢RDGIMNHY[biZTQpMNQYXpÖGOBDGHY©D¬[bKQYJ~IKºpFB[b_GHYÆ k [bOBÃPDYy t r t É y*D¬F QpIKJ~HYOJ~Q
MNDPOBQp¢H.:DJLHYSBHYF DG\H.µ_GQYOBSB[b¸PÄ9DPSBD¼_PQpOJ~QpIKOBQByzHY_GIKDGSB[¶JLH°jRD^TD³BMµH´IRDGFTIRDGKDGOJLH.¸aªYQ¿IRDGHYb[xKJ~H´SBQ
!
#"
$
%
'& ()"
*&
+
#"
$
DGR_PQHYMDGOJ~QF QpRRHKDGI
Qp|TJ~[xS1HT
z#MDPJRQ9SBQYbQpXp[bHYÔSTDECiEDz{0U#¬~ªYQRDPMNDPbZ1H.O,JRDGkOBQdKDGOJ~[xSBQTDiHYM|BHYgOBDG_PDGRK[xJ~HYMHKQpbB¸GªYQ
OTMNPIR[b_GH¬JRIR[xSB[bMDGOBK[bQpOBHYDJ~I~H.OBR[xDGOJ~DS1HY
DG,1HY¸PÄ9DPESBDVEHa¯[bDPIjmJ~Q.DGPnUgMd|}QpIRHQY
MQSBDGxQp
{%Uk
_GQpOJ~[xO,1HYM H D¹9[bXY[bI»MµHYxZ1HYIRDP\H.JR[x¯.HYMDGOJ~D<IRD1O1HYSBHYGy4F QpRKÁx¯pDPH KQpbT¸aªYQ STDDGK_GQH.MNDPO,JRQp³H
OÒTMNDPIRQpnSBDlnD lOBQpxSBn|}DPM®RBF DGIK[bQpIKDG
HYQpnQp|9J~[bSTQp6_GQpMÀCii´ÆÈTH.XHYTJGy o upu ¤É
]^DPRMQnTD#[xOT:QpIRMNHY¸PÄ9DPRQp|TIRDkHY0MNDPOBQpIKDG0DGK_aHYbHY*SBQ
DGR_PQHYMDGOJ~QnJ~TIR|BBxDGOJ~QnKDmÑRHYMÏIKDGxDP¯.HYOJ~DPGy
DGM MdB[xJ~HYiR[¶J~1H.¸GÄDGiKT1_P[bDGOJRDTMµHSBDPR_PIR[b¸GªYQ¢SBQ¢DPR_GQpHYMNDPOJ~QMNPSB[bQT©J~G_POB[b_GHSBDvMGSB[bHµSBD
l
[D l9OTQpbSBS1HY¬DPBHY¸GÄDGNSBDÂzHa¯9[xDGImjJRQ YDP¼Æ8l
Ei É BRBHYbMDGOJ~D»DGMFBIKDGXHYSBH²FBHYI~H<H<STDGR_PIR[x¸aªYQ
SBQDGR_PQHYMDGOJ~QMGSB[xQ<ÆÈ9F DGÃP[\HYxDYy tpt É dCzDNH._GQpIKSBQ¢_GQpMDGJLH¢J~G_POB[b_GHTy*,1HYxTDGI©FBIKQpFBIR[xDGS1H.SBDSBQ
DGR_PQHYMDGOJ~Q¿F Q9STD¼RDPI¢SBDG_PQpMNF QpJLH4DGM BMNH,1HYOJ~[xS1HYSBD¼MGST[\HD³SBDÂBMµH×BTJ~1H.¸aªYQ¿HYKRQ_G[bHYS1H
Ú^J~BIK|BBxÖGOB_P[\HT^EFBx[b_aH.OBSBQÂDPKJ~HÂSBDG_PQpMF}QpK[b¸GªYQ¼H^JRQ9SBHYHÂFTIRQpFBIK[bDPS1HYSBDPdSBQ¼DPR_PQHYMDGOJ~QByWF QSBDjRD
SBDGSBTÃG[bIBMNH¢DG,1HY¸GªYQ^FBHYI~H»H¢SBDGK_GIR[x¸aªYQ»SBQ»DGK_GQHYMDGOJRQÂMGSB[xQH.J~IRH¤¯YGSBDBMµH¢MGSB[bHµJ~DPMNF QpI~H.
S1HYkDG,1HY¸PÄ9DPSBDzEHa¯[bDPIj,J~Q .DGGkUWKJRDzFTIRQ_GDGST[bMDGOJ~QIRDPRB¶JLHOBQHYFBHYIRDP_G[bMDGOJRQVSBD
OBQ¤¯pQYkJRDGIRMQpkSBD
QpIRSBDPMÀKBF}DPIR[xQpIO1H.ÅDG,1HY¸PÄ9DPGy1QpBHY[b#DGO¯pQp¶¯pDPM®_GQpIKIRDP\HY¸PÄ9DPÅDGOJ~IKDE×1TJR1HY¸PÄ9DP6SBDE¯pDPbQ_G[xS1HYSBDPGW
Z1HY|B[xb[bSBHYSBDDvHµXpDPOBDGIRHYb[xS1HYSBDSBDGJLHJ~P_GOB[x_aHµFBHYI~HµFTIRDP¯YDGIi¯.HYxQpIRDPEMGSB[xQpESBDPF}DPOBSBDvSBQYiMNQSBDPbQp
SBD
:DG_LZ1HYMDGOJRQ»FBHYI~HSBDJ~DPIRM[bO1HY¸GªYQµSTQp©MNQYMNDPO,JRQpESTDQpIRSTDGM KBF DGIR[xQpIGUWJ~DvMPJ~QSBQF DGIKMN[¶J~DVQ¢BRQ
SBD6MµH.bZ1HY¦|}DPM MDGOTQpÍIRD1O1HYSBHYGy,DÅQ©DPMNFBIKDGXpQESBD6ZB[bF ºYJRDGRDPWR[xMNFBx[x1_GHYSBQpIRHY*JLHY[xÍ_GQYMNQiDPR_PQHYMDGOJ~Q
|B[bSB[xMNDPOBR[xQpO1HY'y IRDGXY[bMDdF DGIRMNHYOBDPOJ~DYy*DJ~_.dUWM _PQpOBKDG BÖGOT_G[\H9y%TMµHIKDGSBB¸GªYQ¢SBIR«YKJR[b_aHSTQp©IRDP_GBIKRQp
_GQpMFBTJ~HY_G[xQpO1HY[xÅQp|TJ~[xS1HT
|BTR_aH»SBD¬MNDJ~QSBQpxQpXp[\H.EHY¶J~DPIRO1H.JR[x¯.HYi¬BMNH«YIRDGH¢SBD¬F}DPR,B[bRH»DPM HY| DGIJ~QBy0BMNHµ¯pDPÃN,BDNHY
QpF}¸PÄ9DP¦ST[bRF QpOBÁ¶¯pDP[b0OBQ
MNQpMDGOJRQ
OBªYQzRªYQEFTbDGOBHYMNDPOJ~Dg~H.JR[b8H.J~ºpIK[\HYP0zDPKJ~D#_GQpOJRD¹J~QBy.Qp%MNJ~QSBQp0SBD
J~I~H.OBRF QpIKJRDVSBH:BOB¸GªYQSBDGOBK[bS1H.SBDdSBDFBIKQp|1HY|B[xb[xS1HYSBD¬Æ8egC WÉ F}QpK[b_P[bQpO1H.M¬jRD©_GQYMNQ¬BMNHNH.xJ~DPIRO1H°J~[x¯.HTy
IRDGbH.J~[¶¯.HYMNDPOJ~DWF QpB_GQ
D¹9FBxQpI~H.S1HTy;O1HnMNQSBDGbHYXpDPM S1H6J~BIK|BBxÖGOB_P[\HÆ'e%QpF}D.y tpt q e¦QpF DYy o upupu É %zDPKJ~DPGy
TJ~[xb[bÃGH°j±KDEBMNHDG,1H.¸aªYQSBDiJ~IRHYOBKF}QpIJ~D©F1H.I~HSBDPR_GIKDP¯YDGIiHvegC _GQYO°ÑKBOJLHvSBDiJRQ9S1H.nHY6FBIRQYFBIR[xDGS1HYSTDG
SBQ×BB[bSBQTÍUWKJRDGkMNJ~QSBQpWF Q9SBDPMRDPIgDGMFBIRDPXHYSBQpWKDGF1H.I~HYS1H.MNDPO,JRDzQYNH._GQpFBbHYSBQpgH©Qp9J~IRQYkMPJRQ9STQp
JLHY[x6_GQpMQl
Ei¢D{%Uk¢F1HYIRHSBDPR_PIRDP¯YDGIzQ_PQpMF}QpIJLHYMDGOJRQvSBQp6J~DPOBRQpIKDG
SBDQpIRSTDGM®KBF}DPIR[xQpIG
3*20)9?:/B7 ) 2%/ 3 ¦"¦&£¤§B34) ©& 1p3 / ´)9- £¤3 & "%+ ¦"¦?:)-}£¤3 &
J~TIR|BBxÖGOB_P[\HTy*_PQpOT:QpIKMND¯[xKJ~QOBQYV_GHYFBÁxJRBbQY©HYOJ~DPIR[bQYIRDGPy0F QpIR[WKº^TM :DGOBÐYMNDPOBQ|1HYKJ~HYOJ~D
_GQpMFBbDι9QB Ó%DGOTSBQ¿DGM ¯[xKJLH>H4ST[bR_PBRRªYQ¿SBDGKDGO¯pQYx¯[bS1H>OBQY¢F1HYI~«.XpI~H.:QYHY_P[bMNHTy6³DGKF}DPI~HYSBQ¿,BD
HFBIRDPSB[b¸GªYQ¢S1H[bOJRDGI~H.¸aªYQDPOJ~IRD¬_PQpM|BBJLªYQ¢DVJ~BIK|BBbÖPOB_G[bHHY_GHYIRIKDPJ~DvTMXpIRHY³SBDvSB[¶1_GTbS1HYSTDHY[xOBS1H
MµHY[xQpIG¦zQ_GHYRQSBDnDGK_GQH.MNDPO,JRQpgIRDGH.J~[¶¯pQpPy,HYÍJ~P_GOB[x_aHYgSBDnCiE¬D
{0UkdJ~DGOTSBDGMH©KDnJRQpIROBHYIRDPMHY[xOBS1H
MµHY[x0IRDGJ~IK[xJLH.ÍHzDPR_PQHYMDGOJ~Qp¦_GQpM|1H.[¶¹9QEO,ÒBMDGIKQpÔSBDl
[D lOBQpbSTGyYDPO¯pQp¶¯pDGOTSBQ©XpDGQYMNDJ~IR[bHY0DM[bJ~BIRHY
R[bMFBxDGSBDÂXH.RDGµF}DPIK:DG[¶J~QpPe¦QpINDGKJRD¼MQYJ~[¶¯pQBy#MNQSBDGxQpTDÂTJR[bb[xÃaHYM¾HYbXpTMµH¼:QpIKMµH²SBD¼MGSB[bH
J~DGMF QpI~HY SBDPRDGMF DGOBZ1H.M®BMF1HYF DGDPRKDGOB_P[\HYOBHFBIRDPSB[b¸GªYQvSBDiDPR_GQpHYMNDPOJ~Qp6IKDaH.JR[x¯pQYÅ_GQpMFBxD¹9QpGy9Qp
BHY[bn~ª.QNH¬MNHY[bQpIK[\HSBQpnFBIRQY|BbDPMµHYSBD[bOJ~DPIRDGKRDFBI~«°J~[b_PQB
ÊMµH.[bQpIK[\HS1H.ÔMQ9SBDP\HYXYDGOB0F1HYIRH
DPR_PQHYMDGOJ~Qp%J~BIK|BBxDGOJ~Qp¦IRDGH.J~[¶¯pQp%~ªYQzSBDGIK[x¯.HYS1H.%SBHYÔDPBHY¸GÄDG
SBDE_PQpOBRDPIK¯.HY¸GªYQSBDzMµHYK~HTy,,1HYOJR[bS1HYSTDESBDzMNQ¤¯[bMDGOJ~Qb[xOBDaH.IGyDGOTDGIRXY[\HVD
DGKF}P_G[xDGÅ,BÁxMN[x_aHYPÍCEDPO,JRIRD
HYzMDPJRQ9STQpbQpXY[\HYÅDPMNFTIRDGXpHYS1HYPy HNMNHY[b6BK1HY0_GQYOBR[xKJ~DO1HHYFBx[b_aH.¸aªYQByBHNDGJLHY
DG,1H.¸GÄDGGy S1HY
MGSB[bHY
SBDl
[D lOBQpbST6Qp¢SBD Ha¯IRDYyTDGKJ~HvÒBxJR[bMNHTJR[bx[bÃaH.S1HV,1HYOTSBQ¬RDiJ~IRH.JLHVSBD©DGK_GQHYMDGOJRQp6_GQpMSBDPOBR[xS1HYSBD
¯YH.IR[\«a¯YDGWÆ8{0HYBOBSBDPI6HYOBS»F1HYbST[bOBXBy tÇ hZ1H.R~H.[bXpOy o upupu É ÍzÅMNPSB[\H.SBD©lnD lOBQYbSBÅDESBD H¤¯IKDiSBD
BMµH¯.HYIK[\«a¯pDP Â~ªYQIRDPFBIRDPRDGOJ~HYS1HY
F}QYI ÂD 0y1IRDPRF DG_PJR[x¯.HYMDGOJ~D.y1DSBDP1OT[bS1HYn_PQpMNQ
_
-
N
- b
Æ'Ç9 oYrpÉ
Æ'Ç9 o.É
QpOBSBD BM½[bOJ~DPIK¯.HYbQ³STDJ~DGMF Q<KT1_P[bDGOJRDGMDGOJ~D»XpI~H.OBSBD¢,1HYOBSTQ´_PQpMNFBHYI~HYSTQ²Ú<SBTI~HY¸GªYQ²S1HY
×1TJ~BHY_ ¸GÄN DGgJ~BIK|BBxDGOJLHYPWfzK1HYxMNDPO,JRDnFBIRDPR~ª.QdDnSBDGOTR[bSBHYSBDn~ªYQSBDP_GQpMF}QYKJLH.WTJ~[xb[bÃGHYOBSBQ°j±RDÅHMGSB[bH
SBDnl
[D lOBQpbSTGypDPOB,1HYOJ~Q,BD6HYÔSBDGMNHY[b¦FBIRQYFBIR[xDGS1HYSTDGÍRªYQiSBDP_GQpMF}QYKJLH.Ô¯[\HEMGSB[bHzSBD Ha¯IRD.WeÔH.I~HiH
SBDGK_GIR[x¸aªYQ_GQYMNFBxDPJ~HiSBQDGR_PQHYMDGOJ~QJ~TIR|BBxDGOJ~QIKDaH.JR[x¯pQTy
OTDG_GDPRR«YIR[xQdHYFTb[b_GHYIÍDPKJ~DnFBIKQ9_PDGSB[xMNDPOJ~QSBD
MNPSB[\HvDGJLH.JRÁbJ~[b_GHvHYQ¬_GQpO;ÑKBOJ~QSBDDG,1HY¸PÄ9DPzXpQ¤¯YDGIROBHYOJ~DGPÓ¦HY*FBIKQ9_PDGSB[xMNDPO,JRQvIRDPRB¶JLH¬DGM®DPBHY¸GÄDG
MNPSB[\HYkSBDnJ~IRHYOBRF QpIJ~DESTD 2 DnJ~DPIRMQpkSBD
×BTJ~1H.¸aªYQvH.RRQ_G[bHYSBQp#H©J~BIK|BBbÖPOB_G[bHTyQp#,1H.[bkOBDG_PDGRK[xJ~HYM
MNQSBDGbHYXpDPM^ ¨ J~DGIKMNQYFBIRQ¤¯YDGOB[xDGOJ~DP^S1H.»DP,1HY¸GÄDGSBD²,1HYOJR[bS1HYSTD³SBD³MNQ¤¯[bMDGOJRQ>b[bOTDaHYIN~ªYQ
SBDPJRDGIRM[bOBHYSBQpkH.JRI~Ha¯pPSBD
MNQSBDPbQpWSBDnJ~TIR|BBxÖGOB_P[\HTÔUWM|}QYI~H©QdFBIKQ9_PDGKRQdSTDz_PQpM|BBJLªYQ[bO9×1BDGOT_G[bDnQ
J~I~H.OBRF QpIKJRDÅSBD#DGOBDPIRXp[bHEOBQiMDG[xQzIKDaH.JR[x¯pQTypRDPI~«ES1H.S1HEÖGO98HYRD6H.T[BHYF DGO1H.ÍÚEMQ9STDG\H.XpDGM S1HzDG,1HY¸GªYQ©SBD
J~I~H.OBRF QpIKJRDdSBDVMµH.R~HNS1HYEDPRF G_P[bDGETÁbM[b_aH.Gy F}QY[b
OBDGbHNIRDPR[xSBDGM HYxXpBOB
SBQpzFBIR[xOB_G[xF1HY[bnFBIKQp|BxDGMNHY
SBD©:DG_LZ1HYMDGOJRQDPOB_GQYO,JRI~HYSTQpGgE6DP,1HY¸GÄDGnSBDiJRI~HYOTRF QpIKJRD©SBD©MµH.R~HvS1H.6DGRF G_P[bDP
,BÁxMN[x_aHY#F}QSBDPM
RDGI
DGK_GIK[xJLH.zH.FBb[x_aHYOBSTQ.j±KD©HvMNPSB[\HSBDlnD lOBQpxSB
Ú¬Ug ¦ÆÈÇ Ç É
, 2 , , -/
2 , 4 7 6 8
, 9 < : = 'Æ Ç9 o Ç É
zDGJLHiDPBHY¸aªYQTy / D 2 IRDPFBIRDPRDPO,J~HYMHY%×1TJR1HY¸GÄDGÔSBD¯pDPbQ_G[xS1HYSBD#DSBD:IRHY¸aª.QESBDÅMNHYK~HES1HzDGRF G_P[bD
- / 2 ©BK1HYbMDGOJRDi_GQpOTZBDG_P[bSBQ
!¢DPMJRQpIROBQvSBHY6IRDP
RF DG_PJR
[x¯.HY6MGSB[bHYSTD Ha¯IRD. ¨ JRDGIRMQ -/ 2
_GQpMQV×1¹TQdSBDilnD lOBQpxSBSBHVDGKF}P_G[xD !O1HVSB[bIKDG¸aª.Q yF}QpI#HYO1
H.
bQp
Xp
[bHHYQpg
J~DG
OT
RQpIKDGÅSBDEl
D[lOBQpbST / /
UgJ~DÅJRDGIRMQiIKDGFBIKDGRDPOJLHQEJ~IRHYOBRF QpIJ~DÅSBDMµHYK~HESBHYÍDGKF}P_G[xDGW,BÁbM[b_GHYÔFTIRDGKDGOJ~DPgOBQ©DGK_GQHYMDGOJRQ©
RQp
|
QD:DG[¶J~QS1H¬HYXY[xJLH.¸aªYQdJRBIR|TBbDPO,J~HTgeÔH.I~Hd:DG_LZBHYMNDPOJ~Q¬SBQ¬R[xKJ~DPMµH9y9J~QYIRO1H°jRDiOTDG_GDPRR«YIR[xQNHvMQ9STDG\H.XpDGM
SBQN×1¹TQNSBDVl
D[l9OTQpbSBPy |}DPM_GQpMQ¬QNJ~DPIRMQ¬SBDVFTIRQSBB¸aª.QµMGSB[xQSBH ! / GÃP[bMNHDPRF G_P[bDTÁbM[b_aH9y < :
ÆQpIKXpZB[0HYOTSÂhZBHYMNFT[bQpOy o upupu e¦DJ~DGIKGy o upupu É
UWMDGK_GQH.MNDPO,JRQpE,B[xMN[x_aHYMDGOJRD[xOBDGIJ~DPGy QpzJRDGIKMNQpnSBD×1TJR1HY¸aª.QµFBIKDGRDPOJ~DGEO1HYEDP,1HY¸GÄDGzMNÎj
SB[\HYnSBDDGOTDGIRXY[\H¬DDPRF G_P[bDGz,BÁbM[b_GHY6~ªYQ¬:IRDPBDGOJ~DPMNDPOJ~DMQ9STDG\H.SBQpnH.JRI~Ha¯pPzSBDBMNHvZB[bF ºYJ~DPRDSBD
¯9[xR_PQpR[xS1HYSBDJ~BIK|BBbDPOJLH¼Æ Ì D lO1HYOJRDHYOBS Ì DGI¯9[xR_LZy o upu o #I~H lDPJiHYȶy tpt qÉ 6
Qµ_aH.RQµIKDaH.JR[x¯YQµDGJLH
ZB[bF ºYJ~DPRD¬OBDPMRDPMNFBIKD¬TMµH¢| QHHYFBIRQa¹9[bMNHY¸GªYQByDPMF1HYIJ~[b_PB\H.IiOBQ_aHYKQ^STD_PQpM|BTKJLª.Q»DPMXHYKDG
FBIRÎj±M[bKJRBI~H.SBQpGhQYMNQRDPI~«¢¯[bKJRQ»HYSB[\H.O,JRDYy%H¢RQpxB¸aª.Q»STDDP,1HY¸GÄDGF1HYIRH¢Qp©×19¹9QpJ~BIK|BBbDPOJ~Qp
BMµHvMNHYOBDP[bI~HSTDD¯[xJLH.InH¬9J~[bx[bÃGHY¸aªYQdS1HZT[bF ºYJ~DPRD©SBD©¯[bK_GQpK[bS1HYSTDJRBIR|TBbDPO,J~HT
SB[¶1_GTbS1HYSTD¼SBD³FBIKDP¯[bRªYQ¿SBQ>J~DGIKMNQ>STD³FBIRQSBB¸GªYQ>MNPSB[bQ>STD³DGRF G_P[bDP»,BÁxMN[x_aHYµDGM DPR_PQH°j
MNDPO,JRQp©J~BIK|BBxDGOJ~Qp©DPKJ~«^HYKRQ_G[bHYS1HÚ:QpIKJRDSBDGF DGOTSBÖGOB_P[\HS1H¢JLH°¹TH¢SBDvIRDGHY¸aª.Q»_PQpM HJ~DPMNF DGIRH.J~TI~H
UW ÍÆ'Ç9 sÉ ±KJRQHY_GHYIRIKDPJLH9y}DPMF1HYIKJR[b_PB\HYIPy HN[xMNF QpRK[b|B[xb[xS1HYSBDzSBDdTJR[bx[bÃaH.Ij±KDi_GQYOB_GDPO,JRI~HY¸PÄ9DPiMGSB[bHY
DJRDGMF}DPI~H.JRBI~H.
MGST[\HYÅFBHYI~HvQ_a«Yx_GBxQvS1HY6JLH°¹THYnMGSB[bHYÅSBDFBIKQ9STB¸aªYQSBDDGKF}P_G[xDG
Æ'Ç9 o.É
9[;\= > = @2B6C 9<;(= > = @B 6 C
/
/
eÔHYIRHN_GQYO,JRQpIROBHYIzDPKJ~HNSB[¶1_GBxS1HYSBD.y SB[x¯YDGIRKQp
MNQSBDGxQp6:QpI~H.M®SBDGKDGO¯pQYx¯[bSBQYGy}HYbXpTOBnSBQp
BHY[b
RDPI~ªYQ
HY|}QYIRS1HYSTQp
H¬KDGXpT[bIG
9[¶J~1H.¸GÄDGdDPMÙTDQÂJ~DPMNF Q^JRBIR|TBbDPO,JRQBy yÍMT[xJ~Q»F DG,BDGOTQ<ST[\HYOJ~DNSBQÂJRDGMF}Q^TÁbM[b_GQTy LD y
¯pDGIHY [xXpGÅÆÈÇ9 u°jmÇ9 ;opÉ yÔDHYv×1TJ~BHY¸GÄDGvS1H.N DPRF G_P[bDG¬DJRDGMF}DPI~H.JRBI~H³~ª.Q<F DG,BDPO1HYPy¢Q²ÒBOB[x_GQ
_aHYKQ^DPM TDTMµH¢| QHHYFBIRQa¹9[bMNHY¸GªYQ¢F1HYIRH¢J~H°¹TH¢SBD¬IRDaH.¸aªYQ»MNPSB[\H¬Qp|9J~[bSBH»H°J~I~Ha¯YGS1HTJ~[xb[bÃGHY¸aª.Q
S1H_PQpMF}QpK[b¸GªYQvDS1HJ~DGMF DGI~H°J~BIRH¬MGST[\HY5Æ QpIRXYZB[*HYOBS^hZ1H.MNFB[xQpOy o upupu É
f
MµHHYxJRDGIKO1H.J~[¶¯.H¬FBHYI~HNH¤¯.HYx[\HYInH¬JLH°¹THSBDVIKDaHY¸GªYQ_PQpOBR[xKJRDVDPM STDGRDPO¯pQp¶¯pDGI©DPMRPIR[bDVSBDÓÔH lbQpIPy
J~IRTOB_aHYSBH4OBQ>RDPXpBOBSBQ>JRDGIRMQBy6Q4JRDGIRMQ4SBDÂFBIRQSBB¸GªYQ>SBD¼DPRF G_G[xDG¢,BÁxMN[x_aHY¼Æ IRH l DPJ¢HYȶy tpt q Ì D lO1HYOJ~DH.OBS Ì DGI¯9[xR_LZy o upu opÉ DiIKDGRQYx¯pDPIÅDG,1H.¸GÄDGÅF1H.I~HdQp#¯YH.bQpIKDGMGST[bQpkS1HVJRDGMF}DPI~H.JRBI~HdDES1HY
_GQpOB_PDGOJ~IRHY¸GÄDGP©e¦QYIRGM»yDPRKDFBIRQ_GDPSB[bMDGOJRQµRºµbDP¯.HNHµ|}QYOBEIKDGRTxJLH.SBQpEFBHYI~HDGR_PQHYMDGOJ~QYiQpOBSBDdHY
×1TJ~BHY¸GÄDGgSBDÅJRDGMF}DPI~H.JRBI~HEOBªYQD¹9_GDPS1HYM SBQ©¯.HYbQYIÔMGSB[xQByYQ©,BDnSB[¶1_G[xbMDGOJ~D#Q9_PQpIRIKDÅO1HiFBIR«.J~[x_aH
Æ HYIRO1H°J~ÃDPJzHY'xy tptpt É
f
M¾MNJ~QSBQ²[bOJ~DPIRDPR~H.O,JRD^FBHYI~H²RQpxB_G[xQpO1HYIdQp¬FBIRQp|TbDGMNHYv_GHYB~H.SBQpF}DP\H¼:QpIRMNHÂ:BOB_P[bQpOBHYÅS1H
JLH°¹THÂSBDNIRDGHY¸aªYQÂMNPSB[\HH^HYFBIRQa¹9[bMNHY¸GªYQ^DPKJ~H.J~ÁxKJ~[x_aH»B~HYOTSBQÂ:BOB¸GªYQ¼SBDPOBR[xS1HYSBDNSBDµFTIRQp|1H.|B[bx[bS1HYSTD
- /
/
, /
!
<
<
Æ'egC WÉ fnJ~[bx[bÃGHYOBSBQ.jRD©HZB[bF ºYJRDGRDSBDVDGIKXpQ9ST[b_G[xS1HYSBDÆ'hZ1HYK~HY[xXpOy o upupu É y HNMGST[\HJ~DPMNF QpI~H.*_GQpM9JLH
_GQpMHMGST[\HdSBDBM_GQpO;ÑKBOJ~Q¬SBD©IRDGHYb[xÃaHY¸PÄ9DPÅSBD©BMMNDPRMQvDGK_GQHYMDGOJRQ¬JRBIR|TBbDPO,JRQBgUWKJ~HMGSB[bH
SBD_GQpO°ÑKTO,JRQNF QSBDRDGInTJR[bx[bÃaH.S1HTyDGM®F1H.IKJ~[x_GBbHYIÅO1HvSBDJ~DPIRM[bO1HY¸GªYQ¬SBD
Æ'Ç9 o t É
< > 6 2 C < > 6 2 C E> 6 2 C 6 2 : K
: K
K
K
QpOBSBD E> $6 2 C nH©egC _PQpO°ÑKBOJLH©SBD > 6 2 C DGMBMS1H.SBQ©F}QYO,JRQ©SBQDGK_GQHYMDGOJRQµÆ8e¦QpF DYy t rpÉ
9DHvegC K _GQpO°ÑKTO,J~HvS1HFBIRDPRRªYQBy1S1HdJRDGMK F}DPI~H.JRBI~HDiSBH¬_PQpMF}QpK[b¸GªYQi_PQpOBZBDP_G[bSBHTy1HdJLH;¹BHSTD©IRDaH.¸aªYQ
MNPSB[\HF Q9STDRDPIQY|TJ~[xS1HF}QYIi[bOJ~DPXpI~H.¸aªYQ<5Æ I~H l¼DJHYȶy tYt q,É VUWOJ~IRDJLHYOJRQBy%Hµ:QpIRMNHµSBDPKJLH»egC Rº
N_PQpOBZBDP_G[bSBH»_PQpM D¹TH.JR[bS1ªYQF1H.I~H_G\H.RRDPVSTDNDPR_GQpHYMNDPOJ~QpF1HYIJ~[b_PB\H.IRDG©_PQpMQBy0F}QpI©Dι9DGMFBbQByTÑRH.JRQp
b[x¯IKDG6Qp¢_GHYMµH.S1HYÅx[bM[xJ~DPG DPb[xÃGMDGOJ~D.yBHD¹9F DGIK[bÖGOT_G[\HvMQpKJRI~Hd,BDDPKJLH.
XYDGQpMDPJRIR[\H.R[xMNFTb[xB_aHYS1H.
HYFBIRQa¹9[bMNHYM»yTSBDMNHYOBDP[bI~HIRHYÃGQp«¤¯YDG'yBSB[x¯YDGIKRQp
R[xKJ~DPMµH.6FBI~«.JR[b_PQpG
Uͯ[bSBDPOJ~DGMDGOJRDYy,BMNHi[bOJ~DPXpI~HY¸GªYQ©SB[xIRDPJ~HES1HUW ÆÈÇ9 o t É OBQ_aHYKQSTD6DGR_PQHYMDGOJ~QYÍJ~IR[xSB[bMDGOTR[bQYO1HY[b
D_GQpOTR[bSTDGI~H.OBSBQ.jRDµTM·MDG_GHYOB[xRMQ^SBDJLHYxZ1HYSBQ^F1HYIRH¼H^SBDPR_PIR[b¸GªYQ¼SBQÂFBIRQ_GDPRRQ³,BÁxMN[x_GQ»µ[xO,¯[b«¤¯YDG'
ERK[bM»y#OBDP_GDPR~«.IR[bQ´HYSBQ.JLHYIZT[bF ºYJ~DPRDG¬K[bMFBb[¶1_aHYSTQpI~HYPyÍJLHYOJRQ<OTQ²JRQ9_GHYOJ~D»H³SBDGK_GIK[b¸aª.Q´SBQ³JRDGIRMQ
SBDdFBIKQ9STB¸aªYQ[bOTKJLH.O,J~`YOBDPQBy BHYOJ~QµSBHµegC _PQpO°ÑKBOJ~HNS1HY
FBIKQpFBIR[xDGS1H.SBDG
SBQDGR_PQHYMDGOJ~QT6 KDGXpT[bI
RDGIRªYQ¢SB[xR_G9J~[bSBHYE|BIKDP¯YDGMDGOJ~D¬HYxXpBMNHYnF}QYRR[x|B[bx[bS1H.SBDG
OBQµJRQ9_GHYOJ~DHNDGRF DG_P[x1_GHY¸aª.Q¢SBDGJLH¢egC }E
R[bMFBx[x1_GHY¸GÄDG#O1HSBDGK_GIK[b¸aª.QvSBQvFBIRQ_GDPRKQ,BÁxMN[x_GQSTDGRDPO¯pQp¶¯9[xS1HY6O1HKDG¸GªYQ^ÆÈÇ9 opÉ KDGI~ª.QvD¹THYM[bO1HYSBHY
HxBéSBQ¬FBIRQ_GDPRKQµSBD_GQYM|BBJLªYQ¬DGMÀDGR_PQHYMDGOJ~Q¬J~TIR|BBxDGOJ~QT
8 1 32%)?:/B7 ) 20/ 1p!3 ¦"¦&P£a§B34) )& 1p3 / )-}£¤3 & )¦+ 3+*5'&P£¤"%+;/1203 &
QE_aH.RQESBHE_GQpMd|BBKJ~ªYQEDPMDGR_PQHYMDGOJ~QYÔDGM,BD#BMµH
_LZ1HYMNHnJRBIR|TBbDPO,J~HERD#FBIRQYF1HYXHnDGMIRDP\HY¸GªYQ
HNBMNHFTIRjMN[xKJRBI~HvZBQpMQpXpÖPOBDaH9y HNSBDPR_GIK[b¸GªYQNMNHY[x
K[bMFBbDP6SBQµFTIRQ_GDGKRQNSBDV_PQpM|BTKJLª.QµF1HYK~HF}DP\H
:QpIRMT\HY¸GªYQHYFTIRDGKDGOJLH.S1H»OBHRDG¸GªYQ<ÆÈÇ o opÉ V
DGJLHµ:QpIKMB\H.¸aªYQNQ¢FBIRQ_GDPRRQ,BÁxMN[x_GQµvSTDGR_PIR[¶J~Q¢F QpI
BM½ÒBOT[b_GQ³DPR_GHY\HYIdIRDaH°J~[x¯YQBy UW 6ÆÈÇ9 u É ²EFTb[b_GHYOBSBQ°j±RDH¼MNPSB[\HÂSTDl
[D l9OTQpbSBH²DPKJ~H¼DG,1HY¸GªYQBy
Qp|TJ~PM¬jRD
- / 'Æ Ç9 s u É
zDGJLH¬DG,1HY¸GªYQHMNPSB[\HVSBQvJ~DGIKMNQdSBD©J~I~H.OBRF QpIKJRDiMQpbDP_GBbHYIk:QY[OBDGXYb[bXYDGOB_P[\HYSBQVSB[\H.O,JRDiSBQvJ~DPIRMQvSBD
J~I~H.OBRF QpIKJRDiJ~BIK|BBxDGOJ~QB ¨ J~DPIRMQvSBD©FBIKQ9SBT¸aªYQvF Q9STDiRDPI6Qp|TJ~[xSBQvH.JRI~Ha¯pPnS1HvHYFBx[b_aH.¸aªYQvHvUW 0Æ'Ç9 o t É
S1HYnZB[bF ºYJRDGRDPnR[bMFBx[x1_GHYSBQpIRHYSBDPRDPO,¯YQpx¯[xS1HY
RDG¸GªYQ³Æ'Ç9 o oYÉ y
- /
< :
/
- < 9
:
Æ'Ç9 s9;É
< > C E> C :
32%)?:3}&¬/1b &a&G" 458-%2%3 15'-43£;51p/76"¦$54551p/³+ )Ô582%/
e¦HYI~Hv_LZ1HYMNHYÅJRBIR|BTbDGOJ~HYnFBIRQpFBHYXHYOBSTQ.j±KDiOBQ¬IRDPXp[bMDiSBDDGxDGMDGOJ~QY6SBD©_LZ1HYMNHTyB[xKJ~Qv.y1F1HYIRH¬TM
OÒTMNDPIRQµSTD HYIRxQ¤¯9[¶J~ÃF DG,BDGOTQByHDGKF}DPRRTI~HSBQNDGbDPMNDPOJ~QSBDd_LZ1H.MµHV[xOT:DGIK[bQpInÚMNDPOBQpInDGK_aHYbHNSBQ
MNQ¤¯[bMDGOJ~Q¢STD¬HYXp[xJ~HY¸aª.QµJ~BIK|BBxDGOJ~Q´Æ #I~H l²HYOBS<e%DPJ~DPIRPy tpt q,É zDPKJRDIKDGXp[xMNDdHekC SBH¢¯.HYIK[\«a¯pDP
SBDH¤¯.HYOT¸GQS1HIKDaHY¸GªYQBy E> C yBHYRKBMNDBMNH:QpIRMNH|B[xMNQS1HY
Æ'Ç9 spopÉ
> C > / C > C > / C<
9
QpOBSBD > C ´H4:BOT¸aªYQ¿SBDPxJLH>SBD<CE[xI~HY_.zQ.J~DjRD²,BD²DGJLH¿D¹9FBIRDPRRªYQ IKDGRF DG[¶JLH¿HY¢_PQpOBSB[x¸GÄDGSBD
OBQpIRMNHYx[bÃaH.¸aªYQS1HegC E> C D > C y9DzTDiQdKDGXpBOTSBQvMNQYMNDPO,JRQVSBHV¯.HYIR[b«¤¯YDG SBD
H¤¯.HYOT¸GQS1HIKDaHY¸GªYQ¬F}QSBD©bKDGI
DGR_PIR[¶J~Q¬_GQpMQ b
Æ'Ç9 sYsÉ
& > / C[
eÔHYIRH»Qp|9J~DGImj±KDvBMµH¢DιTFTIRDGK~ªYQ^F1HYIRHQ¢JRDGIRMQ¢SBD¬FBIKQ9SBT¸aªYQBy*v[xOJ~DGIKDGK~HYOJ~DDGK_GIKDP¯pDPIH¢DG,1H.¸aªYQ»SBD
J~I~H.OBRF QpIKJRDµF1H.I~H^Q^RDPXpBOBSBQÂMNQpMDGOJRQ^S1H¯.HYIR[b«¤¯YDGkSBDHa¯.HYOB¸PQÂS1H»IRDGHY¸aªYQTyÔ,BDF Q9STDNKDGIdSTDGIR[¶¯.HYS1H
MBxJR[bFBx[b_GHYOBSBQ.jRDnHVUg ÆÈÇ9 u É F QpI yBH.FBb[x_aHYOBSTQ.j±KDzHMNPSB[\HSBDEl
D[l9OTQpbSB#DEKB|TJ~IRHY[bOTSBQdQIKDGKBxJ~HYSBQ
S1HNUW %ÆÈÇ s u É MBxJR[bFBx[b_GHYS1HVF QpI &
- /
- / &
/
/
- / /
- D
9
- <
QpOBSBD #D VHJ~H°¹THSBDSB[xRK[bF1HY¸GªYQvS1HY6×19J~1HY¸PÄ9DPzSTD y
D ]
: Æ'Ç9 s.q,É
&
Æ'Ç9 sprpÉ
e
f
J~[xb[xÃaHYOBSTQ.j±KD©H¬Ug ¦ÆÈÇ soYÉ F}QpKRÁ¶¯pDG0DιTFTIRDGK~HYIzHYn_GQYIRIRDP\HY¸PÄ9DP6,BDHYF1HYIKDG_GDPMOBDGJLH¬DG,1HY¸GªYQ
Æ'Ç9 sYÉ
Æ'Ç9 s Ç É
< > / C < :
b
: QpOBSBD < E> C @ < > C y1Q,1HY0SBDGF DGOTSBDHYF DGOBHYnS1H:QpIKMµHSTD < UWKJLH.zIKDG\H.¸GÄDG
F}QSBDGMÙb KDGI[xO,b JRIRQ: SBBÃP[bS1HYO1H^Ugb : ÅÆÈÇ9 sYq,É DYyÍF QpI_GQpMF1HYIRHY¸aª.QÂ_GQYMHÂUg ÆÈÇ9 s u É yÔ: DPOB_GQpOJRI~H°jRDBMNH
D¹9FBIRDPRRªYQF1HYIRH¬HvJ~H°¹THSTDIKDaHY¸GªYQ
D
Æ'Ç9 sYÉ
< /
/ :
¨ MQ9STDGbQ^MµH.[bdTRb 1HY#F1HYIRH³H^JLH°¹TH¼SBDµSB[bKRF1HY¸GªYQ³S1HY×BTJ~1H.¸GÄDGSBD ¢HY,BDPbD,BD¢KBF}ÄDBMNH
HYO1HYxQpXp[\HDPOJ~IRDSB[xRR[xF1HY¸GªYQ¬D×19J~1HY¸GªYQSBQNDPR_GHY\HYInDSB[bKR[xF1HY¸aª.QBy y1D×1TJ~BHY¸aªYQS1H¬DGOBDPIRXp[bH_P[bOBJ~[x_aH
SBQNMQ¤¯[bMDGOJ~QJRBIR|BTbDGOJRQBy !}y
/ & > /
C / 'Æ Ç9 s t É
QpOBSBD vBMNH_GQpOBJLHYN OJRDNSBDvQYIRSBDPM ¨ ²RD±ÑRHTy%H¢ZB[bF ºYJ~DPRDvSBDvIKDaHY¸GªYQ,BÁbM[b_GHµI~«YFT[bS1H[xMNFBx[b_GH
DGMÙ,BDµH»IRDGHY¸aªYQ»_GQpOJ~IKQp\H.S1H»F DGxQ¢J~DGMF Q^_GHYI~HY_J~DPIRÁbJ~[x_GQ»S1HJRBIR|TBbÖPOB_G[bHTe%QpIBM^y%Q»JRDGIKMNQ»SBD
FBIRQSBB¸GªYQNF QSBD©RDPI
DPR_PIR[xJRQN_PQpMQ
D
& !
<
> / C
'Æ Ç9 q u É
Qp KDmÑRHTynH³JLH°¹TH<SBD^b _PQpO¯pN DPIR~ª.Q>^MN«°¹9[bMNH³BHYOBSBQ´BMµH²,1HYOJ~[xS1HYSBD^[bSBÖPOJ~[b_GH<STD^XH.RDG:IRDPR_GQYµD
TDG[bMNHYSBQYzDPOB_GQpOJRI~HYMvj±KDVDPMBMS1HYSBQ¯pQpxBMDSTD×1T[bSBQBy ['D.xy ,1HYOBSTQ 0( 6zQYJRDjRDTDdDGJ~D
MNQSBDGxQF1HYI~H»H»J~H°¹TH»STDNIKDaHY¸GªYQ^:Qp[WQY|ÑKDPJRQ^SBDNSB[x¯YDGIK~HYMNDPbZBQYIR[\H.Gy0HY,1HY[b©¯[bRHYM [bOT_GbT[bIiD:DG[xJRQp
SBQ¢DGJ~[bIRHYMDGOJ~Q¢DSBHIR[b,BDPÃaH¢S1HM[bJ~BIRHNO1H_PQpO¯pDGIK~ªYQ»DGOJRIRDvIRDGHYXpDPO,JRDGDFBIKQ9STTJ~QpvÆ IRH lÂDPJH.ȶy
tpt I~Hl¢DJEH.ȶy tpt
IRH lDPJzHYȶy tpt o #I~Hl¢DPJzHY'xy o upupu I~Hl¢DJzHYȶy o uYu ;É
e¦HYI~HdQV:DG_LZ1HYMDGOJRQvS1HUW *ÆÈÇ s u É EOTDG_GDPRR«YIR[xQvMNQSBDGbHYIgQd×19¹9QvSBDil
D[l9OTQpbSB / W MµHYOTDG[bIRH
BR1H.SBDiFTIRQ_GDGSTDGI_PQpMDGR_GHY\H.IRDG#,B[bM[b_GHYMNDPOJ~D
[bOBDPIKJ~DPzTJ~[xb[bÃGHYIgBMNHVZB[xF}ºYJRDGKDEXpIR
HYSB
[bDPOJ~DYy9[bJ~Qd.y
b[bXpHYI*Q
×B9¹9QESBDl
D[l9OTQpbSB¦HYQ
XpI~H.SB[bDPO,JRDgS1HzXpIRHYOBSBDPÃaHnJ~I~H.OBRF QpIKJ~HYS1HnMNPSB[\HnH.JRI~Ha¯pPÔSBDkBM _PQ9D1_G[xDGOJ~D
SBDSB[x:BRªYQvJ~BIK|BBxDGOJ~QBy y
< :
/
/
<
/ /
N
N
Æ'Ç9 qT;É
e%QpIRPM^yiOTQ _aH.RQ STD´BM MDG[xQ¿_GQpOBJ~[¶J~BÁxSBQ¿BOB[b_GHYMDGOJ~D<SBD<XHYRDP»:IKDGK_GQp^D´SBD<FBIKQ9SB9J~Qp»SBD
_GQpM|TBKJ~ªYQBy1F Q9SBDÎj±KDMQpJ~I~H.IÅ,BD
/ U> / C > / / / C[
Æ'Ç9 qopÉ
b
QpOBSBD / D / ~ªYQHY¯pDPbQ_G[xS1HYSBDPMGSB[bHY#STQDGK_GQHYMDGOJRQOBQpÅXpHYRDPÅ,BDG[xMµHYSTQp#DEOBQpXpHYRDP:IRDPR_GQYGy
IRDGKF}DP_PJR[x¯.HYMb DGOJ~D.6fzMNH¯pDGÃV,BDdI~H.ÃGQ«a¯pDP¦DPRF DGIRHYIz,BD / / y Q¬×19¹9QµSBDSB[¶:B~ªYQvJRBIR|BTbDGOJ~HN
F}QpK[xJR[x¯pQTyBHYb,BDPI#,BD
RD±ÑRHQR[xO1HY1SBQXpI~H.SB[bDPO,JRD6SBD Wf
MµH©MNHYbOBDP[bI~HiF QpKRÁx¯YDG F1HYIRH_PQpOJ~QpIKO1HYIgDGJ~D
FBIRQp|TbDGMNHNdDGR_PIRD¯pDGIBMNHµDPBHY¸aªYQ¢STDdJ~IRHYOBRF QpIJ~DF1H.I~H / ©UWKJ~HDG,1HY¸GªYQBy,BDv[xO,JRIRQSBBÃVOBQ¤¯pQp
J~DGIKMNQYzH.|}DPIKJ~QY6OBDG_PDGRK[xJ~HYOBSBQNSBDMNQSBDGbHYXpDPM^yO1ªYQ¬RDPI~«HY| QpIR
S1H.S1H¬HY,B[È
32%)?:3}&¬/1&a&G" 458-%2%3 15'4- 3£;5 1p7
/ 6"¦5$ 455 1p7
/ 1p3 @ )?::3 15'20/120
) Ô-¦5A£¤/
CE[¶¯pDPIRRQYÅSBDGKDGO¯pQYx¯[bMDGOJ~QY6RDiFBIKQpF Q9DPMHbD¯YH.IDGM_GQYO,J~HdDP:DP[xJRQpSBDz_G[xOBPJR[b_aHVTÁbM[b_aH_GQYM¯YDj
bQ_G[bSBHYSBD©1OB[¶JLH¬RQp|BIKDdH¬JLH°¹THSBDVIKDaHY¸GªYQµDPMDGK_GQHYMDGOJRQNJ~TIR|BBxDGOJ~QNFBIRÎj±M[bJ~BIRHYSBQBCEDGOJ~IKDDGJ~DPGy
BMµH¢H.xJ~DPIRO1H°J~[x¯.Hµ_PQpOBK[bKJRD¬DGM8H.ÃGDGIH.F1HYIRDP_GDPIGy0O1HD¹9FBIKDGK~ªYQ^S1HJLH°¹THSBD¬FBIKQ9SBT¸aªYQ UW kÆ'Ç9 q u É y*H
¯pDGxQ9_P[bS1H.SBDdSBDd_LZ1HYMNHµ\HYM[bOBHYI6Dd[xOB_GQpIKF}QYI~HYIzHµDGJLHµQYiDP:DP[xJ~QYESBDVIR[b,BDPÃaHO1ª.QµBOB[¶JL«YIK[\HTy _PBIK¯.H.JRBI~H
S1HN:IRDPOJ~DSBDd_LZ1HYMNHTy}DdDGKJR[bIRHYMNDPOJ~QH.DGIRQSB[xO1`YM[b_GQTy1F}QpIzD¹9DGMFBxQB ¨ TJRI~HµF QpKR[b|T[bb[xS1HYSBD©dDGR_PIRD¯pDGI
SB[bIKDPJLH.MNDPO,JRDBMNHDG,1HY¸GªYQF1HYIRH¢HµJLH°¹TH¢SBDFBIKQ9STB¸aªYQ¢JRBIR|BTbDGOJ~HTdUWJLH¢DG,1HY¸GªYQ¢:DGOBQYMNDPOBQpbºYXp[b_GH
F}QpKRB[%BMXpIRHYOBSBDO,ÒBMDGIRQNSBDJ~DGIKMNQYzDPMÕHY|}DPIKJRQµ,BDdIKDG,BDPIRDGMÕMQ9STDG\H.XpDGMÙ5Æ QpIKXpZB[0HYOBS¼hZ1HYMvj
FB[bQpOy o upupu É
]ÂH.[bkIRDG_PDGOJ~DPMNDPOJ~DYy9:Qp[1[bOJ~IKQ9STBÃG[xS1HTMµHVHY|}QYIRS1HYXYDGMSBDPOBQpM[bO1HYSBH %+ 8+%),+-(¦Æ'e%DPJ~DPIRPy o upuYu É y,O1H
BHYBÅSBD1OB[xSBQ©BMDPR_GHY\HYIÔO1ªYQ©IRDGH.J~[¶¯pQByYQi,1HYB6x[bXHYSTQEÚiF QpR[x¸aªYQERBF DGI:Áb_G[xDÅSBDÅ_LZBHYMµH9Ô DG,1H.¸aªYQ
TDSBDGK_GIKDP¯pDµDGKJRDDGK_aHYbHYI[bOB_PQpIRF QpI~H¢SB[¶¯pDPIRRQYDP:DP[xJ~QYFTIRQ¤¯pDPOB[bDPO,JRDGvSBDBMÙO,ÒBMDGIRQ^SBDCEHYM pbDPI
1OB[xJRQB
f
MµH>F QpRK[b|B[xb[bSBHYSBD¼,BD²JLHYMd|}PM R[xSBQ Dι9FBbQpIRHYS1H>´HÊIKDGRQYbB¸GªYQ¿S1H DPBHY¸aªYQÊSBD²J~IRHYOBRF QpIJ~D
F1HYI~HH¢:BOB¸GªYQSBDGOBK[bS1H.SBD¬SBD¬FBIRQp|BHY|B[bx[bS1H.SBDdSBQ»DGK_aHYbHYI©IRDGH.J~[¶¯pQBy E> C ¬
DGJLHDG,1HY¸GªYQBy0,BD¬F}QSBD
RDGIdSBDGIK[x¯.HYS1H^HYFBb[x_aHYOTSBQ.j±KDµH.VJ~P_GOB[x_aHYVSBD_G«Yb_PBbQ»DGJ~Q_a«YJ~[b_PQ¿Æ HYIKSB[bOBDPIGy t r e%QpF DYy t rpÉ y¦Qp
FBIRQ_GDPRRQYESBDV_GQpO¯pDP_G¸GªYQDSBDVIKDaHY¸GªYQµ,BÁxMN[x_aHvO1ªYQOBDP_GDGKR[¶JLHYMÕSBDMNQSBDP\HYXpDPM^kUWM_GQYMNF DGOBRHY¸aª.QBy
QÂFBIKQ9_PDGRKQÂSBDM[b_GIKQ.j±M[bJ~BIRHHYF1H.IRDG_PDN_PQpMQJRDGIKMNQ^HY| DGIKJRQBy0|}DPM _GQpMQ»Q»JRDGIRMQSBD¬×1TJ~BHY¸aªYQ^SBD
FBIRDPR~ª.Q³ÆÈ9HY|}DP OB[ .Q¤¯¢HYOBS [xXpBDG[xI~HdSBHµ9[xx¯.HTy o upu oYÉ
32%)?:/B7 ) 20/ 1p!3 ¦"¦&P£a§B34) )& 1p3 / )-}£¤3 &-%§B3 )¦+ 3+*5'&P£¤"%+;/1203 &
1HYOTSBQ²HÂ_LZ1HYMNHÂJ~TIR|BBxDGOJLH¼KDGF1H.I~H¼_GQYM|BBJ~Áx¯YDGÅDµQ¤¹9[xS1HYOJ~D.ykµF}QpKRÁ¶¯pDGSBDP1OT[bIBM·DGK_aHYbHYI
F1HYRK[x¯YQByBH©:I~HY¸GªYQSBDEM[bJ~BIRH UW Æ'Ç9 Gq,É y,SBDzMQSBQV,BDzHY#_GQpOB_PDGOJ~IRHY¸GÄDG#S1HYkDGKF}P_G[bDP,BÁxMN[x_aHYgD
HJ~DPMNF DGIRH.J~TI~HVDPKJ~ªYQHDGbD
IRDP\HY_P[bQpOBHYSBQpkH.JRI~Ha¯pPS1HVUg ÆÈÇ9 ¤sÉ ÍDG,1HY¸GªYQSBDnJ~IRHYOBRF QpIJ~DESTQV¯.HYbQYI
MNPSB[bQ¬SBDPKJ~DDPR_aH.\HYInF1HYKR[¶¯pQ
- /
- / /
Æ'Ç9 qpsÉ
z DGJLH¢DG,1H.¸aªYQHYF DGOBHYiQµ×1¹TQ¢STDvl
D[lOBQpbST / OBDG_PDGKR[xJ~H¢SBDMQ9SBDP\HYXYDGM»ihQpOJRI~HYIK[\HYMDGOJ~DdHYQ
_aHYKQVSBD6FTIRQpF1H.XHY¸aª.Q©SBD6_LZ1HYMNHYWDGMFBIRÎj±M[bKJRBI~H.
Gyp
F QpIÔJRI~H.J~HYIjRD6SBQ©×19¹9Q©J~TIR|BBxDGOJ~QSBD6TMDGK_aHYbHYI
F1HYRK[x¯YQBy*HµTJR[bx[bÃaH.¸aªYQSBDBMNHNZT[bF ºYJ~DPRDdJR[bF QµXpIRHYSB[bDPOJ~DdFBHYI~HµSTDGR_PIRD¯pDGIDPKJ~DVJ~DGIKMNQµMB[¶JLHYn¯pDPÃGDG
RT1_P[bDPO,JRD
'Æ Ç9 qYq,É
N
QpOBSBD ²BM _GQDP1_P[bDGOJRD<STD<ST[x:BRªYQ>J~BIK|BBbDPOJ~QBzRR[xM^yzbD¯YH.OBSBQ.jRD³DGM _GQpOJLHÊHYZB[xF}ºYJRDGKDG
R[bMFBx[x1_GN HYSBQpIRHYiSBDPRDGO¯YQpx¯[bSBHYO1H»KDG¸GªYQ4Æ'Ç9 o spÉ y0HYSB[¶¯pDGIK~HYFBIKQpFBIK[bDGSBHYSBDGSBQ»DGK_GQH.MNDPO,JRQBy0_GQpMQ
/ /
F}QpInDιTDPMNFTbQvJ~DPMNF DGIRH.J~BIRHTy9:IRHY¸GÄDGnSBDMNHYRRHTyBDJ~_Y¶y F}QSBDPMÀRDPIzQY|TJ~[xS1HY6F QpI6[bOJ~DPXpI~H.¸aªYQ
>
>
C E
'Æ Ç9 qrpÉ
HV:BOB¸GªYQvSBDGOTR[bSBHYSBDiSBDEFBIRQp|BHY|B[bx[bS1H.SBDz_PQpO°ÑKBOJ~HSBQDGK_aHYbHYI
C
QpOBSBD IRDGFTIRb DGKDGOb JLH > 6 2 C D E> C
F1HYRK[x¯YQNDSBDRBH¬J~H°¹THSBDSB[xRK[bF1HY¸GªYQB
32%)?:3}&¬/1&a&G" 458-%2%3 6"¦5$ 455 1p/³+ )Ô5820/
¨
FBIR[xMNDP[bIRQYÅMNQSBDPbQpnH¬IRDGHYb[xÃaHYIKDGM®_PQpM®RT_GDGKRQH¬FBIRDPSB[b¸GªYQS1HN_PQpM|BBJLªYQDGMM[bJ~BIRHY6J~BImj
|BBbDPOJLHYzTJ~[xb[bÃGHYI~H.MÀHZB[bF ºYJ~DPRDSBDd,BDdHIKDaHY¸GªYQµ,BÁxMN[x_aH¬DGOB_PQpOJ~IRH°j±KDdDGMDP,B[bxÁb|BIK[bQBzDGJ~DV_aHYKQBy
> C > C D E> C E> C ¨ _GQpMF}QYIKJLH.MNDPO,JRQvSBQp6DPR_aH.\HYIKDG ÂOBQ¬DG,B[xbÁb|TIR[bQd©S1HYSBQ¬O1H
[bXB*ÆÈÇ9 É
e%QpIRPM^yÔHY[bOBSBH^OBDG_PDGRR«YIR[xQ³SBDPJRDGIKMN[xO1HYIH»:QpIKMµHS1H¼egC SBD V»e¦HYI~HÂDPR_PQHYMDGOJ~QpVR[xMNFBxDGPy
DGKJ~HE_PQpOBZBDP_G[bSBHV_GQYMNQ:BOB¸aª.QSBQp#SBQp[bkFBIK[bMDG[bIKQpgMNQYMNDPO,JRQpkS1HdegC y D & We%QpIDι9DGMFBbQByOBQ
_aHYKQ^S1H¢IKDGXp[bªYQFBxDGO1HYMDGOJRDvSBDGKDGO¯pQp¶¯[bS1HSBDzÑRH.JRQp©_GQ.j±H°¹9[\HY[xESBD¬_PQpM|BBJ~[¶¯pDGÔ
Dv
SBDHYI¬Æ BÃPOBDPJRRQ¤¯
HYOBSÂTHY| DG OB[ YQ¤¯ y tptpu É
>
&
C 9<;\=
/
/
&
Æ'Ç9 qpÉ
&
[bKJRQ^& .yÍH»SB[bJ~IR[x|BB[x¸aªYQ¢DPKJLH°J~ÁbJ~[x_aHSBD NTMµHSB[bJ~IK[b|BB[x¸aªYQ HYBKR[\H.O1H»_PQpM MGSB[bH D¯.HYIK[\HYOT¸aH
vzRR[xM^yJRQpIROBH°j±KDvOBDG_PDGRR«YIR[xQ^IKDGKQpx¯YDGIBMNHDG,1HY¸GªYQ^STD¬JRI~HYOTRF QpIKJRDvF1HYI~HH¯.HYIR[b«a¯pDGÔMNPSB[\H UW
¦ÆÈÇ9 qsÉ yBDQp9J~I~HvF1H.I~H & yB¯.HYIR[bHYOB¸GHSBD &
- /
& ##
- / /
QpOBSBDQ¬×19¹9QNSTDVlnD lOBQYbSB
- - ]
- / &
/ &
e
/
/
- Æ'Ç9 q Ç É
DVHJ~H°¹TH¬STDST[bRK[bF1H.¸aªYQ¬S1HY6×19J~1HY¸PÄ9DPnSBQNDPR_GHY\HYIPy
Æ'Ç9 qpÉ
OBDG_PDGRK[xJ~HYMKDGIzMNQSBDGbHYSBQpPnzQYJRDjRDd,BDdDGKJ~HµDG,1H.¸aªYQBy}_GQpxQ9_GHYS1HHYF DGO1HYzF1HYIRHN[bxBKJRI~HYI
HYzSB[xB_GBØj
S1HYSBDPNDPO,¯YQpx¯[xS1HY¬O1H³MNQSBDP\HYXpDPM^yW& OBªYQ²RD»HYFBx[b_aH³H³DPR_GQpHYMNDPOJ~Qp¬SBDdÑRH.JRQpJ~BIK|BBxDGOJ~Qp¬|B[xSB[bMDGOj
R[bQYO1HY[bP ¨ ×1¹TQdSBDElnD lOBQYbSB /
BR1H.bMDGOJ~D
MNQSBDP\HYSBQMDGSB[bHYOJ~DzHTMµHZB[bF ºYJRDGRD
XpIRHYSB[bDPOJ~D
HYO1«YxQpXH
HzS1HzUg TÆÈÇ9 qpq,É ¦ÊJLH°¹TH
SBD
SB[xRK[bF1HY¸GªYQ
SBQEDPR_aH.\HYI%F1HYKR[x¯YQiF Q9SBDkRDPIÔMQ9STDG\H.S1HzH.FBb[x_aHYOBSTQ.j±KD
BMµH¬HYOBHYbQpXY[\HdDPO,JRIRDQ¬J~I~H.OBRF QpIKJRD©SBD,1HYOJ~[xS1HYSBDSBDMQ;¯[xMNDPO,JRQvDSBDDGR_GHY\H.I
FBHYRK[x¯pQTy1[ÈDY¶y
&
<
Æ'Ç9 q t É
QpOBSBD BMNH¬_PNQpOBJLHYOJ~DSBDQpIKSBDGM
32%)?:3}&20) ©?:)´)9- £¤3 &2%) //
¨
MNQSBDGxQpnSBDDGbDPMNDPOJ~Qp
SBDd_LZBHYMµH¬F1HYIRHNDPR_GQpHYMNDPOJ~QpzSBDVXpHYRDPEO1ªYQNFBIRÎj±M[bJ~BIRHYSBQpnF1HYIJ~DPM
SBQ³FBIRDPRKBF}QYKJ~Q³STD,BD¢HÂ_LZ1H.MµHJ~BIK|BBbDPOJLH¼µTM_PQpO°ÑKBOJ~QÂSBDDGxDGMDGOJ~QYdSBD_LZBHYMµH»\HYM[bOBHYIRDP
_GQpOJ~[xO,1HYMDGOJ~D¬J~IRHYOBRF QpIJLHYSBQY©DDPKJR[bI~H.SBQpF}DPbQDGK_GQH.MNDPO,JRQB ¨ DP:DP[xJRQ»STQ»DPKJR[bI~H.MNDPO,JRQRQp|BIKDNTM
DGbDPMNDPOJ~Q²SBD¢_LZ1HYMNH³\HYM[bOBHYI©:Qp[ÅD¹THYM[bOBHYSBQ³O1H¼KDG¸aª.Q Æ'Ç9 o sÉ
DGJ~D_aHYKQBy#HYvFBIRQYFBIR[xDGS1HYSTDGvSBQ
DGR_PQHYMDGOJ~Q<IRDGH.J~[¶¯pQ > 6 2 C ~ªYQ³:BOT¸GÄDG¬SBQ²DGK_aHYbHYIvF1HYKR[x¯YQ ®D¢S1H³K1H²J~H°¹TH³SBD¢SB[bKR[xF1HY¸aª.Q <
UgJLH¼SBDPF}DPOBSBÖPOB_G[bHÂ:BOB_G[xQpO1HYgF DGIKMN[¶J~DNHÂ_GQpOTKJ~IKB¸aª.Q¼SBD|B[x|Bb[xQYJ~DP_aHYSBDµDGbDPMNDPOJ~QpVSBDµ_LZ1H.MµHTyÔO1HY
BHY[b > 6 2 C ~ª.Q4JLHY|BT\HYS1H.µF1HYIRH4SB[x¯YDGIKRQp¯.HYxQpIRDPSBDGJ~DP»STQp[bFBHYI~`YMDPJRIRQp¼Æ'e%DPJ~DPIRPy t YqÉ
DGRF DG_P[x1_GHY¸aª.Q»SBH»egC _PQpO°ÑKBOJ~HSTD DSBD ´y E> C yvBK1HYbMDGOJRDIRDGHYb[xÃaHYS1HNF1HYIKJR[bOBSTQ.j±KDdSBQ
FBIR[xOB_GÁxFB[bQ,BDH¬JLH°¹THµSBDVSB[bKR[xF1HY¸aª.QNVb[bXpHYS1H¬ÚYEF DG,BDPO1HYiDPR_GHY\HYzSBQµDPR_PQHYMDGOJ~QBy}DG,1HYOJRQ,BDdQ
DGR_GHY\H.I
FBHYRK[x¯pQ[bOT×BBDGOB_P[\HYSTQvF}DP\HY6XpIRHYOBSBDPzDPR_GHY\HY6STQNMQ¤¯9[xMNDPOJ~QBy9Q,BD[bMFBx[b_aHDGM
Æ'Ç9 r u É
> C > C E> C[
TD»µ_GQpOBZTDG_G[xS1H³_GQpMQ¼ZB[xF}º.J~DGKDSBD¢[xOBSBDGF DGOTSBÖGOB_P[\H³DGJLH.JRÁbJ~[b_GHÂSBD QpbMQpXpQpIKQ¤¯ Æ BÃGOTDPJ~KQ¤¯¿HYOBS
THY| DG OB[ YQ¤¯ y tptpu É vegC SBD SBDGF DGOBSTDNSBQ¢JR[bF Q»STDDPR_PQHYMDGOJ~Q»_GQpOTR[bSTDGI~H.SBQBy0_GQpMQdÑR«¢MNDPO9j
_G[bQYO1HYSBQB%zHnDPR_GHY\H6SB[xRR[xF1H.JR[x¯.HSBQp*DPR_PQHYMDGOJ~Qp*JRBIR|BTbDGOJRQp*FBbDPO1HYMDGOJ~DWSTDGRDPO¯pQp¶¯9[xSBQp*¯pDPIR[¶1_aH°jRD
BM_GQYMNF QpIKJ~HYMDGOJ~Q©BOT[x¯pDPIRRHYÈy,D E> C F Q9STD6RDGIgSBDPR_PIR[xJ~H©F}DP\H©D¹9FBIKDGRRªYQd_P\«YKR[x_aHÆ BÃPOBDPJRRQ¤¯HYOBS
THY| DG OB[ YQ¤¯ y tptpu É
>
C > 9[;\=
/
QpOBSBD D GD JLªYQIRDP\HY_P[bQpOBHYSBQpÅF QpI
9[;\=
9
& 9<;\=
0( & & /
C
&
Æ'Ç9 r;É
Æ'Ç9 rYopÉ
'Æ Ç9 r.sÉ
¨ TJRIRQp©MQ9STDGbQY©|1HYRDGHYSBQpO1H.DP,1HY¸GÄDGMGSB[bHYi:QpI~H.M FBIKQpF}QYKJ~QYGy0SBDGJ~[xO1HYSBQpDPMF1HYIJ~[b_PB\H.I
HµFBIRD¯pDPI©Hµ[bXYOB[b¸GªYQ¬DGM DGR_PQHYMDGOJ~QYiF1HYIK_G[\H.bMDGOJ~DFBIKj±M[bJ~BIRHYSBQpP
zDGJLHµ_GH.J~DPXpQpIK[\HNSTDGKJ~HY_aH.M¬jRD
Q»]^Q9STDGbQ ±OJRDGIRM[xJRDGOJ~D{%H.XpI~HYOTXpDaHYOTQ<ÆÈ] m{Wy<#QpIRXpZT[Èy t pÉ DdQ¢MNQSBDGxQSBD DP_LZ1HYMDGOJ~QSBQp]»Q.j
MNDPO,JRQpEhQpOBSB[x_G[bQYO1HY[bÆ'h6]¼hEy [bxXpDGIPy tpt s x[bMDGO.QHYOBS #[bbXYDGIGy tptpt BÌ D[lO1HYOJ~DdHYOBS Ì DPIK¯[bK_LZy
o upu opÉ ¨ FTIR[bMDG[xIRQ©TJR[bx[bÃaHiIKDaH.JRQpIRDP#FBHYIR_P[\HYxMNDPO,JRDÅM[bKJRBI~H.SBQpgF1HYIRHFTIRDP¯YDGIHIKDaHY¸GªYQV,BÁxMN[x_aHTy,BD
b[bXpHYS1HnHYQ
DGR_PQHYMDGOJ~QzMNPSB[bQnF QpI0BMNHzegC _GQpO°ÑKTO,J~HzS1H6:I~H.¸aªYQ
SBDkMN[xKJ~TI~HTy Vy°D#SBDkBMÏJRDGMF}Q
_aHYImj
HY_PJRDGIRÁxKJR[b_GQSBD
[bXYOB[b¸GªYQBÔwp«QRDPXpBOBSTQdIRDPRQp¶¯pDnDG,1H.¸GÄDGkSBDzMQpMDGOJ~QYW_GQpOBST[b_G[xQpO1HY[xÍS1H_GQpMF QpR[x¸aªYQB
EM| QpQpMNQSBDGxQp©~ª.QÂSB[¶1_G[xbMDGOJ~DvXpDPOBDGIRHYb[xÃa«a¯pDP[bF1HYIRH»K[xJR1HY¸GÄDGDPM TDN¯.«YIR[xQp©IRDGHYXpDPO,JRDGV~ªYQ
[bO°ÑKDJLHYSBQY6RDGFBHYI~HYSBHYMNDPOJ~DO1Hv_a`YMNHYI~HvSBD_PQpM|BBJLªYQT
32%)?:3}&20) +;/1-%&)W3 +;£a)¼20/
(
¨ 6MQ9SBDPbQpSBD©_LZ1HYMNHY6O1ªYQ¬FBIKjMN[xKJ~TI~HYS1H.6HY,B[0HYFBIKDGKDGOJLHYSTQpnOBDG_PDGRK[xJ~HYM,BDRDmÑRHvFBIKDGK_GIR[¶JLH
BMµH:QpIRMNHNSBDdegC F1HYIRHHYz:IRHY¸GÄDGzSBDMNHYRRHµQp¼STDMN[xKJRBI~HTzUWKJ~HZB[bF ºYJ~DPRDVF}QSBDdKDGIiIKDGbH°¹THYS1H
BHYOBSBQ
RDkIRDPRQp¶¯pDgBMNHÅDG,1HY¸GªYQzSTDgJRI~HYOTRF QpIKJRDkFBHYI~HnHÅ:BOB¸GªYQzSTDGOBK[bS1HYSTDkSTDkFTIRQp|1H.|B[bx[bS1HYSTDÔ_GQYO°ÑKBOJLH
S1HYv_GQYOB_GDPO,JRI~HY¸PÄ9DPGykS1HÂJ~DPMNF DGIRH.J~TI~HTyWS1H¯YDGxQ9_P[bS1HYSTDµD¢S1H¼FBIKDGK~ªYQB<E¯.HYOJ~HYXpDGOTSBDGJLH¼J~P_GOB[x_aH
~ªYQ¼,BDµQÂJ~DPIRMQÂSBDNFBIRQSBB¸GªYQ¼,BÁbM[b_GH»DµHÂ_GQYO,¯YDG_P¸aªYQ³O1ª.Q¼OBDG_PDGKR[xJ~HYM·MNQSBDGbHYXpDPM^y0DµQY|TJ~PM¬jRD
[bOT:QpIKMµH.¸aªYQ
DGJLH.JRÁbKJR[b_GHE_GQpMFBxDPJLHnRQY|BIRD6HzDP¯pQYbB¸GªYQiS1HYÔXpI~HYOTSBDGÃGHYÔJ~TIR|BBxDGOJLH.GÍe%QpIRPM^yYOBDG_PDGRK[xJ~HYM
SBD¼:DG_LZ1H.MNDPO,JRQ¿Q¿JRDGIKMNQ4STD¼J~I~H.OBRF QpIKJRD³SBDP¯[xSBQ¿Ú4MN[x_GIKQ.j±M[bJ~BIRH<D¼J~HYM| GM Q>SBD³XpI~H.SB[bDPO,JRD³SBD
:TJ~1H.¸aªYQSBDFBIRDPRRªYQ¼Æ8e¦QpF DYy t rpÉ
DG,1HY¸GªYQ>SBDÂJRI~HYOBKF}QYIKJ~D^F1HYIRH4H4egC _PQpO°ÑKBOJLH4SBHYµFBIKQpFBIK[bDGSBHYSBDGµSBQ4DGK_GQH.MNDPO,JRQ>IRDGH.J~[¶¯pQ
F}QSBD
RDGI#SBDGIK[x¯.HYS1HHF1HYIKJR[bIgSBQ_a«Yx_GBxQVST[x:DGIKDGOB_P[\HY1DPKJRQ9_G«YKJR[b_GQµÆ HYIKSB[bOBDPIGy t pr e¦QpF DYy t r e%QpF DYy
tpt q,É gUWKJLH¬DG,1H.¸aªYQSBDGK_GIKDP¯pDdHvDP¯pQYbB¸GªYQ¬S1H¬ekC OBQDGKF1HY¸PQ:ÁxR[b_PQvD©OBQDGRFBHY¸GQSBDFBIRQYFBIR[xDGS1HYSTDG
SBQDPR_GQpHYMNDPOJ~QB ERK[bM»y#STDP¯[bSBQH<XYI~HYOBSTD»ST[bMDGOBRªYQ´STQ´K[bKJRDGMNH´H²RDPINIKDGKQpx¯[bSTQBy#OTQpIRMNHYbMDGOJRD
IRDG_PQpIRIKDjRDH^JRG_GOT[b_aH¼STDF1HYIJ~Áb_PB\H.VDPM½_GQQpIKSBDGO1H.S1HYv{0HYXpIRHYOBXpDGHYO1HYÆÈ]^QYO,JRDjmhÅHYIRxQ É F1H.I~HÂKQpbB¸GªYQ
SBDNJ~HYgR[bJ~DPMµHÆ'e¦QYF}D.y tÇ e¦QYF}D.y t r HYOBS>e%QpF}D.y o upuYu É zdDPBHY¸GÄDG,BDNSBDGK_GIKDP¯pDPM¾H
DP¯pQYbB¸GªYQS1HYF1HYIKJRÁb_PB\HYg×1B[xS1HYk_GQpOJRGMJRDGIKMNQpkSBDJ~DGIKMN[xOBÁbJ~[x_GQpkDzJRDGIRMQp#SBDz×19J~1HY¸GªYQvHYxDaH.JRºpIR[xQpGy
F}QpIJLHYOJRQByBMPJ~QSBQp6O,ÒBMDGIK[b_PQpnDGRF DG_PÁx1_PQp
~ªYQ¬OBDP_GDGK~«YIK[bQp
F1HYIRHvIRDGKQpx¯YDj\HYÆ8e¦QpF DYy tYt rpÉ
&
&
/
3 - 1?8"¦& 0)&
DGKJRD_aH.FBÁxJRBbQFBIRQ_GTIRQp9jRDV_GQpxQ9_GHYIGy SBDdMNHYOBDP[bIRH|BIKDP¯YDYyQFTIRQp|BxDGMNHSBHµ[bOJ~DPI~HY¸GªYQµDPOJ~IRDd_GQpMvj
|BBKJ~ªYQD
J~BIK|BBbÖPOB_G[bHTÍ HY| QpIRS1H.XpDGMDPR_GQYbZB[xS1HTyTDERDEH.J~PMHV_aH.RQpÅK[bMFBbDPgSBDEK[bKJRDGMNHYkIRDaH°J~[x¯YQp
SBDGK_GIR[¶J~Qp¬F QpIDPBHY¸GÄDG¬MQpOBQSB[bMDGOBK[bQpOBHY[bD¢DGJLHY_P[bQpO1«.IR[\H.GyWSBD¯pDRD»HYFBIKDGDPOBSB[bSBH²OTQ³RDGÊ_aH.I~«.JRDGI
[bOJ~IKQ9SB9J~ºpIK[bQB Ì QYbBOJLH.IR[\H.MNDPO,JRDYySBDG[ع9Qp9j±KDSBDDGOT8H.JR[bÃGHYIÅIRDPRB¶JLHYSTQp6DGKF}DP_GÁxB_GQp
D©_GQpMF1HYIRHY¸GÄDG6DPO9j
J~IRDÂMNQSBDGxQpµDÂD¹9F}DPIR[xÖGOB_P[\HYPyzF Qp[bNDGJ~DG¢RªYQ¿HY|BTOBS1HYOJ~DPMNDPOJ~D³_GQY|}DPIKJ~QYOBQp¢x[x¯IRQpD³F DGIR[xº9ST[b_GQY
DGRF DG_P[\HYx[bÃGHYSBQpP
UWRF DGIRH°j±KD#,BDkDGJ~Dk|BIRD¯pDkRQp|TIRDP¯YÐ9QzS1Hn_GQpM|TBKJ~ªYQzDPMÏDGK_GQH.MNDPO,JRQp0J~BIK|BBbDPOJ~Qp%DgRB|BKÐpOB[x_GQp%SBD
XHYRDPÅF QpRRHbDP¯.HYIkQxDG[xJRQpI#HdHY| QpIRSBHYI#JRD¹J~QpMµHY[x#_PQpMFBbDJ~QpkDEJ~ºYFB[b_PQp#STDiF}DPR,B[x~HvH.JR1HY[bPWCEDPO,JRIRD
DGKJRDGPyESBDPKJLH._aHYMvj±KD³H_GQYM|BBJLªYQ>DPM M[bJ~BIRHYµDPKJ~IRH.J~[¶1_aH.S1HYSBDÂXHYRDP<Æ'{0HYZ°ÑRH.[b l4DPJHY'xy tpt É y
H<[xO,JRDGIRHY¸aªYQ²DPO,JRIRD_GQYM|BBJLªYQ<D¢J~BIK|BBbÖPOB_G[bH³DGM½8HYKDSB[bKF}DPIR~H9y#D»H²[bOJ~DPI~HY¸GªYQ²DGOJ~IKD»_PQpM|BTKJLª.QBy
J~BIK|BBbÖPOB_G[bH¢D_PQpMFBIRDPRR[x|B[bx[bS1H.SBDHYDPIRQSB[bOB`YMN[x_aH³Æ8CEDGKZ1HY[xDGDPJHY'xy tYtÇ É hÅH.S1H¢BMSBDPKJ~DPJRDGMNHY
J~I~H.õ_GQYOBR[xXpQÂ[xOÒTMNDPIRQpVSBDGRH.1QpPyWTD_GDPIKJLH.MNDPO,JRDµ_PQpOJ~[bO,1H.I~ªYQÂHÂDGJ~[bMdB\HYIQÂJRI~HY|BHYbZBQ»SBDÑKQ¤¯YDGOB
F}DPR,B[bRHYSBQpIKDGzHYQ¬bQpOTXpQvSBQpnFBIKº¤¹9[xMNQpnH.OBQpG
\} 7 +;/12%) 155 )-}£¤3 &
UWKJRDkJRI~HY|BHYbZBQÅ:QY[IRDaH.b[bÃGHYSBQ6SBTI~HYOJ~DkBMÏF DGIKÁbQSBQnSBDgb[x_GDGOT¸aH6SBQ + ('+ 8(5"$ !$% + % + +- +
-"+ ("
+ < -$% 8( $%" '+ +
$#
)-(5"$
+-( +
-( $ " +kÆ I~HYOB¸GH É _GQpM
| Qpx~Hnegl ¨ STQ©hÅEeW
¨ HYTJRQpInHYXpIRHYSBDG_PDHYn_GQpOJ~IK[b|BT[b¸GÄDG6STDV ¨ 1
[bDP*_ YDGxDVDCV ±IK[bXpQYO¢SBD ±IR[bXYQpOHDPKJRDMNHYO,BK_GIR[¶J~QB
) ),+ - 15:/1&
EOBQpO lMQpBGy o uYu q yTZJKJ~F Ë 55.M[b_PIRQpXpIRHa¯9[¶J lpXpIR_.OBHY~HTXpQ¤(¯ 5._GQYM|BBJ~[bQYFO 59
ÅHY\H IK[bKZBO1HYOy %HYOTS [bxb[\H.MNPy 0d¶y tpt q y¦Ó%BIR|TBbDPO,J¬hQpM|BBJ~[xQpO4lnDGXp[xMNDP©:QpI k l9F DGIKRQpOT[b_
eWIRQpFBTbR[xQpO¼UWMFBbQ l[bOTX k lSBIKQpXpDPO9j±z[bIzCE[ }BR[xQpO bHYMDGGy wYQpBIROBHY¦Q.kegIKQpFBBxR[xQpO¼HYOTS²e¦,Q DP"I .y
Ì QpÈ uTy1
QB s yBFTF qsYq c qsp
ÅHYBx_LZyCd.{WxyphQp|}QYGy,hEYwTxyhQ¤¹}yl;d¶yUWRKDGIGyhE¶y I~H.
O ype¦¶ywYTKJayYÓ©xy DPIRIGypwT.Vxypeg[xbx[bOBXBy°]<pwT¶y
Ó¦IKQ9D.ykwTxy HY YDGIPygl ¶y#H.OBS HYIRO1H°J~ÃYykwT¶y tpt o yWUͯYH.b1H.JRDGS [xOBDPJR[b_CEH.JLH^:QYI¬hQpM|BTKJ~[xQpO
]^QSBDGxb[bOTXBy KwYQpTIRO1HY QY¦eWZ l9K[b_GHYHYOTS»hZBDGM[b_GHYlnDP:DPIRDPOB_GDCiH°JLH .y Ì QYÈ o9 y9zQB s yTFBF qBp cTÇ sp
[bxXpDGIPyTlxy tpt s yThQpOBST[xJ~[xQpO1HY]^QpMDGOJ
hxQpRTIRDi:QpI#Ó¦BIK|BBxDGOJ
l
DGHY_PJR[bOBX b,
Q y meWZ lK[b_GnQY xB[bST
.y Ì Qp' r y
QB o y1FTF qsp
QpIRXYZB[Èyl¶y t p y Ó¦BIK|BBxDGOJVhQpM|BTKJ~[xQpO²]^QSBDPb[bOTXBy meWIRQpXpIKDGKi[bO³UWOBDPIR2
X lÂHYOBS<hQYM|BBJ~[bQYO²9_G[Øj
DGOB_PD .y Ì Qp' aq y1FTF o.q,r c o t o
QpIRXYZB[ÈylpH.OBSNhZ1HYMFB[bQpOy,]´¶y o upupuTy K]^QSBGx[bRH.J~[xQpOVDJgÓ6ZBGQYIR[bD6STDG bHYMNMDG .y WSB[xJR[bQpOTÔÓ%DG_LZBOB[xFy
eÔHYIK[bPy I~HYOB_PDY
I~
H lpy ¶yW{*[b|B| lpyge%xygH.OBS [bxb[\H.MNPy xy tpt q y k [bXpZ>9F}DPDGS>Ó%BIR|TBbDPO,JNhQYM|BBJ~[bQYOy GÓ¦TIR|BBxDGOJ
l
DGHY_PJR[bOBX b,Q n" .yBFBF upt;c Ysp T6_GHYSBDPMN[x_egIKDGK ±OB_.
I~
H lpy *0hExy¦hZ1H.MNFB[xQpOy0]<xy%HYOBS<{*[b|T| lYy0e¦Vxy tYt y*eWIRDPMN[ع9DGS \H.MNDPE[bO´J~HYXpO1H°J~[bOTXÓ¦TIj
|BBxDGOB_PD Ë eÔH.IKJ LBÓ6ZBD DGOBDPI~HY QpIKMBbH.J~[xQpON:QpI
hQYBOJ~DGI×1,Q n[bOBXNJRIRDGHYMNnH.OBS^9I~HYST[bDGOJz]^QSBDPb
:QpI6Ó%BIR|BTbDGOJ
Ó%I~HYOBKF}QYIKJay KhQpM|TBKJR[bQpO»HYOBS bHYMND .y Ì Qp' Yq y zQB s j q yBFTF s t c qB uT
I~
H lpy *0hExy¦hZ1H.MNFB[xQpOy0]<xy%HYOBS<{*[b|T| lYy0e¦Vxy tYt o y*eWIRDPMN[ع9DGS \H.MNDPE[bO´J~HYXpO1H°J~[bOTXÓ¦TIj
|BBxDGOB_PD Ë eÔHYIJ L}Ó6ZBD / Ó6ZBDGQY$I lÂ:QYIilnDaHY_JLHYOJ~ ±MFB[xOBXp[bOTXNQpO²H HYxÈy KhQYM|BBJ~[bQYO³HYOBS
\H.MND Yy Ì Qp'Bt yBzQB o yTFBF ¤r c ¤p
I~
H lpy T1hE¶y1hZ1HYMFB[xQpOy9]´¶yBHYOBS{*[x|B| lpy9e¦TVxy tpt y9eWIKDGM[¶¹9DGS \HYMDGk[bOJLHYXYO1H.J~[xOBXdÓ%BIK|B9j
bDPOB_GD Ë eÔHYIJ L9Ó6ZBD©]^DaHYO Ì DPbQ_G[¶J~[bDPkHYOBS¢eWIRDPRKBIRDHYOTSµJ~ZBDiCiHYM pZBxDGIzBM| DGIPy hQpM|BTKJ~[xQpO
HYOBS bHYMND .y Ì Qp' p;o y1zQB q y1FBF pspr c rYs
I~
H lpy *0hExy¦hZ1H.MNFB[xQpOy0]<xy%HYOBS<{*[b|T| lYy0e¦Vxy o uYupuTy*eWIRDPMN[ع9DGS \H.MNDPE[bO´J~HYXpO1H°J~[bOTXÓ¦TIj
&
"
"
$
%
$
$
"
'&
&
|BBxDGOB_PD Ë eÔH.IKJ Ì T
D Ó6ZBDGQpIOlµ:QpIkJ~ZBDil
D[l9OTQpbSB6J~IKDGRKDG
HYOBSlnD lOBQYbSB b9¹9DGEFBFBx[bDPSµJ~Q
±MNFT[bOBXp[xOBX xQ,nGy hQpM|BBJ~[xQpO»HYOBS \H.MND Yy Ì QpÈ ;o uTyBzQB j o yBFTF c ¤
I~Hlpy *0hExy¦hZ1H.MNFB[xQpOy0]<xy%HYOBS<{*[b|T|lYy0e¦Vxy o uYu y*eWIRDPMN[ع9DGS \H.MNDPE[bO´J~HYXpO1H°J~[bOTXÓ¦TIj
|BBxDGOB_PD Ë eÔHYIJ Ì ÍUͯ.HYb1H°J~[bQYO´QYz]»Q9SBDPb:QpIVJRZBD¢hZBDPMN[x_aHY9QpTIR_GDµÓ¦DPIRM»y KhQpMd|BBKJR[bQpOHYOBS
\H.MND Yy Ì Qp' ;o Çy1zQB j o y9FBF o u o.s c o u q uT
I~
H lpy 6VnhEÅHYOBSe¦DJ~DGIKGyxy tpt q yE{0HYM[bO1H.I bHYMNDPbDJ~[bO Ó%BIR|BTbDGOJ bHYMNDPGy GÓ¦TIR|BBxDGOJ
l
DGHY_PJR[bOBX b,Q n" .yBFBF ps c pas T6_GHYSBDGM[b_eWIRDPR ±OB_Y
hÅH.J~ZBQYOBOBDPJGy©]´¶y Q9DJRJROBDGIPyiwTÅhExyzHYOBSwpHYMDGPy k xy t 9 y
U͹9F DGIK[bMDGOJLHYiJ~T(S l HYOTS zBMDGIK[b_aH.
]^QSBDGx[bOBX6QY k [xXpZÓ¦DPMNF DGIRH.J~TIRD ¨ ¹T[xS1H.JR[bQpOQYTeWIRQpF1H.OBDkHYOBSVnj #TJLHYOTDYy UW[bXpZJRDGDGOJRZv lMF}QpK[bBM
Æ ±OJ~DPIRO1H°J~[bQYO1HY É QYO>hQpM|TBKJR[bQpO .y%FBF%tpu s c9t ¤s y¦eW[xJKJ~R|TBIRXpZ%Ó6ZTD¢hQpM|TBKJR[bQpO ±OBKJR[xJRTJ~D.yÔÓ6ZBD
hQpM|BTKJ~[xQpO ±OBKJR[xJRTJ~D.
hZ1HYRRHY[bXYOy e¦¶y o upupu9y mÓ%BIR|TBbDP_GDDGOÂ]^G_GHYOB[xTDSTDG bB[xSBDG .y1hGFBHYSB Pj±PSB[xJR[bQpOTGy I~HYOT_GDY
CEDGKZ1HY[bDPGy E¶y [bXYBDG[xI~H²S1H49[xx¯.HTy{g ¶y6HYOBS l
DPOBjmhQpI~HY[xÈyÅ]´xy tptÇ9ynQpMND DGOBDPIR[b_ÂeWIRQp|BxDGM
l
DP\H.JRDGS¼JRQÂhQYM|BBJ~[bQYO³QY k lSBIRQpXYDGO´HYOBS²E[xIi[bO´9BF DGIKRQpOT[b_ xQ nPy%hZ1HYMFB[bQYOy0]´0HYOTS´CzDj
RZ1H.[bDGPy E¶yÍDGST[xJ~QYIRGy mfzÓ%©] lMNF QpR[xBMÙQpO¿hQpMd|BBKJR[bQpO[bO>BF}DPIRKQpOB[b_ b,Q n YyÔFBF ;r c q,o y
CEQpIKSBIRDP_LZ,JG mfzÓ%©]´y b #DGIn6_aH.SBDGM[b_eWB|Bx[bRZTDGIRPy ±OB_Y
Ug_LZTD ,[ÈyÓ©.HYOBSv]»BOBXHY'yp]< xy tptYuTyYe¦HYIKJR[b_PbDgÓ¦IRHY*_ ,[bOBXE[bOVHE{0HYM[bO1HYI0eWIKDGM[¶¹9DGS \HYMDYy megZ lR[x_G
QY bB[xSBÅ Yy Ì QpÈ o y1zQBBtTy1FBF ;rYoYs
QpH.Jay°Ó©xy #HYFy °e%xyYHYOBS ZBHYOBXBy v¶y o uYu y°Ó6ZBD#¯[bK1HYx[b~H°J~[bQYOHYOBSdMNHYFBFT[bOBX
QYTJRBIR|TBbDPO,J¦FBIKDGM[¶¹9DGS
[bMFB[bOTXp[bOBX× HYMDGPy KhQpMd|BBKJR[bQpO»HYOTS bHYMD .y Ì QYÈ ¤opr y1
QB j o yTFBF Ys t;c r
xy t r y k HYOBSB| QQ QYvJ~Q_LZ1HYJ~[x_<]^DPJRZBQ9ST»:QpIeWZ lR[x_GGyhZTDGM[bKJR$I l H.OBSJRZBD
HYIKSB[bOTDGIGyihE EH.JRBI~H.09_G[xDGOB_PDG Yy FBIR[xOBXpDGI Ì DPIRbHYXBy DPIRx[bO k DP[bSBDPb| DGIKXB
hE¶y o upupuTy HYneWZ1HYKDhQpMd|BBKJR[bQpO^hZBDPMN[xKJR$I l .y 9FBIK[bOBXpDPI Ì DGIK\HYXByBzD kQpI
HYIKSB[bOTDGI
wYIG¶y y Lxy tpt y KhQpM|TBKJR[bQpO .y96_aHYSBDPMN[x_egIKDGKGy1J~ZB[xIRSDGST[xJ~[xQpO
bHYRKMµHYO
Q YD.y0]´Cdxy0H.OBS<]^[bxbDPIGywTd¶y t Y y k l|BIR[xS²zD 6JRQpFO 5.Ó6[xMNDÎj
IK_aHYIPy0wT HYOBSy lwTxy%MNQ
±OJ~DGXYI~H.JR[bQpO eWIRQ_GDGSTBIRD<:QpI»JRZBD9Qpb9J~[bQYOQ.J~DGHY(S lYyV{0HYM[bOBHYIGy ¨ OTDjmCz[bMDGOBK[bQpO1H.ÈyieWIKDGM[¶¹9DGS
\H.MNDPGy ±Ó #DGOJ lj [xIRJN lMNF QpR[xBM Æ ±OJ~DPIRO1H.JR[bQpOBHY É QpO hQpM|BBJ~[xQpO .yWFBF ÇpÇ s c Ç o yWeW[¶JRJ~mj
|BBIKXpZBÓ6ZBDdhQpM|TBKJR[bQpO ±OBJ~[xJRTJ~D.y1Ó6ZBDVhQpM|BTKJ~[xQpO ±OBKJR[xJRTJ~D.
D kQpI y DGST[xJ~[xQpO
k [bOTÃGDYy wT ¨ ¶y t r tTy mÓ%BIK|BBbDPOB_GD .y ]^_ I~H Åj k [bxÈy9z
y RP lpy LxyfWѯ.«YIR['y}]´xyÓ¦BIR«YO l[ÈyÓ©¶y
k BXpZTDGGy ¶yÓ%QpMb[bOy Vxy k HYMF1HYIJ~KQpBM[\HYOy U6¶y*z[xMNMQBy ¶4
h\HYXYBDYyVxyHYOBS<eW[bbx[bOBXTy]<xy o uYu HTy}EO ±O¯pDPKJ~[xXH.JR[bQpO²QY ±MF}QpIJLHYOJ HYiegZBHYRDlnDaHY_J~[bQYOBiQY
z[¶J~IRQYXpDGO²F}DP_G[bDPi:IRQpMÕJ~ZTD9[bMT\H.JR[bQpO»QY B ÂUÔ¹9F}DPIR[xMNDPO,J~HYÍCEH.JLH[xO<hQpM|BBJ~[xQpO< lKJRDGMGy
KhQpMd|BBKJR[bQpOH.OBS \HYMD .y Ì QpÈ ¤o.q yTFTF r Ç s c rY tT
O l[ÈygÓ©¶yÅhbHYXpBD.ygd¶yHYOTS eW[xbb[xOBXByÔ]´¶y o uYu |ykCED¯pDGxQpFBMDGOJNHYOBS4JRDGKJR[bOBX²QYzH
k BXpZTDGGy xygÓ%BI~«Y
_GQpMFBIKDGZBDPOBR[¶¯pDd_LZTDGM[b_aH.%MDG_LZBHYOB[bKM:QpI6J~ZBDVQ¤¹9[xS1H.J~[xQpO»QYWMDPJ~ZBHYOBDYy ±OJRDGIROBH.J~[xQpO1HY%wYQpTIRO1HY%QY
hZBDGM[b_GHY [bOTDPJ~[x_G Yy Ì QpÈ sps yBFBF r9¤s c r.sp
±OB_GIKQpF}DPI~HTy 0e¦¦HYOBSCED [¶JRJayÔCd¦e¦¶y tpt y BOBS1HYMDGOJ~HYb©QY k DaH°JHYOTS¿]ÂHYKdÓ%I~HYOB:DGI YyÍwYQpZBO
[bxbD lQpOBGy
D kQpI y q DGSB[¶J~[xQpO
Q YD.y.]´;Cd¶yYHYOTSd]»[bbxDGIPy;wT¤d¶y t r y; QpIJ~I~H.OegIKQpXpIRHYM :QpI%]»Q9SBDPb[xOBX
DPDYy.l¤wTxy IK_aHYIPy.wT ¶yYMNQ
J~DGHY(S l{%H.MN[xO1HYI ¨ OTDjmCz[bMDGOBK[bQpO1H.TeWIRDPMN[ع9DGS bHYMNDPGy.Ó¦DP_LZBOB[b_GHY lnDGF QpIKJkiEC r j po.q u 5YfEhkj q y
THYOBST[\HvEH°J~[bQYO1HY{0HY| QpIRH.J~QpIK[bDPG
D lpy 0]<xy¦HYOBS´]^[xbbDPIGy0wT*Vxy tYt q y*Ó6ZBDNhZBDPM ,[bO<Ó6ZBDPIRMQ9(S lO1H.MN[x_vCiH.J~HY|1HYKDYy
DPDYy¦l*wTxy%lnBFBb[
Ó¦DP_LZBOB[x_aHY0lnDGF QpIKJziEC Ç;j po9;r Ey1THYOBSB[bHvEH.JR[bQpOBHY*{0HY| QpI~H.JRQpIR[xDGP
O .QByÔVÔH.OBS [xbXpDPIGy¦l¶y tptYtTyWhQpOTSB[xJR[bQpO1H.k]^QpMDGOJ¬hxQpRBIKDµ:QpIÓ¦TIR|BBxDGOJhQpMd|BBKJR[bQpOy
x[bMDG
eWIRQYXpIRDPRn[bOUWOBDPIR2X l»HYOTS¼hQpMd|BBKJR[bQpO^9_P[bDPOB_GD Yy Ì QYÈ oYr y1zQT yBFBF r t r c p Ç9
TÃGOBDJ~RQ¤¯ y Ì glgHYOBS THY| DG OT[ YQ¤¯ y Ì Wd¶y tYtpuTy mÓ%BIR|TBbDPOB_GD^HYOBS hQpM|BTKJ~[xQpO .y k DGM[bKFBZBDPIRD
eWB|Bb[xRZB[xOBXhQpIKFxy
D kQpI
{%H.Z°ÑRHY[b lpy k xy HYIKMNDPSynCd¶yihZ1H.MNFB[xQpOyn]<xyzHYOBS #IRBDPÈy
e¦¶y tpt y ±OJRIRQSBB_PJR[bQpO QYCE[bxTJ~[xQpOÊ[bO
~J ZBD 6]Â{ MNQSBDG Ë EFBFBx[b_GH.J~[xQpO¼J~QÂHÂJ~HYXpO1H°J~[bOTX»Ó%BIK|BBbDPOJ bHYMDYy KhQYM|BBJ~[bQYO49_P[bDPOB_GDNHYOBS
Ó¦DP_LZBOBQpxQpX2l .y Ì Qp' ¤sr yTFBF ;rYs c Ç s
{%H.BOBSBDPIGy:E}U6HYOTS²9F1HYxSB[bOTXByCV<E¶y tpÇ y {*DG_J~BIKDGi[xO³]ÂH.JRZBDGMNH.JR[b_aH.Ô]»Q9SBDPbiQ.WÓ¦TIR|BBxDGOB_PD .y
6_aHYSTDGM[b_eWIRDPRGy {*QpOBSTQpOy JnDGSB[¶J~[bQYO
{0DPR[xDGBIPyi]´¶y tptÇy mÓ%BIR|BTbDGOT_GD¼[xO bT[bSB Yy x DPI6_aHYSTDGM[b_³eWB|Bx[bKZBDGIKGy ±OB_Y¶yzCEQpIRSTIRDG_LZJGy s
DGSB[¶J~[xQpO
{0-D n[bP4y E*HYOBS¼¯YQpO<UWb| DYy xy t T y KhQpM|TBKJR[bQpOy \HYMDGEHYOBS²UÔ¹9FBbQYR[bQYOB©QY H.RDG .y6_aHYSTDGM[b_
eWIRDGKGy z-D kQpI
]^Qp[bOyBe¦THYOBS]^HYZBDGKZy xy tpt yTCE[xIRDP_PJ6
BMDGIR[x_aHY9[xMB\H°J~[bQYO Ë ÏÓ¦QQp [bOÓ%BIK|BBbDPOB_GDlnDGKDaHYIK_LZy
mzOBO,1HY*lnDP¯[b-D ÏQY xB[bS»]^DP_LZ1HYOB[x_G Yy Ì Qp' s u9yBFBF rYs t;c r Ç
e¦DGDJ~DPIRGyÔÓ© %wT¶yÔJ~IKQpMNMDGIPy%e¦0e¦¦wT¶y¦STD Ì IK[bDPGyÔwT0Un¶y¦l
QDa8H °HYDPIKJRGyÔwT0Un¶yÍH.OBS k Q9QYXpDGOBSTQ9QpIKM^y
hE wTxy tpt q y1hQpMNFBHYI~H.JR[x¯YDU͹9F DGIK[bMDGOJLHYHYOBS^zBMDGIK[b_aH. ±O¯pDGJ~[xXH.J~[xQpOQYÔHeW[xbQYJRDGSÓ¦TIR|BBxDGOJ
EH.JRBI~H. H.nCE[ }BR[xQpO \H.MND.y oYr J~Z^ lMF}QpK[bBMÆ ±OJ~DPIRO1H°J~[bQYO1HY É QYOÂhQYM|BBJ~[bQYO .yBFBF ;o°qB c
;o.q TÓ6ZBDdhQpM|BTKJ~[xQpO ±OBKJR[xJRTJ~D.
e¦DPJRDGIKGy V¶y t Yq y9{0HYM[bO1HYIkCE[ TR[bQYO bHYMNDPbDJ#]^Q9STDGb#[bOµzQpO9j±eWIRDGM[¶¹9DPSÓ¦TIR|BBxDGOJ
hQpMd|BBKJR[bQpOy
eWIRQYXpIRDPRn[bOUWOBDPIR2X l»HYOTS¼hQpMd|BBKJR[bQpO^9_P[bDPOB_GD Yy Ì QYÈ uTyBFBF s9 t;c sps tT
e¦DPJRDGIKGy}V¶y o upupuTy mÓ%BIR|TBbDPO,JEhQpMd|BBKJR[bQpO Yy1hÅHYM|BIK[bSBXpDifzOB[¶¯pDGIKR[¶J l»egIKDGKGy}hÅHYM|BIK[bSBXYDYy1f
e¦DPJRDGIKGy9V,HYOBS [xbb[bHYMGy pVxy t Ç9ypÓ6ZBDnEO lMNFTJRQYJ~[x_
J~IKB_PJRBIRDnQYJRQp[b_LZB[xQpMDPJ~IK[b_]^DPJRZ1HYOBDÎj±z[bI
\H.MNDPGy hQpM|BTKJ~[xQpOHYOBS bHYMND .y Ì Qp' p yTFBF ¤r c o uÇ9
eg[xQpMDGbx[Èy<fV¶y tYtptTy>{0HYIKXpDj±UgST(S l9[bMdB\H.JR[bQpO Ë 6_LZT[bDP¯YDGMDGOJHYOTS hZ1HYxbDPOBXpDGPy eWIKQpXpIRDPR [bO
6DGIKQpRF1H._GDd9_G[xDGOB_PDG" .y Ì Qp' sr yBzQB j o yBFTF spsr c spo
e¦QpF DYyV}¶y tÇ yiÓ6ZBDegIKQp|1HY|T[bb[¶J l zFBFBIKQHY_LZ JRQ JRZBD4]»Q9SBDPbx[bOBX>QYdÓ¦TIR|BBxDGOJÂl
DGHY_PJR[bOBX xQ nPy
KhQpMd|BBKJR[bQpOH.OBS \HYMD .y Ì QpÈ o Ç9y1zQT s y1FBF o tpt;c s9;o
e¦QpF DYy0 xy tpt q y}{0HYXpI~H.OBXp[\H.O¼egC ]^DJ~ZBQSBE:QpIzÓ¦TIR|BBxDGOJ x,Q nGy ±EOBO,1H.ÍlnDP¯[b-D QY bT[bS³]»Dj
_LZ1HYOB[x_G Yy Ì QpÈ o. yBFBF o.s c ps
e¦QpF DYyÔ}¶y tpt r y0e¦HYIKJR[b_GxD]^DPJRZBQS<:QpI©Ó%BIK|BBbDPOJ x,Q n Ë ±OJ~DPXpI~H.JR[bQpO²QYÅJRQ9_LZ1H.KJ~[x_N]^Q9STDGgUW,1H°j
J~[xQpOBGy KwYQpBIKO1HYQ.WhQpMFBTJ~H.J~[xQpO1HYeWZ lK[b_G .y Ì QpÈ Y Ç9yBFBF spso c s.q tT
e¦QpF DYy}}¶y o upupu9y mÓ%BIK|BBbDPOJ b,Q n" .y hÅHYMd|BIR[xSBXpDfzOT[x¯pDPIRK[xJ leWIRDPRPy}f
OB[xJRDGS [bOBXYSBQpM»
e¦QpF DYy E¶y t pr yTegC ]^DJ~ZBQSBÅ:QpI#Ó¦TIR|BBxDGOJnlnDaHY_J~[¶¯pD xQ nPy megIKQpXpIKDGR[bO¢UWOBDPIR2X lHYOBS»hQpMvj
|BBJ~[bQYOÂ_G[bDPOB_GD .y Ì QpÈ p yBFBF p t;c t o
l
[xXpXpGy Exy tYt o yzIR_LZ1HYDPQpbQYXp[b_GHYvUͯ[bSBDPOB_GDÊQY [bIRDÊhDPIR[xMNQpOT[\HYx[bRM [xO JRZBDÊ{0H.J~DÊeWIRDPZB[bJ~QpIK[b_aH.
9QpTJRZBDGJay ml
DPRDaH.IR_LZ¼
QYJ~DPnQY¦JRZBD I~HYO k ]^_ahbBOTX]^TRDGTM .y Ì Qp' p
THY| DG OB[ YQ¤¯ y Ì ¶yWCEDPRZ1HY[xDGPy ExyÍHYOBS [xXpBDP[bI~H¢S1H¼9[b¶¯YH9yÔ{W¶y tpt yÍlnDP¯[bK[xJ~DPS bHYMDGbDJV]^QSBDGk:QpI
zQpOjmeWIRDPMN[عTDPS<hQpM|BTKJ~[xQpO²[bO<9TF}DPIRRQYOB[b_vÓ%BIR|TBbDPO,J x,Q nGy hQpM|BBJ~[xQpO²HYOBS bHYMND .y Ì Qp'
paq yTzQB s j q yBFTF r ÇpǤc rYYq
THY| DG OB[ YQ¤¯ y Ì 0HYOBS [bXpTDG[bIRHS1H^9[b¶¯YH9y*{Wxy o upu o y0eÔHYIJ~[\H.b l¼JR[bIRIKDGS´l
DGHY_PJRQpI Ë JRB(S l²QY#J~ZBDN9DPO9j
R[¶J~[x¯[¶J lÂQYkJ~ZTDµ]»QpOJ~DjmhÅHYIRxQ»9[bMdB\H.JR[bQpO^J~Q¢J~ZBD
BM| DGI©QYÅJ~Q_LZ1HYJ~[x_¬eÔHYIJ~[b_PbDP n[xJ~Z³JRZBD¬BRD
QY%H¬9DPMN[Øj±EOBHY l,J~[x_Yy9JRDaHY(S ljmJLH.JRDYyB9Qpb9J~[bQYOµJ~QdJRZBDegC UW,1H.J~[xQpOy KhQpM|TBKJR[bQpO¢H.OBS \H.MND Yy
Ì QpÈ ;o tTyTFBF ¤Yq c Ç
THYXHY9Jay¦e¦¶y o upu y m{0HYIRXpDUWSB(S l9[xMBbH.J~[xQpOÂ:QpI ±OB_PQpMNFTIRDGKR[x|BbD b,Q n YyÔ9FBIK[bOBXYDGI Ì DGIK\HYXBy DPIRx[bO
k DP[bbSTDG| DGIRXT
T8H °HYIGy1V HYOBS^9QBy l¶y tptÇ9y9 hIR[xJR[b_GHYUͯ.HYbBH.J~[xQpO¢QYÔzDaH.Ij HYxÓ #Q.j±Ug,1H°J~[bQYOÂ]»Q9SBDPbnEXpHY[bOBJ
CE[bIKDG_J6zTMNDPIR[b_GHY}9[bMdB\H.JR[bQpOCiH°JLHTy ±OJ~DPIRO1H.JR[bQpOBHY}wYQpBIROBHYQY k DaH.JÅHYOBS bB[xS xQ .y Ì Qp' ¤ y
zQB o yBFBF tǤc o u
THYI °HYIPy }¶y}UWIKbDG|BHY_LZBDGIPy ¶y HYOBS k BK~HY[xOB[Èy ]< xy tpt y CE[xIRDP_PJE9[bMdB\H.JR[bQpOµQYghQpMFBIKDGRK[b|BxD©Ó¦TIj
|BBxDGOB_PD³[bO HÊ9ZBDGHYI b,Q y mÓ6ZTDGQpIKDPJ~[x_aHYiHYOBS hQpMFBTJLH°J~[bQYO1HY bB[xS hC lO1HYM[b_P" .y Ì QpÈ o yzFTF
otcsur
9DGKZ1HYSBIK[Èy HYOTS´e%DPJRDGIRPy%V¶y tptpu9yÓ6ZBD ±OBOBDPIJ~IKB_PJRBIRDvQ.Å]»DPJ~ZBHYOBDjE[xI \H.MNDPGy hQpM|BTKJ~[xQpO
HYOBS bHYMND .y Ì Qp' T yTFBF t c p¤
9Z1H y E¶y6CEI$lYDGIPy xy [xbx[\HYMGy ¶yÅH.OBS k HYXpXHYIKSynwT E¶ynwTxy t p yÅ9QQYJ~[xOBX<HYOBS CE[xRIKBFTJ~[xQpOÊ[bO
9FBZBDPIR[x_aHYxlÂlMNMDPJRIR[x_aHYÔhQpM|BTKJ~[xQpO²QY#CEDG_GHYOBDCEIKQpFBbDJ~©[xO³E[bIPym6_JLHzKJ~IKQpO1HY9J~[b_GH.y Ì Qp'
Ç9yBFTF p t r c ;o u o
9F}DPÃG[bHYbD.y1hE xy tpt yTÓ%BIR|BTbDGOT_GD]^QSBDGx[bOBXV:QpIÅÓ6[bMDj±CEDGF DGOTSBDGOJ
lniiH.OBS Ì {0Uk Ë lnDP¯[bD-y
m ±E wYQpBIKO1HY Yy Ì QpÈ sp y1
QB o y1FBF Ç s c aYq
ÓÔHYOy xynCEHYXHYTJGy6e¦¶yzhÅH.J~ZTQpOBOBDJay
]´¶y
HYOBS #Q9DJRJ~OTDGIGyzwT#hE¶y tpt q y ¨ ¹9[bSBH.J~[xQpO H.OBS [bXYOB[xJR[bQpO¿QY
MNDJ~Z1H.OBDjFBIRQpFBHYOBD6HYOTSNMDPJRZ1HYOBDÎj±DPJRZ1HYOBDÎj±FBIKQpF1HYOTD6MN[ع9JRBIRDP Ë D¹9F DGIR[xMNDPOJ~kHYOBS¬MQ9SBDPb[xOBXBy hQpMvj
|BBJ~[bQYOÂ_G[bDPOB_GDHYOTS^Ó%DG_LZBOTQpbQpX l.y Ì Qp' u s yBFBF asps c ;r
Ì D lO1HYOJ~D.yTCVpHYOBS Ì DPIK¯[bK_LZy,{Wxy o uYu o ypÓ%BIR|TBbDPO,J#hQYM|BBJ~[bQYO¬]^QSBDGx[bOBXBy eWIRQYXpIRDPRW[bO¬UWOBDPIR2X lHYOBS
hQpM|BTKJ~[xQpO^9_G[xDGOB_PD .y Ì Qp' oY yTFBF t s c oYp
I l QY k [bXpZ Ó%DGMF}DPI~H.JRBIRD<hQYM|BBJ~[bQYOQ.dz °HYOBDP»TFJRQ ¨ _JLHYOBD.y
HYIKO1H.JRÃYywT¶y t Yq yEhZBDGM[bJ~$
m4
Ó DPOJ~[bDJ~ZN lMF}QpK[bBM®Æ ±OJ~DPIRO1H°J~[bQYO1HY É QpONhQpM|BBJ~[xQpO .ypFBF Yq,r c prY yeW[xJKJ~K|BBIRXYZpÓ6ZBDzhQpMvj
|BBJ~[bQYO ±OTKJ~[¶J~TJRDYy1Ó6ZBDVhQpMd|BBKJR[bQpO ±OBJ~[¶J~TJRDY
Y
H
IKO1H.JRÃYy#wTxy#]ÂHYHYGykfV¶ykHYOBS¿CE[x|B|BxDYykl xy tYtptTy hQpM|BBJ~[xQpO¿eWZ lK[b_aH.6HYOBS hZBDPMN[x_aHY TO9j
S1HYMDGOJLH.bGy1]^Q9STDGb[xOBX¬HYOBSÂ9[xMB\H°J~[bQYOyTUÔ¹9F DGIR[xMNDPOJ~Gy e%QpbxTJLHYOJ QpIKMµH.JR[bQpO YyT9FBIK[bOBXYDGIGy DGIKb[bOy
o OBSDGST[xJ~[xQpO
Q yWhE 0H.OBS4CEOI lpDPIGy 0{W¶y t Yq yÔhZBDGM[b_GHY [bOBDJ~[x_]^Q9STDGb[xOBXQY k l9STIRQ_aHYIK|}QpOhQpMvj
DPKJ~|TIRQ
|BBJ~[bQYOy eWIKQpXpIRDPRn[bO»UWOBDPIR2X lH.OBS¼hQYM|BBJ~[bQYOÂ_G[bDPOB_GD .y Ì QpÈ uTyBFBF c r Ç9
b
[
bx[\HYMGy 9Vxy t r y KhQYM|BBJ~[bQYOÓ6ZBDGQY$I l .y DPO°ÑRHYM[bFO 5phTMNM[bOBXY#eWB|Tb[bKZB[bOTXvhQpMF1HYO lpy ±OB_Y¶y
RDP_GQpOBS»DGST[xJ~[xQpO
ywT
HYOBS e¦QpF DYy xy o uYupuTyiegC hÅHYb_PB\H°J~[bQYOB¢QYdJRBIR|TBbDPO,J»OBQYOBFBIRDPMN[ع9DGS ×1HYMNDP n[xJ~ZbQ_aH.
D¹J~[xOB_PJR[bQpOy KwYQYBIRO1H.*QYWhQYMNFB9JLH.JR[bQpO1H.eWZ lR[b_P" .y Ì QpÈ ;oYs yBFTF oYT c s uÇ9
DG SBQ¤¯[b_LZy v¶:
y ÅHYIKDGO,|B\H°JRJay ¶y{*[x|BIRQ¤¯[b_LZy Ì ¶y*HYOBS<]^8H ,Z,¯[x\HYSBÃPDYy ¶y t pr y ±Ó6ZBD¬]ÂH.JRZBDGMNH.JR[b_aH.
Ó6ZBDGQY$I l¢QYÍhQpM|TBKJR[bQpO»HYOBS^UÔ¹9FBbQpK[bQpOT" .y hQpOBKBxJ~HYOJ~ BIKDaHYy zD kQpI
) 9-%2%5 1p)
z#DPBHY¸GÄDG#SBD
JRI~HYOTRF QpIKJRDzSBD
MNHYRRHTy9,1H.O,JR[bS1H.SBDzSTDzMQ¤¯9[xMNDPOJ~QByDPOBDGIKXp[\HDzDPRF G_P[bDGTÁbM[b_aH.
F1HYI~H¬BMNHDGK_GQHYMDGOJRQNIKDaH.JR[x¯pQvJRI~HYOBK[bDPO,JRDF}QSBDGMÀRDGInDPR_GIK[xJ~HYn_GQpMQ^Æ [bxb[bHYMNPy t rYÉ
,.- 1
0(
, 9
,
- /
, 9
>
K
9
<
C
9 2 Y
, - / / > - 2 Y
W2
<
C
, 9
9
9
K
,2 - 2 8
! 2[
> -52 < = /
W C
, 9
9 :
6
-
zDGJLHYvDP,1HY¸GÄDGPy Q¼JRDGMF}QTy HÂSBDGOTR[bSBHYSBDYy Q¼¯pDJ~QpI¯YDGbQ_G[xS1HYSBD.y ¢H¼FBIKDGK~ªYQBy ¢H
DGOBDPIRXp[bH¼[bOJ~DPIRO1H¼DPRF DG_GÁ¶1_aH9y HÂJ~DPMNF DGIRH.J~BIRH¼D µH¼MNH.J~IK[bÃN[bSBDPO,JR[bS1H.SBDY<K zQ²,BD¢KD¢IRDP:DPIRDÚ
!,j±PÃG[bMNHDGKF}P_G[xD,BÁxMN[x_aHTyTH:I~HY¸GªYQ¬SBDMµHYK~HTyTQ¬¯YDPJRQpIzSBHYÅ:QpIR¸GHYnSBD_GQpIKF}QTyBQv¯pDPJRQpInS1Hv¯pDGxQ9_P[bS1H.SBD
SBDdSB[¶:B~ª.QBy HNDPO,J~HYbFT[\HvDGJL«.JR[b_aH9y QJ~DPIRMQNSBDFBIKQ9SBT¸aªYQNMNQpbHYIÅDdHMNHYRRHNMQp\H.IÅ~ªYQNS1HYSBQYzF QpI 2 y
Y y W y M y < D = y}IKDGKF}DP_PJ~[¶¯.HYMNDPOJ~DYn DGKJ~HYEDP,1HY¸GÄDGEVOBDP_GDPR~«.IR[bQHY_GIKDGR_PDGOJLH.IiBMNHNDG,1H.¸aªYQ
SBDDGKJ~HYSBQ :
K
2 = - B6 HY,B[0DGR_PIR[¶JLHvF1HYIRH¬TMµHvM[bKJRBI~HSTDXpHYRDPzF DGI:DG[xJRQpGyTBMµHvDPBHY¸aªYQ¬J~DPIRMQ9ST[bO1`YM[b_GHVF1H.I~Hv_aHYSBHBMNH
S1HY8DPRF G_G[xDG
,BÁbM[b_GHY
M
b
9
G 6
,
K- 9
b
QpOBSBD b HvDGOJLHYxFB[\HSTDi:QpIRMNHY¸aª.QvD G , ©Q¬_aH.bQpIÅDPRF DG_PÁx1_PQµHFBIKDGK~ªYQ_GQpOTKJLH.O,JRDYy DiJLH.M|}PMÀBMNH
IRDGbHY¸aª.Q_PQpOBJ~[xJRTJ~[¶¯.HF1HYI~HvQ¬J~DPOBRQpInSBD©JRDGOBKÄ9DPn¯[xR_GQY~HY
<
>
/
C
>
9
C
1F HYI~H>BM ×1B[bSTQ¿zD6JRQpOB[bHYOBQ>_GQYM ¯[bR_PQpR[xS1HYSBD³STD²¯YQpbTMND¼O,BbH4D²QpOBSBD ²H4¯[bR_PQpR[xS1HYSBD.
¯pDGxQ9_P[bS1H.SBDSBDSB[x:BRªYQvS1HE!,j±PÃG[xMµHDPRF G_G[xD_GHYb_PB\H.S1HIRDPRQp¶¯pDGOTSBQ.j±KDVQ¬K[bKJRDGMNH
h
9
]
I
- e I
>
R
6
2 W
/
/
C
6
2 R
2 /
>
9
C ]
K
e
K
6
I
6
R
!
QpOBSBD «µ:I~H.¸aªYQ¢MQp\H.IGy ¦vQ¢_PQ9D1_G[xDGOJ~DvSBD¬SB[¶:B~ª.Q|B[bOB«YIR[xQD 6 Q»_PQ9D1_G[xDGOJ~DvSTDvSB[x:BRªYQ
J~GIKMN[x_aHT ¨ J~DGIK_GDP[bIRQ6JRDGIRMQnÚ6SB[bIKDG[¶JLHSBDPKJ~H
DPBHY¸aªYQTy.,BDgD¹9FBIK[bMDÍQ6J~IRHYOB RF QpIJ~DWS1HY0DPRFG[bDP0TÁbM[b_aH.
RQp|HHY¸aª.Q©SBQXpI~HYST[bDGOJRDÅSBDÅJ~DPMNF DGIRH.J~TI~HTyp6_PQpOBZBDP_G[xSBQ_GQpMQ©DP:DP[xJ~QQpIRDJaÔ |BHYIRQSB[x:T~ªYQBy.RDPXpBOBSBQ
J~DGIKMNQEÚ
ST[bIRDP[xJ~HTy;IRDGFTIRDGKDGOJLHiQ
J~IRHYOBRF QpIJ~DkS1HY%DGRF G_P[bDPÍ,BÁbM[b_GHY*RQp|dDP:DG[¶J~Q
SBQEXYI~HYSB[xDGOJ~DkSBDkFBIRDPRRªYQB
EM| QpnDGJ~DGnJ~DPIRMQpnHYXpDPM®SBD©:QpIKMµHSB[¶:DGIKDGOB_P[\HYS1HKQp|»DGRF G_P[bDPzSBDMNHYRRHYnMNQY\HYIKDGÅSB[¶:DGIKDGOJ~DPG
e%QpI61M^yTQ¬×B9¹9QNSBD_GHYbQpI <DPR_GIKDP¯YDj±KD
/
6
9
- 2 M
W
9
B6
Q
]
6
= e
>
/
C
9
QpOBSBD ¿iQ×B9¹9QvSBD©_aHYxQpI#JRI~HYOTRM[xJ~[xSBQF}QpII~HYSB[bHY¸aª.QdD Hd_GQpOTSBTJ~[¶¯[bS1HYSTDEJ~PIRM[b_aHVS1HdM[bKJRBI~H9
ÏbDP[}SBD QpTIRIR[xDGIkS1Hd_PQpOBSBB¸GªYQ¬SBDi_GHYbQpIkiQvFBIK[bMDG[xIRQJ~DGIKMNQÚdSB[bIKDG[¶JLHTyRDPXpB[bSTQF}DPbQdJRI~HYOTRF QpIKJRDiSBD
_aHYxQpInSBDP¯[bSTQÚ¬SB[x:BRªYQSBDVMNHYK~HT ¨ D:DG[¶J~QNCET:QpBInJ~DPIR_PDG[bIKQJRDGIKMNQNÚNSB[xIRDP[xJLHvSBDPKJ~HN[bXY1HYbSBHYSBDYyTVQ
J~I~H.OBRF QpIKJRDSBD_aHYxQpI6RQp|D:DG[xJRQ¬S1HST[x:BRªYQJ~PIRM[b_aHvSB[¶:DGIKDGOB_P[\HYS1HSBHYnDGRF G_P[bDPz,BÁxMN[x_aHYP