>hfZrgyy jZ[hlZ ihobfbb aZ deZkk j_r_gb_aZ^Zqbamq_[gbdZ ©ObfbydeZkkª EK=ma_c<<KhjhdbgJIKmjh\p_\Z F©>jhnZª]
mq_[ghijZdlbq_kdh_ ihkh[b_
KH>?J@:GB? =E:<:
=E:<: AZ^Zqbd AZ^Zqbd AZ^Zqbd AZ^Zqbd AZ^Zqbd =E:<: AZ^Zqbd AZ^Zqbd AZ^Zqbd AZ^Zqbd AZ^Zqbd AZ^Zqbd AZ^Zqbd AZ^Zqb d
=E:<: AZ^Zqbd AZ^Zqbd AZ^Zqbd AZ^Zqbd =E:<: AZ^Zqbd AZ^Zqbd AZ^Zqbd AZ^Zqbd AZ^Zqbd AZ^Zqbd AZ^Zqbd AZ^Zqbd AZ^Zqbd AZ^Zqbd AZ^Zqbd AZ^Zqbd
=E:<: AZ^Zqbd AZ^Zqbd AZ^Zqbd AZ^Zqbd AZ^Zqbd AZ^Zqbd AZ^Zqbd AZ^Zqbd AZ^Zqbd AZ^Zqbd AZ^Zqbd =E:<: AZ^Zqbd AZ^Zqbd AZ^Zqbd AZ^Zqbd AZ^Zqbd AZ^Zqbd AZ^Zqbd AZ^Zqbd
IJ:DLBQ?KDB?A:GYLBY IjZdlbq_kdh_aZgylb_ J_r_gb_wdki_jbf_glZevguo aZ^Zqihl_f_ ©J_Zdpbb\ jZkl\hjZowe_dljheblh\ª IjZdlbq_kdh_aZgylb_ Bamq_gb_\ebygbymkeh\bc gZkdhjhklvobfbq_kdboj_Zdpbc IjZdlbq_kdh_aZgylb_ Ihemq_gb_ZffbZdZb bamq_gb__]hk\hckl\ HagZdhfe_gb_khk\hckl\Zfb \h^gh]hjZkl\hjZZffbZdZ IjZdlbq_kdh_aZgylb_ JZkihagZ\Zgb_fbg_jZevguom^h[j_gbc IjZdlbq_kdh_aZgylb_ Ihemq_gb_ KH b bamq_gb__]hk\hckl\JZkihagZ\Zgb_dZj[hgZlh\ IjZdlbq_kdh_aZgylb_ J_r_gb_ wdki_jbf_glZevgucaZ^Zqihl_f_ ©:ahlb nhknhjª IjZdlbq_kdh_aZgylb_ DZq_kl\_ggh_hij_^_e_gb_ m]e_jh^Z b\h^hjh^Z\ hj]Zgbq_kdbo\_s_kl\Zo IjZdlbq_kdh_aZgylb_ Ihemq_gb_wlbe_gZb bamq_gb__]hk\hckl\
IjZdlbq_kdh_aZgylb_ Bamq_gb_k\hckl\ )Hb _]hkh_^bg_gbc IjZdlbq_kdh_aZgylb_ J_r_gb_wdki_jbf_glZevguoaZ^Zq ihjZa^_em©F_lZeeuª
E:;HJ:LHJGU?HIULU Hiul Bkke_^h\Zgb_\_s_kl\ gZwe_dljbq_kdmxijh\h^bfhklv Hiul Bamq_gb_^\b`_gbybhgh\ \we_dljbq_kdhfihe_ Hiul Ijh\_^_gb_j_Zdpbb h[f_gZ \jZkl\hjZowe_dljheblh\ Hiul HagZdhfe_gb_ kh[jZapZfb k_ju b__ ijbjh^gufbkh_^bg_gbyfb Hiul JZkihagZ\Zgb_kmevnZlh\ Hiul
=E:<: >hfZ gZdmog_fufh`_fgZ[ex^ZlvlZdgZau\Z_fh_]Zr_gb_ kh^umdkmkghcdbkehlhc MjZ\g_gb_ j_Zdpbb 1D+&2 &+&22+ &+&221D&2n +2 beb]hj_gb_ijbjh^gh]h]ZaZ MjZ\g_gb_j_Zdpbb&+ 2 &2 +2
B F_g^_e__\ZGZ^Zggucfhf_gl _keb ihkfhlj_lvnZjaZpmq_[gbdZ hldjulhobfbq_kdbowe_f_glh\ Qbkehobfbq_kdbo\_s_kl\bkqbkey_lkyfbeebhgZfb
Qbkehobfbq_kdboj_Zdpbchq_gv\_ebdhb bolhqgh_dhebq_ kl\hgZa\Zlvljm^gh
Ijbf_jhf hq_gv f_^e_gghc obfbq_kdhc j_Zdpbb fh`_l kem `blvdhjjhaby`_e_aZ )H2 +2 )H2 +2
Ijbf_jhfhq_gv[ukljhcobfbq_kdhcj_Zdpbbfh`_lkem`blv j_Zdpby f_`^m \h^hjh^hf b dbkehjh^hf dhlhjZy khijh\h`^Z_lky kbeh\uf\aju\hfb \u^_e_gb_f[hevrh]hdhebq_kl\Zl_ieZ G H GH Ijbf_jhf obfbq_kdhc j_Zdpbb kdhjhklv dhlhjhc fh`gh [u eh[uwdki_jbf_glZevghbaf_jblvy\ey_lkyj_Zdpbykheyghcdbkeh luk dZj[hgZlhfgZljby 1D&2 +&O 1D&O+2 &2n < oh^_j_Zdpbb\u^_ey_lkym]e_dbkeuc]Zadhlhjucfuijhimk dZ_fq_j_ajZkl\hj]b^jhdkb^ZdZevpby &D2+ &2 &D&2p +2 Ih dhebq_kl\m \uiZ\r_]h hkZ^dZ KZKH fh`gh hp_gblv kdh jhklvj_Zdpbb ?keb `_ m]e_dbkeh]h ]ZaZ [m^_l hq_gv fgh]hlhj_Zdpbyihc^_l ^Zevr_ KZKH KH GH KZGKH
Fu [m^_f gZ[ex^Zlv jZkl\hj_gb_ bkq_agh\_gb_ hkZ^dZ dZj[h gZlZdZevpbyqlhlZd`_fh`gh[m^_lhibkZlvfZl_fZlbq_kdbb hp_ gblvkdhjhklvobfbq_kdhcj_Zdpbb Wdahl_jfbq_kdb_j_Zdpbb² j_Zdpbbdhlhju_b^mlk \u^_e_ gb_fl_ieZ Z =hj_gb_]ZaZKG H KHn GH [ =hj_gb_m]e_jh^ZK H KHn
Wg^hl_jfbq_kdb_ j_Zdpbb ² j_Zdpbb dhlhju_ b^ml k ih]eh s_gb_fl_ieZ Yjdbf ijbf_jhf wg^hl_jfbq_kdhc j_Zdpbb fh`_l kem`blv jZa eh`_gb_dZdhcgb[m^vkhebGZijbf_jjZaeh`_gb_]b^jhdZj[hgZlZ gZljby W 1D+&2 1D&2 &2n +2 bebi_jfZg]ZgZlZdZeby W .0Q2 0Q2 .0Q2 2n K ih]ehs_gb_f l_ieZ wg^hl_jfbq_kdb fh]ml jZkl\hjylvky g_ dhlhju_kheb\ \h^_gZijbf_jgbljZldZeby² .12Wlhfh`gh e_]dhh[gZjm`blvldijbjZkl\hj_gbb^Zgghckheb\ \h^_ijh[bj dZklZgh\blkyoheh^ghc AZ]heh\dblZ[ebpu\aylv\ mq_[gbd_kljlZ[e
Obfbq_kdb_ H[jZam H[jZam nhjfmeu Ijhbkoh^blobfbq_kdZy _lky _lky kf_rb\Z_fuo j_ZdpbyihmjZ\g_gbx kf_kv jZkl\hj \_s_kl\ 1D+2 1D+2 1D2++n 6L2+2 ± 1D&O+2 1D&O 1D &O &+2+, &+2++2 &D&2+2 &D&2+&O &D&2 +&O &D&O +2&2n +&O+2 =Q&X =Q+62 =Q+62 =Q62 +n
GH
Z \ G HG
Z \ GHH
0U + 0U + 0U 2
0U 2 0U + 0U 2
|
|
G H GH P+ fhev QG 0U + P 2 fhev QH 0U 2 IhmjZ\g_gbxj_Zdpbb\b^ghqlh^eyj_Zdpbb[ fhevH ihlj_ [m_lkyo fhevG Ld dbkehjh^ gZoh^blky \ g_^hklZld_ lh [m^_f kqblZlv ih db kehjh^m Lh]^ZQG QH fhev\h^hjh^ZmqZ kl\h\Zeh\ j_Zdpbb Ihemqbehkv'G2 Q+ fhev\h^u Lh]^Z\ j_Zdpbhgghfkhkm^_hklZehkv QGH fhev P+2 0U+2 QG2 ] QH P2 QG ± fhev P+ 0U+ QG ] Hl\_lP+2 ]P+ ] Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_
Zlhf + +H /L & 1 2 ) 1H
qbkehwe_dljhgh\
qbkeh\Ze_glguowe_dljhgh\
Zlhf 1D $O 6 &O . &D 5E %U &V ,
qbkehwe_dljhgh\
Hl\_lkfhljbl_\ mq_[gbd_
qbkeh\Ze_glguowe_dljhgh\
Hl\_lkfhljbl_\ mq_[gbd_
< Zlhf_ dZeby bf__lky we_dljhgh\ dhlhju_ aZgbfZxl hj[blZe_c
< Zlhf_ oehjZ bf__lky we_dljhgh\ dhlhju_ aZgbfZxl hj[blZe_c (
(
(
(
S V S V
V
/L
1D
)
&O
=E:<: AZ^Zqbd
Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_
DjbklZeebq_kdZy j_r_ldZ ² wlhi_jbh^bq_kdbih\lhjyxsZy ky\ ijhkljZgkl\_kljmdlmjZ Hl\_lkfhljbl_\ mq_[gbd_
Hl\_lkfhljbl_\ mq_[gbd_
;he__ Zdlb\guf \_s_kl\hf y\ey_lky hahg lZd dZd ijb ^bkkh pbZpbb hg ^Z_l qZklbpm H dhlhjZy y\ey_lky hq_gv kbevguf hdbk ebl_e_f H H H DjbklZeebq_kdb_\_s_kl\Z&X&V&O
&2 1 ² \_s_kl\Z k fhe_dmeyjghcdjbklZeebq_kdhcj_r_l dhc )H6L2 ² \_s_kl\Zk ZlhfghcdjbklZeebq_kdhcj_r_ldhc
1D&O/L+²\_s_kl\Zk bhgghcdjbklZeebq_kdhcj_r_ldhc
AZ^Zqbd
L_fi_jZlmjZ ieZ\e_gby fhe_dmeyjguo \_s_kl\ ih\urZ_lky k jhklhffhe_dmeyjghcfZkku Hl\_lkfhljbl_\ mq_[gbd_
0U+&O 0U+%U 0U+, Ld 0U+&O 0U+%U 0U+, ke_^h\Zl_evgh l_fi_jZlmjZ ieZ\e_gby Lie +&O 7ie +%U 7ie +,
=jZnbdb aZ\bkbfhklb l_fi_jZlmj dbi_gby b ieZ\e_gby m]e_ \h^hjh^h\ hl fhe_dmeyjghc fZkku fh`gh ihkljhblv [he__ lhqgh Bkihevamy ^Zggu_ lZ[ebpu mq_[gbdZ fu ij_^eZ]Z_f ijbf_j guc]jZnbdaZ\bkbfhklb W
±
0U&Q+Q
aZ\bkbfhklvl_fi_jZlmjudbi_gbyhlfhe_dmeyjghcfZkku aZ\bkbfhklvl_fi_jZlmjuieZ\e_gbyhlfhe_dmeyjghcfZkku IjbdhfgZlghcl_fi_jZlmj_ =ZauQ @b^dhklbd Qd L\_j^u_l_eZd Q
KhklZ\iZjZnbgZdhe_[e_lkyhlKG ^hKGke_^h\Zl_ev ghl_fi_jZlmjZieZ\e_gbyhij_^_ey_lky LieKG d LieiZjZnbg d LieKG K d LieiZjZnbg d K Z 0U&2 0U&2 Ld0U&2 !0U&2 ke_^h\Zl_evghKH[m^_ldbi_lvijb[h e__gbadhcl_fi_jZlmj_ [ 0U62 0U62 Ld0U62 !0U62 ke_^h\Zl_evgh6H [m^_ldbi_lvijb[h e__gbadhcl_fi_jZlmj_
AZ^Zqbd
Hl\_lkfhljbl_\ mq_[gbd_
Hl\_lkfhljbl_\ mq_[gbd_
( V S V
V
1D
( S
( S V S
V
V
V
V
&
Hl\_lkfhljbl_\ mq_[gbd_
6L
< Zlhf_ gZljby aZiheg_gguo Zlhfguo hj[blZe_c h^gZ ba dhlhjuo\Ze_glgZyV± \Ze_glgZy < fhe_dme_ 1D aZiheg_gguo fhe_dmeyjguo hj[blZe_c FH P1D f] ] P 1D fhev Q1D 0U 1D 11D 1: Q1D ± Zlhfh\ ld^\ZZlhfZ1Dh[jZamxlFHlh 1 1D 102 Hl\_l102 hj[blZe_c Hl\_lkfhljbl_\ mq_[gbd_
Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_
AZ^Zqbd
>Zgguc bhg fh`_l ©ijblygmlv d k_[_ª kdhevdh m]h^gh bhgh\ ijhlb\hiheh`gh]h agZdZ ]eZ\gh_ qlh[u lZdh_ ijhkljZgkl\_ggh_ iheh`_gb_[uehwg_j]_lbq_kdbb ]_hf_ljbq_kdb\u]h^guf Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_
< maeZodjbklZeebq_kdhcj_r_ldb&XgZoh^ylkyZlhfu&X < maeZo djbklZeebq_kdhc j_r_ldb hdkb^Z m]e_jh^Z gZoh^ylky fhe_dmeuKH < maeZo djbklZeebq_kdhc j_r_ldb ]b^jb^Z eblby gZoh^ylky bh ± gu/L b + Hkgh\Zgby ² wlh\_s_kl\Z^bkkhpbbjmxsb_gZbhguf_lZe ± eZb HG
Kheb ² wlh \_s_kl\Z h[jZah\Zggu_ f_lZeehf b dbkehlguf hklZldhf Hl\_lkfhljbl_\ mq_[gbd_
Kheb y\eyxlky bhggufb kh_^bg_gbyfb ld hgb khklhyl ba iheh`bl_evgh aZjy`_gguo bhgh\ f_lZeeh\ b hljbpZl_evgh aZjy `_gguodbkehlguohklZldh\
&O y\ey_lkydbkehlgufhklZldhfkheyghcdbkehlu+&O ± ) y\ey_lkydbkehlgufhklZldhfnlhjh\h^hjh^ghcieZ\bdh\hc dbkehlu+) ± 62 y\ey_lkydbkehlgufhklZldhfk_jghcdbkehlu+62 ±
Kh_^bg_gb_ 1D+ &D2+ /L1 .2+ 0J2 )H2 )H2+ 1D62 &D62 $O) &D32 0J&2
Hl\_lkfhljbl_\ mq_[gbd_
bhgu ± 1D+ ± &D 2+ ± /L 1 ± .2+ ± 0J 2 )H2± ± )H2+ 1D62± &D62± ± $O) &D32± 0J&2±
AZ^Zqbd
>Zevgbcihjy^hd² mihjy^hq_gghklvkljmdlmjubhggh]hdjb klZeeZih\k_fmdjbklZeem ;eb`gbc ihjy^hd ² mihjy^hq_gghklv kljmdlmju bhggh]h djb klZeeZgZ[ebadbojZkklhygbyob g_mihjy^hq_gghklvgZ^Zevgbo LieGH K LieG ±K Lie: & 0U+ 0U+H
Hl\_lkfhljbl_\ mq_[gbd_
Dhg^_gkbjh\Zggh_ khklhygb_ \_s_kl\Z ² `b^dh_ b l\_j^h_ khklhygb_\_s_kl\Z Kdhjhklv obfbq_kdhcj_Zdpbb² \_ebqbgZoZjZdl_jbamxsZy [ukljhlmijhl_dZgbyobfbq_kdhcj_Zdpbb
Q_f [hevr_ dhgp_gljZpby j_Z]_glh\ l_f [hevr_ kdhjhklv obfbq_kdhcj_Zdpbb
>eylh]hqlh[um\_ebqblvkdhjhklvj_Zdpbbk mqZklb_fl\_j ^uo \_s_kl\ gm`gh m\_ebqblv iehsZ^b ih\_joghkl_c j_Z]bjmx sbo\_s_kl\gZijbf_jjZaf_evqblvbo Obfbq_kdh_ijbf_g_gb_.0Q2 ² fZj]Zgph\dZ, ² bh^ Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_
=E:<: AZ^Zqbd
Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_
DbkehlguchklZlhd² lhqlhhklZ_lkyhldbkehluihke_lh]h dZdhgZijh^bkkhpbbjm_l ± ± +&O + &O &O ² dbkehlguchklZlhd &O V V S V S dhebq_kl\hwe_dljhgh\jZ\ghihwlh fmlZdh_`_we_dljhggh_kljh_gb_bf__lwe_f_glk ihjy^dh\ufgh f_jhf² $UZj]hg ±
Hkgh\ghklvdbkehlu² wlhdhebq_kl\hijhlhgh\G dhlhjh_ ± fh`_l ^Zlv dbkehlZ ijb ^bkkhpbZpbb +&O + &O dhebq_kl\h G ke_^h\Zl_evghdbkehlZy\ey_lkyh^ghhkgh\ghc +62 + 62± ijhlhgZ² dbkehlZ^\mohkgh\gZyb lZd^Ze__ EZfihqdZaZ]hjblky\ jZkl\hj_we_dljheblZlh_klv\ kemqZ_ +62 + 62±
EZfihqdZ g_ aZ]hjblky _keb \_s_kl\h eb[h g_jZkl\hjbfh \ \h^_eb[hg_y\ey_lkywe_dljheblhf < ^ZgghfkemqZ_&DK2 b &X2g_jZkl\hjylky\ \h^_b eZfihqdZ g_aZ]hjblky Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_
EZfihqdZ aZ]hjblky _keb h[jZam_lky jZkl\hj we_dljheblZ Wlhijhbahc^_l\ kemqZ_k 1D2+$J12&D2 &D2+2 &D2+ <_s_kl\Z )H2+ $J&O )H2 g_jZkl\hjbfu \ \h^_ ihwlhfm eZfihqdZg_aZ]hjblky D bhggufkh_^bg_gbyfhlghkylky&D&O1D62.2+
G_we_dljhebluKHKGG Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_
Z
bhgu ± &D12 ± $O &O ± +2+32 ± &U 12 $O62± ± .0Q2
Hl\_lkfhljbl_\ mq_[gbd_ &D&O ² bhgu&D&O ± )H&O ² bhgu)H&O ± .&O² bhgu. &O
\_s_kl\h &D12 $O&O +32 &U12 $O62 .0Q2
±
Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_
AZ^Zqbd
DbkehlZ ijb \aZbfh^_ckl\bb k \h^hc h[jZam_l bhg ]b^jhdkh gbyGH Baf_g_gb_hdjZkdbbg^bdZlhjh\\uau\Zxlh[ZbhgZ Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_
Hkgh\Zgb_ \ \h^_ ^Z_l HG± ihwlhfm ko_fZ hkgh\Zgby kh^_j `blHG±lh_klvlZqlhke_\Z Z IhkqblZ_fdhebq_kl\hbhgh\6U \ e_\hcko_f_² 16U 1HG± 1HG± 16U nhjfmeZ² 6U2+ [ IhkqblZ_fdhebq_kl\hbhgh\6U \ ijZ\hcko_f_² 1 6U 16U 162± 1 62 nhjfmeZ² 6U62 6U2+ 6U HG
±
6U2+ jZkl\hjbf \ \h^_ b _]h jZkl\hj \uau\Z_l baf_g_gb_ hdjZkdbbg^bdZlhjZ6U62 g_jZkl\hjbf\ \h^_ Hl\_lkfhljbl_\ mq_[gbd_
Hl\_lkfhljbl_\ mq_[gbd_
AZ^Zqbd
KeZ[uc we_dljhebl ² \_s_kl\h dhlhjh_ keZ[h^bkkhpbbjm_l gZbhgu
©J_ZdpbhggZy kf_kvª ² kf_kv \_s_kl\ dhlhju_ j_Z]bjmxl f_`^mkh[hc Hl\_lkfhljbl_\ mq_[gbd_
©DhgklZglZ ^bkkhpbZpbbª ² wlh dhgklZglZ jZ\gh\_kby aZib kZggZy^eyj_Zdpbb^bkkhpbZpbb Hl\_lkfhljbl_\ mq_[gbd_
< dgb]_kdZaZghqlh >HG @ ± fheve\ fe ± ± ± ± QHG K 9 fheve fhev Z \k_]hbhgh\[m^_l 1HG± 1: QHG± ± ±
?keb d jZkl\hjm 1D+6 1D +6 ^h[Z\blv +&Olhihqm\kl \m_lkyaZiZolmoeuoybp² h[jZam_lky+6 ± +6 + +6n ±
Hl\_lkfhljbl_\ mq_[gbd_
> @>
@
+6+2 +6± +2 +6 + 2 . ihkdhevdm\h^uhq_gvfgh]hlh__ dhgp_gljZ >+ 6@ >+ 2@
pbyihklhyggZb.
>+6 @ >+ 2 @
AZ^Zqbd
>+ 6@
Fgh]hhkgh\gZy dbkehlZ ²wlhdbkehlZdhlhjZyijbjZkl\hj_ gbb \\h^_^Z_l[hevr_h^gh]hijhlhgZfhe_dmeZdbkehlu +62 + 62 +32 + 32± )H2+ )H2+ 2+ )H2+ )H 2+± ± +6 +6 + ± +6 + 6± ± +6L2 +6L2 + ± ± +6L2 6L2 + ± $O2+ $O2+ 2+ ± $O2+ $O2+ 2+ ± $O2+ $O 2+
±
Hl\_lkfhljbl_\ mq_[gbd_
± ± ., >+6 @>+@>+6@.,, >+@>6±@>+6 @ ., >)H2+ @>+ @>)H2+ @.,, >)H @>2+±@>)H2+ @ ., >+6L2±@>+@>+6L2±@.,, >+@>6L2±@>+6L2±@ ., >$O2+ @>2+±@>$O2+ @.,, >$O2+ @>2+±@>$O2+ @
Kbem we_dljheblZ fh`gh hij_^_eblv ih dhgklZgl_ ^bkkhpbZ pbbQ_f[hevr_dhgklZglZ^bkkhpbZpbbl_fkbevg__we_dljhebl
Hl\_lkfhljbl_\ mq_[gbd_
we_dljhebl &D2+ +62 .+62 1D62 +&O
bhgu >&D@>2+±@ >+@!>62±@ >.@>+@ >62±@ >1D@!>62±@ >+@ >&O±@
>ey\k_olj_odbkehlih^oh^blaZibkv +Q5 Q+ 5Q± +12 + 12±Q +6 + 6±Q +32 + 32±Q Hl\_lkfhljbl_\ mq_[gbd_
DZlbhguZgbhgu 1D
AZ^Zqbd
&O± 1D&O
62± 1D62
&2± 1D&2
Hl\_lkfhljbl_\ mq_[gbd_
FZehjZkl\hjbfu_ \_s_kl\Z ² \_s_kl\Z iehoh jZkl\hjbfu_ \ \h^_GZijbf_jKZKH$J&O < mjZ\g_gbyo we_dljheblbq_kdhc ^bkkhpbZpbb 1D2+ 1D&O &D&O&D2+ +&ObkihevamxlagZd© ªihlhfmqlhwlb\_s_kl\Z kbevgu_we_dljheblub j_Zdpby^bkkhpbZpbbg_h[jZlbfZ
G_ ke_^m_l ijbgbfZlv \h \gbfZgb_ \hafh`ghklb \aZbfh^_c kl\by h^ghbf_gguo bhgh\ \ jZkl\hjZo we_dljheblh\ ihlhfm qlh hgbhllZedb\Zxlky hl ± hl± Ihegh_ bhggh_ mjZ\g_gb_ j_Zdpbb ² mjZ\g_gb_ \ dhlhjhf mdZaZgu\k_bhgukhklZ\eyxsb_\_s_kl\Zdhlhju_j_Z]bjmxl KhdjZs_ggh_bhggh_mjZ\g_gb_j_Zdpbb² mjZ\g_gb_\ dhlh jhfg_mdZaZgubhgug_ijbgbfZ\rb_mqZklby\ j_Zdpbb
<_s_kl\Z kh^_j`Zsb_ dZj[hgZl bhgu 1D&2 0J&2 &D&2 Hl\_lkfhljbl_\ mq_[gbd_
Kmsghklv j_Zdpbb g_cljZebaZpbb khklhbl \ lhf qlh h[jZam _lkykeZ[h^bkkhpbbjmxs__\_s_kl\h\h^Z G HG± GH %D&O +62 %D62p +&O %D &O± + 62± %D62p + &O± %D 62± %D62p 1D&O$J&Oz j_Zdpbyg_b^_l .62 %D12 .12 %D62p . 62± %D 12± . 12± %D62p %D 62± %D62p )H62 1D2+ )H2+ p 1D62 )H 62± 1D 2+± )H2+ p1D 62± )H 2+± )H2+ p +&O$J12 $J&Op +12 + &O± $J 12± $J&Op + 12± $J &O± $J&Op .&2 &D&O &D&2p .&O . &2± &D &O± &D&2p . &O± &D &2± &D&2p &D2+ )H&O &D&O )H2+ p &D 2+± )H &O± )H2+ p &D &O± )H 2+± )H2+ p 1D&O.62 z j_Zdpbyg_b^_l .&2 +62 .62 &2n +2 . &2± + 62± . 62± &2 +2 + &2± +2&2n
1D&O+62 1D &O± + 62± 1D &O± + 62±
< jZa[Z\e_gguo jZkl\hjZo +&O g_ me_lZ_l Z \ dhgp_gljbjh \Zgguo\ul_kgy_lkyk_jghcdbkehlhc
< j_Zdpbb&D&2 +&O &D&O &2n +2g_jZkl\hjb fh_\_s_kl\h² KZKH]Za² KHKeZ[ucwe_dljhebl² GHJ_ Zdpby g_h[jZlbfZ lZd dZd h[jZamxlky ]Za b keZ[uc we_dljhebl Ba kn_juj_Zdpbbm^Zey_lky]ZaKH L J_Zdpby bhggh]h h[f_gZ ijhl_dZ_l ^h dhgpZ \ j_amevlZl_ h[jZah\Zgby ]ZaZ ijb keb\Zgbb jZkl\hjh\ dZj[hgZlZ gZljby b k_j ghcdbkehlu
L J_Zdpbybhggh]hh[f_gZb^_l^hdhgpZf_`^m]b^jhdkb^hf f_^b,, b kheyghcdbkehlhc L Hl\_lkfhljbl_\ mq_[gbd_
Ijb\_^_ggu_\ wlhfiZjZ]jZn_j_Zdpbbhlghkylkyd lbimj_ Zdpbch[f_gZ +62 1D2+ 1D62 +2 +&O&D2+ &D&O +2
L KhdjZs_ggh_ bhggh_ mjZ\g_gb_ j_Zdpbb khhl\_lkl\m_l \aZbfh^_ckl\bxjZkl\hjh\gbljZlZk_j_[jZb oehjb^ZgZljby LHl\_lkfhljbl_\ mq_[gbd_ $J &O± $J&Op )H 2+± )H2+ p
H^gh\j_f_ggh \ \h^ghf jZkl\hj_ fh]ml gZoh^blvky bhgu &D1D12±&O± Hl\_lkfhljbl_\ mq_[gbd_
AZ^Zqbd
DbkehlZ ² kh_^bg_gb_ ^bkkhpbbjmxs__ k h[jZah\Zgb_f G GH HljbpZl_evgh aZjy`_gguc bhg h[jZamxsbcky ijb ^bkkhpbZ pbb dbkehlugZau\Z_lkydbkehlgufhklZldhf
?keb dbkehlZ ^bkkhpbbjm_l g_h[jZlbfh ² hgZ kbevgZy _keb h[jZlbfh² keZ[Zy
Jy^ gZijy`_gbc f_lZeeh\ ² jy^ oZjZdl_jbamxsbc kbem k dhlhjhcf_lZee\ul_kgy_lG ba\h^uIhkljh_gihijbgpbimkijZ \ZgZe_\hihf_j_m[u\Zgbykbeu\ul_kg_gbyG kihkh[ghklb\hk klZgZ\eb\ZlvG &X2+ 62± &X 62± +2 )H2+ + &O± )H &O± +2 %D &O± + 62± %D62p + &O± &D &O± 1D &2± &D&2p 1D &O± &D &O± . &2± &D&2p . &O± + 62± &D32 +32 &D62 + 1D &O± 62± +&On 1D 62± $J 12± 1D &O± $J&Op 1D 12±
DZq_kl\_ggZy j_Zdpby oZjZdl_jgZy ^ey ^Zggh]h kh_^bg_gby ih g_c fh`gh hij_^_eblv _klv eb ^Zggh_ kh_^bg_gb_ \ jZkl\hj_ bebg_l KbevgZy dbkehlZ \ul_kgy_l keZ[mx ba __ kheb ihlhfm qlh \ j_amevlZl_h[jZam_lkykeZ[ucwe_dljheblkeZ[ZydbkehlZ + 12± )H2 )H 12± +2 MjZ\g_gb_j_Zdpbb+ 2+± +2 KmffZdhwnnbpb_glh\jZ\gZ [
DbkehlZhkgh\ghchdkb^ \h^Zkhev &X2+62 &X62 +2 )H2 +12 )H12 +2 .2+32 .32 +2
AZ^Zqbd
Hkgh\Zgby ² \_s_kl\Z dhlhju_ ijb jZkl\hj_gbb h[jZamxl bhg HG± b iheh`bl_evgh aZjy`_ggu_ bhgu f_lZeeZ beb bhgu Zf fhgby1+
S_ehqb ² hkgh\Zgby jZkl\hjbfu_ \ \h^_ Ijbf_j .2+ 5E2+&V2+
>bkkhpbZpby]b^jhdkb^ZZffhgbyh[jZlbfZ 1+ +2 1+ 2+±
Ihemq_gb_dZmklbq_kdhckh^u &D2+ 1D&2 &D&2p 1D2+ &D &2± &D&2p
7 S_ehqbg_j_Z]bjmxlk hkgh\gufbhdkb^Zfb\ Z 1D 2+± 62 1D 62± +2 62 2+± +262± [ %D 2+± 12 %D 12± +2 12 2+± 12± +2 \ )H &O± 2+± . )H2+ p . &O± )H 2+± )H2+ p
AZ^Zqbd
Kheb ² \_s_kl\Z ijb jZkl\hj_gbb \ \h^_ ^Zxsb_ iheh`b l_evgh aZjy`_ggu_ bhgu f_lZeeZ beb Zffhgby 1+ b hljbpZ l_evghaZjy`_ggu_ bhgudbkehlguohklZldh\ %D &O± . 62± %D62p . &O± %D 62± %D62p [ 62± %D %D62p \ )H &2± )H&2p
7 Ih\Zj_ggZykhev\ \h^ghfjZkl\hj_j_Z]bjm_lk $J12 \
L Hl\_lkf\ mq_[gbd_
=E:<: AZ^Zqbd Z
1D
0J
V
V
S
V
V
V
S
V
V
S
GZ \g_rg_f we_dljhgghf keh_ ZlhfZ 1D gZoh^blky h^bg we_d ljhg Z m ZlhfZ 0J ² ^\Z ke_^h\Zl_evgh hl ZlhfZ 1D e_]q_ hlh j\Zlvwe_dljhgq_fhlZlhfZ0J [ 3
6
V V
V
S
V V
S S
DZd \b^gh ba jbk hl ZlhfZ nhknhjZ e_]q_ hlhj\Zlv we_d ljhgq_fhlZlhfZk_ju Hl\_lkfhljbl_\ mq_[gbd_
J_Zdpby^_fhgkljbjmxsZy\ukhdmxZdlb\ghklv1D 1D&O 1D&O
J_Zdpby^_fhgkljbjmxsZy\ukhdmxg_f_lZeebq_kdmxZdlb\ ghklvoehjZ W &O )H )H&O Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_
/L) ² bhggh_ kh_^bg_gb_ h[jZah\Zggh_ we_f_glZfb \lhjh]h i_jbh^Z
51D ! 50J ld m 0J [hevr_ aZjy^ y^jZ b [hevr_ qbkeh we_dljhgh\ ihwlhfm kbeZ \aZbfh^_ckl\by we_dljhgghc h[hehqdb k y^jhf[hevr_ke_^h\Zl_evghjZ^bmkf_gvr_ 53 !5&O ² ZgZeh]bqgh < ]jmiiZojZ^bmkZlhfh\m\_ebqb\Z_lkyk\_jom\gbaihwlhfm 5/L 51D 5) 5&O
AZ^Zqbd
Hl\_lkfhljbl_\ mq_[gbd_ 1D 0J $O 6L 3 6 &O $U /L %H % & 1 2 ) 1H
>V V S@ >V V S@ >V V S@ >V V S@ >V V S@ >V V S@ >V V S@ >V V S@
V V V S V S V S V S V S V S
>V@ >V@ >V@ >V@ >V@ >V@ >V@ >V@
V V V S V S V S V S V S V S
/L % % & 1 2 )
1H
We_dljhgu\g_rg_]hmjh\gy\ ZlhfZo6L36&O$UgZoh^ylky gZj :H
< k\hbokh_^bg_gbyowe_f_glu/Lb Dijhy\eyxl\Ze_glghklv ,Z KZb
Bg_jlghklv we_f_glh\ 9,,, ]jmiiu aZdexqZ_lky \ aZ\_jr_g ghklbwe_dljhgghch[hehqdb
we_f_gl 6 3 6L 1 &O
\ukrZy\Ze_glghklv 0J+
gbarZy\Ze_glghklv
0J [+ [ +
+) + [ ) \Ze_glghklv + ² , ) ² , +2 + [ 2 [ + \Ze_glghklv + ² , 2 ² ,, 1+ + [ 1 [ + \Ze_glghklv + ² , 1 ² ,,, [ +
3+
&+
+ [ 3 [ + \Ze_glghklv + ² , 3 ² ,,, [ +
+ [ + [ & [ + \Ze_glghklv + ² , & ² ,9 [ +
Hl\_lkfhljbl_\ mq_[gbd_
6&O
[[ [ [ &O [ [[
[[ 6 [ &O [[ [[
AZ^Zqbd
Hl\_lkfhljbl_\ mq_[gbd_
Dhhi_jZpbyhagZqZ_lh[t_^bg_gb_q_]heb[h
Dh\Ze_glgZy k\yav ² k\yav dhlhjZy h[jZam_lkyf_`^mZlhfZ fb g_f_lZeeh\ ijb g_ hq_gv kbevgh kf_s_gghc we_dljhgghc iehl ghklbf_`^mZlhfZfb Hl\_l kfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_
3&O ² dh\Ze_glgZy&D6² bhggZy1D3² bhggZy62 ² dh\Ze_glgZy,KO² dh\Ze_glgZy+6² dh\Ze_glgZy 3&O± 1D3± &D6± 62± ,&O± +6± Hl\_lkfhljbl_\ mq_[gbd_
Z 1D&O±0J&O±$O&O± [ 1D6±0J3±$O6L± Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_
AZ^Zqbd
Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_
2+ 2 [ +
2+± 2 [ +
S_ehqb² hkgh\ZgbyjZkl\hjbfu_\ \h^_
Kgb`_gb_hljbpZl_evgh]haZjy^ZgZdbkehjh^_\ ]b^jhdkb^Zo ijb\h^bld h[e_]q_gbxhls_ie_gbybhgZ\h^hjh^Zihlhfmqlhq_f f_gvr_ hljbpZl_evgh]h aZjy^Z gZ dbkehjh^_ l_f f_gvr_ ijbly`_ gb_f_`^mgbfb ijhlhghfG ² iheh`bl_evgufaZjy^hf :fnheblZfb gZau\Zxlky we_dljheblu dhlhju_ fh]ml [ulv b dbkehlhcb hkgh\Zgb_f Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_ \mq_[gbd_
K_jgZy dbkehlZ+62 + 62± OehjgZy dbkehlZ+&O2 + &O2
>bkkhpbZpbyk_jghcdbkehluijhbkoh^bl\ f_gvr_ckl_i_gb ih\lhjhcklmi_gb Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_
Hl\_lkfhljbl_\ mq_[gbd_
>eyZffbZdZ1+ +2 1+2+ Ijbf_gyxlnhjfmeuhlebqZxsb_kygZh^gmfhe_dmem\h^u
J_Zdpbb ]b^jhdkb^Z Zexfbgby k dbkehlZfb b s_ehqZfb g_ h[jZlbfu ihlhfm qlh h[jZamxlky bhgu Z fhe_dmeu hlkmlkl\mxl g_h[jZlbfZyj_Zdpby
Hl\_lkfhljbl_\ mq_[gbd_ Hdkb^ 1D2 0J2 $O2 6L2 3 2 62 &O2
N_ghenlZe_bg Jhah\uc Jhah\uc Jhah\uc ;_kp\_lguc ;_kp\_lguc ;_kp\_lguc ;_kp\_lguc
EZdfmk Kbgbc Kbgbc Kbgbc DjZkguc DjZkguc DjZkguc DjZkguc
=b^jhdkb^ N_ghenlZe_bg G H 1D2+ Jhah\uc 0J2+ Jhah\uc $O2+ Jhah\uc +6L2 ;_kp\_lguc +32 ;_kp\_lguc +62 ;_kp\_lguc +&O2 ;_kp\_lguc
F_lbehjZgl DjZkguc DjZkguc DjZkguc @_eluc @_eluc @_eluc @_eluc
EZdfmk
Kbgbc Kbgbc Kbgbc DjZkguc DjZkguc DjZkguc DjZkguc
1D2 0J2 $O2 6L2
3 2
F_lbeZfbg DjZkguc DjZkguc DjZkguc @_eluc @_eluc @_eluc @_eluc 62
&O2
1D2+ 0J2+ $O2+ +6L2 +32 +62 +&O2
=E:<: AZ^Zqbd
Hl\_lkfhljbl_\ mq_[gbd_
L We_dljhggh_ kljh_gb_ \g_rg_]h wg_j]_lbq_kdh]h mjh\gy ZlhfZ6 6>1H@V S VS D < kh_^bg_gbyo k dbkehjh^hf k_jZ ijhy\ey_l iheh`bl_evgu_ kl_i_gb hdbke_gby lZd dZd m dbkehjh^Z [hevrZy we_dljhhljbpZ l_evghklv Hl\_lkfhljbl_\ mq_[gbd_
Hdkb^k_ju9, ² 62 62 +2 +62
< [ulmbkihevamxlkyebfhggZymdkmkgZydbkehlZGZ\dmk\k_ ijh[h\Zeb Zkdhj[bgh\mx dbkehlm Ijbjh^gu_ dbkehlu fmjZ\vb gZykheygZymdkmkgZyb l^ Ihemq_gb_k_jh\h^hjh^Z\ eZ[hjZlhjbb )H6+62 )H62 +6n Hl\_lkfhljbl_ \ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_
LHl\_lkfhljbl_\ mq_[gbd_ LHl\_lkfhljbl_\ mq_[gbd_ LHl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_
L Hl\_lkfhljbl_\ mq_[gbd_ L Hl\_lkfhljbl_\ mq_[gbd_
Hl\_lkfhljbl_\ mq_[gbd_
+62 6+2 +6² \hkklZgh\bl_evH ² hdbkebl_ev
L +62 0+62 u ]fhev ]fhev 0U 6 Z+626 0U + 62 Hl\_l[
Ijbf_jkbgl_aZffbZdZ² 1 + l 1+ Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_
AZ^Zqbd
J_Zdpbykh_^bg_gby 62 2 o 62 J_ZdpbyjZaeh`_gby 62 o62 2
Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_
+ 2 l +24 1 2 l 124 Z ^eyi_j\hcb \lhjhcj_ZdpbcjZ\gh\_kbykf_klylky\ijZ\hld j_Zdpbykhijh\h`^Z_lkymf_gvr_gb_fh[t_fZ [ ^eyh[_boj_Zdpbc\e_\hldwlhj_Zdpbbwdahl_jfbq_kdb_b jZ\gh\_kb_kf_sZ_lky\ klhjhgmwg^hl_jfbq_kdhcj_Zdpbb Hl\_lkfhljbl_\ mq_[gbd_
6b )H6 62 62 4 )H6 2 )H2 62n 4 Ijbk`b]ZgbbfhevibjblZh[jZamxlkyfhev62 b fhev )H2ihwlhfm4 !4 Hl\_lkfhljbl_\ mq_[gbd_
L_fi_jZlmjZ ijb dhlhjhc hdbke_gb_ 62 \ 62 [m^_l b^lb k \uoh^hfijh^mdlZih]jZnbdmW| & Hl\_lkfhljbl_\ mq_[gbd_
Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_
AZ^Zqbd
DZlZeblbq_kdbc ijhp_kk ² kihkh[ ijh\_^_gby j_Zdpbb h[ e_]qZxsbc b mkdhjyxsbc __ ijhl_dZgb_ \ j_amevlZl_ h[jZah\Zgby ijhf_`mlhqguoijh^mdlh\ DZlZeba ² baf_g_gb_ kdhjhklb beb \ha[m`^_gb_ obfbq_kdhc j_Zdpbb dZlZebaZlhjZfb dhlhju_ mqZkl\mxl \ ijhf_`mlhqguoklZ ^byoj_Zdpbbghg_\oh^yl\ khklZ\dhg_qguoijh^mdlh\ 12 b 62 >bhdkb^u² kh_^bg_gby\ dhlhjuogZh^bgZlhfwe_f_glZijb oh^blky ^\ZZlhfZdbkehjh^Z M]e_dbkeuc]Za² &2>Zwlh^bhdkb^ Hl\_lkfhljbl_\ mq_[gbd_
< j_Zdpbb12 62 1H 62n 12 ² hdbkebl_ev\hkklZgZ\eb\Z_lky 62 ² \hkklZgh\bl_evhdbkey_lky
AZ^Zqbd
Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_
MjZ\g_gb_ j_Zdpbb ih dhlhjhcfh`ghm^ZeblvhdZebgmk ih \_joghklbf_lZeeZ )H2 +62 )H62 +2
Ijb ijb]hlh\e_gbbjZkl\hjZnhknhjghcdbkehlug_h[oh^bfh eblv dbkehlm \ \h^m ld iehlghklv dbkehlu [hevr_ iehlghklb \h ^uijbh[jZlghfijbeb\Zgbbfh`_lijhbahclbjZa[jua]b\Zgb_db kehluqlh\ k\hxhq_j_^vijb\_^_ld obfbq_kdhfmh`h]m
Ijb ijb]hlh\e_gbb jZkl\hjZ ]b^jhdkb^Z gZljby g_h[oh^bfh eblvs_ehqv\ \h^mldiehlghklvs_ehqb[hevr_iehlghklb\h^u ijb h[jZlghf ijbeb\Zgbb fh`_l ijhbahclb jZa[jua]b\Zgb_ s_eh qbqlhijb\_^_ld obfbq_kdhfmh`h]m =b^jZlu² kh_^bg_gbykh^_j`Zsb_\h^m 1+ +2)H2 Q+2
DjbklZeeh]b^jZlu ² djbklZeebq_kdb_ ]b^jZlu hij_^_e_ggh ]hkhklZ\ZgZijbf_j1D&2 +2 Hl\_lkfhljbl_\ mq_[gbd_
Dhgp_gljbjh\ZggZy k_jgZy dbkehlZ emqr_ ih]ehsZ_l \h^m ihwlhfmbf_ggh__ bkihevamxl^eyhkmrdb]Zah\ Hl\_lkfhljbl_ \ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_
@_e_agucdmihjhk)H62 +2 Pbgdh\ucdmihjhk² =Q62 +2 + 2+± +2 &D2+ +62 &D62 +2 %D 62± %D62p
K_jgZy dbkehlZ ijhy\ey_l h[sb_ k\hckl\Z dbkehl \ i_j\hc j_Zd pbb
K_jgZydbkehlZj_Z]bjm_lk kheyfb^jm]bodbkehl_kebijh bkoh^bl m^Ze_gb_ dZdh]heb[h \_s_kl\Z < gZr_f kemqZ_ wlh khev Ihwlhfm wlh fh]ml [ulv kheb %D&D3E$JfZehb iehohjZkl\h jbfu_kheb+62 7 JZa[Z\e_ggZyk_jgZydbkehlZg_j_Z]bjm_lk k_j_[jhfldhgh² fZehZdlb\gucf_lZee hl\_lZ
L K jZa[Z\e_gghc k_jghc dbkehlhcfh]mlj_Z]bjh\Zlvh[Z\_s_kl \Z`_e_ahb )H2+ hl\_l[ 7 +62 =Q =Q62 +n ¦ Ihegh_bhggh_mjZ\g_gb_ + 62± =Q +n 62± =Q ¦ KhdjZs_ggh_bhggh_mjZ\g_gb_ + =Q +n =Q ¦ Hl\_l]
L Dhgp_gljbjh\ZggZyk_jgZydbkehlZg_j_Z]bjm_lk `_e_ahf\ L +62 .2+ .+62 +2 fhevfhevfhev ] fhev.+62
7 +62 =Q =Q62 +n P =Q ] fhev Q=Q 0U =Q ]fhev IhmjZ\g_gbxj_Zdpbbbafhev=QihemqZ_lkyfhevG
Ke_^h\Zl_evgh QG Q=Q 9+ e Hl\_l[ e
L )H6 o 62 o 62 o +62 P + 62 ] Q+62 0U + 62 ]fhev Q)H6
Q+62 fhev
fhev
P)H6 Q)H6 0U)H6 lhgg Hl\_l] l LHl\_lkfhljbl_\ mq_[gbd_
62 2 l 62 62 +2 +62 \uiZ^Z_l k ^h`^_fkg_]hf
AZ^Zqbd
J_qvb^_ldZdh ijhklhf\_s_kl\_lZdb hobfbq_kdhfwe_f_g l_=Zahh[jZagucZahlkh^_j`blky\ djh\bex^_c`b\hlguoObfb q_kdbcwe_f_glZahl\oh^bl\ khklZ\fhe_dme[_edh\gmde_hlb^h\b l^dhlhju_khklZ\eyxl`b\hchj]Zgbaf L We_dljhggZynhjfmeZZahlZ1D V V S
7 We_dljhggZy nhjfmeZ \g_rg_]h wg_j]_lbq_kdh]h mjh\gy ZlhfZZahlZ D V S < khklZ\\ha^moZ\oh^bl Zahl1 ² dbkehjh^H ² m]e_dbkeuc]ZaKH ² bg_jlgu_ ]Zau $U .U ² ½ ¾ iZju \h^u GH b ^j ¿ A_e_gufbjZkl_gbyfbbkihevam_lkyH ^ey^uoZgbyiZju\h^u KH ^eyijhp_kkZnhlhkbgl_aZ
01 0\ha^ iehlghklvZahlZg_fgh]hf_gvr_iehl ghklb\ha^moZU a F U\ha^ U1 :ahlg_bf__lgb aZiZoZgb p\_lZ :ahliehohjZkl\hjy_lky\ \h^_ Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_
/L1 /L1 /L² \hkklZgh\bl_ev1² hdbkebl_ev /L H 1
H
/L
1
:ffbZd1+ kl_i_gvhdbke_gby1² ± +² \Ze_glghklvZahlZ² L Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_
AZ^Zqbd
Kbgl_a ² h[s__ gZa\Zgb_ ijhp_kkh\ ihemq_gby [he__ keh` guo ih khklZ\m b kljh_gbx kh_^bg_gbc ba g_kdhevdbo [he__ ijh kluo 1 + l 1+ Qbkoh^guo \ \ Q 1 Q + Qijh^mdlZ Q 1+ Ld9 Q 9Q lhh[t_f\ oh^_j_Zdpbbmf_gvrZ_lky\ ^\ZjZaZ
MklZgh\db \ukhdh]h ^Z\e_gby ^he`gu [ulv ijhqgufb \h ba [_`Zgb_jZajmr_gby hgb^hjh]b_
L:ffbZdijbghjfZevguomkeh\byo² [_kp\_lguchkljhiZo gmsbc]ZaHl\_l] LIjhfure_gguckihkh[ihemq_gbyZffbZdZ 1 + 1+ \ Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_
1D&O1D621D12 b 1+&O Ijbeb\Z_f\h\k_ijh[bjdbjZkl\hj%D12 %D12 1D62 %D62p 1D12 [_euc hkZ^hd < hklZevguoijh[bjdZogbdZdbobaf_g_gbcg_ijhbahc^_l < hklZ\rb_kyijh[bjdb^h[Z\bfjZkl\hj &D2+ b gZ]j__f W &D2+ 1+&O &D&O 1+n +2 [m^_lqm\kl\h\Zlvkyj_adbcaZiZoZffbZdZ\ h^ghcbaijh[bjhd Ijbeb\Z_fjZkl\hj$J12 $J12 1D&O $J&Op 1D12 [_euchkZ^hd < hklZ\r_ckyijh[bjd_[m^_l1D12 Hl\_lkfhljbl_\ mq_[gbd_
GZ]j_\Zgb_kf_kbkhebZffhgbyb ]Zr_ghcba\_klb\ j_Zdpbb ihemq_gby ZffbZdZ g_h[oh^bfh qlh[u m^Zeylv jZkl\hjb\rbcky \ \h^_ ZffbZd ld jZkl\hjbfhklv ZffbZdZ \ \h^_ ijb m\_ebq_gbb l_fi_jZlmjumf_gvrZ_lky Hl\_lkfhljbl_\ mq_[gbd_
L IjbjZkl\hj_gbbZffbZd\ \h^_j_ZdpbykeZ[hs_ehqgZy 1+ +2 1+2+ 1+2+ 1+ 2+± ] S_ehqgZy W 1+ &X2 &X+21n &X H 1
H
&X
1
ke_^h\Zl_evgh&X2² hdbkebl_ev1+ ² \hkklZgh\bl_ev
AZ^Zqbd
L1+2 1+2 kmffZdhwnnbpb_glh\j_Zdpbb Hl\_lZ $U3W $U5K
71+ 2 pbb Hl\_l[
3W
12 +2 kmffZdhwnnbpb_glh\j_Zd
H ² we_dljhgZgZ\ukr_fmjh\g_ Hl\_lkfhljbl_\ mq_[gbd_
1 + 1+ 1+ +&O 1+&O
AZ^Zqbd
9, +62
9 +32
9,, +&O2
, +&O
L< hkgh\_ ijhba\h^kl\ZZahlghcdbkehlue_`blp_ivij_\jZ s_gbc [ 1+ o 12o 12 o +12
7< ijhfure_gghklbZahlgmxdbkehlmihemqZxlihj_Zdpbb \ 12 2 +2 +12 7< eZ[hjZlhjbbZahlgmxdbkehlmihemqZxlihj_Zdpbb \ W 1D12 dj +62 dhgp 1D62 +12n Z[\] Qm\kl\m_f
Kihkh[ihemq_gbyZahlghcdbkehlu\ eZ[hjZlhjbb < dhe[m gZkuiZlv 1D12 djbklZeebq_kdbc ijbeblv dhgp +62b hl]hgylv+12 \ dhe[mh[eh`_ggmxev^hf Kihkh[ihemq_gbykheyghcdbkehlu +62dhgp 1D&Ol\ 1D+62 +&On Ijh\h^blky\ dhe[_dbkehlZ^h[Z\ey_lkyihdZieyf
Z 1 2 12mkeh\by² fhegby 122 12 12 2 +2 +12 [ 62 o 62 mkeh\by² l_fi_jZlmjZ 62 2 +2 +62 mkeh\by² gZebqb_12 \ Zlfhkn_ j_ ld 62 12 62 12
GZkus_gguc jZkl\hj Zahlghc dbkehlu ijb]hlh\blv g_evay ld+12 kf_rb\Z_lkyk \h^hc\ ex[uokhhlghr_gbyo
JZkl\hj dhgp Zahlghc dbkehlu bf__l `_elmx hdjZkdm ld +12 dhgp jZkiZ^Z_lky k h[jZah\Zgb_f 12 12 ² [mjuc ]Za \ \h^_^Z_l`_elmxhdjZkdm L0J+12 0J12 1n +2 ]
L KZ +12 jZa[ o &D12 1+12 +2 kmffZdhwnnbpb_glh\\ mjZ\g_gbb \
L &X +12 jZa[ KX12 12n +2 kmffZ dhwnnbpb_glh\\ mjZ\g_gbb[ Hl\_lkfhljbl_\ mq_[gbd_
Ljm[dZ KdeygdZ KdeygdZ
1+ 2 dZl 12+2 12 2 +2 +12 :ffbZd i_j_ghkblky k \ha^mohf ba ZffbZqgh]h jZkl\hjZ
AZ^Zqbd
Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_
K m\_ebq_gb_f Zlhfgh]h ghf_jZ ]Zeh]_gZ ih\urZ_lky fhe_ dmeyjgZyfZkkZqlh\e_q_lih\ur_gb_ W² ieZ\e_gbyb dbi_gby Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_
Z ;eZ]h^Zjy gZebqbx k\h[h^guo GZlhfguo hj[blZe_c gZ \g_rg_f wg_j]_lbq_kdhf mjh\g_ nhknhj h[jZam_l agZqbl_evgh [h e__ijhqgu_kh_^bg_gbyk dbkehjh^hfq_fZahlIhwlhfm12 [h e__j_Zdpbhgghkihkh[_gq_fJH [ JZaf_jZlhfZ6E[hevr_q_fjZaf_jJ ijhqghklvkh_^bg_ gby mf_gvrZ_lky hl JH ^h 6E2 Ihwlhfm 6E2 [he__ kbevguc hdbkebl_evq_fJH K m\_ebq_gb_fjZaf_jZkh_^bgyxsbokyZlhfh\ijhqghklvob fbq_kdhc k\yab mf_gvrZ_lky 1+ mklhcqb\__ JG Z JG mklhc qb\_cq_fJH Hl\_lkfhljbl_\ mq_[gbd_
Hl\_lkfhljbl_\ mq_[gbd_
JZaf_j ZlhfZ 6 [hevr_ jZaf_jh\ ZlhfZ H ijhqghklv kh _^bg_gbymf_gvrZ_lkyhlGH ^hG6GH [he__mklhcqb\Z Hl\_lkfhljbl_\ mq_[gbd_
Hl\_lkfhljbl_\ mq_[gbd_
:eehljhiby ² y\e_gb_ kms_kl\h\Zgby obfbq_kdbo we_f_g lh\ \ \b^_ g_kdhevdbo ijhkluo \_s_kl\ gZoh^ysboky \ h^ghf nb abq_kdhf khklhygbb gh hlebqZxsboky kljh_gb_f b nbabq_kdbfb k\hckl\Zfb
Ijb hdbke_gbb [_eh]h J \ha^mohf ² \Ze_glghklv ,,, 32 ijb]hj_gbbdjZkgh]hnhknhjZ² \Ze_glghklv932 Hl\_lkfhljbl_\ mq_[gbd_
>bkkhpbZpbyfgh]hhkgh\guodbkehlgZb[hevrZygZi_j\hcb gZbf_gvrZygZihke_^g_cklmi_gyoWlhlwnn_dlk\yaZgk jZkij_^_ e_gb_f we_dljhgghc iehlghklb \ fhe_dme_ dbkehlu Ijb ihl_j_ hq_j_^gh]h ijhlhgZ G \k_ [hevr_ we_dljhklZlbq_kdbo kbe m^_j `b\Zxlihke_^mxsb_ijhlhgu Hl\_lkfhljbl_\ mq_[gbd_
1D32 +&O 1D&O+32 WlZj_Zdpbyb^_lihlhfmqlhkheygZydbkehlZ gZfgh]hkbevg_c q_fnhknhjgZy Ijhfure_gguckihkh[ihemq_gbynhknhjghcdbkehlu 32 +2 +32 &D32 +62 &D62 +32
Nhknhjgu_m^h[j_gby >>b]b^jhnhknZl dZevpby kmevnZl dZevpby@ ² ijhklhc km i_jnhknZl >b]b^jhnhknZl dZevpby² ^\hcghckmi_jnhknZl NhknZldZevpby² nhknhjblgZyfmdZ =b^jhnhknZldZevpby² ij_pbiblZl >b]b^jhnhknZlZffhgby² Zffhnhk =b^jhnhknZlZffhgby² Zffhnhk J_qvb^_lh[Zffhnhk_lZfkh^_j`blkyZahlb nhknhj Hl\_lkfhljbl_\ mq_[gbd_
AZ^Zqbd
Hl\_lkfhljbl_\ mq_[gbd_
GZih\_joghklb`_e_agh]hba^_ebyijb_]hhdbke_gbbgZ\ha ^mo_h[jZam_lkyj`Z\qbgZ)H2 +2 Ijb]hj_gbbgZ\ha^mo_b^_lj_ZdpbyK H KHn Ijh^mdlhdbke_gby² hdkb^m]e_jh^Z9, Hl\_lkfhljbl_\ mq_[gbd_
DhjjhabhggZy klhcdhklv f_lZeeZ ² wlh kihkh[ghklv f_lZeeZ khijhlb\eylvkydhjjhabb B^_lj_Zdpby
W & &X2 KHn KX Ihjhrhd&Xbf__ldbjibqghdjZkgucp\_l Hl\_lkfhljbl_\ mq_[gbd_
Hdkb^m]e_jh^Z,, h[eZ^Z_l\hkklZgh\bl_evgufbk\hckl\Zfb ihlhfmqlh\ KHm]e_jh^bf__lg_\ukrmx\Ze_glghklv LJ_Zdpbyhdkb^Zm]e_jh^Z,, k dbkehjh^hfwdahl_jfbqgZih lhfmqlhbaf_g__mklhcqb\h]hKHihemqZ_lky[he__mklhcqb\h_kh _^bg_gbyKHHl\_l[
L GZ jbkmgd_ bah[jZ`_gZ fh^_ev djbklZeebq_kdhc j_r_ldb KH Hl\_l[
L >ey ihemq_gby KH \ eZ[hjZlhjbb bkihevamxl j_Zdpbx dZj[hgZlZdZevpbyk kheyghcdbkehlhc Hl\_l[ Hl\_lkfhljbl_\ mq_[gbd_
Kh^_j`Zgb_ m]e_dbkeh]h ]ZaZ \ \ha^mo_khklZ\ey_lih fZkk_ LHl\_lkfhljbl_\ mq_[gbd_
LM]e_dbkeuc]Zakh^_j`blky\ Zlfhkn_j_ Hl\_l]
KH kihkh[kl\m_lijhp_kkmnhlhkbgl_aZ
Hl\_lkfhljbl_\ mq_[gbd_
0&2 u ]fhev F\ha^ ]fhev KH ly`_e__\ha^moZ Hl\_lkfhljbl_\ mq_[gbd_
Kmohc e_^ bkihevam_lky ijb hoeZ`^_gbb q_]heb[h gZijb f_jdZdoeZ^Z]_glijbojZg_gbbfhjh`_gh]h Hl\_lkfhljbl_\ mq_[gbd_
KH GH GKH Ijb jZkl\hj_gbb m]e_dbkeh]h ]ZaZ \ \h^_ kj_^Z keZ[hdbkeZy JZkl\hjGKH bkihevamxl\ ]Zabjh\ZgguoebfhgZ^Zo DZj[hgZlu² khebk KH± =b^jhdZj[hgZlu² khebk GKH± W 1+ &2 1+n &2n +2 I_dZjkdbcihjhrhdbkihevamxl\ jhebjZajuoebl_ey W 1D+&2 1D&2 +2n &2n Hl\_lkfhljbl_\ mq_[gbd_
1D&2 &D&O 1D&O&D&2p 1D &2± &D &O± 1D &O± &D&2p &D &2± &D&2p WlZj_Zdpbyb^_lldKZKH moh^blbajZkl\hjZhkZ`^Z_lky W &D&2 &D2&2n
< lhf qlh \u^uoZ_fuc q_eh\_dhf \ha^mo kh^_j`bl [hevr_ m]e_dbkeh]h ]ZaZ q_f Zlfhkn_jguc fh`gh m[_^blvky k ihfhsvx ke_^mxs_]h wdki_jbf_glZ Fh`gh \aylv ljm[hqdm b ih^mlv \ jZk l\hjKD2+ KD2+ &2 &D&2p +2 H[jZam_lky [_eZy fmlv Z _keb ijh^m\Zlv \ha^mo q_j_a wlhl `_ jZkl\hj lh gbq_]h g_ [m^_l Ijb ba[uld_ KH j_Zdpby ihc^_l ^Zevr_ KH KZKH GH KZGKH
Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_
AZ^Zqbd
Hl\_lkfhljbl_\ mq_[gbd_ >+@ ± fheve
< dbkeuojZkl\hjZo]b^jhdkb^bhg_klvgh\ hq_gvfZeuodh ebq_kl\Zo>H+±@± fheve Z 1D32 ² s_ehqgZykj_^Z [ 1+&O² dbkeZykj_^Z \ 1D6L2 ² s_ehqgZykj_^Z ] &X62 ² keZ[hdbkeZykj_^Z
JZkl\hjkmevnb^ZgZljbyiZog_lk_jh\h^hjh^hfld\ ijhp_k k_ ]b^jhebaZ1D6h[jZam_lky+6 1D6+2 1D 2+± +6 +6iehohjZkl\hjy_lky\ \h^_b qZklbqghme_lZ_lbajZkl\hjZ
Ijb ^h[Z\e_gbb d jZkl\hjm `b^dh]h kl_deZ dZieb n_ghenlZ e_bgZ jZkl\hj klZgh\blky fZebgh\uf qlh ^hdZau\Z_l s_ehqgmx kj_^mjZkl\hjZ +62 ² keZ[ZydbkehlZ Hl\_lkfhljbl_\ mq_[gbd_
Kheb 1+ 6L2 b &X&2 jZaeZ]Zxlky \h^hc ihwlhfm h gbo g_l^Zgguo\ lZ[ebp_jZkl\hjbfhklb
AZ^Zqbd
< ^hdZaZl_evkl\h lh]h qlh dj_fgb_\Zy dbkehlZ y\ey_lky keZ [hc fh`gh ijb\_klb ke_^mxsbc nZdl jZkl\hj 1D6L2 bf__l s_ ehqgmxkj_^m P6L2 Q+2
+6L2 +6L2
P P
Q Q
LHl\_lkfhljbl_\ mq_[gbd_
Ba^_eby ba kl_deZ dhlhju_ bkihevamxl jZagu_ _]h k\hckl\Z ieZnhgu exklju ihkm^Z ^ey j_Zdlb\h\ hdhggu_ kl_deZ kheg_q gu_hqdbbaheylhju
=E:<: AZ^Zqbd
KljmdlmjgZy nhjfmeZ Zlhfu kh_^bg_gu ]_jlhqdZfb ]_j lhqdZ² iZjZwe_dljhgh\
M]hevgZy dbkehlZ g_ y\ey_lky m]e_\h^hjh^hf ld ihfbfh Zlhfh\K bG hgZbf__lZlhfuH Ijhba\h^gu_wlZgZ
+ +
+²&²&²2+
+ +
+ +
+²&²&²&O
+ +
+ +
+²&²&²12
+ + + +
+²&²&²1+ + +
+
+²&²&
+ + +
+²&²&
2
2
+ 2²+
Hj]Zgbq_kdb_\_s_kl\Z GKHHGGKHKGHGKG wlZg KGHKG f_lZg
Hj]Zgbq_kdb_ \_s_kl\Z +&&O oehjhnhjf &+2+ f_lZ ghe &&O l_ljZoehjf_lZg &+1+ f_lbeZfbg 1+ &2fhq_ \bgZ &6 k_jhm]e_jh^ Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_
AZ^Zqbd
JZ^bmkZlhfh\\ ]jmiiZom\_ebqb\Z_lkyk\_jom\gbaihwlhfm 56L !5& KZfuc[hevrhcZlhf² . kZfucfZe_gvdbcZlhf² )
KZfuffZe_gvdbfZlhfhfh[eZ^Z_lwe_f_gl\h^hjh^Z kZfuf [hevrbf0Wf_clg_jbc
fhe_dmeZ + 1D
kljmdlmjgZynhjfmeZ +±+ 1D±1D
1
1{1
2
2 2
Hl\_lkfhljbl_\ mq_[gbd_
we_dljhggh_kljh_gb_ +u+ 1Du1D [[ [ [ [ 2 [ 2 [ [
[ 1 [[ 1
Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_
:lhfu nhknhjZ dj_fgby [hjZ fh]ml h[jZah\u\Zlv p_ihq_q gmx k_lqZlmx dZjdZkgmxfhe_dmeyjgu_kljmdlmjuldbo\Ze_gl gu_\hafh`ghklb[hevr_^\mo
:efZa h[jZam_l dZjdZkgmx kljmdlmjm k\yav K²K kZfZy ijhqgZy\ lZdhckljmdlmj_[he__ijhqgh_\_s_kl\h\jy^ebfh`gh ihemqblv 6L+ 2 o 6L2 +2&+ 2 &2 +2 K\yav6L²+keZ[__\ 6L+hgZaZ\bkblhlf_`Zlhfgh]hjZkklhy gbym 6L²+hgh[hevr_ihkjZ\g_gbxk K²G Hl\_lkfhljbl_\ mq_[gbd_
&+ 2 &2 +2 6L+ 2 6L2 +2 &+ [he__ijhqgZy6L+ [he__j_Zdpbhgghkihkh[gZy KG [he__ijhqgZyfhe_dmeZq_f6L+ l_k\yav6L²+keZ[__ k\yab K²G 6L+ [he__ j_Zdpbhgghkihkh[gZy fhe_dmeZ q_f KG ldk\yab6L²+keZ[__q_fk\yavK²G Hl\_lkfhljbl_\ mq_[gbd_
AZ^Zqbd
+
+
+
+
+
&
&
+
+&+ q +&&lh`_qlh\ f_lZg_
+
+
&
+
+ +
&
+
&
+
+
+
+&& +&+ &&&hgbjZ\gu Hl\_lkfhljbl_\ mq_[gbd_
+ + + +
+²&²&²&²&²+ + + + +
;mlZg
+ + + + +
+²&²&²&²&²&²+ + + + + +
+ + + + + +
+²&²&²&²&²&²&²+ + + + + + +
Hl\_lkfhljbl_\ mq_[gbd_
I_glZg
=_dkZg
+ + +
+²&²&²&²2+ + + + + + + +
Ijhibeh\uc kibjl
;mlbeh\uc kibjl
+²&²&²&²&²2+ + + + +
KGHG ² f_lZghe KGHG ² wlZghe KGHG ² ijhiZghe KGHG ² [mlZghe
Kibjlu ² hj]Zgbq_kdb_ kh_^bg_gby bf_xsb_ nmgdpbh gZevgmx]jmiimHG
AZ^Zqbd
=hfheh]bq_kdbc jy^ ² jy^ kh_^bg_gbc h^gh]h deZkkZ hleb qZxsbcky^ey^Zggh]hb ihke_^mxs_]hqe_gZgZKG]jmiim :edZgZfbgZau\Zxlm]e_\h^hjh^ukhklZ\Z&Q+Q KG ² wlbeKG ² ijhibe
M]e_\h^hjh^uh[s_c nhjfmeu&Q+Q gZau\ZxlkyZedZgZfb KG ² ]_dkZgKG ² ]_ilZg Z
&+
&+²&²&+²&+²&+
&+ &+ ² i_j\bqgu_Zlhfum]e_jh^Z ² \lhjbqgucZlhfm]e_jh^Z ² lj_lbqgucZlhfm]e_jh^Z ² q_l\_jlbqgucZlhfm]e_jh^Z
; GZb[he__ j_Zdpbhgghkihkh[_g lj_lbqguc Zlhf \h^hjh^Z gZbf_g__² i_j\bqgu_ < KG ² ^bf_lbehdlZg = KG²KG²KG²KG²KG²KG²KG²KG ² hdlZg
I_j\bqguc² Lj_lbqguc²
Wlbnhjfmeui_glZgZjZaebqgulhevdhgZ[mfZ]_ bahf_jZ IjhiZgKG²KG²KG IjhiZghe KG²KG²KGHG ² i_j\bqguc &+²&+²&+ 2+
² \lhjbqguc
AZ^Zqbd
Bahf_juKGKG{K±KG b GK K KG Bahf_ju]hfheh]b KG²KG²KG²KG b &+²&+²&+ Hl\_lkfhljbl_\ mq_[gbd_
&+
Bahf_jijhibe_gZ² pbdehijhiZg ijhibe_g pbdehijhiZg +&
&²&+
+
b
&+
&+ ² &+
G_ y\ey_lky
:ed_gZfbgZau\Zxlkym]e_\h^hjh^ukhklZ\Z&Q+Q
:edbgZfbgZau\Zxlkym]e_\h^hjh^ukhklZ\Z&Q+Q± :j_gZfbgZau\Zxlkym]e_\h^hjh^ukhklZ\Z&Q+Q± Lhemhe
&+
P_ivihebwlbe_gZkhklhblbaa\_gv_\²KG² KG² Fhe_dmeyjgmxb fheyjgmxfZkkmihebwlbe_gZgZa\Zlvg_ev ayHgbfh]mlbaf_gylvky\ rbjhdboij_^_eZo J_Zdpbyihebf_jbaZpbb² wlhkh_^bg_gb_fgh]bofhe_dme\ h^gm
Ij_^_evgufb gZau\Zxlky m]e_\h^hjh^u g_ kh^_j`Zsb_ djZlguok\ya_c Ihebwlbe_gy\ey_lkyij_^_evgufm]e_\h^hjh^hf
&+ Q &+ &+
Q&+ &+&Oo&+±&+&O± Q
&+
²+&²&+²
Q
AZ^Zqbd
M]e_\h^hjh^u ijbjh^gh]h ]ZaZ bf_xsb_ bahf_ju [mlZg i_glZg Fhe_dmeyjgZyfZkkZ[mlZgZf_gvr_fhe_dmeyjghcfZkkui_g lZgZihwlhfmLdbi KG Ldbi KG
< ijbjh^ghf ]Za_ kh^_j`Zlky m]e_\h^hjh^u 7dbi & khklZ\Z &Q+Q ]^_ Q ² < g_nlyghc `b^dhklb 7ie Ldbi ! kh^_j`Zlkym]e_\h^hjh^ukhklZ\Z&Q+Q]^_Q ²
E_lmq_klv ² kihkh[ghklv bkiZjylvky Gbadhfheyjgu_ ld bf_xlfZe_gvdmxfZkkm emqr_me_lZxlq_f\ukhdhfheyjgu_
AZ^Zqbd
L_iehl\hjgZy kihkh[ghklv ² hp_gdZ m]e_\h^hjh^gh]h lhieb\Z ihdhebq_kl\ml_iehlu\u^_eyxs_ckyijb k]hjZgbbd]lhieb\Z 1+ 2 1 +2d>` fhev Q P0 01+ ]fhev Q ]fhev fhev fhevo d>` fhevo O d>` O d>` l_4 F>` Hl\_l4 F>`
KG H KHn GH d>`
KG H KHn GH d>`
Bahf_jh\ m hdlZgZ fgh]h ij_^eh] bah ih^jZamf_\Z_l kljmd lmjmhlebqgmxhlebg_cghcgZijbf_j &+ ²&+²&+ ²&&+ &+
M bahhdlZgZ l_iehlZ h[jZah\Zgby hlebqgZ hl l_iehlu h[jZah\Z gbyghdlZgZ l_iehlZk]hjZgbyjZagZy Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_
@b^dh_lhieb\h[_ahiZkg__]Zahh[jZagh]hm^h[g__l\_j^h]h
< wdheh]bq_kdhfieZg_]Zahh[jZagh_lhieb\hemqr_`b^dh]h \ ijZdlbq_kdhf² l\_j^h]h L\_j^h_lhieb\h\ ieZg_[_ahiZkghklbemqr_b `b^dh]hb ]ZaZ
AZ^Zqbd
G_nlv ² wlh kf_kv m]e_\h^hjh^h\ ij_bfms_kl\_ggh ZedZgu b Zj_gu I ² fbeebhgih_a^h\
G_nlvljZgkihjlbjm_lkyk f_klZ^h[uqbih_a^Zfb beb\h^guf ljZgkihjlhf DkbeheuijbgZ^e_`Zld ]hfheh]bq_kdhfmjy^mZj_gh\ Hjlhdkbehe
&+
Ij_^r_kl\m_llhemhe
&G
&+
Lhemhe
L_fi_jZlmjZ dbi_gby ² l_fi_jZlmjZ ijb dhlhjhc \_s_kl\h gZqbgZ_l i_j_oh^ ba `b^dh]h khklhygby \ ]Zahh[jZagh_ Q_f \ur_ ^Z\e_gb_l_f[hevr_l_fi_jZlmjZdbi_gby
Hl\_lkfhljbl_\ mq_[gbd_
>_p_ghlghkblkyd Zed_gZfZ ^_dZg² ZedZg KG±KG ±KG ² ^_dZg KG±KG ±KG KG ² ^_p_g Hl\_lkfhljbl_\ mq_[gbd_
>_dZg\oh^bl\ khklZ\g_nlyghcnjZdpbbeb]jhbg MjZ\g_gb_dj_dbg]Z^hdhaZgZ Wq
KG o KG KG KG±KG ±KG b KG±KG ±KG KG MjZ\g_gb_dj_dbg]ZljbdhaZgZ KG±KG ±KG KGKG±KG ±KG Wq
KG o KG KG Wq
KG o KG KG KG±KG ±KGKG±KG ±KG KG
Ijb dj_dbg]_ g_nlb ihemqZ_lky kf_kv ij_^_evguo b g_ij_ ^_evguom]e_\h^hjh^h\ Ldbi KG ±K Ldbi KG K Ldbi KG K Ldbi KG K
Lie KG ±K Lie KG ±K Lie KG ±K Lie KG ±K
AZ^Zqbd
IZjZnbgihemqZxlbanjZdpbbfZamlZ
Ijbf_ju j_Zdpbc k mqZklb_f ij_^_evguo m]e_\h^hjh^h\ ]h j_gb_f_lZgZijhiZgZ\ aZ`b]Zed_ [_gabgZ KG H
Wq
KG H
KH GH
Wq
KH GH
L_ieh\hc wnn_dl j_Zdpbc k m]e_\h^hjh^hf kh^_j`Zsbf [hevr__dhebq_kl\hm]e_jh^Z\ fhe_dme_² [hevr_ Wq
KG o KG K G KG±KG ±KG b KG±KG ±KG KG Hl\_lkfhljbl_\ mq_[gbd_
AZ^Zqbd
NmgdpbhgZevgZy ]jmiiZ ² kh\hdmighklv Zlhfh\ hij_^_eyx sZyoZjZdl_jgu_obfbq_kdb_k\hckl\Z^Zggh]hdeZkkZkh_^bg_gbc
Kibjlu ² wlh ijhba\h^gu_ m]e_\h^hjh^h\ bf_xsb_ ]b^jh dkbevgmx]jmiim KG±KG±HG ² wlZghe KG±KG±KG±HG ² ijhiZghe
²HG ² ]b^jhdkbevgZy]jmiiZ
KGHG ² m]e_\h^hjh^gucjZ^bdZek ]jmiihc±HGwlbeh\uc kibjl Wq
KGHG H KHn GH QKGHG ]]fhev fhev fhevo e fhevo O e O fhev efhev e
>_]b^jZlZpby² j_Zdpbyk hls_ie_gb_f\h^um \_s_kl\Z &X2+
Wq
&X2+2n
dhgp KG±HG KG±KGHG o KG±H±KG±KG GH
+ 62
K+ H H
Wq
KHn GHn
Ijhklhc wnbj ² ijh^mdl f_`fhe_dmeyjghc ^_]b^jZlZpbb k mqZklb_f^\moh^bgZdh\uobebjZaebqguokibjlh\
Hj]Zgbq_kdb_ dbkehlu ² ijhba\h^gu_ m]e_\h^hjh^h\ kh ^_j`Zsb_²KHHG dZj[hdkbevgmx]jmiim Wlbeh\uckibjlKGHG bmdkmkgZydbkehlZ &+²& 2 2+
KGKHHGKZKH KGKHH KZGH KHn MdkmkgZy dbkehlZ kbevg__ m]hevghc ihwlhfm \ul_kgy_l __ ba kheb
Keh`gucwnbj² ijh^mdl^_]b^jZlZpbbdZj[hgh\hcdbkehlu b kibjlZ 5²&
2
2 5c
KGHG ² f_lZghekibjl KG H ² ^bf_lbeh\ucwnbjijhklhcwnbj Hi_qZldZ² lZdb_\_s_kl\Zg_kms_kl\mxl
AZ^Zqbd Wlbe_g]ebdhev
&+²&+
2+
2+
KGKG KHHG² kl_Zjbgh\ZydbkehlZ KGKHHG² he_bgh\ZydbkehlZ @bj[he__dZehjbcguc
:fbghdbkehlu² hj]Zgbq_kdb_dbkehluh[s_cnhjfmeu 1+²&+²&22+ 5
]^_5² wlhm]e_\h^hjh^gucjZ^bdZe
&+²&+²1+ &22+ 2
&+²6²&+²&+²&+²1+ &22+
&22+
1+²&+²&²1+²&+ + &²
&+ ²6²&+
>Z _kl_kl\_ggh [_edb ijbjh^gh]h ijhbkoh`^_gby y\eyxlky ihebf_jZfb KGH ² d>`ihjbk Oehjhnbebf__la_e_gucp\_l
DZq_kl\_ggZyj_ZdpbygZdjZofZe² k , KGH H KH GH 4 P]exdhau ] F]exdhau ]fhev P Q]^xdhau fhev 0 d>` 4 d>`fhev fhev Hl\_ld>`fhev
=E:<: AZ^Zqbd
J_ZdpbyaZf_s_gby² j_Zdpby\ dhlhjhch^bgZlhfaZf_gy_l ky^jm]bf Hl\_lkfhljbl_\ mq_[gbd_ =Q)H62 =Q62 )Hp =Q+62 =Q62 +n
Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_
$O=Q)H6Q3E&X² jy^Zdlb\ghklb
GZljbc g_evay bkihevah\Zlv \ j_Zdpbb ihlhfm qlh gZljbc \aZbfh^_ckl\m_lk \h^hc 1DGH 1D2++n ² gZ[ex^Z_lky\u^_e_gb_\h^hjh^Z L] gZljbckfhljbaZ^Zqm
.0J1D0J)H² ^Zggucjy^khhl\_lkl\m_ljy^mZdlb\gh klbf_lZeeh\ Hl\_lkfhljbl_\ mq_[gbd_
AZ^Zqbd
L F_lZeeu ijb \aZbfh^_ckl\bb k g_f_lZeeZfb ijhy\eyxl [ \hkklZgh\bl_evgu_k\hckl\Z L F_lZeebq_kdZy Zdlb\ghklv s_ehqguo f_lZeeh\ k\_jom \gba Z mkbeb\Z_lky Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_
Hkgh\gu_kihkh[uaZsbluf_lZeeh\hldhjjhabbkfZadZih djZkdZbebe_]bjmxsZy^h[Z\dZ < dZq_kl\_e_]bjmxsbo^h[Z\hdd `_e_agufba^_ebyfijbf_ gyxlojhfgbd_evheh\hb ^jm]b_ Ijh\hehdZ² ]b[dhklvb ijhqghklv J_r_ldZ² l\_j^hklvijhqghklv =\ha^v² l\_j^hklvdh\dhklv
< i_j\hc]jmii_ld\ g_cgZoh^ylkykZfu_Zdlb\gu_f_lZeeu Hl\_lkfhljbl_\ mq_[gbd_
Hl\_lkfhljbl_\ mq_[gbd_
AZ^Zqbd
GZihke_^g_f\Ze_glghf keh_m $OgZoh^blkywe_dljhgZ :exfbgbcijhy\ey_l\Ze_glghklv² ?]haZsbsZ_lhdkb^gZyie_gdZ$O2
:exfbgbc bkihevam_lky dZd kljhbl_evguc fZl_jbZe baaZ k\h_ce_]dhklbGZijbf_jihkm^ZkZfhe_ludZjdZkub ^jkfhljb jbk Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_
$O&O qZklbqgh]b^jhebam_lky\ \h^_ $O&O +2 $O2+ &O +&O Kj_^ZdbkeZyihwlhfmf_lbehjZg`² djZkguc Hl\_lkfhljbl_\ mq_[gbd_
Hl\_lkfhljbl_\ mq_[gbd_
Hl\_lkfhljbl_\ mq_[gbd_
Hl\_lkfhljbl_\ mq_[gbd_ Wq
$O&2 $O2 & < wlhcj_Zdpbb$O² \hkklZgh\bl_evZ KH ² hdbkebl_ev Hl\_lkfhljbl_\ mq_[gbd_
LZ $O1D2++2 1D>$O2+ @+ [ $O+12dhgp ² j_Zdpbyg_b^_lldZexfbgbciZkkb\bjm _lky\ dhgp_gljbjh\ZgguodbkehlZo \ $O&X&O &Xp $O&O ] $O+&O $O&O +n
AZ^Zqbd
GZihke_^g_f\Ze_glghf keh_m KZgZoh^blkywe_dljhgZ KZijhy\ey_l\Ze_glghklv²
LAZibr_fj_ZdpbxKZGH KZHG Gn KmffZdhwnnbpb_glh\² Hl\_l[ &D&O &D&O KZ6 &D6 &D2 &D2
%D2 %D2 %D+ %D+ %D&O %D&O %D+2 %D2+ +n
J_ZdpbyjZaeh`_gby&D&2 ² wg^hl_jfbqgZldgZj_Zdpbx aZljZqb\Z_lkyl_ieh &D&2
Wq
Hl\_lkfhljbl_\ mq_[gbd_
&D2&2n
J_Zdpby ©]Zr_gby ba\_klbª² wdahl_jfbqgZldl_ieh\u^_ ey_lky &D2+2 &D2+ 4
N_ghenlZe_bg\ jZkl\hj_KZHG ijbf_lfZebgh\mxhdjZkdm Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_
< j_amevlZl_ih]ehs_gbyKH ba\ha^moZ
GKH ² m]hevgZy dbkehlZ HgZ g_mklhcqb\Z b jZaeZ]Z_lky gZGH bKH Hl\_lkfhljbl_\ mq_[gbd_
&X62 +2&D2+ &X2+ &D62 +2 7 [ h[jZam_lkyg_jZkl\hjbfh_kh_^bg_gb_ .&2 &D&O &D&2p .&O
7 ] &D&2 + &D +2&2n IhegZyj_Zdpby&D&2 +&O &D&O +2&2n 7 Z &D+&2 ² \j_f_ggZy`_kldhklv L [ &D62 ² ihklhyggZy`_kldhklv Hl\_lkfhljbl_\ mq_[gbd_
AZ^Zqbd
Hl\_lkfhljbl_\ mq_[gbd_
< f i_jbh^_ kh^_j`blky we_f_glZ \h f b f ² ih we_f_glh\ \ f b f ² ih Qbkeh we_f_glh\ hij_^_ey_lky wg_j]_lbq_kdbfmjh\g_f Dhebq_kl\h\Ze_glguowe_dljhgh\m &Ob 0Q² we_dljhgh\ m 6b &U²
Hl\_lkfhljbl_\ mq_[gbd_
AZ^Zqbd
Hl\_lkfhljbl_\ mq_[gbd_
Z &U2+&O &U&O +n [ &U2 1D2+ 1D&U2 +2 &U2 +&O &U&O +2 \ &U2 1D2+ 1D&U2 +2
Dbkehlguc 7L2 9 2 5H2 :2 7D2 2V2
:fnhl_jguc )H2 =Q2
Hkgh\ghc 7L2 92 )H2 &X2 &X2
Hl\_lkfhljbl_\ mq_[gbd_
AZ^Zqbd
N_jjhfZ]g_lbaf ² kbevgh_ ijhy\e_gb_ fZ]gblguo k\hckl\ hl©n_jjhª² `_e_aguc Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_
)H+ 62± )H 62± +n )H2+&O )H&O +2
Z )H2 +&O )H&O +2 )H&O 1D2+ )H2+ p 1D&O )H2+
Wq
)H2 &
)H2 +2 Wq
&2n )H
[ )H2+ 2 +2 )H2+ p )H2+ +12 )H12 +2
Ijhbkoh^blqZklbqguc]b^jheba)H&O )H&O +2 )H2+ &O +&O J_ZdpbydbkeZyl_hdjZkdZ² djZkgZy Hl\_lkfhljbl_\ mq_[gbd_
Hl\_lkfhljbl_\ mq_[gbd_
H[smxnhjfmemj`Z\qbgufh`ghij_^klZ\blvlZd )H2 Q+2 J`Z\qbgZbf__l[mjucp\_l
@_e_agu_ ba^_eby fh`gh aZsblblv hl dhjjhabb k ihfhsvx kfZadbdjZkdbb e_]bjmxsbof_lZeeh\
AZ^Zqbd
Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_ ReZd² &D6L2
Wie )H &
Hl\_lkfhljbl_\ mq_[gbd_ Hl\_lkfhljbl_\ mq_[gbd_
IJ:DLBQ?KDB?A:GYLBY IjZdlbq_kdh_aZgylb_ J_r_gb_wdki_jbf_glZevguoaZ^Zqihl_f_ ©J_Zdpbb\ jZkl\hjZowe_dljheblh\ª
Z Ijh\_^_fj_Zdpbxf_`^mjZkl\hjZfbDKH b +12>eywlh ]hkhev_f^Zggu_jZkl\hju .&2 +12 .12 +2&2n KbevgZy dbkehlZ +12 \ul_kgy_l g_mklhcqb\mx b keZ[mx db kehlm GKH dhlhjZy aZl_f jZaeZ]Z_lky k \u^_e_gb_f m]e_dbkeh]h ]ZaZihy\eyxlkyimaujvdb GKH KHn GH
[ Ijh\_^_fj_Zdpbx f_`^mjZkl\hjZfb)H&O b DHG )H&O .2+ )H2+ p .&O Ihke_ keb\Zgby jZkl\hjh\ \uiZ^Z_l [mjuc klm^_gbkluc hkZ^hd < ^Zgghcj_Zdpbbkbevgh_hkgh\Zgb_DHG\ul_kgy_lkeZ[h_b ieh ohjZkl\hjbfh_² )H2+ \ Ijh\_^_fj_Zdpbxf_`^mjZkl\hjZfb1D2+b +62 1D2++62 1D62 +2 < wlhc j_Zdpbb ijhbkoh^bl \aZbfh^_ckl\b_ f_`^m dbkehlhc b hkgh\Zgb_f l_ b^_l ijhp_kk g_cljZebaZpbb
] Ijh\_^_fj_Zdpbxf_`^mjZkl\hjhf+&Ob dmkhqdhff_eZbeb fjZfhjZKZKH &D&2 +&O &D&O &2n +2 Ijb ihiZ^Zgbb KZKH \ jZkl\hj +&O gZqbgZ_lky \u^_e_gb_ m] e_dbkeh]h]ZaZ
^ Ijh\_^_fj_Zdpbxf_`^mjZkl\hjZfb&X&O b DHG &X&O .2+ &X2+ p .&O Ijb keb\Zgbb jZkl\hjh\ \uiZ^Z_l ]hem[hc klm^_gbkluc hkZ^hd ;he__ kbevgh_ hkgh\Zgb_ DHG \ul_kgy_l keZ[h_ b iehoh jZkl\hjb fh_&X2+ Bhggu_mjZ\g_gbyj_Zdpbc Z &2± + +&2 +2&2n [ )H 2+± )H2+ p
\ + 2+± +2 ] &2± + +&2 +2&2n ^ &X 2+± &X2+ p
Ijh\_^_f ke_^mxsb_ij_\jZs_gby &X62 o &X2+ o &X2o &X&O >ey ihemq_gby ba jZkl\hjZ &X62 g_jZkl\hjbfh]h &X2+ g_ h[oh^bfh _]h \ul_kgblv k ihfhsvx dZdh]hgb[m^v jZkl\hjbfh]h hkgh\ZgbygZijbf_j1D2+ &X62 1D2+ &X2+ p 1D62 >eylh]hqlh[uihemqblv &X2jZaeh`bf]b^jhdkb^f_^bgZ]j_ \Zgb_f &X2+
±&
&X2 + 2
ey ihemq_gby ba hkgh\gh]h hdkb^Z &X2 kheb &X&O g_h[oh ^bfh^h[Z\blvkhhl\_lkl\mxsmxdbkehlml_+&O &X2+&O &X&O +2
J_Zdpby g_cljZebaZpbb ² wlh j_Zdpby f_`^m dbkehlhc b hkgh \Zgb_f gZijbf_j jZkl\hju k_jghc dbkehlu +62 b ]b^jhdkb^Z gZljby1D2+ >h[Z\bf eZdfmk kgZqZeZ d bkoh^guf jZkl\hjZf < dbkehc kj_^_ eZdfmkbf__ldjZkgmxhdjZkdm\ s_ehqghckj_^_² kbgxxhdjZkdm +62 1D2+ 1D62 +2 + 2+± +2 < g_cljZevghckj_^_eZdfmkhdjZkdmg_f_gy_l
Ihemqbf)H2+ j_Zdpb_cjZkl\hjZ)H&O k 1D2+ )H&O 1D2+ )H2+ p 1D&O ey_]h hl^_e_gby ijhnbevljm_f kf_kv LZd`_ \ j_Zdpbb fh`gh bkihevah \ZlvjZkl\hjDHG
DKH +&O .&O+2&2n &D&2 +&O &D&O +2&2n
Ijh\_^_fg_kdhevdhj_Zdpbc Z <_s_kl\Z ^he`gu kh^_j`Zlv bhgu
IjZdlbq_kdh_aZgylb_ Bamq_gb_\ebygbymkeh\bc gZkdhjhklvobfbq_kdboj_Zdpbc
J_Zdpbyb^_l[uklj__\ ijh[bjd_k fek_jghcdbkehlu $O+62 $O62 +n
;uklj__b^_lj_Zdpby\ gZ]j_lhcijh[bjd_
K fjZfhjghc djhrdhc j_Zdpby b^_l [uklj__ l_ aZdhgqblky jZgvr_ &D&2 +&O &D&O +2&2n
IjZdlbq_kdh_aZgylb_ Ihemq_gb_ZffbZdZb bamq_gb__]hk\hckl\ HagZdhfe_gb_khk\hckl\Zfb \h^gh]hjZkl\hjZZffbZdZ
Ihemq_gb_ZffbZdZ IjZ\bevgh_iheh`_gb_ijh[bjdbih^[
Ijh[bjdb^he`gu[ulvkmobfbldZffbZdj_Z]bjm_lk \h^hcb \ j_amevlZl_h[jZam_lky]b^jhdkb^Zffhgby 1+ +2 1+2+ J_Zdpbyihemq_gbyZffbZdZ W 1+&O&D2+ 1+n &D&O +2 Bamq_gb_k\hckl\ZffbZdZ
:ffbZdohjhrhjZkl\hjy_lky\ \h^_ 1+ +2 1+2+ BaaZ jZkl\hj_gby ZffbZdZ \ ijh[bjd_ mf_gvrZ_lky ^Z\e_gb_ qlh ijb\h^bl d \kZku\Zgbx \h^u \ ijh[bjdm Ihemq_gguc jZkl\hj k n_ghenlZe_bghf ^Z_l fZebgh\uc p\_l ihkdhevdm 1+2+± hkgh 1+2+ 1+ 2+± \Zgb_
< ijh[bjd_k 1+ h[jZam_lky[_euciZj 1+ +&O 1+&On 1+ +12 1+12n K k_jghcb nhknhjghcdbkehlhchiulg_ihemqZ_lkyihlhfmqlh 1+ 62 b 1+ 32 g_e_lmqb 1+ +62 1+ 62 1+ 62 1+ 62± 1+ +32 1+ 32 1+ 32 1+ 32± JZkl\hj h[_kp\_qb\Z_lky ihkdhevdm k_jgZy dbkehlZ g_cljZebam _l ZffbZd l_ kj_^Z klZgh\blky g_cljZevghc < g_cljZevghc b db kehckj_^_n_ghenlZe_bg[_kp\_lguc 1+2++62 1+ 62 +2 1+2++62 1+ +62 +2 K ba[uldhf+62 h[jZam_lkydbkeZykhev
IjZdlbq_kdh_aZgylb_ JZkihagZ\Zgb_fbg_jZevguom^h[j_gbc
HsmsZ_lkyaZiZoZffbZdZ
W
1+ +2 1D12
GZljb_\Zyk_ebljZ² 1D12 1D12 +62dhgp &X 1D62 &X62 12n +2 F_^vjZkl\hjy_lky
KmevnZlZffhgby² 1+ 62 1+ 62 %D&O %D62p 1+&O
DZeb_\Zykhev² .&O .&O$J12 .12 $J&Op
IjZdlbq_kdh_aZgylb_ Ihemq_gb_KH b bamq_gb__]hk\hckl\ JZkihagZ\Zgb_dZj[hgZlh\
FjZfhjbf__lmijhs_ggmxobfbq_kdmxnhjfmem² KZKH GZibr_f_]hmjZ\g_gb_j_Zdpbbk jZkl\hjhf+&O &D&2 +&O &D&O +2&2n DZjlhggufdjm`dhfklZdZgijbdju\Zxl^eylh]hqlh[ug_me_ lmqb\Zekym]e_dbkeuc]Za
Ijb \g_k_gbb \ klZdZg k m]e_dbkeuf ]Zahf kibqdZ lmog_l ld m]e_dbkeuc ]Za g_ ih^^_j`b\Z_l ]hj_gby M]e_dbkeuc ]Za fh`gh i_j_eb\Zlv ba h^gh]h klZdZg \ ^jm]hc ld hg ly`_e__ \ha^moZ b hk_^Z_lgZ^g_ Nbabq_kdb_k\hckl\Z KH ² [_kp\_lguc ]Za jZkl\hjbfuc \ \h^_ ly`_e__ \ha^moZ ijb l_fi_jZlmj_ ±K i_j_oh^bl \ l\_j^h_ khklhygb_ ©kmohc e_^ª fbgmy `b^dmx nZam Y\ey_lky dbkehlguf hdkb^hf ijb jZk l\hj_gbb\ \h^_h[jZam_lg_mklhcqb\mxm]hevgmxdbkehlm &2 +2 +&2 + &2 ± EZdfmkhdjZkbeky\ djZkgucp\_lld\ \h^_ihke_ijhimkdZgby KH h[jZam_lkym]hevgZydbkehlZ IjbgZ]j_\Zgbbm]hevgZydbkehlZjZaeZ]Z_lkyh[jZlghgZKH b GH W +&2 +2 &2 KH me_lZ_leZdfmkijbgbfZ_li_j\hgZqZevgucp\_l
GZ[ex^Z_lky ihfmlg_gb_ jZkl\hjZ gZ ijZdlbd_ wlh bkihevam_l kyijbih[_ed_kl_gIjhbkoh^blj_Zdpby KZHG KH KZKHp GH Ba[ulhd KH jZkl\hjy_l dZj[hgZl dZevpby H[jZam_lky dbkeZy khev KZKH GH KH KZGKH Ijb ^h[Z\e_gbb ba\_kldh\hc \h^u hiylv h[jZam_lky dZj[hgZl dZevpbyjZkl\hjfmlg__l KZGKH KZHG KZKHp GH IjbgZ]j_\Zgbb]b^jhdZj[hgZljZaeZ]Z_lky &D+&2
W
&D&2 +2 &2
Ijh\_^_fj_Zdpbxf_`^mjZkl\hjZfb%D&O b 1D&2 %D&O 1D&2 %D&2p 1D&O %D &2± %D&2p ± %D &O 1D &2± %D&2p 1D &O± H[jZam_lky[_euchkZ^hd >hdZ`_fqlhhkZ^hdkh^_j`blZgbhguKH±>eywlh]hijbev_f dbkehlmgZijbf_j+&O %D&2 +&O %D&O +2&2n %D&2 + &O± %D &O± +2&2n %D&2 + %D +2&2n
IjZdlbq_kdh_aZgylb_ J_r_gb_wdki_jbf_glZevgucaZ^Zqihl_f_ ©:ahlb nhknhjª
J_Zdpby g_cljZebaZpbb ² wlh j_Zdpby f_`^m dbkehlhc b hkgh \Zgb_f Ke_^h\Zl_evgh gZf gZ^h \u[jZlv hij_^_e_ggu_ dbkehlm b hkgh\Zgb_ ijb \aZbfh^_ckl\bb dhlhjuo ihemqZ_lky g_h[oh^bfh_ \_s_kl\h Z ey hij_^_e_gby 1+ 62 kgZqZeZ ^hdZ`_f qlh \u[jZggh_ \_s_kl\h kh^_j`bl dZlbhgu Zffhgby 1+ >h[Z\bf d \_s_kl\m jZkl\hj1D2+b gZ]j__fkf_kv 1+ 62 1D2+
W
1D62 1+ +2
1+ 62± 1D 2+± 1D 62± 1+n +2 ?kebihy\bekyaZiZoZffbZdZagZqbl\_s_kl\hkh^_j`Zeh1+ L_i_jv^hdZ`_fqlh\_s_kl\hkh^_j`bl62± >eywlh]h^h[Z\bfd g_fmjZkl\hj%D&O %D&O 1+ 62 %D62p 1+&O %D &O± 1+ 62± %D62p 1+ &O± ?keb\uiZ^_l[_euchkZ^hdlh\_s_kl\hkh^_j`bl62±Ke_^h \Zl_evghwlh1+ 62
D dZ`^hc ijh[bjd_ ijbeb\Z_f jZkl\hj $J12 Ijh[bjdZ k 1+&O ^Zkl [_euc hkZ^hd $J&O k 1+ +32 ² `_eluc hkZ^hd $J32Z k1+12 ² hklZg_lky[_abaf_g_gbc $J 12± 1+ &O± $J&Op 1+ 12± $J 12± 1+ +32± $J32p 1+ + 12±
Ihke_^h\Zl_evgh ijbeb\Z_f jZkl\hj ba h^ghc ijh[bjdb d jZk l\hjZf ^jm]bo ?klv \ZjbZglZ \uiZ^Z_l [_euc hkZ^hd beb jZk l\hju\ ijh[bjdZog_baf_gylky< hfkemqZ_kheygZydbkehlZ\ lhcijh[bjd_\ dhlhjhchkZ^hdg_\uiZe\h\lhjhf² kheygZydb kehlZ ² \ lhc ijh[bjd_ dhlhjmx fu ^heb\Zeb d ^\mf ^jm]bf ;_ euchkZ^hd%D32 %D &O± 1D 32± %D32 p 1D &O± Qlh[uijh\h^bfu_j_Zdpbb[uebgZ]ey^g_cfh`ghkhklZ\blv lZ[ebqdb %D&O 1D32 +&O
%D&O
[_euchkZ^hd ²
1D32 hkZ^hd[_euc ²
² ²
+&O
Lh]^Z lZ ijh[bjdZ k dhlhjhc gbq_]h g_ ijhj_Z]bjh\Zeh b kh ^_j`bl+&O
Ijh\_^_fmdZaZggmxj_Zdpbx 1+12 &D2+ &D12 1+n +2 Bo g_evay kf_rb\Zlv ld \ j_amevlZl_ \aZbfh^_ckl\by \u^_ey _lkyZffbZd
IjZdlbq_kdh_aZgylb_ DZq_kl\_ggh_hij_^_e_gb_m]e_jh^Z b \h^hjh^Z\ hj]Zgbq_kdbo\_s_kl\Zo
Z KlZdZg aZihl_e ihlhfm qlh ijb ]hj_gbb ]ZaZ kibjlZ \u^_ eyxlky KH b \h^Z iZj IZj dhg^_gkbjm_lkygZoheh^guokl_gdZo klZdZgZ b hg aZihl_\Z_l < kemqZ_ k ]b^jhdkb^hf dZevpby [_eu_ iylgZihy\eyxlkybaaZh[jZah\ZgbyKZKH KZHG KH KZKHp GH Ba hiulZ ke_^m_l qlh \ k]hj_\r_f \_s_kl\_ _klv m]e_jh^ b \h ^hjh^
[ Wdki_jbf_glijh\h^blkyZgZeh]bqghhiulmZ MjZ\g_gb_j_Zdpbb]hj_gbyiZjZnbgZ
W 2 &2 + 2 >ey h[gZjm`_gby k\h[h^gh]h m]e_jh^Z \ ieZf_gb k\_qb gm`gh ih^_j`Zlv qbklh_ kl_deh gZ^ ieZf_g_f Kl_deh ihkl_i_ggh aZdhi lblkyWlhb _klvk\h[h^gucm]e_jh^ \ MjZ\g_gb_j_Zdpbb & +
&+ &X2
W
&2 +2 &X
Ba\_kldh\Zy \h^Z ih[_e__l \ke_^kl\b_ h[jZah\Zgby g_jZkl\hjb fh]h dZj[hgZlZ&X62 ihkbg__lbaaZh[jZah\ZgbydjbklZeeh]b^jZ lZ&X62 +2
IjZdlbq_kdh_aZgylb_ Ihemq_gb_wlbe_gZb bamq_gb__]hk\hckl\
Ihemq_gb_wlbe_gZ Dhgp_gljbjh\ZggZyk_jgZydbkehlZh[eZ^Z_lk\hckl\hfhl[bjZlv \h^m m ^jm]bo \_s_kl\ Wlh k\hckl\h bkihevah\Zgh ^ey ihemq_gby wlbe_gZ &+2+
+62 dhgp W
&+ +2
W
&2 +2
IjZdlbq_kdh_aZgylb_ Bamq_gb_k\hckl\ )Hb _]hkh_^bg_gbc GZ[ex^Z_lky \u^_e_gb_ ]ZaZ Wlhl ]Za ² \h^hjh^ dhlhjuc h[ jZam_lkyijbj_Zdpbb )H+62 )H62 +n )H +&O )H&O +n =\ha^v\g_k_gguc\ &X&Oihdju\Z_lkyf_^vx\ke_^kl\b_we_d ljhobfbq_kdhcj_Zdpbb )H&X&O )H&O &Xp )HR &X &XR )H < h[hbokemqZyohdkb^`_e_aZjZkl\hjy_lkyijbgZ]j_\Zgbb W )H2 + &O± )H &O± +2 W )H2 + 62± )H 62± +2
< h[_boijh[bjdZoh[jZamxlkyklm^_gbklu_hkZ^db HkZ^hd)H2+ ² [mjucZ )H2+ ² [_eucgh[ukljh[mj__l baaZh[jZah\Zgby)H2+ hdbkey_lky\ha^mohf )H &O± 1D 2+± )H2+ p 1D &O± )H &O± 1D 2+± )H2+ p 1D &O± Ijb ^h[Z\e_gbb kheyghc dbkehlu d ]b^jhdkb^m `_e_aZ,, ]b^ jhdkb^ jZkl\hjy_lky ijb ^h[Z\e_gbb ]b^jhdkb^Z gZljby ² g_l < kemqZ_ )H2+ ]b^jhdkb^ jZkl\hjy_lky dZd ijb ^h[Z\e_gbb 1D2+ lZdb +&O &O± )H2+ + +2)H &O± &O± )H2+ + +2)H &O± 1D )H2+ 2+± 1D >)H2+ @± HkZ^hdih[mj_e)H2+ hdbkebeky\ha^mohf^h)H2+ )H2+ 2 +2 )H2+
Ihke_keb\ZgbyjZkl\hjh\h[jZam_lkykbgbcjZkl\hj )H&O .>)H&1 @ .)H>)H&1 @.&O
H[jZah\Z\rbckydhfie_dkgZau\Z_lkylmjg[mee_\Zkbgv Ijbkeb\ZgbbjZkl\hjh\)H&O b .6&1h[jZam_lkyyjdhdjZkguc jZkl\hjHdjZkdmjZkl\hjmijb^Z_ljh^Zgb^`_e_aZ,,, ² )H6&1 )H&O .6&1 )H6&1 .&O < jZkl\hj_ijhbkoh^blqZklbqguc]b^jheba\_s_kl\Z )H62 +2 )H2+ 62 +62 BamjZ\g_gbyj_Zdpbb\b^ghqlh\ j_amevlZl_]b^jhebaZh[jZam _lky dbkehlZ l_ jZkl\hj kheb bf__l dbkemx j_Zdpbx kj_^u Ih wlhfmeZdfmk\ jZkl\hj_)H62 djZkguc
IjZdlbq_kdh_aZgylb_ J_r_gb_wdki_jbf_glZevguoaZ^Zq ihjZa^_em©F_lZeeuª
,ucgZ[hj <_s_kl\Z 1D&20J&O%D&O Ijbeb\Z_fjZkl\hjeZdfmkZd dZ`^hcijh[bjd_lZf]^_eZdfmk ihkbg__lgZoh^blky1D&2 s_ehqgZykj_^Z 1D&2 +2 1D2+1D+&2 D ^\mfhklZ\rbfkyijh[bjdZf^h[Z\ey_f)H62 lZf]^_\u iZ^_l[_euchkZ^hdgZoh^blky%D&O %D&O )H62 )H&O %D62p < hklZ\r_ckyijh[bjd_gZoh^blkyke_^h\Zl_evgh0J&O ,,hcgZ[hj <_s_kl\Z 1D&2&D&O.&O EZdfmkhfhij_^_ey_f1D&2dZd\ i_j\hfgZ[hj_ D ^\mfhklZ\rbfkyijh[bjdZf^h[Z\ey_fjZkl\hjdZj[hgZlZgZ ljby ijh[bjdZ \ dhlhjhc \h^Z ihfmlg__l kh^_j`bl &D&O hklZ\ rZykyijh[bjdZk .&O &D&O 1D&2 &D&2p 1D&O ,,,bc gZ[hj <_s_kl\Z$O&O%D&O)H62 D dZ`^hcijh[bjd_^h[Z\bfjZkl\hj.>)H&1 @`_elhcdjh\y ghckheb jZkl\hjhdjZkblky\ kbgbcp\_l² lZf)H62
)H62 .>)H&1 @ .)H>)H&1 @p .62 D ^\mf hklZ\rbfky ijh[bjdZf ijbeb\Z_f eZdfmk lZf ]^_ eZd fmkihdjZkg__lkh^_j`blky$O&O dbkeZykj_^Z $O&O +2 $O2+ &O +&O
KgZqZeZjZkl\hjbfihjhrdb\ \h^_bao ihjhrdh\jZkl\hjbl kylhevdhkh^Z D hklZ\rbfky ^\mf ihjhrdZf ijbev_f jZkl\hj +62 \u^_e_ gb_imaujvdh\]ZaZmdZau\Z_lgZKZKH f_e hklZ\r__ky\_s_kl\h ² ]bik&D62 +62 &D&2 &D62p +2&2n + 62± &D&2 &D62p +2&2n <j_f_ggZy`_kldhklv &D+&2 &D2+ &D&2p +2 W &D+&2 &D&2p +2&2n MkljZg_gb_ihklhygghc`_kldhklb &D62 1D&2 &D&2p 1D62
Ijh\_^_fg_kdhevdhj_Zdpbc Z &D2+ o &D&2 o&D+&2 o &D&2 o &D&O &D2+ &2 &D&2p +2 &D&2 &2 +2 &D +&2± W &D+&2 &D&2p +2&2n &D&2 + &O± &D&O± +2&2 &D&2 + &D&2n +2 [ 0J2o 0J&O o 0J&2 0J2+ &O± 0J &O± +2 0J2+ 0J +2 0J &O± 1D &2± 0J&2p 1D &O± 0J &2± 0J&2p
Ihemqbf $O2+ >ey wlh]h ijh\_^_f j_Zdpbx f_`^m jZkl\h jZfb$O&O b 1D2+ $O&O 1D2+ $O2+ p 1D&O $O 2+± $O2+ p
?keb ZddmjZlgh ijbeb\Zlv s_ehqv lh \uiZ^_l [_euc klm^_gb kluchkZ^hd]b^jhdkb^ZIhemq_gguchkZ^hdjZahev_fgZijh[bj dbD h^ghc^h[Z\bf+&Od ^jm]hcba[ulhd1D2+< h[hbokemqZyo hkZ^hd jZkl\hjblky Ke_^h\Zl_evgh$O2+ ² Zfnhl_jguc]b^jh dkb^ $O2+ 1D2+ 1D>$O2+ @ $O2+ 2+± >$O2+ @± $O2+ +&O +2$O&O $O2+ + $O +2 Khev_fjZkl\hju&D&O b 1D&2 &D&O 1D&2 &D&2p 1D&O Khev_fjZkl\hju1D2+b +&O 1D2++&O 1D&O+2
Ijbeb\Z_f .>)H&1 @ d )H62 h[jZam_lky oZjZdl_jguc kbgbc jZkl\hj )H 62± . >)H&1 @± .)H>)H&1 @. 62± D jZkl\hjm )H62 ijbeb\Z_f .6&1 ihemqZ_f djZkguc jZk l\hj )H 62± . 6&1± )H6&1 . 62± KgZqZeZihemqbfKZKH baKZHG b 1D&2 &D 2+± 1D &2± &D&2p 1D 2+± &D &2± &D&2p Ihemqbf&D62 ba+62 b &D2+ &D 2+± + 62± &D62p +2 KgZqZeZihemqbf]b^jhdkb^`_e_aZ )H&O 1D2+ )H2+ p 1D&O HkZ^hdhlnbevljm_fb ijhdZebf W )H2+ )H2 +2n
:exfbgbcjZkl\hjbf\ dbkehl_aZl_fhkZ^bf_]h]b^jhdkb^aZ l_fk ba[uldhfs_ehqbihemqbfjZkl\hjbfucdhfie_dk $O+&O $O&O +n $O&O 1D2+ $O2+ p 1D&O $O2+ 1D2+ 1D>$O2+ @
E:;HJ:LHJGU?HIULU Hiul Bkke_^h\Zgb_\_s_kl\ gZwe_dljbq_kdmxijh\h^bfhklv
KgZqZeZ bkke_^m_f gZ we_dljhijh\h^ghklv djbklZeebq_kdbc 1D&O ?keb ih^g_klb kmob_ we_dljh^u ijb[hjZ d kmohc kheb lh fu m\b^bf qlh l\_j^uc 1D&O g_ ijh\h^bl lhd eZfihqdZ g_ aZ ]hjZ_lky Ijh\_jbf we_dljhijh\h^ghklv ^bklbeebjh\Zgghc \h^u HdZau \Z_lkyqlhqbklZy\h^ZlZd`_g_ijh\h^bllhd L_i_jv jZkl\hjbf djbklZeebd kheb \ ^bklbeebjh\Zgghc \h^_ b \g_k_f \ ihemq_gguc jZkl\hj we_dljh^u ijb[hjZ Fu m\b^bf qlh eZfihqdZyjdhaZ]hj_eZkvl_jZkl\hj1D&O ijh\h^bllhd We_dljbq_kdbc lhd ijh\h^yl lhevdh l_ \_s_kl\Z dhlhju_ kh ^_j`Zl k\h[h^gu_ bhgu gZijbf_j jZkl\hju
Hiul Bamq_gb_^\b`_gbybhgh\ \ we_dljbq_kdhfihe_
Kfhq_gguc \ s_ehqb dhg_p gbldb hdjZkblky \ fZebgh\uc p\_l aZ kq_l n_ghenlZe_bgZ Kh \j_f_g_f hdjZr_ggZy qZklv gblb [m^_l m\_ebqb\Zlvkyb ihkl_i_gghhgZklZg_lfZebgh\hc\kyWlhy\e_gb_
ijhbkoh^bl baaZ i_j_f_s_gby ]b^jhdkhZgbhgh\ HG± \^hev gblb ih^ ^_ckl\b_f we_dljbq_kdh]h lhdZ HljbpZl_evgh aZjy`_ggu_ bh guijbly]b\Zxlkyd iheh`bl_evghfmwe_dljh^ml_HG± i_j_f_sZ _lkyhldZlh^Z©±ª d Zgh^m©ª
Ijh\_^_fZgZeh]bqguchiulk jZkl\hjhf&X62 =hem[Zy hdjZkdZ i_j_f_sZ_lky hl Zgh^Z ©ª d dZlh^m ©±ª HgZ\hagbdZ_laZkq_l&Xdhlhjucijbly]b\Z_lkyd hljbpZl_evgh fmwe_dljh^m
Hiul Ijh\_^_gb_j_Zdpbbh[f_gZ \ jZkl\hjZowe_dljheblh\
Ijh\_^_fg_kdhevdhj_Zdpbc Z
\
]
1D2++&O 1D&O+2 2+± + +2
^
I_j_qbkebf \k_ j_Zdlb\u jZkl\hju 1D2+ &D2+ +&O 1D&2.&2&D&O)H&O.12n_ghenlZe_bg GZfgm`ghihemqblvKZKH>eywlh]hih^hc^ml.&21D&2 b &D2+ &D&O AZibr_f\k_\hafh`gu_j_Zdpbb .&2 &D2+ &D&2p .2+ 1D&2 &D2+ &D&2 1D2+ .&2 &D&O &D&2p .&O 1D&2 &D&O &D&2p 1D&O
LZd`_ fh`gh ihemqblv KZKH ijh^m\Zy q_j_a jZkl\hj KZHG m]e_dbkeuc]Zak ihfhsvxljm[hqdb KZHG KH KZKHp GH
Hiul HagZdhfe_gb_ k h[jZapZfbk_ju b __ijbjh^gufb kh_^bg_gbyfb
Nbabq_kdb_k\hckl\Zk_ju K_jZy\ey_lkyl\_j^uf\_s_kl\hfg_jZkl\hjbfuf\ \h^_ijb ihiuld_ jZkl\hj_gby \kieu\Z_l gZ ih\_joghklv jZkl\hjbfZ \ g_ dhlhjuo hj]Zgbq_kdbo \_s_kl\Zo bf__l `_eluc p\_l [_a aZiZoZ e_]dhieZ\blkybf__lg_kdhevdhfh^bnbdZpbc Hibr_fijbjh^gu_fh^bnbdZpbbk_ju
GZa\Zgb_ k_jguc dheq_^Zg pbgdh\Zy h[fZgdZ k\bgph\uc [e_kd f_^guc dheq_^Zg Zg]b^jbl ]bik
fbjZ[bebl
NhjfmeZ )H6 =Q6
Nbabq_kdb_k\hckl\Z Z]j_]Zlgh_ p\_l l\_j^hklv khklhygb_ k\_leh l\_j^uc ojmidbc `_eluc l\_j^uc
[_euc
l\_j^uc
3E6
l\_j^uc
q_jguc
ojmidbc
)H&X6
l\_j^uc
q_jguc
ojmidbc
l\_j^uc
[_euc
l\_j^uc
&D62 &D62 +2 1D62 +2
l\_j^uc l\_j^uc
[_euc [_euc
ojmidbc
l\_j^uc
Hiul JZkihagZ\Zgb_kmevnZlh\
GZ[ex^Z_lky ihy\e_gb_ [_eh]h hkZ^dZ \ ijh[bjd_ k kmevnZlhf gZljby< ^jm]boijh[bjdZo\b^bfuobaf_g_gbcg_gZ[ex^Z_lky %D&O 1D62 %D62p 1D&O %D &O± 1D 62± %D62p 1D &O± %D 62± %D62p
>ey hij_^_e_gby &X62 gZ^h m[_^blvky qlh \u^Zggu_ djbklZe eukh^_j`Zl&X b 62±>eywlh]hkgZqZeZ^h[Z\bfg_fgh]h1D2+ d jZkl\hjmba\u^ZgguodjbklZeeh\ &X62 1D2+ 1D62 &X2+ p
< ijh[bjd_ k k_jghc dbkehlhc \uiZ^_l [_euc hkZ^hd < ^jm]bo ijh[bjdZogbq_]hg_ijhbkoh^bl %D&O +62 %D62p +&O
Hiul
Ijb keb\Zgbb jZkl\hjh\ 1+&O b 1D2+ \b^bfuo baf_g_gbc g_ ijhbkoh^blGZ]j_\Z_fihemq_ggmxkf_kvihqlb^hdbi_gbyg_aZ [u\Zcl_h l_ogbd_[_ahiZkghklb Ih^ghkbfd ijh[bjd_kfhq_ggmx \h^hc[mfZ`dmeZdfmkZeZdfmkkbg__lBaijh[bjdb\u^_ey_lky]Za k j_adbfoZjZdl_jgufaZiZohfWlhZffbZd W 1+&O1D2+ 1+n +21D&O >ey hij_^_e_gby 1+ 62 gm`gh hl^_evgh hij_^_eblv bhgu 1+ b 62± KmevnZlbhg hij_^_ey_lky k ihfhsvx dZlbhgZ %D gZijbf_j jZkl\hj%D&O 1+ 62 %D&O %D62p 1+&O h[Z\ey_fjZkl\hj1D2+b gZ]j_\Z_f W 1+ 62 1D2+ 1D62 1+n +2
Hiul HagZdhfe_gb_k Zahlgufbm^h[j_gbyfb
KhklZ\bfij_^eh`_ggmxlZ[ebpm
GZa\Zgb_ m^h[j_gby ZffbZqgZy k_ebljZ gZljb_\Zy k_ebljZ kmevnZl Zffhgby fhq_\bgZ
Obfbq_kdZy nhjfmeZ 1+12 1D12
1+ 62 2
&
1+ 1+
JZkl\hjbfhklv \ \h^_ ohjhrZy ohjhrZy ohjhrZy
fZeZy jZkl\hjbfhklv \ \h^_
QZklvhibehd\ hiul_jZkl\hjy_lkykeurghrbi_gb_ihy\ey_l ky[mjh_h[eZqdhijh[bjdZaZf_lghgZ]j_\Z_lky >ZggZyj_Zdpbyih^l\_j`^Z_lgZebqb_12± 1+12 +62dhgp 1+ 62 12n +2 2n :gZeh]bqgZy j_Zdpby [m^_l ijhoh^blv k gZljb_\hc k_ebljhc 1D12 Ijb gZ]j_\Zgbb gZqbgZ_l \u^_eylvky ]Za k j_adbf oZjZdl_jguf aZiZohfEZdfmkhdjZrb\Z_lky\ kbgbcp\_lWlhl]ZaZffbZd W 1+12 1D2+ 1+n +21D12
Hiul HagZdhfe_gb_k nhknhjgufbm^h[j_gbyfb
KhklZ\bfij_^eh`_ggmxlZ[ebpm
GZa\Zgb_ m^h[j_gby ^\hcghc kmi_jnhknZl nhknhjblgZy fmdZ
Zffhnhk
Obfbq_kdZy nhjfmeZ &D+32 &D32
1+ +32 1++32
JZkl\hjbfhklv \ \h^_ ohjhrZy
hq_gviehoZy ohjhrZy
GZa\Zgb_ m^h[j_gby
Obfbq_kdZy nhjfmeZ
ijhklhc kmi_jnhknZl
&D+32 &D62
ij_pbiblZl
&D+32
JZkl\hjbfhklv \ \h^_ kj_^gyy kj_^gyy
Ijb ^h[Z\e_gbb d h[hbf jZkl\hjZf \uiZ^Z_l `_eluc hkZ^hd $J32 $J12 &D+32 $J32p +12 &D12 $J12 1+ +32 $J32p 1+12 +12 $J12 1++32 $J32p 1+12 +12 Ijb^h[Z\e_gbb\ ijh[bjdb+12 hkZ^dbjZkl\hjyxlky $J32 +12 $J12 +32 ;he__kbevgZydbkehlZ\ul_kgy_l[he__keZ[mx
Hiul HagZdhfe_gb_khk\hckl\Zfb dZj[hgZlh\b ]b^jhdZj[hgZlh\
Ijb ^h[Z\e_gbb +&O \u^_ey_lky [_kp\_lguc ]Za Kibqb \ ijh [bjdZoihlmoebl_]Zag_ih^^_j`b\Z_l]hj_gb_Wlhl]Za² m]e_ dbkeuc &D&2 +&O &D&O +2&2n &D&2 + &O± &D &O± +2&2n &D&2 + &D +2&2n 1D&2 +&O 1D&O+2&2n 1D &2± + &O± 1D &O± +2&2n &2± + +2&2n
[ Ijb gZ]j_\Zgbb 1D+&2 hieu\Z_l b mf_gvrZ_lky \ h[t_f_
< mq_[gbd_ ^hims_gZ hrb[dZ ih \k_c \b^bfhklb \ i_j\mx ijh [bjdmgZebebfejZkl\hjZ1D&2\ ^jm]mxihf_klbebdmkhdf_eZ KZKH b ^hebebfe\h^u>h[Z\beb\ h[_ijh[bjdbih²dZieb n_ghenlZe_bgZ < ijh[bjd_ k jZkl\hjhf 1D&2 n_ghenlZe_bg hd jZrb\Z_lky \ fZebgh\uc p\_l < jZkl\hj_ ijhbkoh^bl qZklbqguc ]b^jhebadZj[hgZlZgZljbyl_jZkl\hjbf__ls_ehqgmxkj_^m 1D&2 +2 1D+&2 1D2+ F_eiehohjZkl\hjy_lkyb \ijh[bjd_gbq_]hg_ijhbkoh^bl Ijbj_ZdpbbjZkl\hjh\1D&2 b &D&O \uiZ^Z_l[_euchkZ^hd 1D&2 &D&O &D&2p 1D&O &2± &D &D&2p Ijb ^h[Z\e_gbb jZkl\hjZ+12 hkZ^hdjZkl\hjy_lky
Hiul HagZdhfe_gb_k ijbjh^gufbkbebdZlZfb
D\Zjp bkihevam_lky ^ey \ukhdhdZq_kl\_ggh]h l_jfhklhcdh]h kl_deZ b ijb jZaebqguo obfbq_kdbo kbgl_aZo Ihem^jZ]hp_gguc dZf_gv yrfZ bkihevam_lky \ dZq_kl\_ ih^_ehqgh]h Dj_fgbc bk ihevam_lky \ ihemijh\h^gbdh\hc l_ogbd_ I_khd bkihevam_lky \ ijhba\h^kl\_kl_deZb \kljhbl_evkl\_
KhklZ\bfij_^eh`_ggmxlZ[ebpm GZa\Zgb_ KhklZ\ K\hckl\Z kbebdZlZ f_lZkbebdZl [_eucp\_l 1D6L2 gZljby fy]q_kl_deZ f_lZkbebdZl [_eucp\_l .6L2 dZeby fy]q_kl_deZ hjlhkbebdZl [_eucp\_l 1D6L2 gZljby fy]q_kl_deZ kf_kvd\ZjpZ ihe_\h]hriZlZ ]jZgbl a_jgbkluc b kex^ 6L2 [_euc
dZhebg
.2$O2 6L2
$O6L2 2+
[_euc
kex^Z
.+$O6L2
ojmidZy
Zk[_kl
0J6L22+
ihe_\hcriZl
lZevd
GZa\Zgb_
hdhggh_
eZ[hjZlhjgh_ d\Zjp_\h_
0J6L2HG
[_euc h]g_mihjguc [_euc h]g_mihjguc
Ijbf_g_gb_
^_eZxlde_c b kl_deZ ^_eZxlde_c b kl_deZ ^_eZxlde_c b kl_deZ
hl^_edZ kljhbl_evgu_ fZl_jbZeu khklZ\ghc dhfihg_gl ]jZgblZ ba^_ebyba ]ebgu khklZ\ghc dhfihg_gl ]jZgblZ h]g_mihjgu_ fZl_jbZeu h]g_mihjgu_ fZl_jbZeu
Hiul HagZdhfe_gb_k \b^Zfbkl_deZ
Kujv_^eyihemq_gby Ijbf_g_gb_ 6L21D&2&D&2 hdgZ ^h[Z\db0J2)H2%2 6L21D&2.&2&D&2 eZ[hjZlhjgZy ih ^h[Z\db 0J2 )H2 %2 km^Z $O2 6L21D&2.&2&D&2 \ukhdhdZq_kl\_g ^h[Z\db %D2 $O2 )H2gZy eZ[hjZlhjgZy %2 ihkm^Z gZ]j_\Z gb_b l^
Hiul Ba]hlh\e_gb_fh^_e_cfhe_dme hj]Zgbq_kdbokh_^bg_gbc
: Ihlhfmqlhwlhlm]hec gZb[he__\u]h^_g^eyfhe_dmeu ihemqZ_lky kbff_ljbqgZy kljmdlmjZ Zlhfu b jZ\gh hl^Ze_gu ^jm] hl^jm]Zb gZoh^ylkygZh^bgZdh\hfjZkklhygbbhlZlhfZK:lhfu \h^hjh^Zh[jZamxll_ljZw^jijbq_fZlhf&jZkiheh`_g\ p_glj_ IjhkljZgkl\_ggh_kljh_gb_g_baf_gbehkv
H[s__ m]eu f_`^m k\yayfb h^bgZdh\u ^ey jZaguo fhe_dme c Ab]aZ]hh[jZagh_ kljh_gb_ m]e_jh^ghc k\yab h[tykgy_lky m]ehf c b kihkh[ghklvx k\h[h^gh \jZsZlvky IjhkljZgkl \_ggu_ bahf_ju g_evay \u^_eblv ihlhfm qlh m]e_\h^hjh^gu_ jZ ^bdZeu\jZsZxlkyk\h[h^ghhlghkbl_evgh^jm]^jm]Z JZaf_j\Ze_glguom]eh\khojZgy_lky
M ^boehjf_lZgZ bahf_jh\g_lM ^boehjwlZgZ² bahf_jZ &O&+²&+&O² ^boehjwlZg &O&+²&+ ² ^boehjwlZg ;F_lbeZfbgy\ey_lkyijhba\h^guf&+ b 1+
Ijhba\h^gh_ ZffbZdZ ^\Z ZlhfZ G aZf_s_gu ^\mfy jZ^bdZev gufb]jmiiZfb²KG
Hiul I_j_]hgdZg_nlb
KjZ\gbfk\hckl\Zi_j\bqgh]hb \lhjbqgh]hdhg^_gkZlhjh\
I_j\bqgucdhg^_gkZlhj e_]dhih^\b`guc hkljucaZiZo gZihfbgZxsbcd_jhkbg \j_fy\ukuoZgbyk_dmg^
\j_fy\ukuoZgbyk_dmg^
Hiul G_nlvb ijh^mdlu__ i_j_jZ[hldb
AZihegbflZ[ebpm
K\_leu_g_nl_ijh^mdlu GZa\Zgb_ Ijbf_g_gb_ ^\b]Zl_eb ;_gabg Z\lhfh[be_c Z\bZpbhggh_ D_jhkbg lhieb\h
L_fgu_g_nl_ijh^mdlu GZa\Zgb_ Ijbf_g_gb_ =Zahcev
KfZahqgu_ \_s_kl\Z
lhieb\h^eyLWK
Ijh^mdlui_j_jZ[hldbdZf_ggh]hm]ey
L\_j^u_ijh^mdlu ]^_ gZa\Zgb_ bkihevam _lky f_lZeemj dhdk ]by
kfZadZ
@b^db_ijh^mdlu =Zahh[jZagu_ijh^mdlu ]^_bkihev ]^_bkihev gZa\Zgb_ gZa\Zgb_ am_lky am_lky obfbq_kdbc k\_lbevguc kfheZ h[h]j_\ kbgl_a ]Za obfbq_kdZy ZffbZd ijhfure_g ghklv
Hiul HagZdhfe_gb_k f_lZeeZfb
JZkkfhljbf$O&X)H=Q Z H[sb_ k\hckl\Z \ukhdZy l_ieh b we_dljhijh\h^bfhklv f_ lZeebq_kdbc[e_kd [ &X² djZkgucp\_l^hklZlhqghbg_jlgZyd obfbq_kdbf\_s_ kl\Zf )H² l_fghk_jh_h[eZ^Z_lfZ]gblgufbk\hckl\Zfbl\_j^h_ =Q² k\_lehk_juc^hklZlhqghZdlb\gucfy]dbc $O² k_j_[jbkluce_]dbcfy]dbchdkb^gZyie_gdZ \ =Q$O&X)H ] &X$O)H=Q
Hiul HagZdhfe_gb_khkieZ\Zfbf_lZeeh\
Ki_pbZevgh ihemq_ggu_ kieZ\u l\_j`_ f_lZeeh\ b ijhqg__ JZaebqgu_kieZ\uh[eZ^ZxljZagufbk\hcql\Zfb KieZ\u i_j_gbfZxl k\hckl\Z h[jZamxsbo bo f_lZeeh\ gh djhf_ lh]h ijbh[j_lZxl k\hb l\_j^hklv ijhqghklv ih\ur_ggZy we_dljhijh\h^bfhklvbebgZh[hjhl
Hiul Bamq_gb_\aZbfh^_ckl\by f_lZeeh\k jZkl\hjZfbkhe_c
GZ[ex^Z_lky\u^_e_gb_gZ]jZgmeZopbgdZf_lZeeh\ =Q)H&O =Q&O )Hp =Q&X&O &Xp =Q&O $O&O =Q $Op =Q&O
:exfbgbc\ul_kgy_lf_^vb `_e_ah`_e_ah² lhevdhf_^v $O)H&O $O&O )Hp $O&X&O $O&O &Xp )H&X&O &Xp )H&O Wdki_jbf_glZevgucjy^\hkklZgh\bl_evghckbeuf_lZeeh\ $O=Q)H&X kh\iZ^Z_lk jy^hfZdlb\ghklb
Hiul Bamq_gb_obfbq_kdbok\hckl\Zexfbgby
J_Zdpby kgZqZeZ b^_l f_^e_ggh ld ih\_joghklv Zexfbgby ih dju\Z_l hdkb^guc kehc Ihke_ _]h jZkl\hj_gby gZqbgZ_l j_Z]bjh \Zlv kZf f_lZee Ihy\eyxlky imaujvdb ]ZaZ dhlhjuc fh`gh ih^ `_qv_kebhl\h^blv_]hq_j_a]Zahhl\h^gmxljm[dm $O2 +&O $O&O +2² jZkl\hj_gb_hdkb^gh]hkehy $O+&O $O&O +n ² jZkl\hj_gb_f_lZeeZ G H GH ² ]hj_gb_\h^hjh^Z :exfbgbcihkl_i_gghjZkl\hjy_lky\ s_ehqb $O1D2++2 1D>$O2+ @+n + 2 +2² ]hj_gb_\h^hjh^Z
Hiul Bamq_gb_Zfnhl_jguok\hckl\]b^jhdkb^ZZexfbgby
Ijb ^h[Z\e_gbb d jZkl\hjm kheb Zexfbgby s_ehqb h[jZam_lky klm^_gbkluchkZ^hd $O&O 1D2+ $O2+ p 1D&O $O 2+± $O2+ p < h[_boijh[bjdZohkZ^hdjZkl\hjy_lky $O2+ +62 $O62 +2 $O2+ + $O +2 $O2+ 1D2+ 1D>$O2+ @ $O2+ 2+± >$O2+ @±
Hiul HagZdhfe_gb_k Zexfbgb_fb _]hkieZ\Zfb
Koh^kl\hf_`^mkZfbfZexfbgb_f b_]hkieZ\Zfbk_j_[jbkluc [e_kd \ukhdZy we_dljhijh\h^ghklv \ukhdZy l_iehijh\h^ghklv e_]dhklvfZeZyiehlghklv Hlebqby$O² fy]dbcf_lZeekieZ\uqZs_\k_]hl\_j^u_ AZihegbflZ[ebpm GZa\Zgb_kieZ\Z
kbemfbg ^mjZexfbgbc
KhklZ\kieZ\Z ²6L ²0J ²0Q ²&X ²0J ²0Q
Ijbf_g_gb_ ^eyhleb\db^_lZe_c ihjrgb dhjh[db kdhjhkl_c ^ey h[rb\db kZfh e_lh\Z\lh[mkh\
Hiul HagZdhfe_gb_k ijbjh^gufbkh_^bg_gbyfbdZevpby AZihegbflZ[ebpm GZa\Zgb_ NhjfmeZ &D62 +2 ]bik Zg]b^jbl
&D62
nhknhjbl
&D32 2+
fjZfhj
&D&2
f_e
ba\_klgyd
&D&2 &D&2
ihebdjbklZee ihjhrhd
Ijbf_g_gb_ f_^bpbgZ kljhbl_evguc fZl_jbZe m^h[j_gby ibkvfh ih[_edZ kljhbl_evguc fZl_jbZe kljhbl_evguc fZl_jbZe
MjZ\g_gbyj_Zdpbb W &D&2 &D2&2n ² ihemq_gb_``_ghcba\_klb &D2 +2 &D2+ ² gZ[ex^Z_lky Zdlb\gh_ \aZbfh^_ckl\b_ k \h^hcb \u^_e_gb_l_ieZ² ihemq_gb_]Zr_ghcba\_klb N_ghenlZe_bghdjZrb\Z_ljZkl\hj\ fZebgh\ucp\_l
Hiul HagZdhfe_gb_k qm]mghfb klZevx
AZihegbflZ[ebpm GZa\Zgb_kieZ\Z
KhklZ\kieZ\Z &² 6L² 0Q² qm]mgebl_cguc 3² 6 &² 6L² klZevfZjl_gh\kdZy 0Q² 3g_[he__ 6g_[he__ & 6L² ojhfhgbd_e_\ZyklZevg_ 0Q² j`Z\_xsZyb dbkehlhklhc 3 dZy 6
Ijbf_g_gb_
ijhba\h^kl\hklZeb hleb\dZqm]mgguo ^_lZe_cfZrbg ba]hlh\e_gb_^_lZe_c fZrbgb \\b^_ ihemnZ[jbdZlh\ ba]hlh\e_gb_^_lZe_c fZrbgb \\b^_ ihemnZ[jbdZlh\