Химия. 9 класс. Рудзитис Г.Е., Фельдман Ф.Г. 1999 год.

Page 1

>hfZrgyy jZ[hlZ ih obfbb aZ deZkk

d mq_[gbdm ŠObfby deZkkª = ? Jm^ablbk N = N_ev^fZg F ŠIjhk\_s_gb_ª ] mq_[gh ijZdlbq_kdh_ ihkh[b_

KH>?J@:GB?

=eZ\Z , †† ± klj †† ± klj =eZ\Z ,, †† ± klj † klj ± =eZ\Z ,,, †† ± klj =eZ\Z ,9 †† ± klj †† ± klj ± †† ± klj ± =eZ\Z 9 †† ± klj ± †† ± klj =eZ\Z 9, †† ± klj ± =eZ\Z 9,, † klj ± †† ± klj ± † klj =eZ\Z 9,,, †† ± klj ± =eZ\Z ,; †† ± klj =eZ\Z ; †† ± klj †† ± klj EZ[hjZlhjgu_ jZ[hlu EZ[hjZlhjgu_ hiulu , ,, ,,, klj

IjZdlbq_kdZy jZ[hlZ ‹ klj EZ[hjZlhjgu_ hiulu ,9 9 9, klj EZ[hjZlhjguc hiul 9,, klj IjZdlbq_kdZy jZ[hlZ ‹ klj EZ[hjZlhjgu_ hiulu 9,,, ,; klj IjZdlbq_kdb_ jZ[hlu ‹ ‹ klj EZ[hjZlhjguc hiul ;, klj IjZdlbq_kdZy jZ[hlZ ‹ klj EZ[hjZlhjguc hiul ;9 klj EZ[hjZlhjguc hiul 9,,, klj IjZdlbq_kdZy jZ[hlZ ‹ klj IjZdlbq_kdb_ jZ[hlu ‹ ‹ klj EZ[hjZlhjgu_ hiulu ;,; ;; klj

=eZ\Z ,

†† ¹ klj <hijhk ‹

Ihykgbl_ ihq_fm jZkl\hj kZoZjZ g_ ijh\h^bl we_dljbq_kdbc lhd Z jZkl\hj oehjb^Z gZljby ijh\h^bl

Hl\_l JZkl\hj ih\Zj_gghc kheb y\ey_lky we_dljheblhf Ijb jZkl\h j_gbb \ \h^_ bhggZy djbklZeebq_kdZy j_r_ldZ 1D&O jZajmrZ_lky 1D&O 1D KO JZkl\hj kZoZjZ g_ y\ey_lky we_dljheblhf Fhe_dmeu kZoZjZ bf_xl dh\Ze_glgmx g_iheyjgmx k\yav ijb jZkl\hj_gbb kZoZjZ \ \h^_ jZajmr_gb_ _]h fhe_dmeu b h[jZah\Zgb_ aZjy`_gguo bhgh\ g_ ijhbkoh^bl ihwlhfm lZdhc jZkl\hj we_dljbq_kdh]h lhdZ g_ ijh\h^bl

<hijhk ‹

I_j_qbkebl_ hkgh\gu_ ijbqbgu \uau\Zxsb_ jZkiZ^ g_dhlhjuo \_ s_kl\ gZ bhgu ijb jZkl\hj_gbb bo \ \h^_ beb jZkieZ\e_gbb

Hl\_l Fhe_dmeu \h^u iheyjgu <ke_^kl\b_ wlh]h gZijbf_j ijb jZkl\hj_gbb oehjb^Z gZljby fhe_dmeu \h^u ijbly]b\Zxlky k\hb fb hljbpZl_evgufb ihexkZfb d iheh`bl_evgh aZjy`_gguf bhgZf gZljby Z iheh`bl_evgufb ihexkZfb Âą d hljbpZl_evgh aZjy`_g guf oehjb^ bhgZf < j_amevlZl_ k\yav f_`^m bhgZfb hkeZ[ey_lky b djbklZeebq_kdZy j_r_ldZ jZajmrZ_lky Wlhfm ijhp_kkm kihkh[ kl\m_l lZd`_ [hevrZy ^bwe_dljbq_kdZy ijhgbpZ_fhklv \h^u dhlh jZy ijb ƒK jZ\gZ Obfbq_kdZy k\yav f_`^m bhgZfb \ \h^_ hk eZ[ey_lky \ jZa ih kjZ\g_gbx k \Zdmmfhf Ijb jZkl\hj_gbb \ \h^_ \_s_kl\ k dh\Ze_glghc kbevghiheyj ghc k\yavx gZijbf_j dbkehl ih^ \ha^_ckl\b_f fhe_dme \h^u ijhbkoh^bl baf_g_gb_ oZjZdl_jZ k\yab b hgZ ij_\jZsZ_lky \ bhg gmx ihke_ q_]h ijhp_kk jZkl\hj_gby ijhbkoh^bl dZd m \_s_kl\ k bhgghc k\yavx Ijb jZkieZ\e_gbb we_dljheblh\ mkbeb\Zxlky dhe_[Zl_evgu_ ^\b`_gby qZklbp \ j_r_ld_ qlh ijb\h^bl d hkeZ[e_gbx k\yab f_ `^m gbfb < j_amevlZl_ djbklZeebq_kdZy j_r_ldZ jZajmrZ_lky b \_s_kl\Z jZkiZ^Zxlky gZ bhgu

<hijhk ‹

Knhjfmebjmcl_ hkgh\gu_ l_hj_lbq_kdb_ iheh`_gby we_dljheblbq_ kdhc ^bkkhpbZpbb b ihykgbl_ bo

Hl\_l Ijhp_kk jZkiZ^Z we_dljheblZ gZ bhgu ijb jZkl\hj_gbb _]h \ \h^_ beb jZkieZ\e_gbb Âą we_dljheblbq_kdZy ^bkkhpbZpby We_dljheblu Âą wlh \_s_kl\Z dhlhju_ ijb jZkl\hj_gbb \ \h^_ beb \ jZkieZ\_ jZkiZ^Zxlky gZ bhgu Bhgu Âą wlh Zlhfu beb ]jmiiu Zlhfh\ h[eZ^Zxsb_ iheh`bl_evguf dZlbhgu beb hljb pZl_evguf Zgbhgu aZjy^hf Bhgu hlebqZxlky hl Zlhfh\ ih kljh_gbx b ih k\hckl\Zf 1Dƒ H H OH Âą Zlhf gZljby 1D H H Âą dZlbhg gZljby < jZkl\hj_ b jZkieZ\_ we_dljheblZ bhgu ^\b`mlky oZhlbq_ kdb Ijb ijhimkdZgbb ihklhyggh]h lhdZ q_j_a jZkl\hj beb q_j_a jZkieZ\ dZlbhgu ^\b`mlky d hljbpZl_evghfm we_dljh^m Âą dZlh^m Z Zgbhgu Âą d iheh`bl_evghfm we_dljh^m Âą Zgh^m

<hijhk ‹

Oehj \oh^ysbc \ khklZ\ oehjb^Z gZljby b kheyghc dbkehlu g_ hdZ au\Z_l \j_^gh]h ^_ckl\by gZ hj]Zgbaf q_eh\_dZ Z \^uoZgb_ g_[hevrh]h dhebq_kl\Z ]Zahh[jZagh]h oehjZ \uau\Z_l m^mrv_ b ihjZ`_gb_ hj]Zgh\ ^uoZgby H[tykgbl_ wlh y\e_gb_

Hl\_l < khklZ\ fhe_dmeu oehjb^Z gZljby b kheyghc dbkehlu \oh^bl bhg oehjZ KO Hg hlebqZ_lky ih k\hckl\Zf hl Zlhfh\ oehjZ \oh ^ysbo \ fhe_dmem ]Zahh[jZagh]h oehjZ Ihwlhfm \^uoZgb_ gZ ijbf_j oehjb^Z gZljby g_ \uau\Z_l \j_^gh]h \ha^_ckl\by Fhe_dmeZ ]Zahh[jZagh]h oehjZ khklhbl ba ^\mo Zlhfh\ oehjZ k\yaZgguo dh\Ze_glghc g_iheyjghc k\yavx =Zahh[jZaguc oehj g_ y\ey_lky we_dljheblhf Wlh `_elh a_e_guc ]Za k j_adbf jZa^jZ `Zxsbf aZiZohf \^uoZgb_ dhlhjh]h \uau\Z_l m^mrv_ b ihjZ`_ gb_ hj]Zgh\ ^uoZgby

<hijhk ‹

KmevnZl f_^b ,, Âą [_eh_ ihjhrdhh[jZagh_ \_s_kl\h ijb _]h jZk l\hj_gbb \ \h^_ jZkl\hj ijbh[j_lZ_l ]hem[mx hdjZkdm Q_f wlh fh`gh h[tykgblv"

Hl\_l Ijb jZkl\hj_gbb &X62 \ \h^_ ijhbkoh^bl ^bkkhpbZpby &X62 &X 62

Ijb jZkl\hj_gbb \ \h^_ &X62 lZd `_ ijhbkoh^bl obfbq_kdZy j_Zdpby ]b^jZlZpbb \ j_amevlZl_ dhlhjhc h[jZam_lky djbklZeeh ]b^jZl kmevnZlZ f_^b JZkl\hj ijbh[j_lZ_l ]hem[mx hdjZkdm &X62 G H o &X62 ˜ G H [_eh]h p\_lZ

]hem[h]h p\_lZ

<hijhk ‹

MdZ`bl_ hlebqby \ kljh_gbb b k\hckl\Zo bhgh\ b Zlhfh\ gZijbf_j ^ey dZevpby b nlhjZ

Hl\_l :lhf dZevpby ± KZ _ _ _ _ Bhg dZevpby ± KZ _ _ _ :lhf dZevpby kha^Z_l gZjm`gu_ we_dljhgu ihwlhfm obfbq_ kdb Zdlb\_g y\ey_lky s_ehqgha_f_evguf f_lZeehf \aZbfh^_ckl \m_l k ]Zeh]_gZfb hdbkey_lky \ kmohf \ha^mo_ wg_j]bqgh j_Z]bjm _l k dbkehlZfb ijb gZ]j_\Zgbb \aZbfh^_ckl\m_l k lZdbfb \_s_kl\Zfb dZd ) 6 + 1 K J Bhg dZevpby g_ hl^Z_l we_dljhgu ihwlhfm g_ hdbkey_lky l _ g_ y\ey_lky obfbq_kdb Zdlb\guf :lhf nlhjZ ± ) H H Bhg nlhjZ ± ) H H :lhf nlhjZ fh`_l ijbkh_^bgblv g_^hklZxsbc h^bg we_dljhg y\ey_lky kZfuf Zdlb\guf ]Zeh]_ghf h[jZam_l kh_^bg_gby ijZd lbq_kdb kh \k_fb we_f_glZfb djhf_ bg_jlguo ]Zah\ ± nlhjb^u kbevguc hdbkebl_ev b Zdp_ilhj Bhg nlhjZ g_ fh`_l ijbkh_^bgblv we_dljhgu l d \g_rgyy h[hehqdZ bhgZ iheghklvx aZiheg_gZ \oh^bl \ khklZ\ khe_c nlhjb^h\

<hijhk ‹

Qlh lZdh_ bhg ]b^jhdkhgby b dZd hg h[jZam_lky" DZdhc lbi k\yab \ wlhf bhg_"

Hl\_l Ijb ^bkkhpbZpbb dbkehl h[jZamxlky bhgu \h^hjh^Z b dbkehl gh]h hklZldZ +&O + &O H^gZdh ijb ^bkkhpbZpbb fhe_dme dbkehl h[jZamxlky g_ k\h [h^gu_ bhgu \h^hjh^Z Z bo ]b^jZlu ± bhgu ]b^jhdkhgby G G H o G H bhg ]b^jhdkhgby

:lhf dbkehjh^Z ij_^klZ\ey_l h[smx we_dljhggmx iZjm ^h ghj bhgm \h^hjh^Z Zdp_ilhj ªG º G KO + H G o « » K ¬G H G ¼ +&O + 2 o + 2 &O±

<hijhk ‹

GZibrbl_ mjZ\g_gby ijhp_kkh\ ^bkkhpbZpbb hjlhnhknhjghc dbkeh lu ]b^jhdkb^Z dZeby b kmevnZlZ Zexfbgby

Hl\_l G JH l G + 3H ± G JH ± l G +3H ± GJH ± l G 3H ± DHG o D HG± $O 62 o $O 62 ±

<hijhk ‹

Ijb\_^bl_ hij_^_e_gby dbkehl hkgh\Zgbc kj_^gbo b dbkeuo khe_c k lhqdb aj_gby ij_^klZ\e_gbc h[ we_dljheblbq_kdhc ^bkkhpbZpbb

Hl\_l Dbkehlu ± keh`gu_ \_s_kl\Z ijb ^bkkhpbZpbb dhlhjuo \ \h^ guo jZkl\hjZo \ dZq_kl\_ dZlbhgh\ h[jZamxlky lhevdh bhgu \h^h jh^Z GK o G KO± Hkgh\Zgby ± keh`gu_ \_s_kl\Z ijb ^bkkhpbZpbb dhlhjuo \ \h^guo jZkl\hjZo \ dZq_kl\_ Zgbhgh\ hls_ieyxlky lhevdh ]b^jh dkb^ bhgu DHG o D HG± Kj_^gb_ kheb ± keh`gu_ \_s_kl\Z ^bkkhpbbjmxsb_ \ \h^guo jZkl\hjZo gZ iheh`bl_evgh aZjy`_ggu_ dZlbhgu f_lZeeh\ b hljb pZl_evgh aZjy`_ggu_ Zgbhgu dbkehlguo hklZldh\ .12 o 12 ± Dbkeu_ kheb ± keh`gu_ \_s_kl\Z dhlhju_ ^bkkhpbbjmxl \ \h^guo jZkl\hjZo gZ iheh`bl_evgh aZjy`_ggu_ dZlbhgu f_lZeeh\ b \h^hjh^Z b hljbpZl_evgh aZjy`_ggu_ Zgbhgu dbkehlguo hklZl dh\ GZijbf_j 1DG62 o 1Z +62 ± +62 ± l G 62 ±

<hijhk ‹

Bkihevamy ihgylb_ Škl_i_gv ^bkkhpbZpbbª h[tykgbl_ kfuke ihgylbc ŠkbevgZy dbkehlZª b ŠkeZ[Zy dbkehlZª

Hl\_l KbevgZy dbkehlZ Âą we_dljhebl dhlhjuc ijb jZkl\hj_gbb \ \h^_ iheghklvx ^bkkhpbbjm_l gZ bhgu +&O G 6H G1H KeZ[Zy dbkehlZ Âą we_dljhebl dhlhjuc ijb jZkl\hj_gbb \ \h^_ ^bkkhpbbjm_l gZ bhgu g_agZqbl_evgh G KH G <H G H

<hijhk ‹

Ijb\_^bl_ ijbf_ju kbevguo b keZ[uo we_dljheblh\ =^_ gZ ijZdlbd_ g_h[oh^bfh mqblu\Zlv kbem we_dljheblh\"

Hl\_l Kbevgu_ we_dljheblu Âą ijZdlbq_kdb \k_ jZkl\hjbfu_ \ \h^_ kheb dbkehlu +&O G 6H G1H s_ehqb ]b^jhdkb^u [Zjby b dZevpby KeZ[u_ we_dljheblu Âą g_dhlhju_ dbkehlu G <H G H KG KHHHG \h^Z KbeZ we_dljheblZ oZjZdl_jbam_lky kl_i_gvx ^bkkhpbZpbb Âą hl ghr_gb_ qbkeZ ^bkkhpbbjh\Zgguo fhe_dme d h[s_fm qbkem fhe_ i dme gZoh^ysboky \ jZkl\hj_ D 1 ]^_ D Âą kl_i_gv ^bkkhpbZpbb Q Âą qbkeh ^bkkhpbbjh\Zgguo fhe_ dme 1 Âą h[s__ qbkeh jZkl\hj_gguo fhe_dme >ey kbevguo we_d ljheblh\ D [ebadZ d < aZ\bkbfhklb hl we_dljheblh\ D fh`_l f_gylvky hl ^bkkhpbZpbb g_l ^h ihegZy ^bkkhpbZpby

†† ¹ klj <hijhk ‹

>Zgu jZkl\hju Z i_jfZg]ZgZlZ dZeby .FQ2 [ kmevnZlZ dZeby . 62 \ ojhfZlZ gZljby 1D &U2 ] kmevnZlZ f_eb ,, &X62 ^ oeh jb^Z gbd_ey 1L&O DZd jZaebqblv wlb jZkl\hju"

Hl\_l <k_ j ju fh`gh jZaebqblv ih \g_rg_fm \b^m j j .FQ2 hd jZr_g \ yjdh nbhe_lh\uc p\_l j j 1D &U2 Âą \ `_eluc b j j &X62 Âą \ ]hem[hc JZkl\hj 1L&O hdjZr_g \ k\_leh a_e_guc p\_l Z j j . 62 [_kp\_l_g LZd `_ _keb ^h[Z\blv d j jZf oehjb^Z gb d_ey b kmevnZlZ dZeby jZkl\hj s_ehqb < i_j\hf kemqZ_ \uiZ^_l hkZ^hd ]b^jhdkb^Z gbd_ey \h \lhjhf \b^bfuo baf_g_gbc g_ ijh bahc^_l 1L&O 1D2+ 1L 2+ p 1D&O

<hijhk ‹

>Zgu jZkl\hju kh^_j`Zsb_ bhgu $J 62 ± G ,± K ihfhsvx dZ dbo j_Zdpbc fh`gh hij_^_eblv wlb j ju" GZibrbl_ mjZ\g_gby j_Zdpbc

Hl\_l $J $J &O± o $J&Op $J

32 ±

62 ± 62 ±

[_euc hkZ^hd

o $J 32 p `_eluc hkZ^hd

%D o %D62 p

[_euc hkZ^hd

G G bg^bdZlhju o baf_g_gb_ hdjZkdb ,± ,± $J12 o $J,p 12 ±

`_eluc hkZ^hd

, G 62 ± o , + 6n + 2 ±

dhgp nbhe_lh\uc p\_l

<hijhk ‹

>Zgu jZkl\hju Z kmevnZlZ pbgdZ b gbljZlZ [Zjby [ kmevnZlZ f_^b ,, b ]b^jhdkb^Z dZeby \ kmevnZlZ pbgdZ oehjb^Z fZ]gby b hjlh nhknZlZ gZljby ] oehjb^Z `_e_aZ ,,, b kmevnZlZ fZ]gby Ijb keb\Z gbb dZdbo j jh\ j_Zdpbb h[f_gZ ihc^ml ^h dhgpZ b ihq_fm" KhklZ\vl_ mjZ\g_gby wlbo j_Zdpbc \ fhe_dmeyjghf iheghf b khdjZs_gghf \b^_

Hl\_l Z =Q62 %D 12 o =Q 12 %D62 p [_euc hkZ^hd

j_Zdpby ihc^_l ^h dhgpZ l d %D62 \uiZ^Z_l \ hkZ^hd =Q 62 ± <Z 12 ± o =Q 12 %D62 p <Z 62 ± o %D62 p [ &X62 DHG o &X 2+ p D 62 kbgbc hkZ^hd

J_Zdpby b^_l ^h dhgpZ l d KX HG \uiZ^Z_l \ hkZ^hd KX HG± o KX HG p KX 62 ± D HG± o KX HG p 62 ± D \ J_Zdpbb b^ml ^h dhgpZ l d =Q 32 b 0J 32 g_jZkl\hjbfu =Q62 1D 32 o =Q 32 p 1D 62 A=Q 62 ± A=Q 32 ±

[_euc hkZ^hd

1D 32 ± o =Q 32 p 1D 62 ± o =Q 32 p 0J&O 1D 32 o 0J 32 p 1D&O

[_euc hkZ^hd

0J KO± 1D J2 ± o 0J 32 p 1D KO 0J JH ± o 0J 32 p ] )H&O 0J62 l )H 6H 0J&O )H KO± 0J 6H ± o )H 6H ± 0J KO± )H 62 ± jZkl\hjbfZy khev 0J&O ± jZkl\hjbfZy khev agZqbl j_Zdpby )_K a 0J62 ijhl_dZlv g_ [m^_l

<hijhk ‹

>Zgu ko_fu Z G KH ± o [ + 6 ± o \ + 62 ± o KhklZ\vl_ mjZ\g_gby j_Zdpbc \ fhe_dmeyjghf \b^_

Hl\_l Z DjZldh_ bhggh_ mjZ\g_gb_ G KH ± o G H KH n Ihegh_ bhggh_ mjZ\g_gb_ + & D KH D & G H KH n Fhe_dmeyjgh_ mjZ\g_gb_ +& D KH o DK G KH o DK G H &2 n [ DjZldh_ bhggh_ mjZ\g_gb_ + 6 ± o + 6n Ihegh_ bhggh_ mjZ\g_gb_ + & 1D 6 1D & + 6n Fhe_dmeyjgh_ mjZ\g_gb_ +& )H6 o )H&O + 6n \ DjZldh_ bhggh_ mjZ\g_gb_ + 62 ± o G H 6H n Ihegh_ bhggh_ mjZ\g_gb_ + 6H 1D 62 G H 6H n Fhe_dmeyjgh_ mjZ\g_gb_ + 62 1D 62 o 1D 6H G H 6H n

<hijhk ‹

>Zgu mjZ\g_gby j_Zdpbc Z G 2 : G 9 H 9 [ KX 2+ : KX2 G 2 \ 1 2 G 2 : +12 ] KX62 )H : )H62 &X ^ )H &O : )H&O DZdb_ ba wlbo j_Zdpbc y\eyxlky hdbkebl_evgh \hkklZgh\bl_evgufb b ihq_fm" MdZ`bl_ hdbkebl_ev b \hkklZgh\bl_ev

Hl\_l Hdbkebl_evgh \hkklZgh\bl_evgufb y\eyxlky ke_^mxsb_ j_Zdpbb G 2 ± : G 9 H 9 H± H ± _ : H \hkklZgh\bl_ev hdbkey_lky G _ : G hdbkebl_ev \hkklZgZ\eb\Z_lky KX 62 )H : )H 62 &X ±

H± )H ± H : )H &X H : &X

)H &O

\hkklZgh\bl_ev hdbkey_lky hdbkebl_ev \hkklZgZ\eb\Z_lky

W o )H &O ±

H± )H ± H : )H \hkklZgh\bl_ev hdbkey_lky &O H : &O± hdbkebl_ev \hkklZgZ\eb\Z_lky <h \k_o j_Zdpbyo Zlhfu we_f_glh\ f_gyxl k\hx kl_i_gv hdbk e_gby \ hlebqb_ hl ^\mo hklZevguo j_Zdpby ]^_ kl_i_gv hdbke_ gby hklZ_lky ij_`g_c W KX 2 ±+ o KX 2 ± G 2 ±

1 2 ± G 2 ± : + 1 2 ±

<hijhk ‹

>Zgu mjZ\g_gby j_Zdpbc Z =Q &O =Q&O [ =Q +&O =Q&O + 9 IjhklZ\vl_ gZ^ agZdZfb khhl\_lkl\mxsbo obfbq_kdbo we_f_glh\ kl_i_gb bo hdbke_gby b ihdZ`bl_ i_j_oh^ we_dljhgh\

Hl\_l Z =Q &O

W o =Q &O ±

H± =Q ± H : =Q \hkklZgh\bl_ev hdbkey_lky &O H : &O± hdbkebl_ev \hkklZgZ\eb\Z_lky ± o + &O =Q &O ± + 9 [ =Q

H± =Q ± H : =Q + H : +

\hkklZgh\bl_ev hdbkey_lky ± =Q hdbkebl_ev \hkklZgZ\eb\Z_lky ± +

<hijhk ‹

>Zgu ko_fu mjZ\g_gbc j_Zdpbc Z &X6 +12 jZa[ : &X 12 6 12 G H [ D 62 + 62 .0Q2 : D 62 0Q62 + 2 KhklZ\vl_ mjZ\g_gby hdbkebl_evgh \hkklZgh\bl_evguo j_Zdpbc ihevamykv j_dhf_g^Zpb_c ijb\_^_gghc gZ klj

Hl\_l Z &X 6 ± + 1 2 : &X 1 2 ± 6 1 2 G H 6 ± ± H± : 6 12 ± + H± : 12 + 2

6 ± ± H± : 6 gh lZd jZkklZ\eylv dhwnnbpb_glu 1 H± : 1 keh`g__ [ D 6 2 ± + 6 2 ± . 0Q 2 ± : D 6 2 ± 0Q 6 2 ± + 2 ± 6 2 ± + 2 ± H± : 6 2 ± + 0Q 2 ± + H± : 0Q + 2 62 ± + 2 ± H± 0Q2 ± + H± : 62 ± + 0Q + 2 ijhba\h^bf khdjZs_gby 62 ± 0Q2 ± + : 62 ± 0Q + 2 beb 6 ± H : 6 0Q H : 0Q

<hijhk ‹

DZdb_ kheb ih^\_j]Zxlky ]b^jhebam b ihq_fm" H[tykgbl_ wlh gZ ijbf_jZo gbljZlZ pbgdZ kmevnZlZ dZeby b kmevnb^Z gZljby

Hl\_l =b^jhebam ih^\_j]Zxlky kheb h[jZah\Zggu_ Z keZ[uf hkgh \Zgb_ b kbevghc dbkehlhc [ kbevguf hkgh\Zgb_f b keZ[hc db kehlhc Wlh ijhbkoh^bl hl lh]h qlh \ khklZ\_ lZdbo khe_c bf_xlky bhgu dhlhju_ fh]ml k\yau\Zlvky k bhgZfb G beb HG± gZ dhlh ju_ g_agZqbl_evgh ^bkkhpbbjm_l \h^Z GZijbf_j =Q 12 G H : =Q 2+ 12 +12 dbkeZy kj_^Z =Q 12 ± G H : =Q2+ 1H ± G =Q + 2 : =Q2G + Khev h[jZah\ZgZ kbevghc dbkehlhc b keZ[uf hkgh\Zgb_f D 6H G H : D 62 ± ± + 2 : . 62 ± + 2 Khev h[jZah\ZggZy kbevghc dbkehlhc b kbevguf hkgh\Zgb_f ]b^ jhebam g_ ih^\_j]Z_lky

1D 6 G H : 1D+6 1D2+ s_ehqgZy kj_^Z 1D 6 Âą + HGÂą : 1D +6Âą HGÂą 6 Âą + 2 : +6Âą 2+Âą ?keb khev h[jZah\ZgZ kbevguf hkgh\Zgb_f b keZ[hc dbkehlhc lh ]^Z ]b^jheba b^_l k h[jZah\Zgb_f s_ehqghc kj_^u Kheb h[jZah\Zggu_ keZ[hc dbkehlhc b keZ[uf hkgh\Zgb_f ih^ \_j]Zxlky gZb[he__ iheghfm ]b^jhebam < wlhf kemqZ_ j_Zdpby kj_^u aZ\bkbl hl kl_i_gb ^bkkhpbZpbb ijh ^mdlh\ ]b^jhebaZ &+ &221+ G H : KG KHHÂą 1+ + H : KG KHHG 1+ 2+ Âą Zp_lZl Zffhgby

<hijhk ‹

GZq_jlbl_ \ l_ljZ^b lZ[ebpm b aZihegbl_ __

Hl\_l JZkl\hju khe_c

oehjb^ pbgdZ =Q&O dZj[hgZl dZeby D KHa kmevnZl gZljby 1D 62

eZdfmk djZkg__l

P\_l bg^bdZlhjZ f_lbeh\uc N_gheÂą hjZg`_\uc nlZe_bg

kbg__l

p\_l g_ f_gy_lky

jhah\__l `_el__l

p\_l g_ f_gy_lky

MjZ\g_gby j_Zd pbb ihykgyxsb_ baf_g_gb_ p\_lZ bg^bdZlhjZ p\_l g_ =Q&O G H f_gy_lky =Q 2+ &O GKO klZgh\blky D KHa G fZebgh\uf DGKHa DHG p\_l g_ f_gy_lky

Âą

AZ^ZqZ ‹

< jZkl\hj kh^_j`Zsbc ] kmevnZlZ f_^b ,, ihf_klbeb ] `_ e_aguo hibehd DZdb_ \_s_kl\Z h[jZamxlky \ j_amevlZl_ j_Zdpbb b dZdh \Z bo fZkkZ"

>Zgh P &X6 ] P )H ] P )H6H Âą " P &X Âą "

]

]

m ]

o ]

&X62 )H : )H62 &X; ]

]

]

]

0 &X ] fhev 0 )H ] fhev 0 &X62 ˜ ] fhev 0 )H62 ˜ ] fhev Hij_^_ey_f dZdh_ \_s_kl\h ^Zgh \ ba[uld_

] )H Âą ] &X6H

˜ | ] P &X62 \klmib\r_]h \ j_Zdpbx Âą ] hgh ^Zgh \ ba[uld_ @_e_ah j_Z]bjm_l iheghklvx agZqbl fZkku ijh^mdlh\ hij_^_ ey_f ih `_e_am ] )H Âą ] )H6H ] )H Âą ] &X ] )H Âą m ] )H62 ] )H Âą o ] &X ˜ [ ] | ] \ Hl\_l \ j_amevlZl_ j_Zdpbb h[jZah\Zehkv ] f_^b b ] kmevnZlZ `_e_aZ

] )HÂą o ] &X6H

[

AZ^ZqZ

D ] jZkl\hjZ kh^_j`Zs_]h kmevnZlZ `_e_aZ ,, ^h[Z\beb ] jZkl\hjZ dhlhjuc kh^_j`bl ]b^jhdkb^Z gZljby <uqbkebl_ fZkkm h[jZah\Z\r_]hky hkZ^dZ

>Zgh P SÂąSD ] P jÂąjZ ] & )H62 & 1D2+ P hkZ^dZ Âą "

]

]

o ]

)H6H 1D2+ : )H 2+ ; 1D 62 ]

˜ ]

]

GZoh^bf fZkku \_s_kl\ \ jZkl\hjZo P )H62 ˜ ] P 1D2+ ˜ ] <ukqblu\Z_f hlghkbl_evgu_ fhe_dm eyjgu_ fZkku bkoh^guo \_s_kl\ b ihemqb\r_]hky \_s_kl\Z 0 )H62 ˜ ] fhev 0 1D2+ ] fhev F )_ HG ˜ ] fhev Hij_^_ey_f dZdh_ \_s_kl\h gZoh^blky \ ba[uld_ O ] )H62 Âą [ ] 1D2+ ˜ | [ ] )H62 Âą ] 1D2+ < j_Zdpbx \klmibeh ] 1D2+ \_s_kl\h gZoh^blky \ ba[uld_ <uqbkey_f fZkkm )_ HG \uiZ\r_]h \ hkZ^hd ih )H62 ] )H6H Âą [ ] )H 2+ ˜ | ] )H62 Âą ] )H 2+ [ Hl\_l P )H 2+ ]

=eZ\Z ,,

†† ± klj <hijhk ‹

GZ hkgh\_ l_hjbb kljh_gby Zlhfh\ ihykgbl_ ihq_fm dbkehjh^ y\ey _lky [he__ kbevguf hdbkebl_e_f q_f k_jZ

Hl\_l 2 V V S 6 V V S V S :lhfu h[hbo we_f_glh\ bf_xl ih we_dljhgh\ gZ \g_rg_f we_dljhgghf mjh\g_ b ^ey ihkljh_gby mklhcqb\hc \hkvfbwe_d ljhgghc \g_rg_c h[hehqdb g_ o\ZlZ_l lhevdh ^\mo we_dljhgh\ 6 H o 6 2 H o 2 Gh dbkehjh^ bf__l f_gvrbc Zlhfguc jZ^bmk q_f k_jZ b _]h we_dljhgu ijbly]b\Zxlky kbevg__ d y^jm Hlkx^Z ke_^m_l qlh hdbkebl_evgu_ k\hckl\Z m H \ujZ`_gu kbevg__ q_f m k_ju

<hijhk ‹

Ihevamykv ^Zggufb lZ[ebp b h[tykgbl_ ihq_fm m Zlhfh\ oehjZ kl_i_gb hdbke_gby \ujZ`Zxlky g_q_lgufb qbkeZfb Z m Zlhfh\ k_ju ± q_lgufb Ihq_fm dbkehjh^ ijhy\ey_l ihklhyggmx \Ze_glghklv Z k_jZ ± i_j_f_ggmx"

Hl\_l Z K_jZ gZoh^blky \ r_klhc ]jmii_ i_jbh^bq_kdhc kbkl_fu > B F_g^_e__\Z Z oehj ± \ k_^vfhc Wlh agZqbl qlh m k_ju gZ ih ke_^g_f we_dljhgghf mjh\g_ gZoh^blky ± _ Z m oehjZ ± _ >ey h[jZah\Zgby mklhcqb\hc \hkvfbwe_dljhgghc h[hehqdb oehj klj_ fblky eb[h hl^Zlv k_fv we_dljhgh\ eb[h ijbkh_^bgblv h^bg lh _klv g_q_lgh_ qbkeh k_jZ `_ klj_fblky eb[h ijbkh_^bgblv ^\Z eb[h hl^Zlv r_klv lh _klv q_lgh_ qbkeh [ K_jZ gZoh^blky \ lj_lv_f i_jbh^_ i_jbh^bq_kdhc kbkl_fu > B F_g^_e__\Z Z dbkehjh^ \h \lhjhf wlh agZqbl qlh m Zlhfh\ k_ju gZ _f wg_j]_lbq_kdhf mjh\g_ bf_xlky g_aZiheg_gguo G± hj[blZe_c gZ dhlhju_ fh]ml i_j_oh^blv V b j we_dljhgu \ j_ amevlZl_ q_]h m k_ju ihy\ey_lky q_luj_ beb r_klv g_kiZj_gguo we_dljhgh\ b khhl\_lkl\_ggh k_jZ fh`_l [ulv lZd`_ q_luj_o b r_klb\Ze_glghc

<hijhk ‹

KjZ\gbl_ k\hckl\Z dbkehjh^Z b hahgZ djbklZeebq_kdhc b ieZklbq_ kdhc k_ju GZ hkgh\_ wlbo ijbf_jh\ ihykgbl_ kmsghklv Zeehljhibb

Hl\_l :eehljhiby ± wlh kihkh[ghklv obfbq_kdh]h we_f_glZ h[jZah \u\Zlv g_kdhevdh ijhkluo \_s_kl\ Obfbq_kdbc we_f_gl dbkehjh^ h[jZam_l ^\Z ijhkluo \_s_kl\Z ± dbkehjh^ 2 b hahg 2 Nbabq_ kdb_ k\hckl\Z dbkehjh^Z b hahgZ jZaebqZxlky dbkehjh^ ± ]Za [_a p\_lZ b aZiZoZ hahg h[eZ^Z_l j_adbf aZiZohf k\_`_klb b hdjZr_g \ ]hem[hc p\_l K_jZ lZd`_ h[jZam_l Zeehljhigu_ fh^bnbdZpbb ± djbklZeeb q_kdmx b ieZklbq_kdmx k_jm DjbklZeebq_kdZy k_jZ ± l\_j^h_ ojmidh_ \_s_kl\h ieZklbq_kdZy k_jZ ih nbabq_kdbf k\hckl\Zf gZihfbgZ_l j_abgm

<hijhk ‹

I_j_qbkebl_ ijbjh^gu_ kh_^bg_gby k_ju gZibrbl_ bo obfbq_kdb_ nhjfmeu b hij_^_ebl_ \ gbo kl_i_gb hdbke_gby k_ju

Hl\_l Kmevnb^u k\bgph\uc [e_kd 3E6 f_^guc [e_kd &X 6 pbgdh \Zy h[fZgdZ =Q6 ibjbl )H6 k_jh\h^hjh^ + 6 KmevnZlu ]bik &D6H ˜ G 2 fbjZ[bebl 0J62 ˜ G 2 ]eZm[_jh\Z khev 1D 62 ˜ G H

<hijhk ‹

KhklZ\vl_ mjZ\g_gby j_Zdpbc ijb dhlhjuo ba ijhkluo \_s_kl\ h[ jZamxlky keh`gu_ \_s_kl\Z nhjfmeu dhlhjuo ke_^mxsb_ /L 6 =Q6 + 6 62 &6 b 6) Bkihevamy ^Zggu_ lZ[ebpu ihykgbl_ dZdb_ k\hc kl\Z hdbkebl_evgu_ beb \hkklZgh\bl_evgu_ ijhy\ey_l k_jZ \ wlbo j_ Zdpbyo

Hl\_l

/L 6

W o /L 6 ±

_± /L ± H : /L 6 H : 6 ±

=Q 6 H±

W o =Q 6 ±

\hkklZgh\bl_ev hdbkey_lky hdbkebl_ev \hkklZgZ\eb\Z_lky

=Q ± H : =Q 6 H : 6 ±

\hkklZgh\bl_ev hdbkey_lky hdbkebl_ev \hkklZgZ\eb\Z_lky

H± + ± H : + 6 H : 6 ±

\hkklZgh\bl_ev hdbkey_lky hdbkebl_ev \hkklZgZ\eb\Z_lky

\hkklZgh\bl_ev hdbkey_lky hdbkebl_ev \hkklZgZ\eb\Z_lky

\hkklZgh\bl_ev hdbkey_lky hdbkebl_ev \hkklZgZ\eb\Z_lky

+ 6

W o + 6 ±

6 2

W o 6 2 ±

H± 6 ± H : 6 2 H : 2 ±

6 )

W o 6 ) ±

H± 6 ± H : 6 )H H : )H±

AZ^ZqZ ‹

Ba\_klgh kh_^bg_gb_ kh^_j`Zs__ fZkkh\uo ^he_c beb nhknhjZ b fZkkh\uo ^he_c beb k_ju GZc^bl_ _]h ijhkl_crmx nhjfmem

$U 3 $U 6 J ± J 6 ± [ 6

˜ | [ ] ± dhebq_kl\h Zlhfh\ k_ju gZ h^bg Zlhf nhknhjZ ] AgZqbl \ wlhf \_s_kl\_ gZ h^bg Zlhf nhknhjZ ijboh^blky ZlhfZ k_ju l d \ khklZ\ \_s_kl\Z fh`_l \oh^blv lhevdh p_eh_ qbkeh Zlhfh\ agZqbl nhjfmeZ \_s_kl\Z [m^_l 3 6 >Zgh Z J Z 6 6]3\ ± "

Hl\_l 3 6

AZ^ZqZ ‹

Ijb h[jZah\Zgbb fhev hdkb^Z k_ju ,9 ba we_f_glh\ \u^_ey_lky d>` Kdhevdh \u^_eblky l_iehlu ijb k]hjZgbb ] k_ju"

>Zgh Y 6 fhev 4 d>` P 6 ] 4 ± "

]

[ ]

6 H : 62 d>` ]

]

0U 6 0U 62 ˜ [ ] 62 ± ] 6 ] 6H ± ] 6 ˜ P ] Y 62 fhev P 62 ] [ 0 fhev 62 ± o d>` fhev 62 ± d>` [ d>` Hl\_l 4 d>`

† klj ± <hijhk ‹

Dhgp_gljbjh\ZggZy k_jgZy dbkehlZ ijb gZ]j_\Zgbb j_Z]bjm_l k jlm lvx b k_j_[jhf ih^h[gh lhfm dZd hgZ j_Z]bjm_l k f_^vx KhklZ\vl_ mjZ\g_gby wlbo j_Zdpbc b mdZ`bl_ hdbkebl_ev b \hkklZgh\bl_ev

Hl\_l

+J + 6 2

H± +J ± H : +J 6 H : 6

$J + 6 2

H± $J ± H : $J 6 H : 6

W o +J 62 6 2 + 2

\hkklZgh\bl_ev hdbkey_lky hdbkebl_ev \hkklZgZ\eb\Z_lky

\hkklZgh\bl_ev hdbkey_lky hdbkebl_ev \hkklZgZ\eb\Z_lky

W o $J 62 6 2 + 2

<hijhk ‹

KhklZ\vl_ mjZ\g_gby j_Zdpbc dhlhju_ ijZdlbq_kdb hkms_kl\bfu bkihevamy ijb\_^_ggu_ ko_fu &X62 +&O : GJ + 62 dhgp : &X +&O : 1D12 +&O : 0J&O + 62 dhgp : 1D62 + 62 : 1D2+ + 62 : $O 2+ + 62 : Ijb khklZ\e_gbb mjZ\g_gbc j_Zdpbc mdZ`bl_ mkeh\by bo hkms_kl\e_ gby < l_o kemqZyo ]^_ wlh lj_[m_lky khklZ\vl_ mjZ\g_gby \ bhgghf b khdjZs_gghf bhgghf \b^_

Hl\_l &X62 +&O : g_ j_Z]bjm_l GJ + 6 2 dhgp

W o +J 62 6 2 9 + 2

±

H GJ ± H : GJ \hkklZgh\bl_ev hdbkey_lky 6 H : 6 hdbkebl_ev \hkklZgZ\eb\Z_lky &X +&O : g_ j_Z]bjm_l 1D12 +&O : g_ j_Z]bjm_l g_l fZeh^bkkhpbbjmxs_]h \_s_kl\Z

0J&O + 62 dhgp : 0J62 +&On 0J &O± + 62 ± : 0J 62 ± +&O± &O± + : +&On 1D62 + 62 : 1D62 + 62 : 1D 62 62 n + 2 1D 62 ± + 62 ± : 1D 62 ± ± + 62 62 ± + : + 62 : 62 n + 2 1D2+ + 62 : 1D 62 + 2 1D 2+± + 62 ± : 1D 62 ± ± + 2 2+± + : + 2 $O 2+ + 62 : $O 62 + 2 $O 2+ + 62 ± : $O 62 ± + 2 $O 2+ + : $O + 2

<hijhk ‹

GZah\bl_ hdbkebl_ev \ j_Zdpbyo Z jZa[Z\e_gghc k_jghc dbkehlu k f_lZeeZfb [ dhgp_gljbjh\Zgghc k_jghc dbkehlu k f_lZeeZfb

Hl\_l =Q + 62 : =Q 62 + n H± =Q ± H : =Q + H : +

H± KX ± H : &X 6 H : 6

&X + 6 2 dhgp

\hkklZgh\bl_ev hdbkey_lky hdbkebl_ev \hkklZgZ\eb\Z_lky

W o KX 62 6 2 n + 2

\hkklZgh\bl_ev hdbkey_lky hdbkebl_ev \hkklZgZ\eb\Z_lky

AZ^ZqZ ‹

DZdhc h[t_f dbkehjh^Z ihlj_[m_lky ^ey k`b]Zgby Z d] k_jh\h ^hjh^Z [ f k_jh\h^hjh^Z

Z >Zgh P G 6 d] ]

]

˜ ]

9 2 " [

˜

o e

+ 6 2 G H 62 n ˜ e fhev

] G 6 Âą o e 2

] + 6 Âą e fhev H

e f

Hl\_l 9 H f [ >Zgh 9 + 6 f 9 G 6 " [

˜

f

Hl\_l 9 H f

f o e

G 6 H G 2 62 ˜ f

˜ f

f G 6 Âą o f H

f G 6 Âą f H

AZ^ZqZ ‹

DZdh\Z fZkkZ jZkl\hjZ kh^_j`Zs_]h fZkkh\u_ ^heb k_jghc db kehlu dhlhjZy jZkoh^m_lky gZ j_Zdpbx k ] Zexfbgby

>Zgh Z + 62 P $O ] ZjÂąjZ "

G 6H : : : 6H G n ˜ ]

˜ ]

0U G 6H ˜ 0U $O [ ] G 6H Âą ] $O ] G 6H Âą ] $O

˜ P G 6H ] ] P + 62 ] P jÂąjZ Z + 62 [

Hl\_l PjÂąjZ ]

=eZ\Z ,,,

†† ¹ klj <hijhk ‹

< lZ[ebp_ klj mdZaZgu mkeh\by \ebyxsb_ gZ kdhjhklv obfb q_kdbo j_Zdpbc b ^Zgu ijbf_ju GZah\bl_ ^ey dZ`^h]h mkeh\by h^bg ^\Z ^hihegbl_evguo ijbf_jZ khklZ\vl_ mjZ\g_gby j_Zdpbc b ^Zcl_ h[hkgh \Zgb_ bo hkms_kl\e_gby

Hl\_l Kdhjhklv obfbq_kdbo j_Zdpbc aZ\bkbl hl ijbjh^u j_Z]bjmx sbo \_s_kl\ =Q GK : =Q&O + n Âą kdhjhklv j_Zdpbb \ukhdZy l d kheygZy dbkehlZ h[eZ^Z_l \ukhdhc obfbq_kdhc Zdlb\ghklvx =Q G KH : =Q&2 G n Âą kdhjhklv j_Zdpbb gbadZy l d m]hev gZy dbkehlZ hq_gv keZ[Zy >ey \_s_kl\ \ jZkl\hj_gghf khklhygbb b ]Zah\ kdhjhklv obfb q_kdbo j_Zdpbc aZ\bkbl hl dhgp_gljZpbb j_Z]bjmxsbo \_s_kl\ =Q +&Ohq jZa[ : =Q&O + n YD =Q GK : =Q&O + n YE YD YE wlh fh`gh gZ[ex^Zlv ih kdhjhklb \u^_e_gby ]ZaZ >ey \_s_kl\ \ l\_j^hf khklhygbb kdhjhklv j_Zdpbb ijyfh ijh ihjpbhgZevgZ ih\_joghklb j_Z]bjmxsbo \_s_kl\

)H baf_evq GK o )H&O + 9 Âą wlZ j_Zdpby b^_l hq_gv bgl_gkb\gh _keb bkihevah\Zlv `_e_aguc ihjhrhd Ijb ih\ur_gbb l_fi_jZlmju j_Zdpbb gZ dZ`^u_ ƒK kdhjhklv [hevrbgkl\Z j_Zdpbc m\_ebqb\Z_lky \ Âą jZaZ [ukljh

G &O o GK Âą ijb h[uqguo mkeh\byo j_Zdpby b^_l hq_gv f_^e_ggh gh ijb gZ]j_\Zgbb ijhbkoh^bl \aju\ W

)H 6 o )H6 Âą wlZ j_Zdpby [_a gZ]j_\Zgby ihqlb g_ b^_l ijb gZ]j_\Zgbb kmevnb^ `_e_aZ h[jZam_lky ^hklZlhqgh [ukljh Kdhjhklv obfbq_kdbo j_Zdpbc aZ\bkbl hl ijbkmlkl\by g_dhlh juo \_s_kl\ dZlZebaZlhjh\ W

1+ ] ] o 12 ] + 2 Âą wlZ j_Zdpby b^_l ^hklZ lhqgh [ukljh lhevdh \ ijbkmlkl\bb dZlZebaZlhjZ Âą jZkdZe_gghc ieZlbgh\hc ijh\hehdb hgZ hklZ_lky \ khklhygbb djZkgh]h dZe_gby \ jZkl\hj_ ZffbZdZ \iehlv ^h hdhgqZgby j_Zdpbb 3W

<hijhk ‹

Ihykgbl_ d dZdhfm lbim hlghkylky i_j_qbke_ggu_ gb`_ obfbq_kdb_ j_Zdpbb b h[tykgbl_ bo kmsghklv Z \aZbfh^_ckl\b_ jZkl\hjZ oehjb^Z `_e_aZ ,,, k ]b^jhdkb^hf gZljby [ jZaeh`_gb_ oehjZlZ dZeby ijb gZ ]j_\Zgbb \ hdbke_gb_ hdkb^Z k_ju ,9 ] jZaeh`_gb_ dZj[hgZlZ dZev pby ijb gZ]j_\Zgbb ^ \aZbfh^_ckl\b_ Zexfbgby k k_jhc KhklZ\vl_ mjZ\g_gby wlbo j_Zdpbc

Hl\_l Z <aZbfh^_ckl\b_ jZkl\hjZ oehjb^Z `_e_aZ ,,, k ]b^jhdkb^hf gZljby )H&O 1D2+ )H 2+ ; 1D&O Wlh g_h[jZlbfZy j_Zdpby bhggh]h h[f_gZ \ j_amevlZl_ dhlhjhc h[jZam_lky g_jZkl\hjbfh_ hkgh\Zgb_ b ihwlhfm j_Zdpby b^_l ^h dhgpZ [ JZaeh`_gb_ oehjZlZ dZeby ijb gZ]j_\Zgbb DK 2 DK 2 n Wlh g_h[jZlbfZy hdbkebl_evgh \hkklZgh\bl_evgZy j_Zdpby \ dh lhjhc oehj \ fhe_dme_ DK 2 y\ey_lky hdbkebl_e_f b \hkklZgh\b l_e_f h^gh\j_f_ggh &O ± H : &O \hkklZgh\bl_ev hdbkey_lky &O H : &O± hdbkebl_ev \hkklZgZ\eb\Z_lky \ Hdbke_gb_ hdkb^Z k_ju ,9 o 6 2 ± 4 6 2 2 m Wlh h[jZlbfZy hdbkebl_evgh \hkklZgh\bl_evgZy j_Zdpby kh_^bg_ gby ijhbkoh^ysZy \ ijbkmlkl\bb dZlZebaZlhjZ b k \u^_e_gb_f wg_j]bb wdahl_jfbq_kdZy 6 ± H : 6 \hkklZgh\bl_ev hdbkey_lky 2 H : 2 ± hdbkebl_ev \hkklZgZ\eb\Z_lky ] JZaeh`_gb_ dZj[hgZlZ dZevpby ijb gZ]j_\Zgbb

92

KD&2 o KD2 K2 n Wlh h[jZlbfZy j_Zdpby jZaeh`_gby k ih]ehs_gb_f l_iehlu wg^hl_jfbq_kdZy ^ <aZbfh^_ckl\b_ Zexfbgby k k_jhc W

$O 6 o $O 6 ± 4 Wlh g_h[jZlbfZy hdbkebl_evgh \hkklZgh\bl_evgZy wdahl_jfbq_ kdZy j_Zdpby $O ± H : $O \hkklZgh\bl_ev hdbkey_lky 6 H : 6± ± hdbkebl_ev \hkklZgZ\eb\Z_lky W

<hijhk ‹

o +J 2 ± 4 >Zgu mjZ\g_gby j_Zdpbc +J2 m W

o 1+ 4 1 + m j

S W m o 12 ± 4 S o + 2 m + 2 4

1 2

< dZdmx klhjhgm kf_klblky jZ\gh\_kb_ ijb ih\ur_gbb Z l_fi_jZ lmju [ ^Z\e_gby"

Hl\_l

+J2 m o +J 2 ± 4 Ijb ih\ur_gbb l_fi_jZlmju W jZ\gh\_kb_ j_Zdpbb kf_sZ_lky \ijZ\h ijb ih\ur_gbb ^Z\e_gby jZ\gh\_kb_ kf_sZ_lky \e_\h \ klhjhgm mf_gvr_gby h[t_fZ W

1 + m o 1+ 4 Ijb ih\ur_gbb l_fi_jZlmju W jZ\gh\_kb_ kf_sZ_lky \e_\h ijb ih\ur_gbb ^Z\e_gby j ± kf_sZ_lky \ijZ\h j

1 2 m o 12 ± 4 B ijb ih\ur_gbb l_fi_jZlmju W b ijb ih\ur_gbb ^Z\e_gby j jZ\gh\_kb_ kf_sZ_lky \ijZ\h S W

+ 2 m o + 2 4 Ijb ih\ur_gbb l_fi_jZlmju W jZ\gh\_kb_ kf_sZ_lky \e_\h ijb ih\ur_gbb ^Z\e_gby j jZ\gh\_kb_ kf_sZ_lky \ijZ\h S

<hijhk ‹

K_jgmx dbkehlm fh`gh ihemqblv ba ke_^mxsbo bkoh^guo ijh^mdlh\ Z kmevnb^Z pbgdZ [ k_jh\h^hjh^Z \ kmevnb^Z kmjvfu 6E 6 KhklZ\vl_ khhl\_lkl\mxsb_ mjZ\g_gby j_Zdpbc

Hl\_l Ihemq_gb_ 62 =Q6 H =Q2 H Z

+ 6 H + 2 6H [

6E 6 6E 2 6H \

Ihemq_gb_ 62 62 H 6H Ihemq_gb_+ 62 62 + 2 + 6H

<hijhk ‹

KhklZ\vl_ mjZ\g_gby j_Zdpbc ijb ihfhsb dhlhjuo fh`gh hkms_kl \blv ij_\jZs_gby Z 7H : 7H2 : + 7H2 : 1D L_H 7H2 : 1DGL_H + 7H2 : 1DGL_H [ 6H : + 6H : &D6H + 6H : 6_H + 6H : KZ G6H

Hl\_l

o L_H Z L_ H L_H ba[ 1D L_H \h^g G H : 1DGL_H L_H G H : G L_H G L_H 1D2G : 1D L_H G H + L_H ba[ 1DH+ : 1DGL_H G H W

o + 6_ + 6H H o G H 6_H [ 6_ + + 6H ba[ KZ HG : KZ G6H + 2 + 6H KZ HG : KZ6H + 2 W

W

<hijhk ‹

KhklZ\vl_ mjZ\g_gby j_Zdpbc kh]eZkgh ko_f_

Hl\_l

6 + o G 6 W

6 )H o )H6 W

G 6 o + 6 G 6 )H : )H6 + )H6 +&O : )H&O + 6 + 6 H : G H 62 n 6H 2 : 62 6H + 2 : + 62 %U + 6 : + 62 +%U + 62 dhgp : %U + 69 + 2 )H6 : )H 2 62 n 6H + 2 : + 62 + 62 : + 2 6H n + 62 H : + 62 + 62 1DH+ : 1D 62 + 2 6H + 2 : + 62 + 62 1DH+ : 1D 62 + 2 )H62 1D 6 : )H6; 1D 62 W

AZ^ZqZ ‹

<uqbkebl_ kj_^gxx kdhjhklv j_Zdpbb : < : K _keb gZqZevgZy dhgp_gljZpby \_s_kl\Z : jZ\gZ fhev e Z q_j_a k Âą fhev e DZd baf_gbeZkv aZ wlh \j_fy dhgp_gljZpby \_s_kl\Z <"

>Zgh

F $ fhev e F : fhev e 'W k Y Âą " 'k < Âą "

Y

k k

'W

fhev e ˜ k

Hl\_l Y ˜ Âą fhev e ˜ k dhgp_gljZpby \_s_kl\Z < baf_gbeZkv lZd `_ dZd b : gZ fhev e

AZ^ZqZ ‹

<h kdhevdh jZa m\_ebqblky kdhjhklv j_Zdpbb ijb ih\ur_gbb l_fi_ jZlmju hl ^h ƒK _keb ijb ih\ur_gbb l_fi_jZlmju gZ ƒK kdh jhklv j_Zdpbb m\_ebqb\Z_lky \ ljb jZaZ"

'W ƒK Âą ƒK ƒK

>Zgh

'W

W ƒK W ƒK 'Y Âą "

' Y

Hl\_l 'Y kdhjhklv j_Zdpbb m\_ebqbeZkv \ jZaZ

AZ^ZqZ ‹

DZdh\Z fZkkZ k_jghc dbkehlu dhlhjmx fh`gh ihemqblv ba l jm ^u kh^_j`Zs_c ^bkmevnb^Z `_e_aZ )H6 "

)H6 o )H H 62 62 H o 62 62 + 2o + 62 agZqbl )H6 o + 62 beb )H6 o + 62 )H6 o + 62

>Zgh Pjm^u l Z )H6 P + 62 Âą " P )H6

˜

l

0U )H6 0U + 62 ˜ ˜

o l G 62 ± l )H6

l + 62 ± l )H6

Hl\_l P + 62 l

[

˜ l

AZ^ZqZ ‹

Kdhevdh lhgg gh]h jZkl\hjZ k_jghc dbkehlu fh`gh ihemqblv ba l ibjblZ"

>Zgh Z P )H6 l P + 62 ± " o

˜

l

ol

)H6 o G 62 ± ih ZgZeh]bb k aZ^ l

l

o l G 62 o )H6 l G 62 o l )H6 ˜ l l G 62 P G 62

Hl\_l P G 62 l

=eZ\Z ,9

†† ± klj <hijhk ‹

KhklZ\vl_ mjZ\g_gby j_Zdpbc ijb dhlhjuo h[jZamxlky Z ^b]b^jh hjlhnhknZl Zffhgby [ ]b^jhhjlhnhknZl Zffhgby \ hjlhnhknZl Zffhgby

Hl\_l 1G G JH ba[ o 1+ + 3H

^b]b^jhhjlhnhknZl Zffhgby

1G G JH ba[ o 1+ +3H

]b^jhhjlhnhknZl Zffhgby

1G G JH g_^hkl o 1+ + 3H

hjlhnhknZl Zffhgby

<hijhk ‹

=b^jhdZj[hgZl Zffhgby bgh]^Z ijbf_gy_lky ijb \ui_qd_ dhg^bl_j kdbo ba^_ebc DZdb_ k\hckl\Z wlh]h \_s_kl\Z ijb wlhf bkihevamxlky"

Hl\_l Kheb Zffhgby ijb gZ]j_\Zgbb jZaeZ]Zxlky 1+ +&2 o 1+ n &2 n + 2 <u^_eyxsbcky ijb wlhc j_Zd pbb m]e_dbkeuc ]Za ijb^Z_l l_klm iurghklv b \ha^mrghklv

<hijhk ‹

GZq_jlbl_ \ l_ljZ^b lZ[ebpm b \ khhl\_lkl\mxsbo ]jZnZo aZib rbl_ fhe_dmeyjgu_ b bhggu_ mjZ\g_gby j_Zdpbc ihykgyxsbo oZjZdl_j gu_ obfbq_kdb_ k\hckl\Z khe_c nhjfmeu dhlhjuo ^Zgu \ lZ[ebp_

Hl\_l

Kheb

1+ &O 1+ &2

Obfbq_kdb_ k\hckl\Z h[sb_ k ^jm]bfb kheyfb ^bkkhpbZpby

1+ &O : 1+ &O±

1+ &2 : 1+ &2 ±

Ki_pbnbq_kdb_ k\hckl\Z jZaeh`_gb_ ijb gZ ]j_\Zgbb

1+ &O o 1+ 9 &O9 W

1+ &2 o 1+ 9 &2 9 + 2 W

Kheb

1+ 6

1+ 62 1+ &O

1+ 6

1+ 62

1+ &O

1+ &2

1+ 6

1+ 62

Obfbq_kdb_ k\hckl\Z h[sb_ k ^jm]bfb kheyfb 1+ 6 : 1+ 6 ± 1+ 62 : 1+ 62 ± j_Z]bjmxl k dbkehlZfb 1+ &O + 62 dhgp : o 1+ 62 G&O 1+ &2 +&O : o 1+ &O + 2 &2 9 1+ 62 ± g_ j_Z]bjm _l l d k_jgmx dbkehlm ba khe_c ^jm]b_ dbkehlu g_ \ul_kgyxl j_Z]bjmxl k ^jm]bfb kheyfb 1+ &O :J12 : o 1+ 12 $J&O; 1+ &O± :J 12 o :1+ 12 ± $J&O; :J &O± : $J&O; 1+ &2 &D&O : o 1+ &O &D&2 ; 1+ &2 ± &D &O : 1+ &O± &D&2 ; &D &2 ± : &D&2 ; 1+ 6 3E 12 : o 1+ 12 3E6; 1+ 6 ± 3E 12 ± : 1+ 12 ± 3E6; 3E 6 ± : 3E6; 1+ 62 <D&O : o %D62 ; 1+ &O 1+ 62 ± <D &O± : %D 62 ; 1+ &O± <D 62 ± : %D62 ;

Ki_pbnbq_kdb_ k\hckl\Z

1+ 6 o 1+ 9 &2 9 + 69± 1+ 62 1+ 9 + 62 9 j_Z]bjmxl kh s_ehqZfb 1+ &O .2+ : .&O 1+ 9 + 2 1+ &2 1D2+ : 1D &2 1+ 9 + 2 1+ 62 &D 2+ : o&D6 1+ 9 + 2 W

ih^\_j]Zxlky ]b^jhebam 1+ &O + 2 : o 1+ 2+ +&O 1+ &O± + 2 : o 1+ 2+ &O± + 1+ + 2 1+ 2+ + 1+ &2 + 2 : o 1+ 2+ + &2 1+ &2 ± + 2o : 1+ 2+ + &2 1+ 6 + 2 : o 1+ 2+ + 6 1+ 6 ± + 2 : o 1+ 2+ + 6

1+ 62 + 2 : o 1+ 2+ + 62 1+ 62 + 2o : 1+ 2+ + 62 1+ + 2 : o 1+ 2+ +

AZ^ZqZ ‹

] oehjb^Z Zffhgby kf_rZeb k ] ]b^jhdkb^Z dZevpby b kf_kv gZ ]j_eb DZdhc ]Za b kdhevdh _]h ih fZkk_ b h[t_fm \u^_ebehkv g m "

>Zgh P 1+ &O ] P &D 2+ ] P ]ZaZ ± " 9 ]ZaZ ± " g m

]

]

o]

˜ ]

]

˜ ]

1+ &O &D 2+ &D&O 1+ 9 + 2 FU 1+ &O 0U &D 2+ ˜ < g_^hklZld_ ^Zg KZ HG l d 1+ &O ± o ] KD 2+ ] 1+ &O ± ] KD 2+

˜ ˜ ] P &D 2+ ± g_h[oh^bfZy ^ey j_Zdpbb ] ± \ g_^hklZld_ b ih g_fm ijhba\h^bf jZkq_lu FU 1+ ˜ ] KZ HG ± o ] 1+ ] KZ HG ± ] 1+ ˜ ] P 1+ ] o ] 1+ ± o e ˜ ] ] 1+ ± e o o

Hl\_l P 1+ ] 9 1+ e

AZ^ZqZ ‹

DZdh\u h[t_f b fZkkZ ZffbZdZ dhlhju_ ihlj_[mxlky ^ey ihemq_gby l gbljZlZ Zffhgby"

>Zgh P 1+ 12 l P 1+ ± " 9 1+ ± "

ol

l

l

l

1+ +12 : 1+ 12

FU 1+ ˜ FU 1+ 12 ˜ ˜

o l 1+ ± l 1+ 12 l 1+ ± ] 1+ 12 ˜ ] P 1+ ± l o l ± o f l ± ˜ f

o

˜ ˜ ˜ ˜ f

Hl\_l P 1+ ± l 9 1+ ± f

†† ± klj ± <hijhk ‹

Ijb \aZbfh^_ckl\bb jZa[Z\e_gghc +12 k g_dhlhjufb f_lZeeZfb 0J =Q fh`_l \u^_eblvky hdkb^ ZahlZ , beb Zahl GZibrbl_ khhl \_lkl\mxsb_ mjZ\g_gby hdbkebl_evgh \hkklZgh\b l_evguo j_Zdpbc

Hl\_l FJ +1 2 : 0J 12 1 n + 2 0J ± H : 0J \hkklZgh\bl_ev hdbkey_lky 1 H : 1 hdbkebl_ev \hkklZgZ\eb\Z_lky FJ +1 2 : 0J 12 1 Hh + 2 0J ± H : 0J \hkklZgh\bl_ev hdbkey_lky 1 H : 1 hdbkebl_ev \hkklZgZ\eb\Z_lky =Q +12 : =Q 12 1 n + 2 =Q ± H : =Q \hkklZgh\bl_ev hdbkey_lky 1 H : 1 hdbkebl_ev \hkklZgZ\eb\Z_lky =Q +12 : =Q 12 1 2n + 2 =Q ± H : =Q \hkklZgh\bl_ev hdbkey_lky 1 H : 1 hdbkebl_ev \hkklZgZ\eb\Z_lky

<hijhk ‹

< ihq\_ m^h[j_gghc gZ\hahf h[jZam_lky dZj[hgZl Zffhgby Z \h \j_fy ]jhau ± gbljZl Zffhgby Q_f wlh h[tykgy_lky" GZibrbl_ mjZ\ g_gby j_Zdpbc

Hl\_l < gZ\ha_ kh^_j`blky bhg Zffhgby 1+ < ihq\_ kh^_j`blky dZj[hdkbevguc bhg KH ± dhlhjuc h[jZam_lky \ j_amevlZl_ ^bkkh pbZpbb khe_c m]hevghc dbkehlu Bf__f j_Zdpbx 1+ &2 + 2 : 1+ &2 <h \j_fy ]jhau \ g_[hevrbo dhe \Zo h[jZam_lky hdkb^ ZahlZ ,, 1 2 o 12 dhlhjuc aZl_f hdbkey_lky 12 2 12 Ijb j_Zdpbb 12 k \h^hc h[jZam_lky ZahlgZy dbkehlZ 12 + 2 2 +12 we jZajy^

HgZ \ k\hx hq_j_^v ihiZ^Z_l \ ihq\m k ^h`^yfb lZd `_ dZd b m]hevgZy dbkehlZ h[jZah\Z\rZyky \ j_amevlZl_ kh_^bg_gby \h^u b KH Zlfhkn_jgh]h \ha^moZ KH G H : + &2 b k\yau\Z_l bhg Zffhgby k h[jZah\Zgb_f gbljZlZ Zffhgby 1+ 2+ +12 : 1+ 12 + 2

<hijhk ‹

KhklZ\vl_ mjZ\g_gby j_Zdpbc ijb ihfhsb dhlhjuo ba ZffbZdZ ihem qZxl Zahlgmx dbkehlm

Hl\_l 1G H 12 + 2 4 12 2 12 12 + 2 2 l +12 4

<hijhk ‹

Hij_^_ebl_ \ dZdmx klhjhgm kf_sZ_lky jZ\gh\_kb_ j_Zdpbb f_`^m hdkb^hf ZahlZ ,9 \h^hc b dbkehjh^hf ijb baf_g_gbb Z l_fi_jZlmju [ ^Z\e_gby Ihq_fm"

Hl\_l

12 + 2 2 m o +12 4 J_Zdpby wdahl_jfbqgZ ihwlhfm ijb ih\ur_gbb l_fi_jZlmju jZ\gh\_kb_ j_Zdpbb kf_sZ_lky \e_\h Ijb ih\ur_gbb ^Z\e_gby jZ\gh\_kb_ kf_sZ_lky \ijZ\h \ klhjhgm h[jZah\Zgby h^gh]h \_ s_kl\Z l d ijb wlhf ba k_fb bkoh^guo fhe_dme h[jZamxlky lhev dh q_luj_ fhe_dmeu +12 l _ h[t_f mf_gvrZ_lky S

<hijhk ‹

GZibrbl_ mjZ\g_gby j_Zdpbc \ fhe_dmeyjghf bhgghf b khdjZs_gghf bhgghf \b^_ ijb ihfhsb dhlhjuo fh`gh jZaebqblv kheygmx k_jgmx b Zahlgmx dbkehlu

Hl\_l + 62 <ZKO : %D62 ; +&O + 62 ± <Z KO± : %D62 ; + &O± <Z 62 ± : %D62 ; +&O $J12 : $J&O; +12 + &O± $J 12 ± : $J&O; + 12 ± $J &O± : $J&O; +1 2 KX o &X 12 1 2 n G H [mjuc ]Za

< bhgghf \b^_ j_Zdpbx g_evay gZibkZlv l d wlh g_ j_Zdpby h[f_ gZ wlh hdbkebl_evgh \hkklZgh\bl_evgZy j_Zdpby \hkklZgh\bl_ev hdbkey_lky &X ± _ o & hdbkebl_ev \hkklZgZ\eb\Z_lky 1 _ o 1

<hijhk ‹

Ijb\_^bl_ mjZ\g_gby j_Zdpbc Z oZjZdl_jgu_ lhevdh ^ey Zahlghc dbkehlu [ h[sb_ ^ey Zahlghc b ^jm]bo dbkehl

Hl\_l J_Zdpbb k f_lZeeZfb ih f_j_ jZa[Z\e_gby =Q +12 dhgp o =Q 12 1H n G H =Q +12 o =Q 12 1H n G H =Q +12 o =Q 12 1 n G H =Q +12 o =Q 12 1 Hn G H =Q +12 o =Q 12 1G 12 G H Hdbke_gb_ g_f_lZeeh\ J +12 dhgp o +JH 12 n G H Hdbkey_l kheygmx dbkehlm kf_kv +12 b +&O ± pZjkdZy \h^dZ hq_gv kbevguc hdbkebl_ev jZkl\hjy_l ^Z`_ ahehlh +12 +&O o 12&O &O + 2 K hkgh\gufb hdkb^Zfb D H +12 o .12 G H K hkgh\Zgbyfb +12 KZ HG o KZ HG G H K kheyfb [he__ keZ[uo dbkehl +12 &D&2 &D 12 G H KH n JZaeh`_gb_ ih^ ^_ckl\b_f k\_lZ +12

k\_l o + 2 12 n H

<hijhk ‹

GZibrbl_ mjZ\g_gby j_Zdpbc ijhl_dZxsbo f_`^m k_j_[jhf b jZa [Z\e_gghc Zahlghc Z lZd`_ dhgp_gljbjh\Zgghc Zahlghc dbkehlhc Ih dZ`bl_ i_j_oh^ we_dljhgh\ b ih^q_jdgbl_ hdbkebl_ev h^ghc q_jlhc Z \hkklZgh\bl_ev ± ^\mfy

Hl\_l $J +12 jZa[ o $J 12 1 2n G H H± $J ± _ o $J 1 _ o 1

\hkklZgh\bl_ev hdbkey_lky hdbkebl_ev \hkklZgZ\eb\Z_lky

$J +1 2 dhgp o $J 12 1 2 n G H

HÂą $J Âą _ o $J 1 _ o 1

\hkklZgh\bl_ev hdbkey_lky hdbkebl_ev \hkklZgZ\eb\Z_lky

<hijhk ‹

< ^\mo ijh[bjdZo gZoh^ylky jZaebqgu_ gbljZlu [_eh]h p\_lZ Ijb gZ]j_\Zgbb h^ghc kheb \u^_ey_lky [_kp\_lguc ]Za \ dhlhjhf le_xsZy emqbgdZ \kiuob\Z_l Ijb gZ]j_\Zgbb \lhjhc kheb \u^_ey_lky ]Za [mjh]h p\_lZ DZdb_ wlh gbljZlu" GZibrbl_ khhl\_lkl\mxsb_ mjZ\g_gby hdbkebl_evgh \hkklZgh\bl_evguo j_Zdpbc

Hl\_l LZf ]^_ emqbgZ \kiuob\Z_l \u^_ey_lky 2 ke_^h\Zl_evgh \ ijh[bjd_ gZoh^blky gbljZl Zdlb\gh]h f_lZeeZ GZijbf_j 1D12 1D12 2 &D 12 &D 12 2 LZf ]^_ \u^_ey_lky [mjuc ]Za Âą wlh hdkb^ ZahlZ ,9 12 ke_ ^h\Zl_evgh \ ijh[bjd_ gZoh^blky khev h[jZah\ZggZy f_lZeehf dhlhjuc \ jy^m f_lZeeh\ gZoh^blky ijZ\__ f_^b $J12 $J 12 n H

<hijhk ‹

Ijb ]jhah\uo jZajy^Zo \ ihq\_ bgh]^Z fh`_l h[jZah\Zlvky gbljZl dZevpby GZibrbl_ mjZ\g_gby khhl\_lkl\mxsbo j_Zdpbc

Hl\_l

1 2 o 12 12 2 o 12 12 + 2o +12 12 +12 &D&2 o &D 12 + 2 &2 n we jZajy^

AZ^ZqZ ‹

DZdhc h[t_f ZffbZdZ g m ihlj_[m_lky ^ey ihemq_gby l jZkl\h jZ kh^_j`Zs_]h fZkkh\uo ^he_c Zahlghc dbkehlu"

>Zgh P jÂąjZ l Z +1H g m

9 1G Âą " g m

1+ 2 o 12 G H 12 2 o 12 12 G H 2 l +12 1+ o +12 P +1H ˜

of

l

1+ o +12 ˜ f

l

P +1H P jÂąjZ ˜ Z +1H ˜ l o f ˜ f 1+ Âą Q 1+2 ˜ ˜ [ ˜ f Hl\_l 9 1+ f

AZ^ZqZ ‹

D ] jZkl\hjZ kh^_j`Zs_]h fZkkh\uo ^he_c ]b^jhdkb^Z dZeby ijbebeb ] jZkl\hjZ kh^_j`Zs_]h fZkkh\uo ^he_c Zahlghc db kehlu DZdh\Z j_Zdpby ihemq_ggh]h jZkl\hjZ g_cljZevgZy dbkeZy beb s_ehqgZy" Kdhevdh ]jZffh\ kheb h[jZah\Zehkv"

>Zgh P SÂąSD ] P SÂąSD ] Z .2+ O Z G1H

]

]

o ]

]

]

]

DHG +12 o .12 G H

J_Zdpby ihemq_ggh]h jZkl\hjZ dbkeZy l d +12 ^ZgZ \ ba[uld_ kf j_r_gb_ P DHG P SÂąSD ˜ Z DHG ] P D1H Âą " P G12 P SÂąSD ˜ Z G12 ] 0U .2+ 0U +12 ˜ ] DHG Âą [ ] +12 ] .2+ Âą ] +12 ˜ ] o FZkkZ +12 g_h[oh^bfZy ^ey j_Zdpbb Âą ] agZqbl +12 ^ZgZ \ ba[uld_ Ijhba\h^bf jZkq_l ih \_s_kl\m ^Zgghfm \ g_^hklZld_ DHG 0U .12 ˜ ] .2+ Âą o ] .1H ] DHG Âą ] .12 ˜ ] o Hl\_l P D12 ] kj_^Z dbkeZy l d ZahlgZy dbkehlZ ^ZgZ \ ba[uld_

†† ± klj ± <hijhk ‹

Ijb \aZbfh^_ckl\bb Zahlghc dbkehlu gZ nhknhj ihemqZ_lky hjlh nhknhjgZy dbkehlZ KhklZ\vl_ mjZ\g_gb_ wlhc j_Zdpbb _keb ba\_klgh qlh \ g_c mqZkl\m_l \h^Z b \u^_ey_lky hdkb^ ZahlZ ,,

Hl\_l 3 +1 2 + 2 o + 3 2 1 2n \hkklZgh\bl_ev hdbkey_lky 3 ± _ o 3 hdbkebl_ev \hkklZgZ\eb\Z_lky 1 _ o 1

<hijhk ‹

KhklZ\vl_ fhe_dmeyjgu_ b bhggu_ mjZ\g_gby j_Zdpbc hjlhnhknhj ghc dbkehlu k Z dZevpb_f [ hdkb^hf dZevpby \ ]b^jhdkb^hf dZevpby \ayluf \ ba[uld_ \ g_^hklZld_ Ih^ nhjfmeZfb aZibrbl_ gZa\Zgby kh hl\_lkl\mxsbo \_s_kl\

Hl\_l AKZ G J2 o KZ JH p AG n hjlhnhknZl dZevpby

AKZH G J2 o KZ JH p AG H hjlhnhknZl dZevpby

AKZ H+ ba[ G J2 o KZ HG JH AG H hjlhnhknZl dZevpby

KZ H+ G o KZ HG± JH ± AG H ± HG G o G H KZ H+ G J2 ba[ o KZGJH G H

]

±

KZ H+ G HG± G o G H

±

J2 ±

]b^jhnhknZl dZevpby

J2 ±

o KZ G JH ± AG H

<hijhk ‹

I_j_qbkebl_ \Z`g_crb_ Zahlgu_ m^h[j_gby KhklZ\vl_ mjZ\g_gby j_Zdpbc gZ dhlhjuo hkgh\Zgh ijhba\h^kl\h wlbo m^h[j_gbc

Hl\_l 1D &2 12 1D12 1D12 &2 ± ihemqZ_f gbljZl gZljby 1D12 1+ &2 &2 1+ ± fhq_\bgZ + 62 1+ 1+ 62 ± kmevnZl Zffhgby +12 1+ 1+ 12 ± gbljZl Zffhgby

<hijhk ‹

GZibrbl_ mjZ\g_gby obfbq_kdbo j_Zdpbc ijb ihfhsb dhlhjuo ihem qZxl \Z`g_crb_ nhknhjgu_ m^h[j_gby

Hl\_l Ijhklhc kmi_jnhknZl + 62 &D 32 &D + 32 &D62 >\hcghc kmi_jnhknZl + 32 &D 32 &D + 32

<hijhk ‹

KhklZ\vl_ mjZ\g_gby j_Zdpbc kh]eZkgh ko_fZf b

Hl\_l Ko_fZ ‹ Z 1+ &O &D 2+ o &D&O 1+ n G H beb 1+ &O o 1+ n +&On [ 1+ +&O o 1+ &O \ 1+ &O + H o 1+ HG +&O 1+ + H o 1+ HG + ] 1+ HG l 1+ + H W

5K 3W o 12 + H W H 1 2 o 12 W o 0J 1 ` 1 0J

^ 1+

gbljb^ fZ]gby

a 0J 1 + H o 0J 2+ 1+ n b 12 2 o 12 d 12 HG o G12 12

e G12 o G H 12 n 2 n f G12 DHG o D12 G H W k\_l

o $J 12 n 2 n g $J12 R 1 2 DHG o D12 + 2 i 12 G H o G12 G12 W

ZahlbklZy dbkehlZ

j G12 DHG o D12 + 2 gbljbl dZeby

k G12 =Q o =Q 12 12 + 2 l 1+ +12 o 1+ 12

Ko_fZ ‹ Z J H o J H

o G J2 [ J H + 2 \ J +12 + 2 o G J2 12n ] G J2 DHG o G J2 12n W

o G J2 D&On ^ D J2 GKO H J H DHG o D J2 + 2 ` G J2 o G J 2 + 2 W

^\mnhknhjgZy dbkehlZ

a KZ JH K 6L2

W o &D6L2 3 &2

o KZ J b KZ J d KZ J + 2 o JG KZ HG e Q+ 2 Q J H o +32 Q W

f_lZnhknhjgZy dbkehlZ

o +32 + 2 G J H f G32 DHG o DJH G H W

f_lZnhknZl dZeby

AZ^ZqZ ‹

Kdhevdh hjlhnhknhjghc dbkehlu fh`gh ihemqblv ba l hjlh nhknZlZ dZevpby _keb \uoh^ dbkehlu khklZ\ey_l fZkkh\uo ^he_c beb ih kjZ\g_gbx k l_hj_lbq_kdbf"

>Zgh P KZ J2 l ijZdl \uo ± fZkkh\uo ^he_c beb P G J2 ± " l

[ l

KZ JH + 62 o &D62 + 32 l

˜ l

FU KZ JH ˜ ˜ ˜ FU G JH ˜ ˜ JZkkqblZ_f l_hj_lbq_kdbc \uoh^ G JH l KZ JH ± o l G 32 l KZ JH ± l G 32 ˜ l [ IjZdlbq_kdbc \uoh^ G 32

l G 32 ± o l G 32 ± ˜ [ l

Hl\_l P G 32 l

AZ^ZqZ ‹

Kh^_j`Zgb_ iblZl_evgh]h we_f_glZ nhknhjZ \ nhknhjguo fbg_ jZevguo m^h[j_gbyo hij_^_eyxl \ i_j_kq_l_ gZ hdkb^ nhknhjZ 9 Kdhevdh wlh]h hdkb^Z \ ijhklhf b ^\hcghf kmi_jnhknZl_"

KZ JH G 62 o KZ + JH &D62 ijhklhc kmi_jnhknZl

FU KZ + JH ˜ FU &D6H Pijhklh]h kmi_jnhknZlZ ˜ FU J H ˜ ˜ ˜ | Z J H

KD + JH ± ^\hcghc kmi_jnhknZl FU KZ + JH ˜ ˜ | Z KZ + JH

Hl\_l Z J H ijhklhc kmi_jnhknZl

Z KZ + JH ^\hcghc kmi_jnhknZl

AZ^ZqZ ‹

Kdhevdh lhgg ^\hcgh]h kmi_jnhknZlZ ihlj_[m_lky qlh[u aZf_gblv l ijhklh]h kmi_jnhknZlZ"

>Zgh P ijhF kmi_jn l

FU ij kmi nhkn kf ij_^u^msmx aZ^Zqm FU ^\ kmi nhkn P ^\ k n ± " FU J H Z J H Z J H ˜ l \ l i k ± l J H

\ l ^ k ± l J H ˜ l o l ^ k ± l J H o Hl\_l lj_[m_lky l ^\hcgh]h kmi_jnhknZlZ

=eZ\Z 9

†† ± klj ± <hijhk ‹

KhklZ\vl_ mjZ\g_gby j_Zdpbc ijhl_dZxsbo ijb gZ]j_\Zgbb m]ey kh ke_^mxsbfb hdkb^Zfb hdkb^hf `_e_aZ ,,, hdkb^hf heh\Z ,9 Ih dZ`bl_ i_j_oh^ we_dljhgh\ b ih^q_jdgbl_ h^ghc q_jlhc hdbkebl_ev Z ^\mfy ± \hkklZgh\bl_ev

Hl\_l

)H 2 & o

H± & ± H o & )H H o )H

W

)H & 2

\hkklZgh\bl_ev hdbkey_lky hdbkebl_ev \hkklZgZ\eb\Z_lky

\hkklZgh\bl_ev hdbkey_lky hdbkebl_ev \hkklZgZ\eb\Z_lky

6Q 2 & o 6Q & 2

H± & ± H o & 6Q H o 6Q

W

<hijhk ‹

DZdhc ba ]Zah\ y\ey_lky [he__ p_gguf lhieb\hf ]_g_jZlhjguc beb \h^yghc" Ihq_fm"

Hl\_l =_g_jZlhjguc ]Za ± KH <h^yghc ]Za ± KH G <h^yghc ]Za [he__ p_g_g

<hijhk ‹

KhklZ\vl_ mjZ\g_gby j_Zdpbc ijhl_dZxsbo k h[jZah\Zgb_f hdkb^Z m]e_jh^Z ,9 \ ijbjh^_ \ [ulm \ eZ[hjZlhjbb b \ ijhfure_gghklb

Hl\_l \ ijbjh^_ ± ]hj_gb_ K H KH \ eZ[hjZlhjbb &D&2 +&O &D&O &2 + 2 ± j_Zdpby aZf_s_gby

\ ijhfure_gghklb &X2 & &X &2

<hijhk ‹

Ijb ijhimkdZgbb hdkb^Z m]e_jh^Z ,9 q_j_a jZkl\hj ]b^jhdkb^Z dZev pby \gZqZe_ h[jZam_lky \a\_kv dhlhjZy aZl_f jZkl\hjy_lky GZibrbl_ mjZ\g_gby khhl\_lkl\mxsbo j_Zdpbc

Hl\_l KH KZ HG o &D&2 p G H ± ihfmlg_gb_ Ijb ^Zevg_cr_f ijhimkdZgbb &2 h[jZam_lky jZkl\hjbfuc ]b^ jhdZj[hgZl dZevpby KZKH G H KH o KZ GKH

<hijhk ‹

DZd kf_klblv ijhp_kk h[jZlbfhc j_Zdpbb Z \ijZ\h b [ \e_\h &2 + 2 + &2 4" Ihq_fm wlZ j_Zdpby h[jZlbfZy"

Hl\_l

o G K2 4 KH G H m Wlh wdahl_jfbq_kdZy j_Zdpby Ijb ih\ur_gbb W jZ\gh\_kb_ j_Zd pbb [m^_l kf_sZlvky \e_\h Kf_klblv jZ\gh\_kb_ j_Zdpbb \ijZ\h fh`gh m\_ebqb\ ^Z\e_gb_ WlZ j_Zdpby h[jZlbfZ S

<hijhk ‹

>ey bamq_gby obfbq_kdbo k\hckl\ m]hevghc dbkehlu \ h^bg jZkl\hj gZkus_gguc hdkb^hf m]e_jh^Z ,9 himklbeb heh\h \ ^jm]hc ± fZ]gbc Z \ lj_lbc ± gZljbc < dZdhf kemqZ_ m^Zehkv ^hdZaZlv qlh m]hevgZy dbkeh lZ ohly b g_Zdlb\gh gh \k_ `_ j_Z]bjm_l k f_lZeeZfb" Ihq_fm"

Hl\_l J_Z]bjm_l lhevdh k Zdlb\gufb f_lZeeZfb G KH 0J o 0J&2 + n G KH 1D o 1D &2 + n

<hijhk ‹

Ihq_fm \ h]g_lmrbl_eyo bkihevamxl ]b^jhdZj[hgZl gZljby Z g_ dZj[hgZl gZljby"

Hl\_l Ijb g_[hevrhf gZ]j_\Zgbb ]b^jhdZj[hgZlZ \u^_ey_lky &2 1DG&2 1D&H + 2 &2 n >ey dZj[hgZlZ gZljby gm`gu \ukhdb_ l_fi_jZlmju ihwlhfm hgb g_ bkihevamxlky

<hijhk ‹

KhklZ\vl_ mjZ\g_gby j_Zdpbc khhl\_lkl\mxsbo ke_^mxs_c ko_f_

Hl\_l 1D &2 + 2 o 1D &2 ˜ + 2 dZevpbgbjh\ZggZy kh^Z

djbklZeebq_kdZy kh^Z

JZkl\hj_gb_ kh^u \ \h^_ b ihke_^mxs__ \uiZjb\Zgb_

1D &2 ˜ + 2 o 1D &2 + 2 ijhdZeb\Zgb_

1D &2 + 2 &2 o 1DG&2 W

1DG&2

W o 1D &2 &2 n + 2

<hijhk ‹

Bkihevamy jbkmghd khklZ\vl_ mjZ\g_gby obfbq_kdbo j_Zdpbc dh lhju_ ijhbkoh^yl ijb djm]h\hjhl_ m]e_jh^Z \ ijbjh^_

Hl\_l

>uoZgb_ & G H H o &2 n + H Nhlhkbgl_a &2 n + H o & G H H n n_jf_glu

=hj_gb_ m]ey & H o &2 =hj_gb_ hj]Zgbq_kdbo \_s_kl\ g_nlv ijbjh^guc ]Za b l i &G H o &2 + H K`b]Zgb_ lhieb\Z [_gabg b l i W

& G H o &2 + H ;jh`_gb_ ih^ ^_ckl\b_f ^jh``_\uo n_jf_glh\ & G H o &2 n K + HG W

]exdhaZ

wlZghe

JZaeh`_gb_ ba\_klgydZ h[`b] KZKH

AZ^ZqZ ‹

W o KZH KH

DZdhc h[t_f hdkb^Z m]e_jh^Z ,9 \u^_eblky g m ijb h[`b]_ l ba\_klgydZ kh^_j`Zs_]h fZkkh\mx ^hex ijbf_k_c"

>Zgh

P KZKH l Zijbf_k_c 9 KH ± " g m

l

KZKH l

ol

o KZH KH n W

l

Pijbf_k_c ˜ l P &D&2 ± l

0U &D&2 ˜ 0U &2 ˜ l KZKH Âą o l KH l KZKH Âą l KH o Ăœ l P &2 l l KH Âą ˜ f KH l KH Âą o f KH o ˜ ˜ ˜ Hl\_l 9 KH f

AZ^ZqZ ‹

Kdhevdh ihlj_[m_lky djbklZeebq_kdhc kh^u ^ey iheghc g_cljZebaZ pbb ] k_jghc dbkehlu"

>Zgh P G 62 ]

P G &2 ˜ + 2 Âą "

o ]

]

]

]

1Z KH ˜ G H G 62 o 1Z 62 KH ˜ G H

0U G &2 ˜ + 2 ˜ ˜ ˜ ˜ 0U G 62 ˜ ˜ o ] 1Z KH ˜ G H Âą ] G 62 ] 1Z KH ˜ G H Âą ] G 62 ˜ o ] Hl\_l P G &2 ˜ + 2 ]

AZ^ZqZ ‹

Kdhevdh ihlj_[m_lky jZkl\hjZ kh^_j`Zs_]h fZkkh\uo ^he_c beb oehjh\h^hjh^Z ^ey j_Zdpbb k ] dZj[hgZlZ gZljby"

>Zgh P G &2 ] Z GKO P SÂąSZ Âą " o

˜

]

Hl\_l P jÂąjZ ]

]

o ]

]

˜ ]

1Z KH GKO o 1Z&O G H KH n 0U G &2 0U GKO ] 1Z KH Âą o ] GKO ] 1ZKH Âą ] G&O P jÂąjZ

˜

]

AZ^ZqZ ‹

< ] \h^u jZkl\hjbeb ] djbklZeebq_kdhc kh^u Hij_^_ebl_ fZkkh\mx ^hex b ijhp_glgh_ kh^_j`Zgb_ [_a\h^ghc kheb 1D &2 \ ih emq_gghf jZkl\hj_

>Zgh P + 2 ] P G &2 ˜ + 2 ] Z G &2 Âą " Z 1D &2 Âą "

P 1D &2 ]

P 1D &2

Z 1D &2 P j jZ

Z 1D &2

P jÂąjZ ] 0U 1D &2 ˜ ˜ 0U 1D &2 ˜ + 2 ˜ \ ] 1Z KH ˜ G H Âą ] 1D &2 \ ] 1Z KH ˜ G H Âą o ] 1D &2 ˜ o

Hl\_l Z 1D &2 fZkkh\uo ^he_c Z 1D &2

AZ^ZqZ ‹

] kf_kb khklhys_c ba dZj[hgZlZ b ]b^jhdZj[hgZlZ gZljby kbevgh ijhdZebeb HklZlhd ihke_ ijhdZeb\Zgby \_kbe ] <ujZabl_ khklZ\ kf_kb \ fZkkh\uo ^heyo

>Zgh Pkf_kb ]

PhklZldb ]

khklZ\ kf_kb \ fZkkh\uo ^heyo Âą "

Ijb gZ]j_\Zgbb jZaeZ]Z_lky lhevdh ]b^jhdZj[hgZl gZljby o ]

1Z GKH ˜ ]

]

o 1Z KH G H KH n W

]

>ey lh]h qlh[u gZclb _]h fZkkm gm`gh magZlv fZkkm \u^_eb\ rboky \_s_kl\ P G H KH P kf_kb Âą P hkl Âą ] FU G H KH 0U 1D+12 o ] 1D+&2 Âą ] + H KH ˜ ] ] 1D+&2 Âą ] + 2 &2 o P 1D+&2 ]

Z 1D+&2 Z 1D+&2 Âą beb

Z 1D+&2

Hl\_l Z 1D+&2 f ^ Z 1D+&2 Z 1D &2 f ^ Z 1D &2

†† ¹ klj <hijhk ‹

DZd ihemqZxl k\h[h^guc dj_fgbc \ l_ogbd_ b \ eZ[hjZlhjbb" GZib rbl_ mjZ\g_gby wlbo j_Zdpbc b ijhZgZebabjmcl_ bo k we_dljhgghc lhqdb aj_gby

Hl\_l < ijhfure_gghklb bkihevamxl \ dZq_kl\_ \hkklZgh\bl_ey m]e_ jh^ 6L2 & 6L &2 < eZ[hjZlhjbb bkihevamxl fZ]gbc 6L2 0J 6L 0J2

<hijhk ‹

DZdh\u nbabq_kdb_ b obfbq_kdb_ k\hckl\Z dj_fgby" Ijb\_^bl_ mjZ\ g_gby khhl\_lkl\mxsbo obfbq_kdbo j_Zdpbc Ihykgbl_ dZdb_ k\hckl\Z dj_fgby bkihevamxl \ l_ogbd_

Hl\_l Nbabq_kdb_ k\hckl\Z djbklZeebq_kdbc dj_fgbc h[eZ^Z_l f_lZeebq_kdbf [e_kdhf lm]hieZ\dbc hq_gv l\_j^uc ihemijh \h^gbd Obfbq_kdb_ k\hckl\Z dj_fgbc fZehZdlb\_g Z ijb ih\ur_gguo l_fi_jZlmjZo Âą ƒK

6L 2 6L2 6L &O 6L&O 6L 6 6L6 6L + 6L+ [ ba keh`guo \_s_kl\ dj_fgbc j_Z]bjm_l kh s_ehqZfb 6L 1DHG G H 1D 6L2 G n \ j_Z]bjm_l k f_lZeeZfb k h[jZah\Zgb_f kbebpb^h\ KZ 6L o &D 6L W

0J 6L o 0J 6L < l_ogbd_ bkihevamxl ihemijh\h^gbdh\u_ k\hckl\Z dj_fgby _]h `Zjhijhqghklv b dbkehlhmihjghklv ijhba\h^kl\h dj_fgbkluo klZe_c W

<hijhk ‹

DZd fh`gh ihemqblv dj_fgb_\mx dbkehlm ba hdkb^Z dj_fgby ,9 " GZibrbl_ mjZ\g_gby j_Zdpbc

Hl\_l 6L2 1D2G o 1D 6L2 G H 1D 6L2 +& o G 6L2 p 1D&O

<hijhk ‹

DZdb_ ba khe_c kbevg__ ih^\_j]Zxlky ]b^jhebam ± kbebdZlu beb dZj [hgZlu" Ihq_fm"

Hl\_l KbebdZlu ihlhfm qlh dj_fgb_\Zy dbkehlZ keZ[__ m]hevghc Ijb ]b^jheba_ kbebdZlh\ h[jZam_lky dj_fgb_\Zy dbkehlZ 1D &2 + 2 1D+&2 1D2+ 1D 6L2 + 2 G 6L2 p 1D2+

<hijhk ‹

KhklZ\vl_ mjZ\g_gby j_Zdpbc \ j_amevlZl_ dhlhjuo h[jZam_lky kl_deh Z h[udgh\_ggh_ [ dZeb_\h_ \ ojmklZevgh_

Hl\_l

o 1D 6L2 &2 n Z 1D &2 6L2 W

&D &2 6L2 o &D 6L2 &2 n W

1D 6L2 &D 6L2 6L2 o 1D 2 ˜ &D2 ˜ 6L2 W

o D 6L2 &2 n [ D &2 6L2 W

o D 2 ˜ &D2 ˜ 6L2 D 6L2 &D 6L2 6L2 W

o D 2 ˜ 3E2 ˜ 6L2 \ D 6L2 JE2 6L2 W

<hijhk ‹

KhklZ\vl_ mjZ\g_gby j_Zdpbc kh]eZkgh ko_fZf b

Hl\_l Ko_fZ

W o KH W o K G KG W o : KZ AK :

K 2

K KZ o KZK KZK G H o KZ HG K G

KH G H l G KH

W

W o K G [G H W $O &O + 2 o AKG : HG jZa[ dÂąlZ

&+ 2

&2 2 o KH W

o KH KH K KH ba[ 1D2+ o 1D+&2 &2 0J o 0J2 & W

o K G KG 1D+&2 +& o 1D&O G H &2 n 1D+&2 1D2+ o 1D &2 + 2 1D &2 &2 + 2 o 1D+&2 &2 1D2+ o 1D &2 + 2 1D &2 +&O o 1D&O + 2 &2 n W

+ K

2

2

+

62 W G o + 2 &2n

fmjZ\vbgZy dbkehlZ

Ko_fZ

W o 6L2 W 6L2 0J o 0J2 6L

6L H

1D 6L2 &D6L2 6L2 o 1D 2 ˜ &D2 ˜ 6L2 1D &2 6L2 o 1D 6L2 KH n 1D 6L2 +&O o + 6L2 1D&O + 6L2 o + 2 6L2 6L DHG G 2 o D 6L G

AZ^ZqZ ‹

Kdhevdh ihlj_[m_lky hdkb^Z dj_fgby ,9 kh^_j`Zs_]h fZkkh\u_ ^heb ijbf_k_c qlh[u ihemqblv d] kbebdZlZ gZljby"

>Zgh

Zijbf_k_c P 1Z 6L2 d] P 6L2 Âą "

o d]

6L2 1D &2 d]

d]

o 1D 6L2 KH n W

d]

0U 1D 6L2 ˜ ˜

0U 6L2 ˜ o d] 6L2 ± d] 1D 6L2 d] 6L2 ± d] 1D 6L2 ˜ P 6L2 d] o Bs_f fZkkm 6L2 k ijbf_kyfb d] 6L2 ± o d] 6LH ± ˜ P 6L2 k ijbf_kyfb d] o Hl\_l d]

AZ^ZqZ ‹

Kdhevdh ihlj_[m_lky kujvy ^ey ihemq_gby l kl_deZ"

>Zgh P 1D H ˜ &D2 ˜ 6L2 l P 1D &2 ± " P KZKH ± " P 6L2 ± " o d]

[ d]

[ d]

d]

d]

d]

d]

d]

1Z KH KZKH 6L2 o 1D 2 ˜ &D2 ˜ 6L2

FU kl_deZ ˜ ˜ FU 1Z KH ˜ ˜ FU KZ KH ˜ FU 6LH o d] 1Z KH ± d] kl_deZ d] 1Z KH ± d] kl_deZ ˜ [ d] P 1Z KH d] o d] KZKH ± d] kl_deZ d] KZKH ± d] kl_deZ ˜ [ d] P KZKH d] o d] 6LH ± d] kl_deZ d] 6LH ± d] kl_deZ ˜ [ d] P 6LH d] Hl\_l P 1Z KH d] P KZKH d] P 6LH d]

=eZ\Z 9,

†† ¹ klj ¹ <hijhk ‹

;jhf fh`gh ihemqblv Z ^_ckl\my gZ jZkl\hj [jhfb^Z dZeby oehj ghc \h^hc [ ih^\_j]Zy jZkl\hj [jhfb^Z dZeby we_dljhebam Qlh h[s_]h \ kmsghklb wlbo ijhp_kkh\ b q_f hgb hlebqZxlky"

Hl\_l .%UÂą &O o .&O %U n

.%UÂą + 2 o %U DHG G we_dljheba

Zgh^

dZlh^

Wlh hdbkebl_evgh \hkklZgh\bl_evgu_ j_Zdpbb ijb hdbke_gbb bh gh\ <U¹ H^gZdh \ i_j\hf kemqZ_ hdbkebl_e_f y\ey_lky oehj Z \h \lhjhf kemqZ_ ¹ we_dljbq_kdbc lhd gZ Zgh^_ Š ª

<hijhk ‹

GZq_jlbl_ \ k\hbo l_ljZ^yo gb`_ijb\_^_ggmx lZ[ebpm b \ khhl \_lkl\mxsbo ]jZnZo gZibrbl_ mjZ\g_gby ijZdlbq_kdb hkms_kl\bfuo j_Zdpbc mdZ`bl_ mkeh\by bo ijhl_dZgby kf ko_fm

Hl\_l

J_Z]bjmÂą MjZ\g_gby ijZdlbq_kdb hkms_kl\bfuo j_Zdpbc xsb_ k f_lZeeZfb \_s_klÂą 1D &D =Q &X $J \Z H 1D 2 o &D 2 o =Q 2 o &X 2 o Âą o 1D 2 o &D2 o =Q2 o &X2 1D + 2 &D + 2 =Q + 2 o Âą Âą G H o 1D2+ o &D 2+ =Q2 + n + n + n 3E 1H 1D + 2 &D + 2 o 3E 12 Âą Âą \ jZk o 1D2+ &D 2+ =Q o l\hj_ =Q 12 + n + n 3E 1D +&O &D +& =Q +&O Âą Âą GKO o 1D&O o &D&O o =Q&O + n + n + n

J_Z]b MjZ\g_gby ijZdlbq_kdb hkms_kl\bfuo j_Zdpbc jmxsb_ k f_lZeeZfb \_s_kl\Z 1D &D =Q &X $J + 62 1D &D =Q 62 o &X G 62 Âą G 62 o G 62 o =Q62 o &X62 62 o 1D 62 o &D62 + n + 2 + n + n

<hijhk ‹

KieZ\ `_e_aZ ihf_klbeb \ \h^m kh^_j`Zsmx Z dbkehjh^ [ dbkeh jh^ b hdkb^ m]e_jh^Z ,9 < dZdhf kemqZ_ dhjjhaby kieZ\Z [m^_l ijhl_ dZlv bgl_gkb\g__ b ihq_fm" GZibrbl_ mjZ\g_gby j_Zdpbc

Hl\_l Z )H \aZbfh^_ckl\m_l k dbkehjh^hf b \h^hc )H G H H : )H 2+ )H 2+ G H H : )H 2+ [ MjZ\g_gby Z bf_xl f_klh gh lZd`_ b^_l j_Zdpby k G &H G H l + &2 + &2 G l +&2 Âą +&2 Âą : G &2 Âą )H G : )H + l _ )H + &2 : )H&H p G 9 Dhjjhaby [m^_l ijhl_dZlv bgl_gkb\g__ \ kemqZ_ [

<hijhk ‹

D dmkdm `_e_aZ gZoh^ys_fmky \ jZkl\hj_ kheyghc dbkehlu ijbdhkgm ebkv pbgdh\hc ijh\hehdhc Ih\eby_l eb wlh gZ kdhjhklv b oZjZdl_j ob fbq_kdhc j_Zdpbb `_e_aZ k dbkehlhc"

Hl\_l Pbgd Zdlb\g__ `_e_aZ ihwlhfm [m^_l b^lb j_Zdpby =Q +&O =Q&O + ijb wlhf jZkl\hj_gb_ `_e_aZ aZf_^eblky

AZ^ZqZ ‹

Ijb we_dljheba_ jZkl\hjZ oehjb^Z f_^b ,, fZkkZ dZlh^Z m\_ebqb eZkv gZ ] DZdhc ]Za \u^_ebeky b dZdh\u _]h fZkkZ b h[t_f g m "

>Zgh

PdZlh^Z \hajhkeZ gZ ] P]ZaZ Âą " 9]ZaZ Âą "

&X&O jÂąj

we_dljheba o KX KO 9 ]

dZlh^

]

o ]

Zgh^

]

0U &X 0U &O ˜

] &X Âą [ ] KO ] &X Âą ] KO ˜ [ ] ] KO Âą [ e &X ] KO Âą e &X

P &O ] [

˜ e 9 &O e

Hl\_l P &O ] 9 &O e

AZ^ZqZ ‹

Ijb we_dljheba_ \h^gh]h jZkl\hjZ gbljZlZ k_j_[jZ , \u^_ebehkv e ]ZaZ Kdhevdh ]jZffh\ f_lZeeh\ hleh`behkv gZ dZlh^_"

>Zgh F]ZaZ e P $J Âą "

e H Âą [ ] H

$J12 + 2 o $J 2 9 +12 we_dljheba

[ ]

]

dZlh^

Zgh^

˜ ]

0U $J

]

e H Âą ] H

[

˜ ] P H ]

˜ ] $J Âą ] H

[

˜

o ] $J Âą ] &X

Hl\_l P $J ]

] P $J ]

AZ^ZqZ ‹

Ijb we_dljheba_ \h^gh]h jZkl\hjZ oehjb^Z dZeby h[jZah\Zehkv d] ]b^jhdkb^Z dZeby DZdb_ ]Zau \u^_ebebkv b dZdh\ bo h[t_f g m "

>Zgh P DHG ] P]ZaZ Âą " 9]ZaZ Âą "

D&O G H

we_dljheba o DHG G KO ]

o e

m e

˜ ]

0U DHG FZkkZ fhev DHG Âą ] Z Âąo fhev Âą ] agZqbl gZ fhey DHG \u^_ey_lky ih fhex G b &O Ba wlh]h fh`gh k^_eZlv \u \h^ qlh h[t_fu ]Zah\ [m^ml h^bgZdh\u b jZ\gu 9 + 9 &O fhev Ăœ e fhev e Hl\_l 9 + e 9 &O e

AZ^ZqZ ‹

< jZkl\hj kh^_j`Zsbc ] kmevnZlZ f_^b ,, ihf_klbeb ] `_ e_aguo hibehd DZdb_ \_s_kl\Z h[jZah\Zebkv b dZdh\Z bo fZkkZ"

>Zgh P KX62 ] P )H ] Ph[jZah\ \±\Z ± "

]

]

o ]

]

]

]

m ]

&X62 )H : )H62 KX

]

0U KX62 ˜ 0U )H62 ˜ 0U )H 0U KX )H ± \ g_^hklZld_ KX62 ± \ ba[uld_ ^Zevg_crb_ jZkq_lu \_^_f ih `_e_am ] )H ± o ] )H62 ] )H ± ] )H62 ˜ ] P )H62 ] o ] )H ± m ] KX ] )H ± ] &X ˜ ] P &X ] o Hl\_l P )H62 ]

P &X ]

AZ^ZqZ ‹

@_e_agmx ieZklbgdm fZkkhc ] ijh^he`bl_evgh_ \j_fy \u^_j`b\Z eb \ jZkl\hj_ kh^_j`Zs_f ] kmevnZlZ f_^b ,, AZl_f ieZklbgdm ba jZkl\hjZ \ugmeb \ukmrbeb b \a\_kbeb Q_fm jZ\gZ __ fZkkZ"

>Zgh P )H ] P KX62 ] PieZklbgu ± "

]

]

m]

]

]

]

o]

)H &X62 : )H62 KX

]

0U )H 0U KX 0U KX62 kf aZ^Zqm

0U )H62 ] KX62 ± \ g_^hklZld_ JZkq_lu ijhba\h^bf ih KX62 ] KX62 ± o ] &X ] KX62 ± ] &X ˜ ] P &X ] o ] KX62 ± \ ] )H62 ] KX62 ± ] )H62

o

˜

]

P )H62 ]

0U )H

0U )H62 Z )H Z ˜ P )H62 ˜ ] < j_amevlZl_ j_Zdpbb bajZkoh^h\Zehkv ] )H FZkkZ `_e_aghc ieZklbgdb ihke_ j_Zdpbb [m^_l jZ\gZ P ieZkl P ieZkl ± P )H

P KX ± ]

Z )H

Hl\_l P ieZkl ]

AZ^ZqZ ‹

DZdh\Z fZkkZ hdkb^h\ k\bgpZ b heh\Z g_h[oh^bfZy ^ey ihemq_gby ] ijbihy khklhys_]h ba heh\Z b k\bgpZ"

>Zgh Pijbihy ± ] Z 6Q Z 3E P 3E ± " P 6Q2 ± "

o ]

]

]

]

3E2 & : 3E &2n m ]

]

]

]

6Q2 & : 6Q K2 n

P 6Q ˜ ] 0U 3E2 0U 6Q2 ˜ P 3E ˜ ] [ ] 3E2 ± ] 3E ] 3E2 ± ] 3E ˜ ] P 3E2 ] o m ] 6Q2 ± ] 6Q ] 6Q2 ± ] 6Q ˜ ] P 6Q2 ] o Hl\_l P 3E2 ] P 6Q2 ]

=eZ\Z 9,,

†† klj ± <hijhk ‹

DZdb_ hdbkebl_evgh \hkklZgh\bl_evgu_ j_Zdpbb ijhl_dZxl ijb ih emq_gbb f_lZeebq_kdh]h dZeby Z we_dljhebahf jZkieZ\e_ggh]h oehjb^Z dZeby [ we_dljhebahf jZkieZ\e_ggh]h ]b^jhdkb^Z dZeby" Ihq_fm ^ey wlhc p_eb g_evay ih^\_j]Zlv we_dljhebam \h^gu_ jZkl\hju wlbo \_ s_kl\"

Hl\_l

we_dljheba jZkieZ\Z

D KO± o D KO n dZlh^ D _ : D \hkklZgh\e_gb_ dZeby KO ± H : &O Zgh^ hdbke_gb_ oehjZ we_dljheba jZkieZ\Z

D HG o D G H n dZlh^ D _ : D \hkklZgh\e_gb_ dZeby H ± ± H : H Zgh^ hdbke_gb_ dbkehjh^Z G _ : G dZlh^ \hkklZgh\e_gb_ \h^hjh^Z <h^Z kZfZ ih^\_j]Z_lky ]b^jhebam ihwlhfm g_evay bkihevah\Zlv \h^gu_ jZkl\hju

±

<hijhk ‹

:lhfu dZdbo we_f_glh\ y\eyxlky [he__ kbevgufb \hkklZgh\bl_eyfb ± s_ehqgu_ f_lZeeu beb \h^hjh^" KhklZ\vl_ mjZ\g_gby j_Zdpbc ih^ l\_j`^Zxsbo hl\_l

Hl\_l ;he__ kbevgufb \hkklZgh\bl_eyfb y\eyxlky s_ehqgu_ f_lZe eu l d hgb \hkklZgZ\eb\Zxl \h^hjh^ g_ lhevdh ba dbkehl gh b ba \h^u b ijb wlhf y\eyxlky \hkklZgh\bl_e_f Z \h^hjh^ hdbkebl_ e_f 1D G H+ : 1D 2+ + 9 1D G : 1D+

<hijhk ‹

Qlh h[s_]h b q_f hlebqZxlky j_Zdpbb s_ehqguo f_lZeeh\ k \h^hc b k dbkehlZfb" KhklZ\vl_ mjZ\g_gby khhl\_lkl\mxsbo j_Zdpbc b ihdZ `bl_ i_j_oh^ we_dljhgh\

Hl\_l Ijb j_Zdpbyo s_ehqguo f_lZeeh\ k \h^hc b dbkehlZfb ijhy\ eyxlky hdbkebl_evgh \hkklZgh\bl_evgu_ k\hckl\Z \ h[hbo kemqZ yo s_ehqghc f_lZee \hkklZgZ\eb\Z_l \h^hjh^ 1D G H : 1D 2+ + 9 1D G KO : 1D &O + 9 < j_amevlZl_ j_Zdpbc s_ehqguo f_lZeeh\ k \h^hc h[jZam_lky ]b^jhdkb^ b \h^hjh^ Z k dbkehlZfb ± khev b \h^hjh^

<hijhk ‹

H[tykgbl_ ijhp_kku \ j_a l_ dhlhjuo ba oehjb^Z gZljby ihemqZxl Z f_lZeebq_kdbc gZljbc [ ]b^jhdkb^ gZljby \ dZj[hgZl gZljby Kh klZ\vl_ khhl\_lkl\mxsb_ ko_fu we_dljhebaZ b mjZ\g_gby j_Zdpbc

Hl\_l Z F_lZeebq_kdbc gZljbc we_dljheba jZkieZ\Z

1D KO± o 1D KO 9 KO ± H : &O Zgh^ 1D _ : 1D dZlh^ [ =b^jhdkb^ gZljby

hdbke_gb_ oehjZ \hkklZgh\e_gb_ gZljby

we_dljheba jZkieZ\Z

1D&O + 2 o 1D2+ G 9 &O 9 &O ± ± H : &O Zgh^ hdbke_gb_ oehjZ + _ : + dZlh^ \hkklZgh\e_gb_ \h^hjh^Z \ Ihemqblv ba oehjb^Z gZljby dZj[hgZl gZljby fh`gh g_kdhev dbfb kihkh[Zfb Iml_f we_dljhebaZ ihemqblv gZljbc aZl_f 1D H : 1D 2 i_jhdkb^ gZljby

1D 2 KH : 1D KH H 9 1DKO KH 1+ + H : 1D+&2 ; 1+ KO 1D+&2 : 1D KH KH 9 + H

<hijhk ‹

GZ hkgh\Zgbb dZdbo k\hckl\ fh`gh k^_eZlv \u\h^ qlh i_jhdkb^u ± kheb i_jhdkb^Z \h^hjh^Z"

Hl\_l 1D H + 62 1D 6H + 2 Wlh j_Zdpby aZf_s_gby k_jgZy dbkehlZ aZf_sZ_l [he__ keZ[mx dbkehlm

<hijhk ‹

Ijb\_^bl_ mjZ\g_gby j_Zdpbc khhl\_lkl\mxsb_ ko_f_ ij_\jZs_gbc kf ko_fm

Hl\_l 1D 2 : 1D 2 1D 2 &2 : 1D &2 2 9 1D &O : 1D&O

1D &2 : 1D 2 &2 9

we_dljheba jZkieZ\Z

1D&O o 1D &O 9 1D + : 1D+ 1D + 2 : 1D2+ + 9 1DHG KX&O : &X 2+ ; 1D&O

&+ Âą & + &22 &+ Âą 2+ &+ Âą & + &22 1D2+ o &+ Âą 2+ &+ Âą & + &22

&+ Âą 2+

`bj beb wnbj ]ebp_jbgZ b kl_Zjbgh\hc dbkehlu

]ebp_jbg

1D &2 G&O : 1DKO + 2 &2 9 1D &2 &2 + 2 : 1D+&2 1D+&2 1D2+ : 1D &2 + 2

& + &2 1D kl_ZjZl gZljby

hkgh\Z fueZ

AZ^ZqZ ‹

Kdhevdh ]jZffh\ jZkl\hjZ kh^_j`Zs_]h fZkkh\uo ^he_c beb ]b^jhdkb^Z gZljby ihlj_[m_lky ^ey g_cljZebaZpbb ] jZkl\h jZ kh^_j`Zs_]h fZkkh\uo ^he_c beb k_jghc dbkehlu"

>Zgh P jÂąjZ + 62 ] Z + 62 f ^ Z 1D2+ f ^ P jÂąjZ 1D2+ Âą "

o]

]

˜ ]

]

1D2+ + 62 : 1D 62 + 2

P + 62 P jÂąjZ ˜ Z + 62 ˜ ] 0U 1D2+ 0U + 62 ˜ ˜ o ] 1D2+ Âą + 62 ] 1D2+ Âą + 62 ˜ [ ]

P jÂąjZ 1D2+

]

Hl\_l P jÂąjZ 1D2+ ]

AZ^ZqZ ‹

Ijb we_dljheba_ ] jZkl\hjZ kh^_j`Zs_]h fZkkh\uo ^he_c beb oehjb^Z gZljby \u^_ebehkv e \h^hjh^Z g m Kdhevdh oehjb ^Z gZljby jZaeh`behkv \ fZkkh\uo ^heyo beb ijhp_glZo b kdhevdh ]jZf fh\ ]b^jhdkb^Z gZljby h[jZah\Zehkv"

>Zgh P jÂąjZ 1D&O ] Z 1D&O f ^ 9 + e g m

P 1D2+ Âą " Z 1D&O Âą " o ] ] \ jÂąj_

m]

e ]

1DKO + 2 o 1D2+ + n &O n ˜ ]

we_dljheba

˜ ]

]

P 1D&O P jÂąjZ ˜ Z ˜ ] 0U 1D&O 0U 1D2+ 0U + ˜ e + Âą o ] + ˜ e + Âą ] + [ ] o ] 1D&O Âą ] G ˜ ] 1D&O Âą ] G [ ] P 1D&O ] Âą klhevdh 1D&O jZaeh`behkv \ j_amevlZl_ ]b^ jhebaZ beb Z1D&O m ] 1D2+ Âą ] G ] 1D2+ Âą ] G ˜ ] m P 1D&O ] Hl\_l P 1D&O ]

Z1D&O beb

AZ^ZqZ ‹

DZdZy khev b kdhevdh __ ihemqblky _keb q_j_a fe jZkl\hjZ kh ^_j`Zs_]h fZkkh\uo ^he_c beb ]b^jhdkb^Z dZeby U ] kf ijhimklbeb \_kv hdkb^ m]e_jh^Z ,9 dhlhjuc h[jZam_lky ijb k`b]Zgbb e f_lZgZ g m "

>Zgh 9 jÂąjZ DHG kf fe Z DHG U DH+ ] kf 9 &+ e g m

e

e

]

]

]

]

0U KH ˜ e K+ Âą o ] KH e K+ Âą ] KH ˜ [ ]

P kheb Âą " ]

o]

KG H : K2 + H

DHG KH : DGKH

P jÂąjZ 9 ˜ U kf ˜ ] kf ] P DHG P jÂąjZ ˜ Z ˜ ] 0U DHG ] D2+ Âą o ] KH ˜ ] D2+ Âą ] KH ] P &H o M gZk ^Zgh Âą ] KH agZqbl &2 ^_ckl\m_l \ ba[uld_ JZkq_lu [m^_f ijhba\h^blv ih DHG FU DGKH ˜ ] D2+ Âą o ] DGKH ] D2+ Âą ] DGKH ˜ ] P DGKH ] o Hl\_l P DGKH ]

AZ^ZqZ ‹

< dZdbo fZkkh\uo hlghr_gbyo g_h[oh^bfh kf_rZlv ]b^jhdkb^ gZ ljby b \h^m qlh[u ihemqblv jZkl\hj \ dhlhjhf gZ dZ`^u_ fhe_dme \h^u ijboh^beZkv [u h^gZ fhe_dmeZ ]b^jhdkb^Z gZljby"

< jZkl\hj_ gZ fhev \h^u ^he`gh ijboh^blvky fhev 1D2+ F G H ] fhev FZkkZ fhev G H ] fhev ˜ fhev ] 0 1D2+ ] fhev

fhev G H fhev 1D2+

] G H ] 1D2+

Hl\_l G H 1D2+

] G H ] 1D2+

†† ± klj ± <hijhk ‹

GZ hkgh\_ i_jbh^bq_kdhc kbkl_fu b l_hjbb kljh_gby Zlhfh\ ihyk gbl_ dZdb_ k\hckl\Z fZ]gby b dZevpby y\eyxlky h[sbfb KhklZ\vl_ mjZ\g_gby khhl\_lkl\mxsbo j_Zdpbc

Hl\_l 0J b KZ gZoh^ylky \ h^ghc ,, ]jmii_ \ k\yab k wlbf gZ ihke_^ g_f we_dljhgghf mjh\g_ m gbo ^\Z k\h[h^guo we_dljhgZ b hgb ijhy\eyxl lbibqgh f_lZeebq_kdb_ k\hckl\Z b \ j_Zdpbyo \uklm iZxl \ dZq_kl\_ \hkklZgh\bl_e_c kl_i_gv hdbke_gby 0J & : FJ&O &D & : &D&O H± 0J + & : FJ&O + 9

H± 0J + 2 : FJ 2+ + 9

H± &D + & : &D&O + 9

H± &D + 2 : &D 2+ + 9

H± H± 0J 2 : FJ2 &D 2 : &D2

H± H± GZ \ha^mo_ ih\_joghklv fZ]gby ihdju\Z_lky ie_gdhc ihwlhfm \ hlebqb_ hl dZevpby _]h fh`gh ojZgblv gZ \ha^mo_

<hijhk ‹

DZd hlebqblv h^bg hl ^jm]h]h ke_^mxsb_ ijbjh^gu_ fbg_jZeu ba \_klgyd ]bik b nhknhjbl" KhklZ\vl_ mjZ\g_gby j_Zdpbc

Hl\_l KZKH + 62 : KZ62 G H KH n [_euc fbg_jZe

Ijhbkoh^bl \u^_e_gb_ ]ZaZ KZ JH $J1H : $J 32 ; &D 12 nhknhjbl

<uiZ^Z_l `_eluc hkZ^hd

KZ6H ˜ G H G 2 : >&D62 ˜ G H@ ?keb kf_rb\Zlv ihjhrhd Ze_[ZkljZ `_elh]h ]bikZ k \h^hc ih emqZ_lky ihem`b^dZy ieZklbq_kdZy [ukljh l\_j^_xsZy fZkkZ

<hijhk ‹

DZd ba dZj[hgZlZ dZevpby fh`gh ihemqblv f_lZeebq_kdbc dZevpbc" >ey obfbq_kdbo ij_\jZs_gbc gZibrbl_ khhl\_lkl\mxsb_ mjZ\g_gby j_ Zdpbc

Hl\_l KZKH +& : &D&O G H &2 n ± ^Ze__ \uiZjb\Z_f &D&O Zgh^ dZlh^

we_dljheba

jZkieZ\Z o KZ &O n

&O ± ± H : &O KZ _ : KZ

hdbke_gb_ oehjZ \hkklZgh\e_gb_ dZevpby

<hijhk ‹

Ih^ \ha^_ckl\b_f hdjm`Zxs_c kj_^u f_lZeebq_kdbc dZevpbc ij_ \jZsZ_lky \ dZj[hgZl dZevpby KhklZ\vl_ mjZ\g_gby khhl\_lkl\mxsbo j_Zdpbc

Hl\_l &D H KZH KZH KH KZKH

&D G H KZ HG G 9 KZ HG KH KZKH G H

<hijhk ‹

DZdb_ ij_\jZs_gby ijhbkoh^yl k ]Zr_ghc ba\_klvx ijb bkihevah\Z gbb __ \ kljhbl_evkl\_" GZibrbl_ mjZ\g_gby j_Zdpbc

Hl\_l H[jZam_lky dZj[hgZl dZevpby ih^ ^_ckl\b_f KH \ha^moZ hg aZl\_j^_\Z_l KZ HG KH : KZKH ; G H

<hijhk ‹

GZq_jlbl_ \ k\hbo l_ljZ^yo ke_^mxsmx lZ[ebpm b aZihegbl_ __ mjZ\g_gbyfb khhl\_lkl\mxsbo j_Zdpbc

Hl\_l

J_Zdlb\ KH

KZH KH

KZH

Obfbq_kdb_ k\hckl\Z

W o KZKH

KZ HG KH KZ HG : KZKH ; G H

J_Zdlb\ 1 H GKO

&D2 1 H

KZH

Obfbq_kdb_ k\hckl\Z

o &D 12 W

KZH +& : &D&O G H

G JH AKZH G JH : KZ JH ; AG H

KZ HG 1 H KZ HG : &D 12 G 2 KZ HG +& : &D&O G 2 AKZ HG G J2 : KZ J2 G 2

<hijhk ‹

DZj[hgZl dZevpby \ \h^_ ijZdlbq_kdb g_jZkl\hjbf H^gZdh ba\_kl gydb \ufu\Zxlky \h^hc Q_f wlh fh`gh h[tykgblv" KhklZ\vl_ mjZ\g_ gby khhl\_lkl\mxsbo j_Zdpbc

Hl\_l Ijb \aZbfh^_ckl\bb k \h^hc b hdkb^hf m]e_jh^Z ,9 ba\_klgyd hq_gv f_^e_ggh ij_\jZsZ_lky \ jZkl\hjbfuc ]b^jhdZj[hgZl dh lhjuc b \ufu\Z_lky \h^hc KZKH G H KH : KZ GKH

<hijhk ‹

Ihq_fm `_kldmx \h^m g_evay mihlj_[eylv ^ey hoeZ`^_gby ^\b]Zl_ e_c fZrbg" Hl\_l ih^l\_j^bl_ mjZ\g_gb_f j_Zdpbb

Hl\_l Ijb gZ]j_\Zgbb ]b^jhdZj[hgZlh\ dZevpby b fZ]gby gZoh^y sboky \ `_kldhc \h^_ hgb i_j_oh^yl \ g_jZkl\hjbfh_ khklhygb_ dZj[hgZlu aZkhjyy dZgZeu jZ^bZlhjZ h[jZam_lky gZdbiv W o KZKH ; + H &2 9 W FJ GKH o FJKH ; G H KH 9

KZ GKH

<hijhk ‹

DZdh\u hkgh\gu_ kihkh[u mkljZg_gby `_kldhklb \h^u" GZibrbl_ mjZ\g_gby khhl\_lkl\mxsbo j_Zdpbc

Hl\_l Ijb ^h[Z\e_gbb ibs_\hc kh^u ± dZj[hgZlZ gZljby 1D &2 dZj[hgZlu fZ]gby b dZevpby \uiZ^Zxl \ hkZ^hd KZ GKH 1D &2 1DGKH KZKH FJ62 1D &2 1D 62 FJ&2

<hijhk ‹

KhklZ\vl_ mjZ\g_gby j_Zdpbc d ko_f_

Hl\_l

&D 2 o &D2 &D + o &D+ &D2 & o &D& &2n &D& + 2 o &D 2+ & + n W

&D & o &D& &D +&O o &D&O + n &D2 +&O o &D&O + 2 &D2 + 2 o &D 2+ &D 2+ &2 o &D&2 + 2 W

&D&2 o &D2 &2 n &D2 + 2 o &D 2+ &D&2 &2 + 2 o &D +&2 W

W o &D&2 p + 2 &2 n W &D&2 o &2 &2 n W &D2 &2 o &D&2

&D +&2

&D 2+ + 62 o &D62 + 2

AZ^ZqZ ‹

Ijb ijhdZeb\Zgbb d] qbklh]h dZj[hgZlZ dZevpby _]h fZkkZ mf_gv rbeZkv gZ d] <uqbkebl_ kdhevdh ijhp_glh\ dZj[hgZlZ dZevpby jZa eh`behkv"

>Zgh P &D&2 d] fZkkZ mf_gvrbeZkv gZ d] kdhevdh &D&2 jZaeh` ± "

P jZae &D&2 d] Z &D&2 jZae

Hl\_l Z &D&2 jZae

&D&2 o &D2 &2 n 0U &2 ˜ 0U &D&2 ˜ [ d] &D&2 ± d] &2 d] &D&2 ± d] &2 ˜ [ d]

AZ^ZqZ ‹

] f_lZeeZ kh kl_i_gvx hdbke_gby ijhj_Z]bjh\Zeb k \h^hc b \u ^_ebehkv e \h^hjh^Z g m Hij_^_ebl_ hlghkbl_evgmx Zlhfgmx fZkkm f_lZeeZ b gZah\bl_ _]h

>Zgh P 0H ] 9 + e g m

0U 0H ± "

Hl\_l &D $U &D

0H + 2 o 0H 2+ + n ] 0H ± e + [ ] 0H ± ] + ˜ [ ] $U 0H

AZ^ZqZ ‹

Ba l ba\_klgydZ kh^_j`Zs_]h fZkkh\uo ^he_c beb ijb f_kb ihemqbeb l ]b^jhdkb^Z dZevpby Kdhevdh fZkkh\uo ^he_c beb ijhp_glh\ wlh khklZ\ey_l ih kjZ\g_gbx k l_hj_lbq_kdbf \uoh^hf"

&D&2 o &D2 &2 n &D2 + 2 o &D 2+ beb &D&2 o &D 2+ P ijbf l u l P &D&2 P ba\_klgydZ ± ± P ijbf ± l 0U &D&2 u 0U &D 2+ u

>Zgh P &D&2 l Z ijbf_k_c f ^ beb P>&D 2+ ijZdlbq @ l K >&D 2+ hl l_hj @ ± "

L_hj_lbq_kdbc \uoh^ &D 2+ l &D&2 ± [ l &D 2+ l &D&2 ± l &D 2+ ˜ [ l P &D 2+ l_hj l P §¨ &D 2+ © K &D 2+ hl l_hj P &D 2+

ijZdl l_hj

·¸ ¹

Hl\_l K &D 2+ hl l_hj beb

AZ^ZqZ ‹

H[jZa_p `_kldhc \h^u kh^_j`bl f] e ]b^jhdZj[hgZlZ dZevpby b f] e kmevnZlZ dZevpby Kdhevdh dZj[hgZlZ gZljby ihlj_[m_lky ^ey mfy]q_gby f lZdhc \h^u"

>Zgh \ `_kldhc \h^_ &D +&2 ± f] e &D62 ± f] e 9 + 2 f e P 1D &2 ± " ]

o]

]

]

&D +&2 1D &2 : &D&2 ; 1D+&2

]

\ ]

]

]

KD62 1D&2 : &D&2 ; 1D 62

MagZ_f dhebq_kl\h ih fZkk_ khe_c \ f \h^u e + 2 ± ] &D +&2 e + 2 ± o ] &D +&2 [ ] [ e + 2 ± ] &D62 e + 2 ± [ ] &D62 [ ] [ 0U &D +&2 0U 1D &2 0U &D62 <uqbkey_f fZkkm kh^u g_h[oh^bfhc ^ey kfy]q_gby \h^u ] &D +&2 ± [ ] 1D &2 ] &D +&2 ± ] 1D &2 o ] [ ] &D62 ± [ ] 1D&2 ] &D62 ± ] 1D &2 [ ] [ P 1D &2 ] Hl\_l P 1D &2 ]

† klj

<hijhk ‹

>ey ihemq_gby Zexfbgby ba $O&O \ dZq_kl\_ \hkklZgh\bl_ey fh`gh bkihevah\Zlv f_lZeebq_kdbc dZevpbc HoZjZdl_jbamcl_ wlhl ijhp_kk b khklZ\vl_ mjZ\g_gb_ j_Zdpbb ihdZ`bl_ i_j_oh^ we_dljhgh\ Ihq_fm wlm j_Zdpbx g_evay ijh\h^blv \ \h^ghf jZkl\hj_"

Hl\_l $O &O &D o $O &D &O

H± J_Zdpbx g_evay ijh\h^blv \ \h^_ l d &D [m^_l j_Z]bjh\Zlv k g_c

<hijhk ‹

KhklZ\vl_ mjZ\g_gby j_Zdpbc \ dhlhjuo Zexfbgbc \hkklZgZ\eb\Z _l Z ]Zeh]_gu [ `_e_ah \ bhgu \h^hjh^Z ] k_jm ^ dbkehjh^ IhdZ `bl_ i_j_oh^ we_dljhgh\

Hl\_l $O &O o $O &O ± H±

\hkklZgh\bl_ev hdbkey_lky hdbkebl_ev \hkklZgZ\eb\Z_lky

\hkklZgh\bl_ev hdbkey_lky hdbkebl_ev \hkklZgZ\eb\Z_lky hdbkebl_ev \hkklZgZ\eb\Z_lky

$O ± H o$O + H o +

\hkklZgh\bl_ev hdbkey_lky hdbkebl_ev \hkklZgZ\eb\Z_lky

H± $O ± H o $O 6 H o 6 ±

\hkklZgh\bl_ev hdbkey_lky hdbkebl_ev \hkklZgZ\eb\Z_lky

\hkklZgh\bl_ev hdbkey_lky hdbkebl_ev \hkklZgZ\eb\Z_lky

$O ± H o$O KO H o &O±

$O )H 2 )H 2 )H 2 o $O 2 )H H±

$O ± H o$O )H H o )H )H H o )H

$O + &O± o $O &O + n H±

$O 6 o $O 6 ±

$O 2 o $O 2 ± H±

$O ± H o $O 2 H o 2 ±

<hijhk ‹

KhklZ\vl_ mjZ\g_gb_ j_Zdpbb \ dhlhjhc Zexfbgbc \hkklZgZ\eb\Z_l bhgu f_^b \ \h^ghf jZkl\hj_j_ IhdZ`bl_ i_j_oh^ we_dljhgh\ b mdZ `bl_ hdbkebl_ev

Hl\_l

$O &X &O o $O &O &X H±

$O ± H o $O &X H o &X

\hkklZgh\bl_ev hdbkey_lky hdbkebl_ev \hkklZgZ\eb\Z_lky

<hijhk ‹

Fh]ml eb [ulv hdbkebl_eyfb Z Zlhfu Zexfbgby [ bhgu Zexfb gby" Hl\_l ih^l\_j^bl_ mjZ\g_gbyfb j_Zdpbc

Hl\_l Z :lhfu Zexfbgby g_ fh]ml [ulv hdbkebl_eyfb b ijbgbfZlv we_dljhgu $O 6 o$O 6 ± H±

$O ± H o $O 6 H o 6 ±

\hkklZgh\bl_ev hdbkey_lky hdbkebl_ev \hkklZgZ\eb\Z_lky

\hkklZgh\bl_ev hdbkey_lky hdbkebl_ev \hkklZgZ\eb\Z_lky

[ Bhgu Zexfbgby fh]ml [ulv hdbkebl_eyfb \ j_Zdpbb k kbevguf \hkklZgh\bl_e_f $O &O . o $O . &O H±

. ± H o . $O H o $O

<hijhk ‹

>ey ihemq_gby oehjb^Z Zexfbgby fh`gh \hkihevah\Zlvky j_Zdpbyfb h[f_gZ aZf_s_gby b kh_^bg_gby KhklZ\vl_ mjZ\g_gby khhl\_lkl\mx sbo j_Zdpbc

Hl\_l %D&O $O 62 o %D62 p $O&O Wlh j_Zdpby h[f_gZ

&X&O $O o $O&O &X Wlh j_Zdpby aZf_s_gby $O &O o $O&O Wlh j_Zdpby kh_^bg_gby

<hijhk ‹

D jZkl\hjm kmevnZlZ Zexfbgby ihg_fgh]m ijbeb\Zeb jZkl\hj s_ehqb ^h ba[uldZ Qlh gZ[ex^Zeb " KhklZ\vl_ mjZ\g_gby j_Zdpbc

Hl\_l $O 62 1D2+ $O 2+ p 1D 62 < gZqZe_ j_Zdpbb \uiZ^Z_l hkZ^hd ]b^jhhdkb^Z Zexfbgby $O 2+ 1D2+ 1D>$O 2+ @ beb 1D$O2 ˜ + 2 Ijb ^Zevg_cr_f ijbeb\Zgbb s_ehqb hkZ^hd jZkl\hjy_lky l d ijb \aZbfh^_ckl\bb ]b^jhhdkb^Z Zexfbgby b s_ehqb h[jZam_lky jZk l\hjbfZy khev

<hijhk ‹

KhklZ\vl_ mjZ\g_gby j_Zdpbc kh]eZkgh ko_f_

Hl\_l $O + 2 o $O 2+ p + n Zexfbgbc hk\h[h^blv hl ie_gdb

$O 2 o $O 2 $O 2+ o $O 2 + 2 we_dljheba jZkieZ\Z

$O 2 o $O 2 $O 1D2+ + 2 o 1D>$O 2+ @ + n ZexfbgZl gZljby

$O 2+ 1D2+ o 1D$O2 + 2 $O&O 1D2+ o $O 2+ p 1D&O

AZ^ZqZ ‹

Kdhevdh ihlj_[m_lky Zexfbgby qlh[u ijb j_Zdpbb k kheyghc dbkeh lhc ihemqblv klhevdh \h^hjh^Z kdhevdh _]h \u^_ey_lky ijb \aZbfh^_c kl\bb fhev gZljby k \h^hc"

>Zgh Y 1D fhev P $O ±"

fhev

o fhev

fhev

fhev

1D + 2 o 1D2+ + n fhev 1D ± [ fhev + fhev 1D ± fhev +

[

o fhev + Y $O fhev

o fhev

fhev

fhev

fhev

$O +&O o $O&O + n

o fhev $O ± fhev + fhev $O ± fhev + o fhev $O F $O ] fhev [ P $O 0 ˜ Y ] fhev ˜ fhev ] Hl\_l P $O ]

AZ^ZqZ ‹

GZ kieZ\ Zexfbgby b f_^b ih^_ckl\h\Zeb ba[uldhf dhgp_gljbjh\Zg gh]h jZkl\hjZ ]b^jhdkb^Z gZljby ijb gZ]j_\Zgbb <u^_ebehkv e dZ dh]h lh ]ZaZ g m <uqbkebl_ ijhp_glguc khklZ\ kieZ\Z _keb _]h h[sZy fZkkZ [ueZ ]

>Zgh P kieZ\Z ] 9 ]ZaZ e g m

ijhp_glguc khklZ\ kieZ\Z ± " o]

e

$O 1D2+ + 2 o 1D>$O 2+ @ + n ˜ ]

˜ e

0U $O [ ] $O ± e + ] $O ± e + o ] P $O ] [ f $O

Z $O

P kieZ\Z beb Z &X ± beb Hl\_l Z $O beb

Z &X beb

AZ^ZqZ ‹

>Zgh ] jZkl\hjZ kh^_j`Zs_]h oehjb^Z Zexfbgby Kdhevdh ih lj_[m_lky fbeebebljh\ jZkl\hjZ U ] kf kh^_j`Zs_]h fZk kh\uo ^he_c beb ]b^jhdkb^Z gZljby qlh[u oehjb^ Zexfbgby ihegh klvx ij_\jZlblv \ ZexfbgZl gZljby"

>Zgh P jÂąjZ $O&O ] Z $O&O U SÂąSD 1D2+ ] kf Z jÂąjZ 1D2+ f ^ beb

$O&O 1D2+ o$O 2+ 1D&O $O 2+ 1D2+ o 1D>$O 2+ @ + 2 o ]

]

1D2+ $O&O o1D>$O 2+ @ 1D&O + 2 ˜ ]

]

P SÂąSD 1D2+ Âą "

P $O&O P SÂąSD ˜ Z ˜ ] 0U $O&O ˜ 0U 1D2+ [ ] 1D2+ Âą ] $O&O ] 1D2+ Âą ] $O&O o ] P 1D2+ ] [ P 1D2+ ] P SÂąSD Z 1D2+

P kf | fe 9 SÂąSD S Hl\_l 9 SÂąSD fe

=eZ\Z 9,,,

†† ± klj ± <hijhk ‹

KhklZ\vl_ mjZ\g_gby j_Zdpbc \ j_amevlZl_ dhlhjuo fh`gh ihem qblv f_lZeebq_kdh_ `_e_ah ba _]h hdkb^h\ )H 2 b )H 2 bkihevamy \ dZ q_kl\_ \hkklZgh\bl_ey Z \h^hjh^ [ Zexfbgbc \ hdkb^ m]e_jh^Z ,, IhdZ`bl_ i_j_oh^ we_dljhgh\ b mdZ`bl_ hdbkebl_ev b \hkklZgh\bl_ev

Hl\_l

o )H + 2 Z )H 2 + W

H± H o + )H H o )H

\hkklZgh\bl_ev hdbkey_lky hdbkebl_ev \hkklZgZ\eb\Z_lky

G ± _ : G )H _ : )H )H _ : )H

H±

\hkklZgh\bl_ev hdbkey_lky hdbkebl_ev \hkklZgZ\eb\Z_lky hdbkebl_ev \hkklZgZ\eb\Z_lky

\hkklZgh\bl_ev hdbkey_lky hdbkebl_ev \hkklZgZ\eb\Z_lky

H± $O ± _ : $O )H _ : )H )H _ : )H

\hkklZgh\bl_ev hdbkey_lky hdbkebl_ev \hkklZgZ\eb\Z_lky hdbkebl_ev \hkklZgZ\eb\Z_lky

H± & ± _ : & )H _ : )H

\hkklZgh\bl_ev hdbkey_lky hdbkebl_ev \hkklZgZ\eb\Z_lky

+ ±

)H 2 )H 2 ˜ )H 2 +

[ $O )H 2

H± $O ± _ : $O )H _ : )H

W o )H + 2

W o $O 2 )H

$O )H 2 )H 2 ˜ )H H : :O 2 )H

\ )H 2 & 2 o )H &2

W

)H 2 )H 2 ˜ )H H &2 : )H & 2 H±

& ± _ : & )H _ : )H )H _ : )H

\hkklZgh\bl_ev hdbkey_lky hdbkebl_ev \hkklZgZ\eb\Z_lky hdbkebl_ev \hkklZgZ\eb\Z_lky

<hijhk ‹

KhklZ\vl_ mjZ\g_gby j_Zdpbc \ dhlhjuo `_e_ah j_Z]bjm_l k Z db kehlZfb [ kheyfb \ \h^hc ijb ih\ur_gghc l_fi_jZlmj_ IhdZ`bl_ i_j_oh^ we_dljhgh\ b mdZ`bl_ hdbkebl_ev b \hkklZgh\bl_ev

Hl\_l Z )H G 62 jZa[ :)H 62 + 9 H± )H ± _ : )H + _ : +

\hkklZgh\bl_ev hdbkey_lky hdbkebl_ev \hkklZgZ\eb\Z_lky

H± )H ± _ : )H &X _ : &X

\hkklZgh\bl_ev hdbkey_lky hdbkebl_ev \hkklZgZ\eb\Z_lky

H± )H ± _ : )H )H ± _ : )H + _ : +

\hkklZgh\bl_ev hdbkey_lky hdbkebl_ev \hkklZgZ\eb\Z_lky hdbkebl_ev \hkklZgZ\eb\Z_lky

[ )H &X &O : )H &O &X

\ )H G 2 :)H 2 )H 2 ˜ )H 2 + 9

<hijhk ‹

KhklZ\vl_ mjZ\g_gby j_Zdpbc ijb ihfhsb dhlhjuo fh`gh ihem qblv Z kheb `_e_aZ ,, b kheb `_e_aZ ,,, [ ]b^jhdkb^ `_e_aZ ,, b ]b^jhdkb^ `_e_aZ ,,, \ hdkb^u `_e_aZ

Hl\_l Z )H +&O : )H&O + 9

)H &O o )H&O [ )H&O 1DHG : )H HG ; 1D&O )H&O .HG : )H HG ; .&O beb W

)H HG H G H : )H HG \ )H H : )H 2 ˜ )HH )H H KH o )HH KH 9 )H HG

W

W o )H 2 ˜ G 2

<hijhk ‹

DZdbfb h[sbfb b ki_pbnbq_kdbfb k\hckl\Zfb h[eZ^Zxl hdkb^u b ]b^jhdkb^u `_e_aZ" KhklZ\vl_ mjZ\g_gby khhl\_lkl\mxsbo j_Zdpbc

Hl\_l Z h[sb_ k\hckl\Z DZd b ^jm]b_ hdkb^u b ]b^jhdkb^u f_lZeeh\ hdkb^u b ]b^jh dkb^u `_e_aZ ,, b `_e_aZ ,,, j_Z]bjmxl k dbkehlZfb k h[jZah\Z gb_f khe_c `_e_aZ ,, b `_e_aZ ,,, )HH +&O )H&O + H )H H +&O )H&O + H )H HG GKO : )H&O G 2 )H HG GKO )H&O G 2 [ ki_pbnbq_kdb_ k\hckl\Z =b^jhdkb^ `_e_aZ ,, e_]dh hdbkey_lky \ ]b^jhdkb^ `_e_aZ ,,, )H HG H G 2 )H HG )H HG G 2 : )H HG

<hijhk ‹

HoZjZdl_jbamcl_ h[sb_ b ki_pbnbq_kdb_ k\hckl\Z khe_c `_e_aZ Kh klZ\vl_ mjZ\g_gby j_Zdpbc

Hl\_l Z h[sb_ k\hckl\Z Kheb `_e_aZ ,, b `_e_aZ ,,, \klmiZxl \ j_Zdpbb h[f_gZ kh s_ehqZfb GZijbf_j )HKO 1D2+ )H 2+ ; 1D&O )H 6H 1D2+ )H 2+ ; 1D 6H F_lZeeu klhysb_ \ jy^m gZijy`_gbc ijZ\__ `_e_aZ \ul_kgy xl `_e_ah ba jZkl\hjh\ khe_c `_e_aZ ,, b `_e_aZ ,,, =Q )H&O )H =Q&O =Q )H&O )H =Q&O [ ki_pbnbq_kdb_ k\hckl\Z )H&O &O )H&O

<hijhk ‹

KhklZ\vl_ mjZ\g_gby j_Zdpbc ih ijb\_^_gghc gb`_ ko_f_ lZd qlh[u ijb ihfhsb wlbo j_Zdpbc fh`gh [ueh hkms_kl\blv ke_^mxsb_ ij_\jZ s_gby Z )H o )H 2+ o )H 2 o )H [ )H o )H&O o )H 2 \ )H : )H 2+ : )H 2+ : )H 2 : )H2+&O : )H 2 )H : )H 2+ : )H 2+ &O : )H 62 : )H 2 : )H

Hl\_l Z

)H &O o )H&O )H&O 1D2+ : )H 2+ ; 1D&O W

W o )H 2 + 2 W )H 2 &2 o )H &2 9

)H HG

[

)H &O o )H&O )H&O 1D2+ : )H 2+ ; 1D&O W

)H 2+ o )H 2 + 2 \

)H + 2 2 : )H 2+ )H 2+ + 2 2 : )H 2+ W

)H 2+ o )H 2 + 2 )H 2 +&O : )H&O + 2 )H&O +2+ : )H2+&O +&O )H2+&O 1D2+ : )H 2+ ; 1D&O )H 2+ : )H 2 + 2 )H + 2 2 : )H 2+ )H 2+ + 2 2 : )H 2+ )H 2+ +&O g_^hklZlhd : )H 2+ &O + 2 )H 2+ &O + 62 : )H 62 +&O + 2 W

)H 62 o )H 2 62 9 )H 2 &2 : )H &2 n W

AZ^ZqZ ‹

< dZdhc fZkk_ fZ]gblgh]h `_e_agydZ )H 2 bf_xs_]h fZkkh\uo ^he_c beb ijbf_kb kh^_j`blky l `_e_aZ" Ijhba\_klb \k_ g_h[ oh^bfu_ jZkq_lu

>Zgh

P )H l

Z ijbf_k_c beb

P )H 2 ± "

0U )H 2 ˜ ˜ 0U )H

Z )H 0U )H 2 beb P )H

P )H 2 Z )H l )H 2 ± o l )H 2 ± o

Hl\_l P )H 2 l

AZ^ZqZ ‹

l l

H[jZa_p kb^_jblZ hkgh\gZy qZklv dhlhjh]h )H&2 kh^_j`bl `_e_aZ <uqbkebl_ kdhevdh ijhp_glh\ )H&2 kh^_j`blky \ wlhf h[ jZap_

0U )H ] )H ± ] )H&2 ] )H ± o ] )H&2 ˜ Z )HKH ± " ] o 0U )H&2

˜ ˜ Z )HKH 0U h[j

>Zgh Z )H

Hl\_l Z )HKH beb

=eZ\Z ,;

†† ¹ klj AZ^ZqZ ‹

@_e_agZy jm^Z kh^_j`bl fZkkh\uo ^he_c beb )H 2 b fZkkh\uo ^he_c beb 6L2 <uqbkebl_ ijhp_glgh_ kh^_j`Zgb_ `_ e_aZ b dj_fgby \ ^Zgghc jm^_

>Zgh Z )H 2 f ^ beb Z 6L2 f ^ beb Z )H Âą " Z 6L Âą "

0U )H 2 ˜ ˜ FU )H 0U )H

Z )H 2 0U )H 2

Z )H \ )H 2 f ^ )H Âą f ^ )H 2 o f ^ )H Âą f ^ )H 2

˜ Z )H \ jm^_ beb f ^ 0U 6L2 ˜ FU 6L Z 6L2 beb f ^ 6L Âą f ^ 6L2 ˜ [ o f ^ )H Âą f ^ 6L2 Z 6L \ jm^_ beb f ^

[

Hl\_l Z )H \ jm^_

AZ^ZqZ ‹

Z 6L \ jm^_

DZdh_ dhebq_kl\h l_iehlu \u^_eblky ijb Zexfbghl_jfbq_kdhf \hk klZgh\e_gbb ] `_e_aZ ba _]h hdkb^Z _keb l_iehlZ h[jZah\Zgby hdkb ^Z Zexfbgby jZ\gZ d>` Z hdkb^Z `_e_aZ ,,, Âą d>`"

>Zgh

P )H ] 4 h[jÂąy )H 2 Âą d>` 4 h[jÂąy $O 2 d>` 4 Âą "

]

o d>`

)H 2 $O o$O 2 )H 4 W

˜ ]

d>`

4 jÂąpbb 4 h[jÂąy $O 2 4 h[jÂąy )H 2 Âą d>`

0U )H ] )H ± [ d>` ] )H ± d>`

Hl\_l 4 d>`

o d>`

AZ^ZqZ ‹

DZdhc h[t_f hdkb^Z m]e_jh^Z ,, ihlj_[m_lky g m qlh[u \hkklZ gh\blv `_e_ah kh^_j`Zs__ky \ l )H 2 "

>Zgh

P )H 2 l 9 &2 ± " g m

]

of

)H 2 KH o )H KH n l

˜ ˜ f

W

0U )H H ˜ ˜ FU &2 l )H 2 ± [ f KH ˜ ˜ l )H 2 ± ˜ f KH ˜ f o Hl\_l 9 &2 ˜ f

AZ^ZqZ ‹

Kdhevdh qm]mgZ fh`gh ihemqblv ba l `_e_aghc jm^u )H 2 kh ^_j`Zs_c fZkkh\uo ^he_c ijbf_k_c _keb \ ihemq_gghf qm]mg_ kh^_j `blky fZkkh\uo ^he_c `_e_aZ"

>Zgh

l

ol

P )H 2 jm^Z l )H 2 &2 o )H &2 n ˜ l Z ijbf_k_c f ^ l Z )H \ qm]mg_ P ijbf_k_c P jm^u ˜ Z l ˜ l P qm]mgZ ± " P )H 2 P jm^u ± P ijbf_k_c l ± l l 0U )H 2 ˜ ˜ FU )H l )H H ± o l )H ˜ l )H H ± l )H [ l P )H \ l_hj_l l P )H l_hj_l P )H ijZdlbq l Z )H

Hl\_l P qm]mgZ l

W

AZ^ZqZ ‹

Kdhevdh ihlj_[m_lky fZ]gblghc `_e_aghc jm^u kh^_j`Zs_c fZkkh\uo ^he_c )H 2 qlh[u ihemqblv l qm]mgZ \ dhlhjhf kh^_j`bl ky fZkkh\uo ^he_c `_e_aZ"

>Zgh

P )H qm]mgZ l Z )H Z )H 2 P jm^u )H 2 ± "

[ l

l

)H 2 &2 o )H &2 l

W

˜ l

P )H P qm]mgZ ˜ Z )H l ˜ l l 0U )H 2 ˜ ˜

o l )H H ± l )H l )H H ± l )H ˜ [ l P )H H \ l_hj_l l P jm^u ijZdlbq

l Hl\_l P jm^u l

=eZ\Z ;

†† ± klj <hijhk ‹

Qlh bamqZ_l hj]Zgbq_kdZy obfby" D dZdbf \_s_kl\Zf hlghkyl hdkb^ m]e_jh^Z ,9 hdkb^ m]e_jh^Z ,, dZj[hgZlu dZj[b^u dhlhju_ lh`_ kh^_j`Zl m]e_jh^"

Hl\_l Hj]Zgbq_kdZy obfby ± jZa^_e obfbq_kdhc gZmdb \ dhlhjhf bamqZxlky kh_^bg_gby m]e_jh^Z b bo ij_\jZs_gby < jZfdZo hj]Zgbq_kdhc obfbb bamqZxlky g_ \k_ kh_^bg_gby m] e_jh^Z Z bf_ggh l_ dhlhju_ gZau\Zxlky hj]Zgbq_kdbfb \_s_kl \Zfb OZjZdl_jgufb ijbagZdZfb hj]Zgbq_kdbo \_s_kl\ djhf_ ijh kl_crbo y\ey_lky gZebqb_ \ fhe_dme_ ihke_^h\Zl_evghkl_c Zlh fh\ m]e_jh^Z kh_^bg_gguo ^jm] k ^jm]hf \ p_ib ijhba\hevghc ^ebgu Z lZd`_ [he__ keh`gu_ kljmdlmju kf hl\_l gZ \hi b <lhjuf oZjZdl_jguf ijbagZdhf y\ey_lky gZebqb_ \ kljmdlmj_ fh e_dmeu ]jmii &+ ± ± &+ ± &+ ± <_s_kl\Z gZau\Zxlky hj]Zgbq_kdbfb g_aZ\bkbfh hl lh]h h[jZ ah\Zebkv eb hgb \ `b\uo hj]ZgbafZo beb ihemq_gu bkdmkkl\_g guf iml_f Ijbf_ju hj]Zgbq_kdbo \_s_kl\ f_lZg &+ wlZg &+ ± &+ wlbeh\uc kibjl &+ ± &+ ± 2+ mdkmkgZy dbkehlZ &+ ± &22+ [_gahe K + Zp_lbe_g +& { &+ wlbe_g + & &+ [mlZ^b_g &+ &+ ± &+ &+ b l ^

<hijhk ‹

DZd fh`gh h[tykgblv ihq_fm gZijbf_j m wlbeh\h]h kibjlZ b ^b f_lbeh\h]h wnbjZ h^bgZdh\u_ fhe_dmeyjgu_ nhjfmeu" Qlh gZau\Zxl bahf_jb_c"

Hl\_l Bahf_jb_c gZau\Z_lky y\e_gb_ aZdexqZxs__ky \ lhf qlh \ h^ghc b lhc `_ fhe_dmeyjghc nhjfme_ \_s_kl\Z hlkmlkl\m_l g_ kdhevdh \_s_kl\ jZaebqZxsboky k\hbf kljh_gb_f l _ ihke_^h \Zl_evghklvx kh_^bg_gby Zlhfh\ \ fhe_dme_ b dZd j_amevlZl k\hckl\Zfb Kj_^b hj]Zgbq_kdbo kh_^bg_gbc bahf_jby \klj_qZ_l ky hq_gv qZklh Ijhkl_crbf ijbf_jhf bahf_jbb y\ey_lky bahf_jby wlbeh \h]h kibjlZ b ^bf_lbeh\h]h wnbjZ Hgb bf_xl h^bgZdh\mx fhe_

dmeyjgmx nhjfmem & + 2 gh jZagh_ fhe_dmeyjgh_ kljh_gb_ ih wlhfm hgb bf_xl kms_kl\_ggh jZagu_ k\hckl\Z KjZ\gb wlbeh\uc kibjl ^bf_lbeh\uc wnbj + + + + + & & 2+

+ + `b^dhklv Wdbi &q \ \h^_ jZkl\hjbf j_Z]bjm_l k 1D

+ & 2 & +

<hijhk ‹

+ + ]Za Wdbi ± &q \ \h^_ fZeh jZkl\hjbf g_ j_Z]bjm_l k 1D

DZdh\u \Z`g_crb_ iheh`_gby l_hjbb kljh_gby hj]Zgbq_kdbo kh_^b g_gbc"

Hl\_l kf k hkgh\gu_ iheh`_gby l_hjbb kljh_gby hj]Zgbq_kdbo kh_^bg_gbc :lhfu \ fhe_dmeZo kh_^bg_gu f_`^m kh[hc \ hij_^_e_gghc ihke_^h\Zl_evghklb Ijb baf_g_gbb wlhc ihke_^h\Zl_evghklb ih emqZxlky gh\u_ \_s_kl\Z ± bahf_ju kf hl\_l gZ \hij

:lhfu kh_^bgyxlky \ khhl\_lkl\bb k bo \Ze_glghklyfb ijb wlhf Zlhfu m]e_jh^Z q_luj_o \Ze_glgu <Ze_glghklb \k_o Zlhfh\ \aZbfgh gZkus_gu K\h[h^guo \Ze_glghkl_c \ fhe_dmeZo g_l Ijbf_j Zp_lbe_g +& { &+ mdkmkgZy dbkehlZ &+ ± &22+ K\ \Z \ \ aZ\bkyl hl ihke_^h\Zl_evghklb kh_^bg_gby Zlhfh\ \ fhe_dmeZo GZb[he__ kbevgh ijhy\ey_lky \aZbfh\ebygb_ l_o Zlhfh\ \ fhe_dmeZo dhlhju_ g_ihkj_^kl\_ggh k\yaZgu f_`^m kh [hc :lhfu m]e_jh^Z h[eZ^Zxl k\hckl\hf kh_^bgylvky f_`^m kh [hc h[jZamy p_ib Zlhfh\ m]e_jh^Z P_ib Zlhfh\ m]e_jh^Z fh]ml \dexqZlv b ^jm]b_ Zlhfu gZijbf_j dbkehjh^Z ZahlZ k_ju b ^j Ijbf_j ijhiZg ± ^bf_lbeh\uc wnbj ± + + + + + + & & & + +

+ +

+ & 2 & + +

+

<hijhk ‹

GZ dZdb_ ^\_ [hevrb_ ]jmiiu ^_eyl \k_ hj]Zgbq_kdb_ kh_^bg_gby b dZd ih^jZa^_eyxl m]e_\h^hjh^u"

Hl\_l <k_ hj]Zgbq_kdb_ kh_^bg_gby ^_eyl gZ ^\_ ]jmiiu \_s_kl\Z dhlhju_ khklhyl lhevdh ba m]e_jh^Z b \h^hjh^Z m]e_\h^hjh^u \_s_kl\Z dhlhju_ y\eyxlky ijhba\h^gufb m]e_\h^hjh^h\ kf klj M]e_\h^hjh^u ih^jZa^_eyxlky gZ ljb [hevrb_ ]jmiiu ]jmiim gZkus_gguo m]e_\h^hjh^h\ l _ lZdbo \ dhlhjuo \k_ Zlhfu m]e_jh^Z kh_^bgyxlky f_`^m kh[hc lhevdh h^bgZjgufb k\yayfb ]jmiim g_gZkus_gguo m]e_\h^hjh^h\ l _ lZdbo \ dhlhjuo f_` ^m hl^_evgufb ZlhfZfb K bf_xlky ih djZcg_c f_j_ h^gZ beb [hevr_ ^\hcguo beb ljhcguo k\ya_c ]jmiim pbdebq_kdbo m]e_\h^hjh^h\ l _ lZdbo \ fhe_dmeZo dh lhjuo Zlhfu m]e_jh^Z h[jZamxl aZfdgmlu_ pbdeu =jmiiZ g_gZkus_gguo m]e_\h^hjh^h\ ^_eblky gZ ljb hkgh\guo ih^]jmiiu jy^ wlbe_gZ h^gZ ^\hcgZy k\yav jy^ Zp_lbe_gZ h^gZ ljhcgZy k\yav jy^ ^b_gh\uo ^\_ ^\hcgu_ k\yab jZa^_e_ggu_ h^ghc h^bgZjÂą ghc & & K & =jmiiZ pbdebq_kdbo m]e_\h^hjh^h\ ^_eblky gZ ^\_ hkgh\gu_ ih^ ]jmiiu klj jy^ pbdehiZjZnbgh\ l _ lZdbo m]e_\h^hjh^h\ dhlhju_ \dexqZ xl gZkus_gguc m]e_jh^guc pbde h[jZah\Zgguc h^bgZjgufb k\yayfb & & Ijbf_j

pbdeh]_ikZg

+ & + &

&+

&+

&+

&+

jy^ ZjhfZlbq_kdbo m]e_\h^hjh^h\ l _ lZdbo fhe_dmeu dhlhjuo \dexqZxl aZfdgmlh_ gZkus_ggh_ dhevph hkh[hc kljmdlmju ba r_klb Zlhfh\ m]e_jh^Z <k_ Zlhfu m]e_jh^Z \ wlhf pbde_ gZau \Z_fhf ZjhfZlbq_kdbf kh_^bg_gu h^ghc h[s_c k\yavx dhlhjmx ijbgylh h[hagZqZlv [_gahevguf dhevphf kf fhe_dmeyjgmx nhjfmem [_gaheZ Âą & +

<hijhk ‹

>Zcl_ djZldmx oZjZdl_jbklbdm f_lZgm b jZkkdZ`bl_ ]^_ _]h bk ihevamxl Qlh \u agZ_l_ h nj_hgZo"

Hl\_l F_lZg &+ ± ijhkl_crbc ij_^klZ\bl_ev gZkus_gguo m]e_ \h^hjh^h\ Wlh ihqlb g_jZkl\hjbfuc \ \h^_ [_kp\_lguc ]hjxqbc ]Za [_a aZiZoZ Kf_kv h[t_fZ f_lZgZ k h[t_fZfb dbkehjh^Z hq_gv \aju\h hiZkgZ Lhqgh lZd`_ \aju\hhiZkgu kf_kb f_lZgZ k \ha^mohf dh ]^Z \ha^moZ ijboh^blky gZ h[t_f f_lZgZ hl ^h h[t_fh\ LZ db_ kf_kb y\eyxlky hkgh\ghc ijbqbghc \aju\h\ gZ m]hevguo rZolZo F_lZg hlghkbl_evgh mklhcqb\ d obfbq_kdbf \aZbfh^_ckl\byf < j_Zdpbb \klmiZ_l eb[h ijb \ukhdhc l_fi_jZlmj_ b ijb gZebqbb dZlZebaZlhjZ &+ + 2 o &2 + n

>Z`_ k lZdbf Zdlb\guf \_s_kl\hf dZd oehj f_lZg j_Z]bjm_l lhevdh gZ k\_lm j_Zdpby f_lZe_ikbb klj q K dZl 1L

k\_l o &+ &O +&O k\_l &+ &O &O o &+ &O +&O &+ &O

Ijb l_fi_jZlmj_ hdheh qK f_lZg jZaeZ]Z_lky k h[jZah\Z

o & + + n gb_f Zp_lbe_gZ &+ F_lZg rbjhdh \klj_qZ_lky \ ijbjh^_ <h i_j\uo wlh hkgh\ghc dhfihg_gl ijbjh^gh]h ]ZaZ <h \lhjuo f_lZg h[jZam_lky ijb [_k dbkehjh^ghf [jh`_gbb hklZldh\ jZklbl_evghklb gZ ^g_ [hehl hl kx^Z gZa\Zgb_ ± [hehlguc ]Za < lj_lvbo f_lZg y\ey_lky kimlgb dhf f_klhjh`^_gbc m]ey b fgh]h f_lZgZ \u^_ey_lky ihwlhfm ijb ^h[uq_ m]ey \ rZolZo hlkx^Z _s_ h^gh gZa\Zgb_ f_lZgZ ± jm^ gbqguc ]Za < q_l\_jluo f_lZg khklZ\ey_l hkgh\m Zlfhkn_j jy^Z ieZg_l Kheg_qghc kbkl_fu Hkgh\gh_ ijbf_g_gb_ f_lZgZ dZd lhieb\h dZd kujv_ \ obfb q_kdhc ijhfure_gghklb ^ey ijhba\h^kl\Z \h^hjh^Z Zp_lbe_gZ ljboehjf_lZgZ &+ &O nj_hgh\ b jy^Z ^jm]bo \Z`guo \_s_kl\ Nj_hgu ± wlh gZkus_ggu_ nlhjijhba\h^gu_ f_lZgZ b ^jm]bo m]e_\h^hjh^h\ qZklh kh^_j`Zl Zlhfu oehjZ beb [jhfZ Ijbf_j &)&O &) &O &) &) &+ b l ^ Wlh ]Zahh[jZagu_ beb `b^db_ \_ s_kl\Z obfbq_kdb bg_jlgu_ fZehlhdkbqgu_ Hq_gv rbjhdh ijb f_gyxlky \ oheh^bevguo Z]j_]ZlZo \ Zwjhahevguo miZdh\dZo dZd jZkl\hjbl_eb b qbklysb_ kj_^kl\Z | q K

D kh`Ze_gbx \uykgbehkv qlh fgh]b_ nj_hgu ih^gbfZykv \ \_jogb_ kehb Zlfhkn_ju jZajmrZxl hq_gv \Z`guc ^ey `bagb gZ a_fe_ hahgh\uc kehc ¹ h[jZamxlky lZd gZau\Z_fu_ Šhahgh\u_ ^u juª Ihwlhfm hl ijbf_g_gby g_dhlhjuo nj_hgh\ ijbrehkv hldZ aZlvky

<hijhk ‹

HoZjZdl_jbamcl_ k\hckl\Z wlbe_gZ b _]h ijbf_g_gb_ =^_ bkihevam xlky ihebwlbe_g b ihebijhibe_g"

Hl\_l Wlbe_g Âą \Z`g_crbc ij_^klZ\bl_ev jy^Z g_ji_^_evguo m]e_ \h^hjh^h\ k h^ghc ^\hcghc k\yavx nhjfmeZ Âą + & &+ =Za ihqlb [_a aZiZoZ iehoh jZkl\hjbf \ \h^_ GZ \ha^mo_ ]hjbl k\_ly sbfky ieZf_g_f ;eZ]h^Zjy gZebqbx S Âą k\yab wlbe_g e_]dh \klm iZ_l \ j_Zdpbb ijbkh_^bg_gby + & &+ %U Âą %U o + %U& Âą &+ %U ^b[jhfwlZg

+ & &+ + Âą 2+ o + & Âą &+ Âą 2+ wlbeh\uc kibjl

;eZ]h^Zjy gZebqbx ^\hcghc k\yab fhe_dmeu wlbe_gZ fh]ml kh _^bgylvky f_`^m kh[hc h[jZamx p_ib [hevrhc ^ebgu ba fgh]bo lukyq bkoh^guo fhe_dme WlZ j_Zdpby gZau\Z_lky j_Zdpb_c ih ebf_jbaZpbb Q + & &+ ihebwlbe_g

dZl o

> &+ &+ @Q

Ihebwlbe_g rbjhdh ijbf_gy_lky \ ijhfure_gghklb b \ [ulm Hg hq_gv fZehZdlb\_g g_ [v_lky ohjhrh h[jZ[Zlu\Z_lky Ijbf_ ju ljm[u lZjZ [hqdb ysbdb baheypbhgguc fZl_jbZe ie_gdZ ^ey miZdh\db kl_deZ b]jmrdb b fgh]h_ ^jm]h_ >jm]bf ijhkl_crbf g_ij_^_evguf m]e_\h^hjh^hf y\ey_lky ihebijhibe_g + & &+ Âą &+ Ijb _]h ihebf_jbaZpbb h[jZam_lky ihebijhibe_g Âą ihebf_j Ihebf_j ih k\hbf kh\hdmiguf k\hckl\Zf b ijbf_g_gbx ZgZeh]b q_g ihebwlbe_gm Q + & &+ Âą &+

dZl o > &+

&+

@Q

&+ Ihebijhibe_g [he__ ijhq_g q_f ihebwlbe_g ihwlhfm ba g_]h ba]hlZ\eb\Z_lky fgh]h ^_lZe_c ^ey jZaghh[jZaguo fZrbg Z lZd`_ fgh`_kl\h lhqguo ^_lZe_c gZijbf_j ^ey wdkdZeZlhjh\ Ijbf_j gh ihebijhibe_gZ i_j_jZ[Zlu\Z_lky \ \hehdgZ

<hijhk ‹

DZd ihemqZxl Zp_lbe_g" HoZjZdl_jbamcl_ _]h ijbf_g_gb_

Hl\_l :p_lbe_g ihemqZxl ^\mfy hkgh\gufb kihkh[Zfb ± ba dZj [b^Z dZevpby beb f_lZgZ &D& + 2 o &D 2+ p +& { &+n

&+ o +& { &+ + n >ey ihemq_gby ohjhr_]h \uoh^Z Zp_lbe_gZ ijb \lhjhf kihkh[_ ihemq_gby ijh^mdlu j_Zdpbb hq_gv [ukljh hoeZ`^Zxl DZj[b^ dZevpby ihemqZxl ba dZj[hgZlZ dZevpby ± h[`b]hf k m]e_f :p_lbe_g ± \Z`gh_ hj]Zgbq_kdh_ \_s_kl\h Bkihevam_lky \ hq_gv [hevrbo dhebq_kl\Zo ijb kbgl_a_ jZaghh[jZaguo obfbq_ kdbo \_s_kl\ Ijbkh_^bg_gb_f d Zp_lbe_gm oehjbklh]h \h^hjh^Z ihemqZxl \bgbeoehjb^ ba dhlhjh]h ihebf_jbaZpb_c ihemqZxl \Z`guc ihebf_j ± iheb\bgbeoehjb^ +& { &+ +&O o + & &+&O Q &+ &+&O o > &+ &+ @Q Iheb\bgbeoehjb^ hlebqZ_lky obfbq_kdhc klhcdhklvx q K

<hijhk ‹

=^_ ijbf_gyxlky ^b_gu"

Hl\_l Ba ^b_gh\ lbibqgufb ijbf_jZfb dhlhjuo y\eyxlky [m lZ^b_g + & &+ ± &+ &+ b bahij_g f_lbe [mlZ^b_g + & K K+ &+ \ h]jhfguo dhebq_kl\Zo ihemqZxl jZagh h[jZagu_ kbgl_lbq_kdb_ dZmqmdb Ba wlbo dZmqmdh\ \ k\hx hq_j_^v ijhba\h^blky \k_ &+ h]jhfgh_ fgh]hh[jZab_ ba^_ebc ba j_abgu gZijbf_j rbg ^ey Z\lhfh[be_c \k_\hafh`guo reZg]h\ b l ^

<hijhk ‹

DZd ihemqZxl ZjhfZlbq_kdb_ m]e_\h^hjh^u"

Hl\_l < hkgh\ghf ZjhfZlbq_kdb_ m]e_\h^hjh^u gZb[he__ oZjZdl_j gufb ij_^klZ\bl_eyfb dhlhjuo y\ey_lky [_gahe & + ihemqZxl ijb dj_dbg]_ g_nlb kf klj b ba dZf_gghm]hevghc kfheu h[ jZamxs_cky ijb dhdkh\Zgbb dZf_gguo m]e_c l _ bo gZ]j_\Zgbb ^h \ukhdbo l_fi_jZlmj [_a ^hklmiZ \ha^moZ kf klj Hkgh\guf kihkh[hf ihemq_gby y\ey_lky i_j\uc ± ba g_nlb

<hijhk ‹

DZdh\h agZq_gb_ ijbjh^gh]h ]ZaZ \ obfbq_kdhc ijhfure_gghklb"

Hl\_l < obfbq_kdhc ijhfure_gghklb ba ijbjh^gh]h ]ZaZ ihemqZxl ^\Z \_s_kl\Z wlbe_g b Zp_lbe_g ba dhlhjuo \ k\hx hq_j_^v ijh ba\h^ylky lZdb_ \_s_kl\Z dZd wlbeh\uc kibjl kbgl_lbq_kdbc dZm qmd ieZklfZkku djZkbl_eb mdkmkgZy dbkehlZ f_^bdZf_glu b ^j kf klj ± &+ f_lZg

o & + + n dZl W | q & 2

wlbe_g

Wlbe_g + 2 o wlbeh\uc kibjl o ± [mlZ^b_g o dZmqmd &O o ^boehjwlZg jZkl\hjbl_ev dZl o ihebwlbe_g ihebf_j ijhibe_g o wlbe_g ± ijhibe_gh\u_ dZmqmdb &+

dZl W | q &

| q & we_dljhdj_ dbg] W o & + + n Zp_lbe_g

Zp_lbe_g + 2 o Zp_lZev^_]b^ o mdkmkgZy dbkehlZ +&O o &+ &+&O o iheb\bgbeoehjb^ \bgbeoehjb^

&O o &O &+ ± &+&O jZkl\hjbl_ev l_ljZoehjwlbe_g

+&1 o &+ &+&1 o ieZklbdb ihebZdjbehgbljbevgu_ \hehdgZ hj]Zgbq_kdh_ kl_deh

<hijhk ‹

HoZjZdl_jbamcl_ ]eZ\gu_ ijh^mdlu i_j_]hgdb g_nlb Kdhevdh ijh p_glh\ [_gabgZ ihemqZxl ijb i_j_]hgd_ g_nlb b kdhevdh ijhp_glh\ ih emqZxl ijb dj_dbg]_ g_nlb"

Hl\_l Hkgh\gufb ijh^mdlZfb i_j_]hgdb g_nlb y\eyxlky [_gabg d_jhkbg b fZaml ;_gabg ± njZdpby kh^_j`ZsZy m]e_\h^hjh^u k ± ZlhfZfb m]e_jh^Z \ fhe_dme_ ;_gabg hl]hgy_lky ijb l_fi_jZlmj_ ^h qK D_jhkbg ± njZdpby kh^_j`ZsZy m]e_\h^hjh^u k ± ZlhfZfb m]e_jh^Z \ fhe_dme_ D_jhkbg hl]hgy_lky ijb l_fi_jZlmj_ ± qK

FZaml Âą kf_kv m]e_\h^hjh^h\ hklZxsboky ihke_ hl]hgdb [_g abgZ b d_jhkbgZ Ijb i_j_]hgd_ g_nlb ihemqZ_lky ^h [_gabgZ <uoh^ [_g abgZ ba g_nlb dZd kZfhc p_gghc njZdpbb fh`gh agZqbl_evgh m\_ebqblv \ ijhp_kk_ dj_dbg]Z Âą ^h Dj_dbg] Âą wlh l_jfbq_kdh_ beb dZlhebq_kdh_ jZks_ie_gb_ m] e_\h^hjh^h\ k ^Zgghc m]e_\h^hjh^ghc p_ivx gZ m]e_\h^hjh^u k f_gvr_c fhe_dmeyjghc fZkkhc

<hijhk ‹

HoZjZdl_jbamcl_ \Z`g_crb_ \b^u lhieb\Z

Hl\_l <Z`g_crbfb \b^Zfb lhieb\Z y\eyxlky \ ihjy^d_ m[u\Zgby agZqbfhklb ijbjh^guc ]Za ijh^mdlu i_j_]hgdb g_nlb [_gabg d_jhkbg ^balhieb\h fZaml dZf_gguc m]hev [mju_ m]eb lhjn ^j_\_kbgZ LjZgkihjl ihlj_[ey_l [_gabg Z\lhljZgkihjl ^balhieb\h ]jmah\u_ Z\lhfh[beb b ljZdlhju d_jhkbg Z\bZpby Hl^_evgu_ Z\lhfh[beb bkihevamxl dZd lhieb\h ijbjh^guc ]Za L_iehwe_d ljhklZgpbb ihlj_[eyxl ijbjh^guc ]Za fZaml m]eb lhjn GZk_e_gb_ \ [ulm ihlj_[ey_l \ hkgh\ghf ijbjh^guc ]Za < k_evkdhc f_klghklb gZk_e_gb_f bkihevam_lky dZf_gguc m]hev b ^j_\_kbgZ Ih nbabq_kdbf k\hckl\Zf lhieb\h [u\Z_l l\_j^uf m]eb lhjn ^j_\_kbgZ b ^j `b^dbf [_gabg d_jhkbg fZaml b ^j ]Zahh[ jZaguf ijbjh^guc ]Za \h^hjh^ b ^j DZq_kl\h lhieb\Z hij_^_ey_lky l_iehlhc k]hjZgby l _ dhebq_kl\hf l_ieZ dhlhjh_ \u^_ey_lky ijb k]hjZgbb d] lhieb\Z AgZq_gby l_iehl k]hjZgby jZaebqguo \b^h\ lhieb\Z kf lZ[e gZ klj ;hevrh_ agZq_gb_ bf__l klhbfhklv ^h[uqb b ljZgkihjlbjh\db lhieb\Z Ihwlhfm klZjZxlky bkihevah\Zlv f_kl gu_ \b^u lhieb\Z KZfuf m^h[guf \b^hf lhieb\Z k lhqdb aj_gby klhbfhklb ^h[uqb b ljZgkihjlbjh\db y\ey_lky ijbjh^guc ]Za ;he__ lh]h ijbjh^guc ]Za \ hlebqb_ hl g_nlb g_l g_h[oh^b fhklb h[jZ[Zlu\Zlv gZ ki_pbZevguo aZ\h^Zo ih^\_j]Zlv i_j_]hg d_ b dj_dbg]m JZagu_ \b^u lhieb\Z ijb k`b]Zgbb \ jZaghc kl_i_gb aZ]jyagy xl Zlfhkn_jm KZfuf Š]jyagufª lhieb\hf y\eyxlky m]eb kZfuf Šqbklufª ijbjh^guc ]Za Ihwlhfm bkihevah\Zgb_ m]ey dZd lhieb \Z klj_fbl_evgh khdjZsZ_lky <h \k_f fbj_ b^_l ijhp_kk aZdju lby m]hevguo rZol

<hijhk ‹

DZd h[_ahiZkblv Zlfhkn_jguc \ha^mo hl aZ]jyag_gbc"

Hl\_l K`b]Zgb_ [hevrbo dhebq_kl\ lhieb\Z ijb\h^bl d ihklhyg ghfm m\_ebq_gbx kh^_j`Zgby \ \ha^mo_ hdkb^Z m]e_jh^Z ,9 &2 < j_amevlZl_ wlh]h \hagbdZ_l lZd gZau\Z_fuc ŠiZjgbdh\uc wn n_dlª l _ m\_ebqb\Z_lky kj_^gyy l_fi_jZlmjZ \ fZkrlZ[Zo \k_c ieZg_lu A_fey Wlh hq_gv hiZkgh_ y\e_gb_ ijb\h^ys__ d baf_g_ gbx debfZlZ Ijb k`b]Zgbb lhieb\Z hkh[_ggh m]e_c \ Zlfhkn_jm ihiZ^Z _l [hevrh_ dhebq_kl\h \j_^guo \_s_kl\ lZdbo dZd hdkb^ k_ju ,9 hdkb^u ZahlZ b iuev =eZ\gu_ aZ]jyagbl_eb ¹ [hevrb_ we_d ljhklZgpbb Hkms_kl\ey_lky hldZa hl Š]jyaguoª \b^h\ lhieb\Z b i_j_oh^ d bkihevah\Zgbx Šqbkluoª \b^h\ lhieb\Z lZdh]h gZijb f_j dZd ijbjh^guc ]Za < djmiguo ]hjh^Zo hkgh\guf aZ]jyagbl_e_f Zlfhkn_ju y\ eyxlky Z\lhfh[beb ;hjv[Z k aZ]jyag_gb_f \ha^moZ hkms_kl\ey_l ky g_kdhevdbfb kihkh[Zfb aZij_s_gh bkihevah\Zlv wlbebjh\Zg guc [_gabg b ^jm]b_ aZ]jyagyxsb_ \ha^mo \b^u `b^dh]h lhieb\Z hkms_kl\ey_lky i_j_oh^ Z\lhfh[be_c gZ bkihevah\Zgb_ ijbjh^gh ]h ]ZaZ Z lZd`_ gZ \g_^j_gb_ we_dljhZ\lhfh[be_c kh\_jr_gkl\m xlky ^\b]Zl_eb Z\lhfh[be_c k l_f qlh[u k\_klb d fbgbfmfm aZ ]jyag_gb_ Zlfhkn_ju G_h[oh^bfh \kyq_kdb jZa\h^blv a_e_gu_ gZkZ`^_gby [_j_qv dZ`^h_ ^_j_\h H]jhfgh_ agZq_gb_ \ gZklhys__ \j_fy ijbh[j_lZ_l khojZg_gb_ kms_kl\mxsbo e_kh\ b jZa\_^_gb_ gh\uo [hjv[Z k e_kgufb ih`ZjZfb wdhghfgh_ bkihevah\Zgb_ ^j_\_kbgu b ijh ^mdlh\ __ i_j_jZ[hldb b l ^

<hijhk ‹

JZkkfhljbl_ deZkkbnbdZpbx ijhba\h^guo m]e_\h^hjh^h\

Hl\_l KibjlZfb gZau\Zxlky ijhba\h^gu_ m]e_\h^hjh^h\ \ fhe_ dmeZo dhlhjuo h^bg beb g_kdhevdh Zlhfh\ \h^hjh^Z aZf_s_gu h^ gh\Ze_glgufb ]b^jhdkbevgufb ]jmiiZfb Âą HG Ijbf_ju + + + + + & & +

+wlZg +

o

+ & & 2+

+

+

wlZghe wlbeh\uc kibjl

+

+ +

+ & Âą &+ Âą &+ o

+ & & & +

ijhiZg

]ebp_jbg lj_oZlhfguc kibjl

mdkmkgZy dbkehlZ

wlbeh\uc kibjl

2+ 2+ 2+

DZj[hjgh\ufb dbkehlZfb gZau\Zxlky ijhba\h^gu_ m]e_\hÂą 2 ^hjh^h\ \ fhe_dmeZo dhlhjuo bf__lky ]jmiiZ Zlhfh\ K 2+ gZau\Z_fZy dZj[hdkbevghc ]jmiihc Ijbf_ju fmjZ\vbgZy dbkehlZ mdkmkgZy dbkehlZ sZ\_e_\Zy d lZ 2 2 2 2 K K + K + & K 2 + + 2 2 + 2 + Keh`gufb wnbjZfb gZau\Zxlky kh_^bg_gby dhlhju_ ihem qZxlky ijb \aZbfh^_ckl\bb dZj[hgh\uo dbkehl kh kibjlZfb kf klj 2 Keh`gu_ wnbju kh^_j`Zl oZjZdl_jgmx ]jmiim Zlhfh\ K 2 Ijbf_j 2 2 + & K + & K 2 + &+ Âą &+ Âą 2+ o 2 K+ K+ + 2 wlbeZp_lZl keh`guc wnbj

Keh`gu_ wnbju ]ebp_jbgZ b \ukrbo dZj[hgh\uo dbkehl gZijb f_j iZevfblbgh\hc &+ Âą &+ Âą &22+ kl_Zjbgh\hc &+ Âą &+ Âą &22+ b l i gZau\Zxlky `bjZfb + + Djhf_ keh`guo wnbjh\ kms_kl\mxl ijh klu_ lZdb_ dZd ba\_klguc bahf_j wlbeh + & 2 & + \h]h kibjlZ ^bf_lbeh\uc wnbj +

+

Bo oZjZdl_jguf ijbagZdhf y\ey_lky gZebqb_ p_ihqdb Zlhfh\

& 2 &

<Z`g_crbfb ij_^klZ\bl_eyfb m]e_\h^h\ y\eyxlky ]exdhaZ & + 2 njmdlhaZ & + 2 kZoZjhaZ & + 2 ijbjh^gu_ ihebf_ju djZofZe b p_eexehaZ GZa\Zgb_ m]e_\h^u ijhbahreh hl lh]h qlh \ dZ`^mx fhe_dmem ihfbfh Zlhfh\ K gZ dZ`^uc Zlhf dbkehjh^Z ijboh^blky jh\gh ^\Z ZlhfZ \h^hjh^Z

Ijbf_j kljh_gb_ njmdlhau 2+

2

2+ 2+

kljh_gb_ kZoZjhau

2+

2+

&+ 2+

&+ 2+

2

&+ 2+

2

2

&+ 2+

2+ 2+ 2+ 2+ :fbghdbkehlZfb gZau\Zxlky \_s_kl\Z ijhba\h^gu_ hl dZj [hgh\uo dbkehl \ m]e_\h^hjh^ghc qZklb fhe_dme dhlhjuo ohly [u h^bg Zlhf \h^hjh^Z aZf_g_g gZ Zfbgh]jmiim ± 1+ 2 Ijbf_ju ]ebpbg ZfbghmdkmkgZy dbkehlZ + 1 &+ K 2 + ;_edb ± hq_gv keh`gu_ \ukhdhfhe_dmeyjgu_ hj]Zgbq_kdb_ \_s_kl\Z dhlhju_ h[jZamxlky ijb ijbkh_^bg_gbb hklZldh\ jZa guo Zfbghdbkehl \ jZaebqguo dhf[bgZpbyo kf klj Ihebf_ju ± \ukhdhfhe_dmeyjgu_ kh_^bg_gby fhe_dmeu dh lhjuo h[jZamxlky \ j_amevlZl_ kh_^bg_gby fgh`_kl\Z h^bgZdh\uo a\_gv_\ ± khklZ\guo qZkl_c ihebf_jZ + & &+ l ± &+ ± &+ Q + & &+&O l &+ &+ Q wlbe_g

ihebwlbe_g

\bgbeoehjb^

&O

iheb\bgbeoehjb^

†† ± klj <hijhk ‹

Dhjhldh hoZjZdl_jbamcl_ f_lZghe wlZghe wlbe_g]ebdhev b ]ebp_ jbg =^_ bo bkihevamxl"

Hl\_l F_lZghe &+ 2+ ± ijhkl_crbc ij_^klZ\bl_ev h^ghZlhfguo ij_^_evguo kibjlh\ ;_kp\_lgZy `b^dhklv Wdbi ± qK kh keZ[uf aZiZohf g_hlebqbfuf hl aZiZoZ h[uqgh]h wlbeh\h]h kibjlZ Hq_gv y^h\bl I_j\hgZqZevgh gZau\Zeky ^j_\_kguf kibjlhf l d _]h ihemqZeb ibjhebahf ^j_\_kbgu Rbjhdh ijbf_gy_lky \ dZq_ kl\_ jZkl\hjbl_ey \ hl^_evguo kljZgZo bkihevam_lky dZd Z\lhfh [bevgh_ lhieb\h beb ^h[Z\dZ d [_gabgm \ obfbq_kdhc ijhfur e_gghklb ± ^ey ijhba\h^kl\Z mdkmkghc dbkehlu ieZklfZkk WlZghe & + 2+ &+ ± &+ ± 2+ ± [_kp\_lgZy `b^dhklv Wdbi ± qK kh keZ[uf aZiZohf <lhjhc ij_^klZ\bl_ev jy^Z h^gh

Zlhfguo ij_^_evguo kibjlh\ kf_rb\Z_lky k \h^hc \ ex[hf khhl ghr_gbb M`_ \ ^j_\ghklb q_eh\_dm [ue ba\_kl_g [bhobfbq_kdbc f_lh^ ihemq_gby ba kZoZjhkh^_j`Zsbo \_s_kl\ ih ko_f_ & + 2 ^jh``b o & + 2+ &2 n Ihwlhfm wlZghe kh^_j`blky \ g_[hevrbo dhebq_kl\Zo \ d_nb j_ \ [hevrbo \ dmfuk_ Wlhl `_ ijhp_kk ijhbkoh^bl ijb k[jZ`b \Zgbb khdh\ b ij_\jZs_gbb bo \ \bgh < ijhfure_gghklb wlZghe ^Z\gh m`_ ihemqZxl kbgl_lbq_kdb ba wlbe_gZ + & &+ + ± 2+ dZlZebaZlh j o &+ ± &+ 2+

WlZghe ijbf_gy_lky \ [hevrbo dhebq_kl\Zo ^ey ijhba\h^kl\Z [mlZ^b_gZ Z ba g_]h ± dZmqmdh\ dZd jZkl\hjbl_ev dZd kujv_ ^ey ijhba\h^kl\Z fgh]bo f_^bdZf_glh\ eZdh\ ^mrbkluo \_s_kl\ b l ^ Bkihevam_lky lZd`_ ^ey ijhba\h^kl\Z Zedh]hevguo gZibldh\ WlZghe ± y^h\blh_ gZjdhlbq_kdh_ \ \h Mihlj_[e_gb_ _]h \ [hev rbo dhe \Zo fh`_l ijb\_klb d kf_jl_evghfm bkoh^m WlZghe ih \g_rgbf ijbagZdZf g_hlebqbf hl kf_jl_evgh y^h\blh]h f_lZgheZ Wlbe_g]ebdhev ± ijhkl_crbc ij_^klZ\bl_ev ^\moZlhfguo kibjlh\ Fhe_dmeyjgZy nhjfmeZ ± & + 2 kljh_gb_ + & &+ 2+ 2+ Wlbe_g]ebdhev ± keZ^dZy kbjhihh[jZagZy `b^dhklv Wdbi ± qK Hq_gv y^h\bl G_h]jZgbq_ggh jZkl\hjbf \ \h^_ Bkihev am_lky ^ey ijhba\h^kl\Z Zglbnjbah\ ± g_aZf_jaZxsbo kf_k_c wlb e_g]ebdhey b \h^u ^ey aZeb\db \ jZ^bZlhju Z\lhfh[be_c abfhc \f_klh h[uqghc \h^u :glbnjba kh^_j`Zsbc wlbe_g]ebdhey aZf_jaZ_l lhevdh ijb ± qK =ebp_jbg ± ijhkl_crbc ij_^klZ\bl_ev lj_oZlhfguo kibj lh\ Fhe_dmeyjgZy nhjfmeZ ± & + 2 fhe_dmeyjgh_ kljh_gb_ ± DZd b wlbe_g]ebdhev wlh [_kp\_lgZy kbjhih K+ K+ &+ h[jZagZy `b^dhklv keZ^dZy gZ \dmk < hleb 2+ 2+ 2+ qbb hl wlbe_g]ebdhey ]ebp_jbg g_ y^h\bl =ebp_jbg b]jZ_l \Z`gmx jhev \ `bag_^_y l_evghklb hj]Zgbafh\ ± y\ey_lky h^ghc ba khklZ\eyxsbo `b\hl guo b jZklbl_evguo `bjh\ =ebp_jbg bkihevam_lky \ f_^bpbg_ ibs_\hc ijhfure_gghklb Z lZd`_ bkihevam_lky dZd kujv_ ^ey ijhba\h^kl\Z Zglbnjbah\ \ ijhba\h^kl\_ \aju\qZluo \_s_kl\

<hijhk ‹

HoZjZdl_jbamcl_ fmjZ\vbgmx dbkehlm mdkmkgmx dbkehlm b ebfhggmx dbkehlm =^_ hgb \klj_qZxlky \ ijbjh^_ b dZd bo bkihevamxl"

Hl\_l

FmjZ\vbgZy dbkehlZ + K

2

2

+

Ijhkl_crZy dZj[hgh\Zy dbkehlZ Kh^_j`blky \ y^h\bluo `_e_ aZo fmjZ\v_\ \ djZib\_ \ _eh\hc o\h_ Bkihevam_lky \ dZq_kl\_ ijhljZ\u r_jklb b dh`b i_j_^ djZr_gb_f \ obfbq_kdhc ijh fure_gghklb \ dZq_kl\_ kbevgh]h \hkklZgh\bl_ey Z lZd`_ dZd ku jv_ ^ey ihemq_gby keh`guo wnbjh\ jZkl\hj fmjZ\vbghc dbkehlu \ kibjl_ ¹ ŠfmjZ\vbguc kibjlª bkihevam_lky \ f_^bpbg_ 2 MdkmkgZy dbkehlZ + & K 2 + ;_kp\_lgZy `b^dhklv k j_adbf aZiZohf < nhjf_ \h^gh]h ¹ jZkl\hjZ ba\_klgZ \k_f dZd klheh\uc mdkmk < qbklhf \b^_ mihl j_[e_gb_ mdkmkghc dbkehlu kf_jl_evgh hiZkgh IhiZ^Zgb_ __ gZ dh`gu_ ihdjh\u lZd`_ ijb\h^bl d kbevguf h`h]Zf Hq_gv rbjh dh ijbf_gy_lky \ obfbq_kdhc ijhfure_gghklb ^ey ihemq_gby e_dZjkl\ khe_c bkdmkkl\_gguo \hehdg jZkl\hjbl_e_c kj_^kl\ [hjv[u k gZk_dhfufb b [he_agyfb jZkl_gbc klbfmeylhjh\ jhklZ jZkl_gbc djZkbl_e_c ^ey ldZg_c dbghie_gdb EbfhggZy dbkehlZ ¹ djbklZeebq_kdh_ \_s_kl\h Wie ¹ qK Fhe_dmeyjgZy nhjfmeZ ¹ & + 2 Fhe_dmeyjgh_ kljh_gb_ +

2

2+

2

K K+ K &+ K K

2

2

2

+

2 + Ohjhrh jZkl\hjbfZ \ \h^_ dbkeZy gZ \dmk B]jZ_l \Z`gmx jhev \ ijhp_kk_ h[f_gZ \ \ \ `b\uo hj]ZgbafZo IhemqZxl __ ba g_^haj_euo ebfhgh\ Z lZd`_ hkh[uf [jh`_gb_f kZoZjh\ beb dhj fh\hc iZlhdb Bkihevamxl \ ibs_\hc ijhfure_gghklb ^ey ij \Z dhg^bl_jkdbo ba^_ebc b ijhoeZ^bl_evguo gZibldh\ \ f_^bpbg_

<hijhk ‹

<aZbfh^_ckl\b_ dZdbo \_s_kl\ ijb\h^bl d h[jZah\Zgbx keh`guo wnbjh\" DZdb_ keh`gu_ wnbju h[eZ^Zxl ijbylguf ZjhfZlhf"

Hl\_l Keh`gu_ wnbju h[jZamxlky ijb \aZbfh^_ckl\bb dZj[hgh\uo dbkehl kh kibjlZfb

Ijbf_j + & K

mdkmkgZy dbkehlZ

2

2 +

+2 Âą &+ &+ o + & K wlbeh\uc kibjl

2

2 K+ K+

+ 2

wlbeZp_lZl

wlbeh\uc wnbj mdkmkghc dbkehlu

?keb \ _]h fhe_dme_ keh`guo wnbjh\ qbkeh Zlhfh\ m]e_jh^Z g_\_ebdh lh hgb h[eZ^Zxl ijbylguf ZjhfZlhf Ijbylguc ZjhfZl fgh]bo njmdlh\ p\_lh\ k\yaZg k ijbkmlkl\b_f keh`guo wnbjh\ 2 Ijbf_j mdkmkghbahhfbeh\uc wnbj Š]jmr_\Zy wkk_gpbyª K+ K 2 K+

<hijhk ‹

Qlh lZdh_ fueh b qlh lZdh_ `bju"

Hl\_l FueZ ¹ wlh gZljb_\u_ beb dZeb_\u_ kheb lZd gZau\Z_fuo Š`bjguoª dZj[hgh\uo dbkehl gZijbf_j K + &22¹1D M]e_ jh^guc hklZlhd dZj[hgh\hc dbkehlu ^he`_g \dexqZlv hl ^h Zlhfh\ m]e_jh^Z FueZ ihemqZxl \Zjdhc `bjh\ k 1D2+ beb . &2 GZljb_\u_ fueZ ¹ l\_j^u_ dZeb_\h_ fueh ¹ `b^dh_ @bju ¹ keh`gu_ wnbju ]ebp_jbgZ b h^ghhkgh\guo g_jZa\_l\ e_gguo dZj[hgh\uo dbkehl kh^_j`Zsbo hl ^h Zlhfh\ m]e_jh ^Z lZdb_ dbkehlu ba^Z\gZ gZau\Zxl ³`bjgufb´ dbkehlZfb < hk gh\ghf `bju khklhyl ba ljb]ebp_jb^h\ Ze_bgh\hc & + &22+ iZevf_lbghc & + &22+ b kl_Zjbgh\hc & + &22+ dbkehl < fhe_dmeu ijbjh^guo `bjh\ \oh^yl h[uqgh hklZldb ¹ jZa guo dZj[hgh\uo dbkehl Ijbf_j &+ 2 &2 & + ljb]ebp_jb^ kl_Zjbgh\hc dbkehlu &+ 2 &2 & +

&+ 2 &2 & +

<hijhk ‹

DZd ]exdhaZ h[jZam_lky \ ijbjh^_" =^_ bkihevamxl ]exdham"

Hl\_l =exdhaZ \ ijbjh^_ h[jZam_lky \ jZaebqguo jZkl_gbyo \ ijh

o & + 2 2 n p_kk_ nhlhkbgl_aZ &2 + 2 4 k\_l oehjhnbee

LZdmx `_ nhjfmem bf__l b ^jm]hc ijbjh^guc m]e_jh^ ± njmd lhaZ =exdhaZ b njmdlhaZ ± e_]dhmk\hy_fuc bklhqgbd wg_j]bb `b \uo hj]Zgbafh\ =exdhaZ rbjhdh bkihevam_lky lZd`_ \ dhg^bl_j kdhc l_dklbevghc ijhfure_gghklb ij \_ a_jgZ Zkdhj[bgh\hc dbkehlu ibs_\h]h b f_^bpbgkdh]h wlbeh\h]h kibjlZ

<hijhk ‹

< dZdbo jZkl_gbyo \klj_qZ_lky kZoZjhaZ"

Hl\_l KZoZjhaZ & + 2 ± h[uqguc ibs_\hc kZoZj < hkgh\ghf \klj_qZ_lky \ dem[gyo kZoZjghc k\_deu ± b \ kl_[eyo kZ oZjgh]h ljhklgbdZ ± KZoZjhaZ \ f_gvrbo dhebq_kl\Zo kh ^_j`blky \ khd_ b ^jm]bo jZkl_gbc ± [_j_au de_gZ \ DZgZ^_ g_ dhlhjuo iZevf \ :njbd_ \ ieh^Zo fgh]bo jZkl_gbc

<hijhk ‹

HoZjZdl_jbamcl_ kljh_gb_ fhe_dme djZofZeZ b ]exdhau =^_ hgb bk ihevamxlky"

Hl\_l Fhe_dmeu ]exdhau bf_xl pbdebq_kdh_ kljh_gb_ &+ 2+

+

+2

+ 2+

+

2 +

+

2+

2+

< \h^ghf jZkl\hj_ pbdebq_kdb_ fhe_dmeu ]exdhau jZkdju\Zxlky \ ebg_cgu_ nhjfu fhe_dme ]exdhau Zev^_]b^gZy nhjfZ ]b^jZlgZy nhjfZ 2+ &+2 + & 2+

+2 & +

+ & 2+ + & 2+ &+ 2+

+ & 2+ + & 2+

+2 & +

+ & 2+

+ & 2+ &+ 2+

Bkihevah\Zgb_ ]exdhau ± kf hl\_l gZ \hijhk klj

DjZofZe ± ijbjh^guc ihebf_j ]exdhau Bf__l nhjfmem & + 2 Q ]^_ Q ^hklb]Z_l g_kdhevdbo lukyq We_f_glZjgu_ njZ]f_glu bf_xl pbdebq_kdmx kljmdlmjm kjZ\gb kh kljh_gb_f ]exdhau &+ 2+ &+ 2+ 2 2 + 2 2+

2

2+

Q

2+ 2+ Ih^h[gu_ ijbjh^gu_ ihebf_ju gZau\Zxlky ihebkZoZjb^Zfb >jm]hc ijbjh^guc ihebkZoZjb^ k _s_ [hevrbf agZq_gb_f Q ± wlh p_eexehaZ DjZofZe bkihevam_lky \ ibs_\hc ijhfure_gghklb gZijbf_j kmohc dbk_ev ^ey ihemq_gby l_ogbq_kdhc ]exdhau wlbeh\h]h kibjlZ Z lZd`_ \_s_kl\Z ^_dkljbg

<hijhk ‹

HoZjZdl_jbamcl_ kljh_gb_ fhe_dme Zfbghdbkehl DZdh\Z jhev Zfb ghdbkehl \ `bagb q_eh\_dZ b `b\hlguo"

Hl\_l :fbghdbkehlu ± wlh ijhba\h^gu_ dZj[hgh\uo dbkehl \ fhe_ dmeZo dhlhjuo \ m]e_\h^hjh^ghc qZklb h^bg beb g_kdhevdh Zlhfh\ \h^hjh^Z aZf_g_g gZ Zfbgh]jmiim ± 1+ LZdbf h[jZahf Zfbgh dbkehlu bf_xl \ fhe_dme_ ^\_ nmgdpbhgZevgu_ ]jmiiu Ijbf_ju Zfbghdbkehl ]ebpbg + 1 ± &+ ± &22+ ZeZgbg &+ &+ &22+ 1+

n_gbeZeZgbg ZjhfZlbq_kdZy ZfbghdbkehlZ

]emlZfbg

ebabg Zfbgh]jmiiu \ fhe_dme_

& + &+ &+ &22+

+22& &+ &22+

1+

1+

+ 1 &+ &+ &22+

1+

Jhev Zfbghdbkehl \ ijbjh^_ \ lhf qlh ba gbo h[jZamxlky [_e dh\u_ \ \Z \k_o jZkl_gbc b `b\hlguo ;_edh\u_ \ \Z b]jZxl bk dexqbl_evgmx jhev \ iblZgbb q_eh\_dZ b `b\hlguo l d qZklv Zfbghdbkehl `b\hlgu_ hj]Zgbafu kbgl_abjh\Zlv g_ fh]ml b ihem

qZxl bo \ khklZ\_ [_edh\hc ibsb LZdbfb g_aZf_gbfufb Zfbgh dbkehlZfb y\eyxlky \Zebg e_cpbg bahe_cpbg f_lbhgbg Nmgdpbb [_edh\ hq_gv jZaghh[jZagu Ijbf_jZfb [_edh\ y\ey xlky ]_fh]eh[bg n_jf_glu ]hjfhgu

<hijhk ‹

HoZjZdl_jbamcl_ keh`ghklv kljh_gby fhe_dme Zfbghdbkehl bo jZa ghh[jZab_ b \Z`gmx [bheh]bq_kdmx jhev

Hl\_l :fbghdbkehlu Âą keh`gh mkljh_ggu_ hj]Zgbq_kdb_ \_s_kl\Z bf_xsb_ jZaghh[jZagh_ kljh_gb_ <k_ Zfbghdbkehlu bf_xl \ fh e_dme_ ih djZcg_c f_j_ ^\_ nmgdpbhgZevgu_ ]jmiiu Zfbgh]jmi im 1+ b ]jmiim dZj[hgh\hc dbkehlu Âą &22+ G_dhlhju_ Zfbghdbkehlu fh]ml bf_lv g_kdhevdh dbkehlguo ]jmii ZfbghdbkehlZ ]emlZfbg +22& &+ &22+

1+

g_dhlhju_ Zfbghdbkehlu bf_xl ih g_kdhevdh Zfbgh]jmii ebabg Âą Zfbgh]jmiiu + 1 &+ &+ &22+

1+

< khklZ\ fhe_dme Zfbghdbkehl fh`_l \oh^blv ZjhfZlbq_kdh_ dhevph n_gbeZeZgbg & + &+ &+ &22+

1+ G_dhlhju_ Zfbghdbkehlu \dexqZxl kibjlh\mx ]jmiim ¹ k_jbg Kms_kl\mxl Zfbghdbkehlu mkljh_ggu_ &+ &+ &22+ _s_ [he__ keh`guf h[jZahf <Z`g_crZy [bheh]bq_kdZy jhev Zfbghdbk 2+ 1+ ehl \ lhf qlh hgb y\eyxlky we_f_glZjgufb ³dbjibqbdZfb´ ^ey kljhbl_evkl\Z ]b]Zglkdbo fhe_dme [_edh\ Hk gh\guo Zfbghdbkehl ¹

<hijhk ‹

Qlh gZau\Zxl n_jf_glZfb b qlh Âą ]hjfhgZfb"

Hl\_l N_jf_glu b ]hjfhgu Âą wlh jZagh\b^ghklb [_edh\ h[_ki_qb \Zxsb_ `bag_^_yl_evghklv hj]Zgbafh\ b bo jZa\blb_ N_jf_glu Âą wlh mgbdZevgu_ ih k\hbf k\hckl\Zf [bheh]bq_ kdb_ dZlZebaZlhju [_a dhlhjuo g_ fh]eb [u hkms_kl\blvky \Z` g_crb_ [bheh]bq_kdb_ ijhp_kku Mq_gu_ ^h kbo ihj g_ gZmqbebkv

\hkijhba\h^blv fgh]b_ obfbq_kdb_ ijhp_kku dhlhju_ ijhoh^yl \ de_ldZo `b\uo hj]Zgbafh\ ijb mqZklbb n_jf_glh\ =hjfhgu ± hkh[u_ hq_gv Zdlb\gu_ \_s_kl\Z j_]mebjmxsb_ ^_yl_evghklv hij_^_e_gguo hj]Zgh\ hj]ZgbafZ \ p_ehf b ijhp_k kh\ h[f_gZ \_s_kl\ <ujZ[Zlu\Zxlky ki_pbZebabjh\Zggufb de_l dZfb b `_e_aZfb \gmlj_gg_c k_dj_pbb Ba\_klgh [he__ ]hjfh gh\ q_eh\_dZ b `b\hlguo Ijbf_ju ]hjfhgh\ Z^j_gZebg bgkmebg dhjlbdhkl_jhg ijh]_kl_jhg lbfhabgu >_nbpbl ]hjfh gZ bgkmebg \ hj]Zgbaf_ q_eh\_dZ ijb\h^bl d aZ[he_\Zgbx ± kZoZj guc ^bZ[_l =hjfhgu lbfhabgu \ujZ[Zlu\Zxlky \behqdh\hc `_e_ahc b] jZxl \Z`g_crmx jhev \ hkms_kl\e_gbb ijhlb\h\bjmkghc b ijh lb\hjZdh\hc aZsblu hj]ZgbafZ =hjfhgu lZd`_ b]jZxl \Z`g_c rmx jhev \ hkms_kl\e_gbb j_ijh^mdlb\ghc nmgdpbb hj]Zgbafh\ Fgh]b_ ]hjfhgu y\eyxlky p_gg_crbfb e_dZjkl\Zfb

<hijhk ‹

>Zcl_ djZldmx oZjZdl_jbklbdm ihebwlbe_gZ ihebijhibe_gZ iheb \bgbeoehjb^Z n_ghieZklh\ =^_ hgb ijbf_gyxlky"

Hl\_l Ihebwlbe_g ± ihebf_j h[jZamxsbcky ijb dZlZeblbq_kdhc ihebf_jbaZpbb wlbe_gZ 7L &O $O & + Q + & &+ o > &+ &+ @Q L\_j^uc ihebf_j [_eh]h p\_lZ ijhajZqguc \ ie_gdZo Obfbq_kdb hq_gv klh_d G_ j_Z]bjm_l k s_ehqZfb ex[hc dhgp_gljZpbb jZk l\hjZfb ex[uo khe_c \k_fb dbkehlZfb djhf_ dhgp Zahlghc JZajmrZ_lky lhevdh ^_ckl\b_f &O b ) Z lZd`_ hdbke_gb_f db kehjh^Z \ha^moZ gZ k\_lm hkh[_ggh ijb ^_ckl\bb mevljZnbh e_lh\uo emq_c IjZdlbq_kdb [_a\j_^_g ^ey a^hjh\vy q_eh\_dZ H^bg ba kZfuo p_gguo b jZkijhkljZg_gguo ihebf_jh\ Hq_gv e_]dh i_j_jZ[Zlu\Z_lky \ ]hlh\u_ ba^_eby Fbjh\h_ ijhba\h^kl\h ihebwlbe_gZ khklZ\ey_l [he__ feg lhgg \ ]h^ GZb[he__ rbjh dh ijbf_gy_lky ^ey ijhba\h^kl\Z \k_\hafh`guo ie_ghd [ulh\h]h b l_ogbq_kdh]h gZagZq_gby ij_^f_lh\ ^hfZrg_]h h[boh^Z _fdh kl_c b ZiiZjZlmju b ojZg_gby Z]j_kkb\guo \_s_kl\ Ihebijhibe_g ± [_kp\_lguc l_jfhieZklbqguc ihebf_j Kbgl_abjm_lky iml_f ihebf_jbaZpbb ijhibe_gZ &+ &+ ± &+ Bf__l kljmdlmjm > &+ & + @Q &+

< lhgdbo ie_gdZo ijZdlbq_kdb ijhajZq_g Ijbf_jgh iheb ijhibe_gZ i_j_jZ[Zlu\Z_lky \ kbgl_lbq_kdh_ \hehdgh G_dhlhju_ _]h khjlZ h[eZ^Zxl [hevrhc fhjhahklhcdhklvx ¹ ^h ¹ qK Ijb f_gy_lky dZd we_dljhbaheypbhgguc fZl_jbZe \ we_dljhl_ogbd_ Iheb\bgbeoehjb^ ¹ [_kp\_lguc l_jfhieZklbqguc ihebf_j Kbgl_abjm_lky ba \bgbeoehjb^Z &+ &+&O o > &+ &+&O @Q Klh_d obfbq_kdb Ih kjZ\g_gbx k ihebwlbe_ghf b ihebijhibe_ ghf klh_d d \ha^_ckl\bx Zlfhkn_ju b ljm^gh ]hjxq Bf_ggh ih wlhfm I<O hq_gv rbjhdh ijbf_gy_lky ^ey baheypbb \k_\hafh` guo we_dljhijh\h^h\ b dZ[_e_c ^ey ijhba\h^kl\Z ebghe_mfZ iheh\hc iebldb b bkdmkkl\_gghc dh`b Ba ijhajZqgh]h I<O ba]h lh\eyxl h[t_fgmx lZjm ^ey ibs_\uo ijh^mdlh\ [mluehd b l ^ N_ghieZklu NNK ¹ ieZklfZkku ihemqZxsb_ky iml_f ijh ibldb n_ghenhjfZev^_]b^gufb kfheZfb b ij_kkh\Zgby ijb ih \ur_gghc l_fi_jZlmj_ jZaebqguo fZl_jbZeh\ dZd lh o [ ldZg_c [mfZ]b kl_deh\hehdgZ ^j_\_kghc fmdb beb hibehd N_ghenhjfZev^_]b^gu_ kfheu ihemqZxl \ j_amevlZl_ ihebdhg ^_gkZpbb n_gheZ b nhjfZev^_]b^Z 2 Q & + 2+ Q + K o > & + 2+ &+ @Q Q + 2 2 + Ijb gZ]j_\Zgbb kfhehih^h[guc ijh^mdl j_Zdpbb ihebdhg^_gkZ pbb aZl\_j^_\Z_l l d h[jZamxlky k\yab Škrb\Zxsb_ª ebg_cgu_ fhe_dmeu LZdb_ ieZklfZkku gZau\Zxlky l_jfhj_Zdlb\gufb < hlebqb_ hl ihebwlbe_gZ ihebijhibe_gZ iheb\bgbeoehjb^Z n_ ghieZklu ijb gZ]j_\Zgbb g_ jZaeZ]Zxlky GZebqb_ Škrb\hdª f_` ^m ebg_cgufb fhe_dmeZfb h[_ki_qb\Z_l agZqbl_evgmx f_oZgbq_ kdmx ijhqghklv n_ghieZklh\ qlh iha\hey_l bkihevah\Zlv bo ^ey ij \Z ^_lZe_c fZrbg b ZiiZjZlh\ \ we_dljh¹ b jZ^bhl_ogbq_kdhc ijhfure_gghklb kf lZ[e gZ klj

<hijhk ‹

GZ hkgh\Zgbb \k_]h ba\_klgh]h \Zf fZl_jbZeZ hj]Zgbq_kdhc obfbb khklZ\vl_ lZ[ebpm ih ke_^mxs_c ko_f_

Hl\_l DeZkk kh_^bg_gbc Ij_^_evÂą gu_ gZku s_ggu_ m] e_\h^hjh^u

Lbibqguc ij_^klZ\bl_ev F_lZg &+

H[eZklv ijbf_g_gby

Lhieb\h kujv_ ^ey ob fbq_kdhc ijhfure_ggh klb kf hl\_l gZ \hij klj

DeZkk kh_^bg_gbc G_ij^_ev gu_ g_gZku s_ggu_ m] e_\h^hjh^u jy^Z wlbe_gZ G_ij^_ev gu_ g_gZku s_ggu_ m] e_\h^hjh^u jy^Z Zp_lb e_gZ >b_gh\u_ m]e_\h^hjh ^u :jhfZlb q_kdb_ m]e_ \h^hjh^u =Zeh]_g ijhba\h^gu_ m]e_\h^hjh ^h\ Kibjlu h^ghZlhf gu_

Kibjlu fgh]hZlhf gu_

DZj[hgh \u_ dbkehlu Ijhklu_ wnbju

Lbibqguc ij_^klZ\bl_ev Wlbe_g + & &+ :p_lbe_g +& { &+

±[mlZ^b_g + & &+ ± &+ &+ ;_gahe & +

>boehjwlZg &+ &O ± &+ &O nj_hgu WlZghe &+ ± &+ 2+ =ebp_jbg

&+ &+ &+

2+

2+

2+

MdkmkgZy dbkehlZ 2 + & K 2 +

>bf_lbeh\uc wnbj &+ ± 2 ± &+

H[eZklv ijbf_g_gby

Bkoh^gh_ kujv_ ^ey ih emq_gby ihebwlbe_gZ wlbeh\h]h kibjlZ b ^j \_s_kl\ kf hl\_l gZ \hij klj

Ijhba\h^kl\h mdkmkghc dbkehlu ^j \_s_kl\ Zp_lbe_gh\Zy k\ZjdZ b j_adZ f_lZeeh\ kf hl\_l gZ \hij klj

Ijhba\h^kl\h dZmqmdh\ kf hl\_l gZ \hij klj

Kujv_ ^ey obfbq_kdhc ijhfure_gghklb JZkl\hjbl_eb oheh^bev gu_ Z]j_]Zlu kujv_ ^ey obfbq_kdhc ijhfur e_gghklb kf hl\_l gZ \hij klj

JZkl\hjbl_ev ijhba\h^ kl\h Zedh]hevguo gZibl dh\ ± [mlZ^b_gZ kf hl\_l gZ \hij klj

F_^bpbgkdZy ijhfur e_gghklv ibs_\Zy ijh fure_gghklv obfbq_ kdZy ijhfure_gghklv Zglbnjbau b l ^ kf hl\_l gZ \hij klj

Ibs_\Zy ijhfure_g ghklv obfbq_kdZy k_ev kdh ohayckl\_ggZy ijh fure_gghklv kf hl\_l gZ \hij klj

JZkl\hjbl_ev

DeZkk kh_^bg_gbc Keh`gu_ wnbju M]e_\h^u :fbgh dbkehlu @bju

Lbibqguc ij_^klZ\bl_ev F_lbeZp_lZl 2 + & K 2 K+ =exdhaZ & + 2

=ebpbg + 1 Âą &+ Âą &22+

Ljb]ebp_jb^ kl_Z jbgh\hc dbkehlu &+ 2 &2 & +

H[eZklv ijbf_g_gby

Ibs_\Zy ijhfure_g ghklv iZjnxf_jby ob fbq_kdZy kf hl\_l gZ \hij klj

F_^bpbgZ ibs_\hc ijh^mdl obfbq_kdZy ijhfure_gghklv kf hl\_l gZ \hij klj

Dhfihg_gl [_edh\ f_ ^bpbgkdbc ij_iZjZl kf hl\_l gZ \hij klj

Ijh^mdl iblZgby ijhba \h^kl\h fueZ kf hl\_l gZ \hij klj

&+ 2 &2 & +

;_edb

Ihebf_ju

&+ 2 &2 & +

N_jf_glu ]hjfhgu [_edb fur_qguo ldZg_c Ihebwlbe_g

> &+ &+ @Q

Hkgh\ghc Škljhbl_ev guc fZl_jbZeª `b\uo hj]Zgbafh\ ijh^mdlu iblZgby kf hl\_l gZ \hij klj

Ie_gdb ljm[u _fdhklb ^_lZeb f_oZgbafh\ kf hl\_l gZ \hij klj

Turn static files into dynamic content formats.

Create a flipbook
Issuu converts static files into: digital portfolios, online yearbooks, online catalogs, digital photo albums and more. Sign up and create your flipbook.