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5*S\I9JK7IC>A@CBt4MJ>SKTnz5S@j>S@CBb@9J57@n/5STI K¿IS@KWS9@57@F(B,9JI79J@9<Kg*> S9J8¿;X@9y>AK S\I9 MJ9J8@ S9<K#*5 U.STI96 Sr>AKy1 I99 h> MS#~>SW8 RC9<65 Ul >A@CBl
B,9!Y/9<@CBzRYz5S@oS\I9>766TRX9<BoI9<8WKeRX>*nRC@CB>A@>M9.X9 Sr>A8¿W8 KNMKWS; z>A@CBÇ9yL6 Yz!9 MaK¿>S8:8¿; S\IÁ9 SgK9y> S\Xb9<8@ S*5 UJM57@ S!9 MSTK¿5S@ >A@/zB M5S@ 79!MS\K:79
5S9<Kg6TI5 5*Sy1%·nz9J@oË j9<@ÈaK¿@KJÉ /
b4Ê#I7>~S9H>F>SW8 R19 l ò SZ5
l ¼ B,!9 Y/9<@CFB K¿@ZI RY/57D@ MJ5 XZYz57T6 K[S\K:57@%>A@/B l ¼ Kl6 M5 XZX5S@C8:;
>SB5YFSg9<B21_@wSTI95STI9<K¹I/>A@CBvÂ>m8l>AKgIS9CY/5s6 S\R8¿*> S9yB B,9<ISKg9J9b*5 U
579JKrL6 I5 5 Sn/9<;S57@CzB S\I99<B,I795 U7STIC9 MJ5S@ S,9 MSTK¿S9 M57K9FB R\K K:@CI
STIC9Xj>*K¿@F\69!Q8R9<@M9YIC>S69MJ>S@jK9yF
B RMJ9 l T6 K:I7@ KW>MJ>S4@ Sg8:;71 k 5SK#a9 h*> XZY8¿9 >S6gL6 RXZK¿@I XZK[hFK¿@ÁI n ; IC>AW8 U2*5 U1> YKg9<6gL6 RKg9\6 MJ>A8¿9 I!9 K:4I I4S
nz9J;S57@CBwSTI9Uf5SK\Xj>A89yB,IS9b5*UgSTI¡
9 MJ5S@ S,9 MST K¿S9 M57K49 P K9y66g>A@va9 SX>A8no1 É /
4
b4ÊC@C<B STI/> S!tUf5SK V ò 1 ]»>A@/B ò 1 ] tl K¿«@ STI9
Kr>A@I791iS5¡mZl ¼ J1 l Kl6>A8l65 RC@ M9<LK Sr*> K¿t@ FnRFSI79J@9<Kg>S8:8¿Z; STI45 RI I8SS5 nz9 // S5 / ]l ¼ K¿V@ S\I57619 X5 B9J8l`6 STIC*> SB,5@*5 S!9 XYC8:5;
XR>MI 5S9<Kg6TI5 *
5 SCXKWhFK:@CIC1?45 5768:9<
; Ë 4
9y>~S9<DK É /
8iÊUf5 R@C
B STIC*> S»> / ]±l ¼ É@b1 ]wl ¼ I9Je8 KWRX M57K#9 ÊÁK¿IS@ KWS9yB?@9<5S³
@ Éu>A@/B
5#h,; IS9J@j>S@CB»T6 K:e8 KeMJ5S>@ ÊJnRKg@ K¿@CI MJ9J8@ SKr>A8¿8:;71 IC9JKg9>AKg9>A8l6Á5 K:@/FB KeM<> S\K:57@CJ6 S\IC> S`nC>AKg9 I9<W8 KeRXïM57K9y6
B,5@*5 S+9 hFYz9J\K K:9<@ M9 S\I9HISKg5 OSTI
K¿w
@ M57@s7!9 MSTK¿SÁ9 M57K9 X>766>A@CBv@5SF@ ®X5S@5 S57@ KeM1nza9 I/>~8 K¿5S=K K:±@ C@C>A)8 MJ>STK nz5S@v> nR@CB>S@ M9b69<9Jz@ n D; STI!9 K:K U¦R8¿8'L6 Sg>S=K MJ5 R8@ S9<TK Y/>ATK Sg6<1
OIK¿8:9>S@ /4/ l ¼ Xb5,B,9<J
8 É@]1
Zl ¼ IC9Je8 KWRXÌM57K#9 ÊJK¿IS@ KWS9yBm5 wM9<4@ Sg9JKy1D T6 KeXK¿8l>AK I9<W8 KeRXMJ5SKg=9 Xj>S6g16 É-bC1 bZl ¼ Ê7Uf5SK l O_>S6_>A8l65
Uf
5 RC@CDB nsV; c5 X5 S5 Ë*G>ST6 IKWX5 Sz5 É /
ÊM1
/ p
9 SO9<9JZ@ l >A@/B l 6 Sg9J8¿8¿>SK.9<S57W8 RFS\K:57@bB RTK K¿@I MJ>STK nz5S@>A@/B@C9J5S@ nRKg@ K¿@1I K¿76 Q4RK[Sg9 M5 XZYe8 KNMJ> Sg9<vB OK[S\ICS\I9Kg9<6TK¿BFR/>A8,9½9!MSg6
P a
5*UzB,9JI79J@9<Kg>4M;1 Y8l>~;8K¿@IH >Xj>Æ57K'K578:9+>A@CBF5*.®MJ9J@8S9<K)K¿IS@K[S\K:57@nz9aK¿@I¹STI9+KTRC8:9+Kg>*STI9<K)STIC>S@ÁSTIC9+9ahM9aYSTK¿5S@1 I9MJ>AK\nz5S@F\5#h,;sI79J@
M57K4
9 >A@CB%8l> S9<K STI9#5 h,; IS9<F@ \@9J57V@ M57K49 FK¿6T6 RKgK45 R@CB,9yB n ;m>jL6 S9<a9 YÇB,9J@/L6 KWS;mI7Kg>7FB K:9<8@ S`OI9<K!9 K:@Çe8 K:9y6> STI9<KTXj>S8:8¿;¡YR8l6TK:@IZS\IK¿@
I9<W8 KeRX L6 IC9J8¿8Q1 I9<69F>AKgÁ
9 IK¿I IwX>766!9 Q8RK¿>A8¿9J8@ Sg6 S5%>76; XZYFSg*5 STKNM4I K¿>S4@ S=nKg>S@ MIvL6 Sg>AKr6>S@CvB ½>S6L6 RMI%>Xj>~;on/99J@CB5O9yBoOK[S\I
¤T6 RYz9J\K OK:@/BT6 ¥»*
5 U7RYwS5 /! 9 l ¼ ; 9t~11 ·®U65 .STI9<w@ K¿w@ X57L6 SMJ>S69<6 STIC9 C@C>S8'9JS57W8 RSTK¿5S@C>SK;6 Sr> S9 OK¿8:8.@*5 S1nz9b>%L6 RYz9JKg@5>
nRFSX>S@
#
5 h,; IS9<F@ n@C9J5Sz@ OIK[Sg9»FB O+>SLK U1 ·(@>S@s±; M<>S69 vnz!9 M<*> RC69*5 UJS\I9»6 Sg9J!9 Y
B,9<@CL6 KWS;vI7Kg>7FB K:9<8@ S!T6 RMI
L6 Sg>SKg¹6 OK¿8:8@5 SÁM5S8@ SgTK KenRFSg9
> YYK,9 MKl*> n8¿Z; SZ5 S\I9 ²>A8l> MSTKNMH8@ R>M8¿9J576; 8@ STI9yL6 Kl6+*5 U*> nR@/B>A8@ S@ RM8¿a9 K2e8 KW79#5 h,;sI79Jt@ ,T6 K:e8 KNM5S%@ >A@CVB K:Kg5S@p1
*
; É /
8pf8ÊM1
I9j9 hFKl6 Sg9J@ MJ9b5 U7S\IK¿Á6 K:8@ S9<K9y6 S\K:@CVI nKr>A>@ MI
5 U+L6 S9J8¿8l>AK9J75Se8 RFSTK¿5S«@ O_>S¹6 Y/45 K:8@ Sg9<B5 RFSn ; P >A\K > S,%ja9 Kl6ga6 %Ëj*> >~
lzK¿;7*
> ÆK9 S²>A8n11 É /
Ê_>S@CBÇ45s5s68¿9J4; C49<>~79J,K Ë >7*> X É /
ÊJ/KgL6 SL6 STRCFB K¿9<zB STI98¿*> S9X9<S5Se8 RFS\K:57@5 U /! l ¼ L6 Sg>AKr6>S@CDB Uf5 R@/B
69Ja9 XZK¿@IS8¿;FB K¿\6 MKga9 Y/>A8@ S
Kg9<T6 R[8 Sr6JJ1 _@ S\I957@9 IC>S@CB lzK¿;7*> ÆKC9 S_>A8nW1 OI5FB K¿B»@*5 SgUf5S8¿8:5 O£I ;,B,K57IS9<t@ I9<W8 KeRXo 5S`K MJ>A\K nz5SZ@ nRKg@ K¿@I
nRFS_
> M!MKg9 S9yBb@9J57@»>A@CBj#5 h,; IS9<@578@ S5FÁ> MJ5SKg9*5 USTIC96g*> X9 M45 XZY/5sL6 KWSTK¿5St@ Uf5 R@/ZB STIC*> S
@9<5S@ K¿IS@ KWS9yBj5 OK:@C1I S5X9<8:,9 MSKg5S¡@ M<*> YFS\RKg9
> S+*> nz5 RFS] ú i ÍV/! í I MaX 9$ 1'D B9JIS9<@9JKr> Sg9TK RC@C#> O+>~;F9J@CT6 R9<¡B K:¡@ OIKeMIZS\I98¿576g6*5 UtYCK9y6T6 RKg9 S5X9<8:,9 MSKg5S¡@ M<*> YFS\RKg9 Xb57K9 STIC>S@
M4
5 XZY/9<@C6*> S9ywB Uf571K STI9j\K KlL6 K¿@DI S!9 XYz9JKr> S\RKg9»>A@CwB STIV9 M5SKgZ9 M5S8¿8l*> YC69<wB S5v>@!9 RFSKg5S@ L6 Sg>AKy1j45s5s68¿9J; 9 SF>A8ne1 %OIo5 Uf578:8¿5 O9yB >S@
9J8@ S\K:Kg9 /! l ¼ 6 Sr>A,K >nRS=RC69<±B MJ57>SKg69 ÈJ57@ K:@C¡I K:±@ STIC9 I9Je8 KWRXÌnRK@ K:@I%L6 I9<8:¯8 .Uf5 R@/oB STIC*> S@9<5Sz@ K¿IS@ KWS9yB *5 ÄM9<8@ S9J=K K:@
>»69<TK K¿9<6
5*UL6 SKg5S@CI Ö/>ST6 I9y`6 STIC*> SYKg5 YC>SI7> Sg9<¡B S5 STIC9 M9J8@ Sg9JK*5 U)STIC9X6 Sr>AK STRCK@ K¿@ZI KWSK:8@ Sg5T6 K¿W8 KNM57@Ç>S@CB%*5 STIC9JK#5 h,; IS9<@ nRKg@ K¿@ZI YKg5 B RMSr6J1
^5S8
@ S\K:@ R9yB 9J75Se8 RFSTK¿5Sz@ S\I\K R L6 K¿e8 KeMJ5S±@ nRCK@ K¿@DI YKg5 B RM9yBv>A±@ K¿Kg5Sw@ MJ5SKgÁ9 K:w@ STI9 RCT6 RC>A)8 O_>~V; OIKNMI<MJ5S8¿8¿> YC69<B2=1 ·(4@ Sg9JKg9<L6 STK¿@IS8¿D; STI9
L6 SKg5S@Ib@9J57
@ Öz>ST6 I9<`6 K¿@ S\IK¿6 ɦYz5s57K8¿; ÈJ57@9<>B Ê7X5,B,9<t8 O9<K9²T6 RFî¡MK¿9J8@ SS59 Æ,9 MSSTIC¹9 I ;,B,Kg5SI79J@m9<@ S9J8¿5 Yz9²*> nz5 RFS /! ;S9y>AKr76 nz9 Uf57K9
STIC
9 C@/>A8'9 hFY8¿57T6 K:57z@ OK[S\I<K¿8@ S9<K9y6 S\K:@DI M57@C6,9 Q8R9J@ MJ9<6 Uf5S=K STI9bW8 K¿I I8SMRKgS97¹1 lv5 B9JKg<@ MJ>Se8 MaR8l> STK¿5S@/6@5 OrM<>A8¿)8 K¿8@ SD5 Q4RC9<L6 STK¿5S@ >S8:8
STIC9<6Á
9 M5S>@ Me8 RCL6 K¿5S@/6J1
c
5 X5 S£
5 É /
f> /
p*Ê#G*> nz9 Sro6 É /
m8ÊJlzK¿;7*> ÆKË c5 X5 S£
5 É /
pÊ#>A@/Å
B c45 X*5 S
5 Ë G>ST6 IKWX5 SA
5 É /
ÊÁUf5S8¿8¿5 O9y
B STI9
9J75Se8 RFSTK¿5S@ *5 UJI9<W8 KeRX M57K9y6 K¿z@ STICC9 Xj>S6g6Kg>S@ISC9 ]1 SD5 fC1 l ¼ STICK45 RI I±IC9Je8 KWRX >S@CwB M<>A\K n/57z@ nRKg@ K:@CI 2>S6gL6 RXK¿@I S\IC> S¹STIC9J;
O+
5 R8l
B XZKWXZKNM¡S\I9m9<S5Se8 RFS\K:57@ *5 UU¦R8¿86 Sr>AKr6*5 UUf45 RK S\KWX9yÁ6 S\IC> SX>76!6 >A@C
B R@ M579JKg9<B 65 X9 K¿8@ S9JKg9<L6 STK¿@I 6;,6 Sga9 Xj> S\KeM<6J1 k 5SK
I9<W8 KeRX
MJ5SKg9<Á
6 K¿A
@ STI9Kg>S@ISo9 ],1 ]oSg
5 ]1 iwl ¼ ɦXj> K:@Ï6,9 Q4RC9J@ MJ9L6 Sg>SKg6*5 U> n/45 RFS
z /! l ¼ Ê#@C9J5S@ @9J79JK nRKg@9<B 6 Sr*> n8¿Ä
; K¿@
I ;,B,K5s6 Sr
> S\KeM_,9 Q4RK:e8 KWnCTK KeRXÇ1 I=9 MJ5SKg9ISKga9 O S5 S\I19 ^gI/>A@CB,Kr>S6a9 IC>SK Xj>S6g6
>A@/B@9J57@ K:I7@ K[Sg9<B n ;b9J8¿!9 MSKg5S¡@ MJ> YFSTRCK9*> S~±yi ÍV/!
I MX!9$A1 I99J@CT6 RK¿@IXB,a9 Ö/>AI7Kg*> STK¿5SÁ@ Sg5@ RM8¿9<>SK#6 Sr> STKlL6 STKNMJ>A8C!9 Q8RK¿W8 Ken\K KWRX O+>76> M!M5 XZYC>S@ K¿9<CB ns;bL6 R>MIMJ5 YK¿5 RC6'9<8:,9 MSgK57Z@ M<*> YFS\RKg9
Á
STI/
> S`STI19 M57K¹9 M5S8¿8l*> YC69<B Sg5b>F@a9 RFSgK57@%L6 Sg>S=K É P \K R9J@C@ /
p*]4ÊM1 P 45 R@ MJ9>A@/B»L6 IC5 MZYKg5 Y/>AI7*> STK¿5S@ O+9JKg9L6 STRCFB K¿9<VB n ;jG K¿8:8¿a9 nKr>A@/B S!
c4
5 X*5 S>5 FË 45SW8 ÅÉ /
fÊ P RKKg5 O76 Ë *> SLSTKeX9JK É /
iÊ ,>S@CB lv>~; 8¿¹9 Ë
4 K:8l657«@ É /
ÊOI5 ,> USg9JK65 X¹9 K:@ KWSTKl>At8 MJ5SF@ U¦R/L6 K¿5St@
B,a9 S9J\K XZK:@C9<VB STIC*> SSTIC9 YK9y69<@ M95 U)RC8@ nRK@C9<B@ RM8¿9<>SK U¦R9J'8 K:D@ STIC9 M578:8l*> YCT6 K¿@I MJ5SKg9 MJ*> R/69yB%57@8¿;%> XZK:@57K Yz9JTK STR\K nC> S\K:57@1 I9
9 hFY8¿57T6 K¿5SD@ Xb,9 MIC>A@ K¿T6 XâO_>S6+9<6g69<8@ STKl>A8¿8:; S\I9X6g*> X9>S6 K¿o@ MJ5S8¿8¿> YCT6 K:@I K¿K57D@ MJ5SKg9<6+*5 U)STI9X6g*> X19 Xj>S6gg6
@a9 RS\K K:@Z5 Yz5 O9<K9yB21
G5 O+9JS9<K c45 X*5 S<5 É /
fÊ_5 nC69JKgS9yVB STIC*> S¹IKl16 ],1 m¡l ¼ I9Je8 KeRX M57KÁ9 K¿IS@ K[Sg9<B @9<5Sz@ K¿@
>»69J\K K¿9<65 U
6 SgK57@I»5 >M9<4@ Sg9JK Ö/>ST6 I9<6
STI/
> SFB KlBm@5 S8:9y>S¡B KeXZX9<FB Kl> Sg9J8¿; S5 M57K19 M578:8l*> Y/649 8Kn1 9Se1 STI96g*> X=9 nza9 I/>~8 K¿5SK+5 n/69<K79<¡B n ;j45 5768:9<; 4
9y>~S9<!K FË >S> X É /
Ê
K¿¡
@ STICa9 K¿K /, l ¼ É@]1 pl ¼ I9Je8 KeRXâM57K#9 Ê6 Sr>AKy1 > Sg9JK c5 X5 S5 ËEG>ST6 IKWX5 SV5 É /
ÊK9<8 Kl69<B STICa9 K¿K9y6 S\KWXj> Sg9 Uf57K
@9<5S¡@ K¿IS@ K[S\K:57@
K¿@
>mL6 Sg
> n8¿9L6 Sg>A¹K RYO_>AKrB6 UfKg5 X ],1 mZSgo5 ]1 l ¼ 1 ^8¿9<>SK8¿D; STIKl6 Kl6²>»Kr>A@I79X*5 UJXj>7669<=6 OI9JKgÁ9 S\IÁ9 /@C>A8'9J75Se8 RFSTK¿5Sz@ Kl6²69<@CT6 K[S\K:79
SV
5 X5 B9JKr> SC9 MIC>A@I79<6 K¿z@ S\I9bB9JIS9<@9JKr> MJ;S1 c5 X*5 Sgw5 É /
fÊ_>A8l65%B,9 Sg9J\K XK¿@9yoB STIC*> SS\IC9 MJTK KWSTKNMJ>S'8 Xj>S6g6 Uf57K@9<5S±@ K¿IS@ K[S\K:57@ W8 K¿9<6
> nz5S9 / 1 b8pl ¼ É-M45 XZYC>AKg¹9 S5 / 1 mZl ¼ Uf5SK MJ>STK nz5SV@ K:I7@ KWSTK¿5S>@ Ê1
*
D8¿8 STI9 MJ>Se8 MaR8¿*> STK¿5S@C)6 n ; c45 Xb5 S5H9 S#>A8n1Â>S@CBX45 5768:9<;9 S>A8n'1 K¿Á@ S\IKl6 X>766ÂKr>A@I79
@9<IS8¿!9 MSg9<B X>766.8¿576g6Â>S@CÁB R/69yÁB ÈJ57@ K¿@I S\IC> S
O_>Sg
6 K:@C>7B,!9 Q8RC*> S=9 SC5 Uf5S8¿8:5 OsSTI¹9 STIK:D@ I9Je8 KeRX T6 I9J8¿.8 Ö/>ST6 I9<6_T6 RKgK45 R@CFB K¿@ÁI S\I9²B,9JI79J@9<Kg*> S19 M5SKg9 S\IC> SB,9<S9J8¿5 Y/76 Uf57K I9Je8 KWRXM57K9y6
5 U8:9y6=6 STI/>A@ *> nz5 RFSÁ],1 il ¼ ɦSTI45 RI I69<9 k K¿IC1 / *5 Uc45 Xb5 S5 /
p*ÊÁ1 l 5SKg9Kg!9 MJ9J8@ S8¿z; MJ>Se8 MaR8¿*> STK¿5S@C¹6 n w; ²>AK MKl> P 9JKgK¡5 Ëâ·n/9<@
*
É /
f8Ê tjK[Sg576g6
> v²>S\K MaK¿*> P 9<KKg5 .Ëï·n/9<@ É /
4
m4Ê %²>AK MKl> P 9JKgK>5 >jKWS5s66g> vËï·nz9J£
@ É /
8pÊ v·nz9Jt@ tjK[Sg576g6> t˲>AK MKl> P 9JKgK5
É /
p*Ê +>A@CA
B jKWS576g6g> 7²>AK MKl> P 9JKgK>5 )Ë ·nz9JÍ
@ É /
4
4Ê1IC>~79%>7BB,Kg9<6g69y
B STI9y69ÇB,a9 >MK¿9J@ MaK:9y6 K:@Ï>
L6 STRCB; *5 US\IV9 Yz57L6 SL®I9<W8 KeRX
nRKg
@ K¿@IÇ9J75Se8 RFSTK¿5S@*5 UXj*> K¿@6!9 Q8R9<@ M9jL6 Sg>AKr6²*5 U
1 /! 1 /, 1 iFp>S@CB // 1 l ¼ 1»D8¿8 STIC9<69»6 Sr>AKr6²9 hM!9 YFS1STI9 /4/ l ¼ X5,B,9J8
K¿IS
@ KWS9yB MJ>STK nz5S@m*5 .®MJ9J8@ S9<K+>S@CB»> M5S@ 7!9 MS\K:79J8¿C; nz5 RC@CB,9<VB MJ>STK nz5S@ U¦R/L6 K¿5S@ Ö/*> X19 M5S@ 79J;S9yZB nRKg@ K¿@ÁI Sg5 S\I¹9 MJ9J8@ S9<K5 Up9<4> MIwÉu69J9
>A8l65 KeXZXb9ya6 ,45 5768:9<; FË >S> X /
4
*f8Ê1.3> MImL6 Sg>SK_9J@CB,9yB KWSg6_e8 KWUf9²>76_> S\I9J\K Xj>A8¿8:; YR8¿T6 K¿@IjD P 6 Sr>A`K OK[S\I w> ¤gL6 RYz9J\K OK¿@CB ¥1
I9
C1 /! 1 S>A@CB /, 1 i=l ¼ X5,B,9J8l69 Æ,9 MSg9<B STICa9 K¿JK I ; BK57IS9J@9J@ S9<8:45 YC6>A@/B9<@CB,9yCB RY»>S6'#5 h,; IS9J@ n@9<5SC@ OIK[Sg9FB O_>ATK Uu6'*5 U / 1 / m
9 MS\K:79J8¿;S1G5 O+9J79JK S\I9 /4/ 1 l ¼ X5 B9J)8 IC>SB >S@v#5 h,;sI79J@Ç@9<5S±@ M57K95 U / 1 bm l ¼ >A@CoB YKg9<T6 RXj*> nC8:;
/ 1 ]i/>S@CB / 1 b / l ¼ Kg9<T6 Y/,
OK¿8:
8 /@ K¿T6 I«K[Sr6W8 KWUf9 )M578:8l*> YCT6 K¿@I>76²>A@9J8¿!9 MSgK57«
@ M<*> YFS\RKg9T6 RYz9JKg@5>%>76B,9<\6 M\K Ken/9ywB n w; lzK¿;7*> ÆK'9 SF>A8nZ1 n/a9 Uf5SKg98:5sL6 K¿@DI K[Sr69J8@ STK¿Kg9
9J@ 79J8¿5 Yz9S1 ·®S69<a9 Xj`6 STIC5 R4I IS\IC> S,K:@ÇKg9<>SW8 Kl6 S\KeM¹X5,B,9J8l!6 FSTI9 Xj>766+Kr>A@I7=9 Uf57K9J8¿!9 MSKg5SF@ MJ> YFSTRKg9²L6 RYz9JKg@5>A¹9 Kl6 Q4RK[Sg9@C>AKgK5 O1
I9JKg9F>AKg9X65 XÁ9 K¿@CFB KNMJ> S\K:57@C6 S\IC> S=STIZ9 ^Kg> nvL6 RYz9JKg@5Z> IC>7B > YKg5SIS9<@ KWS5SK6 Sr>AK K¿z@ STIC9 // l ¼ Kr>A@I7¡9 É-c45 X*5 S5m9 S>S8Q1
/
fÊM1
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@ MKg9<>7L6 K¿@Ij> S>SK45 R@CoB b l ¼ É k K¿IC1 / fÊM1 IÁ9 nK¿@CFB K¿@I»9<@9JKgIS;%*5 U#>A8¿%8 Xj> STS9<K5 RFSrL6 KlB,9 S\IÁ9 K¿K57z@ M5SKg9X>A8l6¡5 M9<>769y6 S5 K¿@ MJK9y>S69
>A@/B 9J79J@vB,,9 MKg9<>S69<6>je8 K[STS8¿9S1 IK¿6HT6 RISI79<L6 Sg6 S\IC> S=STIC9 C@C>S'8 YCK5,FB RMSg6*5 U#9 hSgK!9 Xb9<8:o; Xj>S6gT6 K:79F6578¿>SK X9 Sr>A8¿W8 KNMKWS; 6 Sr>AKr6 É-b S5
| /!4 l ¼ ÊXj>~
; nz9F@5 X57K9XFB KWî¡MRW8 SSg5»9 hFY8¿5,B,9 S\IC>Ao@ S\Ia9 K¿K8¿5 O9<K Xj>S6g6 M45 R8@ S9<TK YC>SLK Sr6J14
C9 n/9<W8 K¿9J79 STI/> ST6 RMI 6 Sr>AKr6 IC>~79
STICa
9 K¿K M45 R8@ S9J\K YC>SLK Sr76 K¿@Ç@C> S\RK9>76 ; Yz9 ·n ·M²T6 RY/9<K@C5~>S9H>S@C
B ɦKWU÷7 rs*8:9®¹ fZl ¼ Ê_T6 Rne8 RXZK¿@5 RC6 ; Yz¹9 ·n T6 RYz9JKg@5>A9S1
H#Kg9<T6 RY/9<K@C5~>m6 Sr>AKr6
5 U
8:5 O+9J¹K X9 Sr>A8¿W8 KNMKWSz; IC>~S9bL6 K¿IS@ K[>M<>A8@ S8¿; FB KWz9<K9<4@ SMIC>SKg4> MS9<TK KlL6 STKNMJ!6 z*> SH8¿9<>76 S> S1IK¿I IwXj>766<1 P !9 MJ> RC69
5 US\I9 Xba9 Sg>S8:e8 KeMaK[S; B,!9 Y/9<@CB,9<@ M9*5 UJXj>S6g68¿576g6 ÉZ=·T· k ÊSTIC9 X>766*5 US\I9Fe8 K¿I I8S9y6 S²L6 K¿@IS8¿9L6 Sg>SK Sg5m8¿576Á9 K[Sr¹6 Is;,B,Kg5SI79J@Ç9J@ 79J8¿5 Yz9
*
K¿
@ MKg9<>769y%6 OKWSTIjB,,9 Me8 K:@ K¿@¹I X9 Sg>S8:e8 KNMKWS;F>A@CtB S>A8¿5S@=I OK[S\IZK[S,STI9 Xj>S6g6.*5 U.K[Sr6 I9Je8 KWRX M57K9_> SB,9<*> STI)1 ·(C@ Uu> MS,Uf5SK È<9JKg5 X9 Sr>A8¿W8 KNMKWS;
L6 Sg>AKr!
6 STI9 I9Je8 KWRXÙMJ5SKg9 K:@ MJK9y>S69<6 OKWSTI45 RFSJnz5 R@CZB K¿@j@9y>AJK YKg5 Yz5STK STK¿5SC@ S15 S\I9 Xj*> K¿@»6!9 Q8R9J>@ M9 Xj>S6g6 É k K¿IC81 ] Ê1 ^57@C6,9 Q8R9J8@ S8¿;
STIC¹
9 K¿Kg5SV@ MJ5SKg9<6_>A@/B»#5 h,; IS9J@L6 IC9J8¿v8 X>7669<6+>A8l6C5 K¿@ MKg9<>76Z9 É k K¿IC1 / iÊ>A8¿5S@CI OK[S\IVS\I19 nK¿@CFB K¿@I9J@9<KI7±; É k K:I/1 / m8ÊM1Í
D M5 XZYC>STK Kl65S@
> S1i l ¼ Kl69yFB RMJ*> STK¿5S@C>S8Q1 k 5SK>m6578¿>SK X9 Sg>S8:e8 KNMKWS;L6 Sg>S!K STI9 C@C>A'8 I9Je8 KeRX M5SKg9 Xj>S6g6 Kl6 K¿z@ STIC9FKr>A@I7Á9 b1 mp 1 iUf57K>jKr>A@I79
5 UJXj>7668:5s66Kg*> S9<6!9 Q8RC>S%8 Sg5m5S@C9 S5 STIKg9J9 STKeXb9y6,9 QzC1 É / iÊ1 I9 M5SKgKg9<T6 Y/57@CFB K¿@I K:Kg5S±@ MJ5SKgÁ9 Xj>S6g69y6>SK9 / 1 fi / 1 i / l ¼ >A@/B
*
STIC=
9 nK¿@CFB K¿@I9J@9<KI7;45 RFSgT6 K¿B9 S\I9 K¿K57@ M57K49 1 i / 1 p
Í/, ×+9JKgIC1 IKl`6 MJ5SKg9T6 I5 R8lB nz9@C5 X5SKg9FB KWî¡MRW8 SgSgC5 nC8:5 O£RYSTIC>S@
T6 KWXZK¿8¿>S
K M5SKg9<g6 S\IC> SB,9<S9<8:45 YUfKg5 XïS\I9 / iSg5 ]4il ¼ Xj*> K¿@Ç6,9 Q4RC9J@ MJ9²L6 Sg>SKg`6 S\I5 RCI I8SK9yL6 Yz5S@CT6 Ken8:¹9 Uf57K M5 XZX5S@ÇT6 RY/9<K@C5~>S9S1
\T
6 K:@ÁI STI96g*> X9 YI ;,T6 KeM<a6 4nRFSgOKWSTIXj>7668¿576g6#Kg9<B RM9yCB n ; Ç=i\*4STI9L6 RYz9JKg@51> YKg5SI79J@ KWS57JK M5 XZK¿@1I UfKg5 X C> i l ¼ 6 Sr>AK#5 U
K X9 Sr>A8¿W8 KNMKWSZ; K¿6+S9<K;FB KWz9<K9<8@ S<1 k 57K57@9 S\IK¿@CI KWS6 S\K:8¿8 IC>S6+Á> I ;,B,Kg5SIS9<@j9J@ S9<8:45 Y/9 ɦYKg9<T6 RYz9JKg@5> Xj>S6g76 Klg6 f4
1 l ¼ Ê
/! 9 6578¿>S7
>A@/ZB STI¹9 K¿K57t@ sT6 K¿W8 KNM57t@ ,>A@CB IC9Je8 KWRXâMJ5SKg9 Xj>S6g69y6>SK¹9 ],1 8fC1 ]F >A@CDB ] 1 ]l ¼ Kg9<T6 Y/,9 MS\K:79J8¿;>S@CZB S\I=9 nK:@CB K:@Ib9J@C9JKgIS;b5 RFSrL6 KlB,95 U
STIC=
9 K¿K57@ M57K9 K¿6 ] ú ÍD/! ×_9<KI/'1 ·®SKl6+B K[î¡MRC[8 S`SC5 n/9<W8 K¿9J79 STI/> S`STIKl6_6 Sr>A`K OK:8¿8z>~75 KlZB n/,9 M45 XK¿@IbÁ> n8l> MZI578:97J1 _@C=9 M57@ Me8 RCT6 K:57@
STIC9JÄ
@ Kl16 STIC*> SÁn8l> MwIC5S8¿Z9 Uf5S\K X*> STK¿5S«
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@ STI9j9y>AKg8:;
R
@ K¿S9<Kg6=9 STIC>S@%@5 O1#0 9<9>A8l6P5 Z~[· P $Z[=·L·>S@C8B Z~[=· DF1 I"9 Ç(B,!9 Y/9<@CB,9J>@ M9²*5 U)X>766+8¿576g`6 K¿6 MJ8:9y>AKg8:;»C> Xj> Æ5SK R>@ M9JTK Sg> K:8@ S;
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> J5S8¿8¿> C69 C>~S9> 9<@ gKg>S8 _5 1
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1 %>S6>A@ >~S9<Kg>SIS9 z57@9 :I 9 z9 F> C>A@CBKg>769 />AK >766²5 1 ¼ 1
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5 5s68¿9J; *49<>~79JK
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1 >S@CB 1 ¼ f57KB
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D S`STI9=STKeX9S\I9=K¿Kg5S@MJ5SKg9K:@> / iÁl ¼ 6LSg>SK`MJ5S8¿8¿>YC69y6aSTI9H9J8¿9!MSKg5S@KNM9<@8SKg5Y ;S;YKNMJ>S8:8¿;Kg>S@IS9y6UfKg5X 1 fÁK¿@¡S\I91M9J@8Sg9JKgS5 /
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Xj>S6g6T¥b5U / 1 bfZl ¼ >OIKNMIDKl6K¿@oUu>MSM8¿57691S5¡MJ>S8eMaR8l>S9yB~>S8WRC9<6ÁÉ KWXZX9<6!C45 5768:9<;Ë 4
9y>~S9JK /
4m4ÊM1 k 5SK>¡]4il ¼ 6LSg>SK!
STICC
9 YKg9<T6 RYz9JKg@5¡> M57K99J8@ SKg5 Y ;ÇKr>A@I79<6 UfKg5 X 1 iS5 / 1 2L6 RCISIS9y6 S\K:@CIm>o^gI/>A@CB,Kr>S69aIC>SKXj>S6g65U / 1 p
Vl ¼ 1Ál 5SKg9ÁXj>S6g6TK:79
L6 Sg>AKrC
6 IC>~S¡9 X57K9%9J8@ SKg5 Y ; >A@CvB
5SÄ
@ S\I9>~79JKr>AI79 )YK5,FB R>M9m8l>AKgIS9<K K¿K57@ÅM57K9y6F>S@CBYz576g6LKen8¿;Xb57K9VXj>S6g6LK¿S9»@C9aRFSgK57@ 6Sr>AKr6J1
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B É k K¿IC1 / fÊn D; STI98:5s66H>A@/B K9yFB Kl6 SgTK KenRFS\K:57@v*5 U#9<4@ SgK45 Y V; S\IC> SHF5 MaMRCKg6HFB R\K K:@CI
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> S19 nRKg@ K¿@I»6 Sr>AI79<6<1
I=9 YCK9y69<@ M9H5SK+8¿4> Mj*5 Upa9 h,5s9<K4I KeM8MJ5S@ S,9 MS\K:7=9 MJ>STK nz5S@ nRKg@ K:@CIb*> SgS\I9 M9J8@ Sg9JK_*5 UtS\I96 Sr>AK_>A@C¡B STI9²@ RXCn/9<K_>S@C¡B K¿8@ S9<@CL6 KWS;
5 UÁM<>A\K n/ 57@ MJ5S@ S,9 MSTK¿S9 T6 I9J8¿8l¡6 IC>~79Ç>S£
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B ] l ¼ ÉUf57¡K S\Iw9 MRCKKg9J8@ S¡MI5 KNM9 5 U
L,^¹É-Ò ÕtÊTLØ_1ÊM1 P 9J8¿
5 O³] l ¼ M<>A\K n/57V@ nRCK@C6 MJ5S@ S,9 MS\K:79J8¿;»> SSTIC9 XKlBB,8¿9X5 U%STIC9F6 Sr>AÁK É k K¿IC>1
4Ê > n/5719 K[SnRCK@C6Kg>7FB K¿*> STK¿S9<8:;71
·(<
@ Uu> MS1Uf57K²L6 Sg>SKg¹6 I9y>~ K:9<=K S\IC>AÄ
@ ] l ¼ @!9 K[S\I9JÁK M<>A\K n/57@ @57K²@9J57w@ nRKg@ K¿@IÇ9J79JK> MIK¿9J79<69J@9<KI7; IS9<@9JKr> S\K:57±@ K:@9 hMJ9<6g65 U
@!9 RFS\K K:@C5 8:5s669<6²> SS\I9 XZK¿BCB,8:9j5 UgS\I9»L6 Sg>AKyV1 ^+>A\K nz5S@ 6 S\K:8¿J8 nRKg@CÁ6 MJ5S@ S,9 MS\K:79J8¿z; K:@ 9 h,5 9JKgI KNMbL6 I9<8:8l¡6 É@MU1 S\I9 ]iDl ¼ 6 Sr>AK K¿@
1
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k K:I/'
nRKg
@ K¿@IX!9 YK¿65,B,9<76 K:@»> /
l ¼ L6 Sg>AJK SC5 ]1K¿@mÁ> ] / l ¼ 6 Sr>AKy1 d R\K K:@ÁI STI9y69 MJ5S@ S,9 MS\K:79L6 I9<8:>8 nRKg@ K¿@ÁI YIC>769ya6 STI¹9 M9<4@ Sg9JK*5 USTI9
L6 Sg>AKT6 I9<BC6_9J8
@ SKg5 Y ; n ;»@!9 RFS\K K:@C5b!9 XZK¿6gL6 K¿5S@p1 IK¿64> MaM45 R8@ Sgg6 Uf5S`K S\I9X*> n\K RYFSMIC>S@IS¹9 K¿D@ MJ9J8@ SKr>A8½9J8@ SgK45 Ys; K¿V@ STI9 YKg9<T6 RYz9JKg@5>
X5,B,9J8lÁ
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3
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30
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final mass, remnant mass (solar masses, baryonic)
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very massive stars
massive stars
low mass stars
100
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log Temperature
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9
8
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Ar
Na
Li
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Cr
Zn
Co
Sc
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0
8
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32
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48
56
64
72
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5.0
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K
2.0
B
H
N
C
He
1.0
Si
Cl ArCa Ti
S
P
O
Al
Mg
F NeNa
Sc
Zn
Ni
Cu
V
Fe
Cr
Co
Mn
Li
0.5
0.2
0.1
0
8
16
24
32
40
48
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56
64
72
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R-2
15
V-1
B
20
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t0 8700
8800
8900
9000
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9100
9200
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Ca II
4000
6000
8000
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