Answers to some of the problems in the books

"!$# %
(& '*)+'*,.-(/+0213/546427
8:bd9<c ;=.\3=>;?eg;@9<HJf ;?\iAhjBDCFBDALE.E?kPG:=Il<m:HJnC5oALp"KMq6=>l<;Nr<AOsu9<tN;Pv"AQs`ENlHRowE?q6=>STn<x`=>y*CE?t?AUyWn:9WzPVX{OE?G:Y+=Z_:HJY:E@;?=w9W_F[:\Dj<=>SZ=>;NA.ALBD]^9WY:C5\DA=.H<9WALVX=TE?ALG:=.BiC`AP_a_|9|=>}SZ~:HJSTBD\*=.C<E@9 E
Kd ‡|BD\€x5JyW[+n<=3x`H"ƒWjR<HJŠ`BD\il|HJoW[:‘+\D=*y"`9Wƒ`C^z k6s|rrM‚@ƒƒJ„„„ut…q+†Xt?v"s`lo.q+n<x`y*tNyJnƒ<n†<‡5vWlWr+ˆJ‰JŠ5ƒvW‰J‡x+yJn`yJƒ‹Œ<Œ6"ƒlol|ŽWl|ƒ
’”“
•P–˜—*™›šœ
ž z Ÿ¢¡R£"¤˜¥¡.¦
ž z §¨¤+©¥ ž
ž z ªg¡R£R¦W¤I¥g«§`¬Q¡"ŸO­a¤+®
’”“
•P–˜—*™›š°¯
§|zD¡A@¡"=>®d=.eC^]^±
«HJ®U²<³›=W]5~:S´Ÿ<®u[5³›=.;~:S´9JVX[5\i=.HJ;OC`9J²WVµ~`HWS´²W±(=.AO}NG:E@G5BD\iHR_|EP;@=.¶C^A@] Y+ž =.®dHJ³›·6]¸~:§<S´®[5³›=.;O~:S´9WVµ[5}>=.9W;PC9JE@;?VMBD=.¹OAMBDj"E@G5HW\DHR_:EOBµ¶uSG`~`H"A@j<BD}=
ºM» E@G`HJE›¶X9RKdC
§|z §¨½Ï¶¼C(½¿¥Ä¾Z¦À9W;P¥ÁÀЦ´¥ÑBÂV*¦:HJC`z_öÒV›9WC:BDC\D±ZÓ¨BÂV2¾Ô½Ä½Ï¥g¥Õ¦ZÓ¨Å"Æu¾ÔÀÀµ¥gÖµ¦`Ó×]:¥ÄÅRÆu¦:SÇ]¸=wE@HJG`C`=>A›CØÈʽÉÌËÌÍ+ÈNHJÆ.C`Î5_ÙÅ"ÆuÀgBÌz }>=W9Wz*~:=.\iBÂ_ÙE?G:[5=>=;
½¿HWC±¥C:¡R9<£C:ÖLÚ>À=.;@¥9Z¬Û­[+¡"=.®Ê}.z HJ~`A@=›¦›¾P¦BiAܳÝÞß_|=>à`C:=._5®*B€CE?=>²W=.;µC~:S[+=>;w]5¬áVá9W;Ü= c HWSTY:\€=
§|z â¬ÌH<®F¡.¦Ÿ¥g§Ç¾a¡.âOãg¡wŸ
¬á[5®F­d« ž ¦:¡›¥­›ª<ä´¾
ª ž ãØ«<ª
¬Ì}.®(ª<§W¦Wä`¡wŸ¥ÐŸ|¡w¦Wª´¾ ž ¦Wä›ãg¡w§Jâ
§|z ä¬ÌH<®˜«<¦P¥ÐŸJåU¾§¥^æèç<¡<Ö?Ÿ:ÖL«`Ö?â:Ö.¡.¦:ÖNŸJ¦`ÖL«<¦:éê «W¦
¬á[5®(âW¦P¥ÐŸRë¾§¥^æèç<¡<Ö?Ÿ:ÖL«`Ö?â:Ö.¡.¦:Ö.¡.ª`Ö?ŸJ¦`ÖL«¦|Ö@â<¦éê âJ¦
§|zD¡wŸì¬ÌH<®
Ÿ å ¾ ž ¾§
¬á[5®
ŸJíU¾ ž
¬Ì}.®
ŸRë¾î£
¡
…¬ _`® ž ¾(« ž
§|zD¡>«ÐA@¬ BiUã_|=BDAu®L©«T¥ KdG:©BDX\ =Uã E@G:Ê=©UBi;?AdB€²<C:G9WEuEuG5jRHJHWC`\€Bi_
_ÛzA@BD_|=UBDSTBiAOY:\DŸ|±Iz E?HW·W= T¥ d¥ ¡W]|E?G:=>C(E@G`=P\€=>V E›G`HJC5_
­}>9W¡<;?]Û;@=wE@}ÊG`Ed›=>AQCÙBDENSTHRKXY:E?=Z=>\€BDST=.HWA =>;@C=ÇEO²WHÇ=>EL›KdE@BDBD;@C:Ad9<²5C:HWkZCòZ­O}BDCŸ9<j"C`HW}\€\DBi~`_˜­A@B€B€¡T9<STC^B€Y:STz \DBY:}.\DHRB =.E?AB€9<ŸC^z W~`¡WAL]^EuB E?z =WHWzD·W] = KMÇ¥=Tg_:=>Ÿ:;?ÖB€j<u=¥Vá;?¡<9WÖ S d¥ H
82¡BD¥gC`HJ¦:\D z ± u㠛¥¬ ›ã >® RzµÞ2HJ·W=<]WVá9<;X= c HJSTY:\D=W] Ç¥ u¥ ¡HWC`_ ›¥Á¦:]±W9W~òW=E
§|zD¡w§ì¬ÌH<®F­OŸ ¤ ¢ŸJ¦
¬á[5®(â ¤ ןJ¦
¬Ì}.®F­¡ ž ¤ ן<§
¬…_`®F¡ ¤ ž
’”“
•P–˜—*™›š
ª:zD¡ ¬ÌH<®(_|Þu~`G:}=IE@BDBDjWC`=Ô_|~5H<}ÊA@E@A@BD~:jWST=˜Y|AQE?E?B€=>9<Y^C5k(®¡.¥ ©›ãgŸW©O㠞 © ©dã Xã ã ¬áÀaÀ^©Ø­Á¥ ¡"®Q©O© ãßÀ^å ©Ã¥¬áE@G:=IBDC ¥
©
¬á[5®(ÞuHWA?G:A@=d~:STBDC`Y|_|E@~`BD9W}E@C5BD®ÜjW=›¥ ALE@¬ =.Y^k3¡wå5ã(®L©3ŸJãØå`ã À^åOž å`¥ ã © ãÔ¬…ÀU­(¡"ë ®Qå:ãÃ¥ÕÀ^åO¬ ¥¬áE@G:=›®Q©BDC`_|~5}ÊE@BDjW=
ª:z ŸØBD³OC`9J_|E?~5=W}Êk*E@BD=>jW;?=U;@9<AL;XE@=>BDCIY k E?G:=UY:;?ã 9W[:\D=>© S ã ALE?HRE?=>STã =>CEU+¡ ã :¬áÀ´ã ë ¡w®Xã A@G:9W~:\i_I[+=U¥ÕÀ ©¬|E?¬…G:À´=ã BDC`¡w_|®Ê~5zµ}ÊÞuE@BDG:jW==
¥
H<A@A@~:STY|E?B€9<C5®Ü¥ © © ã å å ë ¥
ª:z ž ¬ÌH<®(BDÞuC`G:_|=›~`}BDC`E@BD_|jW~5=d}ÊHWE@BDA?jWAL=~`SÇAQE?Y:=>E@Y^BDk9WC5ž ®À^©›¥ Ÿ:¬áž À¬L­Ã¬…ÀP¡"­î®"ã¡"®¡`ãaãZ¡"ªJ®QÀ©u­ ¥ ž ž ¥Á¬áÀPŸJ­îÀu¡"ã®Q©5¬ÌªJãÀªJ­ÀP«­ ® ž ŸJÀu¬áE@ãG:=¡
¬á[5®(«5Þu¬…G:ÀT=Ç­aB€C5¡"_|®Q~`©d}Ê¥¢E?B€j<À^=´©2ALãE@=.¬ Y^ž k›À^©2« ­¥âJÀ«IãÔ¾«®2« ¥¢À^© 㠬ហE@G:¬…ÀT=Ç­BDC`Ÿ<_|®Q~`©Û}ãÔE@BDjW«5=T¬áÀTHW­îA?AL~:ŸWST® Y|E?À^B€9<©C5¬á® Vá9W;
À ŸW®
ª:z « BiAu=E?E G`HRE _|=.C:¥9JE?=3E?G:=d© ALBDÚ>]:=MKd9JG:V:BiE?}NG:G(=uBÂY5E?=>9<;NY:HR~:E@\i=wHR_ÃE?B€ÀF9<CE@BD±WST=wHJ=.;2AdÀµ²<B€z2j<Þu=.A G`=XST¥9|_|Ô=>\DB© C:²HWA?AL©~:STz Y|E?B€9<C
ª:z § BiAu=E?E G`HRE _|=.C:¥9JE?=3E?G:=dALBDÚ>=M­ 9JV:E?G:=uY5© 9<Y:z ~:\iHRE?B€9<C±W=wHJ;2Àµz2ÞuG`=XST9|_|=>\DB C:²HWA?AL~:STY|E?B€9<C
©
ª:z ª BiAu=E?E G`HRE _|=.C:¥9JE?=3E?G:=dALBDÚ>ã=M9JV:E?G:=uY59<z Y:~:\iHRE?B€9<C±W=wHJ;2Àµz2ÞuG`=XST9|_|=>\DB C:²HWA?AL~:STY|E?B€9<C
©
ª:z £ß­
!
"
!
$#
&%'%'%
*),+
-/.01+)
+
),+<56.0=)
7
7
(
)2+
-3.40156.40
+98:-
+9;5/+95 7 9
+ ;
7
+<56.0
>%'%'%
),+-3.401+
+@?A-
+9845/+<;5
+
)2+956.40
+98
CB
.ED
.
D
.
+
-/.
)2+
-3.40156.
D
.
6B
F%A%'%
.
+
),+<56.0
.
,) +
-/.01+
),+
-/.0G)2+956.40156.
+
),+95H.0
.
+
),+<56.0
+
+956.
JI
I
I
+
+
-/.
I
I
I
I
K
SK
UK
ML
+
ML
NL
ML
+
O!L
+
NL
+
NL
O
+
+
.
O!L
PL
L
+
-/.
+
-/.
+
-/.
TO
SOL
L
+
-3.
+
-
Ÿ
+
O
Q -3. L Q
R
Ó ­¡
Ó
Z
×
­
¡
Ó
ª:z âÞuG`=BDC`_|~5}ÊE@BDjW=UALE@=>Y k B€C5}=W][±Z\D9WC:²T_|BDjBiA@B€9<C^] ­P¬Ó ­µÓ ®
Ó ­¡
KM=P¸²<ãg=E ¡ ¥Ó ã ¥ ¬áE@G:=´B€C`_:~`}ÊE?B€j<=HWA?AL~`SÇY:E@BD9WC5®M¥ Ó ãÔÓ ã
’”“
•P–˜—*™›š
£z ž ¬ÂÓ ;@Ö 9J9W®WV¸ãF9JV¬ Rº Ö "9W®ÜST¥ÕS¬~:Ó E?WHRÖ E?B€j<"=U®WãF\DH"¬KÁRVáÖ 9W;›"HW®µ_`¥Õ_|B¬E?Ó B€9<6C^ã k RÖ "®µ¥ ¬ Ûã @Ó Ö J®Ü¥ ¬ Ö J®Wã
¬ @;@Ó 9Ö 9WV¸J9J®ÜV ¥Õº ¬9WRSTÖ wS®¸~:ãgE?HR¬ÂÓE?B€Öj<J=U® \DH"KÁVá9W;dS~`\ÂE?B€Y:\DBi}>HRE?B€9<C^k
¬ÂÓ ;@Ö 9J9W®uV¸¾a9JV ¬ R» Ö Bi"AL®3E@;?¥ B€[:~:¬ Ó E@RBDjWÖ ="\i®3H"K¥k ¬ ?Ó¸Ö J®3¥Õ¬ RÖ w®d¾a¬ÂÓ Ö J®
Ó ¬Â¬ÂÓÓ ÖÖÊJJÖ ®M®u¾Ô¾a6®¬L¬ ʬ ¥ RÖ ÛÖ "®¬ Ó®^ã¢2¬Ö ÊÖ ÛÛ®L®2®Üã ¥Õ¬Â¬Ó Ó Ö ÊJÖ ®X¾FÛ¬®´¥Äã ¬ Ó RÊÖ Ö "6®2®Ü㥠¬ Ó¬ Ó¸Ê¬Ö Ç6®ã ¥ L®Ê¬ Ó Ö Ö J6®›®Ü¾ ¥¨¬ RÓ Ö "´®*ãã
£z « 8`9W;d;NHRE?B€9<C`HJ\ÛC~:S´[5=.;?A ¥ ] ¥ HWC`_ Ü¥ ]:9<C:=UG`HWA
|¬ uã L®Ü¥ © ¬ © ã © ®Ü¥ © © ©ã © © ¥ © © ã © © ©
¥ © © ©© ã © ©© © ¥ © © ã © © ¥ Mã
£z §ì¬ÌH<®Ôç.¤ k:¡ ¤ ß§ ž é
¬á[5®Ôç.¤ k:­ ëí ¤ í é
¬Ì}.®Ôç.¤ kJ¤ Э ë 9<;u¤ ëå é
¬…_`®Ôç.¤ kJ¤ Э 9W;u¤ í é
£z £¨{A@Y+AL=>BDC:=._²TE?9JG:V›=UE?G:V…HW=(}Ed;@~:E@C`G`C:HJEO=>;Ç9WC:BDA(=U¡wSTªBD\€ST=B€Bi\DAO=.A §W"ŸWG:âW9<¦~:Vá;Ç=>=>Y:E.\€]5~5HWAÇC`â _(âî9WC:Vá=>=U=>G:E R9<A@~:=.; }>9Wž C`ª<_^¦W¦Ç]*E@ALG`=wHJ}9<EÇC`Bi_:A(A.¡.]|ª(E@G:¾ =
E?§<G`ŸJHRâ<E›¦ BiAž ªWž ¦<Ÿ ¦d ŸJ㢪Wª<â ªWª â(W¥ Vá=>=E å Rí?A@© =.}>9WC`ã _Ûz å å ¥ ë?ë å å ¥ å Vá=>=E RA@=.}>9WC`_Û]
£z â¬ÌH<®(¦ «ŸWâ<§£¡^«ŸJâ<§£¡Û«Ÿ
¬á[5®(¦ D¡w§ ž âW«<ªd¡"§ ž âW«<ªu¡"§
¬Ì}.®(¦ ŸJäW«`¡<¡"£RªW«£J¦<§Jâ<âWŸ ž §ÜŸRäJ«`¡W¡
£z ä¬ÌH<® ž «§Wª
¬á[5®(¦ §Jä£J§
£zD¡.¦¬ÌH<®˜«Ÿ Rä<ä:]<E@G`HJE›BDA¡.« žWž
ž
+
+956.
+956.
+
+
Q -/.
-3.
%A%'%
+
Q /
- .
-/.
+
+
-/.
! " $# ! &% #
%
)
.
-,-.
"
-,-.
B
.
.
.
.
* .
.
.
.
;
.
.
+
.
.
.
0/
.
.
21
.
I
63
7RR
/
%
%,%
%
%,%
%
R
.
.
/
43
7/8 / 5
7 RR
7RR
9%2%
%
%
B
' $( (
;
.
B
. 765
%,%
.
/
%
%
!
-,-.
-,-.
.
;
B
43
%
/
/
R 5
. 7
7RR
/
R
.. 7 . 74R
74RR
63
.
¬á¬Ì[5}.®(®˜«âWâ`ŸWäW¡W¦¡ §RäWRä<ä<äWäWää<äWä
£zD¡W¡ ¬á¬Ì[5H<®® ··BDBDY:Y:Y`Y`HWHWAA
@B
B
¬…}w®
-4
82B€²<~:;?=Ç¡<k
-2
0
2
4
¬…_`® ·BDY:Y`HWA
£zD¡wŸ
£zD¡ ž ¬Q¡X㦠¦Wä®
’”“
•P–˜—*™›š
ä:zD¡
ä:z Ÿì¬á¬Ì[5H<®a®a¬Q¬Q¡w­¦:¡wÖ ¦:Ö.¡>® «
¬Ì}.®Ôç<­¡.«`Ö?ª:Ö?Ÿ<Ÿ|Ö ž ¦|é
ä:z ž ¬L­ ¢Ö?¦<® å Ö å å
ä:z « ;N_:HJ9WC`SZ²WHJ=WBDkMC^çJku£Jçw§|¦`ÖÊÖ>£J¡<§ Ö?Ÿ|¦`Ö¡Wž ÖN£WÖ@«`§ Ö?¦W§:â`Ö@ª`ÖN£JÖN§£Ö?Ÿâ:£Ö?ÖNä£Wé<§ ] ªW«:ÖN£Jª ŸW§Ö DÖ@⟠ŸWäé
ä:z § Ð¥ ¦:Ö §J¦ ] Ð¥ ¦`Ö?§W¦
ä:z ª¢ç¡WÖ ë Ö Ö Ö Âé
ä:z £ ¥ ¥ ¬L­ ¢Ö ®z }9W~`\D_˜[5=PHWC±ÃAL=>EO}9<C<ENHJBDC:BDC:² ¥Õ¬…¦`Ö>¡
ä:z â¬á¬Ì[5H<®Ô®Ôç.ç.¤¤ kJkJ¤¤ ¥¥­O­OŸ´Ÿ´HWHWC`C`_(_(¤¤ ¥¢¥Á«ZŸ|é HWC`_ä ¥g§é
¬Ì}.®Ôç.¤ kJ¤ ¥­¡ JŸ´HJC5_˜¤ ¥Áâ|é
ä:z ä¢ç"¦:Ö.¡WÖ?Ÿ:Ö ž ÖL«:é
ä:zD¡.¦ |·BDY:Y`H<A
ä:zD¡W¡ ¬ÌH<®U¬…[5®Ê] ¬Ì}.®dA@·B€Y`Y`HWA
ä:zD¡wŸ |·BDY:Y`H<A
ä:zD¡ ž |·BDY:Y`H<A
ä:zD¡>« |·BDY:Y`H<A
ä:zD¡w§ |·BDY:Y`H<A
«
%
R
+
.
.
.
%
.
. '%2%
. 7
.
.
%
%
#
$#
#
$#
-,-.
#
U
%
%
%
U
%
A%,%
%
!
-,-.
%
%
-,-.
CB
%
#
$#
"
4
2
-4
-2
2
-2
-4
82B€²<~:;?=Ÿ:k
’”“
•P–˜—*™›š
¡.¦:zD¡ ¬ÌH<® T¥¢«W¤I­×¡
¬á[5® ­¨ŸP¥­ © ¬á¤T㨫®
¬Ì}.® ­Ø£¥¢¦
¬…_`® T¥­£ «W¤´ã Ÿ<£
¬…=w®˜¤˜¥ ­ ž
¬áV?® T¥­ ž ¤´ã §
¡.¦:z Ÿì¬ÌH<® T¥ ëí ¤Ã­ ë í
¬á[5® T¥­ å© ¤Tã ©í
¬Ì}.®˜¤˜¥ ¡ ž
¬…_`® T¥¢«
¬…=w® T¥¡.¦W¤´ã £
¬áV?® T¥­OŸR¤Z­×¡
¡.¦:z ž ¤
¥­ ¡.¦:z « |=>=UE@G`=Y:\€9WE›9JV¸E@G:=UVá~:C5}ÊE@BD9WC5Ad[5=.\€9RKz
¡.¦:z § Ü=wA
¡.¦:z ª Ü=wA
¡.¦:z £ ¬ÌH<®a¬Q­d« W£|Ö?Ÿ <£J®
§
.
%
7
%
%
B
B
4
7
6
5
4
y
3
2
1
0
−1
−2
JH82C5B€²<_ ~:Z;?= ¥ ž k © b¤´ã¢Y:\D9J¡IEd¬ 9WV E@G`®=zOVᬠ~`C`;@9<}ÊE?[:B€\D9<=>C`S A T¡.¦`¥ z «® © ¤¨¬ ®] T¥ © ¤Z­FŸ˜¬QzD z ®] T¥ © ¤ã¨«(¬ z ®
¬á[5®a¬ ž § |¡W¡WÖNŸWŸ ž ¡<¡w®
¡.¦:z â Z¥­ ¬…¤Ã­ ž ®
¡.¦:z ä¬ÌH<® T¥g¦ D¡>¤´ãg¡ ä
¬á[5® T¥­¡.¦W¤´ã¢¡"Ÿ
¡w¦:zD¡.¦¨¤HWC`_(פ ¤ © ­aߤ ¦B€ST¦:Y:]:\DB E@=.G`AÜHJ¤ Eu©© Bi­IAd¤+¤ © © ¥ ¤+¬á¤ © ©z ã
¤ ®¬á¤ © ­I¤ ® ¦`]<[+=.}.HJ~`A@=d¤ © ã(¤ ¦
©
©
¡w¦:zD¡W¡ |=>=UE@G`=Y:\€9WE?Au9WV¸E?G:=UVá~:C`}E@BD9WC`Ad[+=>\D9RKz
¡w¦:zD¡wŸ |=>=UE@G`=Y:\€9WE?Au9WV¸E?G:=UVá~:C`}E@BD9WC`Ad[+=>\D9RKz
¡w¦:zD¡ ž |=>=UE@G`=Y:\€9WE?Au9WV¸E?G:=UVá~:C`}E@BD9WC`Ad[+=>\D9RKz
¡.¦`z€¡.« =.=Y:\€9WEd[5=.\€9RKz
¡w¦:zD¡w§ |=>=Y:\D9JE›[+=>\D9RK
¬ÌH<® T¥¢¤5©XãØ«W¤Tã§¥Õ¬á¤Ç㠟W®L©X㢡
¬á[5® T¥ÁŸR¤ © ­ÙŸJ¤Z­ © ¥gŸ`¬á¤I­ © ® © ­×¡
¬Ì}.®T¥­ å ¤+©X㠟R¤Z­ß¡O¥­ å ¬á¤I­ ž ®L©3ãŸ
¡w¦:zD¡.ªì¬ÌH<®
©
¬á[5® ¬Q­¡"® ©
ª
0
1
2
3
x
.
4
5
.
6
.
.
B
B
.
. R
%
.
<%
.
1
.
.
.
S
S
.
.
+
+
.
.
.
.
-
-
.
P
.
25
20
15
a
10
5
c
0
b
82¬ B€²<;@~:9<[:;?=Ã\D=>«`S k ¡.¦`\Dz€9J¡<ET¡w® 9JV›E?G:=(Vá~:C`}E@BD9WC`AZH® ×¥ ªJ¤+©J]3[+® ߥ ­ ë ¤5©J]MHJC`_ }.® ×¥ ëå ¤+©Wz
−5
−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
.
̬ }.® © ã
¬…_`® ¬ÌŸ ãg¡w®
¬…=w® ë ¤5ë
¬áV?® ¤5©
¡w¦:zD¡"£ ¬ÌH<® © ¬ 㠟W®L©
¬á[5® í ë ¬ ­ ¡.«® ©
¬Ì}.® ë å ¬ ãØ«®L©
¬…_`® ¬ ­Ø£J®L©
¡w¦:zD¡.âì¬ÌH<®F­d«OãØªW¤I­ÙâJ¤5©M㢡<¡>¤5åu­×¡.ªW¤5í
¬á[5®˜«<â­Ø£JŸJ¤´ãتW¤ © ­Ùâ£R¤ å ãg¡wŸR¤ í
¬Ì}.®F­OŸdãØªW¤Ç㠟R¤5©MãØªW¤5åu­a¤`ëMãØ«W¤+í
¬…_`®F­›âJ¤+©3㢡wªJ¤+åu­aªW¤`뛭¨ŸR¤+íX㢡R£"¤ ãŸWâJ¤
¬…=w®F­›â›ã¢¡"ŸR¤´ãg¡>«<¤5åXãØ«W¤5ëd­aªW¤5íd­Ø£"¤
¬áV?®(«W¤+©d­¨ŸR¤5å3ãâJ¤+íd­¨ŸR¤ 㨤 ­F«<¤
¬…²®F­›â›ã¢¡"ŸR¤Z­¨ŸR¤+©X㢡"§R¤+å3㨫<¤`뛭ס.¦W¤5íu­Ø£"¤
¬áG5®F­›â›ã¢¡"ŸR¤´ãØ«W¤ © 㢡"ŸR¤ å 㨫<¤ ë 㠟R¤ í ­ÙŸJ¤ ­ÙªJ¤ ­F«<¤
¬…Bi®F­¡.ªW¤5©5㠞 ŸR¤5å^­(¡"ŸR¤5ëÛ­Ç«<¤5í6ãI«ŸR¤ ­
¡.ªJ¤ 㘪<ŸJ¤ ã(ŸR¤ ­
¡"£R¤ ­IŸJâJ¤ ©
£
+ .
+
+
-
+
+
-
+9 56.
+
-
+9 5
R
.
5
R
.
) 56.40
R
-/.
.
-
/
/
7
7
7
7
/
. R
.
25
20
a
15
b
10
c
5
82¬á¤TB€²<ãØ~:;?¦ =´§<§|®Qk ©Jz›¬\€9WE?;?A9W[:9J\DVµ=>E@S G`=¡w¦:Vá~:zD¡wC5ŸW}ÊH<E@BD® 9WC5AH® (¥Ñ¬á¤(­ØŸW®Q©W]6[5® ¥ ¬á¤IãС §W®L©J]ÛHJC5_î}.® (¥
0
−3
−2
−1
0
1
2
3
<%
%
¡w¦:zD¡.äì¬ÌH<®˜¤5©MãŸJ¤ ã ©
¬á[5®˜¤5åM㠞 ¤5© 㠞 ¤ ©3ã å
¬Ì}.®˜¤5园 ž ¤5© 㠞 ¤ ©u­ å
¬…_`®˜¤`ëu㨫<¤5å ãªJ¤5© ©3㨫<¤ åXã <ë
¡w¦:z ŸJ¦Ó Ó © ¥
¤
¡w¦:z Ÿ|¡ÔÚ.Þu=>G`;?=M9Y+Vá9W9W;X\D±¦:C:]D¡W9W] STŸ|]Biž HJ]\"«`Ó¸] §|¬…¤+]WHW®3C`¥ _Tž G`ª<HW¦JAܤuE@­´G:=äW«Y:ŸR;?¤+9WY+©<ãZ=>;@EQäW±P«<äWE@¤5G5å:HRE­´Ó2«<¬áâ<¤+¦J®¤`ë|ã
ã ¡ ž ¦J¤+Kdí|G:­Ã=.¡wCIâJ¤¤ ãZ¤ ã BDA
V…E?HWH<G:C`}Ê=_ZE?9W[+Ó2;?=>=.¬áG`¤+_ZH"® jBDCBD9WE@9;w­z Ó¸¬á¤6®3Kd¥gG:=.¤¸CÔ¬á¤Ç¤ ­¨¡w®>­ ¬á¤Çg­Ô]+ŸWA@®>=>¬á=´¤Y:­ \€9Wž E?®QA©<[5¬á¤Ç=.\€­9RK«z®Þu¬…¤´G:=P­îY+§<9W®Ê\D]|±KdC:9WG:STBi}NGÃBiHJ\*= c }>Y`HW\DCîHWB€[5C`=A
¡w¦:z ŸWŸ ¬ÌH<®BDC`};?
=.H<ALBDC:²TB€
CîHWCB€CE?=>;?j"
HW\3 "¬ +Ö!®M#BÂV $&%'¢¤ ) (+*,-!./B€ST.10Y:2 \DB =.b A4Vá3*~`¬…C`¤+}Ê® E?B€59<C)3*3F¬ :BD®ÊA z
G`8:;?H<9WAMSÄE@G:¤5=PåOA?HJ­ ST|=åUAL¥ BD²WC
© ¬áHW¤˜Au­ ¤Ã|­ ®>¬á6¤+]|©MG:ã =.C`|}©X=ãg¤+åU¬…¤TBDAdã BDC`:}>®Q;@©w=w®uHWA@BÂB€EC:BD²5Az AL=.=>C(E@G`HJEO¤5åO­ å
¬á[5® BDb SÇY`Vá~:\€BDC`=.}A E@BD3*9W¬…5C ¤+® 3¢BiAZ3*_|¬ :=w}®;?zI=.HW8:A@;?BD9WC:S ²FBD¤5C¢ëHJ­ C×B€ëZCE?¥¿=>;?j"¬…¤
HW\P­ ¬ +Ö:®>¬…®¤IB€ã V |®>¿¬á¤+©O¤ ã |©. ®B€EPBDA
A@=>=>C˜E@G5HRE›¤ ë ë BÂVµ¦ ¤ 6]:HJC5_ä ë ë B€V*¤ ߦ:z
¡w¦:z Ÿ #ž Y`6 \€=9WVáE›9W;?[5S=.\€~`9R\DKHJE@z BD9WCî9WVÜY:;@9<[:\D=>S
k \D9JEE@G:=ÇST9WC:9<STBDHW\DA›Vá9W;Ç­OŸ ¤ Ÿ|z =>=´E@G:=
U
'
U
'
T
.
'
/
R
A
. .
R
U
;
5 .
6
5
7
!
N
.
"
I
!
I
â
"
12
10
8
6
4
b
2
c
0
a
−2
82¬ B€²<;@~:9<[:;?=u\D=>ª`S k ¡.¦`\€9Wz€¡E?A*ž H9J®V+E@G`=uVá~:C`}ÊE?B€9<C`AÜH® T¥ß¤+©^­ ž ]W[5® T¥g¤5©5ã(Ÿ:]WHJC`_T}w® T¥g¤5©Û­Z¦ §|z
−4
−3
−2
−1
0
1
2
3
%
¡w¦:z ŸR« 6Ÿ:ÖL= ¤ Vá9W^ã;?îSŸ ~`\D]HJKdE@BDG:9W=>C
;?=›9JV*¤Y:›H;?W9W;@[:=d\D=>E?S
G:=k A@±\DST9JEdSÇE?=>G:E@=P;?±´Y+9W9<\D;X±HWC:C<9WE?STB ¼BiA@HJ±\iSTAMVáST9W;›=E?BD;@C(±´E@Y5G:9<=PB€CBDCEME@9J=.VÛ;@jRE@HJG`\i=OAuY+¤9Wd­\D±
C`}>9W9W;?TS @; =wBDHWALY+\Ìz*9WÞuC5_|G:B€=MC`²WY5\D9<±ZB€C¤EµB¤ iA›BiHJAµCA@E?±BDSTA@±STSÇ=STE?;@=>±E@;?Y+±I9WY5BDC9<E2B€CB€V`EdVáB€9<V6;µÓ2HJ¬áC¤±3ã¤Ø]¤+Ó2®3¬á¤ ¥ãÇ­µ¤+Ó¸®3¬á¤¥¨u­Ó¸a¬…¤¤+®z­P¤6=>®Ê= ]
E?G:=:Y \D9JENAdB€C(à`²<~:;?=[+=>\D9RKz
¡w¦:z ŸW§ |=>=Y:\D9JENAu[5=.\€9RK 9JV2Y:B€=w}=.KdBDA@=UY59<\€±C:9<SÇBiHJ\iA.z
’”“
•P–˜—*™›š
¡W¡WzD¡ ¬ÌH<®Ôç.¤ kW¤ ¥ å HWC`_(¤ ¥¡Wé
¬á[5®Ôç.¤ kW¤ ¥¢¦ZHWC`_ä ¥gŸÇHJC`_(¤ ¥ ­ © é
¬Ì}.®Ôç.¤ kW¤ ¥¢¦:é
¬…_`®Ôç.¤ kW¤ ¥¢¦ZHWC`_ä ¥­ å© é
¬…=w®Ôç.¤ kW¤ ¥ ©å HWC`_(¤ ¥­d«`é
¬áV?®Fç.¤ kW¤ ¥­OŸÇHJC5_˜¤ ¥ ­¡Jé
¡W¡Wz Ÿì¬ÌH<® ¬ 㢡"®¼¤ ¬…¤I­ ¡"® ¬Ì³›9JE?=STBDA@Y:;?B€CE.kd¡w¦W¦ÇALG`9W~:\i_Ã[+=Z¡.¦Ÿ ®
¬á[5® å ©
¡W¡Wz ž ¬ÌH<®(6¬³›á9W¤ÇE@=uã ST:BD®ÜA@Y:¥ ;?B€¤C´Ewk ã 3*¬á¤6u®3¥ ¥ 3*<¤¬áX¤6®ã ã ÜA@3*G:¬ 9<:~:®Êz\D_´[+= 3*¬…¤+®3¥ ¤ z ;?99JVQk 3*¬…¤Xã :®µ¥
ä
(
(
S
-, #
-, #
-, #
-, #
#
-, #
$#
-, #
. . $#
.
#
.
.
$#
R .
$#
.
-
U
30
25
20
15
10
c
5
a
0
−5
b
28 B€¬á²<¤
~:­;?=
ž £®L©k ­g\D¡Ç9JE?VáA´9W;T9JVO­ E@ž G:=˜Vá~:¤ C`}E@BDž9WC`zTAT³›H<9W®ÃE@=T­ E?© G:¬á=T¤î¤ ­HW¡wC`®L©_ ãÐ ¼Ÿ|}]Ü99W[5;N®Ç_|BDŸ:C`¬…HR¤
E?=.ãÐAŸW9J®LVX©E@G:­g=T§î= c HJE?C5;@_=.SÇ}.=®
Y+å 9WBDC<ENA>]^¬áE@G:=Y+9WBDCE?AuKdG:=.;@=E@G`=UVá~:C`}ÊE?B€9<C˜G5HWAuSZH c 9<;uSÇBDC(j"HW\€~`=w®Êz›¬ ;?9W[:\D=>S ¡.¦:zD¡>«®
¬á[5® E@G5;?HR9E›9JVQBiAk 6¬6¬……¤d¤Çã ã::®Ü® ¥ ¥¬á6¬¤›…ã¤+® :ã®Q©Û¬¥¢:¤5®X©^~:ãC:\DŸR=.¤A?Ad3¤˜ã ¥g|©›¦ÇHJC`9<;_ ÇÛ¬á¥g¤6®¦`ã z Û¬ :®Ü¥g¤5©Ûã|©J]
¡W¡Wz « ¬ÌH<® © å ¥ß¤T㠞
¬á[5® © © ë ¥ß¤I­a«
¬Ì}.® ë © ¥ß«W¤Ã­ÙŸ<Ÿuã å
¬…_`® å © å © ¥ß¤5©u㨤T㢡
¬…=w® í © ë ë ¥ í© ¤I­¨Ÿ›ã © ë ©
¬áV?® ë í ë ¥¢¤5©d­a¤I­a«
¬…²® ¥¢¤+íX㨤+©Xã ¬áG5® ¥g¤ ãØ¤ ©Xã wãØ¤5©u㨤˜¥ ¤
¡W¡Wz §ì¬ÌH<® ž ¬ ŸR¤+©3㢡"®*­Ù§¥ÁªJ¤+©d­ÙŸ
¬á[5®
Ÿ:¬ ë ®L©X㢡¥ å?© 㢡
¬Ì}.® å ë í
¬…_`® ž ¬ Ÿ:¬ ë ®Q©M㢡"®2­Ù§P¥ ž ¬ å?© ãg¡w®2­¨§P¥ ­¨Ÿ
¡W¡Wz ª³O3 9JE?=3 SÇ¥ BiA@Y:;@BDCE.k
HJ;?¤ = R¤ © .( A@=.G:h9W~`~`HJ\D_\ ]Vá[59W=¨;d=¡ c "HJ¤¸STz Y:3 \D=Vá 9<3;d© ¤(¥ ¥«+¡<z¬ ®XãŸØ¥ ë 㠟aHJC5_
© ë ©
¡.¦
−10
−3
−2
−1
0
1
2
3
.
.
(
(
#
;45
-3.
;:-
;5
-
-
56.
-3.
5 7
845
;5
5
; 5
.
5 7
5
85 7
; 5
?:-
.
)
;5H.
;-
56.
-3.
- .
8 3
Q -3.
-3.
;
; 5
-
56.
-
;:-3.
8 -3.
+
-/.
+
-
+ -3.
.
;
-
7
;
.
B
.
5
;
@B
.
.
30
25
20
b
a
15
10
5
0
−5
c
ž82®LB€©3²<~:ã;?=Ÿâ:Vá9<k ;P­\D9JžENA39WV^¤ E@G`=Ož Váz›~:C5¬ }ÊE@;@BD9<9W[:C5\DAM=>S H®›¡w¬…¤¦:zDãa¡w§WŸW® ®L©¸ã ¡W][5®uŸ:¬…¤P­ © ®Q©Ü­Ù¡HJC`_˜}.®O­ å ¬á¤´­
¡W¡Wz #£ HW3 ;@=´ 3 =.© h~`¥ HW\¸6¬B€VMʤµHWãC`_®w9Wã C`\€X±¥ B€V ÊUã¤*ã UÛ㥠*XHJC`ã_5]3 Û© Kd 3G:Bi}N¥ GîBiJAO¬ <¤E?µG:=Tã }>HW®.ãA@=PP¥Vá9<;= ¤c *HJãSTY:<\D=´ãB€V
T¥¡HWC`_ ›¥ ¡W]Vá9<;›HJC± HJC`_ 5]:9W;d9WE@G:=.;@KdBiAL=B€V T¥ 9W; u¥ z
¡W¡Wz â¬ÌH<®Ôç.¤ kW¤ ¥¢¦ZHWC`_ä ¥ ë é
¬á[5®Ôç.¤ kW¤ ¥¡PHWC`_ä ¥ © HWC`_ä ¥ å© é
’”“
•P–˜—*™›š
¡wŸ|zD¡ |3*B€¬…C`¤ }>=
®>ê ê 3*¬á¤ ¡.ª+®3ê ¤ ­ ­´3*¬á¤ ¤ © ê"®.Váê59W¥Ä;µ¤ ê ¤+ÖL© ¤ ­¨¤+©© ­›ê`¥Äâ`Ö@âê ¤ Ò]JHJã×C5_(¤ © ê 3*ê€ ¤¬á¤ ­¨®-­ ¤ 3*© ¬áê ]Û¤ KM®.=ê G5H"â<jW¦W=(¦+ê ê3*¤ ¬á¤ ­´®Ü¤ ­ ê
©
©
Vá9<;d¤© ÖL¤ © €­d«<¦<¦:©ÖNŸJ¦W¦ z ©
¡wŸ|z ŸØ8`ê ã9W; +ÖJêD P­ €J¡.ê ¦`×Ö>¡ ŸWž ª5µê 9WP­C:=TJG`ê H<AIê 3*¬ |®3­ 3*¬ ®.ê^¥ ê ©­ ©<ê^¥ ꀬ Çã ®¬ Z­ >®>êÛ¥
¡wŸ|z ž 8`>®|9W­Ã; +֟:¬ Üã ®­O¬ X­Ÿ:Ö?Ÿ ^>®>9<ê.C:¥ =G`ꀬáH<«3A­Ãê 3*Ÿ M­¬ |®Ã*­Ÿ ®>3*¬ ¬ M­®>ê¥ ®>ê.ê ¥Õ« ­ê «3¨­ÃŸ ©Ÿ X­dí¢Ÿ ¬áJ« êDXM­­¨Ÿ JÊê ©>®.ꥡwŸ5êê M­«5¬ ­JêÂ]
[+=.}.HJ~`A@=Iê «­ØŸ ­ÙŸ Jê «ãŸ5ê Ûê>㠟`ê Jê «ã¨«ãØ«´¥¡"Ÿ|]Vá9W; +Ö €­OŸ|Ö?Ÿ z
¡wŸ|z « «|®>B€C`ê ¤ }>=(­aê 3*¤ ¬á¤ êÂ]:®ÜKX­ =U3*G`¬…H"¤ j<© = ®>ê:¥ ¥ ê ¤5¡wå Ÿ:z­¨¤5å© ê|¥ ê ¤ ­Ù¤ © êD ¤+© 㤠¤ © ã ¤5©© ê Õ¬á«ã«ã
©
¡wŸ|z § |3*G:¬…¤ 9RK ®>êWE@¥G`HJêDEO¤ Vá9W;ê"­¢HJ\Dê ¤ ¤ ê€ Ö@¤ © ]+ê ¤ KM=P­aG`¤ H"jWê=ÃHJêDC`¤ _ ØêJ­g¥ ê ¤ ¡W© z ê€ ê ¤ ­¨¤ © êÂzOÞuG~`AÇê 3*¬…¤ ®Ü­
©
©
©
¡W¡
−10
−3
−2
−1
0
1
2
.
#
-, #
#
.
',
N
,
.
'
N
-/.
.
.
.
.
<
<
,
:
#
.
.
U
.
.
.
,
.
-3.
#
.
'
-, .
.
3
9
<
<
.
,$
.
.
E
.
.
.
U
.
.
.
.
.
.
50
0
−50
−1
4
x 10
4
0
1
2
3
4
5
6
2
0
−2
−4
−2
−1
0
1
2
3
4
5
6
7
4000
2000
0
−2000
28¡.âWB€²<¤ ~:;?ãß=uä`¤ k2Þu]¸G`E@G:;@=.=I=ME@Y`9W\€Ya9WE?à`Aµ²<9W~:V+;?E?=IG:AL=dG:Y+9R9WK›\D±AUC`Kd9WB€STE@G¨BDHWSZ\ ž HJª<E@¦J\iHJ¤[Ù­IC:äJ9J«ENŸJHR¤5E?©:B€9<ã(CFäJ¤×«äJ¥ ¤+å6­›­Z¦ «<DâW¡˜¦Wk¸¤`¦ë5ãF¦W¦:¡ ¡˜ž ¦Jk¸¤+§ í6D­¡W]
E@m G`m=Ç|Œ3ST‚QBi†_:mM_|‚Ò\Dm^=Z<¤¨]SÇ¥Ä=wHJ­OC`ŸAdk6E@G`¦ HJ¦<EO¦:¤F¡ZHWk ;@£=U]¸E?HJG:C`=P_FjR[5HJ\D9W~:EL=.E?AO9WS AQENHJ¤Ø;@E@¥ÄBDC:²Z­Kd¡IBÂE?kÛGª:zTm:ŒÃÞuHWG:C`=T_(SZB€C`HR}>E@\i;@HJ=w[aHWA@C:B€C`9W²ZE?HRKdE?B€BÂ9<E?GC
BDC<E?=>;?jRHJ\^†mI~:CE@BD\^m^BiAd;@=wHW}NG:=w_Ûzd¬ ;@9<[:\€=.S ¡.¦`z Ÿ:¡w®
−4000
−1
7
0
1
2
3
4
5
6
%
%
%
%
¡wŸ|z ª ²<6 ;@.= w= HJHR\DE?B Ú>=.=´ALEX¬…jR[HJ±Ç\D~:Y`=\€9WC:ELE@=.BDHWC:;X²-¤ 3*¬á¤6®L¤®ÜE@G`HJE.]²WŸ:BDz2jWÞ2=.CÔHJ·<ê ¤=¤ ­
¥Á¤ © Ÿ´ê ]^HJê 3*C5¬á_Z¤ ¤ ®6­"¥Ð3*Ÿd¬á¤ ­ © ®>wê]HJKdELG:E?HW=.B€;@C5= A3uB€E?BDAA
HTA@ZS HJ\D^C~:S[+=>;wzµÞuG:=>CA@G:9R©KgE?G`HRE´ê 3*¬á¤ ®*­ 3*¬á¤ © ®.ê ž Ÿ`© ê ¤ ­a¤ © ê z
¡wŸ|z £¨8` 9W; +Öê ­ J€ê¡WÖ?Ÿ `«69Wê ­C`=dG`JHWêÂ]|AO[+ê 3*=.}>¬ |®HW:~`­A@=Z3*ê 㬠®.ê<¥Jê ×ê «Z­ HJC` _ êW©¥ ê © ¡Wz êW¥Õê êW¥
¡wŸ|z â E?|G:G:=>9RC
K A@G:E@G`9RHJK¢E
E@êG`3*= ¬á¤ B€®MY5A@­ }NG:3*B€E@¬áÚ¤ © }>®>9Wê CE@BDC~:BÂEQ±Z KdB€ E@G ê ¥ß¤ «5­ z*¶Ò¤ Eu© BiêA.zÔ]|G:8`9R9WKX;´=.¤ jW=.Ö@;.¤ ]© Y59A@A@BDÂ[:­O\€Ÿ:=Ö?E@Ÿ 9
_:9([+ =E@E@ =.;PHJC`]`_ÔHREd²W=¤ E Ð¥¢¥ ¤ ž ¥ ž R¡ â`]ÛKdž G:z BD}NGa=.=UBiAOE@G:E?G:==ZY:SZ\D9JE›H c 9WBDV SE?~:G:S BDAdVájR~:HJC`\D~:}ÊE?=ZB€9<HRC
E@E?[5HW=.B€C:\€9R=wK_îz [±
©
¡wŸ|z ä¬ÌH<® ¥¡w¦W¦
¬á[5® ¥¡w¦W¦<¦W¦
¬Ì}.® ¥¡w¦W¦<¦W¦W¦<¦
¡"Ÿ|zD¡.¦Ø8`9W=Eu;¸¤¤(¥¥¡ "E@ÀµG`=Ö Ç^¥BDY`A?¡ }NJG:ŸJB€E@ÀµÚ3ÖLÀ(BDC:=w¥h<~5¡WHJÖ?Ÿ:\DBÂÖEQ±ž Ö SZH"3±HJ[+C5=3_IKd9W;?[5BÂE@ALE@=.=.;@C˜j<=dê 3*E@G`¬…¤+HJ®wE­ ê 3*3*¬á¬ ¤6:®^®>ê ­:ê ¤µ3*­¬ :Û®>êê :ê ¤P›­ z
^êW¥ÐŸ XÀ^©J]|KdG`BD}NG
BiAu²W;?=.HRE?=>;ME@G5HJCHJC± Vá9W;dÀ JŸz
¡"Ÿ|zD¡wŸ ¬…H® 8:9<;µ¤ ¥ P9WC:=›}.HJCTKd;?BÂE?=uE@G:= B€Y`A?}NG:B€E@ÚdBDC:=.h~`HW\€B EQ±´H<A›ê 3*¬…¤+®­ 3*¬ |®.ê `ê ¤O­
¡wŸ
.
.
.
.
.
;
,$
5
U
;
K
5 ;
; 0=) .5
) .5
;
5 ;
; 0G) .45
.
;
;
; 0
;
A
.
;:;
I
.
#
;
) 5
;
0G) ;
;
,
.
@B
0
K
@B
B
.
; 0
.
#
K
.
T
) .5
T B
@B
K
'%'%A%
1
B
PB
B
40
30
20
10
b
0
a
−10
−20
c
−30
`¤82ëB€²<Bi~:Ad;?=.=ZjW¡.=>¦:C k zu¬ \D9J;?EN9WAd[:9J\D=>VÜS H®u¡.¤5¦:å<z Ÿ ]5ž [+® ®u¤`ëÇHJC`_}w®d¤5í<zd³›9WE@=PE?G`HRE¤5åHWC`_
¤5í´HJ;?=P9|_:_
KdG:BD\€=
^ê ¦Uê ­ ¡ ê `ê ¢B¦­ß€E@GF¬Q­¤F¡ ¥ Ô¦˜®>ê<HJ¥ C`_ ¨(]:Kd¥ G`­BD}NG(¡ BDA›\DHWKM;@=²<=>G`;XH"E@j<G`= HW3*C
¬á¤6HWC®Ü± ­ 3*¬Vá9W:;®>ê :ê ¤Ã­O^z ê:¥
¬á[5® Ü=.A
¡"Ÿ|zD¡ ž ¶Ò_:V*BDA?E?}G:9<= C<E?^B€BDCY`~:A?9<}N~`G:AMB€E@VáÚP;?9W}SÑ9<C`ALHÇE?HJY:C;NEHW}ßE@Bi}>BiAdHJ\Û= cY+E?9W;@BD=.CSÇE›\D9J±ÃV2\ijHJBD;?=>²WK=z E?G:=>C
E?G:=Vá~:C`}E@BD9WCBiAO}>\€9AL=E@9
¡"Ÿ|zD¡>«³OA@G:9J9<E?~:=O\D_aSTBD[+A@=FY:;?ê B€WCê Ew3 k z 3 © F=­ I3 ©G5H"A@jWG:=î9W~`êÂ\D¬ _Z3 [+¬…¤+= ®M3 ­ ­ 3 3 ©¬…¤+HW®LC`®d_Ç­ÐE@G`¬ 3 = ^¬ :BDY`®MA?­ }NG:3 B€E@Ú¬ :}>®@9W®>C`ê AL¿E?HWCê 3 E39J¬á¤6V ®M3 ­
©
©
3 ¬ :®.ê€ã(ê 3 © ¬…¤+®"­ 3 © ¬ :®>ê Ь ã © ®>ê ¤Ü­ ^êwHJC`_(ê 3 ¬á¤6®"­ 3 ¬ :®>ê ê Wê>ê 3 ¬á¤+®R­
3 ¬ :®.ê ê Wê ê ¤I­ ÛêÂz
¡"Ÿ|zD¡w§¨³O;@9J9<E?[:=U\Dà`=>S ;?ALEd¡"E@Ÿ|G5zD¡>HR«`EzTH Þu^G:BDY`=.A?Ca}NG:~5B€ALE@BDÚPC:²î}9<ÞuC`ALG:E?=.HJ9WC;?Ed=>S Vá9<; ¡"3*Ÿ|zD¬á¡´¤+®MKM¥¢=T;@¤ =wHW_|9WBDC \€±Ô­ 9W[|JENÖ HJ^BDCFBiAdE?ÀG:=I_|=wAL]`BD;@A@=w=>_=
;?=.A@~:\€E.z
¡"Ÿ|zD¡"£ØÝ¡ [53 AL=.¬ ;@:j<®>=¸ê E?G`HRê EX3 ¡ ¬á¤+3 ®3© ­BiA 3 B€Y`¬ :A?}N®>G:ê "B€½E@ÚÜ© STzPB€³OE@G 9RKB€Y`E@G:A?}N=ZG:B€ÞuE@ÚÜG:=.}>9W9W;?C`=>ALS E?HWC<Vá9WEµ\D¡ 9R"K›½
A›©JVá]";?AL9WBDC`S }=OÞuêÂG:¡ =.9W3 ©;?=>¬…¤+S ®Ê­
¡"Ÿ|z «`© z © ©
¡"Ÿ|zD¡.âì¬ÌH<® ^BDY`A?}NG:B€E@ÚUKdBÂE?G Ø¥¡ žWž ~`ALBDC:²ÇE@G`=UVá9W;?S~:\iHÇB€CÙ¡wŸ:z€¡.«`z
¬á[5® ^BDY`A?}NG:B€E@ÚUKdBÂE?G Ø¥¡wª Rä`z
¬Ì}.®(E@³›G`9W=E ²W^BDjWBDY`=>A@C(}NG`BDC<BÂE?E?ÚU=>;?}>jR9WHJC\ zE@BDC~:9W~5AX[±IÞuG:=.9W;?=>S ¡"Ÿ|z ž ][5=w}>HW~`AL=UC:9WEd[59<~:C`_|=w_Ã9<C
¬…_`® ^BDY`A?}NG:B€E@ÚUKdBÂE?G Ø¥ ž Ÿ|]~`A@=PÞuG:=>9<;@=.S ¡wŸ:z ª`z
¡ž
−40
−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
N%
B
@B
CB
B
1
JK
.
.
.
.
.
K
CB
/
/K
K
B
K
K
B
K
K
/
.
"
.
+
@B
K
.
.
@B
.
.
/ +
-/.
CB
.
40
30
20
c
10
0
a
−10
b
−20
−30
82¬ B€²<;@~:9<[:;?=Ç\D=>¡<S ¡Wkµ¡.H<¦`®Xz Ÿ Biž Ad® Y:\D9JE@E@=._(BDC˜BDCE@=.;@jRHJ\ Ò«`] ¦ Ò]|[5®MBDA›Y:\€9WELE?=._(B€C ?¡<] ž ]:HWC`_˜}w®MB€C ž ]€¡ z
−40
−4
−3
−2
−1
(
0
1
2
$ (
3
(
%
1
1
28 BD²W~:;?=T¡wŸ|kµÞ¸9ÇE@G:=\D=V E›Y:;?9W[`\€=.SÑH<®uHWC`_IE?9TE@G:=;?BD²WGEM[+®ÊzO¬ ;?9W[:\D=>S ¡w¦:z ŸW§<®
¡"Ÿ|zD¡.䨤8`9W\D€9R¦:K›Ö.AM¡ ÒVá;?z 9WS ÞuG:=>9<;@=.S ¡wŸ:z §´[+=.}.HJ~`A@= ¤Zã © ¬Q¡›­a¤+® STBDC ¬ Ö © ® ߦÇVá9W;
’”“
•P–˜—*™›š œ
¡ ž zD¡
¡ ž z Ÿ
¡ ž z ž ¬ÌH<®Ôç ž é
¬á[5®Ôç.« é ©
¬Ì}.®Ôç¬L­¡w® é ©
¬…_`®Ôç<¡3㠞 é
¡>«
-2
-1
1
2
-2
-1
1
2
"
,
"
R
.
.
S
I
.
"1
0.7
0.6
0.5
0.4
0.3
0.2
0.1
2
0
−2
−1.5
−1
−0.5
0
0.5
82¡wŸ:B€²<z â~:® ;?=Ô¡ ž k b Y:\€9WEÇ9WV›E@G`=ÃVá~:C5}ÊE@BD9WC
¤
) .45
0
−1
1
1.5
.
5 ;
; 0G) .45
−2
2
; 0
;
¤©
1
BDC €­OŸ|ÖNŸ 3¾ €­OŸ|Ö?Ÿ z¢¬ ;?9W[:\D=>S
…¬ =w®Ôç ž ­×¡Jé
¬áV?®Fç"§ é å
¡ ž z « ¬ÌH<®Ùê å ­Ù¦5êJ¥ å ›BÂV ž ÀI㢡 ]
E@G5HRE›BiAuBÂV*À KdG:=>;?= ¥ å z
¡ ž z §Áê ­a¦+ê ›BÂV›¬ © ® .]E?G`HRE›BiAdB€VµŸ z
¡ ž zª
¡ ž z £ ¬ÌH<® A@º ~`G:}N9G 9<A@=IHJC± ”¦:z˜³O9RK KM=IG`H"j<=ÇE@9ÔA@G:9RK E?G`HREE@G:=.;@=I= c BDALE?APHWC
E@G5HR¥E¬­d«WÀîãgãÕ¡w® ¡ "«5°z ­ Vá9<;THW\€uÀ ¨z F=A@=>=˜E@G`HJEÇE?G:BiATBDA´E@;?~:=(Vá9W;
¬á[5®˜¶ÒV \DB S À å ¥ èE@G`=>CAL~`;@=.\€±
\€BDS À å ã¨À © ¥ g]:ALBDC`}=À å ×À å ãØÀ ©
VáÀ^9Wå ;dÀ ¡W]zVá9W;d9TÀ BÂE›BiA›¨A@~zµIÞu}G:BDBi=>AdCBiEdAME@E@95;?]~:Vá=U9WVá;›9WHW; C± ¥ צ:]åJà`z C`_HWC °A@~`}NG(E@G`HJE
¡ ž z â . ( &.5k G:9<~:\D_([+= СW]:C`9JEê :ê Ÿ:z
Vá8`9<9W;›;ÜHJHW\DC± ߦ:]JKM=dKuHJCE*E@9ALG`9RKØE@G5HREµE@G`=>;?=d= c BDALE?AµHWC ÄA@~`}NGÇE@G`HJE
¡w§
-
.
-
/
/
+95H.
I
+
.
I
.
1
M
I
1
+
1
-3.
B
+
+
/
1
/
I
+
+95H.
1
1
1
.
I
+
1
−n
f(n) = 2
1
0.5
0
0
1
2
3
4
5 6
−n
f(n) = 5
7
8
9
10
0
1
2
3
4
5 6
−n
f(n) = 10
7
8
9
10
0
1
2
3
4
7
8
9
10
1
0.5
0
1
0.5
0
5
6
−n−1
f(n) = 10/9⋅ (1−10
)
1.1
1.05
1
0
1
2
3
4
5
¡.ª
6
7
8
9
10
À ¨zM~|E À\DC ×\DC À \DC ¬ ®Ê]
A@9T\€=>E ¥¢\DC ¬ ®z
¡ ž z ä¬ÌH<® í ¥ÁŸ ž
¬á[5® ž ¥ß«
¬Ì}.® í © ¥ © z
¡ ž zD¡.¦ì¬ÌH<®
¬á[5® ¥ z
¡ ž zD¡W¡ b \€¸HJ;?==wh~`HJ\6E?9
ç å© Ö ëí Ö å Ö í Ö Êé
= c }=>Y:E¬á=w®MKdG`BD}NG
BiAç ëí Ö å Ö í Ö é<z
¡ ž zD¡wŸ ¬ÌH<
® © í ë
¬á[5® © © å
¬Ì}.® © ©
¡ ž zD¡ ž :Þ 6 6]:E@;?BDHWC:²W=.\€9<\€BD·G:=E?=>CÃ[ 9W ;d[+=>G`HWC`_|\iHWAu;?=._:HWC˜B^·RHWY
ª`]:;NHRE@BD9WC5HJ\6C~:S[+=>;NA>z
ÞuG`=UE?HWA@·IBiAME@9ZY:;?9RjW=E@G`-= ( & (µkOê ã Jê ê 6êwãÁê Jê<Vá9<;›HJ\D 5Ö "z
¶ÒV ¦:] ¦:]|E?G:=>CØê ã JêW¥ ã u¥Õê ÛêwãÁê JêÂz
¶ÒV ߦ:] ¦:] Uã ¦`]|E@G`=>CØê Uã WêW¥ Uã Э ã u¥Õê ÛêwãÁê JêÂz
¶ÒV ߦ:] ¦:] Uã ¦`]|E@G`=>CØê Uã WêW¥­ P­ ­ ã M¥ ê ÛêwãÁê JêÂz
ÞuG`=;@=.STHWB€C`B€C:²Z}.HWA@=.AuHJ;?=UY:;@9Rj<=._ÃB€CHTALBDSTB€\iHJ;dKuH"±Wz
;@99WV¸9JVu¬Q¡ ž z £J®Êk›ê ­ JêW¥Õê ´­ µã Üã Wê ê P­ WêwãÁê Üã JêÂz
¡ ž zD¡>«Þuê G`=X­ E?;@´BiHJêwC`ãÁ²W\Dê=XBDC:­=.h(~`HWê ]`\€B KdEQ±G:²W=>BD;?jW==wE@AdG:êÂ=U¬ ;?B€²<­ G<E›A@®<BD_:­˜=P¬ (}>HJ­ C(´[+=®.êWST¥ H<ê€_|¬ =HW­ AdA@SZ®WHJ­(\D^¬ HWAd­ _|=w´AL®.BD;@ê =w_
[±ÃE?HJ·BDC:²TÀFA@~ I}BD=>CE@\D±Ã\iHJ;?²W=<z b C:9JE?G:=>;OY:;@99WV2}>HWC˜[+=UVá9W~`C`_(B€C
|=.}ÊE?B€9<CÙ¡ ž z §|z
¡ ž zD¡w§Ù¶ÒV*ÀaBDAdA@~ I}BD=>CE@\D±Ã\iHJ;?²W=<]E@G:=.C
ê ­ Çê © ê ´ê|HWC`_aê ­ ˜ê © ê ˜êÂ]`A@9ÇE@G`HJE
ê ê<¥Õê ­ ×ã!Çê ê ­"´êwãÁê ´ê å© ê Çê ]5HJC`_
ê ˜ê¥ ê ­ ã ê ê ­ êwãÁê ê © ê ˜êwãÁê êÂ]`HJC5_
ê ê © ê (ê ]`HWC`_ # © zÜ8`9W;d\iHJ;?²W=
ÀaKM=E?G~`Ad²W=>E
¡"£
1
1
+
1
1
#
#
.
. - 1) .
.-
.
0
#
B
0
?
. -
.-
8
.
R
;
.
. - 1) #
0
.45
.
#
/
. 7 '%A%'%
/
5 ),+95
Q 01;
+
5 ),+
- 01;
Q ;
+
5 ),+
-/.01;
Q +
. 7 A%'%'%
-
U
I
I
I
U
I
U
I
U
U
T
+
+
U
U
T
U +
+
+
.
$
+
+
I
+
+
.
Q
T
+
+
T
+
+
.
+
U
+
.
.
/
+
+
­ # ¥ ­ # ã # ­# ¥ # ¬ ­ ®^ã # ¬ ­ ®
# ê ­ ê.ã # ê ­ Çê ž # ê ­ ˜ê>ã # ê ­ Çê
KdG`=>;?=E?G:=;?B€²<G<E›A@BD_:=P}>HJC([+=STH<_|=HWAdA@SZHJ\D^HWAd_|=wALBD;@=w_
[±ÃE?HJ·BDC:²TÀFA@~ I}BD=>CE@\D±Ã\iHJ;?²W=<z
b C:9JE?G:=>;OY:;@99WV2}>HWC˜[+=UVá9W~`C`_(B€C =w}ÊE@BD9WCa¡ ž z §:z
¡ ž zD¡.ªì¬ÌH<®F¡
¬á[5®(À_|BDjW=.;@Ÿ ²<=>CEXE?9˜ã ¢]|[+=.}.HJ~`A@= ¥gÀ^©W¬…«­aªWÀ ® À^©Vá9W;
¬Ì}.®(¦:]|[+=.}.HJ~`A@=Iê ­Ù¦5êW¥¢À ©
¬…_`®F¡ ž
¬…=w®(_|BDjW=.;@²<=>CE.][+=.}>HW~`A@= ¥ B€Y`A
¬…HWY:Y:;?9 c B€SZHRE?=>\D±:®Ü[+=EQKM=>=.C HJC`_F­ KdG:=>C
ÀaBDAu\iHJ;?²W=
¬áV?®Ÿ
¬…²®F­d«¬…HW\€ =.h~`HJ\µ­d«®
¬áG5®F­O§ Jâ
¬…Bi®(_|BDjW=.;@²<=>CEXE?9˜ã ¢]|[+=.}.HJ~`A@=
¥gÀ © í ŸJÀ
¬@®a­¡
¡ ž zD¡.äÁê ¦ äWä Qä<ä ­ ¡êW¥¬Ì¦ D¡w® ¥Á¦ ¦W¦ Q¦`¡
Vá9<;dÀ ¨]|B€V °BiA
E?G:=BDC`_|= c 9JV2E@G:=Uà5;?ALEdC:9WC ÒÚ>=.;@9T_|=w}BDSTHW\ÛB€C wz
³O9JE?=PHJ\iAL9´E@G`HJE.]:~5ALBDC:²TE@G`=²W=>9<ST=E@;?Bi}A@~:S
]
¦ ä<ä QäWä ¥g¦ ä ¬…¦ €¡"® ¥Á¦ ä ¡u¡d­×­a¬Ì¦ ¦ D€¡w¡ ® ¥¡d­×¬Ì¦ D¡w® z
’”“
•P–˜—*™›š
¡>«`z Ÿì¬ÌH<® =.=I¬á[5®z
¬á[5® bÞuG:A?A@=.~:C STÊ= ©QÓ¥ Ó©¥ W]2HWC`I_ÙKdALG`BDC`=>;?}>==PÓ¨\DHW;@BD²<A=.Y:ALET;?B€ST}>9W= STa¥ST9WCßÓ
_|gB€jVáBi9WAL;9<;ZA@9W9JSTV =HXW]*C`HW_ C`_F˜BiE@A
G~`¡WA z
A@ÊB€©LC`ÓØ}>=u¥ÓîÓ5_|© B€¸j©ZBi_|9<=.;Au[+Ê©I9JE?¥G ÃHÓ ¸J©ÃC5_ HJC`"_FzÜeÔE@GHJ~`·WA =ÇA@~:¥;?=Ó ±<Ü9Wz(~˜Þu~:G:C`Bi_|A=.;?BDAALE?HHWC`}_
9WCHJE?\D;?^H<_|_|=BDEN}HJE@BDBD\9WA.C^z ]
¡>«`z ž « åWÖ ž ëW]:« ë<]|=E?}Wz
¡>«`z ä b A@A@~:STY|E?B€9<CI²WBDjW=´ê JêJ¥ ­ dHJC5_îê ÛêW¥ ­ Ç¥ ¬ ­ |®5­ ¸­
¡.â
Q
Q
Q
Q
Q
Q
Q
Q
.
+
Q
+
Q
T
;
+
+
.
$
+
.
+
"
-3.
I
+
I
-
+
CB
+
)1-/.0 Q
5/+
;
.
.
/
+
B
5/+
7 -
+
%
I
8
%
+
I
;45 +
+
;
%
+
+
(
%
%
+
+
-/.
%
%
%
+
%
%
R
+
$B<
"
U
.
.
.
N
’”“
•P–˜—*™›šU¯
¡w§|z Ÿ ¬á[5® OH"®>j<ê<=u¥ÕE@G`ê ^HJêDEU¤ê ¤­I¤ ­Ã꼤 ã¨ ê ¤ êWꀥÕdꀭ ¬á¤U ­˜ê ¤ ® ê M^ê㟠¤ ãÙ¬ ›¬@­ê ¤2 ê¼ã
®.ê ¦ €¡"®L꟬…¤­˜]WKd¤ G`® =>^;?êQ=›ãKXê ¤=d~5¬ ›AL=w­ _
E@Vá9WG`; =PV…HW}EÇ«5zê ¤ ꥔ꀬᤠ­Ù¤6®¸ã¤2ê Õê ¤ ­Ù¤2ê"ãÐê ¤2ê ÁŸ ã ê ¤2ê Á¦ €¡Xã ê ¤2ê
¡w§|z «¤¤ ¥ ¦ ¥gž ¦ £ ž ž £ £Pž ¾a£ ¡ 6«`HJ¡›C5_ ¥Áa¦ ¥ §WŸ|¡R£Ÿ]¤ ¥¿ ¡ «5¥Á¡>«¦ Ÿ:ž ¡ £ž ž +¾a²WBD¡jW=T«`¡>¤ «P ¥Á¦ ¥ §WŸ<¦ £Rž «Ÿ<¾ Ÿ|]W¡ =>«E?}W¥ z ¦ «Ÿ|]
©©
åå
¡w§|z §ØY+³O9<9`A@]XB€E@[5BDjW=w=W}>]5HJ~5HJC`AL=
_ B€VOE@G`=¥ \€BDSTBÂEZ¤¢¥ KM¡d9W~:­ \i_Ø[+=
\€=w¡dA@AÇ­ E?G`Ç¥HJÁC ¤Ç¡Ãã E?G:TV=>C á9<;ߥ ¬L¡P­ß`]`¤+E@®G`WHJŸFE›BDBDAA
Vá9<; ­Ù¡W]KdG:BD}NG˜}9WCE?;?H<_|BD}EÜE@G`=HWA?A@~:STY|E@BD9WCZE?G`HREç é}9<CjW=>;?²W=wA2E@9´¤ z
¡w§|z â¬ÌH<®Ôç.¤ k`­OŸ Ÿ ¤ ¢§ Ÿé
¬á[5®Ôç.¤ kW¤ ן Ÿ­¨Ÿ ž 9<;d¤ ߟ Ÿ›ãŸ ž é
¡"§|zD¡W¡¬ÌH<®(ÞuG:=3A@=.h~:=.C`}=µBiA*ç éO¬á9W·E@9›A@G:B€V E^E@G`=ÜB€C5_|= c ALBDC`}>=µKX=ÜHW;@=µ9<C:\€±}9<C`}=.;@C:=w_
KdB€V B€E@ÖGP E?G:= HJC5( _®Êzµ8`9W¥ ;dê ­ z êW¥ ê êW¥
¥ ã
©
¡"§|zD¡wŸ Çb A@¥ A@~:°ST=˜HJC5E@_G`HJE ¥©˜BDãgATH¡<z º º HW9W~`ST}NGY:±¨~|E?AL=Ã=wh<ê ~`©u=>­C`}><=W©z ê|HJº C5G:_˜99<_|A@=.= ;@BDjW=ÄHT}¦F9<CHWE@C`;N_ HW_|¨Bi}Ê]3E?B€HW9<C`C^_¨z ENHJ·<=
¡"§|zD¡ ž ¬á[5®F¡ ž
¡"§|zD¡w§ Vá9<=;›
E HJO \D _:=>C:9WE@Ø=¬ E@ÊG:®=Uz A@ST9 HW \€DBi=.AMALE@EuG`9J=V2\€HWBDST\€ BÂREOk A.[z ±Zº E?G`G:9=U9VáAL9W=U;?SZHJC HJ\^_|×=>à`¦:C:zÜB€E@ÞuBD9WG:C^=.zC Ü ­ ¤ ¡"§|zD¡.â ¡ «5Ÿa¡ ¥ž «<âW¡ ä«`£ ¡>ž « €] ^3*²<¬QB€j<¡ =.«5A ¡>«3*®*¬L¡ ¥Ð«¦®«5¥ ¡>«`¡Rë£Rª<ë ä:© ¡.¥â§ ¦ D]W«5=>¡WE?¡R}W£RzªJ«|¬ OS£ TDS(] 3*]+\D¬Q9¡ 9<«5·|¡wAM®V…HJ¥ STB€\DBië HJë ;w]:© \€BD·W¥ =
Ÿ­×¡Wz º 9<~:\D_˜B€E›[5=UE?G`HRE43*¬ Ÿ<®Ü¥ © © © ¥ Ÿ­ ¡ º G:=.}N· ®Êz
¡"§|zD¡.äØª
¡"§|z Ÿ ž ¬ÌH<®a¬Q­OŸ:ÖL«
¬á[5®a¬Q­ ž Ö>­¡"® a¬L­¡WÖ?Ÿ
¬Ì}.® €­OŸ|Ö>­OŸ ¦:Ö ®
¬…_`®a¬Q­ gÖ@¦® a¬Q¡WÖ ®
¡"§|z ŸR« Ÿ|Ö ž ®
¡"§|z ŸJâØ8`9W; +Ö î9WC:=(G`HWAê 3*¬ |®u5­ 3*¬ >®>ê3¥ ê (­ RêX¥ ê êÜ¥
ê êW¥ ê P­ JêKdG:=.;@= Ø¥ © -
%
-
-
%
I
%
%2%,%
%
<%
I
56.
.
-, -, %
.
<%
%
%
;
.
.
5 .
H
;
-1
B
.
I
.
5 .
6
56.
.
<%
B
. -/.
5H
56.
%,%
%
I
%
%
.
.
;
B
;
-
;
;
;
;'-
;
;
;
;
5
;
;
.
;
.
;
;
-1
CB
K
1
<%
<%
%,%2%
%,%2%
%
1
3
%
.
%
8
.
8
%
5
%2%,%2%
%
8
.
%2%,%
.
8
.45
.
5
-
5
1
-
.
5
¡.ä
)
5
0G)
5
-
0
’”“
•P–˜—*™›š
#
¡.ª:zD¡FE?{9TAL=´E@G:E@=G`==whMB~`iHRALE?=wB€}Ê9<E@C˜BD9W¤ÇC ãb \D¦ ²W 9W§d;?ãB€E@G:ŸÜS }9<E@A9˜Û¤˜à`C`¥g_F¦ÇHÃ9WA@C(9W\DE?~|G:E@=UBD9WB€C C]6E@=.H<;@}>jR}>HW~:\ ;?HJ¦ E@=§:Ö>E@9á § KdzB€E@G`B€Cס.¦ ©R]
¡.ª:z ŸØ;N{HRALE?=O=E@E@G:9Z= KdMBB€E@DA@G:=.BD}CÙE@BD¡.9W¦ C b ëJz \€²<9W;?BÂE?G:SÕE?9Pà`C5_IHJCÃHWY:Y:;?9 c B€SZHRE?B€9<CÇE@9 ž E?G`HREMBDAMHW}.}~
¡.ª:z ž E?82B€BD9<C`CI_
E?HT9[5E?G:9<=~:C`=wh_Ã~`VáHR9WE?;uB€9<E?CÃG:=¤5Cåµ~:ãÔS¤´[+­
=>;›«´9W¥ÁV¸B€E@¦P=.;?9<HJCIE@BDE@9WG`C`=AuBDC:C=.E@=.=>;?_|jR=wHJ_I\ E?Â9I¡<ÖLHJ« Y:+Y`E?9´;@9 HWc C˜BDSTHWHJ}.E@}=U~:;NHTHW}>AL9<±´\€~9WV
¡w¦ åRz
¡.ª:z « 9Wb VXE@H(;?9WAL~`=.SDzWGBi}9JBD;NVX}KM\D=HJKdE@=>B€;E@GÔ9JVÜ;NHW\D=>_:C:B€~`²WAE@G Ãg¥ ¥ ¡´¡.Vá9¦T9JVáEw=.z =EU¢GG``HW=>ACFHIà`}>\€;@D=.9_ÔA@AKdALBÂ=wE?}ÊGFE@BD9WKuCÔHRE?B€=>CÔ;E@E@G:9˜=ÇKdALG`BÂE?HWG:Y5B€C =
E?HÃG:_|=UBDALVá9WE?HW;?SC`}~`= \DH 9JV*E?G:=PE?9WY^]`E@G:=´jW9W\D~:ST= ¥ ¡wŸ « 3 QåU9WV*E@G:=´KMHJE@=>;OBDAO²WBDjW=>C
[±
¡"Ÿ «P¥¡.¦ ¦ § íÙHJ;N}>A@B€C T­ ¬L¡d­ © ® ©
» =E?=>;?STB€C:=UE?G:=P_|=.Y|E@G
9JV2E@G`=KMHJE@=>;uE?9TKdBÂE?G:B€C¦ ¦`¡Vá=.=Ewz
¡.ª:z § E?|G:~:=>Y:;?Y+=Z9<HJA@;?= =´3*HW¬…CÔ¤+®9|G`_:HW_FAC9W~`C`S\€±[+=>A@;UB€ST9JY:V3\D;?=´9;?9J9EN9JAEN9WAOV BDC 3*¬á¬¤65Ö®¥ ®ÊzU¦˜¶ÒV B€Cß3*¬¬ |®+Ö 3*>®Ê¬ zP® ¶ÒV 3*¦`¬ |®]ÛAL3*G:9R¬ K® E?G`HR¦:E ]
BDA@C¨G:9R¬ K+Ö E?>G`®ÊzHREE@G:=.;@=ÇHJ;?=HJCî=.jW=.CîC~:S[+=>;T¬áY+9<A?ALBD[:\D±
Ú>=>;?9®›9JVÜ;?99JE?AO9JV 3*¬…¤+®›¥¦
¡.ª:z ª Bi|A›G:}>9R9WKaC`ALE@E?G`HWHJC<E^EwE@z G:= MBDA@=.}E@BD9WCST=E?G:9|_}9WCj<=>;?²W=.A6\DB C:=.HW;@\D±W].E@G`HJE¸BiA>]w\DB€S
¡.ª:z £¨82BDC`_
HJ\DÛE@G`=;@99JENAM9JV2E@G:=UVá~:C5}ÊE@BD9W"C 3*¬…¤+®3¥g}9<A:¤I­a}>9<A ž ¤ z
¡.ª:z â82BDC`_˜E@G:=;?99JEd9W;d;?99JENAu9JV¸\DC D¬Q¡MãØ¤+® |¬L¡d­F¤+©w® 6¥g¦`z
¡.ª:z ä82 BDC`­ _
ž Kd¤˜G:¥Á=.;@=U¦TE?}G:9W=P;?;?²W=.;N}ÊHJEMY`E@G`9TAuVá9J9<V~:;›Z_|¥ =w}ž BD¤îSTHWHJ\^C`_|_ BD²WIB€E?¥ A.z BDCE@=>;NA@=.}ÊE›[±Ãà`C`_|BDC:²I;?99JE?Au9WV
¡wª:zD¡.¦ ²<º ~`9<HJC`;NA@HJBDC_|E?=.=>;µ=UE@G`HJ=›C
[:HJBiY:ALY:=w}Ê;?E@9 BDc 9WB€CZSZSTHJE@=>BDE@9WG:CÃ9|9W_ÛV*]HÇ_|=;?E?9=>9J;?STEuE@B€C:9Z=OA@BG:c 9RK_:=.SZ}BDSZHWCHJ±Ç\^AQY`E?\D=>H<Y`}AX=.AHJ;?¬…=u;@9<;@~:=wC`h<_|~`=wB€;?_`=.®Ê_´z E@9
¡wª:zD¡W¡ =wM±hT~`HR²WE?;NB€HJ9<Y`C˜G:BD\D}.C HJ¬Q\5¡uSÇã¨=>¤6E@G:® 9|ãÙ_:A.ENHJ]C\€9|¬ }.ŸRHR¤6E@®Ü=¥gHJY:¦`Y`z ;@9 c BDSTHJE@BD9WC`AµE@9THJ\D5;?99JE?A39JVÛE?G:=C`9WC:\DB€C`=.HJ;
¡wª:zD¡w
Ÿ STXh=>~`E@G:HR9|E?B€_˜9<C E@9Z¤ =w AQ E?B€­ÁSZHRŸ E?= ¥°´¦aKdB€G`E@G:H<BDAICHÙAL=.ALjWBDST=.C(Y:_|\€==w};?BD9SZ9JHJE \^a_|BDB€²WC B€E?A.¦:z Ö>¡ zg{AL=
E?G:=[:BiAL=w}ÊE?B€9<C
¡wª:zD¡ ž Vá{9<AL;d=P=.E@H<G:}N=´G˜[:=wh<BDA@~5=.HR}E@E@BDBD9W9WCC z ST=E?G:9|_(E@9Zà5C`_Û]6HWAOH<}>}>~:;?HJE@=.\€±ÃH<A›±<9W~}>HWC^]5HW\€¸;@=wHJ\^;?99JE?A
¬ÌH<®˜¤5园F¤+©d­F¤Ã­ ¡¥g¦
ŸJ¦
%
%
%
-
(
-
(
-
%
%
%
.
%
%
U
1
+
B
%
# Q - #
# Q - #
¬á[5®˜¤5©¥ ¬Ì}.®˜\DCê ¤*ê<¥¢A@BDCd¤
¡wª:zD¡>« b }>=>;@E?HWB€C˜E@=w}NG:C:Bi}>HJ\ÛY`;@9<[:\€=.SÑ;?=.h~:BD;@=wAuAL9<\€~|E?B€9<C˜9WV E?G:==.h~`HJE@BD9WC
Ÿ|¡ €¡ ž ­ ž « âW¦ ­Ù§ ¦<âµ\D9W² g¥g¦
VáA@9<G:;X9<~:HU\DE?_î=>ST\€BD=Y:;N[+HR=E?EQ~:KM;@=>= =.PCîz2«<Þ¸¦<¦=.P}NG`HWC:C`BD}._îHJ\:§J¦<BDC|¦ VáJ9<z;@SZ{OHRA@=PE?B€9<E?G:CZ=B€C5[`_|BDA@BD}.=.HR}E?E@=.BD9WAµCîE?G`STHR=EXE?E@G:G:9|=›_
E@=>E@9˜STY+=.AL=>E@;NBDHRSZE?~:HRE@;@==
E?G:=P_|=wALBD;@=w_IE?=>STY+=>;NHRE@~`;@=UE?9ÇC`=.HJ;?=.ALE›_|=>²<;@=.=Wz
¡wª:zD¡w§¨9W{V AL=3*¬…E@¤+G:®3=Ç¥g[:BiALALBD=wCd}ÊE?¤ B€R9<¤C9WSÇC(=>E@B€CG:E?9|=>_Ô;?j"KdHW\ BÂE?GÔµÖNALŸ 9< STÒz=´}>HW\D}>~:\D~`AdE?9Ià`C`_E@G:=ÇSTB€C:BDS~`S jRHW\€~:=
-
;
%
B
%
¡.ª:zD¡ ¥Á¦ £¡W¡
¡.ª:z Ÿ ž ë ¥¡ £ ž ŸW¦
¡.ª:z ž © ¥¡ ž £Râ£
¡.ª:z « å ¥g¦ D¡.ª`¡"£AL9ÇE@G`=P_|=>Y|E›BiA ­ ¡d­Ù¦ D¡.ª:¡R£¥g¦ ⠞ âPVá=.=E
¡.ª:z £×ç"¦:Ö JŸ|Ö µÖ ž JŸ|Ö Ÿ Lé
¡.ª:z âØ¤
¥¢¦
¡.ª:z ä¦ ª`¡.ä<¦Wª:Ö ¡ §:¡wŸ:¡ ž
¡wª:zD¡.¦ŸW¦TAQE?=>Y`A
¡wª:zD¡W¡¨_:ç"¦:=.}Ö ;?=.
ë H<ãAL=wA>z Ö å ë ã Ö í ë ã Ö Êé<]5KdG:=>;?=ÇALE?HW;LENA›HREOHWY:Y:;?9 c BDSZHRE?=>\€EU¡ JŸÇHJC5_
¡wª:zD¡wŸ P¥Á¦ â<§WŸWªW¦§W§
¡wª:zD¡>«Ø«|£J§ ’”“
•P–˜—*™›š
¡.â:z Ÿ Ü=wA ¥¡<Ö ´¥¡ ž
¡.â:z ž ¬ ®ÊÖP¬ >®
¡.â:z « ³O9
¡.â:z ª³O9
%
%
.
%
.
6B
%
"
%
.
6B
%
@B
%
CB
%
%A%'%'%
A%'%A%
%
Ÿ|¡
y
y=x
y=g(x)=100+0.2x
100
x
_
x
82B€²<~:;@=T¡.«`k ;?9W[:\D=>S ¡wä:zD¡
’”“
•P–˜—*™›š
¡.ä:zD¡ Û¬M;á?¤6=.®3HW·´¥ =.¡.jW¦W=>¦›CÃãBÂV¸¦ A?HJ ŸR\D=.¤¸A3z ¤˜=wh~`HJ\iA3= c Y5=.C`AL=wAO¡w¦W¦ÜãÔ¦ ŸR¤ ]E?G`HREMBDAMB€V^¤(¥ Û¬á¤6®ÜKdG`=>;?=
¡.ä:z Ÿì¬ÌH<®(¤58:9<å›;P­F= ¤+c ©dHWSÇ­ÙY`ŸJ\€¤I= ­×3*¬…¡›¤+®¥Á¥ ¦ © ­ ¤×¥Ñ¦9W; 3*¬…¤+®´¥ ¤5åU­Ð¡U­¤¸¬…¤(ãgŸ<®P¥
¬á[5®(8:9<;d= c HJSTY:\D= 3*¬á¤6®3¥ß¤+훭a¤5åXãØ«­F¤˜¥Á¦Ç9W; 3*¬…¤+®Ü¥ ë ­ ¡¥Á¦:z
¡.ä:z ž ¬ÌH<®(8:¬ 9<¤5;ÃíM= ãc HWST® Y:\€=Ôå ¤ ¥ Û¬á¤+®î¥ ¤Ù­Á¦ D¡<¬Ò£"¤5í­g«W¤+åPãŸW®Z9<;I¤ ¥ Û¬á¤6®î¥
¬á[5®(¤˜8:ë9<¥ ;˜6¬= c …¤+HJ®3©ST¥ Y:\D=Ô¬ ž ¤T¤”ã ¥ © Û¬® á"¤+«`®az ¥ ¤F㦠ž ¬ © ­Ð¤5å"®Z9<;˜¤ ¥ Û¬á¤6®F¥ © 9W;
¡.ä:z « |·BDY:Y`H<A
ˆm:"‡r:‰|Š6n<o<xdž´vRr+¥g¥ßˆJ‰Wm:Œ Š|Œ m¥ ˆ"m|n†<`‰5ˆ.Š|rÛ¬ 6Ö@m|Œ5ÖÒq+l<m ˆwr:n<x6ÖLr:‰|o®
mZm ¥ßŠ`nWm „Ç¥Á‰|o<n† :l|o5¬ :®
¡.ä:z § „sÛmTˆWo¥¢n`ˆ"m r:n<‰xo<† aq6l<m ˆ"r:n<x Pl 6y:¬ám Š`nW„­am ‰|o<†|® r:‰|o
mˆ"r:Š`nWnJxT„Ç¥¥Ðˆ"n r::nWlxUo5ãÁ¬ |®
mZnWŠ:¥ß† m Š`nW„
¡.ä:z ª 6HWC`=>_îKd;?;?BÂ=.E?A?=d}>HWE@G:\€==[=.±
h~`BDHJCE@E@BD;?9W9CZ_:~`¤¸}¬ÌBD¦ C:¦<² Ÿµ
ãŸJ¤+¡.®L¦<©u¦J¥ ¤ÔE@¡ 9Ãâd9<¡.[|¦ E?HWíuB€C HWAO6¬¡.Ÿ¦<¦µãߤ¸Ÿ ¬ |Ÿ*® ãÔ© Ÿu¥ ¡.¦<¡wâ:¦µz ¤+®La;©X?¥ BÂE?B€¡.C:â:² ]
E?G:BiAÜHWA T¥ 6¬ :®Ü¥ © © ]RE@G:=uà c =w_Y+9WBDCEµBÂE?=>;NHRE@BD9WC5A ¥ Û¬ ®¸_:9=wA*C:9JE
ŸWŸ
%
%
8-3.
5
-
-
8
%
.
.
%
8
B
8
1
)
%
. /
5 0 ;
<%
-
56.
}>9WCjW=.;@²<=WzuÞ ;?±(B€C`ALE@=wHW_ Ã¥ Û¬ :®u¥”¬ Pã © © Ÿ ® J¦<ŸÇ¦W¦<Vá¦W9<¦W;O¦<Kd¦W¦<G:¦WBi}N¦WG
¦<¦WE@¦JG`¦ =B€E@=>;NHRE?B€9<C
¡¡ ¦<¦<ªWªWäW¦`«W¡.«W¦ «<ž «WäW«<ª`«W¡"«W£R«<â «Wž «J§R«¦
¥6¬ ®MKdBÂE?G ¥ÁŸ´²WBDjW=wAME@G:=PA@=.h~:=.C`}= ¡¡ ¦<¦<ªWªW¦¦ŸJŸJ¦W¦â<£|ªW¡ ªž<ž£W££W£W¡"§JŸJä¦Wž§
¡¡ ¦<¦<ªWªW¦¦ŸJŸJ¦¦£|£|¡w¡w§W§<ª:§Jâ<¡.â§§J£J¦J§Rªª
¡ ¦<ªW¦ŸJ¦£|¡w§<§JâWªŸ ž §
E?G`HRE›BiA.]:¤˜¥ |¡.¦W¦ ¦ ¦`¡.¦<ªW¦<ŸW¦£|¡w§W§Wä:z
.¡ ä:z £ 6Ÿ :=>®QKd©O;?¥ BÂE?=u¡ E@ §<G:£=dz =wa;h<~5@HRB€E@E@=UBD9WE?CÇG:¤¸BiA›¬Ì¦ HWA ¦ žZ£Û¥ ãÃÛ¬ŸJ¤+:®Q®3©O¥ ¥¡ §<£Mí ¡w¦ HWC`Kd_(B€E@}G 9WÇST¥ Y:~:¡.E@¦<= ¦W ¦J¤THWA ¥ ÛÛ¬¬ ž £Û ã ®
å ©
KdB€E@G ¥ ¡E@9Z9<[|E?HWB€C
¦¦¡ ¦W¦W¦W¦<¦`¦`¦W¡W¡W¦W¡>¡>««¦<¦WªWªW¦<ª<ª<¦WäJâW«¦W¦ ¦<ž§ «¦WžW¦<žž ¦JäWŸW¦§£ E@G`HJE›BDA.]|¤(¥ |¡.¦<¦W¦ ¦ ¦W¦<¦W¦<¦:¡W¡.«<ª<ªWâW¦ ž z
¦ ¦W¦`¡W¡>«ªWª<âW¦ ž «§W¦ ž
.¡ ä:z â 6HWC`=>_Kd;?}BÂ9<E?ST=d=.Y:h~|~`E@HR=´E?BÂB€E?9<=>C
;NHR¡›E?=.¥ Ad¤ å ë ¥ Kd6¬B€…E@¤ GT¤(®dKd¥ BÂE?ÁGîH<¤ A*¤(¥¥ Ÿ|Û¬z›áÞu¤6G`®ÜBD¥¢AO²W¤OBDjW­(=.Ad¡ E@§`G:¬ =Çå AL=w h<~`=>­
C`}>¡w=®
9WV2Ÿ B€¦WE@=.¦<;?¦WHJ¦WE@¦<=w¦WA ¦<¦W¦W¦<¦W¦<¦J¦
¡¡ ¦WŸ<ä<£WäŸWžŸW§J§W«`¦ ž¡"ä:§WŸW¡WŸW¡ â<ž «|§J«£Jž£
¡¡ ¦<¦W¦ŸWä<£WŸJ£â<¡wªWäWª`¦ ž¡WäW¡.â<ª<äW¦<ä`Ÿ<ŸJ¡>âŸ
¡¡ ¦W¦W¦`¦<¦J¡.«<ä<ä`§£R¡Wª<¡w¦ä<ž§Jâ<ª<ªWä:ª¡wâJ£"ââ
¡¡ ¦W¦W¦<¦<¦:¦W¦¡wžŸ<¦ŸJä`£ ž¡wŸJ§J¦W¦<«`ä:¡¡"ž§W££
¡¡ ¦W¦W¦<¦<¦W¦W¦W¦W¦¦`£R¡.äª<âJŸ|«¡.¦<Ÿ:â:¡w§W¡wªJªJ¦ä
¡¡ ¦W¦W¦<¦<¦W¦W¦W¦W¦<¦<¦J¦:«¡"âWŸJ¦<¦W¦<ŸªW£Jâ`Ÿ:¡¡«ž
¡¡ ¦W¦W¦<¦<¦W¦W¦W¦W¦<¦<¦W¦W¦¦<¦ž ¦W£J¦`§W¦J¡"«£J¦RŸR«ª
¡¡ ¦W¦W¦<¦<¦W¦W¦W¦W¦<¦<¦W¦W¦<¦<¦:¦W¦J¡.«âªW£Rä<ª<¦W¦<Ÿ£
¡¡ ¦W¦W¦<¦<¦W¦W¦W¦W¦<¦<¦W¦W¦<¦<¦W¦W¦:¦W¦¡<ŸJ¡"ä£WžŸJ§¡
}>9WCjW=.;@²<B€C`²PE@9¡<z
¶ÒB€E@E?=.=>;?;NHJHRE@E?=wB€C:A ²˜KdBÂE?G Û¬á¤6®O¥ ¤ZãߟW¦`¬ å ­¢¡w®HJC`_¤ ¥Õâò<B€j<=.AOH(A@=.h~:=>C5}=9WV
Ÿž
B
. /
5 0 ;
%
)
%
%
%
R
56.
%
%
%
%
B
%
%
<%
<%
)
R
-
8
.
56.
5 0 ;
<%
%
B
%
%
%
)
;
530 ;
56.
%
.
%
<%
<%
<%
<%
<%
<%
<%
<%
<%
<%
<%
<%
<%
<%
<%
<%
<%
<%
)
. 7
5
0 ;
R
)
. 7
5
0 ;
ââ ¦WäW¦<â ¦Wž ¦WªW¦<äW«`¦W¦<¡"¦WŸJ¦Wâ:¦<¡"¦W§J¦<¦<¦J¦J¦ä
äâ ¦WäW¦`ä<ä¡.â<£RäŸJ«<£"«|¦£J£Rä<ŸJâWŸ«£Râ<ŸªJ£"äª
äâ ¦WäW¦<ä<¦WäW¦<äWäŸ<ŸW£"«§W¦JäW«ä<ŸW§<¦:§Jª<¡"ªWŸR¦§
äâ ¦WäW¦<ä<¦WäW¦WäW¦<ä<¦<äWä<ŸªW£Wä:£Râ¡ žŸ<¦£ žJž ¦ž
äâ ¦WäW¦<ä<¦WäW¦WäW¦<ä<¦WäW¦<ä<¦äWžäW«ª`ŸJ¡.â<ä<âJäJäª
ä ¦W¦<¦W¦W¦<¦W¦<¦W¦W¦W«Ÿ ž «
}>9WCjW=.;@²<B€C`²PE@9Iä`zd¬ 3h~`HJE@BD9WC
}>HWC(HW\DA@9T[5=PA@9W\DjW=w_ÃHJC5HJ\D±<E?BD}.HJ\D€±IVá9W; ®
¡.ä:z ä Û¬6 á=>¤6Kd®P;?¥BÂE?=´¦ E?G:¦`=Z¡W¡d=.ãßh~`«HJ§E@BD|9W¬ Cןãg¬ÌŸU§Wã ¦ Rí ¤5©>®®¬ HWC`­_Ù¦}9<¦:SÇ¡<Y`¡w®O~|E@¥ =IB€ž E@=.¾Ø;?HJ¡wE@§Ã=wAUKd¤ B€E@Ga¤¨¥ ¥ Û¬ ᤠHW®AUKd¤¨BÂE?¥ G
¤ ¥ÐŸJ¦E@9Z9W[:E?HJBDC
ŸJŸ|¦¡ ¦<ž ¦WŸR«<¦W¦<¦<¦Wª ¦<ž ¦W¦J«`¦W¦<¡w¦Wâ<¦<Ÿ¦J£w«<¦W¦ä
Ÿ|Ÿ|¡¡ ž<ž<žž âJäW«äžŸJ¦Wª«`£JŸ<¡.¦£R«Wž «§<§ŸJž§ ªž
Ÿ|Ÿ|¡¡ žž «<«<¦W¦W¦<¦<â<äWâŸJ«<§J¦<äŸ<£J¦§Jª<£|¦<¡w£R£J¦§
Ÿ|Ÿ|¡¡ žž «<«<¦:¦:¡w¡w¦W¦W¦¦W«ŸJâ:§Jª<¡Rä£JŸW£<ä|£"âW¡wª§
Ÿ|Ÿ|¡¡ žž «<«<¦:¦:¡w¡w¦W¦W¦W¦W««£J£W§<£|ŸJ¡.¦<¦W«â ž£R«ä
Ÿ|Ÿ|¡¡ žž «<«<¦:¦:¡w¡w¦W¦W¦W¦W««£W£W££ žž ¦Ÿ<ŸRŸJ¦§Jä£
¡wä:zD¡.¦ ;@99WV¸[±IBDC`_|~`}E@BD9WC^kÜÞ¸;@~`=UVá9W;dÀ
¥ ž z b A@A@~:ST=E@;?~:=UVá9W;dÀµzÜÞuG`=>C
¤¥ ¥ ë ¤ã ã ë ¥ ë ã¬ ë ¤ ¥ ã ã ë ®¸ã ë Ö
ë © ë ë ë ë
A@G:9RKdBDC:²ÇE@G`HJEdVá9W;?S~:\iH´j"HW\€Bi_˜Vá9W;dÀI㢡<z
¡wä:zD¡W¡¬ÌH<®˜¤ ¥ÁŸ ¤ ã ë Ÿ
¬á[5®([+8:9<=.}>;ÇHWHW~`CA@±F= ²<B€j<=>C Ÿ ¥¬Q¡d¦Ô­¨KXŸ =(G`H"®>j<¬Q=Z¡›­¨E@G`ŸWHJ®ÜE´¥Á¤ Ÿ ­×¡WB€VOz À¢BiA´\iHJ;?²W=Ã=>C:9<~:²WG^]
¡wä:zD¡wŸ ¬ÌH<®˜¤ ¥ ¬ åë ® ã å ë ¬á[5®(82B€;NALE*KM=uY59<B€CEÜ9<~|E*E@G`HJE ½ BDC|Vw¬ ëå ® ¦:z*ÞuG:=>CÇKM=M\D99W·HJE*E@G:=›A@~:S
å ë ¥ å ¬ åë ® ¥ å ¥ å ¥ ëå
¡wä:zD¡ ž ¤ ¥¢½ ¤ 㠟R«
%
%
%
%
%
%
%
%
%
%
%
R
%
%
;
B
B
56.
R
%
%
%
%
%
%
%
%
%
%
%
%
.
+956.
.
Q
+
+
+ +
+
+
.
R
+ ..-
.
Q
Q
.
Q
.
.
.
+9 56.
.
+
1
+956.
.
+ +
R
.
+<56.
R
+
+
.
.
1
.
+ .
+9 56.
.
R
.
+
.
+
+
+ 56.0
. .- ) 8 0 <
?
.- 8
?
.
.-
.
?
8
.
y
1
y=g(x)
¡.ä:zD¡>«
x
1
28 BD²W~:;?=T¡w§:k ;@9<[:\D=>S ¡.ä`z€¡wª:z
a=ê ½(I¤TA@ã G:9RMK­×E@G5¬…½HRE 6¬ã …¤+®U®>ê¥ ¥”½(ê ½Ù¤ZêDã ¤˜­BiÛAêH(¥ }>9WCê ¤IE@;N­HW}E@^BDê9Wz Cî SZHWY:¡PY:A@BDC:9 ²`˜BkIiê A›6¬…HI¤+®X}>9W­CE@Û¬;NHW:}®>E@ê6BD9W¥ C
SZÞuG`HW=PY:Y:ALBD9<C:\€~|²E?HWB€9<C`C˜_BiE?A G:=M¤˜ à ¥ c Y59<|B€¬LC¡uE*­FBÂE?½=>;NHR®ÊzE?B€9<CG`H<A¸H~:C:Bih~:=MA@9W\D~|E?B€9<C[±PÞuG:=>9<;@=.S”¡.ä:zD¡Wz
¡wä:zD¡>« ¤» ;NH"K €¡ Vá §|9<ÖN;3Ÿ = Òcz HWSTY:\€=›E@G:=OVá~:C`}ÊE?B€9<C Û¬á¤6®Ü¥ÁŸJ¤­ ž Vá9<;3KdG:Bi}NG 6¬…¤+® ¦:Ö>¡ ]KdG:=.C
¡wä:zD¡w§¨³OA@9W=>\DjW=w_=E?E@G:9˜BDA›·C:Y:9R;@9<K [:\DE@=>G:S
=Tz ALY+=.}>BÂà+}à c Y+9WBDC<EVá~:C`}E@BD9WC`A~`A@=._BDCE?G:=˜¡wä:z ž Y:;?9W[:\D=>SÄE@9
¡wä:zD¡.ª¨¶ÒBDCV E@=.…¬;@ájR¤6HJ®M\ z BDAu[+¬…9W¤+~`®›C`¥ _|=._˜BD©Cà E?G:=UB€æ CE@=.ß;@jR¥HW\6STE@G:H =.c C Û¬á¤6®3Biê A ^© BD Y`A?}NG:ê B€E@Ú¡ }9<æC<E?B€C`kB€9<~`AM+ÖB€C˜E@G: =
+ÖE?G`HREÒ]6B€V3E@G5E?G:HRE=ÇBDALA E?HWB;LE?iB€AUC`²˜H˜Y+}>9W9WCBDCE@;NEHWBD}CÔE@BDE?9WG:Cî=´SZà HJc Y`=._FY:B€C`Y5²`9<zB€ CM±EU
BÂE?=>E?;NG:HR =>E@9<BD9W;@=.CFS ¤ ¡.ä:z ŸZ+ÖKM=Ç*C:E?9RG:K =>CFG`H"E@G:j<==
A@=.h~:=.C`}=U²<B€j<=>C([±IE@G:=B€E@=.;?HJE@BD9WC
}9WCj<=>;?²W=.A3E@9IH ¤ 5Ö Òz
¡wä:zD¡"£Ù{AL¥ BDC:¡W²
ÖNŸ|ê ¤ Ö ž ÖL«­˜Kd¤BÂE? GZê _:HREN H Váê ;@¤ 9<S­˜E@¤ G:=›êJE?KMHJ=O[`\€}>=<9Wz2STÞuY:G:~|=dE?=´;?=.¬@A@ê~:¤ \€ EÜBDA3­Ã¦:z ⤠£J §›ê :Váê 9W¤ ; ­Ã¥¤ ¡Wê ® ÖNŸ|Ö ž VáÖL9W«5; ]
G`=>C`}>= ¨¥Á¦ â£W§|z
¡wä:zD¡.⨶ÒBDCV E@=.;@¬ájR¤6HJ®M\ z BDAu[+…¬á9W¤6~`®XC`¥ _|=.ë_˜ BDCÃE?G:=UB€CE@© =.;@jRHW\6 E@ G:=.C æ Û¬á¤6®3BiA ^BDY`A?}NG:B€E@Ú}9<C<E?B€C`B€9<~`AMB€C˜E@G:=
ë
©
¥ÏSZH c ê
¦E?G`¦HR§ Edž B€V ÕE?G:¡Ä=AQæ ENHJ;@E@
BBDC:D²´AUY+HI9W}>BD9WCCEdE@B€;NC˜HW}E@E@G: BD=9WCà c SZ=w _IHJ Y`Y+Y:ê´9WB€C`BD¥C<²`Edz X±B€êE@(=.;?E?HJëG:E@=>BD9W9<CÃ;@=.ã ¤S°¡wä:©Âz ŸT­¡<KMÖ>êÇ=¡ 6¥C:E?9RG:K=>å ©C˜G`H"E@G:j<==
A@=.h~:=.C`}=U²<B€j<=>CÃ[±ZE?G:=B€E@=>;NHRE?B€9<C(}>9WCjW=.;@c ²<=.AÜE@9ZH ¤ 뀭 ¡WÖ.¡ Òz IBDAu© C:9WE› HÇ }>9WC
E?;?H<}ÊE?B€9<CSZHWY:Y:BDC:²dB€C ¼ä:z ä:] ä:z ä Òz ¨¥gSZH ê
ê<¥
ê ë ã © ê ߟ W¡.¦ ]|KdG:Bi}NG(BiAu\iHJ;?²W=>;ME?G`HJCÙ¡Wz
'B
",$
,
%
<%
K
) .45
; 0 ;
) .45
; 0 ;
2,$
56.
R
.
$
,
R
B
56.
.
R
.
%
K
%
8) . R -
01;45
) . R 0 ?
) . R 0 ?
8') . R 01;5
) . R 0 ?
) . R 0 ?
-3. . ) . R 3
- .40 ;
2,
(
) . R
5 8 8
- 8
0 ;
) . R
5 8 ?
- 8
0 8
- 8 8 ŸW§
/
) . R -/.0 8
R
,$
"
8 ) . R 0 ;45
) . R -
"
(
) . R 0 ?
0
?
¡wä:zD¡.äØ{A?}NALG:BDB€C:E@²˜ÚZE@}G:9<=TC`ALSTE?HJ=CE?EG:9|E@9
_î[+Vá;?=I9WS ¦:z ªWä<;@§J9<«`[:]Û\D¦:=>Sz ª:¡"¡.§Wä`Ÿ:z€]+¡R¦`£Çz §WKXâW=Ǫ£|²W]Û=>E¦:z E?§JG:ªW=T⠞ =.ALVáE@9<BDSZ; HRE@=w¥ÄAVá¡W9WÖN;Ÿ|Ö E@ž G:ÖL= «5^]+BD;?Y =
²E?<A@G:Y+B€j<=.=.=.A@}ÊAd=PE?B€¦`j<}9<z=>ª<\DST±Wä<z§RY:«˜~|b E?]`\ÂHJE?¦:E@=>BDz ;?§R9WC`«<C`HR« AdE?ž B€A@j<G:]`=>9R¦:\DKÁ±z § KXž<E@G`ž =T«ÃHJ}>Ed]5HWE@CÔ¦:G:z =P§|}¡.9<}>ªSÇ9W§UCY`jWVá~|9<=.E@;;@=î²<=>ê ¤C`¥ }> =O¡WBiÖNAuŸ|­¨ÖC:ž 9J¤ ÖLE› «5ê\D]<:B€C`;?ê ¤=.=.A@HJY+;w­Ø=.z }ʤE?B€ j<=>\D±Wê5z KdM9G:JBi}NE?GG
¡wä:z ŸJ¦ì¬ÌH<®˜E@¶ÒVG`=´BD¬áC¤6E@®*=>Bi;?AµjRHJ[5\ 9<z ~:C`_|¬á=w¤6_T®OB€¥ CTE?ŸRG:¤+=›©JzBDCÁE@=>;?¥ jRHJST\|E?H G:c =>C Û¬á¤6®*BiA ^BDêY`A?}N¬…¤+G:®.BÂE?ê+ڛ¥Ä}9<ê C<Ÿ E?|B€C`¬ B€9<®Q~`©Aµê`BD¥ C
© ©
©
¦ §|z
¬á[5®
¬Ì}.®˜E@¤ G5HR¥ E ¤˜Û¬ á¥Á¤ ¦´KM®Ü=U¥ ²W6¬=>E.¤kO ãaê ¤ ¤ ­ ¤2 ê<­ ¥Õ¤Û ê®Ü© ¥ ¬…¤ ©å ¬ ¤P ­ ãg¤6 ¬á¤® å ê ­ ¤6 ®@®Qå<zµ{OA@B€C:²ÇE?G:=V…HW}ÊE
¡wä:z Ÿ|¡Ô{AL=PHWST9WC:²AQEu9JE?G:=>;uE?G:B€C`²<AuE?G`HRE›¤ å Ÿz
¡wä:z ŸWŸ ¬ÌH<®˜¤5©+ãZ¤d­Tª¥¢¦ ¤2¬á¤Xãî¡w®3¥Áª ¤˜¥ zµÞuG:=u=.;@;?9W;*BiA*=.ALE@BDSTHJE@=w_
[¤ ±aê ¤ êÂ]^­KdG:¤* =>ê<CF¥ E@G`ê Û¬=TᤠA@=.h~:®*=.C`­ A@=´Û¬ 9W¤6 V3®>E@ê<G`¥ =´à c =w_ÔY+­9WBDC EBÂE?=>;NHRêE@BD9W CF G` HW AU}>ê 9WCjW©å=.;@ê ¤I²< =.­ _
HJC5_ä ¤2 z
¬á[5®˜¤5 ©Û㘤Oz¸­IÞuG`ªP=X¥g=.;@¦;?9WHW;¸_:BD_|A¸BD=.C:AL²E@BD¤+SZ©dHR9WE@CT=w_P=.~`H<}NA@GZBDC:²ALBi_|¤( =d¥Ð²WBDŸ›jW=wHWA>C`k2_ŸR¤5¤ ©Û㘥 ¤˜Û¬¥ß¤µ ã(¤+©6¬á¤ ã(ª ­ ¤+ ®@¤˜®Ü¥¥
© ¥ ë © zdê ¤ ­ ¤µ êW¥Õê Ÿ3㠭ԟ5êJ¥
ë
í
ê © í ê ¡wä:z Ÿ ž BiÞuAXG`²W=3BDjW=.=>hCÃ~`HJ[E@± BD9WÇC¥ Vá9<;^3*E?¬á¤G:=3\DB€C`®5=Üã E@G` ;@9< ~: ²W GE?¬ 3*G:=3¬…¤ Y+9W®6BD"­ CE?3*AM¬á¬á¤ ¤ ®ÜÖ 3*Kd¬áG`¤ BD}NGZVá®L9<® ; HJZC`_Ã¥¢¬á¤¦G`Ö 3*HWA3¬á¤ E@G:®L=®
AV…@H<9W}Ê\D~|E?9WE?B€; 9< CÔ¤ ¥ ¤ ­ 3*¬á¤ ®>¬á¤ ­¨¤ ® |¬ 3*¬á¤ ®3­ 3*¬á¤ ®@®Êz º 9WCjW=.;@²<=>C`}>=
’”“
•P–˜—*™›š ŸJ¦:zD¡ ;@99WVM¬á= c HJSTY:\D=W]:HJC5HJ\D±<E?BD}.HJ\ ®X9JV ¬ ®X¥¬ ® +k M±Ã_:=à`C:B€E@BD9WC
¸¬ |®3
¥ ¬ ܬ Ö © ®L®X¥ ¸¬ Ö © ®3¥ ¬ ¸¬ ®Ö ¸¬ © ®L®
HWC`_
¬ ® T¥ ¬ ®¬ Ö © ®Ü¥ ¬@¬ ® Ö.¬ ® © ®
S´ÞuG`~:=\€E@BD_|Y:=w\€ALBi}>BD;?HJ=.E@_ZBD9WBiC^_|z =>CE?BÂEQ±ÇE@G~`AXVá9<\€D9RK›AµVá;?9WS E@G`=H<A@A@9|}BiHRE@BDjW=d\iH"KßVá9W;M;?=.HJ\5C~:S[+=>;
ŸJ¦:z Ÿ SZ3*¬…HJ¤+E@®3;?B ¥gc Bi¤´A 㠟:¬ ¬á¤6®¼¤˜­F¤6®Ü¥ÁŸ ¬…¤+®*­a¤(¥gŸ P­a¤ zÜÞuG`=P}9W;?;?=.A@Y59<C`_|BDC:²
Ÿ ­×¡
Ÿ Ÿ Ÿ ­×¡ ŸJª
K
:(
B
56.
(
-3.
MK
.
-3. . %
-/.
-3.
-/.
-3.
-/.
7
-3.
)
7
-/.
56.0
7
56.
7 )
56.
-
)
-
0 ;5 7
01015H.
-
5
5 )
56.
-
01;
)
-/.
-
01;
01;
0
5H.0 ;
-/.
;45 7
56.
5 )
) 5)
)
56.
-
-/.
-3.
-
-3.
/
/
.
L
4
.
.
/
;;
/
5
<L
; ;
-3.
-3.
-/.
/
B
-/.
;
;; ;
;;
.
/
.
%
%
JŸ ¦:z ž ¬ÌH<® ¡ ž ¬…[5® ¡"£ ¬…}w® §WŸ ¬…_`® â ¬…=w®U¬ ž Ö?Ÿ<® ¡ ž ¬áV?®¬L¡WÖL«® ¡R£
ŸJ¦:z « ê êW¥Õê¬ Ö ®.ê<¥ ¬ ® © ãÁ¬ ® © ¥ ã ¥ ¥ ¡¥¡
ŸJ¦:z §g©¬…[5® ã © ã ¥ÄÊ© ê ã ÛêDê W© êQã}9Ÿ A>¬ <® ãîêŸ ÛêDê JêÂz ¥ ¬ÌH<ê Ûꮩ6ê ããØê JJê ©+ê ©ãî¥ Ÿ ¬ ã ê Ûê ©6®Q©dãØãê J¬ ê ©Û©ã㠟`ê Ûê© €ê®LJ©êR¥¥
©©
¬?ê ÛêwãÁ© ê Jê ®Q© ©
ŸJ¦:z ªÁ¬ÌH<®›£ ¬…[5®d§ ¬…}.®›¦
ŸJ¦:z £¢¬ÌH<®] ¬…}w®uHJC`_Ù¬á="®MSZHJ·W=wAuAL=.C`AL=<z
ŸJ¦:z â ´¥gHJ;N}>}>9<A¬ © í ®
ŸJ¦:z ä C`b 9W\€;?ST
¥HW\ܬ̬Ÿ:Ö>¡wÖ ®XY`© ®OH<A@A@A@~`BDC:}NGÔ²ÇE@E@G:G`;?HJ9WE~:Ÿ ²<G^]ãVá9W;›©= c ¥ÕHJSTŸ:Y:z \D=Wb ]E@\DG`B C:==´Y5BD9<CîB€CE?EG:= ¬…¦`Ö?Ÿ<Ö ®Êz © Y:\iHJC:=<]ÛKdBÂE?G
ŸW¦:zD¡.¦g¬ÌH<® ¬ ®I¥ ˜¥ íí ¬L¡WÖ?Ÿ<®Z¥ ¬Q¡<Ö?Ÿ<® ¬…[5® ¬ ®I¥ í ¬L¡WÖ?Ÿ<®Z¥ ¬…¦`Ö@¦® ¬…}.®
¬ |®Ü¥ í ¬L¡WÖ?Ÿ<® ¬…_`® ¬ |®Ü¥ å í © ¬Q¡WÖNŸW®
ŸW¦:zD¡W¡ ¥ Oã aKdG:=>;?= ¥ ­ ˜HJC`_Ь…H<® ¥ ¬ ®Z¥ ¥ í å ¬L¡WÖ?Ÿ<® ¬á[5®
›¥ í ¬Q­OŸ:Ö>¡w® ¬Ì}.® ›¥ ¬ÌŸ|ÖNŸW® ¬…_5® ›¥ ë © ¬ Ÿ:Ö ŸW®
ŸW¦:zD¡wŸgêê WÛêê © ©M¥ãÁêê ¸­Jê ©u­ÙWê © Ÿ ¥Õ ¬ d¥Õ­ ê Ûê ©X® © ãÁã˜ê¬ Jê ©©u­ ­ÙŸ5© ®ê Ûê© D¥ê WêQ}9© A>ã ¬ +®©© ã © ã ©© ­PŸ`¬ ã © ­PŸW®*¥
ŸW¦:zD¡ ž |=>=Y:;?=>jBD9W~`AMY:;?9W[:\D=>S
z
ŸW¦:zD¡>«Á¬…¬Ì«`H<®Ö?ª<›® ¤Ð¥ ¬Ì§|Ö.¡W¡"® HWC`_ *¤Á¥ ¬ £|Ö>¡w¦<® ¬á[+® O¤Ð¥ ¬ ž ÖN£W® HWC`_ *¤Á¥
ŸW¦:zD¡w§¢¬ÌH<® «¡wäž Ÿ<§W
¦Ÿ ¬…[5® žŸ ž¡ «ž «ª ¬…}w® žŸJªâ«Wž «¦ ¬…_`® ž¡R䣟§ žž ¬…=w® ŸW¡.ä
Ÿ¡wŸ § «§Wž¦ ­O§ ¬ §VN® Ÿ<¡wä
Ÿ «§J¦ž ¡ì ¦ ¬…²® ­O¡ Ÿ§ ­›¦ §¡ ¬áG5® ž­d«§ ­OŸ ž§
¬…Bi® ­¡.¦ £W§ « £J§ ¬@® ¦ ¡
ŸW¦:zD¡.ªØÞuH<A›G`BD=CSZ;@9RHRK E?;@B ˜c HJ=.C`\€=._ST}>=>9WC\DE~:STBDCîC ;?9RK 9WV HJ´C5_®›BD}A›9W\DE@~:G:ST=C A?}>˜HW\DHW9J;›V›Y:¬ ;?9|´_|® ~` }ÊE¬…Kd9JVµG:;@BD}N9RGÔK BDÃAOE@9JG:V=Ç A@HWHJSTC5_ =
E?}>G:9W9J=\DV~:A@ST}.HJC HJ\iHJC`;M_(9JY:V ;?;?9R9IK _:z˜~`Z}ÊÞuEd9WG:V 9J=ZV¸SZ;@zÜ9RHRÞuK E@G`;?BHRc 9WE›V =>BiA>\D=>]:STØE@G:=>HJ=CC5EPSZ_˜BDHRCÙ}>E?9W;@;@\DBi9R~:}K=wSTAC ¬ THJC`´9W_ÙV ® }>9WdHW\D~:C`]ST_ E@G`C HJEuîBi A.9J]|V 9JV¸G5}>H"9WjW\D=~:ÐE@STG:BDC =A
A?HJST=U=>\D=>ST=.C<ENA›HJC5_˜HW;@=E@G`=>;?=Vá9W;?=U=.h~`HW\Ìz
ŸW¦:zD¡"£ß¬ÌH<® BiAdAL±STST=E?;@Bi}Jz ¬…[5® BiAdB€Cj<=>;@E@BD[:\€=UKdB€E@G
BDCj<=>;NAL= Iz
;
@
.
<
. R
M
L
.
.
5
.
;
.
.
R
PL
"
.
E
. 7
P
<
;
;
.
L
-3.
9
;
; 5
/
B
;; ;
<
7
; ;
9
L
.
B
;
.
L
.
/
/
.
5
;
.
.
.
.
<%
%
%
%
%
%
%
!
Ÿ<£
%
ŸW¦:zD¡.âØÞuG`=ŸÇ¾
Ÿ SZHRE?;@B c }9W;?;?=.A@Y59<C`_|BDC:²PE?9TE@G:=Y:;?9 Q=w}ÊE?B€9<C ¬ ®MBiA
¡êÛê © © ©© © ©
Ý[jBD9W~`A@\€±<] ¨¥ Tz º 9WSTY:~:E@BDC:²`]:9<C:=à`C`_:AdE@G`HJE
¥ ê Ûê¡ ë ëå ã © ã© ©© å© å ©© ©ã © ã åë©© ¥ ê 6ê¡ ë © ê Ûê© ê© Ûê © ©©© êê ÛêÛê ©© ¥
ŸW¦:zD¡.ä }A@B€9C A>¬ ¬ <<® ® ­}AL9BDC^A>¬¬ ®® ¤¤ © ;?9JE?HJE@=wAu¤
E@G:=PHWC:²W\D= Ç}>9W~:CE@=.;›}\D9|}N· ÒKdBiAL=<z
ŸW¦:z ŸJ¦ |=>=UE@G`=PAL=w}ÊE@BD9WC
HJ[+9W~:E 6 = =w}ÊE?B€9<C(HW[59Rj<=
ŸW¦:z Ÿ|¡¬ÌH<®­d« ¬á[+®d¦ ¬…}.®¡w¦
’”“
•P–˜—*™›š Ÿ|¡Wz Ÿ ÝC`\€±ÃE@G:=;?B€²<GE@ST9<ALEM9<C:=Wz
Ÿ|¡Wz «Ð¬L­£ÖNŸ|Ö>¡"®
Ÿ|¡Wz §Ÿ
Ÿ|¡Wz ª £WŸ JŸ
Ÿ|¡Wz £¢¬ÌH<®uHW;?}.}9<A>¬ í å ®U¬á[5® í å ¬Q¡<Ö>¡WÖ.¡w®¬…}w®U¬Q¡<Ö@¦:Ö.­¡w® Ÿ(¬…9W;P¬Q­¡<Ö@¦`Ö>¡w® ŸW®
Ÿ|¡Wz âÁ¬L­¡WÖ?¦:Ö>¡"®
Ÿ|¡Wz äÁ¬ÌH<®XE?;@~:=<] ¬á[+®XE@;?~:=W] ¬Ì}.®XE?;@~:=
Ÿ:¡WzD¡wŸ
¦¡ }9<Aw¦ ¬ ® ­
A@BDC ¬ <¦ ® }¦ 9A>¬ <® ¦¡ ­ALBDC^¬ ¦ ® }>A@BD9<C A.¬ ¬ <<® ® ­}>9<A@B€A>C^¬ <¬ <® ® ¦¦
¦ ALBDC ¬ ® }9<A.¬ <® A@B€C ¬ <® ¦ }9A>¬ ® ¦
¦ ¡ ¬Q¡w ®
Ÿ:¡WzD¡>«
¦¡ì¦¡ ¦¦
¬ÌŸW®
¦ ¦ ­¡
Ÿ:¡WzD¡"£ß¬L­¡WÖ.­ ž Ö@ª®Ê]= c }>=>Y|E?B€9<C^z
Ÿ:¡WzD¡.⨶¼KdCB€E?E@=>G(;NALE?=wG:}Ê=E@BD¤9WCß­F9WV¤ E?G:Y:=
\DHWEQC:KX=W9¨k›Y`¬Ì¦:\DHWÖ?¦:C:Ö@=.¦A.®Êk ]9J Vµ¬ Ÿ|}Ö.9<­~:;N¡WALÖ>=<­z ¡"®Ê]MB€CE?=>;NAL=w}ÊE@BD9WC×9JVEQKM9¨Y:\DHWC:=.A
©
Ÿ:¡Wz ŸJ¦ Oã J¬ P­¨Ÿ |®Ê] ¬ ¦<®]|KdG:=>;?=Z¬…A@=>=Uà`²<~:;@="® M¥ P­¨Ÿ +] Ç¥ Àµz
@(
L
L
.
.
.
L
L
U
L"L
.
.
.
U
U
.
.
.
U
.
L
.
.
.
(
.
U
<B
B
..
B
..
.
9L
+
P
I
ŸJâ
9L
+
L
+
5
+ + ;
’”“
•P–˜—*™›š ŸWŸ|z Ÿg¬ÌH<® © ¬…[5® åí ¬…}w® © B€V¥g¤´ã 6z
ŸWŸ|z ž ¬ÌH<®dŸ ž 㠟 ¬á[5® å ©?© ¬Ì}.® å@ë ë ©?©
ŸWŸ|z §g¬Ì¬…[5H<®®¬Ì}Ÿ:9<¬ÌA.}¬…9ä<¦A>¬á«®§Ö@A@B€®C Ö@A@¬ÌäWB€C2¦¬á>«®L§® ®@®
¬Ì}.® ë å ¬Ì}9A.¬ ­ 6®ÊÖ?ALBDC ¬ ­ 6®L®]`KdG:=.;@=¥ b ;?²`¬ÌŸO㠞 ®] ˜¥ b ;?²`¬Ì§›ãØ« ®Êz
ŸWŸ|z ªÁ¬Ì¬…[5H<®® ¥Õ¥Õ¬…¬…}}99A>A>¬¬…«§X>«®Ê§ Ö@A@BD®ÊC Ö?AL¬á«BDC §¬ >®@X®Ê]«§ © ®@¥ ®Ê] ¬…}9¥A.¬L¡W¡ ÖNž Ÿ|§Ö ®DÖ@Ö@â`A@B€z C ¬L¡ ž §®@®
¡w¬Ì¬Ì_`}.âW® ®u¦G:®LBD®C¥ ]:E.Kdk*­ G:à`©=>;N;?ALã =EdA@9W:¥ \D¬…jW}>=9<ê"A.­Vá9<¬ ;ž WRgŸW«®Ê¥Ö?­ ALBD©C êWO¬ ¥g E?J9T§Ÿ<"à`®L®Û«ZC`HW_˜HJC`C5E@
_ _G5HR© E ¥¥b­ ;?© ²`ã ¬Q­ ž :"¬Ì«U}9<­ A.¬ ®Wz Ÿ<ã´¡wâW¦Ê®Ö@A@B€C¸¬ WŸ<ã
¥ ž ¬Q¡X㠟 ®^ã :¬…}9A>¬ JŸ<®ÊÖ@A@BDC ¬ WŸW®@®
Ÿ
HWC`_ ¥ ž ¬Q¡u㟠®^ã |¬…}9A.¬ JŸ›ãg¡.â<¦ ®Ö@A@B€C2¬ WŸ›ã¢¡wâW¦ ®@®ÊÖ
© Ÿ
Kd¥G`=>;?¡<= Ö?Ÿ:Ôz ¥ê Ÿ<£ "«Ç­Ð¡"§ êÛHWC`_ F¥ b ;?²5¬ÌŸ£ R«´­Ð¡w§ ®zîÞuG:=>CØA@9W\DjW= ©˜¥ ]
ŸWŸ|z £¢¬Ì¬…[5H<®®ç笅¬á¦:¤ Ö Ö ::®3®Mk kJ ¤ Z*éÃ¥¬…¡WÞ¸éT9Z¬ ALX==.w=U}>KdHW~`GAL±<= ]:;?©=>OKd¥ ;?BÂE?¬…=U¤5©dH<AP­ ê U­|©JßÖNŸR¬Q¤ ­ :®@®.® êW¥Õê ­ ê ®
¬Ì}.®ç¬á¤ Ö :®uk5ê Ûê ¤^éz
ŸWŸ|z âØ¶Ò6V ®¥Ö@A@B€C2¬¬Ì}­ 9A.+¬ <®@®Ê®Êz Ö?ALBDC ¬ ®L®µHWC`_ ¥ +¬Ì}9A.¬ +®Ö@A@B€C2¬ 6®L®]JE?G:=>C ¥ ¬ |®¬…}>9<Aw¬ 2­
Ÿ<Ÿ|zD¡.¦gHW¬ÌH<C`®_ÃÞuALE@G:;?=´=.}N}>G`9W=.ST_IY:[\D=±Tc E?G:Y:=\iHJV…C:HW=´}ÊE?BD9WAO;à`ê ;NÛêAQÂE]E@;@G:9W;?E?9WHJ~`E@=.²W_ÔGIHJE?;?G:9W=~:SC`_(~:\DE?BÂE?G:B€=ÇY`\€9WBi}>;?HJB€²<E@B€BDC
9WC(E?G:9J=ÇV Ç[HWC:²W± \D= +]bE@;@G:² =.C
E?¬…;?[5HW®C`ÞuA@\DG:HJ=˜E@=._˜}9W[ST±ZY:E@\D=G`c =PCHW_:~`_|SB€E@[+BD=>9W; C
Ô¥9WV "z ¬Ì}9A.¬ <®ÊÖ?ALBDC¸¬ <®L®UBiASZHJY`Y5=w_Ù9WCE@9(E@G`=Ã}9<S
Y`ST\€=9|c _|~:C\D~:~`SA›[+A?h=>~`; HJR;?©<=.¬Ì_^}z9A>¬ÌŸ <®ÊÖ?ALBDC ¬ Ÿ <®@®Ê]|E?G`HREuBDAME?G:=UHJ;?²W~:ST=>CEuBDAu_|9<~:[:\D=._˜HJC`_ÃE@G:=
’”“
•P–˜—*™›š Pœ
Ÿ ž zD¡ a;\D=.H<?_:BÂE?AX=E@¤59´åE@G:¥ =¬ Bi¤T_|=>ãØCE@¤ZB€EQ­±Z¤5¤6 å®LåO¥ ¥ ¤+ ¤+å*åXã 㠞 ž¤5 ¤5©W ©<¬…¤´¬á¤I­ ­ ¤6 ¤6®+ ®^ã 㠞 `¤2¬…¤ ¬á¤IÖ ¤Û ­ ®Ê]|¤Û Kd®Q©3B€E@ãÁG˜E@¬áG`¤Ã=­ =.;@¤6 ;?®L9Wå ;3`E@Þu=>;?G`S BDA
5¬…¤ Ö ¤6 ®Ü¥ ž ¤2 ¬á¤Z­ ¤6 ®Q©3ãg¬á¤Z­ ¤6 ®Qå<zܳ›9WE@=E@G`HJEê 5¬á¤¸Ö ¤µ ê<¥Õê Ÿ ¤´
HWC`_˜E@G~`AME?G:=P_|=>;?BDj"HJE@BDjW=U9JV*¤5åUBiA ž ¤5©JzÜÞuG`=Y`;@99JV¸Vá9W;d¤5ëPBDAdA@BDSÇ BDãa\iHJ¤2;wz ꀬá¤I­ ¤+ ®L©W]
.
R
.
; 5 ;
-
.
-
-
R
.
.
.
.
.
B
A%,%
B
B
.
B
B
B
B
.
B
B
B
B
B
<B
',
+
B
<B
(
"
9%
ŸJä
Ÿ ž z ŸØÞuG`¤Û =¨®­=>;?;@¡ 9<J;˜Ÿ E?=>¤6;?S®¬á¤ BiA ­ ¤Û 5®Ê¬áz ¤¸Ö 8:¤Û ~`®;LE?¥ G:=>;?ST¤Ø9W;?­ = ¡ |¤Ø ¬ ­”¤F¬áã¤Ø­¤6¤6 ®® J­ Ÿ ¡ ¤¿W Ÿ ¥¤Ä ¬L¡¥ :¬ ¤a¤¨ ã­
²<¡ =R¤ÛEâ ® ¤ :å ¬ © ¬á¤¸]¤O VáÖ 9Wã ¤Û ;d® ¤Ô¤+}>®@\€Ÿ 9AL=¬…¤( ¤ E@9¥Ö ¤Û ¤¸®¬ ¤U¬…z ¤
­Ã­ ¤+¤6® |®L¬©´Kd¤O B€E@ã G ¤6®Q©"¬á¤ Ÿ Ö ¤6 ¤¸®z ¥ º 9<¡ \€:D=.ꀬ }E@BD¤ÃC: ²Uã E@G:=¤Û;@®Q=w©wALŸ ~`\ÂEN¤2Aµê KX=
Ÿ ž z ž a=3 U¬ ¤Û }>® HJ\i}~`3\DHJE@¬ =¤Û E@®ÇG:¥ =U_|¬ =>3*;?¬BDj"¤( HJãE@BDjW+=®u9J­ V 3*¤
¬ ¤+ HR®@E® ¤˜ Ø¥gVá9<¦ ; §P ~`AL¥ BDC:²Ÿ E@G:=UVá9<_|;B Ø=.;@¥¿=.C`}¦`=UÖ>¡<hÖ~:9JE?ÊB€ÖL=.«C<¦E
E?~5B€AL9<BD?CC:Ó ² SZ¬ HR¤Û |E?®I]2\DHW¥Kd[^G:zIê=>3 Þu;?= G:¬ ¤Û=>?®dCÙÓ T5­ KMBi=IA3 E?}>¬ G:HW¤Û \D=î>}>êÂ~:A@z×ST\DHJ{E@HW=Ç\€ALDBD=.E@C:ALG`²FEP=ZCVá=>9W~:;?;?S;@S9<[+;~:=>\iBD;H CaB€¬C¨E@Ÿ G:ž eî=Zz ŸCHJ£J~:E@®\iSTHJKX[¨=.=(;@HJBi}>²WC`HW=>_ \ÜE HJ Y::Y:¬á;?¤¸9 Öc ¤ÛB€SZ® H¥
¡ |¬Ìâ ¤5 å ©.®z =>=UE?G:=Uà`²W~`;@=<z
@B
O
@B
%
B
CB
CB
'%'%A%
-
9(
@B
>O
B
B
@B
B
@B
@B@O O
(
0
10
−1
10
−2
10
−3
10
−4
10
−5
10
−6
10
−7
10
−8
:YBi82Ad;?B€²<=.H´_|~:\DBi;?9W}Ê=I²E?=.¡.\D_
ª`9W²ÇkM9<Y|ÞuY:E@\DG:BD9JSZ=E ›¬HJ=>;?\¸;@}N9<G`;?; 9W9W[`Bi}\€==.SÄBD9JCV Ÿ E@îG:ž =´z STž ®CHW~:;@ST·<=.=>_(;?BD[}.HJ±(\ HT_|=.j<;@=>BD;@jRE@HRBiE?}>B€HWj<\ =_:HWHWAA@G:HT=w_
Vá~:\€C`BDC:}E@=WBDzd9WCî³O9J9WE@V =PîE@G`HJHJC5EO_
E@E@G`G:BD=A
10
−14
10
−12
−10
10
10
−8
10
−6
−4
10
−2
10
10
0
10
<(
Ÿ ž z « {Ÿ ž ALzDBD¡C:ž ²×KXÞ¸=H"²W±=>\D9WEX;NE?ATG:Vá=9WVá;?9WS\D€~:9R\iKdHØBDC:HW²PC`_¢Vá9<;@Y:S´;?9|~:}\iHP=>=wVá_|9<BD;3C:²ØE?G:=UBDC¢9WY|E@G:E?B€=aSZA@HJHW\ÛST}NG:=î9<KMBD}>H"=±ß9WV HWAÃk B€C º G`HJY:E@=>¥ ;
¬BDFC ?Ó E@G:=Z_|<B ® =.;@åW=.]MC`Kd}=ZBÂE?Gh~:9WE@×BD=>C¥ EUH<3 AUHI¬ ¤6 Vá®~:RC5ª`}ÊzßE@BD9W8`CÙ9W;9WV 3*Ù¬…¤+HW®(A¥ KM=>\D*¤¢H<AKME@=G:=ÇALG`E@9RG`K =ÇY`E@ G`;@=w=_| =>BD} ;?E@;@=w9<_ ;
9<|Y E@BDSZHJ\ Ù¬…jW=.;LE?BD}.HJ\^_:H<ALG:=w_Ã\DB C:=w®z
Ÿ ž z §Ø8`9W;µA@B€STY:\DB }>BÂEQ±<]J}9<SÇY`~|E@=XE@G:=d_|=.;@BDjRHRE?B€j<=XHRE ¤˜¥ ¡W z¸ÞuG`=>CPE?G:=u;@=.\DHJE@BDjW=X=>;?;@9<;^Vá9W;
HUHVáA@=.Y5K¢=w}_|B€à5B }u=>}N;?G:=>9WCBiE3}=M}NG:9J9<V BDÃ}>=.¥gA*9W¤MV6­À
¤ZHJ;?BD=uA Y: \D9J¬ EL5E?®Ü=._Z¥ H<A2Vá~:C`}ÊE?B€9<CZ9Jz*V ÞuZG:BD=uCÇ;@E@=.G:\DHJ=dE@à5BDjW²W=M~:=>;?;?=u;@[59<;?=.A\€9RVáK9W; z
8`9W;ÜÀî¥ ¡M9<C:=›A@G:9W~:\i_T}NG:99<A@=›HU\DHW;@²<=XjRHW\€~:=O9JV ZALBDC`}>=uE@G:=›\DB C:=.HW;@BDÚ.HJE@BD9WCÇ=>;?;@9<;
ž¦
@B@O .
O
B
+
) Q
+
- +
(
0
10
−2
10
−4
10
−6
10
−8
10
−10
10
−12
:YBi82Ad;?B€²<=.H´_|~:\DBi;?9W}Ê=I²E?=.¡"\D_
£|9W²ÇkM9<Y|ÞuY:E@\DG:BD9JSZ=E ›¬HJ=>;?\¸;@}N9<G`;?; 9W9W[`Bi}\€==.SÄBD9JCV Ÿ E@îG:ž =´z ST«®CHW~:;@ST·<=.=>_(;?BD[}.HJ±(\ HT_|=.j<;@=>BD;@jRE@HRBiE?}>B€HWj<\ =_:HWHWAA@G:HT=w_
Vá~:\€C`BDC:}E@=WBDzd9WCî³O9J9WE@V =PîE@G`HJHJC5EO_
E@E@G`G:BD=A
10
−14
−12
10
−10
10
−8
10
−6
10
10
−4
−2
10
0
10
10
<(
Bi8`AU9WÚ>;d=.\i;@HJ9
;?²WHJ=.C5;M_ÔÀÔKME@=TG:=.9W;@C:=\D±BiAdC:HJ=>C
=w_î9<Y|E?E@9
BDSZKXHJ9<\Û;@jR;?±HJ\D~:HJ=[+9W9J~|V E^;?z 9W~:C`_ 9 J}9WSTY:~:E?HRE?B€9<C`HJ\2=>;?;?9W;wz
Ÿ ž z ª _:==.à`;@G5C:HJ=wY`_
AOALBDE@C G:¬á=Z¤6®d}>9WHJ;?C5;@=w_˜}ÊE}>9<HWA>C`¬…¤+A@KX®]`=.[:;O~|E?E›9˜KME?G:=PBiAALE@h<BD\€~`^=.SZALE@H"BD±T9WCÔà`C5BiA_ÃC:E?9`G:]¸=PAL}BDC`9<;@};?=Ç=.}KME›=´HJG`C`H"A@j<KX=´=.;.C`z 9JEU±W=E
Þuê ¤2KMêÂz9¢ÞuHJG:\€E@=.=.C;@C`~`HJA@E@=˜BDjW=wE@G:A>k=(;@¬á=.B ® \DHJE@6 BD9W=.C`HW\€AÇBDÚ>A@=ÙB€C ²W¬…=.¤+9W®›ST­×=E?A@;@B€BiC¸}>¬ HW¤Û\€D®T±ß¥ E@G5ŸµHREîA@B€C ALBDC ¬…¤+® }>9<A ¤ Vá9W; ALSZHJC5HW\€_
}E?>9´9<A.;?¬á=.¤+HW®d\€BD­×Ú>=}>_|9<B€A>;?¬ =.¤6}®ÇE@\D±T¥ ²W­O=>9<ŸµSTALBD=C E@;?Bi}> HJ© \D ± E?A@B€G`C HREM E@G:© =U _|z=.;@¬áBDBDjRi®HRE@ÞuBDjWG:=O=Ã9JV¸A@=.A@}>B€© C¸9WC`¬á¤+ _¨®3HWBiAM\ÂE?}>=>9<;?C`A.© ¬áHR¤+E? ®XB€j<HJ=ZC5BD_ A
E?G:=P_|=.;@BDjRHRE@BDjW=U9WV*}>9<A>¬…¤+®MBiA­ALBDC^¬á¤6®Êz
Ÿ ž z £¨Vá{~`ALC`=}ÊE?ÞuB€9<G:C(=.9WBiAd;?=>;?S =.HW\€Ÿ D±ž zD^¡IBDY`E@9aA?}N²WG:=>BÂE?EIÚPHÔ}9<\DC<9RKXE?B€=.C;´~:9<[+~`9WAu~`KdC`_ØB€E@G(Vá9<E@; G:Bi A OHWC`z _ØE?G:=>CßA@G:9RK E@G5HRETE@G:=
Ÿ ž z âÛ¬{…AL¦=(®^E?ã¢G:=(¬…¤ZV…HW­F}ÊET¦<® E?G`HR¬…¦E ®Û3*㠬ᤠ®I¬á¤ ¥ Ö@3*¦<®¬…¦]|®3KdãG:Bi}N¬áG˜¤a²<­¢B€j<¦<=.®A 3 3*¬…¬á¦¤ ®3®Üã ¥g ¤3 ¬á¤ ¬…¦Ö?®^¦<ã®´HJ C`_ ¬á¤ 6¬…Ö?¤ ¦<®3®IVá9W¥ ;
3(HWC`_´E@G:=OA?HJST=uVá9<; +z » B€jBi_|=›[±´¤˜HJC`_Ç;?=.HJ\DB Ú>=uE@G5HREÜE?G:=›\DB€STB€E3BDA 3 ¬Ì¦<® ¬…¦®Êz
Ÿ ž z äÞuG`BDAdY`;@9<[:\€=.SÑA@G:9W~:\i_˜Y5=.;@G`HWY`Au[+=B€C(E@G`=C:= c EO}NG`HWY|E@=.; Þu G`=.C:==>\€;NBDSTHJ\DBBÂÚ>ENA›=Ü
\HJ ;?O9=TW¡Y:JB€E?Ÿ´HW\HJ C5A¸_ ;@~:\D=Üz E?9O¤ ¤THJC`_P}>9WSTY:~|E?=ÜE?G:=X_|=.;@BDjRHRE?B€j<=.A HJE ¤(¥¡Wz
(
3
-
-
5
5
K
B
CB
'
ž¡
0
10
−2
10
−4
10
−6
10
−8
10
−10
10
−12
10
DB82SÇB€²<Y`~:;@;?9R=j<=>¡.STâ:k =>Cº Eu9W~`STALY`BDC:HW²Ç;@BiE@ALBDG`9W=PCÇAL[+±=STEQKMST=>==>E@CÇ;?BiE?}G:_|=›B ;?=.=>A@;?~:=>\ÂC5EN}Aµ=BDC Vá9W;?S;?9W~:[:\i\DH:=>ziS ¬ Ÿ;@9<ž [:z ž \D=>HJSÑC`_ZŸ žŸ žz «z ®«`z¸³O9JE?=dE@G:=
’”“
•P–˜—*™›š ŸR«`zD¡FÞuG`=d;@~:\D=.A2Vá9<;Ü_|B =.;@=.C<E?BDHJE@BDC:²U¤ ]JE@G`=›h<~`9JE@BD=>CEµ;?~:\€=<]<HWC`_PE?G:=›}NG`HWB€CÇ;@~`\€=u²WBDjW=wA>k
¡
¤ ã ¤ ¤ ãØ¤ ¥
¡W¡>¤ ã
Ÿ ¤ ã 㠟 ¡ ¡W¡<¡>¤ ¬á¤ ãØ¤ ¬á¤ ®*­a¤ãؤ ¬L­® ¡© D¡>¤ © ãg¡ D¡>¤ ® ŸR«`z Ÿ ¥ ¬…¤ © ãØ¤ ë© ® +¤ © ¬á¤ © ãØ¤ ë© ®Ü¥¢«<¤ å©
ŸR«`z ž a=j<=>I;?²WY:=wAÇ\D9JEE@9¦ Váª<9<ä ;ž ¡Àߥu¥ Ÿ \€ÖNCOŸJŸ:©RÖz €³OÖNŸ 9RKíJk]MBDM±CßîE@BDG`C`= }>;@º =wHWG`A@HJB€Y:C:E@²
=>; Àµ]¸b KX¹µ=Ç=>à`;?C`± _F|E?G:G`9WHR;@E E º 9W}>~:9W;NCA@=
BDC º HJ\i}~:\D~`A.]3KM=A@H"KÑE@G`HJEa\DB€S ¬Q¡Uã À ¡ ® ¥ <z a=îAL=.=(E@G:=}9<C:C:=w}ÊE@BD9WC E@9
\DB€S ¬L¡Xã À ® ¥gŸ:]:[±IC:9JE?B€C`²´E?G`HRE\DB€S ¥ ß ¬…¦<®uHWC`_ ¬…¦®3¥¡
ŸR«`z « G5H"=jW-E =3*Ÿ ¬á¤+®T¥Ð¥ Ÿ Ÿ Ÿ HJ C`]_¨B z =<A@~:z€,] Y:3*Y+¬á9<¤6A@®Ü=I¥ E?G`3*HR¬…EǤKX­ =I¤Û ·® 3*C:9R¬ ¤+K ®zÜ3 Þu¬…G:¦=®I}N¬…G`A@=>HW= B€CZ;?;?~:9W\D[:=O\D²<=>SB€j<=.ŸR'A «53 z ž ¬á® ¤6®3F=¥
3 ¬á¤Ã­ ¤Û ® 3*¬ ¤+ ®Ê]5AL9ÇE@G5HR4
E 3 ¬ ¤Û ®Ü¥ 3 ¬…¦® 3*¬ ¤6 ®
ŸR«`z § ¬…Bi® ã d¥ © ¬…SZHRE?}NG(E?G:=UEQKX9TY:BD=.}>=.AdHJE›¤˜¥¡"®
žŸ
−14
−12
10
−10
10
−8
10
10
−6
−4
10
−2
10
0
10
10
#
...
..
-3.
8.
)
..
-3. 8 .
. . R
. R
. 8.
. 8.
...
8.
-3.
5
.
5
<%
-
8.
<%
8.
R
8.
.
+
.
+
.
%
A%,%2%
.
+
%,%2%
+
+
+
+
K
-
%
.
+
(
À¥¡.¦
À¥¡.¦
À¥ ¡.¦<¦W¦<¦
À¥¡.¦
Àw¦
À¥¡.¦
Àî¥ÐŸ
À¥¡.¦
À¥¡.¦
À ¦<¦W¦<¦W¦W¦<¦W¦<¦:¡
À¥¡.¦
À¥¡.¦
ÀÀ¡.¦ ¡.¦ À¥¡.¦ À.¦ À¥¡.¦ À.¦ À¥¡.¦ À¥¡.¦ À¥¡.¦ Àw¦
\D82=>B€S ²<~:Ÿ;?=Ǟ z §W¡wä:® k 6 =.\DHJE@BDjW=U=>;?;@9<;?AXVá9<;uE@G:=C~:ST=>;?Bi}>HJ\^_:=>;?B€jRHRE?B€j<=H<AMVá~:C`}E@BD9WC9JV ^z›¬ ;?9W[
0
−2
−4
−6
−8
−10
%
−12
−14
−16
−16
−14
−12
−10
−8
−6
−4
−2
0
h
(
ᬠBDi® ¤˜¢¥¥ ¡w­O® Ÿ:] î¥ ©í ¬…SZHRE?}NGßHJ\iA@9ÔE?G:=
\€=>V E ´HWC`_;?BD²WGE ÒG`HJC5_:_|=>;?BDj"HJE@BDjW=wAHRE
’”“
•P–˜—*™›š ¯
ŸW§|z « ¤
! ¥ç<­ .ž ž ¦<Ÿ£Ö>. ­¡ ª`¡.â<¦:Ö@¦ ž ¦<ŸW£|Ö@¦ ª:¡>â<¦|Ö>¡WéW] . ( (* ( (+*, ,
'
* .(
ŸW§|z § ¤
¥ ž ¦Wª<¦Wâ
ŸW§|z £ ;@9<[`HJ[`\€±IHWC˜=.;@;?9W;uBDC˜E?G:=PHWA?A@B€²<C:ST=>CE.z*¤ ¥¡ ž BiAuST9W;?=UB€CE@=.;@=wAQE?B€C`²`z
ŸW§|z â¬ÌH<® ›z ²`z*¤ ­ ¤ ¬á¤ ­ ۬ᤠ®@®
%
4(
%
%
4(
%
%
R
.-
. )
0
žWž
CB
0.86
0.84
0.82
0.8
0.78
0.76
0.74
0.72
0.7
0.68
0
82BD²W~:;?=PŸJ¦`k ;@9<[:\D=>SğJ«`z ž z
5
10
ž«
15