Towards the exact value of the Ramsey number R(3, 3, 4)

Rochester Institute of Technology
RIT Scholar Works
Articles
2001
Towards the exact value of the Ramsey number
R(3, 3, 4)
Konrad Piwakowski
Stanislaw Radziszowski
Follow this and additional works at: http://scholarworks.rit.edu/article
Recommended Citation
Congressus Numerantium 148 (2001) 161-167
This Article is brought to you for free and open access by RIT Scholar Works. It has been accepted for inclusion in Articles by an authorized
administrator of RIT Scholar Works. For more information, please contact [email protected].
!"$#%&')('*+&-,.)0/213453456)7
89:;=<?>%@BADC"<FE9GCIH5EA
Z\[^]_^`badce!aVfFgUh
iV_YjYaVg)k\alcmngLcLaVonpqiV_Yjsr=k
w[xrnyFg?jsrzi{|g)jM}V[5onkzjM_Y~alc€Bh
i?g kl‚
ŠG‹VŒdŽV €Bhiu)g kl‚W‘Ba{ˆiVgh
rzaVg)jxš!]V‰G` ‰
h
iG` ]{
J)KL<F:AMH5NOD<
CP@RQ!SI<>UTVADH5TW9GCIH5EAYX
Z[^]_^`alctbaVpu])f_^[5oIvr=j[5gUrn[
ƒ„a…rny)[5kz_^[5o†mng)kz_YjM_YfF_^[‡alc0w[xrnyFgUaV{ˆaz‰V~
ƒ„a…rny)[5kz_^[5o5’“•”=–— G˜ \|!vF™
ks]oVš„r=k=`›o5jD_^`M[xhVf
œ ,RVWGF
"žŸ WOD<?H5H5AD V<FOISI<¡HnŸV¢':£¡¤¥ŸW; /21s¦G§G4V¨W¨V¨W4n¦
©F7 AMH2K5žŸ+ODŸV<?HzKª¬«®­¯H5£ Lž
K5ž!<GK\K=žŸW;=ŸAMHI:9±°)²x ³9?O´9?;5AD:µ29F¶„K=žŸŸ>UµŸHI9F¶.·%¸¹C†žAD Lž$>9)ŸHI:9K‡ W9:)K=<A´:<:)¢
¡29:9U Lž;=9¡<FK5AM W9¡2ºODŸ³K5Ÿ0H5£¤µ?;=<ºž»·½¼z¾A´:+ ³9?O´9?;"¿=À¶s9;I<FODOBÁqÂÿ.ÂİÅQBÆx:±K5žŸ
¡£O›K=AD W9OD9;I W<?HnŸ 1 °±«ÄÇ 7 ÀUK=žŸ09?:O´¢%E):9GC†:±:9:)K5;=A´ÈAM<FOÉÈG<FOD£ŸqAMH /2134534=3?7„Ê Á
ËUQ
"žŸÌ9:OD¢»9FK=žŸW;q W<?HnŸC†ž9?H5ŸŸVÈG<FOD£<GK=A´9?:$>U9ŸVH‡:9K‡OD99E»ž9º¥ŸWODŸVH=H‡ADH /213453456)7 À
C†žAM Lž+ ³£;=;5ŸV:)K5OD¢½ADH"E:9GC†:±K=9̤¥Ÿ0ŸÍ?£!<FOÅK59 3 ­Ì9; 3 Á¤¢%<:±Ÿ<F;=O´ADŸW;"Cu9;=E½9F¶K5žŸ
<F£K5ž9?;=HVQRÎ-Ÿ;=ŸWº¥9;5K"9?:¹º;59?µ;=ŸVH=H„K59GC"<F;L>H">UŸ ³AM>UA´:µÌC†žAD Lž±9F¶K5žŸHnŸ‡KzCu9ÌAMHuK5žŸ
³9?;5;=ŸV ³KbÈG<FOD£ŸQRÏ\H5AD:µ W9¡2º£UK=ŸW;R<FODµ9;=A´K5ž¡HCuŸ"Hnž9GC•K=ž<GK„<F:¢q ³;=A›K=AD V<FO ³9?O´9?;5AD:µ
9F¶·%ÐnѺ;59GÈAD:µ /213453456)7+ÊÒ3 Á¡£!HzK»H5<FK5AMHz¶s¢ÄH59¡2Ÿ$<>>UA›K=A´9?:<FOº;=9º¥ŸW;5K5ADŸVHVÀ
¤¥ŸW¢9?:>K5ž9)HnŸ†AD¡2ºODA´Ÿ>>UA´;=ŸV ³K5OD¢¤¢0K=žŸI>UŸWÓ:A´K5AD9:HVÀ¶s£;nK=žŸW;Bº;5£:A´:µK=žŸ\H5ŸV<;= Lž
H5º< WŸQ„"žAMH.º;=9µ?;5ŸH5HVÀFK=ž9£µž¹H5£¤HnK=<:)K5AM<FOdÀ?AMHu:9FKu¢Ÿ³K†H5£UÔ½ ³ADŸW:)KK=9OM<F£:! Lž½K5žŸ
Ó:<O<GK5K=< LE%9:¹K5žŸqŸWÕU<? …KIÈG<FOD£Ÿ9F¶ /213453456)7 Q
֥רWÙ WGVÚ Ù Ù Ä*+UVÚ^ Ù
Û : 1s¦G§G45¦VÜ?4W¨W¨V¨³4n¦
©7ݳÞGßÞ
¦ ¿lªÅà¥À ¦á2â Á½¶s9?;¹Á•¬¿Âã°ÅÀBAMH<:ä<H=H5A´µ?:¡2ŸW:)K
9F¶B9?:Ÿ9¶°+ ³9?O´9?;=H†K59%Ÿ< Lž+Ÿ>UµŸA´:$<% ³9¡2ºODŸ³K=Ÿµ?;=<ºžÀÅHn£ LžK5ž<FKA´K‡>U9ŸVH:9K
³9?:)K=<FAD:•¡Ì9?:9U Lž;=9¡<GK=AD Ì ³9?¡ÌºO´ŸWK5Ÿ½H5£¤µ;L<Fºž•· ¼n¾ AD:å ³9OD9;¿LÀ¶s9?;Á»Âæ¿0Âç°ÅQ
JAD¡2A´OM<F;=O´¢?À.<F: 1s¦G§G45¦VÜ?4W¨W¨V¨³4n¦
©è ª 7ÌݳÞGß^Þ
¦ ¿dªÅàåAMH2<F: 1¦
§F4W¨V¨W¨W45¦©F7 ³9?O´9?;5AD:µ-9F¶· ¸ Q
éŸWK"ê 1s¦ § 4W¨V¨W¨V4n¦ © 7 <:>ê 1¦ § 4W¨V¨W¨W45¦ © è ª 7 >UŸW:9K5ŸK5žŸqH5Ÿ³K†9F¶<FODO 1s¦ § 4W¨V¨W¨³45¦ © 7 <:>
1s¦G§G4V¨W¨V¨W4n¦
©è ª 7 W9OD9;=A´:µ?HVÀ?;=ŸVH5º!Ÿ …K=A´È?ŸWOD¢QB"žŸqSI<¡2H5ŸW¢%:)£¡¤¥ŸW; /21s¦G§
4V¨W¨W¨V4n¦
©F7 ADH
>UŸWÓ:ŸV>¹K=9̤¥ŸK5žŸqO´Ÿ<HnKIª$«ë­ÌH5£ Lž±K5ž!<GK"ê 1s¦G§F4V¨W¨V¨³4n¦
©Uè ª 7 AMH†ŸW¡2ºUKz¢?Q
X•ìí?î)îUïWðxñzò…óôˆõÌî)öWðxñ.÷GøùúdûBüVýÉþbÿWðnöVõGñ
Á
Û W9OD9;=A´:µ2£H5AD:µ¹°± ³9?O´9?;=H"C†ADO´O¤!ŸÌ W<O´ODŸV>»<½°)²x ³9?O´9?;5AD:µQ.Æx:»K5žAMHIº<º!ŸV;ICuŸ
³ 9?:H5AD>UŸV;\°)²x ³9OD9;=AD:µ?Hu9:O´¢%¶s9;° Ê Ç 1 ŸÍ)£A´ÈG<O´ŸV:?K†K=9µ;L<Fºž!H 7 9;‡° ÊP3 QBÆx:»K5žŸ
¡£O›K=AD W9OD9;2 W<H5Ÿ 1 ° « Ç 7 ÀBK5žŸ±9:OD¢åE:9GC†:':9?:)K5;=A´ÈAM<FOuÈ
<O´£Ÿ¹9¶†K5žŸ+SI<¡2H5ŸW¢
:£¡¤¥ŸW;"AMH /2134=34=3?7RÊ ÁG
Ë dQ"žŸ‡9?:OD¢9FK5žŸW;† W<?HnŸ‡C†ž9?H5Ÿ\ŸVÈG<FOD£<GK=A´9?:¹>U9ŸVH
:9KOD9)9?E¹ž9º¥ŸWODŸVH=HIAMH /2134534n6)7 ÀC†žAM Lž$ ³£;5;=ŸW:)K5OD¢±ADH\E):9GC†:»K59%¤¥ŸŸÍ)£<FObK59 3 ­
9; 3 Á̤¢$<:-Ÿ<F;=O´ADŸW;‡Cu9;=E+9F¶.K=žŸ½<F£K5ž9?;=
H @.
S lQ IŸV;5Ÿ2CuŸÌ;=ŸWº¥9;5K9:•º;59?µ;=ŸVH=H
K59GC"<F;L>H2>UŸ ³AM>UA´:µ•C†žAD LžÃ9F¶‡K5žŸHnŸ±KzCu9¯ADHÌK=žŸ ³9?;5;=ŸV ³KÌÈG<FOD£Ÿ?Q Û :ëŸWODŸV ³K5;=9:AM >U¢:<¡ÌAM 0H5£;=ȟW¢%9F¶RK5žŸ¡Ì9)HzKI;=ŸV WŸW:)KI;=ŸVH5£O›KLHI9?:±¤¥9£:>HI9?:+SI<F¡H5ŸW¢±:)£¡¤¥ŸW;LH
W<:¹¤¥Ÿ¶s9£:>±9:U²lO´AD:Ÿq<G
K SI<?> dQ
"Cu9¹°)²x ³9OD9;=AD:µ?H†<;5Ÿq¿ Þ ±Þ
¦ ¿ Ý A´¶„K5žŸV;5Ÿ0ŸWÕUADHnK‡<¤A zŸ …K5AD9:+¤¥Ÿ³KzCuŸWŸV:+K5žŸ
ȟV;nK=AD WŸVH9F¶UK=žŸ£:>UŸW;=OD¢)AD:µ ³9?¡ÌºO´ŸWK5Ÿ.µ?;=<ºžHº;=ŸVH5ŸW;=È)AD:µ\<O´O?K5žŸu W9OD9;LH9F¶!ŸV>Uµ?ŸVHVÀ
<F:!>ÌK5žŸV¢2<;5
Ÿ U° ß ¿ Þ ±Þ
¦ ¿ Ý A´¶ÅK5žŸV;5ŸIŸWÕUADHnK=H<q¤A zŸV …K=A´9?:½¤¥Ÿ³KzCuŸWŸW:È?ŸW;5K5AM ³ŸH
C†žAM LžPº;=ŸVH5ŸW;=ȟHK=žŸ-;=ŸWOM<GK=A´9?: 9F¶qKzCu9ßV>Uµ?ŸVH¹ž<
ÈA´:µ'K5žŸåH=<F¡2Ÿ- W9OD9;QçÆlK»ADH
³9?:ȟW:A´ŸV:?KK59K5žA´:E9F¶¥<CuŸV<FEqAMH59¡29;=ºžAMHn¡ <?H< W9¡2º!9)HnA´K5AD9:9F¶º¥ŸW;=¡£K=<GK=A´9?:
9F¶" ³9?O´9?;=HC†A›K=ž•<:-AMH59¡29;=ºžAMHn¡»QÌ音
K ¤!Ÿ<+°)²x ³9OD9;=AD:µ%<F:!
> ã¤!Ÿ<»HnAD¡2ºODŸ
£:>A´;=ŸV ³K5ŸV>'µ;L<FºžQ+Æx:'K5žŸ±HnŸÍ?£ŸWOuCŸ½C†ADODO£H5Ÿ½K=žŸ¹H=<F¡2Ÿ½:9FK=<FK5AD9:ä<?H0AD:åK5žŸ
º;=ŸWÈAD9£Huº<º!ŸV
; @
S lQ
>UŸVµ 1 !¥7
ž " K=žŸ0>UŸWµ?;5ŸVŸ9¶È?ŸW;5K5ŸWÕ ! A´:»µ;L<Fº#
ª 1 7 $À 1 7 " K=žŸq:£¡¤¥ŸW;†9¶È?ŸW;5K5AM ³ŸVH"<:>%Ÿ>UµŸH"A´:»µ?;=<º#
ž % 1 7 $À & 1 7 " K=žŸqȟV;nK=Ÿ³Õ%<F:!>¹Ÿ>UµŸqH5Ÿ³KLH"9F¶Rµ;L<Fº#
ž ' (1 !¥7
ž " K=žŸq:ŸWADµž¤¥9;=ž99U>½9F¶RȟV;nK=Ÿ³Õ ! AD:»µ;L<Fº)
á *¿ " K=žŸqµ;L<Fºž%¶s9;=¡2ŸV>¹¤)¢¹ŸV>Uµ?ŸVH"9¶ ³9?O´9?;"¿.AD:± W9OD9;=A´:+µ ,á
" K=žŸ0 ³9?O´9?;5AD:µÌA´:>£ ³Ÿ>¹AD:-椢%È?ŸW;5K5AM ³ŸHAD:-'
.0/ á21x1(!¥7 á
, 34
" K=žŸqµ;L<Fºž%¶s9;=¡2ŸV>¹¤)¢¹ŸV>Uµ?ŸVH"9¶ ³9?O´9?0; 3AD:» W9OD9;=A´:µ ,
ê 1 4 5
45ÝGèVâ ª 7 "76 © 8 ¸ ê 1 94 5
4=ÝGè ° 7
JŸ …K5AD9:+ÇÌHn£¡Ì¡<;5ADTWŸH.9?OD>±<F:>¹:ŸVC ;5ŸHn£O›KLHWÀ<:>¹H5ŸV ³K5AD9: 3 >UŸH5 W;5AD¤¥ŸVHuK5žŸ
<FODµ9?;5A´K5ž¡2H"<:>» ³9¡2º£K=<GK=A´9?:HVQ
:×<; ë Ù Ä*+)®#%Vs
B@ ;=ŸWÈAD9£H;=ŸVH5£O›KLHb9?:0K=žŸ†SI<F¡H5ŸW¢q:£¡¤¥ŸW; /213453456)7 ¤)¢08q<O´¤>=ŸWAMH5 Lž 1 OD9GCŸV;
¤¥9£:>À? 8q<FOD¤@ 7 <:>±K5žŸ0<F£UK=ž9;LH< @.S<;5ŸqH5£¡2¡<F;=A´TVŸV>±A´:»K=žŸq¶s9?O´OD9GC†A´:µK=žŸ³²
9;=ŸW¡»Q
Ö¥× 3 ­¯Â /Ì1^34=34n67A /21^34534n67  3 Á ACBEDF½/2134534n6)7qÊã3 ÁHG I BEDJF
DK LON G IQP(R>SUTVSSVWXGZY[P*Y B1^34=34n6!è53 ­ 7]\ K L K T[G D^ _Y[` \ R<P(R B PSbaESbT N PcT[G BED ^4L Sedgfh 3 M
R B Y B aSUT[PiS9W !kj dmlnGoPoR-pXVà .n/ Ð 1 1!¥7Ê Á 3Mq+r `@T[PoR$SbT[s K TVS A tR B Y B P L S B Y[P\Á 6
aESbT[PcG \ S[YuY` \ R)P(R B Pep Và4.n/ §v1d1 u 7.Ê pXVà4.n/ Üw1d1 u 7.ÊyxzB{DJF p Và4.n/ Ð 1d1 u 7.Ê Á 3Jq
0G&
Ç
AMHq< 134534n6èV»7 ³9?O´á 9?;5AD:µ!ÀÅK5žŸV:¯¶s9;qŸWÈ?ŸW;=¢+ȟV;nK=Ÿ³Õ ! À , Ð AMH0< 13 À 3 À 3è
p Wà .0/ Ð 1 1(!¥757 ³9?O´9?;5AD:µÀB<:> , À„¶s9;»Áå ¿% ÇUÀBAMH2< 1 ÇUÀ 3 À 6è p 7 9;2< á 1 ÇUÀ 3 À 6è p 7
³9?O´9?;5AD:µ!À;=ŸVH5º!Ÿ …K5ADȟVO´¢?ÀC†žŸV;5Ÿp Ê p Và .n/ á21 1!¥7 Q„Æx:½K5žŸOD<FKnK5ŸV; V<H5ŸVHQ , ADHŸVÍ)£ADÈ)²
<FODŸW:)KÌK59å< 13456è p 7 µ;L<FºžbÀ.HnAD: WŸ±A´K½ W<::9FK2ž<
È?Ÿ¹Ÿ>UµŸH9¶‡ ³9?O´9?;¿LQ O´Ÿ<F;=O´¢?À
p W à4.0/ §il1 1(¥! 7 pXV à4.0/ Üwd1 1¥! 7 p V à4.n/ Ð d1 1(Å! 7†Êg
ÁÀÅ<F:!>±¶s£;nK=žŸW;=¡29;=Ÿ¶s9; ®Ê 3 ­
K5žŸ$ŸVÍ)£<O´A´K5ADŸVH /2134n6)7Ê <:> /2134534=3?7Ê Á
Ëh A´¡2ºOD¢ ³9?O´9?;%>UŸWµ?;5ŸVŸ
¤¥9£:>H
 p V à .n/ §i1 1(Å! 7 À?p V à .n/ Üw1 1(Å! 7  x <:> Á 3  p V à .n/ Ð 1 1(Å! 7n7  ÁQ2"žŸW;=Ÿ
<F;=Ÿ09?:O´¢ 6 p  )x 7 ÀÉ<F:!><FODO9¶„K5žŸV¡®<F;=Ÿ0E:9GC†:
x 134n6è p 7 µ;L<Fºž!H 13 2¶s9;% +
H5A´: WŸ‡K5žŸqŸ<F;=O´¢½Cu9;=E¤¢%8q<FOD¤@= ŸVADH= Lž 8q<O´¤@l Q
£;RE:9GC†ODŸV>Uµ?Ÿ.<F¤¥9£UKRº¥9?H=HnAD¤ODŸ 1^3453453è p W à4.0/ Ð 1 1¥! 7n7 H5£¤Å ³9?O´9?;5AD:µ?HbA´:! ³OD£>UŸVH
K5žŸ¶s9?O´OD9GC†A´:µQ8q<FOD¤@= ŸWAMH= Lž<F:>$JK=<F:)K=9: 80J R º;=9GȟV>±K=ž<GK‡K5žŸW;=Ÿ<F;=ŸŸWÕ< …K=O´¢
Æl¶
KzCu9+:9:AMH59¡29;=ºžAM 134=34=3è Á 7 ³9?O´9?;5AD:µ)HWÀ¤¥9FK=žåȟV;nK=Ÿ³Õ$K=;=<:H5A›K=A´È?ŸQŸWODŸ³K=A´:µ
9:Ÿ0º!9?A´:)KI¶s;=9¡ ŸV<? Lž±ODŸV<?>H†K=92KzC9%:9:AMH59¡29;=ºžAM 134=34=3è Á 7 ³9?O´9?;5AD:µ)HWÀ<:>
<H½º;59GÈ?ŸV>ä¤)k
¢ IŸVA´:;=AM L_
ž IŸVA´>: \K5žŸW;=Ÿ<F;=Ÿ±:9å9FK5žŸW;LHWQ ş+¶s9?£:>ÃK5ž!<GKK5žŸW;=Ÿ
<F;=Ÿ±Ÿ³Õ< ³K5OD
¢ UÁ¹:9:ADH59¡29;=ºžAM 134=34=3è Á 6)7 W9OD9;=A´:µ?HVÀ„C†žAD LžÃAMH2;5Ÿ>U£ ³Ÿ>åK=9
9:O´¢ Á?Á $£ºÃK59¯CuŸV<FEåAMH59¡29;=ºžAMHn¡»
Q £;5K5žŸW;½HnK=<GK=ADHnK5AM WH<¤!9?£UK½ ³9?O´9?;5AD:µ?HÌAD:
ê 13453453è Á 67 W<:½¤!Ÿ¶s9£:>½AD
: @.
S lQ)Æx:¹H5£¡2¡2<;5¢?À?CuŸ\E:9GC <O´O¥9F¶bê 134=34=3èWâ
Á 67 ÀG¤£KR:9FKê 134=34=3è Á 3?7 Q „ÕUž<£HzK=A´È?ŸBµŸV:ŸW;L<GK=A´9?:09F¶¥<FODO 1^34=3453è Á 3?7 W9OD9;=A´:µ)H
AMH.9?:½K5žŸŸ>UµŸ9F¶É¶sŸV<?HnAD¤ADO´A´Kz¢À¤¥ŸV V<F£H5Ÿ\9¶K5žŸVA´;uȟV;5¢ÌOM<F;=µŸI:£¡¤!ŸV;VÀU<F:!>½ŸWÈ?ŸW:½A´¶
K5žŸWAD;¶s£O´OşW:£¡2ŸV;=<FK5AD9:½CuŸW;=Ÿ W9¡2ºODŸ³K5Ÿ>ÉÀA›K†Cu9£OM>:9Ku¤¥Ÿ‡º!9)H5H5A´¤O´ŸK59̺!ŸV;n¶s9?;5¡
¡£! Lž± W9¡2º£UKL<GK5AD9:!H"C†A›K=ž+ŸV< Lž± ³9?O´9?;5AD:µQ
"žŸq;=ŸVH5£O´K=H"9F¶K5žADH†Cu9;=E½<F;=ŸHzKL<GK5Ÿ>±A´:±K5žŸq:Ÿ³ÕK"KzC9ÌK=žŸW9?;5ŸV¡2HVQ
0G& : × /21^34534n67RÊ 3 ÁCG I
B{DJF K DMLON G IQPoR$SbT9S S9WXGZY[PY B‡134534n6è=3 ­ 7]\ K L K T[G D ^
[Y ` \ RHP(R B PSUaSUT N PcT[G BED ^4L S dh 3 ]R B Y B P L S B Y[PP*l K aSUT[P*G \ SbY !b4w#j d lnGoPoR
p W à4.0/ Ð 1l1(!¥7Ê p Và4.n/ Ð 1l1(7BÊ Á 3Mq
G¥ × "žŸ+ W9¡2º£UKL<GK5AD9:!HÌ>ŸVH= ³;=A´¤¥ŸV>äA´: K5žŸ»:ŸWÕKH5ŸV ³K5AD9:ÃHnž9GCuŸV>åK5ž<FK2:9
³9?O´9?;5AD:µA´:ê 13453456è=3 ­ 7 W<:ž<
È?Ÿu<\K5;=AD<:µODŸ]d C†A›K=žÌ<FK„¡Ì9)HzKR9:Ÿ"H5£ LžȟW;5K5ŸWÕÉQ
I9K5ŸK=ž<GK\"žŸV9;=ŸW¡ Áµ£!<F;L<F:)K5ŸVŸVH"<GK†ODŸV<HnKI9:ŸQ
0G& × /2134=3456)7Ê 3 ÁHG I
BEDF K D$LON G IPoR$SbTVS#S9W4GZY[P*Y B-134534n6è=3 ­ 7+\ K L
TK G D^ Y` \ R)P(R B PSUaESbT N S F ^ S G D P(R>S P(RGoT F \ K L K TCR B Y B P L S B Y[P K D S S DJF! K G D P !
[
lnGoP(R#pXVà4.n/ Ð 1d1!¥7Ê Á 3Jq r `@T[PoR$SbT[s K T9S A R B Y B P L S B YPuÇ"aSUT[PcG \ SbYu Y` \ RP(R B P
p W à .0/ §i1 1 u 7.Ê p Và .n/ Ü1 1 u 7.ÊyxzBEDF p Wà .0/ Ð 1 1 u 7.Ê Á 3Mq
G¥ × Û H5H5£¡2ŸK5ž<FKæAMH†< 13453456è=3 ­ 7 ³9?O´9?;5AD:µ!Q9;†ŸWÈ?ŸW;=¢ÈŸV;nK=Ÿ³Õ ! ÀM , Ð ADH
< 13453453èVâ Á 3)7 ³9OD9;=AD:µÀFAD:2C†žAM LžÌŸVȟV;5¢0È?ŸW;5K5ŸWÕADH.<>n <? ³ŸW:)K„K=90<GKBODŸV<HnK.Ç 1 <:>
<GKR¡29?HnK# Ê /2134=3?7" Á 7 ȟV;nK=AD WŸVHA´:̟V<? Lž ³9?O´9?;VQeI
ŸW:! ³ŸÀF¶s9;R<F:¢qŸV>Uµ?Ÿ !M A´:K5žŸ
K5žA´;L>+ ³9?O´9?;†K5žŸV;5Ÿ¡£HnK\¤¥Ÿ<È?ŸW;5K5Ÿ³Õ%$%H5£ Lž±K5ž<FK !M $½¶s9;=¡HI<2K5;=AM<F:µ?O´ŸqAD:+K5žŸ
K5žA´;L>+ ³9?O´9?;†A´:zÌ
Q""ž£HWÀ!¤¢¹"žŸV9;=ŸW¡ ÇÀ$p W à4.0/ Ð l1 1(¥! 7"Ê Á 3 9?; pXV à4.0/ Ð d1 1 7Ê Á 3 Q
3
JAD: ³Ÿ /213453)7Ê ÀŸ< Lž•Hn£¤!HnŸWK9¶È?ŸW;5K5AM ³ŸVH % 1 7 9F¶u9;L>UŸW;žADµžŸW;‡K5ž<:
+¡£HnKÌ ³9?:)K=<FAD:'<F:äŸV>Uµ?Ÿ%AD:åK5žŸ¹K5žA´;L>' ³9?O´9?;VÀ„H599:Ÿ%9F¶IA´K=H̟V:>Uº¥9AD:?KLH ! ž<?H
p Wà .0/ Ð 1 (1 !¥7Ê Á 3 Q
şI ³9:!HnAM>UŸW;K=ž<GKRK5žADHRCu9;=Eqº;=9GÈ)AM>UŸH<?>>UA´K5AD9:<OŸWÈAD>ŸW: WŸK=9qHn£ºº!9?;nKRK5žŸ
³9?:EzŸV ³K5£;=ŸuK5ž<FK /Ì1^34=34n67„Ê 3 ­ @.SlQ £;nK=žŸW;„ŸVO´AD¡2A´:<FK5AD9:Ì9F¶Å<FODOUȟW;5K5AM ³ŸHRC†A›K=ž
>UŸVµ;=ŸWŸ<GK"O´Ÿ<HnK‡Á 6 AD:%K=žŸ‡K5žAD;L>¹ W9OD9;uADH"º¥ŸW;=ž<Fº!H.¶sŸ<H5A´¤O´Ÿ?QRÏ\:U¶s9;5K5£:<GK=ŸWOD¢ÀU9£;
³£;5;=ŸW:)K0<Fºº;59)< LžAMHq:9KŸWÔ½ ³ADŸW:)K0ŸW:9?£µž-K59»º;=9U ³ŸVŸV>• ³9¡2º£K=<GK=A´9?:<FODOD¢C†A›K=ž
<FODO 1^3453453è Á 3)7 ³9OD9;=AD:µ?HVÀUC†žAM Lž+O´ADEŸVO´¢¹ADH\:ŸWŸ>UŸV>»AD:+9;L>UŸW;"K=9½9¤K=<FAD:±K5žŸ0Ó:<FO
<F:!HnCuŸW;Q
× œ ¥GÚV&' Ù !&VUÚ Ù Î•Ÿ¹>UŸH5 W;5AD¤!Ÿ¹<F:'<FODµ9?;5A´K5ž¡ ³9?:HnK5;=£ …K=A´:µ-<FODO 13453456è=3 ­ 7 W9OD9;=A´:µ?H
C žAM Lžåž<
ȟ½<+K5;=AD<:µODŸ+d 3 .C†A›K=žä<GKO´Ÿ<HnK0KzC9+È?ŸW;5K5AM ³ŸH !b4Vkj d¬H5£ Lž
†
K5ž!<GKpXVà/ Ð 1x1(!Å7 À>p Wà/ Ð 1l1U7uâ Á 6 QR"žŸ‡HnK=<;nK=A´:µÌ ³9?:UÓµ£;=<FK5AD9:H.¶s9;"<FODµ9?;5A´K5ž¡
<F;=Ÿº;=9U>U£ WŸV>¹¤)¢½K5žŸµOD£AD:µÌº;59U WŸV>U£;=Ÿ.À<:>K=žŸW:±K=žŸ‡¶s£O´OHnŸ<F;L Lž½ADH
º¥ŸW;5¶s9;=¡ÌŸ>%£!HnAD:µÌK5žŸq9?º!ŸV;=<FK5AD9:Hu
ê .À !"Éê <:$
> #.%
ê '&(*)Q
GbG
ADȟW: 4,+ j ê 1^34=3453èWâ Á 67 À]u j % 1 7 <:> j % 1+%7 H5£ Lž K5ž<FK
‡
0
.
>UŸVµ / Ð 1 1 u 7½Ê >UŸWµ.- / Ð 1 1 7 À¶s9;̟V<? LžäAMHn9?¡Ì9?;5ºžADH5¡0/210' .n/ Ð 1 1 u 7%3 '4- / Ð 1 1 7
³;=ŸV<FK5Ÿ»<•:ŸWC º<F;5K5AM<FO† W9OD9;=A´:µ65 Ê ß87 1 4,+4 u 4 4 / 7 ¤¢'9GȟV;5OM<FººA´:µ +
C†A´K5žHæ
9?:%K=žŸqȟV;nK=AD WŸVH' .n/ Ð 1l1 u 7 £H5A´:µ9/„À!Hn9ÌK5ž!<GK
1 Á 7 ¶s9;†Ÿ< Lž !Hj '
.n/ Ð d1 1 u 7 K=žŸqȟV;nK=AD WŸVH ! <F:!>:/ 1!¥7 <;5Ÿ‡AM>UŸW:)K5A´ÓŸ>»A´:;5åÀ
1 Ç 7 ¶s9;†Ÿ< Lž ! j % 1+¹7 K5žŸqŸ>UµŸ u ! ž<H† W9OD9; 3 A´:<5åÀ
13?7 ¶s9;†Ÿ< Lž ! j % 1 7 K=žŸqŸV>µŸ ! ž<?H† ³9?O´9?; 3 AD:<5åÀ
' - / Ð 1 1 7=?> @ 7
1s6)7 ¶s9;I<O´O ! j % 1 7 1 ' .n/ Ð 1 1 u 7=?> Au @ 7 <F:!> Hj % 1B+%7 1 "
K5žŸqŸV>Uµ?Ÿ !M ;=ŸW¡<FAD:H"£:! ³9OD9;=ŸV>Q
"žŸ†:ŸVCà W9OD9;=A´:µ5 ž<?HR:9GC ª ÊDC % 1 7EC FC % 1+%7GC ?C ' .n/ Ð 1 1 u 7EC ȟV;nK=AD WŸVHVQ
A´:!<FODO´¢?À?ŸWÕ)K=ŸW:>%5 K59 3 ­ÈŸV;nK=AD WŸVHB¤¢2<>>A´:µ 3 ­ ª»AMHn9?OD<FK5ŸV>2È?ŸW;5K5AM ³ŸH 1 C†A´K5ž%<O´O
<>En < ³ŸV:)K"Ÿ>UµŸH"£: W9OD9;=ŸV> 7 Q
éŸWKHIJ 1 4K+%7 >UŸV:9FK=Ÿ†K5žŸH5Ÿ³K.9¶É<O´O!º<F;5K5AM<FO! ³9OD9;=AD:µ?HL5 C†žAD Lž½ V<F:¤¥Ÿ
9¤K=<FAD:Ÿ>$¤¢ ß7 1 4,++4 u 4 4 / 7 ¶s9?;0Hn9?¡2Ÿ u j % 1 7 Àe j % 1+¹7 <F:>¯H59¡2Ÿ
AMHn9?¡Ì9?;5ºžADH5¡/<?H<F¤¥9Gȟ?Q ¤È)AD9£!HnOD¢À<F:¢ 1^34534n6!è53 ­ 7 ³9OD9;=AD:µH
C†A´K5ž0<:qŸV>Uµ?Ÿ
!$ AD: ³9OD9; 3 <:>»>UŸWµ./ Ð x1 1(Å! 7…4 >ŸWµ. / Ð l1 1 7†â Á 6 W9:)K=<A´:H†<?HI<H5£¤¥ W9OD9;=A´:µ2<:
ŸWODŸW¡2ŸV:?KI9¶IJ 1 4K+%7 À¶s9;IH59¡2Ÿq ³9OD9;=AD:µ?H 4,+mj ê 13453453èVâ Á 67 Q
6
; ?GUÚ Ù ê
xÆ :̟V< LžA´:º£UK„º<F;5K5AM<FO 13453456è=3 ­ 7 ³9OD9;=AD:µÌÀ<?H5H5A´µ?:qK5ž;5ŸVŸº¥9?H=HnAD¤ODŸu W9OD9;LH
K59$ŸV< Lž¯£:! ³9OD9;=ŸV>•Ÿ>UµŸ?À<:>¯A›K=ŸW;L<GK=Ÿ2K5žŸ¶s9?O´OD9GC†AD:µ+º;=9 WŸVH=HWQ%9?;0ŸV<? LžåŸV>Uµ?Ÿ
C†A´K5ž+¡29;=ŸK5ž<:+9:Ÿº!9)H5H5A´¤O´Ÿ0 W9OD9;À>UŸWODŸ³K=Ÿ ³9?O´9?;=HIC†žAD Lž»ODŸV<?>±K59%<̶s9?;5¤AM>>UŸV:
³ODAMÍ?£Ÿ9;‡ÈA´9?OD<FK5Ÿ09?¤È)AD9£!H\>UŸVµ;=ŸWŸ;=ŸVHnK5;=AM …K5AD9:!HIODADHnK5Ÿ>+A´:•HnŸ …K=A´9?:-ÇUQ‡bŸV;5¡2AD:<GK=Ÿ
C†A´K5ž+ŸW¡2ºUKz¢¹9£UK=º£UK\A´¶BHn9?¡2ŸqŸV>Uµ?Ÿqž<H†:9º!9)H5H5A´¤O´Ÿ0 W9OD9;LHWQ„Æl¶RK5žŸW;=ŸqADH†:9½ŸV>Uµ?Ÿ
¶s9;uC†žAM Lž½K=žŸ‡>ŸWODŸ³K5AD9:¹9F¶bº¥9?H=H5A´¤ODŸ W9OD9;LHBAMHuŸW:U¶s9?;= WŸV>ÉÀ?K5žŸV:± W;5Ÿ<GK=Ÿ†K5žŸ9?£UK5º£K
³9?O´9?;5AD:µ
ê 1 7 K5;=ŸV<FK5AD:µ<FODOɟV>Uµ?ŸVH"C†A´K5ž»¡29;=ŸK=ž<F:±9:Ÿ‡º¥9?H=H5A´¤ODŸ0 ³9?O´9?;
<HÌ£:! ³9OD9;=ŸV>Q O´Ÿ<F;=O´¢?À.<F:¢ 134534n6è=3 ­ 7 ³9?O´9?;5AD:µ- W9:)K=<A´:A´:µ¯H5£¤¥ W9OD9;=A´:µ ³9?:)K=<FAD:Hu
ê 1 7 <?H"CŸVO´OdQ
; ?GUÚ Ù L! ê
éŸWKCç
¤!ŸÌ<F:»AD:º£UK‡º<F;5K5AM<FO 1^34=34n6!è53 ­ 7 ³9OD9;=AD:µQu音K䤥Ÿ0K=žŸH5Ÿ³K\9¶R<O´O
ȟV;nK=AD WŸVH±
u Hn£! Lž¹K=ž<GK\K5žŸV;5ŸqAMH\<ÌK=;5AM<F:µ?O´Ÿu !$ AD: ³9OD9; 3 <F:>»>UŸVµ .0/ Ð 1x1(!¥7Iâ Á 6 À
>UŸVµ .0/ § Ð 1 1 7â Á 6 Q 9;ŸV< Lž u j
LžŸ LE$C†žŸWK5žŸV;K=žŸ¹H5£¤Å ³9OD9;=AD:µ+A´:!>U£ ³Ÿ>
¤¢z ž!<H<½º¥9?H=HnAD¤ADO´A´Kz¢»K59±¤¥ŸŸWÕ)K=ŸW:>ŸV>$K59±9:Ÿ9F¶BK=žŸÌK5ž;=ŸWŸÌ:9:Ü ADH59¡29;=ºžAM 1 Ç 4534n6è9?x 7 W9OD9;=A´:µ?HVÀ?<F:!>C†žŸ³K=žŸW;K5žŸ‡H5£¤Å ³9OD9;=AD:µqA´:!>U£ ³Ÿ>½¤¢ ž!<Hu<0º¥9?Hn²
H5A´¤ADODA›Kz¢K590¤¥Ÿ\ŸWÕK5ŸW:!>UŸV>2K=9< 1^34 Ç 4n6!èV?x 7 W9OD9;=A´:µ!QbÆl¶É¶s9?;.ŸV<? Lžu j -K 5žŸ‡<F:H5CŸV;
AMHB<GÔ;=¡2<FK5ADȟ"AD:¤!9K5ž½ W<?HnŸHWÀFK5žŸV:CŸIH=<
¢qK5ž!<GKBK=žŸIº<;nK=AD<O ³9OD9;=AD:µ< H=<GK=ADHnӟH
º;=9º¥ŸW;5Kz¢2
Q ¢¹"žŸW9?;5ŸV¡ Á?ÀUŸWÈ?ŸW;=¢2H5£¤Å ³9?O´9?;5AD:µÌ9F¶eæ
¡£HnK†ž<
ȟº;59?º!ŸV;nKz¢2 Q
º¥ŸW;L<GK5AD9: !"Éê C†ADO´O¥¤!Ÿ\£HnŸ>2K59ŸWODA´¡2AD:<GK=Ÿ\ ³9?O´9?;5AD:µ?H„¶<FADO´AD:µ0º;=9º¥ŸW;5Kz¢2
Q
; ?GUÚ Ù #.ê%'&(*)
éŸWK# !¤ Ÿ-<F:ÄAD:º£UK%º!<F;5K5AM<FO 1^34534n6!è53 ­ 7 ³9OD9;=AD:µÀ"<F:>ëH5£ºº¥9?H5Ÿ ADH%<
H5£¤¥ W9OD9;=A´:µ±9¶"H59¡2Ÿ + j ê 134=3456è53 ­ 7 Q½éŸ³K4 ¤¥ŸK5žŸ%HnŸWK09F¶I<FODOBÈ?ŸW;5K5AM ³ŸVH u
H5£ Lž½K=ž<GK"K5žŸW;=ŸAMH†<0K=;5AM<F:µODŸu !$ AD:¹ W9OD9; 3 <F:>¹>UŸWµ .n/ Ð 1 1(!Å7…4 >UŸWµ .n/ Ð 1 1U7â Á 6 Q
¤H5ŸW;=ȟ\K5ž<FK"¤¢½"žŸV9;=ŸW¡ ÁK5žŸHnŸq W9:>UA´K5AD9:!HAD¡2ºOD¢K5ž<FK"¶s9;u j 'CuŸ¡£HnK
ž<
È?Ÿ p V à- / §i1 1 u 7.Ê p V à- / Ü1 1 u 7.Ê x <:>
p V à- / Ð 1 1 u 7.Ê Á 3 QÎ-Ÿ†ŸWÕºO´9?A›KK5žŸ"OM<GK5K5ŸW;
¤¢K=;5¢AD:µ+K59 W9OD9;H59¡2ŸŸ>UµŸHqA´: AD:'<»º<F;5K<FOD;=ŸV<>¢-<FOD¡29?HnK ³9?O´9?;5Ÿ>-<:>
ODŸV<>A´:µÌK=9ÌODAD¡ÌA´K5Ÿ>»¤;L<F: LžAD:µ!Q
ž99?H5Ÿq<ÌȟW;5K5ŸW
Õ u j ä<:>± ³9OD9;I° jF> Á 4 Ç.@¡<GÕUA´¡2ADTWAD:µK5žŸq:£¡¤!ŸV;†9F© ¶
³9?O´9?;5Ÿ>»ŸV>Uµ?ŸVHA´: © ÀÉADµ:9?;5AD:
µ u+<F:!>$°+µ?A´ÈAD:µ¹ W9¡2ºODŸ³K5ŸÌHn£¤¥ W9OD9;=A´:µ)HI9¶ 1 :ŸV ³ŸH5H=<F;=ADO´¢±9: x ȟW;5K5AM ³ŸH 7 Q\Æl¶BK=žŸW;=ŸAMH:9¹H5£ Lž+º<A´;K5žŸº;=9 WŸVH=H†K=ŸW;=¡ÌAD:<FK5ŸVH
C†A´K5ž+£: Lž!<F:µ?ŸV)
> æ9?:±9?£UK5º£UKVQ K5žŸV;5C†AMHnŸ?ÀŸV<? Lž¹9¶K=žŸqK=ž;5ŸVŸq:9:ADH59¡29;=ºžAM 1 Ç 4534n69è x?7 ³9?O´9?;5AD:µ?H 1 ° Ê Á 7 9?;ŸV< Lž•9F¶K5žŸ2K=ž;=ŸWŸ:9?:ADH59¡29?;5ºžAD 134 Ç 45© 69è x?7
³9?O´9?;5AD:µ)H 1 ° Ê Ç 7 ADHŸW¡¤!Ÿ>>UŸV>$A´:)K=9# AD:-<O´Oº!9)H5H5AD¤O´ŸÌC"<
¢HVÀÅHn9K=ž<GK< ¤¥Ÿ³²
³9?¡2ŸVHu ³9¡2ºODŸ³K=ŸWOD¢½ ³9?O´9?;5Ÿ>2C†žŸW:%K5žŸ‡ÈŸV;nK=AD WŸVH9F¶ 1 Ç 4534n69è x?7\1 9; 134 Ç 4n69è x?757 <F;=Ÿ
AM>UŸW:)K5A´ÓŸ>C†A´K5žK5žŸ† ³9?;5;=ŸVH5º¥9:>UAD:µIÈ?ŸW;5K5AM ³ŸHb9J¶ % 1 7 À?<:>qK=žŸu W9OD9;LHb9¶!<FOD;=ŸV<>¢
³9?O´9?;5Ÿ>%Ÿ>UµŸHIADz
: <F;=Ÿqº;5ŸHnŸV;5È?ŸV>ÉQ \ŸV:9FK=ŸqK5žŸHnŸWK\9F¶B<O´OHn£ Lž»ŸWÕ)K=ŸW:H5AD9:H†¤¢
#%
ê &( ) 1 7 Q \9FK5Ÿ±K=ž<GK%H5£ Lžä¤;=<: LžAD:µ-AMH ³9?;5;=ŸV ³KAD:ÃK5žŸ+H5ŸW:H5Ÿ%K=ž<GK½A´¶
AD:º£UK ãAMH0<+Hn£¤¥ W9OD9;=A´:µ»9¶"< 1 34534n6è=3 ­ 7 W9OD9;=A´:µ + ÀbK5žŸV:'<GK0ODŸV<?HzKq9:Ÿ9F¶
K5žŸqŸWODŸW¡2ŸW:)K=H"9¶J#ê% &( ) 1 7 DA HI<ODH592<ÌH5£¤Å ³9?O´9?;5AD:µÌ9F¶ + Q
œ B !!GÚs& V Ö!× 9?;†ŸV<? Lž¹º<A´;"9¶R W9OD9;=A´:µ)H 4K+mj ê 134=34=3èWâ Á 6)7 W;5Ÿ<GK5Ÿ‡K=žŸ0HnŸWK†9F¶
HnK=<F;5K5AD:µ2º<;nK=AD<OÅ W9OD9;=A´:µ?H Ê IJ 1 4,+%7 Q
µ j ;=ŸWºOM< WŸ C†A´K5žåê 1 7
V :× 9;̟V< Lžåº!<F;5K5AM<FO" ³9OD9;=AD:z
Ÿ ¶s;59?¡ A´¶„
ê 1 7 ž<H\ŸW¡2ºUKz¢»9£UK=º£UK 7 QÏHnAD:µ: Éê$À
1 ;=ŸW¡29GÈ?
>UŸVO´ŸWK5Ÿ†¶s;=9¡ <O´Oº<F;5K5AM<FO W9OD9;=A´:µ?HRC†žAM LžÌ¶<FADOº;=9º¥ŸW;5Kz
¢ 2QRS†ŸW¡29GÈ?Ÿ"¶s;59?¡
AMHn9?¡Ì9?;5ºžAD ‡ ³9?ºADŸVH"9F¶„ ³9?O´9?;5AD:µ)HWQ
V × ÆlK5ŸV;=<FK5Ÿ£:)K5ADO<F¶YK5ŸV;IHzK=ŸWº 13 Q 3)7 AMHuK5žŸ0H5<¡ÌŸq<?H <FK†HnK5ŸVº 13 QDÁ 7 Q
1 Á 7 Û H=H5A´µ?:
Ê Q
µ j <?>:
> #.%
ê &( ) 1 7 K59^Q
1 Ç 7 9?;†ŸV<? Lž¹º<;nK=AD<O ³9?O´9?;5AD:+
µ j Å;=ŸWºOM< WŸ æC†A›K=ž%
ê 1 7 QBÏ\H5A´:µ
13?7 9?;"ŸV< Lž¹º<F;5K5AM<FOÉ W9OD9;=A´:
!"Éê$À>ŸWODŸ³K5Ÿ2¶s;=9¡B<FODOBº<;nK=AD<OB ³9OD9;=AD:)
µ ãC†žAM Lž$¶<A´O.º;59?º!ŸV;nKz¢
2QBS†ŸV¡Ì9GÈ?Ÿ‡¶s;59?¡ÉAMHn9?¡Ì9?;5ºžAD ‡ ³9?ºADŸVH"9F¶„ ³9?O´9?;5AD:µ)HWQ
1s6)7 Û H=H5A´µ?:
Ê ^Q
G¥ × 1 9F¶¥"žŸW9;=ŸW¡ Ç 7 J£ºº¥9?H5Ÿ.K=žŸW;=Ÿ"Ÿ³ÕUAMHzKLH< 134534n6è=3 ­ 7 ³9?O´9?;5AD:µ
ãC†žAM Lž
ž<?H%<åK=;5AM<F:µODŸHd 3 ‡C†A›K=žP<GK±O´Ÿ<HnK%KzCu9'ȟV;nK=AD WŸVH !4w j d®Hn£ Lž K5ž<FK
p Wà / Ð 1d(1 !Å7 ÀepXVà/ Ð 1l1(70â Á 6 QÆlKqAMH‡ŸV<H5¢»K59+H5ŸWŸK5ž<FKK5žŸH5Ÿ³Kq9F¶HnK=<;nK=ŸW;LH‡µŸW:²
ŸW;L<GK=ŸV>$¤)¢ ëA´:'J)K=ŸWºëÁ9¶u<O´µ?9;=A›K=ž¡ ¡£HnKqº;59U>U£! ³Ÿ<¹H5£¤Å ³9?O´9?;5AD:µ±9F¶
'Q"žŸ9K5žŸV;K=ž;=ŸWŸ29º¥ŸW;L<GK=A´9?:HIê 4 Éê <F:> #.ê% &( ) £HnŸ>
AD:<FODµ9;=A´K5ž¡ º;=9>£ ³Ÿ<FK\ODŸV<HnK\9?:Ÿ ³9?O´9?;5AD:µ2A´¶Bº!ŸV;n¶s9?;5¡2ŸV>»9?:Hn£¤¥ W9OD9;=A´:µ)H
9F¶ äQ 9:!HnŸÍ?£ŸW:)K5OD¢ÀRK=žŸ¹H5Ÿ³K ¡£HnK2 W9:)K=<A´:'<-Hn£¤¥ W9OD9;=A´:µ$9F¶ <FKK5žŸ
K5ŸV;5¡2AD:<GK=A´9?:¹9¶ ½À9;†A´¶ Ê K=žŸW:»:9½H5£ L$
ž ŸWÕAMHnK=HVQ
"žŸ$<O´µ?9;=A›K=ž¡ C"<H2;=£:ös9;%<O´OHzKL<F;5K5AD:µ¯º<FAD;=H½9F¶q ³9OD9;=AD:µ?+
H ,4 + j
ê 13453453èVâ Á 6)7 Q+Æx:åŸV< Lž' V<H5ŸA›K̺;=9>£ ³Ÿ>å<F:åŸW¡2ºUKz¢åH5Ÿ³K <F¶YK5ŸW;Ì<H5¡2<O´O
:£¡¤¥ŸW;9F¶ÉA´K5ŸW;L<GK=A´9?:H 1 A´:%¡Ì9)HzKu W<H5ŸVH 6 À 9; 7 9¶JK5ŸWº 3 QR"žADHu ³9?¡2ºO´ŸWK5ŸH„K5žŸ
º;=99F¶9¶R"žŸW9;=ŸW¡ãÇQ
!&VUÚ Ù "žŸ%H5Ÿ³K <F¶YK5ŸW;ÌJ)K5ŸVºÄÁA´:å<FODµ9?;5A´K5ž
¡ Cu<?H0H5ºO´A´KAD:)K59åÁÁ?Á 3 %H5¡<FODO´ŸV;
º<;nKLHWÀ<:>K=žŸ ³9?¡Ìº£UK=<FK5AD9:H‡CuŸW;=Ÿº¥ŸW;5¶s9;=¡2ŸV>$H5ŸWº!<F;L<GK5ŸVO´¢±¶s9?;qŸV< Lž-9F¶BK=žŸW¡»Q
JADµ:A´Ó! V<F:)Kqº<F;5K=H‡9F¶" ³9?¡Ìº£UK=<FK5AD9:HCuŸW;=Ÿ;=ŸWº¥ŸV<FK5Ÿ>$C†A´K5žå<F:•AD:>UŸWº¥ŸW:!>UŸW:)K0AD¡²
ºODŸW¡2ŸW:)KL<GK5AD9:夢-K5žŸ¹HnŸ ³9:!>å<F£UK=ž9;À<:>•K5žŸKzC9$A´¡2ºODŸW¡2ŸW:)KL<GK5AD9:!H<Fµ?;5ŸVŸV>
9:»<FODOº<;nK=AD<OÉ ³9OD9;=AD:µ?Huº;=9U>U£ ³Ÿ>%AD:+H5<¡2ºO´Ÿq V<H5ŸVHVÀU£º±K592ADH59¡29?;5ºžADH5¡»Q
"Cu9‡µ?ŸW:ŸV;=<OUº£¤ODAM †>U9¡<FAD:2º;=9µ;L<F¡HC†;=A›K5K5ŸW:2¤¢ u;=ŸW:><:$ W8q<
¢0CuŸW;=Ÿ
£H5ŸV>%A´:%K5žAMH"C9?;5E 1 DJB `@P N W82ÁU!¶s9?;uK5ŸVHnK5AD:µÌADH59¡29?;5ºžADH5¡ 9F¶ŸV>µŸ ³9OD9;=AD:µ?HVÀ
<F:!> B `@P K Y K D V80ÇR¶s9;q>UAMHzK=;5AD¤£UK=A´:µ z9?¤H‡9GȟV;‡<¹O´9U V<FOR:Ÿ³KzCu9;=EÅQ"žŸK59K=<FO
K5AD¡2Ÿq;5ŸÍ)£A´;=ŸV>½¶s9;†<FODO ³9?¡2º£UK=<FK5AD9:HuC"<H"<F¤¥9£K 6 @Ï ¢?ŸV<;=HVÀ?¡29)HzK=O´¢½9?:»JU£:
ÏIO´K5;L< <:>Á­H5¢UHzK=ŸW¡HWQ„"žAMHuCu<?H<? LžADŸWȟ>AD:±<;5Ÿ<H59:<¤ODŸ\<F¡29£:?K"9F¶K5AD¡2Ÿ
¤¢½ŸW¡2ºOD9G¢A´:µ2<ÌOM<F;=µŸ‡:£¡¤¥ŸW;I9¶ W9¡2º£UK=ŸW;LH†HnAD¡£O´K=<:ŸW9?£H5O´¢?Q
#%l)G Ù SqQIQX‡;=ŸWŸV:)Cu99U><F:!> Û QåQ ‡O´Ÿ<H59:À 9?¡¤AD:<GK=9;=AD<O;5ŸVOD<FK5AD9:H„<:>
Lž;=9¡<FK5AM ¹µ?;=<ºžHVÀ B{DJBXF G BED K `@T DBEL K I B PoR$Sbs B PcG \ YLÀ
1 Á 7 À
Á ËQ
IŸWAD:@ 82QI ŸVA´:;=AM LžÀÉ@B;=9º¥ŸW; W9OD9£;=AD:µ?H\9F¶· § À K `@T DBEL K I P(R>S`Y[P*T BEL G B{D
B P(R>SUs B PcG \9B{L K \ GSbP NA SbT[GSbY À : 1 Á ËË 7 À 6 6 Q
8q<O´¤@! QÌ
QF8q<O´¤>= ŸWAMH5 LžbÀ ž;=9¡<FK5AM Bµ;L<FºžHb<:>SI<¡HnŸV¢ HbK5žŸV9;=ŸW¡»À0R q q
P(R>SbY[GZLY À!ÏI:ADȟV;=H5A›Kz¢%9F¶Î¯<GK=ŸW;=O´99!À? <:)£!<F;=¢+Á Q
80J ! QXÌ
Q8q<O´¤@!= ŸWAMH5 Lž<F:!>ÌS0QXÌ Q)J)KL<F:)K59?:À :ÌK5žŸI¡<GÕUA´¡<OUK5;=AD<:µODŸ³²d¶s;=ŸWŸ
Ÿ>UµŸW²l Lž;=9¡<FK5AM µ?;=<ºžHAD:-K=ž;=ŸWŸ½ ³9?O´9?;=HVÀ K `@T DBEL K I! K s#"UG DJB P K T[G BEL
$R>S K T N À&% 1 Á ?x 7 À U Ç­Q
$ W82Áb ‡
Q Q' V8q<
¢À)( B `@P N £H5ŸW;LH*É µ?£AD>Ÿ 1 ȟV;=H5AD9:äÁ?Q 7 ÀbŸV Lž:AD V<FO„;=ŸWº¥9;5K
†S"² J)² ­F²l­)ÇUÀ 9¡2º£UK=ŸW;JU WA´ŸV: ³Ÿ \ŸVº<F;5K5¡2ŸW:)KÀ Û £HnK5;L<FODAM<F:\<FK5AD9:<O
Ï\:A´È?ŸW;LHnA´Kz¢ÀÉÁ " ­À+-,-,/.1032/24-5768:9-;16</=;>68?;@2:.</A:.@B/</2:CD=FE&2:98?;D,/¥G Q
$ W80Ç ‡
Q Q? W8q<
¢?À`@P K Y K D ÀV<I>UAMHnK5;=A´¤£K5ŸV>0¤<GKL LžHn¢UHnK5ŸV¡P¶s9?;Ï \ÆIH Cu9;=E)²
HnK=<FK5AD9: :Ÿ³KzCu9;=EUH 1KJ ŸV;=H5A´9?: ÁQ 3?7 À!$$S \ R D G \B{LL S K T[
P †S"² J)² F²l­ 3 À
9?¡Ìº£UK5ŸV;»JU WA´ŸV: ³Ÿ \ŸVº<F;5K5¡2ŸV:?KÀ Û £HnK5;L<FODAD<: \<FK5AD9:<O‡Ï\:ADȟW;LH5A›Kz¢?À
Á " À+D,-,/.102-24-576M89-;16<=;>68:;2N*C=?E&28:;D,-A5A:Å9 Q
@.S
[email protected]´C"<FE?9GCIHnEAI<:>ÄJÅQu@RQSI<>UTVADH5TW9GCIH5EA^À 3 ­ Â /2134=3456)7 Â 3 Á?À
K `@T DBEL K IO K sP"bG DB P K T[G B{L B P(R>SUs B PcG \ Y B{DJF K s#"UG DJB P K T[G BEL
K s `@PcG D ^ À : 1 Á "4)x 7 Á 3 F¥ Á 6 ÁQ
S\<>
JÅQ@RQ?S\<>UTVADH5TW9GCIH5EA^ÀJ¡<FODO!SI<¡2H5ŸW¢2:£¡¤!ŸV;=HVÀ-Q L S \ PcT K D G \R K `@T DJB{L K I
K sP"UG DJB P K T[G \ …Y À ¢:<F¡2AM qJ£;=ȟW¢$ÁÀÉÁ F6 U ÇF­?­Á?ÀF;5ŸVÈADH5A´9?:TS x À
+D,-,/.>032-2:U-U/U16V4AFECXWY98:,AZW/4/576IAZ-[D2/\:;DZ]<GU5 Q
Ë