Ануфриев И.Е. Matlab 7 (2005) (1095859), страница 41
Текст из файла (страница 41)
/01232451267 8669:6; ' <=>2?3@A59= +- B5CD=@A59= +%- E % F) G *+ ! & ! <H8BHI 8669:6; JKL ! <H8BHI F) E #-#$ ) #-. F /01232451267 8669:6; ! %! + #-#$ ! /#.$0$ .$1 ƶ½º i¶º¶Ã¾» ºÄÅÄÁþȻÁÒÃÑË Å¶Æ¶Â»ÈÆÄ¸¹Á¶¸Ñ -M % F % N #-. ! ) ! () #-. ! <H8BHI +A 8669:6;- # ) #-.*+#+, & F -. - /# (%.0 123& 4#%56%#17% 189:7% 4 %4#%56%#;8%),! <2 "=<89: <> "=O - 123& 17% <2 <> ! ?% 4# 4%! + #" ƶ½ºi¶º¶Ã¾» ºÄÅÄÁþȻÁÒÃÑË Å¶Æ¶Â»ÈÆÄ¸ ¹Á¶¸Ñ -" #$ %&'(*#P X B5CD=@A59= X <=>2?3@A59= X () B5CD= <=>2?3@A59= ! %"2 +#$+ % B5CD=@A59= %! QF B5CD=@A59= F) % ! ! ! 3#04$ %$0"5 54678 9#4674#$&$:1 F B5CD=@A59= F) ! ! ! %F ¨ »ÈĺÄÂ ÅÆ»ºÄ·ÉÇÁĸÁ»ÃÃÑË ÇÄÅÆµ¼»ÃÃÑË ¹Æ¶º¾»ÃÈĸ3&* qÄ ÉÂÄÁÍ¶Ã¾Ô ¸Ñ·¾Æ¶»Èǵ º¾¶¹ÄöÁÒÃÑ¿ ÅÆ»ºÄ·ÉÇÁĸÁ¾¸¶È»ÁÒ È »Î¾Æ¾Ã¶ ¸»ÆËû¿ ÅÄÁÉÁ»ÃÈÑ Æ¶¸Ã¶ ÃÉÁÔ d Ƶº» ÇÁÉͶ»¸ ¸Ä½ÂļÃÄ ºÄ·¾ÈÒǵÉÇÀÄÆ»Ã¾µ ÇËĺ¾ÂÄÇȾ ¾È»Æ¶Ì¾ÄÃÃÄ¹Ä ÅÆÄÌ»ÇǶ ½¶ ÇÍ»È É¸»Á¾Í»Ã¾µ ξƾÃÑÁ»ÃÈÑ ÅÆ»ºÄ·ÉÇÁĸÁ¾¸¶È»Áµ q¶Æ¶Â»ÈÆ ÇÁɼ¾È ºÁµ ½¶º¶Ã¾µ ξƾÃÑ ¸»ÆËû¿ ÅÄÁÉÁ»ÃÈÑ Á»ÃÈÑ ¸ ¾ÇËĺÃÄ¿ Â¶ÈÆ¾Ì» ö ÄÇÃĸ» ÀÄÈÄÆÄ¿ ÇÈÆÄ¾Èǵ ÅÆ»ºÄ·ÉÇÁĸÁ¾¸¶È»ÁÒ n¶ÀǾ¶ÁÒÃÄ» ;ÇÁÄ ¾È»Æ¶Ì¾¿ ¸ »Èĺ»ÇÄÅÆµ¼»ÃÃÑË ¹Æ¶º¾»ÃÈĸ ÄÅÆ»º»Áµ»Èǵ ½Ã¶Í»Ã¾»Â ¶ ÀƾȻƾ¿ÄÇȶÃĸ¶ ¨ i¶º¶Ã¾» Â¶ÈÆ¾ÌÑ ÀÄ·¾ ¸»ÀÈÄÆÊÉÃÀ̾¾ ¾ÇÇÁ»ºÉ»ÂÄ¿ ½¶º¶Í¾ ½Ã¶Í¾È»ÁÒÃÄÉÇÀÄÆµ»È ¸Ñ;ÇÁ»Ã¾µ v¶¿ÁÊÉÃÀ̾µ ¸Ñ;ÇÁµÔ϶µ Á»¸ÉÔ Í¶ÇÈÒ ¾ÇÇÁ»ºÉ»ÂÄ¿ ǾÇÈ»ÂÑ Ã»Á¾Ã»¿ÃÑË ÉÆ¶¸Ã»Ã¾¿ Ã¶ÅÆ¾Â»Æ ¸ ÇÁÉͶ» Âļ»È¾Â»ÈÒ º¸¶ ¸ÑËĺÃÑË ¶Æ¹É»Ãȶ ¸Ä ¸ÈÄÆÄ ¸Ä½¸Æ¶Ï¶»Èǵ Â¶ÈÆ¾Ì¶ ÀÄ·¾Ç¾ÇÈ»ÂÑ sÄÄȸ»ÈÇȸÉÔϾ¿ ÅÆ¾Â»Æ ƶ½Ä·Æ¶Ã þ¼» d»ÇÈÄ ¶Ã¶Á¾È¾Í»ÇÀĹĸÑ;ÇÁ»Ã¾µ Â¶ÈÆ¾ÌÑ ÀÄ·¾ Á»¸Ä¿ ͶÇȾ ǾÇÈ»ÂÑ Ã»Á¾Ã»¿ÃÑË ÉÆ¶¸Ã»Ã¾¿ÂļÃÄ ½¶º¶ÈÒ »¹Ä ζ·ÁÄÃ È » ƶÇÅÄÁļ»Ã¾» ûÃÉÁ»¸ÑË ÓÁ»Â»ÃÈĸ ¸ ÈĹº¶ ¸ ÅÆÄÌ»ÇÇ» ¸Ñ;ÇÁ»Ã¾¿ ÈÄÁÒÀÄ Ã»ÃÉÁ»¸Ñ» ÓÁ»Â»ÃÈÑÂ¶ÈÆ¾ÌÑ ÀÄ·¾ ·ÉºÉÈ ¶ÅÅÆÄÀǾ¾ÆÄ¸¶ÈÒǵ ÀÄûÍÃѾ ƶ½ÃÄÇȵ¾ ÍÈĽö;ȻÁÒÃÄ ÉÇÀÄÆ¾È ¸Ñ;ÇÁ»Ã¾µ¡Âº¾·ÂÍsÁ»ºÉÔϾ» ƶ½º»ÁÑ ÅÄǸµÏ»ÃÑ ÅÆ¾Â»Ã»Ã¾Ô ûÀÄÈÄÆÑË ÄÅ̾¿ ÉÅÆ¶¸ÁµÔÏ¾Ë ¸Ñ;ÇÁ¾È»ÁÒÃÑÂ ÅÆÄÌ»ÇÇÄ ö ÅÆ¾Â»Æ» ƻλþµ ·ÄÁÒÎÄ¿ ǾÇÈ»ÂÑ ! ûÁ¾Ã»¿ÃÑË ÉÆ¶¸Ã»Ã¾¿ r¶½Ä·Æ¶ÃÄ ÇĽº¶Ã¾» ÅÆ¾Áļ»Ã¾µ Ç ¹Æ¶Ê¾Í»ÇÀ¾Â ¾ÃÈ»ÆÊ»¿ÇÄ ÅÄÁҽĸ¶È»Áµ Ä·Á»¹Í¶ÔÏ»» ¾ÇÅÄÁҽĸ¶Ã¾» ¸Ä½ÂļÃÄÇÈ»¿ 2SWLPL]DWLRQ 7RROER[¢·Ê·¿º·ÃºÃÄ·¾Í¿·½º¿·»¿ÍÇŲ´¿·¿º»r¶ÇÇÂÄÈÆ¾Â ÅÆ¾Â»Æ ƻλþµ ǾÇÈ»ÂÑ Ã»Á¾Ã»¿ÃÑË ÉÆ¶¸Ã»Ã¾¿ ¸ ÀÄÈįĽ¶º¶Ã¾» ¶Ã¶Á¾È¾Í»ÇÀ¾Ë ¸Ñƶ¼»Ã¾¿ ºÁµ ÓÁ»Â»ÃÈĸ Â¶ÈÆ¾ÌÑ ÀÄ·¾ ÇÉÏ»Çȸ»ÃÃÄ É»ÃÒζ»È ¸Æ»Âµ ¸Ñ;ÇÁ»Ã¾¿ o»Ä·Ëĺ¾ÂÄ Æ»Î¾ÈÒ ÅÆ¾¸»º»ÃÃÉÔ Ã¾¼» ǾÇÈ»ÂÉ Ã»Á¾Ã»¿ÃÑË ÉÆ¶¸Ã»Ã¾¿ ) ( [ ) = ºÁµ 3 = [ − [ = − [ + [ − [ = − [Q − + [Q = v¶¿ÁÊÉÃÀ̾µ ¸Ñ;ÇÁµ»È ½Ã¶Í»Ã¾µ ÀÄÂÅÄûÃȸ»ÀÈÄÆÊÉÃÀ̾¾ ¸ ̾ÀÁ» Á¾ÇȾù ) ( [ ) )Q− ( [ ) ! r¶½Â»ÆÃÄÇÈÒ ½¶º¶Í¾ ºÄÇȶÈÄÍÃÄ ·ÄÁÒζµ ¾ À¶À ÂÑ É¸¾º¾Â »» ƻλþ» Âļ»È ½¶ÃµÈÒ ½Ã¶Í¾È»ÁÒÃÄ» ¸Æ»Âµ »ÇÁ¾ û ÅÆ¾Ã¾Â¶ÈÒ ¸Ä ¸Ã¾Â¶Ã¾» ƶ½Æ»¼»ÃÃÉÔ ÇÈÆÉÀÈÉÆÉ ¾ÇËĺÃÄ¿ ǾÇÈ»ÂÑ d º¶ÃÃÄÂ ÅÆ¾Â»Æ» ¸Ñ;ÇÁ»Ã¾» Â¶ÈÆ¾ÌÑÀÄ·¾ º¶»È ÇÉÏ»Çȸ»ÃÃÑ¿ ¸Ñ¾¹ÆÑÎ ¸Ä ¸Æ»Â»Ã¾ n¶Èƾ̶ ÀÄ·¾ ƻζ»ÂĿǾÇÈ»ÂÑ ∂)L ∂[ M L - = M = Q" #$ %&'( )¾Â»»È ºÄÇȶÈÄÍÃÄ ÅÆÄÇÈÉÔ ÇÈÆÉÀÈÉÆÉ ¨ Äö µ¸Áµ»Èǵ ǾÁÒÃÄ Æ¶½Æ»¼»ÃÃÄ¿ÈÆ»Ëº¾¶¹ÄöÁÒÃÄ¿- [ − − [= [Q−− − [Q o¶ÅÄÂþ ÍÈÄ Æ¶½Æ»¼»ÃÃÑ» Â¶ÈÆ¾ÌÑ ÇĽº¶ÔÈǵ ÅÆ¾ ÅÄÂÄϾ ÊÉÃÀ̾¾ ƶ·Äȶ Ç Æ¶½Æ»¼»ÃÃѾ Â¶ÈÆ¾Ì¶Â¾ ÄžǶö ¸ pÍ»¸¾ºÃÄ ÍÈÄ Â¶ÈÆ¾Ì¶ ÀÄ·¾ ÅÆ»ºÇȶ¸Áµ»Èǵ ÇÉÂÂÄ¿ - = ' + ' + ' ƶ½Æ»¼»ÃÃÑË Â¶ÈÆ¾Ì ' ¾ ' ¹º»7 [ ['= [Q− [Q − ' = − fÄÅÄÁþȻ ʶ¿ÁÊÉÃÀÌ¾Ô Ã¶Ëļº»Ã¾»Â ƶ½Æ»¼»ÃÃÄ¹Ä ÅÆ»ºÇȶ¸Á»Ã¾µ ºÁµ Â¶ÈÆ¾ÌÑ ÀÄ·¾ ÀÄÈÄÆ¶µ ¸Ñ;ÇÁµ»Èǵ ¾ ¸Ä½¸Æ¶Ï¶»Èǵ ¸Ä ¸ÈÄÆÄ ¸ÑËĺÃÄ ¶Æ¹É»ÃÈ» »ÇÁ¾ ʶ¿ÁÊÉÃÀ̾µ ¸Ñ½Ñ¸¶»Èǵ Ç º¸Éµ ¸ÑËĺÃѾ ¶Æ¹É»Ãȶ¾ jÇÅÄÁҽɿȻ ÉÇÁĸÃÑ¿ ÄŻƶÈÄÆ ¾ Żƻ»ÃÃÉÔ ºÁµ ůď»ÆÀ¾ ;ÇÁ¶ ¸ÑËĺÃÑË ¶Æ¹É»ÃÈĸ ůď»ÆÀ¶ ;ÇÁ¶ Å¶Æ¶Â»ÈÆÄ¸ Ç ÀÄÈÄÆÑ¾ ¸Ñ½¸¶Ã¶ ʶ¿ÁÊÉÃÀ̾µ ÄžǶö ¸ t»ÀÇÈ Âĺ»ÆÃ¾½¾ÆÄ¸¶ÃÃÄ¿ ʶ¿ÁÊÉÃÀ̾¾ ÅÆ¾¸»º»Ã ¸ Á¾ÇȾù» " ODUJHV\VM #$ %#& !" #NZce!nmgdpby ^ey \uqbke_gby e_\hc qZklb kbkl_fu g_ebg_cguo mjZ\g_gbcb fZljbpu Ydh[b<uqbke_gb_ dhfihg_gl \_dlhj!nmgdpbb ?keb qbkeh \uoh^guo Zj]mf_glh\ [he__ _^bgbpu" lh lj_[m_lky gZclbjZaj_`_ggh_ ij_^klZ\e_gb_ fZljbpu Ydh[b # $FZljbpZ Ydh[b y\ey_lky kmffhc lj_o fZljbp % & ' &$ ' &$(Nhjfbjh\Zgb_ ^bZ]hgZeb fZljbpu & % )*+BgbpbZebaZpby jZaj_`_ggh]h ij_^klZ\e_gby ^ey fZljbpu &$ % Nhjfbjh\Zgb_ \_dlhjZ ih[hqghc ^bZ]hgZeb BgbpbZebaZpby jZaj_`_ggh]h ij_^klZ\e_gby ^ey fZljbpu &$$ % <uqbke_gb_ jZaj_`_gghc fZljbpu Ydh[b % & ' &$ ' &$(+r»Î»Ã¾» ǾÇÈ»ÂÑ Ã»Á¾Ã»¿ÃÑË ÉÆ¶¸Ã»Ã¾¿ ÄÊÄÆÂ¾È» ¸ ʶ¿ÁÅÆÄ¹Æ¶Â» Á¾ÇȾù ¸ ÀÄÈÄÆÄ¿ ½¶º¶ÔÈǵ ;ÇÁÄ Å»Æ»Â»ÃÃÑË ¾ ¸»ÀÈÄÆ öͶÁÒÃĹÄÅÆ¾·Á¾¼»Ã¾µ ¾ ¾ÇÅÄÁҽɻÈǵ ºÁµ ÅľÇÀ¶ ÀÄÆÃ»¿ o¶Î¶ Ì»ÁÒ ÇÄÇÈľȸ ¾ÇÇÁ»ºÄ¸¶Ã¾¾ ÓÊÊ»ÀȾ¸ÃÄÇȾ ÅÆ¾Â»Ã»Ã¾µ µ¸ÃÑË ÊÄÆÂÉÁ ºÁµ ÓÁ»Â»ÃÈÄ¸Â¶ÈÆ¾ÌÑ ÀÄ·¾ ÅÄÓÈÄÂÉ ÇöͶÁ¶ ķƶȾȻÇÒ À ÇÄ ½Ã¶Í»Ã¾»Â ((Å¶Æ¶Â»ÈÆ¶ ÄÃÄ ÉÇȶÃĸÁ»ÃÄ ÅÄ ÉÂÄÁÍ¶Ã¾Ô i¶Â»ÈÒÈ» ÍÈÄ ¸ ÓÈÄÂÇÁÉͶ» ·Éº»È ¸Ñ½Ñ¸¶ÈÒ Ê¶¿ÁÊÉÃÀÌ¾Ô Ç ÄºÃ¾Â ¸ÑËĺÃѶƹÉ»ÃÈÄ ¾ Â¶ÈÆ¾Ì¶ ÀÄ·¾ ¸Ñ;ÇÁµÈÒǵ û ·Éº»È i¶È»Â Âĺ¾Ê¾Ì¾ÆÉ¿È»ÉÅÆ¶¸ÁµÔÏÉÔ ÇÈÆÉÀÈÉÆÉ ÉÇȶÃĸ¾¸ Å¶Æ¶Â»ÈÆ ¸ ½Ã¶Í»Ã¾» ¸ (( ¾ÇÃĸ¶ ÅÆ¾Â»Ã¾È» fÁµ ÀÄÃÈÆÄÁµ ½¶ ¸Æ»Â»Ã»Â Çͻȶ ɺķÃÄ ½¶º»¿Çȸĸ¶ÈÒ ¸ÇÈÆÄ»ÃÃÑ» ÊÉÃÀ̾¾ ¾ '# ( ) )# * % $,,,+ qbkeh i_j_f_gguo, % -$" .+ gZqZevgh_ ijb[eb`_gb_J_r_gb_ kbkl_fu [_a bkihevah\Zgby y\guo nhjfme^ey we_f_glh\ fZljbpu Ydh[b" #$ %&'( * J_r_gb_ kbkl_fu k bkihevah\Zgb_f y\guo nhjfme ^ey we_f_glh\ fZljbpu Ydh[b ! " # $ %& ' $ ( ( $ ) # " * + , , " , - ) * .
/%&*)/.+ $!$ &''(*(+&,+-+&).-+,)*,./)-,'/*-,*..,/'(')*&,(+(.-,(+&+*!(,-/)&-+&,)&('(!&' +,.--*&!.!")*,)(*,&),')*,*+))!./!&$!"$&&*,.-,*.&.,&.,&.,-. % , 0 $$ # 0 # " " " $ 1 ,0 # - 1"0 " # ( $ 1 ,0 #$ "$ # $" 2" - " " " 1 -( ! $ ! 1 " ( ( !1" ' - 3456768956:; <::=>:? $ " " @ " <::=>:? A ( # ( # B , - ( " 3456768956:; <::=>:?¡Âº¾·ÂÁº½À¸·¿ºÑÃ*8,3456768956:; <::=>:? ," " +- $ !1, C1" 1 ! , $ " - D " ( - +- $ - ) = DHD [ + D VLQ D [ + "$( " E( " # " "$ ' , $ , $ "$ . , "$ 1 " " ', , $! ( $ , '$, !"#!$ %&$&'()$!*( , E( - ,F +,-)&).
"&//0( ! "( ," " ( " 1&23 4 "&//0'- . ,$! , G "$( $!1" ! ( 1&2356/78-9 .!1 ! $,( !! ,!! H $" #! $%&' , , :$&5-7 "39 /&,; %$-#3; F<=><? , I" <%)-'&3./0( %&$&'()$0 J 1 <,-4)-). !4- pÀÃÄ ÅÆ¾Áļ»Ã¾µ ͶÇȾ ,,, ! " #$#% &' ( ' ) #$* j»ö ķлÀÈĸ ÅÆ¾Áļ»Ã¾µ ! ÄÀÄÃͶþ» !"# $ % $% '( GZ`ZlZ dghidZ KqblZlv ^Zggu_ <u\h^ ^bZeh]h\h]h hdgZ hldjulby nZceZ Hldjulv nZce k ^Zggufb ! AZibkv \ h[eZklv \\h^Z NZce k ^Zggufb bf_gb nZceZ !! "# Ba\e_q_gb_ ^Zgguo ba nZceZ b aZibkv bo \ ihey kljmdlmju $ "#% $ & '"!#( $ & )"!# KhojZg_gb_ kljmdlmju Ihkljh_gb_ ]jZnbdZ ^Zgguo fZjd_jZfb* $ +% ( !!"#* ,- "# HqbkldZ h[eZklb \\h^Z agZq_gbc iZjZf_ljh\ HilbfZevgu_ iZjZf_lju.
!! !!"" #$ %&'( ) /0 " Kqblu\Zgb_ \_dlhjZ gZqZevgh]h ijb[eb`_gby ^ey iZjZf_ljh\ ba h[eZklb \\h^Z GZqZevgh_ ijb[eb`_gb_. $ 1!+2$! / !!" !#!3# <uiheg_gb_ kljhdb aZibkv gZqZevgh]h ijb[eb`_gby \ \_dlhj +!. Ihkljh_gb_ bkke_^m_fhc nmgdpbb hl gZqZevgh]h ijb[eb`_gby AZ^Zgb_ \_dlhjZ agZq_gbc Z[kpbkk% $ 4%"&4%%" 54%""672&4%%""# <uqbke_gb_ nZce$nmgdpbb bfy dhlhjhc ihevah\Zl_ev \\_e \ kljhd_8 \\h^Z NZce$nmgdpby94 $ !! !#!"( $ 94 +2 %"# Hlh[jZ`_gb_ ]jZnbdZ ^ey gZqZevgh]h ijb[eb`_gby+% ( $$ 0 " AZ^Zgb_ mklZgh\hd ^ey ih^[hjZ iZjZf_ljh\+ +4+( Nhjfbjh\Zgb_ kljhdb k dhfZg^hc ^ey aZkuedb \ \_dlhj +! gZqZevgh]h ijb[eb`_gby. $ 1!+2$! / !!" !#!3# <uiheg_gb_ kljhdb aZibkv gZqZevgh]h ijb[eb`_gby \ \_dlhj +!.
Kqblu\Zgb_ gb`g_c b \_jog_c ]jZgbpu ba h[eZkl_c \\h^Z Gb`gyy ]jZgbpZ b <_jogyy ]jZgbpZ b aZg_k_gb_ bo \ \_dlhju b 1!$! !!" !#!3"#1!$! !! !#!"3"# AZg_k_gb_ \ 94 bf_gb nmgdpbb ba h[eZklb \\h^Z NZce$nmgdpby94 $ !!"# <uah\ nmgdpbb : ^ey ih^[hjZ iZjZf_ljh\+ $ :94 +2 % ( + AZibkv j_amevlZlh\ \ kljhdm HilbfZevgu_ iZjZf_lju. $ 4)+ 7"#. !! ."#*+ Ihkljh_gb_ bkke_^m_fhc nmgdpbb hl gZc^_gguo iZjZf_ljh\% $ 4%"&4%%" 54%""672&4%%""#( $ 94 + %"#*+ $ +% ( !5!"#*+'" !;! ) " 0 "8 HqbkldZ hk_c#+ , "- " ) " ! %&'( '). ) ' ' "½²´²£º¾´À½Î¿Í·´Íɺý·¿ºÑd ÇÄÇȶ¸ 0$7/$% ¸Ëĺ¾È 6\PEROLF 0DWK 7RROER[ ÅÆ»ºÃ¶½Ã¶Í»ÃÃÑ¿ ºÁµ¸Ñ;ÇÁ»Ã¾¿ ¸ Ǿ¸ÄÁÒÃÄ ¸¾º» qƻķƶ½Ä¸¶Ã¾» ¸Ñƶ¼»Ã¾¿ ƶ½ÑÇÀ¶Ã¾»¶Ã¶Á¾È¾Í»ÇÀÄ¹Ä Æ»Î»Ã¾µ ½¶º¶Í Á¾Ã»¿ÃÄ¿ ¶Á¹»·ÆÑ º¾ÊʻƻÃ̾¶ÁÒÃÄ¹Ä ¾¾ÃÈ»¹Æ¶ÁÒÃÄ¹Ä ¾Ç;ÇÁ»Ã¾µ ÅÄÁÉͻþ» ;ÇÁ»ÃÃÄ¹Ä Æ»½ÉÁÒȶȶ Ç ÁÔ·Ä¿ ÈÄÍÃÄÇÈÒÔ ¨ ¸ÄÈ º¶Á»ÀÄ Ã» ÅÄÁÃÑ¿ ŻƻͻÃÒ ¸Ä½ÂļÃÄÇÈ»¿ ÅÆ»ºÄÇȶ¸Áµ»ÂÑ˺¶ÃÃÑ 7RROER[ vÉÃÀ̾¾ 6\PEROLF 0DWK 7RROER[ Æ»¶Á¾½ÉÔÈ ¾ÃÈ»ÆÊ»¿Ç»¼ºÉ ÇÆ»ºÄ¿ 0$7/$% ¾ ·¾·Á¾ÄÈ»ÀÄ¿ ÊÉÃÀ̾¿ µ¸ÁµÔϾËǵ ¸Ñ;ÇÁ¾È»ÁÒÃÑ µºÆÄ 0DSOH ÅÆ¾Í»Â ƶ·Äȶ ¸ 0$7/$% û ÈÆ»·É»È ÉÇȶÃĸÀ¾0DSOH r¶Çξƻþ» 7RROER[ ÅĽ¸ÄÁµ»È ÅÄÁҽĸ¶È»ÁµÂ ¾Â»ÔϾ ÄÅÑÈ Æ¶·ÄÈÑ ¸ 0DSOH ¾ÇÅÄÁҽĸ¶ÈÒ Æ»ÇÉÆÇÑ µºÆ¶ 0DSOH ÅÆ¶ÀȾͻÇÀ¾ ¸ ÅÄÁÃÄ ķл» ¸ÀÁÔͶµ ¾ ÅÆÄ¹Æ¶Â¾ÆÄ¸¶Ã¾» ¸ 0DSOH£º¾´À½Î¿Í·Á·Â·¾·¿¿Í·ºÆÅ¿¼Èººp·Ð»ÀÈÃÄÄÆ¾»ÃȾÆÄ¸¶ÃÃÑ¿ ÅĺËĺ Æ»¶Á¾½Ä¸¶ÃÃÑ¿ ¸ 0$7/$% ÅĽ¸ÄÁ¾ÁǺ»Á¶ÈÒ Æ¶·ÄÈÉ Ç Ç¾Â¸ÄÁÒÃѾ ¸Ñƶ¼»Ã¾µÂ¾ ÅÆÄÇÈÄ¿ ¾ ɺķÃÄ¿ gÇÁ¾ ¸ÑÄǸľÁ¾ ƶ·ÄÈÉ Ç ¶Æ¾Ê»ȾͻÇÀ¾Â¾ ¸Ñƶ¼»Ã¾µÂ¾ ÈÄ Ç¾Â¸ÄÁÒÃÑ» ÅÆ»Ä·Æ¶½Ä¸¶Ã¾µ û ºÄÁ¼ÃÑ ¸Ñ½¸¶ÈÒ ½¶ÈÆÉºÃ»Ã¾¿ Á·¶·½·¿º·Á·Â·¾·¿¿ÍǺÆÅ¿¼Èº»ºÂ²³ÀIJÿº¾ºs¾Â¸ÄÁÒÃÑ» Żƻ»ÃÃÑ» ¾ ÊÉÃÀ̾¾ µ¸ÁµÔÈǵ ķлÀȶ¾ ÀÁ¶ÇǶ V\P REMHFW¸ ÄÈÁ¾Í¾» ÄÈ Í¾ÇÁĸÑË Å»Æ»Â»ÃÃÑË ÀÄÈÄÆÑ» Çĺ»Æ¼¶Èǵ ¸ ¶ÇǾ¸¶Ë GRXEOHDUUD\ s¾Â¸ÄÁÒÃÑ¿ ķлÀÈ ÇĽº¶»Èǵ ÅÆ¾ ÅÄÂÄϾ ÊÉÃÀ̾¾ V\PV lĶú¶!! V\PV [ D EÇĽº¶»È ÈÆ¾ Ǿ¸ÄÁÒÃÑ» Żƻ»ÃÃÑ» [ D ¾ E r¶½Â»Æ ŶµȾ Äȸĺ¾ÂÑ¿ ÅÄÉÂÄÁÍ¶Ã¾Ô Åĺ Ǿ¸ÄÁÒÃÑ» Żƻ»ÃÃÑ» ºÄÇȶÈÄÍÃÄ ·ÄÁÒÎÄ¿ ¨ ÅÄÇÂÄÈ ! ƾȻ ¾ÃÊÄÆÂ¶Ì¾Ô Ä· ÄÅÆ»º»Á»ÃÃÑË ÈÄÁÒÀÄ ÍÈÄ Å»Æ»Â»ÃÃÑË ¸ ÄÀû ·Æ¶É½»Æ¶ ƶ·ÄÍ»¿ ÇÆ»ºÑ ¾Á¾ ¸Ñ½Ä¸¾È» ÀÄÂ¶ÃºÉ ZKRV!! ZKRV [ D1DPHDE[*UDQG WRWDOE6L]H%\WHV&ODVV[V\P REMHFW[V\P REMHFW[V\P REMHFWLV HOHPHQWV XVLQJ E\WHVlÄÃÇÈÆÉ¾ÆÄ¸¶Ã¾» Ǿ¸ÄÁÒÃÑË ÊÉÃÀ̾¿ ÄÈ Å»Æ»Â»ÃÃÑË ÀÁ¶ÇǶ V\P REMHFWůľ½¸Äº¾Èǵ Ç ¾ÇÅÄÁҽĸ¶Ã¾»Â Ä·ÑÍÃÑË ¶Æ¾Ê»ȾͻÇÀ¾Ë ÄŻƶ̾¿ ¾ ķĽöͻþ¿ ºÁµ ¸ÇÈÆÄ»ÃÃÑË Â¶È»Â¶È¾Í»ÇÀ¾Ë ÊÉÃÀ̾¿ Ã¶ÅÆ¾Â»Æ!! I VLQ[ DAFRV[ EAVTUWDEVD EIVLQ[ DAFRV[ EADEVD EAi¶Å¾ÇÒ ÊÄÆÂÉÁÑ ºÁµ ¸Ñƶ¼»Ã¾µ ¸ ĺÃÉ ÇÈÆÄÀÉ Ã» ¸Ç»¹º¶ ɺķö ·ÄÁ»» »ÇÈ»Çȸ»ÃÃÑ¿ ¸¾º ¸Ñƶ¼»Ã¾µ ¸Ñ¸Äº¾È ¸ ÀĶúÃÄ» ÄÀÃÄ ÊÉÃÀ̾µ SUHWW\!! SUHWW\IVLQ[ D FRV[ E_ D E _pÅÆ»º»Á»Ãöµ ÊÉÃÀ̾µ I ȶÀ¼» µ¸Áµ»Èǵ Ǿ¸ÄÁÒÃÄ¿ Żƻ»ÃÃÄ¿ ȾŶ V\PREMHFW ¸ ͻ ûÇÁļÃÄ É·»º¾ÈÒǵ ÅÆ¾ ÅÄÂÄϾ ·Æ¶É½»Æ¶ Żƻ»ÃÃÑËj»ÔϾ»Çµ Ǿ¸ÄÁÒÃÑ» Żƻ»ÃÃÑ» ¾ ÊÉÃÀ̾¾ ÅĽ¸ÄÁµÔÈ Ä·Æ¶½Ä¸Ñ¸¶ÈÒÃĸѻ Ǿ¸ÄÁÒÃÑ» ¸Ñƶ¼»Ã¾µ!! V\PV \!! J H[S\ H[S\JH[S\ H[S\!! K IJKVLQ[ DAFRV[ EADEVD EAH[S\ H[S\!! SUHWW\KVLQ[ D FRV[ E H[S\ _ D E _H[S\" # $% & 's¾Â¸ÄÁÒÃÉÔ ÊÉÃÀÌ¾Ô ÂļÃÄ ÇĽº¶ÈÒ ·»½ ÅÆ»º¸¶Æ¾È»ÁÒÃÄ¹Ä Ä·Ðµ¸Á»Ã¾µÅ»Æ»Â»ÃÃÑË ÅÆ¾ ÅÄÂÄϾ V\P ¸ËĺÃÑ ¶Æ¹É»ÃÈÄ ÀÄÈÄÆÄ¿ µ¸Áµ»Èǵ ÇÈÆÄÀ¶Ç ¸Ñƶ¼»Ã¾»Â ½¶ÀÁÔÍ»Ãöµ ¸ ¶ÅÄÇÈÆÄÊÑ!! ] V\PFAG ]FAG !! SUHWW\]FG fÁµ ķе¸Á»Ã¾µ Ǿ¸ÄÁÒÃÑË Å»Æ»Â»ÃÃÑË Âļ»È ·ÑÈÒ ¾ÇÅÄÁҽĸ¶Ã¶ ÊÉÃÀ̾µ V\P lĶú¶ V\PV D E F ÓÀ¸¾¸¶Á»ÃÈö ÅÄÇÁ»ºÄ¸¶È»ÁÒÃÄÇȾD V\PD E V\PE F V\PFqƾ ƶ·ÄÈ» ¸ Ä·Á¶ÇȾ ÀÄÂÅÁ»ÀÇÃÑË Í¾Ç»Á ÇÁ»ºÉ»È ÉÀ¶½¶ÈÒ ÍÈÄ ÄÅÆ»º»Áµ»ÂÑ» Żƻ»ÃÃÑ» µ¸ÁµÔÈǵ ¸ ķϻ ÇÁÉͶ» ÀÄÂÅÁ»ÀÇÃѾ lÄÂÅÁ»ÀÇÃѻǾ¸ÄÁÒÃÑ» Żƻ»ÃÃÑ» ½¶º¶ÔÈǵ ÀĶúĿ V\PV Ç ÄÅ̾»¿ XQUHDO pÅ̾µUHDO ĽöͶ»È ÍÈÄ Å»Æ»Â»ÃÃÑ» ¾ÃÈ»ÆÅƻȾÆÉÔÈǵ À¶À ¸»Ï»Çȸ»ÃÃÑ» u·»º¾È»ÇÒ ÍÈÄ Æ»½ÉÁÒÈ¶È Ç¾Â¸ÄÁÒÃÑË ¸Ñ;ÇÁ»Ã¾¿ ½¶¸¾Ç¾È ÄÈ ÈÄ¹Ä À¶À¾» Ǿ¸ÄÁÒÃÑ» Żƻ»ÃÃÑ» ¾ÇÅÄÁÒ½ÉÔÈǵ ¨ ¸»Ï»Çȸ»ÃÃÑ» ¾Á¾ ÀÄÂÅÁ»ÀÇÃÑ»p·Ðµ¸¾È» º¸» ¸»Ï»Çȸ»ÃÃÑ» Żƻ»ÃÃÑ» D ¾ E ķƶ½É¿È» ÀÄÂÅÁ»ÀÇÃÄ» ;ÇÁÄ Ç;ȶµ ÍÈÄ D µ¸Áµ»Èǵ º»¿Çȸ¾È»ÁÒÃÄ¿ ͶÇÈÒÔ ¶ E ¨ ÂþÂÄ¿ ¾ ö¿º¾È»ÇÄÅÆµ¼»ÃÃÄ» À ûÂÉ ÅÆ¾ ÅÄÂÄϾ FRQM!! V\PV D E UHDO!! S FRQMD LESD LEqÆÄ¾½¸»º¾È» ¶Ã¶ÁĹ¾ÍÃÑ» º»¿Çȸ¾µ ÅÆ»º¸¶Æ¾È»ÁÒÃÄ Ä·Ðµ¸¾¸ D ¾ E À¶À ÀÄÂÅÁ»ÀÇÃÑ» Żƻ»ÃÃÑ»!! V\PV D E XQUHDO!! T FRQMD LETFRQMD LEp·Æ¶È¾È» ¸Ã¾Â¶Ã¾» ö ½Ã¶Í»Ã¾µ Ǿ¸ÄÁÒÃÑË Å»Æ»Â»ÃÃÑË S ¾ TjÇÅÄÁҽĸ¶Ã¾» ÄºÃ¾Ë ¾ È»Ë ¼» ÄŻƶÈįď ¸ Ǿ¸ÄÁÒÃÑË ¾ ;ÇÁĸÑË ¸Ñƶ¼»Ã¾µË ¸Ä½ÂļÃÄ ·Á¶¹Äº¶Æµ ÈÄÂÉ ÍÈÄ Å¶À»È 0$7/$% µ¸Áµ»Èǵ ķлÀÈÃÄ ( ÄÆ¾»ÃȾÆÄ¸¶ÃÃÄ¿ ǾÇÈ»ÂÄ¿ nÑ Ã» ·Éº»Â ÄžÇѸ¶ÈÒ ¾º»ÄÁĹ¾Ô ķлÀÈÃÄÄÆ¾»ÃȾÆÄ¸¶ÃÃÄ¹Ä ÅÆÄ¹Æ¶Â¾ÆÄ¸¶Ã¾µ ¶ ÅĵÇþ ÇÀ¶½¶ÃÃÄ» ö ÅÆ¾Â»Æ»ÄŻƶ̾¾ ÇÁļ»Ã¾µ fÁµ ÇÁļ»Ã¾µ ;ǻÁ ¾ ;ÇÁĸÑË Â¶ÇǾ¸Ä¸ ¸ 0$7/$%½¶Æ»½»Æ¸¾ÆÄ¸¶Ã ½Ã¶À ÀÄÈÄÆÑ¿ ÅÆ¾¸Äº¾È À ¸Ñ½Ä¸É ¸ÇÈÆÄ»ÃÃÄ¿ ÊÉÃÀ̾¾SOXV ƶÇÅÄÁļ»ÃÃÄ¿ ¸ ÅĺÀ¶È¶ÁĹ» ?WRROER[?PDWODE?RSV? ÄÇÃĸÃÄ¹Ä À¶È¶ÁŶ0$7/$% qÆÄ¸»ÆÒÈ» ÍÈÄ ¾ SOXV ÅÆ¾¸ÄºµÈ À ĺ¾Ã¶ÀĸÄÂÉ Æ»½ÉÁÒȶÈÉ fÁµ Ǿ¸ÄÁÒÃÑË Å»Æ»Â»ÃÃÑË ¾ ÊÉÃÀ̾¿ ¾ÇÅÄÁҽɻÈǵʶ¿ÁÊÉÃÀ̾µ Ç È»Â ¼» ¾Â»Ã»Â SOXV öËĺµÏ¶µÇµ ¸ ÅĺÀ¶È¶ÁĹ»?WRROER[?V\PEROLF?#V\P? ÄÇÃĸÃÄ¹Ä À¶È¶ÁŶ 0$7/$% j½É;Ȼ »» Çĺ»Æ¼¾ÂÄ» ÄÈÀÆÑ¸ ʶ¿Á SOXVP ¸ Æ»º¶ÀÈÄÆ» 0$7/$% û ¸ÃÄǾȻ ¸ û¹Ä ¾½Â»Ã»Ã¾¿ d öͶÁ» Ä·¶ »» ¸ËĺÃÑË ¶Æ¹É»Ãȶ ÅÆ¾¸ÄºµÈǵ À Ǿ¸ÄÁÒÃÄÂÉ È¾Åɺ¶ÃÃÑË ÅÆ¾ ÅÄÂÄϾ ÊÉÃÀ̾¾ V\P ÍÈÄ ÅĽ¸ÄÁµ»È ÇÀÁ¶ºÑ¸¶ÈÒ Ç¾Â¸ÄÁÒÃÉÔŻƻ»ÃÃÉÔ Ç Í¾ÇÁĸĿ ¾ ÅÄÁÉ;ÈÒ Ç¾Â¸ÄÁÒÃÑ¿ Æ»½ÉÁÒÈ¶È f¶Á»» ůď»Æµ»Èǵ ÇĸŶº»Ã¾» ƶ½Â»ÆÄ¸ ¸ËĺÃÑË ¶Æ¹É»ÃÈĸ ÀÄÈÄÆÑ» ÂĹÉÈ ·ÑÈÒ Â¶ÇǾ¸¶Â¾ qÄÇÁ»ºÃµµ ÇÈÆÄÀ¶ Çĺ»Æ¼¾È ¸Ñ½Ä¸ ÊÉÃÀ̾¾ PDSOH ÇÁɼ¶Ï»¿ ºÁµ ķƶϻþµ À ÇÄÄȸ»ÈÇȸÉÔÏ»¿ ÊÉÃÀ̾¾ ¾Á¾ ÄŻƶÈÄÆÉ ¾½ µºÆ¶ ŶÀ»È¶0DSOH ¨ ¸ º¶ÃÃÄ ÇÁÉͶ» Ǿ¸ÄÁÒÃÄÂÉ ÇÁļ»Ã¾Ôeďįµ ö µ½ÑÀ» ķлÀÈÃÄÄÆ¾»ÃȾÆÄ¸¶ÃÃÄ¹Ä ÅÆÄ¹Æ¶Â¾ÆÄ¸¶Ã¾µ ;ÇÁĸѻŻƻ»ÃÃÑ» ȾŶ GRXEOH DUUD\ ķƶ½ÉÔÈ ÀÁ¶ÇÇ ÇÄ Ç¸Ä¾Â¾ »Èĺ¶Â¾ ¸ ÈÄÂ;ÇÁ» SOXV fÁµ ÀÁ¶ÇǶ Ǿ¸ÄÁÒÃÑË Ä·Ð»ÀÈĸ V\P »Èĺ SOXV ŻƻÄÅÆ»º»Á»Ã 0$7/$% ÄÅÆ»º»Áµ»È ÅÄ È¾ÅÉ ¶Æ¹É»Ãȶ ÇÄÄȸ»ÈÇȸÉÔϾ¿ »Èĺ ÀÁ¶ÇǶ ¾ ¸ÑÅÄÁõ»È »¹ÄqÄÁҽĸ¶È»ÁÒ 0$7/$% Âļ»È ÇĽº¶¸¶ÈÒ ÇÄ·Çȸ»ÃÃÑ» ÀÁ¶ÇÇÑ ¾ ÄÅÆ»º»ÁµÈÒ ¾Ë »ÈÄºÑ ¸ ÈÄ ;ÇÁ» ¾ ŻƻÄÅÆ»º»ÁµÈÒ Â»ÈÄºÑ ÅÆ»ºÀ¶ ÀÁ¶ÇǶ dÑÅÄÁûþ» ÅĺķÃÑË º»¿Çȸ¾¿ ÈÆ»·É»È ÅÄþ¶þµ ÄÇÃĸ ķлÀÈÃÄÄÆ¾»ÃȾÆÄ¸¶ÃÃÄ¹Ä ÅÆÄ¹Æ¶Â¾ÆÄ¸¶Ã¾µ sĽº¶Ã¾» ÀÁ¶ÇÇĸ ¸ 0$7/$% ÄžǶÃÄ ¸ ÇÅÆ¶¸ÄÍÃÄ¿ ǾÇȻ» ¸ ƶ½º ²ÄºÈͺ´·¼ÄÀÂÍs¾Â¸ÄÁÒÃÑ» Żƻ»ÃÃÑ» ÂĹÉÈ µ¸ÁµÈÒǵ ÓÁ»Â»Ãȶ¾ Â¶ÈÆ¾Ì ¾ ¸»ÀÈįďÁ»Â»ÃÈÑ ÇÈÆÄÀ Â¶ÈÆ¾Ì ÅÆ¾ ¸¸Äº» ÄȺ»ÁµÔÈǵ ÅÆÄ·»Á¶Â¾ ¾Á¾ ½¶ÅµÈѾ ¶ÇÈÄÁ·Ìĸ ¨ ÈÄÍÀÄ¿ Ç ½¶ÅµÈÄ¿ ȶÀ ¼» À¶À ¾ ºÁµ Ä·ÑÍÃÑË Â¶ÈÆ¾Ì d Æ»½ÉÁÒȶȻ ķƶ½ÉÔÈǵ Ǿ¸ÄÁÒÃÑ» Â¶ÈÆ¾ÌÑ ¾ ¸»ÀÈÄÆÑ À ÀÄÈÄÆÑÂ ÅÆ¾Â»Ã¾ÂÑÂ¶ÈÆ¾ÍÃÑ» ¾ ÅÄÓÁ»Â»ÃÈÃÑ» ÄŻƶ̾¾ ¾ ¸ÇÈÆÄ»ÃÃÑ» ÊÉÃÀ̾¾!! V\PV D E F G H I J K!! $ >D E F G@$> D E@" # $% &> F G@!! % >H I J K@%> H I@> J K@!! & $%&> DH EJ DI EK@> FH GJ FI GK@!! ) $%)> DH EI@> JF GK@lÄÃÇÈÆÉ¾ÆÄ¸¶Ã¾» ·ÁÄÍÃÑË Ç¾Â¸ÄÁÒÃÑË Â¶ÈÆ¾Ì û ÄÈÁ¾Í¶»Èǵ ÄÈ Í¾ÇÁĸÑËÈÆ»·É»Èǵ ÇÁ»º¾ÈÒ ½¶ ƶ½Â»Æ¶Â¾ ÇÄÄȸ»ÈÇȸÉÔÏ¾Ë ·ÁÄÀĸ!! ' >& $ % &@'> DH EJ DI > FH GJ FI >H>JEKDE@GKFG@I DH EJ DI EK@K FH GJ FI GK@p·Æ¶Ï»Ã¾» À ÓÁ»Â»Ãȶ Ǿ¸ÄÁÒÃÑË Â¶ÈÆ¾Ì ¾ ¸»ÀÈįď ůľ½¸Äº¾Èǵ ÅÆ¾ÅÄÂÄϾ ¾Ãº»ÀǶ̾¾ ¸ ÈÄ ;ÇÁ» º¸Ä»ÈÄ;»Â ¾ ¸»ÀÈÄÆÄ ÇÄ ½Ã¶Í»Ã¾µÂ¾ ¾Ãº»ÀÇĸ!! G ' G> FH GJ FI GK!! G G> @G> FH GJFFG@G@fÁµ ɺ¶Á»Ã¾µ ÇÈÆÄÀ ¾Á¾ ÇÈÄÁ·Ìĸ Ǿ¸ÄÁÒÃÑË Â¶ÈÆ¾Ì ¾ÇÅÄÁҽɻÈǵ ÅÉÇÈĿ¶ÇǾ¸!! ' '>H>J> @I DH EJ DI EK@K FH GJ FI GK@ ) Íɺý·¿ºÑÃú¾´À½Î¿Í¾ºÁ·Â·¾·¿¿Í¾ºs¾Â¸ÄÁÒÃÑ» ÄŻƶ̾¾ ÅĽ¸ÄÁµÔÈ Ã¶Ëĺ¾ÈÒ ÈÄÍÃÑ» ½Ã¶Í»Ã¾» ¸Ñƶ¼»Ã¾¿¾Á¾ ½Ã¶Í»Ã¾µ ÇÄ ÇÀÄÁÒ É¹ÄºÃÄ ·ÄÁÒÎÄ¿ ÈÄÍÃÄÇÈÒÔ fÁµ ÅÆ»Ä·Æ¶½Ä¸¶Ã¾µ½Ã¶Í»Ã¾µ ;ÇÁĸĿ Żƻ»ÃÃÄ¿ ¸ Ǿ¸ÄÁÒÃÉÔ ÇÁɼ¾È ÊÉÃÀ̾µ V\P d¸»º¾È»Â¶ÇǾ¸ ȾŶ GRXEOH DUUD\!! $> @¾ ķƶ½É¿È» ÇÄÄȸ»ÈÇȸÉÔϾ¿ »ÂÉ Ç¾Â¸ÄÁÒÃÑ¿ ¶ÇǾ¸!! % V\P$%> @> @qƾ ŻƻËĺ» ÄÈ Í¾ÇÁĸÑË À Ǿ¸ÄÁÒÃÑ ¸Ñƶ¼»Ã¾µÂ ÅÄ ÉÂÄÁÍ¶Ã¾Ô ¾ÇÅÄÁҽɻÈǵ ½¶Å¾ÇÒ Í¾Ç»Á ¸ ¸¾º» ƶ̾ÄöÁÒÃÄ¿ ºÆÄ·¾ dĽÂļÃÑ ¾ ºÆÉ¹¾»ÊÄÆÂÑ ÅÆ»ºÇȶ¸Á»Ã¾µ ;ǻÁ ¸ Ǿ¸ÄÁÒÃÄ ¸¾º» ÀÄÈÄÆÑ» ÄÅÆ»º»ÁµÔÈǵ ½Ã¶Í»Ã¾»Â ¸ÈÄÆÄ¹Ä ¸ËĺÃÄ¹Ä ¶Æ¹É»Ãȶ ÊÉÃÀ̾¾ V\P Ç ƶ½º ÇÅÆ¶¸ÄÍÃÄ¿ ǾÇÈ»ÂÑsĽº¶¿È» ¸»ÀÈÄÆÇÈÄÁ·»Ì!! F> @¾ ½¶Ã»Ç¾È» ¸ ¸»ÀÈÄÆ G »¹Ä Ǿ¸ÄÁÒÃÄ» ÅÆ»ºÇȶ¸Á»Ã¾»!! GV\PFuÂÃļÒÈ» Â¶ÈÆ¾ÌÉ % ö ¸»ÀÈÄÆ G ¨ Æ»½ÉÁÒÈ¶È µ¸Áµ»Èǵ Ǿ¸ÄÁÒÃÄ¿ Żƻ»ÃÃÄ¿ ÅÆ¾Í»Â ¸Ç» ¸Ñ;ÇÁ»Ã¾µ ÅÆÄº»Á¶ÃÑ Ã¶º ƶ̾ÄöÁÒÃѾ ºÆÄ·µÂ¾!! H %GH> @> @jÇÅÄÁҽĸ¶Ã¾» ƶ̾ÄöÁÒÃÑË ºÆÄ·»¿ ÅÆ¾ ¸ÑÅÄÁûþ¾ Ǿ¸ÄÁÒÃÑË ¸Ñ;ÇÁ»Ã¾¿ ĽöͶ»È ÍÈÄ ¸Ç»¹º¶ ÅÄÁÉͶ»Èǵ ÈÄÍÃÑ¿ Æ»½ÉÁÒÈ¶È Ã» Çĺ»Æ¼¶Ï¾¿ÅĹƻÎÃÄÇÈÒ ÄÀÆÉ¹Á»Ã¾µ u·»º¾ÈÒǵ ¸ ¸ÑλÇÀ¶½¶ÃÃÄ ÂļÃÄ Ã¶ ÅÆÄÇÈÄÂÅÆ¾Â»Æ» uÇȶÃĸ¾È» ÊÄÆÂ¶È ORQJ H ºÁµ ÄÈķƶ¼»Ã¾µ ¶ÀǾ¶ÁÒÃÄ ¸Ä½ÂļÃÄ¹Ä Í¾ÇÁ¶ ½Ã¶Í¶Ï¾Ë Ì¾ÊÆ ºÁµ ½Ã¶Í»Ã¾¿ ;ÇÁĸÑË Å»Æ»Â»ÃÃÑË ¾ ö¿º¾È»ÇÉÂÂÉ Í¾Ç»Á ¾ §!! IRUPDW ORQJ H!! H HDQVH" # $% & i¶Å¾Î¾È» À¶¼ºÄ» ¾½ ;ǻÁ ¸ Ǿ¸ÄÁÒÃÑ» Żƻ»ÃÃÑ» ¾ ÇÃĸ¶ ¸Ñ;ÇÁ¾È»ÇÉÂÂÉ!! ODUJH V\PH!! VPDOO V\PH!! V ODUJH VPDOOVr¶Ì¾ÄöÁÒöµ ºÆÄ·Ò µ¸Áµ»Èǵ ÈÄÍÃÑ ½Ã¶Í»Ã¾»Â ÇÉÂÂÑ r¶½É»»Èǵ Ǿ¸ÄÁÒÃÑ» ¸Ñ;ÇÁ»Ã¾µ ÈÆ»·ÉÔÈ ·OÁÒÎ¾Ë ½¶ÈÆ¶È ÀÄÂÅÒÔÈ»ÆÃÑË Æ»ÇÉÆÇĸ ÅÄÇÆ¶¸Ã»Ã¾Ô Ç Ä·ÑÍÃѾdÑ;ÇÁ»Ã¾µ Ç Æ¶Ì¾ÄöÁÒÃѾ ºÆÄ·µÂ¾ ÅĽ¸ÄÁµÔÈ ÅÄÁÉ;ÈÒ ½Ã¶Í»Ã¾» Ǿ¸ÄÁÒÃÄ¹Ä ¸Ñƶ¼»Ã¾µ Ç ÁÔ·Ä¿ ÇȻŻÃÒÔ ÈÄÍÃÄÇȾ È » ö¿È¾ ÇÀÄÁÒ É¹ÄºÃÄÂÃÄ¹Ä ½Ã¶Í¶Ï¾Ë Ì¾ÊÆ Æ»½ÉÁÒȶȶ fÁµ ¸Ñ;ÇÁ»Ã¾µ Ǿ¸ÄÁÒÃÑË ¸Ñƶ¼»Ã¾¿ÅÆ»ºÃ¶½Ã¶Í»Ã¶ ÊÉÃÀ̾µ YSD!! F V\PVTUW!! FQ YSDFFQqÄ ÉÂÄÁÍ¶Ã¾Ô Éº»Æ¼¾¸¶»Èǵ ½Ã¶Í¶Ï¾» Ì¾ÊÆÑ dÈÄÆÄ¿ ºÄÅÄÁþȻÁÒÃÑ¿¸ËĺÃÄ¿ Å¶Æ¶Â»ÈÆ YSD ÇÁɼ¾È ºÁµ ½¶º¶Ã¾µ ÈÄÍÃÄÇȾ!! FQ YSDF FQdÈÄÆÄ¿ ¶Æ¹É»ÃÈ YSD ½¶º¶»È ɺ»Æ¼¾¸¶»ÂÄ» ;ÇÁÄ ½Ã¶Í¶Ï¾Ë Ì¾ÊÆ ÈÄÁÒÀĺÁµ º¶ÃÃÄ¹Ä ¸Ñ½Ä¸¶ YSD fÁµ ¹ÁÄ·¶ÁÒÃÄ¿ ÉÇȶÃĸÀ¾ ÅÆ¾Â»Ãµ»Èǵ ÊÉÃÀ̾µGLJLWV ¸Ä ¸ËĺÃÄ ¶Æ¹É»ÃÈ» ÀÄÈÄÆÄ¿ ÉÀ¶½Ñ¸¶»Èǵ ÈÆ»·É»ÂÄ» ÀÄÁ¾Í»ÇȸÄÌ¾ÊÆd¶¼ÃÄ ÅÄþ¶ÈÒ ÍÈÄ ¸ÑËĺÃÄ¿ ¶Æ¹É»ÃÈ ÊÉÃÀ̾¾ YSD µ¸Áµ»Èǵ Ǿ¸ÄÁÒÃĿŻƻ»ÃÃÄ¿!! ZKRV FQ1DPH6L]HFQ[%\WHV &ODVV V\P REMHFW * fÁµ Żƻ¸Äº¶ Ǿ¸ÄÁÒÃÑË Å»Æ»Â»ÃÃÑË ¸ ;ÇÁĸѻ È » Żƻ»ÃÃÑ» ȾŶGRXEOH DUUD\ ¾ÇÅÄÁҽɻÈǵ ÊÉÃÀ̾µ GRXEOH!! FQXP GRXEOHFQFQXP²ƺɷüÀ·Á·¶ÃIJ´½·¿º·ÆÅ¿¼Èº»d¾½É¶Á¾½¶Ì¾µ Ǿ¸ÄÁÒÃÄ¿ ÊÉÃÀ̾¾ ĺÃÄ¿ Żƻ»ÃÃÄ¿ ÄÇÉÏ»ÇȸÁµ»Èǵ ÅÆ¾ÅÄÂÄϾ H]SORW s¶ÂÑ¿ ÅÆÄÇÈÄ¿ ¸¶Æ¾¶ÃÈ ¾ÇÅÄÁҽĸ¶Ã¾µ H]SORW ÇÄÇÈÄ¾È ¸ÉÀ¶½¶Ã¾¾ Ǿ¸ÄÁÒÃÄ¿ ÊÉÃÀ̾¾ ¸ À¶Í»Çȸ» »º¾ÃÇȸ»ÃÃÄ¹Ä ¸ËĺÃÄ¹Ä ¶Æ¹É»Ãȶ ÅÆ¾ ÓÈÄ ¸ ¹Æ¶Ê¾Í»ÇÀÄ» ÄÀÃÄ ¸Ñ¸Äº¾Èǵ ¹Æ¶Ê¾À ÊÉÃÀ̾¾ ö ÄÈÆ»½À»[−π π]!! I V\P[AVLQ[!! H]SORWIp·Æ¶È¾È» ¸Ã¾Â¶Ã¾» Æ¾Ç ÍÈÄ ¶¸ÈĶȾͻÇÀ¾ ÇĽº¶»Èǵ ÇÄÄȸ»ÈÇȸÉÔϾ¿ ½¶¹ÄÁĸÄÀ qÄ ÉÂÄÁÍ¶Ã¾Ô ¸ À¶Í»Çȸ» ÄÈÆ»½À¶ ö ÀÄÈÄÆÄ ÇÈÆÄ¾Èǵ¹Æ¶Ê¾À ÅÆ¾Ã¾Â¶»Èǵ ÅÆÄ»¼ÉÈÄÀ Żƻǻͻþµ Ä·Á¶ÇȾ ÄÅÆ»º»Á»Ã¾µ ÊÉÃÀ̾¾ ¾ ¾ÃȻƸ¶Á¶ [−π π] dÈÄÆÑ ¶Æ¹É»ÃÈÄ Âļ»È ·ÑÈÒ ½¶º¶Ã ¸»ÀÈÄÆ ǹƶþ̶¾ ÄÈÆ»½À¶ ö ÀÄÈÄÆÄÂ ÈÆ»·É»Èǵ ÅÄÇÈÆÄ¾ÈÒ ¹Æ¶Ê¾À ÊÉÃÀ̾¾!! H]SORWI > @vÉÃÀ̾µ H]SORW ¾Â»»È ûÀÄÈÄÆÑ» ÄÈÁ¾Í¾µ ÄÈ Ç¸Ä»¹Ä ¶Ã¶ÁŶ ¨ ÊÉÃÀ̾¾ISORW ÅÆ¾Â»Ãµ»ÂÄ¿ À ;ÇÁĸÑ ÊÉÃÀ̾µÂ d ͶÇÈÃÄÇȾ ¸Ä½ÂļÃÄ ÉÀ¶½¶Ã¾»Ç¾Â¸ÄÁÒÃÄ¿ ÊÉÃÀ̾¾ ½¶¸¾ÇµÏ»¿ ÄÈ º¸ÉË ¶Æ¹É»ÃÈĸ!! ] V\P[A \A!! H]SORW] > @d º¶ÃÃÄ ÇÁÉͶ» ¸Ñ¸»º»Èǵ Á¾Ã¾µ ö ÀÄÈÄÆÄ¿ ¾ÇÇÁ»ºÉ»ÂÄ» ¸Ñƶ¼»Ã¾» ƶ¸ÃÄ ÃÉÁÔqÆ»º»ÁÑ ¾½Â»Ã»Ã¾µ ÄÅÆ»º»ÁµÔÈǵ ö½¸¶Ã¾µÂ¾ ¶Æ¹É»ÃÈĸ q»Æ¸Ñ» º¸¶Í¾ÇÁ¶ ÇÄÄȸ»ÈÇȸÉÔÈ Å»Æ¸ÄÂÉ ÅÄ ¶Áʶ¸¾ÈÉ ¶Æ¹É»ÃÈÉ ¶ ÅÄÇÁ»ºÃ¾» ¨ ¸ÈÄÆÄÂÉ Ã¶ÅÆ¾Â»Æ ¸ H]SORW] > @ ¹º» ] V\P[A DAÇ;ȶ»Èǵ ÍÈÄ D ¾½Â»Ãµ»Èǵ ÄÈ § ºÄ ¶ [ ¨ ÄÈ § ºÄ qƾ ÅÄÂÄϾ H]SORW ¸Ä½ÂļÃÄ È¶À ¼» ÄÈķƶ¼»Ã¾» Å¶Æ¶Â»ÈÆ¾Í»ÇÀ¾ ½¶º¶ÃÃÑË ÊÉÃÀ̾¿" # $% & + eƶʾÀ Ǿ¸ÄÁÒÃÄ¿ ÊÉÃÀ̾¾ eƶʾÀ Ǿ¸ÄÁÒÃÄ¿ ÊÉÃÀ̾¾ º¸ÉË Å»Æ»Â»ÃÃÑË !" #$### #%!& '$!(# ) * * * * ! * * + ,$!(# "- .'#( #%!'$!(## ( $#%& !/!# .$%!* ! !/!#"* / # " !# '$!(##$& %!!&+ 0#%* "1!# ## ( .'#($* #"-!!%$ ! #+ 23+4+¥ÁÂÀË·¿º·Á·À³Â²¹À´²¿º·º´Íɺý·¿º·´Í²¸·¿º»5-! ."#/(# # #.!%#/(# -!# !( %.$" #! ( 6(#!!% $% $1!#+ #% #!& '$!(# * !!/!!& #/!& "7!# #%!& -!# + 8 %- ## (( !7! ## ! #!%%#* ( # # " "1# .7#%* !!/!! $1!# -!# * ( -!! #%! '$!(##+9## #!%%# #$ / '$!(##) * !* # + :/#!# (6''##! # !& !##% 7%!! ## #!#% '$!(## + :# #7!% # "# .