prob analysis how difficult does it need to be

"#%$'& ()*+&,+ -.&/0132

45 65 879 (1;:=<>79?&A@B C,?EDF &G4H5I> KJML%01<

@ONQP,JSRO@QTSJ

U8V W>X?YX?WZ[Z\W^]_`Wacbdbfe;gOWWbfhiYj kl_mbnV Wo9X Z\e!j?Ypjq_lkl_mbnhr_sYpt?Ykluqbn_mbdh\WsiV t _mv%wqWbx?bfw?syVzY;bdhrV WB{}|_lZ}bnh

Z}oWZ.Wse!t?o1Be;gWth}OYpt3ohrV W1{}e;_`thSbnhr_lg9Yh\WOgOWhrV eo bx=Y;b+YX X k`_lWohreB!We;hrWsyVqt _sYk

X Z\e!j klWgbU8V WcY;o];Yth}Yp!Wb8Yt?o>kl_`gO_lh}Yph\_`e;t?be,hrV WbnWgWh\V eoqbYZ\Wo_brsw?b\bfWox;a_`h\V+X?YZ\hr_sw kmYpZ

Z\W WZrWt?sWhreMhrV WZ\e!klWepbfX?Yphr_Yk?se;ZrZ\WkmYphr_le;t+aVq_siV>_bt e;hY;s^se;w th\W0o e;Z_`t>h\VqWbnWcbf_lgOX k`WgOWh\V

eo bU8V WcX?YXW^Z!eWb=e;t.h\eSoWbrsZ\_`j?WY[gOe;ZrW8Zr_l;e!Z\e!w?b8YX X Z\eY;siVQhre[X Zre;j?Yj _lk`_bnhr_s8!We;hrWsyVqt _sYk

Ypt?Ykluqbn_bx_`tQaV _msyV.ZiYt?oe!g?WkmoQYt?o?t _`h\WcWklW^gOWthgOW^h\V eoe!kle!;_lW0bYZ\W[gWZ\!WoU8V W[ZrWbnw k`hib

V _l!V kl_`;VhsY;bfWb_`taV _siVX Z\e!XW^Z=gOeoWk`_lt epbfX?Yphr_Yk se!Z\ZrWkYh\_le!t_b,_lgOX?e;ZrhiYth^xYpt?o>_`klklw3bnh\Z}YphrWb

h\V _mb8h\V Zre;w !V5Y.bn_lgX klWcWqYpgOX k`WdZrWkYh\_`t +h\e+hrZ\_Y_mYpkse!gOX ZrWb\bf_le;tepYM Zr_shr_le;t3Ypkbne!_lk

#J>RQ.49BTSJ>.

5YptuGbne;wqZisWbOe.w t?sWZrhiY_lthnuAW_bnh_ltG;We!h\WsiV t _msYpkYt?Ypk`u bf_bOZiYt ;_`t / Zre;g

h\V Wg9Yh\WZr_Ypk

X?YpZ}YpgOWhrWZibh\e+hrV Wb\YgOX k`_lt Ypt?oOh\W0bnh\_`t +h\W0syV tq_vw WbKU8V _b8X3YpX?WZcY;oqoZ\WbrbnWb8hrV WSv%wqWbnhr_le;tep

V ea]!YpZ\_mYpj k`W[g9Yh\WZr_YpkX?YpZ}YpgOW^h\WZ}b_lgX?Y;shh\V WSbrY0 Whfu9Yt?o9sebfhde=!We;hrWsyVqt _sYk,oW0bn_l!t,

UZ}Y;o_`h\_le!t?Ypk?!We;hrWsyVqt _sYk Yt?Ypk`u bf_b=w?bfWb=h\V W+{}|Y!sh\e!Z8e=Y Whfu [YX X ZreY;siVO_`t+e;t Wcep hnae[aYuqb

¡¢t) e;w t3o Yphr_le;t3bHYt?Ypk`u bf_b e!ZQW^ YgOX klWx8U,WZ\£0Yp;Vq_¥¤¦b+j?WYpZr_lt sYpX?Y!s_lhfu)Wvw?Yphr_le!t§klW0Y;o b+h\e)Yt

Wbnhr_lg9Yh\W[e8hrV Wh\V WSw klhr_lg9Yh\W[]!Yklw Wx?aV _msyV9_bh\VqWt5o_`]_moWoOjuOh\V W|?Y;shre;ZcepcY0 W^hnuh\eO!_l]W

Ypklk`eaYpjqklWckleY!o_ltq+klW]Wkmb e;Z¨oWbf_l;t ©dklhrWZ\t?Yh\_`]Wklux_ltbnk`e;X?WSbnh}Ypj _`kl_lhfuYpt?Ykluqbn_bxhrV W|?Y;shre;Zep

Y0 Whfu+_mb_lt3sklw?oWo>ju.Z\W0ow?s_`t eph\VqWbnV W0YpZbfh\ZrWt ;hrVOephrV Wbfe;_lk?X Zr_le!Z8h\eSX?WZn e!Z\gO_`t SYMkl_`gO_lh

Wv%wq_lkl_`j Z\_`w gªs^Ypksw kYh\_le!t,=_lhrV WZ8a¨YuxhrV WS|Y!sh\e!ZepY0 W^hnu.Z\W^X Z\WbfWthib8Y>jqkYptq«WhY!sh\e!Zh\V?Yh

_lgOX k`_s_`h\k¬u._lt?sk`w?oWbYklkbfe;w Z}sWbde];YZ\_mYpj _`kl_lhfu9Yt?oBw t?sWZ\h}Yp_lthfuO_ltqV WZ\W^thc_lt#h\V W+!We;hrWsyVqt _sYk

Ypt?Ykluqbn_b

U8V W#YpX X ZreY!syV W0bQoW0b\sZr_lj?Wo_`t/hrV _b>X3YpX?WZ.Yphrh\WgX h>hre5_lt?sk`w?oWOhrV W9WWsh}b>epbne;_`kX Z\e!X?WZ\hfu

];YZ\_mYpj _`kl_lhfu_lt.Y[gOe!Z\W¨b\s_`Wthr_®saYux;w3bn_ltq>bfhiYh\_bfh\_msYpk gWh\V eoqb=¡_lhK_bY;brbnw gOW0o>h\V?YhhrV Wcbne!_lk

X?YpZ}YpgOWhrWZib[_`t1vw Wbfh\_le!tE¯W° O Z\_msh\_`e;t±Ypt !klWxKse;VqWbn_`e;t,xse!gOX ZrWb\bf_lj _`kl_lhfu!xX?WZ\gWYpj _`kl_`hnu?²¨YpZ\W

ZiYpt3oe;gª]!YpZr_Yj klWbh\V?Yh8s^Ypt+j?WdW^X ZrWb\bfWoM_`t+h\V W8 e!Z\gªe,Y[X Zre;j?Yj _lk`_lhfuSoWt?bf_lhfuM wqt?sh\_`e;t,x!h\V Wt

³¢´3µ ¶i·l¸f¹ ¹¶µrº;»=¸f¶¼c¸f½¥¾!¿yÀÁ¦½f¹ Â¸f¹ ¸\¿iµ ½¥¾SÃ¸nÀ^Ä¸fµrºÃ¶ÅÆ¶µ¿yÇ¶¨È0½¾p¶^¶Å¶i·?É[Á¦À¸f¹rº;»=¶Å¦Ç¸nÀºÃ,ÊËÌiÍ^ÌpÎ

Ïr´3µ ¶i·l¸f¹ ¹¶µrº;Ð¸fÑ!¿iµÄ ¼d¸fÀÄ,¶i·3Ò3ÀÓÁ¦À¸f¸nµ Á¦ÀÓcÉ¿yÄ ¾¸f¼[¿iÄÁÆ½n¹rºÐK¿yÅ¦¾¶Ô¹Á¦¸KÕÀÁ¦Ö¸fµ¹ Á¦Ä×º^Ã,¿yÀ!¿iÇ!¿

³¢Â¸f¹ ¸\¿iµ ½¥¾Ø¹ ¹ÁÆ¹Ä¿yÀ^Ä\º!»=¸n¶¼c¸n½¾;¿iÀÁ¦½f¹,Â,¸f¹¸r¿iµ½¥¾SÃ¸fÀÄ ¸fµ\ºÃ¶Å¦¶µ¥¿iÇ¶È0½¾p¶^¶Å¶y·3É[Á¦À¸f¹\º!»=¶Å¦Ç¸fÀºÃ,ÊËÌiÍÌÎ

h\V W_mb\bnwqW8j?Wse!gOWb,e;t WeW0bnh\_`g9Yphr_lt hrV WX Zre;j?Yj _lk`_lhfuSoWt?bf_lhfu[ w t?shr_le;t+e bne;gW8e;wqhise!gOWh\V?Yh

oWX?Wt?o be;t5hrV W_lt Xqw hdZ}Ypt?oe;gÚ]!YpZ\_mYpj k`Wb¨U8V W>e!w h\X wqhsYpt#h\V W^tHj?WS_lth\WZrX Z\WhrWoO_lt9h\W^Z\g9bep

X Z\e!j?Ypj _`kl_`h\_lW0bxklWY!o_ltqMhre+bfhiYphrWgOWthibbfw?syVY;bÛ[{iU8V WoWbn_`;tOk`eY!oe!tOh\VqWÜ e!w t?o Yh\_le!t9a_lklk?!_l]W

YX Zre;j?Yj _lk`_lhfu.epj?WYZ\_ltqOsYX?Y;s_lhfuQYp_`klw ZrW[epÝ

<iÞ

x={iU8VqW>Wg.j?Yptq«gOW^thV3Y;bcYX Zre;j?Yj _lk`_lhfu.ep

bnkle!X?WQYp_`klw ZrWQeÝ

DÞ

xd{iU8VqWOX Z\e!j?Ypjq_lkl_`hfu5epch\VqWOoW0bn_l!t)bnW^h\h\k`WgOWthcklW]Wkmbdj?W_ltqBWqsWWoWoB_b

Ýß

x e;Z+{iU8VqW>X Zre;j?Yj _lk`_lhfuQeh\VqW>bfWWX?Y;WklW^]Wk?W sWWo_`t >hrV WSoWbn_`;t9kl_`gO_lh_mb=Ýà

©áh\Vqe;Z\e!w ;Vw t?oWZibfhiYpt3o_lt 9e8VqepaâZ}Ypt?oe!gã]!YpZr_Yj klWbY0Wsh[hrV WM wqt?sh\_`e;t?bch\V?YhoWX?Wt?oBe!t

h\V Wgä_mbMWbrbnWth\_mYpkOU8V WQ3ZibnhSX?YpZrh>ech\V WOX3YpX?WZ>hrV WZrW e;ZrWObfw gOg9YZ\_bfWb[bfe;gOW+ech\V WQ wqt?o Y0

gOWthiYpk?Zrw klWb8hrV?YphoWbrsZ\_`j?W[h\V _mb8Z\WkmYphr_le;t3bnV _`X,

P.åâIæR+9ç8IMP4HIPTSRON+è7éRO@O#4zå

6@ORO@ON+ç8IP

¡¢thrV _bbnWsh\_le!t,xh\V Wt e!hiYphr_le!t+_bv%w _`h\W=!Wt WZr_s=a_lhrV>Z}Ypt?oe!gâ];YZ\_mYpj k`Wb¯ W°q,êFYt?o+ë² oWt e!h\Wo

_lt9w X X?WZcsY!bnWìYphrWZ_lt9hrV WX?YpX?WZ^xbfXW0s_®sc;We!h\WsiV t _msYpkW YgOX k`Wba_`klkj?W_lt3sklw?oWo

Idíî; ?

ì?WhY[ZiYt?oe;gª]!YZ\_Yj klWêïjWoWbrsZ\_`j?WoMju>hrV Wc=Z\e;j3Ypj _`kl_lhfuSðdWt3bn_lhfu|3wqt?sh\_`e;t9¯ð|²ixñò[¯ó ²}

¡ô¯ ê²c_bYQ w t?shr_le!t5ephrV W.ZiYpt3oe;gä]!YpZr_Yj klW.ê1x,h\VqWt5h\V W.WX?Wsh\W0oB];Yklw W+e8ô¯ ê²ix,_mb_`hib

Y0]W^ZiYp!W];Yklw WSY h\WZ_`hV?Y;bj?WWt9a8W_`;Vh\Wo.juOhrV WS=Z\e;j3Ypj _`kl_lhfuðdWt?bf_lhfu9| w t?sh\_le!t,Û

õ.ö

ô¯ê²÷øGù.ú

ô¯¥ó²fñò[¯ó ²üó

åá?ý)

|_lZ}bnhcBe;gWth^ÛBWYpt

þ ÿ

øõ.ö

êB÷ø

ù.ú

ó?ñpòc¯¥ó²Küó

Wse!t?o9Be;gOWthÛYpZ\_mYpt?sW

ê#÷ø

õö®¯ê

þ ÿ

÷ø

ùOú

¯¥ó

þ,ÿ

ñpòc¯¥ó²Küó

¯ ²

U8V _lZ}oHBe!gOWthÛ=«WatqWb\b

õ.ö¬¯ê

þ ÿ

ùQú

¯¥ó

¯¥ó²üó

¯²

&? > ,Icíî;0 ?

k`_lt W0YpZ wqt?sh\_`e;t9ep

hnae+ZiYt?oe;gÚ]!YpZr_Yj klWb8êéYpt3oHë

õ.öyêë÷ø0õö

êB÷0õö°ë[÷

¯²

U8V WSbnw gFeg.w klhr_lX k`WZiYpt3oe;gÚ]!YpZr_YpjqklWb8ê

x ê

Wh}s;

õ.ö

±ê

1ê !÷,øõ.ö

÷§õö

÷!

Aõ.ö

ê !÷

¯"²

U8V WSbnw gFe= w t?sh\_le!t?b8ep

hnae+ZiYt?oe;gÚ]!YpZr_Yj klWbxêéYpt?o#ë

õ.ö

ñ¯ ê²#ô¯ë²÷ø

õ.ö°ñ¯ê²¥÷$Aõ.ö

ô¯¥ë²÷

¯&%!²

©át e!t kl_`t WYpZ w t?sh\_le!t9ephfa8e.ZiYpt3oe;gÚ]!YpZr_YpjqklWbê

Ypt3o5ësYtBj?W>W^X ZrWb\bfWoHw3bn_ltqOYOUYuk`e;Z

WX3Ypt?bf_le;t

ñ¯ê

ëQ²äø

ñ¯nõ.ö

êB÷

õ.ö

ëM÷²'E¯ ê(§õö

êB÷ ²*)

)

E¯ë+§õ.ö

ëM÷²,)

).-

¯ê§õö

ê#÷²

)

¯¥ë+§õö°ë÷²

)

).-

¯ê§õö

ê#÷²i¯ë+§õ.ö

ë÷ ²

)

)'-

¯¥ë+§õö°ë[÷²}¯ê§õö

êB÷ ²/)

)'-$)

¯0²

h\Vw?b8h\eY3Zibnhe!ZioW^ZepY!ssw Z}Y;suÛ

õ.ö

ñ¯ê

ë+²¥÷øGñ¯nõö

êB÷

õ.ö

ëM÷ ²

¯1²

Ypt?o9h\e.Y.bnWse!t?oOe;Z}oWZÛ

õ.ö

ñ¯ ê

ë+²¥÷Fø

ñ¯nõ.ö

êB÷

õ.ö

ë÷ ²#

.ö

ê#÷

)

ö°ë÷

)

)'-

se]ö

ë÷

)

)'-

Ù2

&? > ,è6

8YZ\_mYpt?sWepY+ZiYt?oe;gï];YZ\_mYpj k`WMê

ê#÷Fø

õö®¯ê

þ ÿ

õö

÷3E¯nõö

êB÷ ²

Ù;Ù

8YZ\_mYpt?sWepY+kl_`t WYpZ w t?shr_le!tHeê

.öyê#÷

õ.ö®¯ ê

þ,ÿ

êB÷

8YZ\_mYpt?sWepY+kl_`t WYpZ w t?shr_le!tHehfa8e+Z}Ypt?oe!gÚ];YZ\_mYpj k`Wb8ê'Ypt?o#ë

ö456iê6ëM÷,ø7

ê#÷6

ö°ë[÷

8se]ö

ë>÷

8YZ\_mYpt?sWepY+kl_`t WYpZ w t?shr_le!tHew t?se;Z\ZrWkYh\WoOZ}Ypt?oe!gF]!YpZr_YpjqklWb

ö:9;

6< pê !÷ø

÷6

ê ;÷

TS%L?qp 5 &

TS0 ?

ep]!YZ\_Yt?sW

se] ö

ëM÷Fø

õ.ö¬¯ê

þ,ÿ

²i¯ë>

²÷

õ.ö

ê5ëM÷@§õö

ê#÷õ.ö

ë[÷

se]ö

ê#÷

õ.ö¬¯ê

þ,ÿ

õ.ö

÷@§¯fõ.ö

êB÷²

ê#÷

"²

e;Z\ZrWkYh\_`e;t

eWBAs_lWth

se],ö

ë÷

%!²

ÙED

DÙ

J>"BIªCRHP Jã.RO49I[R

P IMT+.B4éå

åáIBJGF\C8OP åIHåâI[J>"5.4

U8V W[|_lZibfh

ZioW^Z8Wse!t?o.Be;gOWth¯¥|

%²,gOWhrV eoM_mbY[ZrWkYh\_l]W^klubf_lgOX k`W8gOW^h\V eoep,_`t?sk`w?o%

_lt +hrV WWWshib8e]!YpZr_Ypjq_lkl_`hfu+ep_`t X w h]!YpZr_Yj klWb8e!t5Y+Z\Wbfw klhr_lt oWX?Wt?oWth]!YZ\_Yj klW

U8V W.|_lZ}bnh

Z}oWZ>W0se;t?o5Be!gOWthdgWh\V eo9w?bnW0bMYUYukle;ZbnWZr_lWbdW^X?Yt?bn_`e;t5eh\VqW> w t?shr_le;t

h\e.jWSW]!Ypk`w?YphrWoU8V _bWX?Ypt?bf_le!tH_mbÜhrZ\w t3sYphrWo9Y0 h\W^ZdhrV Wkl_ltqWYpZhrWZ\g5x¯V W^t?sWO{f?Zibfh[e;Z}oWZi²i

U8V WOgOeo_¬?Wo5WX?Ypt?bf_le!t1_b[h\VqWt1w?bfWox=Ykle!t 5a_lhrV1h\V W+?Z}bnh+hfa8e9gOe!gOWthibeph\V W.ZiYt?oe;g

];YZ\_mYpj k`W¯¥bi²ix,h\ezoWh\W^Z\gO_`t Wh\V W.]!YpklwqWb[ephrV W+?Zibfh>hfa8e9gOe!gOWthib8epchrV W.oWX?Wt3oWthM]!YZ\_Yj klW

¯V Wt3sWO{ibfWse!t?oHgOe!gOWthi²i

ðdw W[hre+h\Z\wqt?sYphr_le!tHeh\V WSUYuk`e;ZbfWZ\_`WbY0 hrWZ8?Zibfh8e!ZioWZhrWZ\gbxh\V WY;sswqZiY;suQeh\V W[gWh\V eo

oWh\W^Z\_le!ZiYh\Wb_®KbnW0se;t?o9Yt?oOV _l!V WZoWZ\_`];Yh\_`]Wb=epKh\V Wd wqt?sh\_`e;t#YpZrWbn_`;t _¬sYth^|3wqZ\h\VqWZ\gOe!Z\Wx

h\V W+gOW^h\V eo9hiYp«W0bdt e#Y;sse;w th[ephrV W> e;ZrgãephrV W+X Z\e!j?Ypjq_lkl_`hfuBoWt?bn_`hfu wqt?sh\_`e;t,x oWb\sZ\_ljq_lt

h\V WSZiYpt3oe;g

];YZ\_mYpj k`WbÜw3bn_ltqOe;t k`u9h\V W_`ZdgWYpt#Ypt3o5bnhiYt?o YZiooW]_Yphr_le!t,c¡¢t#h\V W.bf_lgOXqklWd e!Z\g

1x?bf«Wat Wbrb[¯h\Vq_lZio.gOe;gOW^th²_mb8_l!t e;ZrWo

©dt e;hrV WZkl_`gO_lh}Yphr_le;t5ech\V W|

gOWhrV eo5_b[h\V?Yh>t e#WX kl_ms_lhY!sse!w th_mbh}Yp«Wt±epbnX3Yph\_mYpk

se;ZrZ\WkmYph\_`e;t#ephrV W>Z}Ypt?oe;gä]!YpZr_YpjqklW|3e!Z[WqYpgOXqklWx hrV W.bne!_lkX Z\e!XW^Z\h\_`Wb[Yh[hfa8eO!We;hrWsyVqt _sYk

bn_lhrWbse;w kmoV3Y0]WK_oWth\_msYpkgOW0YptYt?obnhiYt?o YZio>oW]_mYphr_le;t3bxV ea8W^]WZ,Yh,e;t Wbn_`h\WxhrV WX Z\e!X?WZ\hr_lWb

se;w kmoO];YZ\uOZ}YpX _moklu. Z\e;gïXe!_lthh\e.X?e;_lth¯{rkleac.bnX?Yh\_Ykse;ZrZ\WkmYphr_le;t9k`Wt ;hrV²ix?Yt?oBYhcYpt e!h\V W^Z

h\V Wuse!w koO]!YpZruQ!ZiY;ow?Ypk`klu5¯{\V _`;V#bnX?Yh\_mYpkse!Z\Z\W^kYphr_le!tOklWtq;h\V3%²iU8V _mb_brbnw Wa_`klk?j?WMZrWh\wqZ\t Wo

h\e.kYphrWZ8_`t9h\V WX?YXW^Z

e;t?bf_oWZcY> w t?sh\_le!t#ñ¯ê

ëQ²ehfa8e+ZiYt?oe!g

]!YZ\_Yj klW0b8ê

Yt?oBë.

U8V WOUYuk`e;Z+WZr_lWbcWX3Ypt?bf_le;tep¨h\V W+ w t?sh\_le!tYpj?e;wqh>h\VqWQgOW0Ypt5]!Ypk`w Wb+¯

þ ÿ

²ix,h\Zrw t?sYh\Wo

Y0 h\W^Z8?Zibfhde!ZioWZhrWZ\gb

Z\e!gFWvw?Yphr_le!t¯J0%²}x ;_l]W0bÛ

ñ¯ê

ëQ²ø

ñ¯

²#E¯ê

)

E¯ë+

)

).-

0²

aV WZ\WSoW^Z\_l]!Yh\_l]W0b8YpZrWW]!Ypklw3Yph\W0oHYh>¯

²}

UeYM?Zibfhde!ZioW^ZepY!ssw Z}Y;suxh\V WWX?WshrWoQ]!Ypk`w WephrV W[ w t?shr_le;t9_mb8;_l]W^tOjuÛ

õ.ö

ñ¯ê

ëQ²÷øGñ¯

þ,ÿ

1²

Ypt?o9h\V W]!YpZr_Ypt3sWjux

.ö°ñ¯ê

ëQ²¥÷ø+.ö¬¯ê

þ,ÿ

)

E¯¥ë+

)

).-

V Wt?sWx

.ö

ñ¯ ê

ëQ²÷øML

)

ó;N

ê#÷$OL

)

)'-

.ö°ë÷$

)

).-

se],ö

ë÷

¡Kê'Ypt3oBëæYpZ\Ww t3se;ZrZ\WkmYph\W0ox

.ö

ñ¯ ê

ëQ²÷øML#)

)

ê#÷$OL#)

)'-

.ö°ë÷

¡¢t9!Wt WZ}Ypk¥x e;ZY wqt?sh\_`e;t9epQP5w t?se!Z\Z\W^kYphrWoQZ}Ypt?oe!gÚ];YZ\_mYpj k`Wbx hrV WS|

äBWhrV eoH!_l]WbÛ

ñ¯ ê

ê !²¥÷ø

SUT

LV)

)

aV WZ\WhrV W[?ZibfhcoWZ\_`]!Yph\_`]Wb8YZ\WW]!Ypk`w?YphrWoHw3bn_ltq+gOWYpt];Yklw W0bM¯

þ,ÿ$W

þ,ÿKX

xll`lx

þ,ÿ<Y

C¨P,å

Idí ý)î@Zc9?#[=&§0p í ?ý/î^ ?)$\]8^:`_.^=^

U8V WQwqt?se;t?t Wo)¯#^

²se!gOX ZrWb\bf_l]W+bfh\ZrWt ;hrVecY#oZiY_lt Woa8^-x_'^=bne!_lk_b[;_`]WtB Z\e!gäh\V W

Be;V Zf

e!w kle!gQj9Wvw?Yphr_le!tBY!bÛ

bBc

hiYt¯<d_

e;t?bf_oWZr_lt +hrV WSskY!b\bf_sYk

e;w k`e;g.j9bnV W0YpZbnh\ZrWt !h\VBkmYaÛ

fBg

øh

hiYt5_

_lh_bgOe!Z\W[ w t?o YgOWthiYkh\eoWYpk,a_`h\V#hiYpti_.^=¯ ZiYh\V WZch\V3Yptj_'^-²¨Y;bh\V WSZiYt?oe;gÚ]!YpZr_Yj klWx?h\Vw?b

Wv%w3Yph\_`e;t¯

²V?Y;bj?WWt9Z\W0YpZ\Z}Ypt !WoBY!bÛ

hiYptV_

1hiYt

<JkfD

"²

UZrWYphr_lt 8^,Ypt?o9hiYt5_'^Y;bw t?se;Z\ZrWkYh\WoOZ}Ypt?oe!gF]!YpZr_YpjqklWbx?Ypt?o9Z\W WZrZ\_`t >hreQWvw?Yh\_le!t¯

²ix

.ö

÷ølL

)

.ö

÷$mL

)

¯h}YptV_

²nN

hiYtV_

%!²

U8V WZ\Wvw _lZrWoOoW^Z\_l]!Yh\_l]W0b8se!gOX w hrWoOYpt3Ypkluh\_msYpk`kluYpZrWM!_l]WtjuÛ

)

bBc

)

hiYt5_@o:

±hiYpt

<kfD

0²

Ypt?o

)

¯hiYtV_

h}Ypti_

1hiYt

_²

<kfD

1²

¡¢h_bdt ea

Xeb\bf_lj k`WQhreBse;gOX wqh\W>hrV W+gOWYt5Yt?obfhiYt?o YpZ}o1oW]_Yh\_`e;t5ep¨h\V W+wqt?se;t?t Wose;g.

X Z\Wbrbn_`]WbnhrZ\Wt !h\V9 e;ZcY+ZiYptq;W>ebfe;_`k,X Z\e!XW^Z\hfuO]!YpZr_Ypt3sWb

©[bQYt§WqYpgX klWx=k`Wh

þ#p

Ù2q2

«q=YYt?o

þ.rsut!v

øähiYtV

2Kw

:%q%GUeYz?Z}bnh.e;Z}oWZ.ep

YpX X Zre_`g9Yphr_le;t x%hrV W[gOW0Ypt.];Yklw Weh\V W[wqt?se;t?t Wo9se!gOX Z\W0b\bn_`]WcbnhrZ\Wt !h\V9_b;_`]WtOjux

þ#xzy

{<"

9«q=Y

e;t?bf_oW^Z[t eaªYQZ}Ypt !WQe¨bnhiYt?o YZiooW]_Yphr_le!t5];Yklw W0bde;th\V W0bnW>_`t X w h];YZ\_mYpj k`Wbx

WXqZ\WbrbnWo[_lthrV Wo_lgOW^t?bn_`e;t k`Wb\b e;Zrgâep3Y

eWBAs_`Wthep@YZ\_Yh\_`e;t.¯&|

~}/

²}¡¢thrV _bWqYpgX klWx

h\V W |

~}/

]!Ypk`w Wb8 e;Zj?e;hrVj8^,Ypt?o9hiYtV_.^,YpZrWh\V WSb\YgOWxh\Vw?b

~}/

rsut!v

rsut<v

rsut!v

¯J

U8V W8X?YZ\hr_YpkqoWZr_l]!Yphr_l]Wbe?h\VqW8w t?se;t?tqWo+se;gX Z\Wbrbn_`]WbnhrZ\Wt !h\VSW]!Ypklw3Yph\W0o>YphKh\V WgOWYpt[ Zre;g

Wv%w3Yph\_`e;t?b=¯

0²,Yt?o+¯

1²,YZ\Wse!t?bnh}Ypthx!Ypt?o;_l]W^t[ju

)

B^ø7

<"cYpt?o

)

¯h}Ypti_.^l²ø

2q2

« =YxV W^t?sW+ e;Z+Y9ZiYt ;WOec_lt Xqw h|

~}/

rs&tv

]!Yklw Wbx=UYpj k`W

!_l]Wb[hrV WQXqZ\Wo_msh\W0oègOW0Ypt

Ypt?o#bnhiYt?o YZioBoW]_mYphr_le;t9eh\V Ww t3se;t3t Wo9se;gX Z\Wbrbn_`]W[bfh\Z\W^t ;hrVH Z\e!gFWvw?Yphr_le!t¯

"²i

J a +P >$\

î& ;&)* )C8OP å

F\ , qqîîqp;H

rsut<v

ö48^°÷

hiYtV_.^¦÷

.ö

xzy

¯i ²fD

¯@5 ²fD

¯i ²

¯ « =Y²

Ùn2K2

2q2

2K2

K0~%

Ù!Ù

2K2

Ù;Ù

2q2

0K K

:%,

2K2

1K "

2q2

"K K

%* q

2K2

~%,0

Ù2q2

2K2

ÙnÙ

2K2

{<0"

2Ù

B*ý/ q= îî?

©dtYpk`h\WZrt?Yphr_l]WSYpX XqZ\eY!syVW]!Ypk`w?YphrWbdhrV W.oWZr_l]!Yphr_l]WbtwqgOWZ\_msYpk`klu!xw?bf_lt #YOsWthrZiYk?tq_lh\W.o_®

WZ\Wt3sWd e;ZrgQwqkYK¡¥tHhrV _bcsY!bnWx hrV WSoWX?Wt?oW^th]!YpZr_Yj klWx

x _bbrYpgOX k`WoOY!sZ\eb\bhnae.bnh}Ypt?o YZio

oW]_Yphr_le!t?b_`tHe!t W[]!YpZr_Yj klWxaV _lk`W[«WWXq_lt Sh\V W[e!h\V W^Z];YZ\_mYpj k`Wd?Wo9Yphh\VqW[gOWYt,=U8V _mb8kYZ\;W

sWth\ZiYko_¬W^Z\Wt?sW+_lth\WZr];Yk=Wt?se;gOX?Y!b\bfWb[Ypj?e!w h "q0

epYklk=]!Yklw Wb[eh\VqWQ_`t X w hX?YZiYpgWh\WZ}b

B^=Yt?oh}YptV_.^ xbne9h\V WYpXqX Z\e_lg9Yh\_le!t5_b[e;tqkluBZrWY;bfe;t?Yj klW_®h\V W+ w t?sh\_le!t

b8c

¯8^

hiYt5_'^m² Zre;g

Wv%w3Yph\_`e;t¯

"%²}x?oeWb8t e!hdWV _`j _lhg.w?syV.t e!t kl_`t WYpZr_lhfu.Y;sZ\ebrbÜhrV _bZiYt ;WU8V W[?t _`h\Wo_®WZ\W^t?sW

e;Z\g.w kmY;bh}Yp«Wh\VqW e!Z\g5Û

)

þ#p

þ.rsut!v

þ#p

þ.rsut3v

øI

¯J

Ypt?o

)

¯ hiYptV_

bBc

rsut!v

rs&t!v

bBc

rsut!v

rsut<v

rsut!v

¯J

U8V W>g9Y_lt#Yphrh\Z}Y;shr_le;t5eh\V _mbdYX X Z\eY;siV,x_mbÜhrV?Yph[e!t?sWSh\V WoWZ\_`]!Yph\_`]Wh\WZrg9bYpZrW.b\vw?YpZrWoBYt?o

bnw j?bfh\_`h\w hrWoO_lth\e+Wvw?Yphr_le!t¯

%!²ix?h\V W]!YpZr_Ypt3sWb8epB^Ypt?o9hiYpti_.^sYpt3sWke!w hx?klW0Y0]_ltq Û

.ö

rsut<v

¯J K ²

¡¢t5hrV _bsY;bfWx

_mb[YOkl_ltqWYpZ w t?shr_le!t5epV8^Ypt?o5_b[bfkl_`;Vh\klu9t e!t kl_`t WYZ[a_lhrV5Z\WbfXW0sh[h\ehiYpti_.^x

bne.h\V Wtw gOWZr_sYk?YpX XqZ\e_`g9Yphr_le!tHae;Zr« b8aWklk Y;bcbnV eatBjuUYj klW

J ] >P0 +3\

î& ;0&A* ,1C8OP å

F\*ý) îî? QH

~}/

rsut!v

bBc

xzy

þ#xzy

~}/

xzy

¯«q=Y%²

¯ « KY%²

¯Ji3²

¯«q=Y%²

¯ « =Y²

* "*

<1K10

K0U%

{<"4

Ù!Ù

Ù2

*<0{q1

Ù;Ù

{<"4

0K1{

:%, K0K"

1K 4

{<"4

Ù;Ù

14"

{<"4

~%,0

Ù!Ù

~%q%

Ùq2

{<"1

{<"4

2q2

¡¢h_mbsklW0YpZ Zre;gÚUYpjqklWb

Yt?o

hrV?Yphch\VqWMZrWbnwqklhib8_`t9h\V _mbsY;bfW>YZ\WWbrbnWth\_mYpklk`uQwqt?syV3Ypt !Wo

RO:[K&A îî?

*& ±?&A&+ý/

¡¢t.h\VqW[Yje]WcWqYpgOX k`Wx!Y?Z}bnhe;Z}oWZYX X Zrep_lgYph\_`e;t+a¨Y;bw3bnWo+h\eSX Z\Wo_sh=j?e!h\VOhrV WdgWYpt.Yt?o

];YZ\_mYpt?sWep

Z\e;gæWvw?Yphr_le!t?b[¯

1%²Ypt3o¯

²}8_lt?sW[h\V W];YZ\_mYpt?sW0b8epQB^Ypt?oOhiYtV_.^YpZ\Wj?e;hrV

«t eat.V ea8W]W^Zx_lh=_mbX?eb\bf_lj k`WdhreZ\W?tqWh\V WWbfh\_`g9YphrW8ep

juS_lt?sklw?o_`t bfWse;t3oe!ZioWZKh\WZrg9b

Z\e;gïWv%w3Yph\_`e;t¯

Ùn2

²klWY!o_ltq+h\e Û

þ#xzy

b8c

rsut!v

²#

.ö

)

hiYt5_

)

¯ hiYt_

se]ö

h}Ypti_

)

¯h}YptV_

¯J {²

aV WZ\WYpk`k=oW^Z\_l]!Yh\_l]W0bdYZ\W>W^];Yklw?Yh\Wo5Yh[h\VqW>gOWYt,5ce;h\_`t .h\V?Yh[_lt5hrV _bcsY;bfW

)

bBc

)

Ypt?o#se]ö48^

hiYpti_.^¦÷ø

x h\VqWMW^X ZrWb\bf_le!tBbf_lgOXqkl_®3Wb=h\e Û

þxy

bBc

rsut!v

²#

.ö

h}YptV_

)

¯ hiYptV_

¯J K²

U8V WSYpt?Ykluh\_s^Ypk e;ZrgFepKh\VqW>bfWse!t?oBoW^Z\_l]!Yh\_l]Wc_b;_`]WtOjuÛ

)

¯ hiYtV_

±hiYpt

<JkfD

hiYt

_.^

1h}Ypt

kfD

¯J K"²

e;g.j _lt _`t >W0v%w?Yh\_`e;t?b[¯J K%²¨Ypt3o¯ q"%²= e!ZdhrV WX?YpZrh\_sw kYZsY!bnWep

Ùn2K2

«q=Y+Yt?o

rsut3v

<%K%SklWY!o bh\e Û

xzy

øh *<"

6"{

1q.ö

hiYt5_

÷« KY

¯J :%!²

UYj klW ObfV eacb[YOZ\Wae;Zr«_`t Qeh\V W.Yt?Ypk`uhr_sYkZrWbnw k`hib8 Z\e!gäUYpj k`W

_lt?sklw?o_`t bnWse!t?oBe;Z}oWZ

h\WZrg9b=_ltOhrV WWbnhr_lg9Yh\_le!tQe

©áse;gOX?YZ\_mbne;tepKh\V W[ZrWbnwqklhib= Z\e!gFh\V Whnae+hiYj klWb_lt?o_sYh\Wb

h\V?Yh+h\V W9bfWse!t?oe;Z}oWZSh\WZrg9b[V?Y]WQg9YZ\!_lt?Yklklu5_`t?sZrWY;bfWo

Yt?o1h\Vw?bMZrWow?sW0o|

U}/

xzy

j w hh\V Wo_¬W^Z\Wt?sWbYpZ\Wcj?YZ\Wk`u+t e;hr_sWYj klWwqthr_lk hrV Wd_`t X w h]!YpZr_Yt?sWcjW0se;gOW0bZ\WkmYphr_l]Wk`uMkmYpZr;W

J8 j >P0 0 +$\

î& ;&§* ±C8OP,å

F\ , îî?

*& ±?&E?&+ý){H

~}/

rsut!v

h}Ypti_.^¦÷

¯i ²

¯«q=Y%²

2q2

q0U%

{""

Ù!Ù

2q2

Ù;Ù

0K q

1q "

"K q

K<%

~%,"

2q2

{0"

K"q 1

1q"

J>"BIª>.BJÚIMP J>åâ@[J>IæåâI[J>"5.4

F\I[å¡H

U8V WSe;_`thcbnhr_lg9Yh\WBWh\Vqeo¯¥²_bYt#YpklhrWZ\t3Yph\_`]W[aYuOe=h}Yp«_lt +_`thre.Y;sse;w thZiYt?oe;g

];YZ\_mYpj k`Wb1ì?_l«W|

oeW0b>t e;h+ZrWv%wq_lZ\W«t eak`Wo;Weph\V WOX3YpZ\hr_swqkYpZ e;Zrg

eph\V W

X Z\e!j?Ypj _`kl_`hnu.oWt?bn_`hfu> w t?shr_le;t.ephrV W[_`t X w h^x%VqepaW]WZã_b8Yj klWch\eY;sse;w th e!Z8w XOhre>hrV Z\WW

gOe;gOW^th}b8¯gOW0Ypt

x ];YZ\_mYpt?sW

x?Ypt3oHbf«Wat Wbrb

²i©b8a_lh\V#|

1xähiY«Wb8t e+WX kl_ms_lh

Y;sse!w thepbfX?Yphr_Ypkse;Z\ZrWkYh\_`e;t,

_mbW0b\bnW^thr_Ypk`kluYca8W_`;Vh\WoY]WZiY;WgOWh\VqeoZrWgO_`t _brsWthep3tw gWZ\_msYpk!_lth\W!ZiYphr_le!tM e;ZrgQw

kY;b_lt]e;k`]_`t O{ibrYpgOXqkl_ltq>X?e;_`th}b\>Yt?o1{\aW_l!Vhr_lt X?YZiYpgWh\WZ}b\=U8V W[X?e!_lth8Wbfh\_lgYph\WgWh\V eo

Z\W]_lWaWoBV WZrWOa_lk`kjWh\V WOhfaeBX?e;_`thSWbnhr_lg9Yh\W+gOWhrV eooW]Wk`e;X?Wojua¢ÜebnWtj k`w Wh\V

1<%*x

1K0

²}

U8V WOe;_lthSbnh\_`g9YphrW+BWhrV eo1bfWW«qbdh\e#Z\WX kmY;sW.Y9se!thr_ltw e;w3bXqZ\e;j3Ypj _`kl_lhfuzoWt?bf_lhfuH w t3sh\_`e;t,x

a_lh\V#Y.o_brsZ\W^h\Wd w t3sh\_`e;t9V?Y]_`t +h\VqW>brYpgOWc?ZibfhdhrV Z\WWsWth\ZiYk,gOe;gWth}b

|_l!w Z\W

£cWa'ðd_bfh\Z\_`j w hr_le;t

Pî¤\r?O ý)îý1 ,5I[å

cðdWhrWZ\gO_`t Wh\VqW[Z\WkmYphr_le;t3bnV _`XQj?Whfa8W^WtOh\VqW[oW^XW^t?oWth8]!YpZr_Yj klWYt?oOZiYt?oe;gï_lt X wqh8]!YpZr_®

Ypj k`Wbd¥

øGñ¯ê

e;gOXqw h\W.h\V WklesYh\_le!t?bMech\V Whnae5brYpgOX k`_lt 9X?e;_`th}b e!Z>WY!syV1_`t X w h]!YpZr_Yj klW#| e;ZY

bn_`t ;k`WMZ}Ypt?oe;gF]!YpZr_Yj klWê1x?a_lhrV#bn«Wat W0b\b

x h\V WSbrYpgOX k`_lt SX?e;_lthibYZ\WS;_l]W^tOjuÛ

ÿ<§

©¨

E¯

Dª

<JkfD

¯J K0²

Ypt?o

ÿ$«

ÿ<§

¯J K1²

aV WZrW

Ypt?o

YpZrW+o_`gOWt?bf_le;tqklWbrb8bnh}Ypt?oqYpZiooW]_Yh\_`e;t9w t _`hib;_l]_ltqQhrV W>k`esYphr_le;t3b

ep h\V Wb\YgOX kl_`t cXe!_lthibh\eh\V WZr_l!VhYpt3ok`W h=ep h\V WcgOWYt>ZrWbnX?Wshr_l]Wk`u,|_`;w ZrW

bfV eacb

h\V W0bnWSb\YgOX kl_`t >X?e!_lthibklesYh\Wo9Yph

þ,ÿ

ÿ<§

òEYt?o

þ ÿ

ÿ$«

¡,h\VqWÜ w t3sh\_`e;t9oW^XW^t?o b=e;t¬PO]!YpZ\_mYpj k`Wbxh\V W^Z\Wca_lklkqjW

b\YgOX kl_`t X?e;_lthibse!Z\ZrWbnX?e;t3o%

_lt hre+Ypk`kse;g.j _lt3Yph\_`e;t?bep,hrV WchnaeSb\YpgX kl_`t [X?e;_`th}b

e;ZWY;siV+]!YpZr_YpjqklWK|_l!w Z\W

bfV eacb

h\V W+k`esYphr_le!t?bdep¨brYpgOX k`_lt .X?e;_`th}bÜ e;ZSYOo_mbnhrZ\_ljqw h\_`e;tBehfa8e.ZiYt?oe!gä];YZ\_mYpj k`Wbdê

Yt?o

ëQ8_`t?sW/PBø

h\VqWZ\WSYpZrW[ e;w Zb\YgOX kl_`t >X?e!_lthib8;_`]Wt9ju

þ,ÿ

ÿ<§

þ,ÿ

ÿ<§

þ,ÿ

ÿ$«

þ,ÿ

ÿ$«

¡bf«Wat Wbrb8_b8_l!t e;ZrWoOe;ZY;brbnw gOW0oQh\e.Wvw?Ypk,£W^Z\e x Z\e!gFWvw?Yphr_le;t3bM¯J K0%²¨Ypt3o¯ q1%²}x

ÿ<§

ÿ$«

¯z

Ypt?o.WY;siVQZ}Ypt?oe;gæ];YZ\_mYpj k`WdV?Y!b8X?e;_lthklesYh\_`e;t?b8hrV?Yph¨YpZ\WcX k`w?b8Yt?oQgO_`tw?be;t Wbnh}Ypt?o YZio

oW]_Yh\_le!tO Z\e;gïh\V WgOWYt,

|_l!w Z\W

e;_lthcbnhr_lg9Yh\Wb= e;Zchnae+ZiYt?oe;gÚ]!YpZr_Yj klWb

cðdWhrWZ\gO_`t W[hrV W>aW_l!Vh}bd

x?h\eO!_l]WWY!syV#ephrV W

X?e;_`thWbnhr_lg9Yh\Wb®;w?bfhY;bYQX Z\e!j?Y0

j _lk`_lhfuoWt?bf_lhfuQ w t?sh\_le!tBWt3sklebnWbcYptA{iYpZrWY;Oew t _`hnux?bneOhrV WX Z\e!j?Ypj _`kl_`hnu9aW_l!Vh}b8gQw?bfh

Ypkmbnebnw gÚh\ew t _lhfuU8V WSa8W_`;VhibcYpkbfeOs^YptBh}Yp«WS_lth\e.Y;s^se;w thse;ZrZ\WkmYph\_`e;t#jW^hnaWWt9hfa8e

e;ZgOe!Z\W[Z}Ypt?oe;gÚ]!YpZ\_mYpj k`Wb

| e;ZcY.bn_ltq;klWZ}Ypt?oe!gÚ];YZ\_mYpj k`W[ê1x?h\V WaW_l!Vh}b8YpZrW>!_l]WtOjuÛ

ÿ<§

ÿ$«

ÿ<§

ÿ$«

¯z

Ù2

ÿ$«

ÿ<§

¯z

| e;ZEPZ}Ypt?oe;gä]!YpZr_YpjqklWbda_`h\V5t e#bf«Wat Wbrbx

V Zr_bfh\_Yt5WhYk¯

1K1K1²[V?Y]WSX Z\WbfWth\Wo#Y

;WtqWZiYk,WXqZ\Wbrbn_le!tO e;Z?t?o_`t +h\V WSa8W_`;VhibxaV _msyV9hiY«Wb8_lth\e.Y!sse!w thhrV WSse;ZrZ\WkmYphr_le;t

seWBAs_lW^th

S4°

j?Whfa8W^Wt9h\V W_±²[Yt?o³±²];YZ\_mYpj k`WbY;b8 e;k`kleacbÛ

X¶µ·µ·µ

SUT

°¸T$SU¹

¯º

S4°

²r²

¯z< ²

U8V W»º

h\WZrg9bdh}Yp«W.h\V Wbn_`;t6

e!Z>X?e;_`th}b[;Z\W0Yph\W^Z>h\V3Ypt1hrV WQgWYpt,x Ypt?oh

e;ZX?e;_`th}b

bng9Yklk`WZ>hrV?YptAh\V W9gOWYt,AU8V W9X Z\eow3sh¼º

w t?oWZQhrV W#bnw gg9Yphr_le;t xoWh\W^Z\gO_`t Wb[h\V W

bn_`;tephrV Wse;ZrZ\WkmYph\_`e;tseW8A9s_`Wthx,Yt?oèhrV Wbnw j?brsZ\_`X hib[eh\VqWQaW_l!Vh

_lt?o_msYphrW+h\V W

klesYh\_`e;t9ephrV WX?e;_lthh\V3Yphc_b8j?W_ltqQaW_l!VhrWo

| e;Z[g.w klhr_lX k`WZiYpt3oe;gä]!YpZr_Yj klWbcaV WZ\W.bf«Wat Wbrb[sYt t e;hj?Wo_bfZ\WYpZioWoxhrV WOse;gOX w

hiYh\_le!t9epa8W^_l;Vhib_bbn_l!t _®sYpth\k`u+gOe;ZrW[se!gOX k`_sYh\Wo¢ebfWtjqklw WhrV,¯

1K0

²X ZrWbnWthibh\V W

a8W_`;Vhib e!Zh\V WSsY!bnWeptø

h\e+j?WSh\V W[ e;k`klea_ltq Û

ø½ò£´

W¾

'¿#´

6º

ò`¿

¯\¯

E¯

²}¯

E¯

<JkfD

¯zK²

U8V Wt e;h}Yphr_le;t_mbh\V Wb\YgOWY!b e;Z,h\VqWXqZ\W]_le!w?bWvw?Yphr_le;ta_lh\V ò

¿'´Àj?W_`t h\VqW=a8W_`;Vh e!Z

]!YpZ\_mYpj k`WdÁx4ÂGW]!Ypklw3Yph\W0oOY;bY+bn_ltq;klWcZiYt?oe!g]!YpZr_Yj klW

ÿ$Ã

_mbhrV W[bf«Wat Wbrbeh\V W[Z}Ypt

oe;g

]!YpZ\_mYpj k`W[o_bnhrZ\_`j w h\_`e;t,| e;ZY[kle!;t e!Z\g9Yk?o_mbnh\Zr_lj wqh\_le!t,x;hrV Wcbn«WatqWb\b=seWBA9s_lWthx

sYpt9j?W+s^Ypksw kYh\Wo Zre;gFhrV W |

U}/

Y;b8 e;klk`eacb¯Ä8W^t*³iYpgO_`tOYt?o

e;Zrt Wklk

1:%

²iÛ

øh

¯|

~}/

¯z<²

cðdWhrWZ\gO_`t Wh\V W.]!Ypk`w W+ep¨h\V WoWX?Wt?oWth];YZ\_mYpj k`WOYhMW0Y;siV5Xe!_lthOì?Whh\VqWbnW.]!YpklwqWb[jW

oWt e!h\Wo9juj¥#ò

e!Z

e;Z

µ·µ·µ·µ

xoWX?Wt?o_`t Ow X?e!t5h\V WSXe!_lth[Yh[aV _msyVj¥

_bjW^_lt

W]!Ypk`w?YphrWo| e;ZVP5ZiYt?oe;gÚ_`t X w h]!YpZr_Yj klWbx¥

_b8W]!Ypk`w?YphrWoBYh

X?e;_`th}b

c¡¥t+;Wt W^ZiYpkx;h\VqWce;_`thbfh\_lgYph\W¨BWh\Vqeo>Wt?YpjqklWbw3b

hre[Wbfh\_lgYph\Wh\V WW^X?WshrWoM]!Yklw Wbep

h\V W[?Z}bnhhrV Z\WWgOe!gOWthib=epKh\VqW>oWX?Wt?oWth]!YpZr_YpjqklWw?bn_`t +h\VqW e!klk`epa_`t .bnwqgOg9Yphr_le!t?bÛ

C .ý)?ý)?

þÆÅ

õöÇ¥G÷ø

SUT

¯z<"²

P,?&Aý)ý)

øõö®¯u¥

þÅ

÷ø

SUT

¯&¥

þÆÅ

¯z$%!²

Ù;Ù

Yklh\W^Z\t?Yh\_l]W^klu

øõöÇ¥

÷3E¯nõ.ö¥G÷²

SUT

¯u¥

¯z<0²

J> &Aý/?ý)

õö®¯&¥

þÅ

RSUT

¯u¥

þÆÅ

¯z<1²

Yklh\W^Z\t?Yh\_l]W^klu

¯nõöÇ¥

÷nÈ õ.öÇ¥G÷ õ.öÇ¥

÷B

¯nõ.ö¥G÷²

²ø

SÇT

¯&¥

þÅ

¯u¥

¯J

MIå

Idí ý)î@ZcH?É[K&§ í ý)î^ ?)$\j8^:`_.^=? 5FP9ø

U8V _b=_bh\V Wb\YgOW8WqYpgX klW¨se;t?bf_oW^Z\Wo>w?bf_lt hrV Wc|

FgOW^h\V eo>WYZ\k`_lWZ_lt+hrV WdX3YpX?WZx_`t]e!kl]

_lt 9oZiYp_`t WoBw t3se;t3t WoBh\Zr_Y_mYpkKse;gOXqZ\Wbrbn_le!tBeY¼

x#_

bne!_lk¥¡¥t5hrV W> e;k`klea_lt b\YgOX k`W+sYk®

sw kYh\_`e;t,x

Ùn2K2

« =Y.Ypt3o

rsut!v

øEhiYtV

2Kw

:%q%xYpt?oj|

ø+|

U}/

rsutv

|3e!klk`epa_`t +h\VqW>bfh\WX3b e;Zc_lgOX k`Wg.Wth\_`t S1Û

cU8V W[ w t?shr_le!tHhreQj?WW]!Ypk`w?YphrWoO_b8hrV WSb\YpgW>Y!b8Wvw?Yphr_le;t±¯

"%²ix t3YpgOWk`uÛ

h}YptV_

E¯

±hiYpt

<JkfD

¯J

c¡¥h_mbY!b\bnwqgOWoMhrV?YphKh\V WZiYpt3oe;g

bnV WYZbnhrZ\Wtq;h\VS]!YpZ\_mYpj k`Wb;

Ypt?o>h}Ypti_

YpZrW8w t?se;Z\ZrWkYh\Wo

Ypt?o9kle!;t e!Z\g9Yklkluo_mbnh\Zr_lj wqh\Woxh\Vw?b Z\e!gFWvw?Yphr_le!t?bM¯J K0²Yt?o5¯ K1²ix

rs&t3v

Ù2

¯J

rs&t!v

cU8V W>aW_l!Vh}b[YpZrW+oW^h\WZrgO_lt W0o e;Z[hrV WM e!w ZbrYpgOX k`_lt .X?e;_`th}bÜ Z\e!g

W0v%w?Yh\_`e;t)¯q²w3bn_ltq

Wvw?Yphr_le;t3b¯

²¨Ypt?o¯

²¯

S4°

²Y;b8 e;k`kleacbÛ

ø+

rsut!v

¯JK ²

rsutv

U8V WZrW e;ZrWx% Zre;gFWvw?Yh\_le!t1¯zK²}x h\V WSbrYpgOX k`_lt SX?e;_lthca8W_`;Vhib8YZ\WÛ

¹¹

{

¯J{²

ø+

û û

"q"K

cU8V W.oWX?Wt3oWth[]!YpZ\_mYpj k`W

bBc

_mbdW]!Ypk`w?YphrWo5YphWY!syV#ep¨h\V W+X?e;_`th}bSUYj klW bnw gOgYpZ\_mbnWb

h\V W]!Ypk`w Wb8eh\V WaW_l!Vh}bxhrV WSb\YgOX kl_`t >X?e!_lthibcYpt?o

bBc

e;Zh\Vq_bcsY;bfWÛ

J8 ËÊ, ¤Ì

-?;:=^ ý)î ,î? ?+ &

L3 *¤\r?OI[å

ÍÍ

hiYt5_

cÎqÎ

¯«q=Y²

¯ « KY%²

{

Ù!ÙÙ

%*"

"q"K

%*"

cU8V WM3Zibnhch\VqZ\WWSgOe;gOW^th}b

bBc

sYtBt eaj?W+W]!Yklw?Yh\WoO Z\e;gÚWvw?Yh\_le!t?b¯<"²ix¯!%;²cYt?o

¯1%²¨Y;b8 e;klk`eacbÛ

xzy

{q¯

Ù;ÙnÙ

²`

¯J"

²Æ

¯z

"²Æ

"K"q¯

%²ø K

1« =Y¯JK²

* ¯

Ù!ÙÙ

þ#xzy

¯"

þ#xzy

"q"K¯

þxy

"K<%

¯«q=Y%²

¯K"²

xzy

{q¯

Ù;ÙnÙ

þ#xzy

¯J"

þ#xzy

¯®

þ#xzy

"K"q¯

þxy

¯<%;²

¢ÜebnWtj k`w Wh\Vz¯

1q0

²t e;hrWbh\V?Yh8 e;Zch\V W[g.w k`h\_lXqklWZiYt?oe!g

]!YZ\_Yj klWSsY!bnWx?bf«Wat WbrbsYpt

e;t k`uOj?WZ\Wk`_YpjqklusYpkmsw kYh\Wo._®Kh\V W]!YpZr_YpjqklWbYZ\W>_`t?oWX?Wt3oWth

©ábfw gOg9YZ\u+e=ZrWbnw k`hib e!Z[o_¬WZ\Wthd|

~}/

^Ï

rsut!v

_b8X ZrWbnW^thrWoO_lt#UYj klW/

J ]Ð >P +$\

î& ;&A*^ ,1I[å

~}/

rsut!v

U}/

¯«q=Y%²

K00

*<""

Ù!Ù

Ù;Ù

Ù!Ù

*<0

1K01

qK "

0K"q0

¡¢h_bsklWYZ Zre;gïY+se;gOX3YpZ\_mbne!tOep

UYj klW0b

Ypt3oËMhrV?Yphc|

äYpt3oHä;_l]WcWbrbnWth\_mYpklk`u+h\V W

b\YpgW[Z\Wbfw klh}b e;Zch\V _mb8WqYpgOX k`WdXqZ\e;jqklWg5

W]WZ}YpkcZ\W?tqWoEe;_`thbnhr_lg9Yh\W5BW^h\V eo bOV?Y]W#jW^WtEX Z\e!X?ebnW0o

h\e1_`gOX Zrep]W9e!t

X?WZ}sW_l]W0o

bnV e!Z\hise;gO_`t be¢ebfWtjqklw WhrV,¤¦b

Xe!_lth8Wbfh\_`g9YphrW8gOWhrV eoO¯W° `Ñde;tq

1K1q0xì?_`t?o

1K0q x@Ñ[YZ\Z

1K0q1x,ì?_

1K1

V Z\_mbnh\_mYptjÒ*Ó®ÔnÕÖ

1q1K1²i

RO@OB4B.å

CI[ç4Ë× CBJ>IªIç8I[åâI[#J@ORQS@QTS"

|3e!ZdZrWY;bfe;t?Yj klu){rkl_ltqWYpZ}X Zre;j k`Wg9bxh\VqW>|

'Ypt?o#

gWh\V eoqboWb\sZ\_lj?WoO_`tBh\Vq_b8X?YXW^Z

YpZ\WYpj k`WQhreBhiY«WOY!sse!w thSepbfe;_lkX Zre;X?WZrhnu5]!YZ\_Yj _lk`_lhfu5_lt±YBbfu bfh\WgYph\_ms>aYu9U8V W.gOWhrV eo b

V ea8W]WZ^xph}Yp«Wt eSY;sse!w th=ep bnX3Yph\_mYpk?se;Z\ZrWkYh\_`e;t,x;aVq_siV>_bh\V WhrWt?oWt3su[ e;Z=X Zre;X?WZrh\_lW0bep bne!_lk

WklWgWth}b{isklebfW8h\e!;WhrV WZ,hredj?Wse;ZrZ\WkmYphrWoxaV _`klWbfe;_lkW^klWgOW^th}b{nYZYpX?YZ\hiYpZ\Ww t3se;ZrZ\WkmYph\W0o

UeY!o oZ\W0b\bMhrV W9se!Z\ZrWkYh\_le!t1_brbnw Wxh\VqWOh\Zr_Yp_Ykse;gOXqZ\Wbrbn_le!tXqZ\e;jqklWgäV?Y!b>j?WWt1ZrWYpt?YkluqbnWo

w?bn_`t #YZ}Ypt?oe;gã?WkmoØ3t _lhrW+WklWgWthcYX X ZreY;siV,x,h\V3Yph>W^t?Ypj k`Wb[bfe;_lkKX Z\e!XW^Z\hfu5]!YpZ\_mYpj _`kl_`hnu#Yt?o

bnX?Yh\_Ykcse;ZrZ\WkmYphr_le;t)hrej?W#Y;sse;w th\Wo e!ZAU8V W9gOWh\Vqeoe;k`e;;u±_lt]e;kl]W0bMh\VqWH!Wt WZ}Yphr_le;tAYt?o

g9YpX Xq_lt 1e.Y1ZiYt?oe!g

?Wko§e 8^[Ypt3o

h}YptV_.^cX Z\e!XW^Z\h\_`WbOe;th\eAY)v%wq_lh\W#Z\W3t Wo§?t _lhrW5WklW

gOWthgOWbnV >| w k`k=Y!se;w th_bdh}Yp«Wt5ek`esYpkY]WZ}Yp!_lt #Ypt3oè]!YpZr_Yt?sW+Z\W0ow?shr_le;t)¯| Wthre;tYt?o

8Yt g9YZisi«W

1K1

²+e]WZSWY;siV)WklW^gOWthxYpt?o)Yt§WX?e;t Wth\_mYpk`kluoWs^Y0u_ltqbnX?Yh\_Ykcse;ZrZ\WkmYphr_le;t

hrV Wt.X?WZn e!Z\gOWo>w3bn_ltq

YOBe;V Zf

e!w kle!gQjOY_lklwqZ\W+sZ\_lhrWZ\_`e;t,¨ðdWhiY_lkmbÜeYObn_`gO_lkmYpZ¨Ypt?Ykluqbn_bcsYt5jW e;w t3oB_lt]ÙcZr_~Ah\V?b

Ypt?o| Wthre;tA¯

q2K2Ù

²iU8V WQgWbnV#_bdhrV WtkleY!oWoYp_Yklklu#w th\_lkKYOg9Yp_lg.w gªYp_`klw ZrW.bnh\ZrWb\bx

bBc

_b+Z\WY!syV W0o§U8Vq_b>Yp_lk`w Z\W9k`eY;o)_b+Z\Wse;ZioWo)Ypt?o§hrV W#Ypt?Ykluqbn_b+_b+Z\W^XW0Yph\W0o/tw gOWZre;w?b>hr_lgOWb

w?bn_`t OBe!thrW

YpZ\k`e.bn_`gQw kmYphr_le;t3b=Y!syV9Z\W0Ypkl_mb\Yh\_le!t9epKh\V WSBe;th\W

YZ\kle.X ZresWb\b_lt]e;k`]Wb=h\V W

b\YpgWMgWYpt,xqbnh}Ypt?o YZio5oW^]_mYph\_`e;t#Ypt3o5bnX?Yh\_Yk=se;Z\ZrWkYh\_`e;t9klWtq;h\V#epbfe;_`k,X Z\e!XW^Z\h\_`Wbx?V ea8W^]WZ

h\V W9bfX?Yphr_Yko_mbnh\Zr_lj wqh\_le!t1epX Zre;X?WZ\hr_lWb]!YpZ\_`Wb Zre;g'e;t WZ\WYkl_brYphr_le;t±h\e5h\VqWOt Whxh\Vw?bMWY!syV

bn_lg.w kmYph\_`e;t+k`WY;o b=hre+Y>o_®WZ\W^th=]!Yklw Wcep

|3e!klk`epa_`t SYH{}bnw$As_lW^th}tw g.j?WZeZ\WYkl_mb\Yphr_le!t?bx

h\V WSbnh}Yphr_bnhr_sb[¯ gOWYt9Ypt?o9bfhiYpt3o YpZ}o5oW]_Yphr_le!t²=eh\V We;w hrX w hv%w?Ythr_lhfu

sYpt#h\V Wt9j?WSse;g.

X w h\W0oU8V WSYpt?Ykluqbn_mbÜV?Y!bÜhrV We;X hr_le!tHe_lt3sklw?o_lt sZ\eb\bcse;ZrZ\WkmYph\_`e;t9j?Whfa8WW^tOX Z\e!X?WZ\hr_lWbYt?o

Ypt _mbne;hrZ\e!X _s.bnX?Yh\_mYpkse;ZrZ\WkmYphr_le;t5k`Wt !h\V?b+¯W° Sh\V W.bfX?Yphr_Ypkse!Z\ZrWkYh\_le!t5klWtq;h\V_ltYOt?Yh\w Z}Ypk`klu

essw ZrZ\_ltq.bnh\Z}Yphrw gFep

bne!_lk_be h\Wt9V _`;V W^Z_ltOhrV W[V e!Z\_l£^e;thiYpko_lZ\W0sh\_`e;t²};dW_`h\V W^Ze=hrV WbfW[e;X

h\_le!t?b=V?Y;b=j?WWt._lt]Wbfh\_lYphrWoM_`t+h\V WcswqZ\Z\W^thbfh\w?ou+h\e[Y;s_`kl_`hiYphrWse!gOX?YZ\_bfe;t?ba_lh\V.h\VqWcbn_lgX klWZ

e;Z\gbep|

äYt?oB1

ì?e;;tqe;Z\gYpk,o_bnhrZ\_`j w h\_`e;t?b=e`B^ Yt?oQh}Ypti_.^ V?Y]Wj?WWtOw?bfWo+_lt.h\V Wsw ZrZ\Wthbnh\w3ou.Ypt?o.g9YpX X?Wo

e;th\e#Y9b\vw?YpZrWQgOW0bnVBe

2K2

WklW^gOWthib[¯0¥tqeoWx=vw?Y!oZ\_`kYphrWZiYk¥xXqkYptqWObfh\ZiY_lt5Wk`WgOWthibi²iU8V W

bne;_`k[X Zre;X?WZ\hr_lWb.a8WZrWY;b\bfw gOWo)h\e)j?W5w t?se!Z\ZrWkYh\Wo¯

²i

UuX _msYpkcZ\WYkl_mb\Yphr_le!t?bQeph\V W

X Z\e!XW^Z\hfu#o_bfh\Z\_`j w hr_le;t3bYpZ\WbnV eat#_lt5|_l;wqZ\W/ _`t9h\V W e;Z\gïepYQ!Z\Wub\sYklW_lt#aV _siV9a8WY«WZ

Z\W!_le;t3bQYZ\W5oqYpZ\«W^ZxYpt?oAbnh\Zre;t !WZ.Z\W!_le;t3bQYZ\WBk`_l!VhrWZ)©dtAWqYpgOX k`WQeSY5Z\WkmYph\_`]Wklubfg9Ypk`k

bnX?Yh\_Yk,se!Z\ZrWkYh\_le!tOklW^t ;hrVOYt?o9YMZ\W^kYphr_l]Wk`u>V _`;V9se;Z\ZrWkYh\_`e;t.klWt !h\V9YZ\WbfV eat,¡¢hbfV e;w kmoOjW

WgOX V?Y!bn_mbnWoh\V?Yh=h\V WgWYptYpt?o.bnh}Ypt?o YZio.oW]_Yh\_le!t+eph\VqWZiYpt3oe;gª]!YpZr_Yj klWjW^_lt X?e;Zrh\ZiYuWo

_bh\V Wb\YpgWM_`t9je!h\VB?!w Z\W0b[U8VqW+bnX3Yph\_mYpkKse;ZrZ\WkmYphr_le;t#klWtq;h\V±¯aV _msyV9V?Y!bdw t _`hibepk`Wt !h\V²_b

oW?t W0oèa_`h\V1ZrWbnX?WshSh\e#h\V W.w t?oW^Z\klu_ltqHtqe;Z\gYpko_bfh\Zr_lj w hr_le!t,x=Yt?o1oWtqe;h\W0o1Y;b ÚÛ

t!p

t<rsut!v

Ä8e;h\VÜ8^=Ypt?ohiYpti_.^a8WZrW.Y;b\bf_l!t WohrV WObrYpgOW+_mbne!h\Z\e!X _s.se!Z\Z\W^kYphr_le!tk`Wt ;hrV_`t5h\V _mbbnh\w3ouO©

se;t]Wt _`WthSt e;tfo_`gOWt?bf_le!t?Ypk`_b\Yh\_`e;t§eSh\V WzbnX?Yh\_Yk[se;Z\ZrWkYh\_`e;t§k`Wt !h\VEs^YptEj?W5Y!syV _`W]Wo1_lt

h\V _mbMs^Y;bnWxju5o_l]_o_`t OjuBh\VqWObf_oW+k`Wt ;hrVÝæech\V W.brv%w?YZ\W.gOWbfVbnV eat_lt±|_l!w Z\W xh\Vw?b

øhÚ

t3p

t<rsut!v

Ý.

High correlation length

Low correlation length

|_l!w Z\W/

e!Z\ZrWkYh\_le!tBk`Wt ;hrV?b8_ltO?tq_lh\WWk`WgOWthBØ^ZiYt?oe;g

3WkoOYX X ZreY;siV

d ý) *&

¡¢t9hrV W[ZiYt?oe!gO_bfWo?t _`h\WWk`WgOWth=gOWhrV eoB¯J¢d|=²

bnh\w3o_lWbx?Y+bnWZr_lWbep

Ypt?YkluqbnWbV?Y]W[j?WWt

XW^Zn e;ZrgOWo[_ltaV _msyVhrV WseW8A9s_`Wthep3];YZ\_mYph\_`e;t |

rsut!v

x!Ypt3o>bnX3Yph\_mYpkqse;ZrZ\WkmYphr_le;tSklWtq;h\V

V?Y]W[j?WWtB]!YZ\_lW0o8¡¥t#Ypk`k=s^Y;bnW0bx h\VqW>gOWYt9bnhrZ\Wtq;h\V#X?YpZ}YpgOW^h\WZ}b8V?Y]WMj?WW^tHVqWko9se!t?bnh}Ypth

Yphh\V Wb\YgOW+]!Ypk`w Wb[se!t?bn_moWZrWoèW0YpZ\k`_lWZc_lth\VqWQX?YX?WZx,t?YgOWklu

Ùn2K2

«q=Y9Ypt3o

rsut!v

hiYpti

2qw

:%q%5U8V W];YZ\_mYph\_`e;t1_`thrV WOgOW0Yptse!gOX Z\W0b\bn_`]W.bnhrZ\Wt !h\V

x=t e;Zrg9Ypk`_bnW0oBa_lh\V

Z\WbfXW0sh8hre>h\VqWoWhrWZ\gO_`t _bfh\_ms]!Ypk`w W[j?Y!bnWoOe;th\V W[gWYpt.]!YpklwqWb

þ#p

þ.rs&t!v

²øh *<"

.« =Y_b

bnV eat5_lt|_l;wqZ\WbY9Ypt3oË;jYpt3oèhrV W>ZrWkYh\_le!t?bnVq_lX5j?Whfa8WW^tHhrV W.seWBAs_`Wth}b8ep]!YpZr_Yphr_le!t5ep

_lt X wqhcbnV WYZ[bfh\ZrWt ;hrV9X?YpZ}YpgOWhrWZibYt?oOe;w hrX w hse;gX Z\Wbrbn_`]W[bfh\Z\W^t ;hrVB_bbfV eatB_`tB|_l;wqZ\WE

0.2

0.4

0.6

0.8

C.O.V.

c’,tan

φ’

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.1

(µ

c’

,µ

tan

φ’

)

Θ=0.05

Θ=0.1

Θ=0.5

Θ=1.0

Θ=5.0

Θ=10.0

FOSM

PEM

-2

4 6 8

-1

4 6 8

0.4

0.5

0.6

0.7

0.8

0.9

1.1

(µ

c’

,µ

tan

φ’

)

C.O.V.

c’,tan

φ’

=0.1

C.O.V.

c’,tan

φ’

=0.3

C.O.V.

c’,tan

φ’

=0.5

C.O.V.

c’,tan

φ’

=0.7

C.O.V.

c’,tan

φ’

=0.9

|_l!w Z\WEqYpZr_Yh\_le!t9ep

þ#xzy

a_lhrVj|

rsut!v

Ypt3o

0.2

0.4

0.6

0.8

C.O.V.

c’,tan

φ’

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.1

C.O.V.

Θ=0.05

Θ=0.1

Θ=0.5

Θ=1.0

Θ=5.0

Θ=10.0

FOSM

PEM

|_l!w Z\W|

]qb®|

~}/

rs&tv

|_l;wqZ\W/"UuX _msYpkoW e;ZrgOWo+gOWbnVYphYp_lk`w Z\W

U8V Wd e;k`klea_ltq+e;j?bfWZ\]!Yphr_le!t?bsYpt9j?W[g9Y!oWd Zre;gïY+se;gOX3YpZ\_mbne!tOepKh\V W{ibn_`gOX k`W[gOWh\Vqeo b8Yt?o

h\V W/¢c|=

ZrWbnw k`hib

²¨|_l!w Z\WbY.Ypt3oË;jB_`t?o_msYphrWMhrV?Yph e;Zc_lth\W^Z\gOWo_YphrW]!YpklwqWbÜe

xhrV W/¢d|K'Z\Wbfw klh}bbnV ea

YObn_`;t _¬sYpthYpklk_lt

Y;b¤|

~}/

^Ï

rsut!v

_b_lt3sZ\WY!bnWodU8Vq_bd_mbdYQ]W^Z\uO_`gOX?e;Z\h}Ypth[o_®WZ\W^t?sW

Z\e;gährV W9|

Ypt?o1

gOWhrV eo bxaVq_siVj?e;hrV)Y]WQW0b\bnW^thr_Ypk`klu#se!t?bnh}Ypth

9¡¥tèY!shx

h\V WS

Yt?oBbfWse;t3oHe;Z}oWZc|

äo_bfX kYuWoYQbfkl_l!Vhßà#áâ8ÒÔ*ã¶Ò_lt

Zre;gÚ|_l;wqZ\WEY

²|_l!w Z\W0b;j

Ypt?o)bnV ea

h\V?Yh e!Z9kYpZr;W]!YpklwqWbQep

xdh\VqWa¢d|=

Z\W0bnw k`hibOh\Wt3o§h\e)h\V W

]Ø0

XqZ\Wo_msh\_`e;t?b> e;ZYpklkc]!Ypk`w WbQe |

U}/

rsut!v

xÜ_`gOX k`u_`t BhrV?YphOhrV W5|

Yt?o

ägOWhrV eo bYpZrWSbnX?Ws_mYpksY!bnWbepQ¢d|Käa_lhrV#YptB_`t?t _`h\Wse;Z\ZrWkYh\_`e;t9klWtq;h\V

%²|_l;wqZ\W5!j9bnV eacb8hrV?YphhrV WdgWYpt.]!YpklwqWbe=hrV W[se;gOX ZrWb\bf_l]Wcbfh\Z\W^t ;hrVQ e;ZcYklk#|

U}/

rsut<v

o_bfX kYuOgO_`t _lgYYphcYZ\e;wqt?o

xYptA_lt?sZ\WY!bnWO_`t

_b>e!j?bnWZr]Wo)Y;b+_lh+V W0Y;o b+j?Y;si«1hrepa¨YpZ}o bhrV W#se;g.

X Z\Wbrbn_`]WObfh\Z\W^t ;hrV/j3Y;bnW0oe;t)h\VqWOgOWo_mYpt±bnV W0YpZ+bfh\ZrWt ;hrV)];Yklw W0b5U8V W0bnWOhrV We;ZrWh\_msYpkZrWbnw k`hib

V?Y]WQj?WWt±_lt?sk`w?oWo5_lt|_l!w Z\W ;j,z©[b>Y5brYpgOX k`W.sYpkmsw kmYph\_`e;t,xh\V WZ\Wbfw klhSse!Z\Z\W0bnX?e;t?o_lt 5hre

rsut<v

BaVqWt

Þåä

_mb>;_`]Wt1ju)BWo_mYpt

~}/

^Ï

rsut<v

<kfD

0K1

K!« =YcYpt3oMBW0o_Yt

rsut!v

þ'rsut!v

¤|

~}/

rsut!v

<kfD

<"U8Vw?b

x¸æ

þp

þ.rsut!v

0*$%,1

%²|_l!w Z\W O_`t?o_s^Yph\W0bdY9bnhrWY;ou5Z\Wow3sh\_`e;t5_lt5hrV WÈ|

~}/

Y;b

_boWsZrWY;bfWoSU8V W|

Ypt?o9ãgOWh\Vqeo b=a_lh\Vqe;w hcY!sse;wqthr_lt e;ZbfX?Yphr_Yk,se!Z\Z\W^kYphr_le!tOY]WcWb\bfWthr_YklkluÈ|

~}/

rsut<v

"%²¨|_l!w Z\W/"+bnVqepacbYhfuX _sYk,oW e;Z\gWogWbnVO Z\e!gFh\VqW¢c|='Ypt?Ykluqbn_b8ðYpZ\«9£e!t Wbbf_l;tq_® u

a8WY«WZbfe;_lkYt?oBoWgOe;t3bnh\Z}YphrW[h\V WgOW0Ypt?oW^Z\_ltq+Ypt3oH_lZrZ\W!w kYZt?Yphrw Z\Weh\V W[Y_lklwqZ\Wbfw ZnY!sWb

4HPTSzPP 0.

@O#4

T+.5TSç894957

RI[åâ@ORÈçèP

U8V WX?YpX?WZcV?Y;bcoWge;t?bfh\ZiYh\Wo.h\V ZrWW[gOWhrV eo b e!Z_lgOX k`Wg.Wthr_¬t X Z\e!j?Ypj _`kl_mbnh\_ms[se!t?sWX h}b8_lth\e

;We!h\WsiV t _msYpk?Yt?Ypk`u bf_b=epYbn_lgX klWX Z\e!j klWg

epKse!gOX ZrWb\bf_l]WbnhrZ\Wt !h\V,U8VqWQ{}bn_lgX klWgOWhrV eo b

a8WZrWMhrV W+|_lZibfh

Z}oWZWse!t?oBBe!gOWth[¯¥|

²Ypt3o5e;_`thcbnhr_lg9Yh\WSBWhrV eo¯²}xYt?o

h\V W#{ibne!X V _mbnh\_msYphrWo +gOWhrV eoHa¨Y;bcYO|_ltq_lh\W

k`WgOWthBØ,¢dYt?oe!gÚ|_lW^koB¯J¢d|=²gOWhrV eoU8V W

e;w hrX w h.bnh}Yphr_bnhr_sbeph\V Wse;gOXqZ\Wbrbn_l]W.bfh\ZrWt ;hrV1ju1|

Ypt?o±

a8WZrWObf_lgO_`kYZMhreBWY!syV

e;h\VqWZx j wqhco_®WZrWo9bn_l!t _®sYpth\k`u Zre;gFhrV W/¢d|=ägOWhrV eo

²=Z\e!j?Ypj _`kl_mbnh\_msÜgWh\V eo.epWZibY>ge;Z\Wb\s_lWth\_¬sÜa¨YuQeYX X Z\eY;siV _ltq+;We!h\WsiV t _msYpkYpt3Ypkluqbn_mbx

_lt+aV _msyV+X Zre;j?Yj _lk`_lhr_lWbeoW0bn_l!tY_lk`w Z\W¨sYpt.j?W[Y!b\bnW0b\bnW0oxZiYphrV WZh\V3Ypt.h\V WYpj?bfh\Z}Y;sh{nY!sh\e!Zep

b\Y0 W^hnuq.YpX X ZreY!syV,èÄ8W_lt +ZrWkYh\_`]Wklu.t WaGV ea8W]W^Zx h\VqW>se;t?sW^X hibcYpZrW+o_UA9swqklh8hreOo_l;W0bnhcW]Wt

_lt9h\V WSbfeOsYklk`Wo{ibf_lgOXqklWgOWh\Vqeo b

²U8V W ¢c|=

gWh\V eo5Y!sh\w3Ypklk`uBgOeoWkbh\V W.X Vu bf_sYkk`esYphr_le!t?b[epaWYp«zYpt?obnhrZ\e!t B£e!t Wb

a_lh\Vq_ltOhrV WbnX?Ws_lgOWt ÉéEVqWt9se!gOX Z\W0b\bnW0oxX Z\e!;Z\W0b\bn_`]WdYp_`klw ZrW[esswqZibxqYpt?oOhrV WdYp_`klw ZrW[gOWsiV

Ypt _mbng

{ibfWW«qb¢e;w h}èhrV WBaWYp«Wbfh+X?YphrV§hrV Z\e!w ;VEhrV W#bne;_`k¥E|_l;wqZ\W¬"bfV eacbQV eaFhrV WHY_lklwqZ\W

gOWsiV?Ypt _mbngâ_bYh\h\Z}Y;shrWo+h\e>hrV Wa8W0Yp«WZc¯¥oqYpZ\«W^Z²,ZrW;_`e;t?bep,hrV WcgOWbnV U8VqW|

ÚYt?oO

V?Y]W[t ese;t?sWX hep

klesYk,£e;t W0b8epaWYp«t Wbrb8h\V?YhcsYptzoe;gO_`t?YphrW[h\VqW>se;gOX ZrWb\bf_l]WbnhrZ\Wt !h\V,

%²KU8V Wi¢d|=ÚgOWh\Vqeo>_lt?o_msYphrWbYbn_l!t _®sYpthZ\Wow3sh\_`e;t+_lt.gOWYt.se;gX Z\Wbrbn_`]W8bfh\ZrWt ;hrV9ow W

h\e5h\VqWOa8WY«WZ>£^e;t WbSoe;g_lt?Yh\_ltqBh\VqWOe]WZiYklkbnhrZ\Wt !h\VAYph+_`thrWZ\gWo_Yh\WS];Yklw W0b>ep

U8V W

e;j?bfWZ\]Wo5Z\W0ow?shr_le;t_lt5hrV W.gOWYptbfh\ZrWt ;hrV1jua¢d|=1x_mb[;Z\W0Yph\W^Z>h\V3Ypt±se;w kmoèj?WOW^X kmYp_`t Wo

juAklesYkY]WZiY;_ltq)Ypk`e;t W

_mbQZ\W0ow?sWo/ wqZ\h\VqWZOV ea8W^]WZx8hrV WZrWB_bY

;ZiY!ow?Yk_`t?sZrWY;bfW+_lt5h\VqWQ]!Ypk`w W+ep

þ#xzy

Y!bbnV eat_lt|_`;w ZrW!j,+| Z\e!gäYOh\V W^e;Z\W^h\_s^Ypk=X?e;_`thep

]_`WaxY;b

j?Wse!gOWb];Yt _bfV _ltq;klu±bngYpklkx=h\V W

þ#xzy

a_lk`kse!thr_ltw WOhre5_lt?sZrWY;bfW9h\eaYZio b>hrV W#Y

oWh\W^Z\gO_`t _bfh\_s8]!Yklw Wj?Y!bnWoOe;t#h\V WEêËÒ,ëKßÔnàOe;t#h\V W[_`t X w hbnVqWYpZcbfh\Z\W^t ;hrVBX?YZiYpgWh\WZ}bK©[b8h\V W

bnX?Yh\_Ykse;ZrZ\WkmYphr_le;t9k`Wt ;hrV#oWsZrWY;bfWbx hrV Wa8WY«WbnhX?Yh\V9j?Wse!gOWb_`t?sZrWY;bf_lt !kluOhre;Z\hrw e;w3bdYt?o

_lhibklWtq;h\Vse;ZrZ\WbfXe!t?o_`t ;k`uOkle!t ;WZ^©[b8Y>ZrWbnwqklhxh\V Wa8WY«WbnhX?YphrVBbfhiYZ\hib8hre+klee!«Q e;Z¨bnV e!Z\h\W^Z

Z\e;wqh\WbSsw h\hr_lt 9hrV Z\e!w ;V)V _`;V WZSbfh\Z\W^t ;hrV1g9YphrWZ\_mYpkQ¡¥th\V W.kl_`gO_lh^x,Y;b

Þä

xhrV WOe;Xqh\_lg.w g

Yp_lk`w Z\WcX?Yh\V9a_lk`kj?Wh\VqWb\YgOW[Y!b8_lt9Yw t _¬ e;Z\gæg9Yh\WZr_Ypk?a_`h\V9bfh\Z\W^t ;hrVOWvw?Ypkh\e+h\VqW[gOWo_mYpt,

]W^Z\u+?t WgOWbfVOa8e!w koOj?Wt WWoW0ohreObfV eah\Vq_b8WWshtwqgOWZ\_msYpk`klu

²U8V W/¢c|=ãX Z\Wo_sh}b8Y+se!t?bn_mbnh\W^th¨Ypt?o9bn_`;t _¬sYthZ\Wow3sh\_`e;tO_`tì|

~}/

Y!b

oW0sZ\WY!bnWbx

ow W[hre+h\V W[Z}Ypt?oe;g?W^koQj?W_`t .se;gXebnWo.epKgOe;ZrWd_`t?oWX?Wt?oWthj _lh}bU8V _mbWWshx se;g.j _lt W0o

a_lh\Vh\VqWQYpk`kl_ltq

x=YphS_lth\WZrgOWo_mYphrWM]!Yklw Wbep

x_lt?o_sYh\Wb[h\V3Yph>hrV W.X Z\e!j?Ypj _`kl_`hnuoWt?bn_`hfu

w t?shr_le;t9e=hrV WSse;gOXqZ\Wbrbn_l]Wcbfh\ZrWt ;hrV9gOe]Wb=h\e.h\V W[k`W hYt?oH!Whib8ge;Z\W{\j w t3syV W0owqX?+Y;b

Ypklkmb

%²KU8V WcX?YpX?WZV?Y;bbnVqepath\V?YhXqZ\e;X?WZ_lt?sklw?bf_le;t+ebfX?Yphr_Ypkse!Z\ZrWkYh\_le!tOY!b=w?bnWo+_lt.h\VqW5¢c|=1x

_b=Wb\bfWth\_Yk e;Zvw?Ypth\_`hiYh\_l]WX Z\W0o_shr_le!t?b=_lt+X Zre;j?Yj _lk`_bnhr_s8!We;hrWsyVqt _sYk?Ypt3Ypkluqbn_mb;éEV _`klW+{}bn_lg.

X klWZ}gWh\V eoqbbnw?siV5Y!b[|

'Ypt3o5

YZ\WSw?bnW wqk e;Z[!_l]_lt +!w _o Yt?sWSe;t5h\VqW+bnW^t?bn_`h\_l]_lhfu

epSoW0bn_l!tEe;w h}se;gWb>h\e]!YpZ\_mYphr_le;t3bQep_`t X w h.X?YZiYpgWh\WZ}bxh\V W^_lZ._lt?Yj _lk`_lhfuhre1bfu bfh\WgYph\_msYpk`klu

_lt?sk`w?oWbfX?Yphr_Ykse;ZrZ\WkmYph\_`e;t#Ypt3oHkles^YpkY]WZiY;_`t .bnW]W^Z\Wk`uQk`_lgO_`hibhrV W_lZw3bnW w k`t Wbrb

"%²U8V WX?YXW^ZV?Y;bcbnV eat#h\V?Yhh\V WE¢c|=ägOWh\VqeoQ_b8hrV W[e;tqklu9swqZ\Z\W^thrklu.Y]!Y0]_lkmYpj k`WdgWh\V eo

Ypj k`W[h\e+X Zre;X?WZrkluY;sse!w th e;ZhrV W[_`gOX?e;Z\h}Ypth8_`t$í?w Wt3sWdebfX?Yphr_Yk,se!Z\Z\W^kYphr_le!t9Ypt?oOk`esYpk Y0]W^Zn

Yp;_`t ¡¥h=_mb=Ypth\_ms_lX3Yph\W0o>h\V?YhXqZ\e;j3Ypj _`kl_bfh\_ms8YpXqX Z\eY;siV Wb=h\e;W^e;h\W0syV tq_sYk Yt?Ypk`u bf_b=a_lk`k_`t?sZ\W0Y;bnW

_lt.Xe!X w kmYpZ\_`hfuxV ea8W]WZK_lha_lk`kj?WYMaV _`klWcj?W e;ZrWdhrV WdgWh\V eoqb

j?Wse;gOWcY!ssWX h}Ypj k`Wd_`tQZre;w hr_lt W

;We!h\WsiV t _msYpk_lt]Wbnhr_lYh\_`e;t?b

îåï5ð<ï5ñ£ï¤òjóèï¤ô

ö@ûü8ý!þ{ú#øÿ$ú¬x

Ù!Ù2

¯0%²}x

1K0*

÷/ ¦U[

V Zr_bfh\_YtYpt?o

ÙSÄ['ÄYpWsiV WZ^e;_`thf¥W0bnh\_`g9YphrWgOWh\VqeoBY;b[tw gOWZr_sYkv%w3Y;oZ}Yph\wqZ\W

ùKû

ÿ øèÿ

õdöÉ÷Æø8x

Ùn

¯1%²}Û~%q%*13%*0q" x

1q1K1

Ypt?oAÑ>;Yptqg9YpZ}sy«W)_lg.w kmYph\_`e;t1eSZiYpt3oe;g

?Wkmo b+]_mYBklesYk[Y]WZ}Yp;W

bnw jo_`]_mbn_le!t,ùÈøèÿ

þ ;õVö÷Æøx

Ù;Ù

"¯0²iÛ

%* q

%<1 x

1K1

ö!÷Sð>4+VÙdZr_~Ah\V?b9Yt?o

ÙSÆ©>| Wth\e;t

Ä8W0YpZ\_`t )sYX?Y;s_lhfu§ebnX?Yh\_Yklk`u§ZiYt?oe!g

bfe;_lkÛ1h\V W

w t?oZ}Yp_ltqWoBskmYuO=ZiYt?ohrk,X Z\e!j klWgïZ\W]_bf_lh\W0o

Kû

þ 3ÿýix'

¯²}Û q

: Kq1 x

K2q2Ù

ö4÷S1¦Ñ[YZ\Z^ !"#$%!û'&(# ")*+,+-.)$/ÿ0ÿjþ1 1%28ÿÿ3 8üÿ;5s{ÙcZ}Y0a½Ñd_`klk¥x ì?e!t?oe;t x.dW^a

Âe!Z\«x

1q0:%

ö4"÷S1¦!Ñ[YpZrZ,=Z\e!j?Ypjq_lkl_mbnhr_sWbnhr_lg9Yh\Wb e!Z8g.w klhr_l]!YpZr_Yh\WYt?Ypk`u bfWb;õ5446ú67"Kû @ú38+-9%!ÿ!x

1K0q1

Ypt?oAU[¦|8;ée;k¬K)KWshQeoW^h\WZrgO_lt _mbnhr_s+Ypt3o/X Zre;j?Yj _lk`_bnhr_sOgOeoW^kbMe!t

bnkle!X?WBZ\W^kl_Yj _lk`_lhfu_lt?oW^A¡¥t§ðS4+®ÙcZ\_UAOhrV?bÈÒ*ÓÔÕx8Wo_`h\e;Z^xdö6!:46Èö@û;"#1%!û;&<===x8X3Yp;W0b

1{*

q2K2K2

Ùhce

Ù2Ù

øÿÿ3 8üÿ@"<ÿ+öA&)8ûB

öA"DC*¶û;&px@q0Û

"<%x

1q1K0

ö41÷FE¬?ì?_5e!_lthMW0bnh\_`g9YphrWQgWh\V eoB e;Z.s^Ypksw kYh\_ltqBbfhiYh\_bfh\_msYpkgOe;gOW^th}bËùaøÿ8

õdö÷Æøx

Ù;Ù

0¯&%!²iÛ

ÙÙ

1K1

Ù2

÷/>

8ì?_`t?oABeoWklk`_lt 5e[wqt?sWZrhiYp_`thfu_lt

o_brsZ\WhrW9out?Ypg_sYkbnuqbnhrWg9bõ5446ú>7"Kû @ú

7*+- %?ÿ;xÆ%Û

1q0K

Ù;Ù

÷FG>®?©dZrgQu

e;ZrX?b[ep¨=t ;_`t WWZ}b¡¥thrZ\eow3sh\_`e;t5h\e9X Zre;j?Yj _lk`_lhfu#Ypt?oBZrWkl_mYpj _`kl_`hnu.gOWhrV eo b

1q1K

tq;_ltqWWZ\_`t .U,WsyVqt _sYkì?Whrh\WZ

Ù!Ù;Ùn2

¸{$%

÷FG>®?©dZrgQu

e;ZrX?b[ep¨=t ;_`t WWZ}b¡¥thrZ\eow3sh\_`e;t5h\e9X Zre;j?Yj _lk`_lhfu#Ypt?oBZrWkl_mYpj _`kl_`hnu.gOWhrV eo b

1q1K1

tq;_ltqWWZ\_`t .U,WsyVqt _sYkì?Whrh\WZ

Ù!Ù;Ùn2

¸KK"

÷SÜ'¢ebnW^tj k`w WhrV,[e!_lthdW0bnh\_`g9YphrWb e;ZX Z\e!j?Ypj _`kl_`hnugOe;gOW^th}b¡¢tHèü{þ*úJIK"KûuúÆõ

þ "+$ú#ö'þ1ú

LÉöõx?tw g.j?WZ

Ù2

xX?Y;WbV K0

! K0

1:%,

!÷SÜ!¢ebfWtjqklw WhrV,U8a8epX?e;_`thWbnhr_lg9Yh\Wb,_lt.X Z\e!j?Ypjq_lkl_`h\_`Wb#õ446ú38"KûM @ú8+-9%!ÿ!xÛ

K Kx

1K0

Wyszukiwarka

Podobne podstrony:
prob analysis how difficult does it need to be
Jak ona to robi I Dont Know How She Does It 2011 RMVB Lektor PL(1)
Third Eye Blind How s It Going to be
How it used to be
How It Feels to be Colored Me
Youyour boss in 20 years „We need to be innovative.”
What Is It Like to Be a Bat
it had to be u
Heinlein, Robert A It s Great to Be Back
Carpenters I Need To Be In Love
and it suppose d to be love
Earthdawn How It Came to Pass
Thomas Nagel What does it all mean a very short introduction to philosophy 1987
Sosnowska, Joanna Adaptation to the institution of a kindergarten – does it concern only a child (2
Does the United States Need to Develop a New Nuclear Earth Penetrating Weapon
David Icke 911 How is it possible to mastermind
It's Easy to Earn Money
How and When to Be Your Own Doctor
Juggler How To Be A Pickup Artist 2nd ed final

więcej podobnych podstron