RH-10-2003 Continuum Branched Polymers Thordur Jonsson

!"$#&%('
)*+-,&
%./
0 143-5764845:9;3-<4=7=3-<
2
>?<4@BA;CD5=7@BEGFH3JILKGMCDNPOJ<46
QR8<41SO;TUOWVXZY\[U] ^?CF`_\aO\A`@b_
KGMCDNPOJ<46
ced4f7gihjlkgmHnpoRqsrutwvixytt{zoi|}~oiw€rv?‚yƒ„yt~ƒ…yq$€wo7†Droi‡!„loˆw„lo7|€‰ |Š‹vi|…Dwr…\xl|xyt
w€oiotŒ‡Z„lruv„:„yƒtŒŽJo7oi…qso7†oi|‚;o7q:r…:„lo‘uƒt’ “ ‰o7ƒ€t7”npo‘oi•\‚yƒr–…ˆw„yoL€oiuƒr–|…:|Š
v—|…Dwr…Dxyxl}˜w€oiot™w|š„lo‘o—•\wo7…ytwr–†oi‰?t
xyqsro7qRqsrutwvi€woiwoLw€oioti”
›UœžŒŸ …Dxy} Ž;oi€ti¡ ” ¢ D ‡‘£ ¤ ” ¥ ¦¨§ £ ¢s” ‰
ƒ…yqs|}!zoi|}šoiw€‰ |€xJƒ…Dwxl}˜zoi|}~oiw€‰Sviƒ…eŽJoL†\r–o7‡ oqeƒt™v—uƒttwrv7ƒ-t
ƒwrut’wruviƒ
}šo7v„yƒ…lruvit |Š`€ƒ…yql|}!zo7|}šo—€wruviƒJ|Ž
o7v—t7¡ ‚yƒw„yt7£Dw€oiot |€™Žl€ƒ…yv„loq2‚;|‰D}šo7€tG£
twxl€’Š ƒv—oti£J„lr–z„loi€Lqsr}~o7…ytwr–|…yƒ }šƒ…lr–Š |uqlti”‹xyƒ…Dwxy} zoi|}šoiw€‰ˆƒ€wrut’otZ…yƒwxl€ƒ–‰ˆr…
‚yƒ€’rvi–oe‚y„D‰stwrv7t ƒ…Jq Dxyƒ…Dwxy}z€ƒ“†\r–
‰£‡Z„loi€o2w„yo2Š xl…yv—wr|…yƒ r…Dwoiz€ƒt xyt’oq Š |€
Dxyƒ…Dr § ƒwr|… ƒ€o2|Š oi… }š|t’ …yƒwxl€ƒ–‰ †Droi‡™o7q ƒt‘ŽJo7r–…yzR"ƒ !oi… |†o7€‘zo7|}šo—€wruviƒ
|Ž o7vGti” ƒ…yqs|} zoi|}šo—w€‰ ƒ€rut’ot‹ƒtw|:r… }2ƒ…\‰ Žl€ƒ…yv„yo7t‹|ŠZv—|…Jqsoi…ytwo7q }2ƒ’oi€
‚l„\‰st’ruvit7£™o” zy”£ r… w„lo t’wxJqs‰$|ŠL‚l„JƒtwoŽJ|xl…yqlƒ€wro7t7£ †o7twrvi–oti£™Žl€ƒ…yv„yo7q ‚J|–‰\}šoi€ti£
Š |ƒ}2t‘o—v
” #l|€ ƒ€oi†\roi‡ |ŠŒw„lrut w„lo7|€‰ xl‚ | % $&$(' £ ‡Z€wr–’oi… Š €|} w„lo:‚J|r–…D |Š
†\r–o7‡ |Š Dxyƒ…xl*
} )yo7q:„loi|€w‰£lt’o7,
o + . - ”
o )J€t’ˆt’wo7‚Hr–…H„lo ƒ…yƒ–‰stwrt2|Š €ƒ…yqs|}zoi|}šoiw€‰$rut?xytwxyƒ–‰$|$qso )y…lopƒ
/ „l
v—uƒtt™|Š4qsrtv—€o—oLƒ‚l‚l€|“•sr–}2ƒr–|…yt w|~w„lo¨zoi|}šoiw€rv7ƒ;|Ž ovGtŒxy…yqsoi€Zr…\†ot
r–zDƒwr|…`”
ƒ )J…lr o …\xl}{ŽJo7€4|Šy‚yƒ€ƒ}šo—wo7€ttw|
/ „lot’oŒqsrutwvi€woiwo ƒ‚l‚l€|“•sr–}2ƒr–|…yt`ƒ€wo™qso7tv—€rŽJoq Ž\‰ 0
w„JƒSw„yoZŠ xl…yv—wr|…yƒlr–…Doiz€ƒut4Ž;o7v—|}šo )y…lr–wožqsr}šoi…ytwr|…yƒlr–…Doiz€ƒut|€ ƒ¨vi|…\†o7€wzoi…D
twxl} |1Š )y…lr–woRqsr}šoi…ytwr–|…yƒ r–…Doiz€ƒut7” / „lo:two7vi|…yq$t
oi‚Wrut „lo:vi|…yt’w€xyv—wr|… |Šžƒ
tviƒr…lz–r}šr ~|ŠŒw„yo2w„lo7|€‰pƒ{ƒ…Wƒ‚l‚l€|‚l€rƒwo2v—€r–wruviƒ ‚J|r–…D” / „yo?twv7ƒr–…yz–r}šr 
|Šw„y
o 2L€wo7oi…ˆŠ xl…yv—wr|…ytžr–…R„lo qsrutv—€o—wo¨„loi|€w‰:ƒ€o‘zoi…yoi€ƒ–‰eŽ;oiroi†oq:w|eqsotwvi€wrŽJo
w„yo xl…yqso7€w‰\r–…yz?v—|…r–…\xlxy} „loi|€w‰” / „yo xl–wr}šƒwo{z|ƒUr–… w„lo t’wxJqs‰R|ŠS}š|\qloiutr…
Dxyƒ…Dxl}!zoi|}šo—w€‰~rt w|{xl…yqso7€t’ƒ…yq2r…:qsoiƒr–;„l|‡ w|~r…oiz€ƒwo|†oi€ „lo‹tw‚yƒv—ož|Š
v—|…Dwr…Dxy|xyt™zo7|}šo—€wruviƒJ|Ž o7v—t7” / „lrtŒ€%o Dxlr€o7t w„lo‘vi|…yt’w€xyvGr–|…?|Šƒ{}~oƒtwxl€o‹|…
w„yo ƒ‚l‚l€|‚y€wruƒoLtw‚yƒvio‹|Š4vi|…Dwr…\xlxl} ‚Jƒw„Jti£ytwxl€wŠ ƒvio7t7£\w€oio7t7£so—v”
3  rutSŠ ƒr€ | twƒ“‰ w„yƒ r…šw„loLviƒtwoZ|ŠUtwxl€’Š ƒv—ot ƒ…yqš„yr–z„loi€ qlr–}šoi…Jt’r|…yƒl}2ƒ…lr–Š |uqlt
w„yo:uƒt’~t’wo7‚W„yƒt{…l|~Ž;oio7…$ƒv„lroi†o7qU” 3 … „loˆv7ƒtwoe|Š‹„lr–z„loi€šqsr}šoi…ytwr–|…yƒ™}2ƒ… r–Š |uqlt o7†oi… „l
o )J€t’{t’woi‚ rut{‚l€w|Žloi}2ƒrv2twr–…Jv—oer…Wzo7…loi€ƒ ŽJ|xl…yqlt ‡Z„lrv„$oi…ytwxl€o
w„yošvi|…\†o7€wzoi…yvio |ŠŒqsrutwvi€woiwošƒ‚l‚l€|“•sr–}2ƒwr|…ytLƒ€o{…y|4
 !\…l|‡Z… £ twoi
o + - ” 3 5
… + 6 - r–‘rt
tw„l|‡Z… „l|‡ |‹r…Dwz€ƒwo™|†oi€v—|…r–…\xl|xytzo7|}šo—€wruv ‚yƒw„yt4ƒ…yq‘„loŒ}~oƒtwxl€o |…~t’xJv„
‚yƒw„yt rtŒvi|…yt’w€xyvGo7qU” |xlz„y–‰2tw‚Jo"ƒ !\r–…yz w„yrt™rut™ƒv„lroi†oq2Ž\‰2qsr–†\ruqsr…lz „loLnHr–o7…loi€
}šo7ƒt’xl€ožŽ\‰~w„yo¨ƒvGr–|…e|Š „lo‘qs8r 7;o7|}š|€‚l„lrut’}!z€w|xl‚e|…:‚yƒ€ƒ}šoiw€r § o7qš‚yƒw„yt7”Snpo
€oi†\r–o7‡$„lrut „loi|€w‰~r–…ew„lo‹…lo—•\ two7v—wr|… ” 3 …šw„yow„yr–€qetwo7vGr–|…2‡ o‹qso7tv—€r–Ž;o œ qs|xy%t 9 t
w„yoi|€‰e|Š€ƒ…yql|} vi|…Dwr…\xlxl}˜€wo7o7t7£yt’o7:
o + " - Š |€ƒ2qsoiƒr–o7qˆ€oi†\r–o7‡ Š |€Z‚l€w|ŽyƒŽyr–rt’t
ƒ…J;
q + "¤ - Š |€žƒšqs<r 7-oi€oi…DZ‚;oi€t’‚;o7v—wr†o ƒr}šo7qˆƒ‚l„\‰stwrvirt’t7”
/ €oiotƒ…Jqv—|…Dr–…\xl|xyt™w€oiotƒ€o‘r–…Doi€o7t’wr…lz2r–…R„loir€|‡Z…R€r–z„žƒtƒ…Roi•sƒ}š‚l–o
|Ѝƒ€wo7ƒwr†oi‰ t’r}š‚lo€ƒ…yqs|} zoi|}~oiw€‰5
” =|€o:r}š‚J|€’ƒ…Dw‰£Œqsrutwvi€woiwoRt’xy€’Š ƒv—o7t
viƒ…$Ž;o:€oi‚y€wot’o7…o7qWƒtšv—oi€wƒr–…$ƒŽJo7–o7q$w€oio>
t + ¢ - tw|pr–~rut~‚J|DtwtwrŽl–o:w„Jƒ2|…loˆviƒ…
qso )y…lo‘r…oiz€ƒwr|…?|†oi€Œv—|…r–…\xl|xytŒ€ƒ…yqs|} t’xy€’Š ƒv—o7tŒŽ\‰er…Dwo7z€ƒwr…lz~|†o7€™€ƒ…Jqs|}
uƒŽ;oi–oq:vi|…Dwr…\xl|xyt™€wo7o7t7”
?
@BACDEA1FG.IHJKL
3 ‹rut‡™oiM!\…l|‡Z…R„yƒ‹w„loN xyvi–ruqso7ƒ…RŠ €wo7o4)yo7q‚y€w|‚yƒzDƒw|€viƒ…ŽJo{o—•s‚l€o7tt’oq?Š |€ }2ƒ–‰:ƒt
g
POCQSR TUVWYX"[Z]\_^a`cb:[ZM\d^aecf(gih j6k4lmnWpoq q r,s0\
‡Z„lo7€wo‘„lo Š xy…yvGr–|…yƒ4r…oiz€ƒ rt‹|†o7€žƒ
sHŠ €|} Z | ^Rƒ…yq s
qso7…l|o7t-„lo oi…lzw„‘|Š(s” œ zo7|}šo—€wruv4‚yƒw„‘rut`ƒ…‘oVDxlr–†ƒ–o7…yv—o viƒtwtU|Šs‚yƒ€ƒ}šo—€wr § oq
‚yƒw„y
t ¡ + \ -!#" xl…yqloi€ „lo?oVDxlr–†ƒ–o7…yv—o2€oiuƒr–|…%$ ‡Z„lo7€wo&'$() r Šƒ…Jq
|…y–‰r ŠZ„loi€oerut ƒ… r–…yvi€woƒtwr–…yz qs<r 7-oi|}š|€‚l„lrut’+
} * |ŠŒw„lo:xl…lr–{r…Dwoi€†ƒ™t’xyv„ „yƒ
) e,.-/*™”
| ^eŽ\#
‰ 1: ZM\d^—” 3 … + V - ƒ
0 oixytZqsoi…y|woL„lo‘t’oiŒ|Šƒ–Uzoi|}šoiw€rv‹‚yƒ„yt™Š €|} Zˆw,
‚l€|ŽyƒŽlr–r–
‰2}šo7ƒtwxl€3
o 2prutZv—|…yt
€wxJvGwoq?|&
… 1: ZM\d^t’xyv„:w„Jƒ
f gh j6k4l m Wpoq g q 5 s _r,s0\
45 s 76 `cf 5 [s 982 e
b:[Z]\_^
‡Z„lo7€wo:w„loVo Dxyƒr 
‰ ƒŽ;|†oˆ}~oƒ…yt~„yƒ2…yƒwxl€ƒqlrtv—€o—oˆƒ‚l‚l€|“•\r}2ƒr–|…yt{w|w„lo
Š xl…yv—wr|…yƒsr–…Doiz€ƒb£o” zJ”–£„loƒ‚y‚l€w|“•sr}2ƒwr|…{xytwr–…lz¨uƒwwruv—oZ‚yƒw„yt4‡Zr–w„šuƒ’rviot’‚Jƒv r…l;
z :;£Dvi|…\†o7€wzo |¨w„lo‹o—•s‚;o7vGƒr–|…~†ƒ–xlož‡Zr „2€wot’‚;o7v— w;
| 2ƒ<t : ” 3 Œv—|}~ot ƒt
…l|2twxl€w‚y€wrut’o‹w„JƒZw„yo ƒŽ;|†oL%o Dxyƒr–
‰e„l|uqltZŽ;o7v7ƒxytwoLw„lo‘}šoƒtwxl€w=
o 2rtŒr…ˆŠ ƒvGžvi|… t’w€xyvGo7qšƒtSƒLr–}šr– |Š-}šo7ƒtwxl€o7t4|…~qsrutv—€o—wr § oq~‚yƒ„yti” 3 … + - 
‡™|¨ql<r 7-oi€oi…D tv„loi}šo7t
ƒ€oŒr–…D€w|sqsxyvio7qU£|…loŒxytwr…lz‘ƒ’rvioZ‚yƒ„yt ƒ…Jq „loZ|„loi€ xyt’r…lz¨‚lruv—o7‡ZrtwoZ–r…loƒ€S‚yƒw„yt
‡Zr–w„$ƒ…Wr–…D€wr…ytwrv?}~oiw€rv” / „lo:oi…ytwxlr…lzpvi|…Dwr…\xlxl} –r}šr tšƒ€oe%o Dxlr†ƒoi…D7” Ÿ r–} rƒ€w‰£ xJt’r…lzRw„yoetwƒ}~o~o7v„l…lr Dxlo7t7£|…lo2viƒ… v—|…Jt
€wxyv— ƒR‚l€w|ŽyƒŽyr–r 
‰}šoƒtwxl€woš|…
w„yo t’‚yƒv—o¨|Šzo7|}šo—€wruvL‚yƒ„ytŒ‡Zr „ƒ…Rƒ€Žlr €ƒ€w‰2o7…yqs‚;|r…D7”
o 2ev7ƒ… ƒtw|ZŽJo™qso7tv—€rŽJoq‘qsr–€o7v—w‰‹r…‘oi€}št`|Š\w„yo nHroi…lo7€`}šo7ƒt’xl€o”
/ „lo }šoƒtwxl€w
o B-|…‘‚yƒ„yt Š €|} Z 0
| ^L‚yƒ€ƒ}šo—€wr § oq
0 oi? >A@UŽJoS„lo nHroi…yoi€}~oƒtwxl€oS‡Zr „ †ƒ€rƒ…yv—<
Ž\‰šw„lo‘xy…lr Zr…Dwoi€†ƒb” / „loi…ˆw„yoL}šoƒtwxl€woL|Š4ƒ{two—Z|Š zo7|}šo—€wruv‹‚yƒ„yDt CFEG1: ZM\d^
rutŒzr†oi…ˆŽ\‰
2GC ae fIH m W oK @L U >M@ N WX C dO8PB
J
‡Z„lo7€wo=Nprut™w„yo¨v7ƒ…l|…lruviƒ-}2ƒ‚y‚lr–…yz~|Š ‚yƒ€ƒ}šo—w€r § o7qe‚yƒ„ytŒ|…Dw|{w„yoir€Zo%Dxlr†“ƒ–o7…yv—o
v—uƒttwo7tSrQ
… 1:[Z]\_^G” / „lrut €o7twxl– rt o7t’ƒŽl–rutw„lo7qšr… + V- |zo—w„yoi€ ‡Zr–w„š„lo‹vi|€€wot’‚;|…yq r…lzš€wot’xl–ŒŠ |€Z‚yƒw„yt‡Zr „Rƒ{Š €oio‘o7…yqs‚;|r…”
2Loi|}~oiw€rve‚yƒ„yt „yƒ“†o2…l| r…Dw€r–…ytwruvet
€wxJvGwxy€woeƒ…yq w„yoi‰ viƒ…y…l| Ž;oe‚yƒ€ƒ}šo— €r § o7q ŽD‰ ƒ€v—oi…lzw„ twr…yv—oˆw„yoir€2–|sviƒZŽJo7„yƒ“†\r–|xl€šrt~„lo tƒ}šoƒt{w„yƒe|ŠLnHr–o7…loi€
‚yƒw„ytŒ‡Z„lruv„R„yƒ“†o¨r… )y…Dwo ƒ€vi–o7…lz„ ” |‡™oi†oi€£Dw„lo‘‚;|r…DtZ|…?„lo‘zo7|}šo—€wruvL‚yƒ„
ƒ€o2r–…loƒ€–‰p|€qsoi€o7qtwr–…yvio?twxyv„ |€qsoi€r–…yz|… ƒ‚yƒ€ƒ}~oiw€r § o7qp‚yƒ„yt rut ‚y€wot’o7€w†o7q
Ž\‰:r…yvi€woƒtwr–…lzeql<r 7-oi|}~|€w‚y„lrtw}2ti” 3 žw„yoi€o—Š |€o }2"ƒ !o7t‹t’o7…yt’o w|:ƒ_t !:‡Z„lo—„loi€¨ƒ2zoi| }šo—€wruvL‚yƒ„:r… " „lr–tZƒšvioi€wƒr…Rt’oiD C(|€Œ‡Z„lo—„loi€r–Z„lr–tƒ~…\xl} Ž;oi€Z|Š }{xswxyƒ–‰
qsru[t |r–…Džtwo—R
t C \
S
STS\UCWV:r–…ˆw„Jƒž|€qso7€7” / „lo¨
‰\‚lruviƒUŠ xl…yv—wr|…yt|…lo vi|xluqˆr–}2ƒzr–…yo
r…oiz€ƒwr…lz{‡Zr–wX „R€o7tw‚JovGŒw|š„lo‘}šo7ƒt’xl€=
o 2ƒ€woLw„yoi€o—Š |€oL|Šw„lo¨
‰\‚;o
… [
\ r–]Š s )y€t
„lr–Dt C.ƒ…yq:w„lo7\
¤ X s GeZY \ |w„lo7€w‡Zrut’o
‡Z„lo7€woWC ƒ…yq[ ƒ€oŒ
‡ |{qsrt |r…D™twxlŽytwo—t |Š " ” 3 …+ 6- ƒ v—|…\†oi…yr–o7…SŠ ƒ}šr–‰š|Š t’oit
|Š™zo7|}šo—€wruv~‚yƒ„ytLw|r…Dwoiz€ƒwo~|†o7€Lrut qso)y…loqU” / „lo7two2t’oit ƒ€wošviƒ–o7qv—‰\r–…Jqsoi€
two—tŽ\‰ ƒ…Jƒ|z‰L‡Zr–w„{w„loZv—‰\r–…Jqsoi€Stwo—t|ŠJ‚yƒ€ƒ}~oiw€r § o7q‘‚Jƒw„Jtƒ…yq r–Srt4tw„l|‡Z… „yƒ
w„yoZ}~oƒtwxl€o7t4|Š-|ŠUv—‰\r–…Jqsoi€ two—t qso )y…lDo 2Rxl…lr Dxloi‰” / „lo}šo7ƒt’xy€wot |Š v—‰\–r…yqso7€ t’oit
viƒ…WŽ;o?oi†ƒ–xyƒwoq r–…$wo7€w}2t{|Š 2L€oioi…WŠ xl…yvGr–|…yt Š |^
€ ]žr€wruv„lo—~‚l€w|‚yƒzDƒ|€ti” / „lo
twr–}š‚lo7t’o—•lƒ}š‚lo¨rt
b4[Z]\_^
\
b:[Z]\_^
2G C_ae
B¢n
‡Z„lo7€wo#C rt{ƒ t’x2vir–o7…Dw‰…yrvio?t’xyŽyt’oi |Š " ‡Z„lruv„$vi|…Dƒr–…yt Z ƒ…Jq ^;£b4
ZM\_^
rut~w„l\
o ]‹r–€rv„y–oi2L€oio7…WŠ xl…JvGwr|… Š |€{„lo o7–}š„l|  § |‚;oi€ƒw|€{‡Zr–w„Hqlƒƒp|… w„lo
Ž;|xl…yqyƒ€‰{|Š C ƒ…y
q C rut „lo¨t’oi™|Š`ƒJzoi|}šoiw€rvž‚yƒ„yt Š €|} Z:w|^2‡Z„lrv„:ƒ€o
v—|…Dƒr…loq?r…ˆw„lo‘two—W
 C ”
L J D
A0A0L
no{Ž;oizr–…pŽD‰ qlrtv—xyttwr–…lz?w„lo{w„yoi|€‰|Š™qsrtv—€o—o €ƒ…yql|} w€oioti”
™‰ qsrutwvi€woiwo{w€oio7t
‡™o™xy…yqsoi€t’ƒ…Jq{€|\|o7q~‚luƒ…yƒ€4w€oio7t7£rb” o”–£|…loZ|ŠJ„loZ†o7€’rvio7t4|Š;oƒv„~w€oioŒrut t’r…lz–oq
|xlžƒ…yqRviƒ–o7q?w„yo €w|\|Zƒ…yq:w„lo w€oio7tZtw„l|xlqˆŽ;o‘w„y|xlz„Z|Š4ƒtZoi}{ŽJoqlqso7qˆr…Rw„lo
‚luƒ…loLt’|{w„Jƒ™w„loL–r… !stŒƒ€o‹vi‰\vi–ruviƒ–‰š|€qsoi€o7q?ƒ€|xl…yqeo7ƒv„?†oi€wwoi•U” / „lo¨t’ƒ…Jqlƒ€q
w„yoi|€‰e|Šqsrutwvi€woiwoLw€oiotŒrtžqs.o )y…yo7qˆŽ\‰2w„lo‘‚Jƒ€wwr–wr|…:Š xl…yvGr–|…
[Z Ge
Z q @ q B_ \
@
¥&
‡Z„lo7€wo?w„loˆt’xl} €xl…yt{|†o7€{ƒ–™€w|\|wo7qW‚lƒ…yƒ€ w€oiot BG£W B
qsoi…l|wot „lo:…\xl}{ŽJo7€{|Š
r–… !st r–#
… B ƒ…yq B_ rt „lož‡™oirz„D Š ƒvG|€ |Š w„yow€oioBG” / ‰\‚lruviƒ–‰~w„lo‹‡ o7r–z„ Š ƒv—w|€
B_Zrutv„l|twoi…ˆ|2ŽJo ƒš‚y€w|sqsxyv—ž|Š4‡™oirz„DZŠ ƒv—w|€tZƒttw|\virƒwoq:‡Zr–w„†oi€wwruv—otŒ|Š4w„lo
w€oio£srB” o”£
> B_ae
' @
rutZ„lo ‡™oirz„DZŠ ƒv—w|€ZŠ |€Lƒš†oi€wwoi•ˆr–…\BŒ|Š4|€qloi€1e-”ŒnHr „w„lot’o
‡Z„lo7€wo
qso )y…lr–wr | …yt™„lo‘‚yƒ€wwr–wr|…ˆŠ xl…JvGwr|…tƒrt_)yo7t™„lo‘o%Dxyƒwr|…
Z Ge Z H
X
WX [ZpS
&
/ „lrut¨%o Dxyƒwr|… viƒ…pŽJoeƒ…yƒ‰st’oq r… |€qsoi€Lw|qsoiwo7€w}šr…lo~w„loevi€wr–wruviƒŽ;oi„Jƒ“†Dr|xy€L|Š
w„yo~qsrutv—€o—wo w„lo7|€‰£-t’o7o>+ ¥l£ 'V- ” / „yo~vi€wr–wruviƒ Ž;oi„yƒ“†\r|xl€‹rt‹xl…lr†o7€tƒ ‚l€|†DruqsoqRw„lo
z|~w| § oi€|štwx ev—roi…D–‰?Š ƒt’Œ‡Zr–w„-”
/ „lo¨‡ o7r–z„D Š ƒv—w|€tŒqs
o )y…lo7q:ƒŽ;|†o‹zr†oL€wrut’o‹w|šƒ{‚l€w|ŽyƒŽyr–r 
‰š}šo7ƒt’xy€woL|…?w€oio7t
‡Zr–w„
ƒ )l•so7qˆ…\xl} Ž;oi!€ |А–r… !sti¡
1:#" e B_Ge%$
@
&('
)
\
$ ‡Z„lo7€wo*$ rtZƒ~…l|€w}2ƒr § ƒr–|…eŠ ƒvGw|€7” œ  oi€…yƒr–†oi‰2|…lo v7ƒ…ˆ‡Z€wr–wo
1:" e B_Ge%$+
¤
-,
X
/.
'
@) \
7 ‡Z„lo7€wo4r B_Œrut™w„yo‘…Dxy} Ž;oi€Z|Š4†o7€’rvio7t™|Š4|€qso7€!:r… GB ” 3 Š
e
\
w„yoi…ƒ-w€oiotŒ‡Zr „ †o7€’rvio7tŒƒ€o¨o%Dxyƒ–‰e‚l€|ŽyƒŽloLƒ…yq
O 1:" e B_ae
e
S
>O B™¡ B
&e
#l|€™w„lo¨Š |–|‡Zr–…yz~qsrutv—xytt’r|…:r rut™}š|t’Zvi|…\†o7…lroi…D |~Š |\vixytŒ|…:w€oiotŒ‡Zr „ˆƒ)l•soq
…\xl} Ž;oi€ |Š †oi€wwruv—ot ƒ…Jqšxyt’ožw„lo‹Š xl…yqyƒ}šoi…DƒyŠ ƒvG
 + - „yƒ w„lo7€wo‹rt™ƒ |…lo| |…lo
v—|€w€o7tw‚;|…yqso7…yv—o ŽJoi
‡ o7oi… €wo7o7tL‡Zr–w„ R †oi€wwruv—ot‹ƒ…yq qsrtv—€o—o{oi•lv—xl€t’r|…Jt 2|Š
qsxl€ƒr–|… S£ rb” o”£ €ƒ…yql|} ‡Œƒ !st‘|…w„yoe‚J|Dt’r–wr†o2r…Dwo7zoi€t¨‡Z„lruv„ ŽJo7zr…Wƒ…yqoi…Jq
ƒ ” / „lrutžvi|€€wot’‚;|…yqloi…yvioLrut‹ŽJot
žoi•s‚lƒr–…yo7qRŽ\‰ˆƒe‚lrv—wxl€o£-twoio #rzy” ”Œno{qs€ƒ“‡
w„yo2w€oioer… „lo?‚luƒ…yo” / „lo?oi•lv—xl€t’r|… PG£‡Z„loi€o ‘rt w„lo?qlrt’ƒ…yv—oe|ŠZw„lo
‡Œƒ !oi€4Š €|} w„yo€w|\| ƒŠ wo7€ 4t
oi‚yt7£Drt ql.o )y…loq2Ž\‰~t’ƒ€’r–…yz ƒ „lo€|D| ƒ…yqš‡Œƒ !\r–…yz
v—|xl…Dwo7€vi–|sv !\‡Zrtwo ƒ€w|xl…yq‘„lo™w€oio£†Drutwr r–…lzL„loŒ†oi€wwruv—ot twxyvio7tt’r†o7–‰‘ƒ…Jq €ƒ“†oi€t’r…lz
|\|
#r–zxl€o ¡ œ €w|\|o7q2‚yƒ…yƒ€ w€oio‹‡Zr „ †oi€wwruv—ot ƒ…yqšw„yoLƒtwtw|sv—ruƒwoqev—|…Dw|xy€ ‡Œƒ !;”
o7ƒv„R–r…!e
‡Zruv—o{ƒtZr…yqsruviƒwo7qRr…Rw„yo4)yzxy€wo” #r–zJ” tw„l|‡t ŒƒtƒšŠ xl…JvGwr|…|Š ”
œ }šo7ƒt’xl€o¨|…qsrutwvi€woiwo¨€wo7o7tŒ|Ž\†\r|xytw–‰:qso.)y…yo7tƒš}šo7ƒt’xy€wo¨|…qsrutv—€o—wo‘oi•lv—xl€t’r|…Jt
†\rƒ‹„ložv—|€w€o7tw‚;|…yqso7…yv—o” s‡™oZqs|‘…l|G !D…y|‡ „l|‡$w| qso )y…ložvi|…Dwr…\xl|xJtw€oio7t
Žlxs w„loLv—|€w€o7tw‚J|…yqso7…yv—oZŽ;o—
‡™oio7…?qsrutwvi€woiwooi•svixl€t’r|…yt ƒ…yq2qlrtv—€o—ow€oiot ƒ–|‡tSxyt
w|eql.o )y…lo vi|…Dwr…\xl|xJtŒw€oiotZƒtŒ„lo |Ž o7vGtƒttw|\virƒwoqe‡Zr–w„ v—|…Dwr…Dxy|xytZoi•lv—xl€t’r|…Jt
r…:„lo tƒ}šo¨‡™ƒ“‰eƒtZqsrtv—€o—oLw€oio7tZƒ€wo‘ƒtwtw|sv—ruƒwoqe‡Zr–w„qsrutwvi€woiwo¨o—•lvixl€twr|…yt7”
0 oi ¡
+ ŽJo¨ƒ vi|…Dwr…\xl|xyt Š xl…yv—wr|…ˆt’xyv„?w„yƒ e £ 6 Š |€
ƒ…Jq 60e Š |€
” Ÿ xyv„pƒeŠ xl…yv—wr|… rut¨twƒrqw|ˆŽJošƒ?vi|…Dwr…\xl|xyt
o—•lvixl€twr|…2|Šqsxl€ƒwr|… ”4noLqso )y…lo¨ƒ ‚ytwoixy|\ql|}šo—€wruv|…ew„yoLvi–|Dt’oq2r–…Doi€†“ƒF + \ Ž\‰e‚lxswwr…lz
8 &\ ) Ge 6R ) O r…sŠ "
7 $# #&% ' % (! %
) & * + *
¢
,)-.-/,10 32
"!
%
$ 3 P™v—|€w€o7tw‚J|…yqsr…lz
#rzxl€o ¡ / „lo¨o—•lvixl€twr|…
|šw„lo¨€wo7o¨|…# rzy” ”
% # )
% $ & * ) %
# ,)- . -, 0 32
ƒ…Jq
, r–…l.Š , 0 3"2 ae zo7…loi€ƒr–|…?|Š w„lo‘uƒt’v—|}~}š|…Rƒ…yv—ot
|€Œ|Š
ƒ…yq$ ) \
) ” / „lrutSrutS…l| ƒ¨}šoiw€rvŒŽ;o7v7ƒxytwoŒ‡ ov7ƒ…š„yƒ“†oD8 &\ ) Ge Š |€ &\ ) + \ - ƒ…yq
‡Zr–w„ e )-ŽlxlD8šrut™o7ƒt’r–‰etwoio7…e|~tƒrt’Š ‰šw„loL€wruƒ…lz–oLr…lo%Dxyƒ–r–
‰”|‡ qso.)y…yoLƒ…
%o Dxlr†ƒoi…yvio¨€wo7ƒwr|…M$.|… + \ - Ž\‰ =$ )`r Š8 &\ ) Ge ” / „loi…ˆ„loUU
O rtZqso )y…loq?|šŽJo¨„lo‘}šo—w€ruv‘t’‚yƒv—o:+ \ - ${”
3 Lrut‹‚Jo7€w„yƒ‚yt‹}~|Dt
¨v—|…D†oi…lroi…D|e„lr–i… !|ŠSw„yo{v—|…Dwr…Dxy|xytžw€oio xJt’r…lze„lo~zo …loƒ|zruviƒ ‚yrv—wxl€o” / „loi… 6{t’„l|xluq$Ž;oˆw„l|xlz„Dš|ŠLƒt{w„loRzo7…loi€ƒr–|…W|Š‹w„lo
r…yqsr†Druqsxyƒ ” 3 Š
)-„loi… ‘rutZƒ…Rƒ…Jv—o7t’w|€Z|Š T) r ŠSƒ…yqˆ|…l–‰?r Š
6Ge r–…lŠ "
i¤ ¢n
3 Ї™oe…l|‡!„yƒ“†o:ƒ}šo7ƒtwxl€oe|… „lo:tw‚yƒv—oe|Šžv—|…Dr–…\xl|xyt oi•svixl€t’r|…yt r ~zr†o7t €wrutwo
w|šƒ{}~oƒtwxl€ož|…?w„lo‘vi|…Dwr…\xl|xyt w€oiot™†Druƒ w„lo‘v—|€w€o7tw‚;|…yqso7…yv—ož‡ oL„yƒ“†oLqso7tv—€rŽJoq
ƒŽ;|†o” no‘‡™|xluq?|Š4vi|xl€two‹8r !oLw|2„yƒ“†oLƒ~}šo7ƒt’xl€o¨|…:w„lo vi|…Dwr…\xl|xJt™w€oio7t™„yƒ
rutšr–… ƒ …Jƒwxy€ƒt’o7…yt’oRƒ–r}šr 2|Šžw„yoˆ}šoƒtwxl€woˆ|… qsrutwvi€woiwoˆw€oioti” / „lrutšrt~"ƒ !o7…
viƒV€wo?|ŠŽ\‰ L ƒw„yoi|€oi} ‡Z„l|Dt’o:}š|t’{zo7…loi€ƒ Š |€} rt~qsxlo:w| œ uqs|xy
t + $ £ 76 - ” 0 o—
B ŽJo:ƒ t
|sv„yƒt’wruvš‚l€|\vio7tt¨‡Z„loi€o ‘rt ƒ
@ ` WX U _+ B - L‡Zr „ qsrutwvi€woiwo‘oi•svixl€t’r|…Rƒ…yq + Z - qsoi…l|wotŒw„lo‘r…Dwo7zoi€ž‚yƒ€wZ|Š Z`” 0 o—=
 [W@ ŽJo ƒ ™€|‡Z…lruƒ…
o—•lvixl€twr|…ˆ|Š qsxl€ƒr–|… ‡Z„lruv„ viƒ…RŽJo‘„l|xyz„Dž|Š ƒtƒ ™€w|‡Z…yrƒ…:}š|r–|…‡Z„lruv„
t’ƒ€wt¨ƒ ƒ¨wr}~o ƒ…yq rut‘v—|…yt’w€ƒr…lo7q w|RŽ;o2‚J|Dt’r–wr†ošxl…DwrSr– €woiwxl€…ytLw| ƒ
wr}š
o Be £ twoi
o + £ V - Š |€ ƒˆ}š|€o2‚l€o7v—rutwošqlrtv—xyttwr–|… G” 0 o— ŽJoew„lo2†ƒ€ruƒ…yvio
|Š w„lošn| 7-tw‚l€r–…lzˆ‚l€|ŽyƒŽlr–r–
‰ qsrut
€wrŽlxsr–|…ƒtwtw|sv—ruƒwoq ‡Zr–w„pw„lo2‡™oirz„DLŠ ƒv—w|€t ”
/ „lrutŒrtZw„lo qsrut’w€r–Žlxlwr|…Rqs.o )y…yo7qˆŽ\‰
&¥ › €w|Ž ” 2v„lrql€wo7… X S
nHr–w„pw„lošƒŽ;|†o~qs.o )y…yr r–|…yti£ œ ql|xy%t 9 t‹„loi|€wo7} t
ƒwot„yƒ¨„lo{‚y€w|sv—otwt @ V vi|… †o7€wzo7t ‡ o"ƒ !\‰2w| WX [ @ ƒt ”
¥
/ „lo*
™€w|‡Z…yrƒ…?o—•lvixl€twr|…:v7ƒ…ˆŽJo v„Jƒ€ƒvGoi€r § o7q?ŽD‰ew„lo sq o7…ytwr 
‰
X L U W L U O V W L U Z U m W j K L U X W )
[Zp e
'
, N , ,
6' ‡Z„lruv„:rutŒ„lo‘‚l€|ŽyƒŽlr–r–
‰?qsoi…Jt’r–
‰eŠ |€ƒ…ˆo—•lv—xl€twr–|…:|Š4qsxy€ƒwr|… |2ŽJo‘|sviƒwo7qˆƒ
Z
ƒr–}šo \ G” / „loZƒŽ;|†o Š |€w}{xluƒ‹qs|\ot „y|‡ o7†oi€ …l|S‰\roiuq }{xyv„ r…ytwr–z„
r…| „lo¨t
€wxyv—wxl€oL|Š „lo‘ƒtt’|sv—ruƒo7q2€ƒ…Jqs|}˜v—|…Dwr…Dxy|xyt w€oiot ŽyxsZr viƒ…eŽ;oLxJt’oq
w|~viƒvixlƒwožtw|}šo‹|ŠUw„yoir€ ‚l€|‚;oi€wwro7t7” #l|€ o—•lƒ}š‚lo£w„yo‹|svivixl‚yƒwr|…eqso7…yt’r–
‰ |Š
w„yo €wo7o{ƒ¨qsrut
ƒ…yvi
o Š €w|} w„lo{€w|\|L‡Z„lruv„Š |€¨ƒezr–†oi… oi•svixl€t’r|A
… >A@Zrt¨qso )y…loq
Ž\‰
8
f X
8PB \
e
&
8
!
‡Z„lo7€wo X
-/,
rt™„lo v„yƒ€ƒvGwo7€wrut’wruvŠ xl…JvGwr|…R|Š`w„yo t’oiWC £l„yƒt™w„lo ƒ“†oi€ƒzo
4 6Ge ¤ m WpU K S
%$ =|€wo¨r…yt’rz„Dr…Dw|~w„lo{t
€wxyv—wxl€o¨rt|Žsƒr…lo7qˆŽ\‰:ƒ2qsr€o7vGvi|…yt’w€xyvGr–|…R|Šw„lo‘€ƒ… qs|} v—|…Dr–…\xl|xyt w€oioŒqsxlo™w| œ uqs|xyti”no™‡Zrs…l|‡W|xlwr–…lo w„yrtSqsr€o7vG vi|…yt’w€xyvGr–|…
‡Z„lruv„ rut‹ŽJƒtwo7q|…ƒn!Dr…lzˆƒe„yƒ Š r–…yo£ v—xl’wr…lzˆr ¨xl‚pr–… ƒ:‚yƒ€’rvixlƒ€ž€ƒ…yql|} ‡™ƒ“‰
ƒ…Jq?z–xlr…lz~w„yo‘‚lr–ov—otŒw|zo—„loi€Œr…ƒ…l|w„lo7€Z‚yƒ€wwruv—xluƒ€Œ€ƒ…yql|} ‡Œƒ“‰”
S
S
SŽJow„ložwr}~ot |ŠUƒ › |rutwtw|…~‚l€|\vio7ttS‡Zr–w„e€ƒo
0 oi e J BG£Urb” o”–£-„lo{€ƒo{r…yviX €woƒtwo7tU r…lo7ƒ €w‰R‡Zr „ r–}šošt’|ˆ‡ ošviƒ…w„yr–… ! |Š „lo r–}šo
t Œƒt
w„yoLvi–ruv !st r…R
ƒ 2Lo7r–zoi€Œv—|xy…oi€™}šo7ƒtwxl€r–…yz w„yoL€ƒqlr–|DƒvGr–†\r–
‰š|Š ƒ~t’xyŽyt
ƒ…yvio‹‡Z„y|two
qsoviƒ“‰ˆ€ƒwo r…yvi€woƒtwo7t‹–r…yƒo7€w‰ˆ‡Zr „ r–}šo”  |…yt
€wxJvGLw„lo~–r…lošt’o7z}šoi…Dt + d\ X Š |€ 0e \ \ \TS
STS ” no~…y|‡ qs.o )y…yošƒ… r… )y…Dwo~€|D|woqw€oio~r…yqsxyv—wr†oi‰” 0 o—3
 B X ŽJo
w„yožr…oi€†ƒ] + \ X S‡Zr–w„ w„lo‹€w|\|” 3 …JqsxyvGr–†oi‰£D–oi B X Ž;ow„yow€oiož|Žsƒr…lo7qš
Ž\‰
zxlr…lzšw„yo r–…Doi€†“ƒa + \ X ™wQ
| B ƒžƒ2€ƒ…yqs|} ‚;|r…D ‹v„l|twoi…R‡Zr–w„R„lo xl…lr–Š |€}
‚l€|ŽyƒŽlr–r–
‰ qlrt’w€r–Žyxswr |… |… B ” / „lo r–}šr–wr…lz w€oio ƒt rute„lo €ƒ…Jqs|}
v—|…Dwr…Dxy|xyt w€oio ƒ…yq:r žv7ƒ…RŽJo tw„l|‡Z…:w|šŽ;o‘w„lo tƒ}šo‘ƒt™„lo‘|…yo¨ƒtwtw|sv—ruƒo7q:‡Zr „
™€w|‡Z…yrƒ…ˆoi•lv—xl€t’r|…`” / „yrt‹€ƒ…yqs|}
w€oio{viƒ… ŽJo €o7ƒ–r § oqR€wrz|€w|xytw–‰?ƒtžƒ2€ƒ…Jqs|}
twxlŽytwo—|ŠSƒ2twxlr ƒŽl*
o Œƒ…yƒv„ˆtw‚yƒv—
o + 76 - ƒ…yqˆ…l|žtwxl€‚l€rtwr–…yz‰2w„lrut€ƒ…Jqs|} twxlŽytwo—
„yƒt ƒxJtwqs|_€ 7 qlr–}šoi…Jt’r|… ”
œ …l|w„lo7€‹‚yrv—wxl€o |Š„lo~€ƒ…yqs|} v—|…r–…\xl|xytZ€wo7o{v7ƒ…Ž;o |Žlƒr…loqŽ\‰:|\n| !\r–…yz
ƒ‹w„loštwxlŽsw€oioštw‚yƒ…l…yo7qŽ\‰ ƒe…\xl}{ŽJo7€¨|Š ‚;|r…tL€ƒ…yqs|}𐁉v„l|twoi… ” 0 oi=
 2$ŽJo{w„lo
}šo7ƒt’xl€oš|…pw„lo2€ƒ…Jqs|} vi|…Dwr…\xl|xJtLw€oio2r…yqsxyvio7qŽ\‰ w„yo 0 oiŽ;o7twzxyo2}~oƒtwxl€o{|…
w„yoZxl…lr– r–…Doi€†“ƒB” |‡ ‡™oŒƒ€woZ†\roi‡Zr…lzLw„lo‹v—|…Dr–…\xl|xytw€oioƒt4ŽJo7r–…lz‘zoi…lo7€ƒwoq Ž\‰
ƒ ™€|‡Z…lrƒ…šo—•lv—xl€twr–|… ”  „y|D|Dt’o ‚J|r–…Dt |…2„lo€wo7ožƒv7v—|€qsr…lz¨| w„yož}šo7ƒt’xl€R
*
o 2S”
/ „lot’o ‚;|r…t™w|zo—„loi€Œ‡Zr–w„:w„lo¨€|\|Zt’‚yƒ…:ƒ~t’xyŽsw€oio¨ƒ-|Š ‡Z„y|two‹†oi€wwruv—o7t „yƒ“†o
|€qso7€ |…lo¨|€™w„l€oi:
o w„lo‘‚l€|ŽJƒŽlr–r–
‰2|]Š )y…yqsr…lz2ƒ~„lrz„lo7€™|€qloi€Œ†o7€’o—•erut § oi€(| ƒ…Jq
:O oizDqso7t ‡Zr–w„ˆ–o7…lz„yt X \ U \
S
STS\ U V WX ” žŠvi|xl€twow„yož€wo7o‹rut™…l|Zv—|}~‚y–oiwoi‰
tw‚Jov—8r )yo7qˆŽ\‰2w„yo‘o7qszoioi…lzw„yt7£sr „JƒtZtw|}šo¨‚yƒ€wwruv—xluƒ€™|‚;||z
‰ U” 0 o—
# # # #
e
U V WYX
X
'
7S
/ „lo7… + 7 £ -
s › €w|Ž 8” \ X \ U \TS
STS.\ U V WYX ae m W K L U \
‡Z„lo7€wo rutƒZ…l|€}2ƒr § ƒr–|…¨vi|…yt’ƒ…D7” 3 rt]xyr o r…oi€o7t’wr…lzZ„yƒ w„lrut`‚y€w|ŽyƒŽlrr 
‰‹rt
r…yqsoi‚;oi…Jqsoi…D|Šw„yo¨w|‚;||z
‰ ˆƒ…yqˆr v7ƒ…RŽJo tw„l|‡Z…?w|ev„yƒ€ƒvGwo7€wr § ožw„lo‘€ƒ…Jqs|}
v—|…Dwr…Dxyxl} w€oioˆxl…lr Dxloi‰” Ÿ oi†oi€ƒ™|w„yoi€š‚l€|‚;oi€wwro7t{|Šž„lov—|…r–…\xlxy} w€oioRƒ€o
qsrutwvixytt’oq?r… + 6 - ”
L.
œ uqs|xyt 9 t‘„loi|€w‰ |Š™„loˆ€ƒ…yqs|} v—|…Dwr…Dxy|xyt w€oioe‚l€|†\rqlo7t ƒ v—|}š‚lo—o>Dxyƒ…xl}
z o7|}šo—€w‰|ŠZ€wo7o7t7”pnoˆ„yƒ“†oˆƒŽ;|†oe|xswr–…yo7q „lrutšƒ‚l‚y€w|Dƒv„ ƒ…yq t
ƒo7qWtw|}šo?|Š
w„yo‘}~|€wo¨r}š‚J|€’ƒ…DZ€wot’xl–t7” 3 …R‚l€r–…yvir–‚y–o‘|…lo viƒ…:xytwo¨w„yrtŒ„loi|€w‰ew|eƒ…Jt’‡™oi€Zƒ…\‰
Dxlo7t’wr|… ƒŽ;|xl¨€ƒ…Jqs|} vi|…Dwr…\xl|xyt‹€wo7o7t7” Ÿ |}šoš‚l€w|‚Jo7€’r–otL|Š™vi|…Dwr…\xl|xJtLw€oio7t
ƒ€o2…l|~v—|}š‚l–oiwo7–‰ xl…yqloi€t
|D|sqU£4o” zJ”–£4r–{rut …l|
 !\…l|‡Z… „l|‡ |pqso )y…l
o ™€|‡Z…lruƒ…
}š|r–|…?|…ˆƒ{vi|…Dwr…\xl|xJt €wo7o‹r…:ƒ{‚l€o7virtwo‹‡Œƒ“‰šoi†oi…e„l|xyz„:tw|}šo¨t’xyzzot
r–|…yt™ƒ€o
‚l€|†\rqsoq2r… + 6 - ” ‹…loLv7ƒ…?w„lo7€woiŠ |€ož…l|Œv7ƒuv—xluƒoLqsr€o7vG–‰š„lo¨t’‚;o7v—w€ƒUqsr}~o7…ytwr–|…
|Šžvi|…Dwr…\xl|xJt‘w€oiot ‡Z„yr–o?„loRt’‚;o7v—w€ƒ qlr–}šoi…Jt’r|… |ŠZw„yoir€~qsrutv—€o—woˆt’rŽlr–…yzt~ƒ€o
!\…l|‡Z…:w|šŽJo ¤ + 6 - ”
/ „lo‘}š|t’r–…Doi€o7t’wr…lz2‚J|wo7…rƒ`ƒ‚y‚l–ruviƒwr|…ˆ|Š œ uqs|xJt 9 tŒw„yoi|€‰e|Š4vi|…Dwr…\xl|xyt
w€oiot2| Dxyƒ…Dwxy}zoi|}~oiw€‰ ‡™|xyq Ž;o | v—|…yt’w€xyvG:ƒW}~oƒtwxl€o |… vi|…Dwr…\xl|xyt
€ƒ…yqs|}twxl€wŠ ƒvio7t?ƒt:twxlzzo7t’woq r–… + ¢ - ” / „lo7€woƒ€o t’|}šo wov„l…lruviƒ‹|Žyt
ƒvi–ot2w|
viƒ€w€‰\r–…yzew„yrt¨‚l€|z€ƒ}š}~o w„l€|xyz„Žlxs‘xytwr–…lzˆ„lo2v—|€€o7tw‚J|…yqsoi…Jv—o~ŽJoi
‡ o7oi…pw€oio7t
ƒ…Jq t’xy€’Š ƒv—o7ttwoioi}2t`w|‹ŽJo w„lo™}š|t’‚y€w|}~rutwr–…lzž‡™ƒ“‰¨|Šlzo—wwr…lz‹ƒ‹„l|uq‘|… r–…Doiz€ƒr–|…
w„yoi|€‰2Š |€Z€ƒ…yqs|} twxl€wŠ ƒvio7t7”
A"ACAC1A0L
+ .-
” œ } Ž€… £ L”]žxl€„\xlxytSƒ…yq / ” |…Jtwtw|… £&‹xJƒ…Dwxl}.zoi|}~oiw€‰ œ t
ƒwrut’wruviƒ
)yo7q:w„yoi|€‰?ƒ‚l‚l€|ƒv„`£  ƒ} Žl€ruqszo…lr†o7€twr–
‰ › €o7tti£  ƒ} Žl€rqlzo, %$&$(' G”
+ 6- L” ]‹xl€„Dxyxyt ƒ…Jq / ” |…ytwtw|…`£ ”]= ƒ„ ” › „\‰st7”5 l ' ¥ $P ' + }2ƒw„ ‚l„ y7y%$"- ”
+ - ]{” œ ql|xyt7£ / „lo‹vi|…Dwr…\xlxl}˜€ƒ…yqs|} €wo7o 3d3 ¡\ƒ…e|†o7€w†\roi‡‘” 3 …`¡ › w€ |sv”]‹xl€w„Jƒ}
tw‰D}š‚ ”Ut’w|sv„yƒt
rv ƒ…yƒ‰st’rut V$n$ £yoqU”;ŽD‰ = ” / ” Œƒ€–|‡(ƒ…yq ” ” ™r–…yz„yƒ}ˆ£
…lr†o7€twr 
‰ › €wotwt7£  ƒ}{Žl€wruqszo, %$&$l —”
 ƒ}{Žl€rqszo
+ ¤"- ]{” œ u qs|xyti£ / €wo7o Žyƒtwo7q$}~|sqso7t~Š |€2€ƒ…yqs|}
› „\‰st7” %$n$ ¥ ¢ ¥ ¤y ”
+ ¢ - › ”  „Jƒrutwtƒ…lzšƒ…Jq2~” Ÿ v„yƒo.7-oi€£
qsrut
€wrŽlxsr–|… |ŠL}2ƒtt7£ ” Ÿ ƒ7”
ƒ…Jqs|} ‚lƒ…yƒ€žƒ’wruv—otƒ…Jq:r…Dwo7z€ƒwoq:twx ‚;oi€Žl€w|‡Z…yrƒ…:oi•svixl€t’r|… £\‚l€oi‚y€wr…D4+ }2ƒ„ ”  ¢ ¥ + ¥ -
” œ } Ž €w… £ ‹
” ]‹xl€w„\xlxJtˆƒ…yq / ” |…ytt’|… £ Ÿ xl}š}šr–…yz |†oi€?ƒ–Lzo7…loi€ƒ Š |€
8 ¡ ƒ{w|‰?}~|sqso7B£ › „\‰sti” 0 oi’” L£ V $n$ ¤b¤D y”
!
+ 'V- ” ™
xl€qyƒl£ ”N €qs}2ƒ…l… £ L” › io wo7€tt’|… ƒ…yq = ™” n ƒ’oi…\Ž;oi€zy£CN •\|wruvRw€oioti£
„› \‰st7” oi†-”; ¥ ¢:+ v—|…yq }šƒ '“¤ ¢ $ + - / ”iNž” ƒ€€rt7£ / „loLw„lo7|€‰e|Š4Žl€ƒ…yv„yr–…lz~‚l€|sv—o7ttwo7t7£ Ÿ ‚l€wr…lzoi€£
o7€wr… %$ ¥ —”
+ $ - ]{” œ uqs|xJti£ / „yoev—|…Dr–…\xlxl}
V $n$y —
y”
€ƒ…yqs|}€wo7o 3 £ / „lo œ …l…yƒt |Š › €w|ŽyƒŽyr–r 
‰£
+ 7 - ]{” œ uqs|xyti£ / l„ o v—|…r–…\xlxy} €ƒ…yqs|}˜w€oio 3d3_3 £ / „yo œ …l…yƒt|Š › €|ŽyƒŽlr–r–
‰ V $n$ ¤ $ ”
+ .- ” #™” 0 o 2¨ƒB£ Ÿ ‚yƒwruƒŽl€ƒ…yv„lr…lzZ‚l€|sv—o7ttwo7t7£i€ƒ…yqs|} tw…yƒ"!o7t ƒ …yq¨‚yƒ€’rƒqsr87;o7€ oi…Drƒ`o%Dxyƒwr|…yt7£ 0 o7v—wxl€o7tžr–… = ƒw„yoi}2ƒrv7tCN /Zxl€rv„ £ ™–r € !\„ ƒ xytwoi€£ Œƒtwoi
V$n$&$ G ”
+ 6-‘¦ ” 3 w| ƒ…yq ” › ” = v ¦ oƒ… £=]žr87;xJt’r|… ‚l€w|svio7tt’ot?ƒ…JqHw„yoir€Rtƒ}š‚lo ‚Jƒw„Jti£
Ÿ ‚l€r…lzo7€7£
™oi€r–… V$ ¢&G ”
+ 7 - ”lnH„lo7ƒwo7€ƒ…yq / ” |…ytt’|… £ / l„ o tw‚JovGw€ƒ qlr–}šoi…Jt’r|…ˆ|Šw„lo‘Žy€ƒ…yv„lo7q:‚;|‰ }šoi€{‚l„yƒtwoe|Š™
‡™| qsr}šoi…ytwr–|…yƒGDxyƒ…Dwxl} z€ƒ“†\r 
‰£ xJv—b” › „\‰st7” L£ + # Ÿ( V$n$ &Œ
¢ ¤($ ¢ “' ¤ + „lo7‚ ƒ $ \' ¤"- ”
$