Adaptive regulation with flow and stock externalities

_@T|i +i}*@|L? | 6*L @?_ 5|LU!

, |ih?@*|it

w,W6 k 5#w @?_ 5A,W W 5A,W5O

Lhi}@? 5ULL* Lu ,UL?L4Ut @?_ t?itt _4?t|h@|L?

Oi**iii? f

DfD ih}i?5@?_!i?

Lh@)

a@?@h) bbH

Devwudfw

Lq frqiurqwlqj d frqvxphu jrrg zkrvh surgxfwlrq surfhvv lv dvvrfldwhg zlwk erwk rz dqg vwrfn h{whuqdolwlhv/ d fruuhfwlyh wd{ lv lqwurgxfhg wr uh0 vwruh hflhqf|1 Wkh remhfwlyh lv wr pd{lpl}h vrfldo zhoiduh ryhu wlph zkhq wkh vwrfn srooxwdqw reh|v dq duelwudu| g|qdplf surfhvv1 Wkh prgho pdnhv lw srvvleoh wr ghulyh wkh rswlpdo fruuhfwlyh wd{ dv d forvhg irup ihhgedfn frqwuro odz1 Wklv ihhgedfn uxoh fdq eh dssolhg iru txdolwdwlyh sxusrvhv vxfk dv sdudphwhu dqdo|vlv ru vwxg|lqj wkh wlph sdwk ri wkh fruuhfwlyh wd{1 Lw fdq dovr eh xvhg iru txdqwlwdwlyh sxusrvhv/ iru h{dpsoh hydoxdwlqj dq dfwxdo srolf| ru dvvhvvphqw ri wkh rswlpdo wd{ iru d fhuwdlq fdvh1 Lw lv khuh xvhg wr vwxg| krz wkh rswlpdo fruuhfwlyh wd{/ erwk dv d ixqfwlrq ri wlph dqg dv d ixqfwlrq ri wkh srooxwlrq ohyho/ ghshqgv xsrq wkh ghfd| ixqfwlrq1 Lw lv vkrzq wkdw/ ghshqglqj xsrq wkh lqlwldo frqglwlrqv dqg wkh vwuxfwxuh ri wkh hfrqrp| dqg wkh ghfd| ixqfwlrq/ prvw rxwfrphv duh srvvleoh1

Nh|zrugv= Sljryldq wd{dwlrq/ rz dqg vwrfn h{whuqdolwlhv1

 W?|hL_U|L?

B*LM@* @h4?} |hL} i4ttL? Lu 2 ? |i @|4LtTihic |i |???} Lu |i L3L?i *@)ihc |L U @t|ic i|Uc @hi @** i @4T*it Lu i |ih?@*|it ? |i iUL?L4) Aihi i t|t @*hi@_) @ @t| *|ih@|hi L? i |ih?@*|it |@| @| *i@t| _@|it M@U! |L }L L @t L?i Lu |i €ht| |L t}}it| @ ULhhiU|i |@ U UL*_ hit|Lhi iUi?U) Lt| Lu |i *|ih@|hi L? T}L@? |@ @|L?c Liihc t @ML| L i |ih?@*|it Lti @h4u* igiU|t _ttT@|i 4Lhi Lh *itt 44i_@|i*) @?_ ?L|

@ML| t|LU! i |ih?@*|it Lti @h4u* igiU|t hi4@? uLh @ *L?} TihL_ 2c

|???} Lu |i L3L?i *@)ih _i |L U*LhLLhLU@hML?tc |L U @t|i @?_ TL**|L?

? }i?ih@* @hi @** i @4T*it Lu t|LU! i |ih?@*|it W? u@U|c | t @h_ |L |?! Lu i @4T*it Lu Thi L i |ih?@*|itc i UiT| ?Lti @?_ t|hL?} *}|c @t 4Lt| T)tU@*

i4ttL?t |i?_ |L @UU4*@|i |L tL4i i |i?|

5|LU! i |ih?@*|it @hi LMLt*) 4TLh|@?| @?_ ThLM*i4t Lu t|LU! i |ih?@*

|it ihi @__hitti_ @*hi@_) ? |i i@h*) b.ft Ekii*ihc 5Ti?Ui @?_ ~iU!@tihc

b.c _<h}i @?_ kL}!c b.c @?_ 6Lht|ihc b.D `| ?Uhi@t?} UL?Uih?

4Vxeplwwhg wr Qdwxudo Uhvrxufh Prgholqj1

@ML| }*LM@* @h4?} _i |L @UU4*@|L? Lu 2 ? |i @|4LtTihi |ihi @t i4ih}i_ @ *|ih@|hi L? |i iUL?L4Ut Lu @UU4*@|L? Lu tLU@**i_ }hii?Lti }@tit U t @ |)TU@* i @4T*i Lu @ t|LU! i |ih?@*|) Lh_@t EbH2 @t L?i Lu |i €ht| |L @__hitt |t @hi@ ? |i iUL?L4U *|ih@|hi M) @t!?} L u@t| |i }*LM@* iUL?L4) tL*_ @**L @ M*_T Lu @|4LtTihU 2 h|L @?_ W?|h*

}@|Lh EbH. @__hitti_ |i ThLM*i4 Lu t|i@_) t|@|i @?@*)tt ? |i Thiti?Ui Lu t|LU! i |ih?@*|it @?_ |i ti Lu @ UL?t|@?| T}L@? |@ kLc w@T@? @?_ 5@?

_*ih Ebb2 i @4?i |i ti Lu @? ?i M*i T}L@? |@ UL4T@hi_ |L @ €ht|Mit|

T@| Lu @ T}L@? |@ |@| @hit UL?|?Lt*) Lh_@t Ebb@ @t uLh4*@|i_

@? iUL?L4U 4L_i* |@| *?!t i4ttL?t Lu }hii?Lti }@tit @?_ U*4@|i U@?}it

@?_ @?@*)3it |i |h@_iLg Mi|ii? |i ULt| Lu hi_U?} i4ttL?t @?_ |i _@4@}i uhL4 }*LM@* @h4?} `h* Ebbe@ tit @ Lh_@t 4L_i* @?_ _tUttit |i |4i T@| uLh |@ @|L? Lu i?ih}) ? |i Thiti?Ui Lu L @?_ t|LU! i |ih?@*|it @t T@h|

Lu t t|_) Lu |i _)?@4U @?_ t|h@|i}U ?|ih@U|L?t Mi|ii? ThL_Uiht @?_ UL?

t4iht Lu uLtt* i?ih}) iU! @?_ AitMih} Ebb2 _i|ih4?i LT|4@* |4i T@|t Lu i4ttL?t UL?|hL* @?_ ULhhitTL?_?} U@hML? |@ it ?_ih @*|ih?@|i @tt4T|L?t

@ML| }*LM@* @h4?} ULt|t Aih 4@? hit*| t |@| @? LT|4@* U@hML? |@ **

|i?_ |L ?Uhi@ti 4L?L|L?U@**) Lih |4i 5?U*@h Ebb2 @?_ bbe @?_ N*T @?_

e

N*T Ebbe UL?t_ih |i LT|4@* |4i T@| Lu @ U@hML? |@ i? |t t *?!i_

|L |i i |h@U|L? Lu uLtt* ui*t @t ?L?hi?i@M*i hitLhUit @?_ _tUttit i|ih

|t |@ tL*_ hti Lh _iUhi@ti Lih |4i Ai) €?_ |@| ? 4Lt| U@tit |i h*i t |L *i| |i |@ _iUhi@ti Lih |4i ? Lh_ih |L TLt|TL?i i |h@U|L?

W? 4Lt| Lu |i *|ih@|hi L? TL**|L? @ 4L?L|L?U@**) ?Uhi@t?} _iU@) u?U|L?

t @TT*i_ 4L?} |i i UiT|L?t @hi 6Lht|ih Eb.D L tit @ ?L?UL?t|@?|

i TL?i?|@* _iU@) u?U|L? @?_ A@L?i? @?_ 5@*L EbbS L ti @ UL?U@i UL?i _iU@) u?U|L? Aiti @hic Liihc tTiU@* U@tit Lu |i _iU@) u?U|L?

@TT*i_ ihi U t UL4T*i|i*) }i?ih@* AihiuLhic 4Lt| Lu |i hit*|t hiuihhi_

|L @MLi U@? Mi uL?_ @t tTiU@* U@tit Lu |i 4L_i* @TT*i_ ihi

Ai @4 Lu |i Thiti?| T@Tih t |L ThL_i @? @?@*)|U@* i ThittL? uLh |i LT|4@* T@| Lu |i ULhhiU|i |@ ? |i Thiti?Ui Lu @ }i?ih@* _iU@) u?U|L?

Ai LT|4@* T@| uLh |i T}L@? |@ ? |i Thiti?Ui Lu ML| L @?_ t|LU!

i |ih?@*|it t _ihi_ @t @ uii_M@U! UL?|hL* 6ii_M@U! UL?|hL*t @i tiih@* @_

@?|@}it Ai) @hi hi*@|i*) i@t) |L 4T*i4i?| @t |i LT|4@* |@ t @ u?U|L? Lu

|i Uhhi?| *ii* Lu TL**|L? L?*)c @?_ tTLh@_U tLU!tc i} t__i? ?UL?|hL**i_

i4ttL?tc @hi @|L4@|U@**) |@!i? U@hi Lu ?@*)|U@* i ThittL?t @hi i4T@t3i_

? Lh_ih |L @**L uLh T@h@4i|ih @?@*)tt @?_ @L_ |i _h@M@U!t Lu ?4ihU@*

D

@?@*)tt tU @t @}}hi}@|L? Lu ?4ihU@* ihhLht Ai 4L_i* U@? Mi ti_ ^@?

||@|i*) ML| |L @ttitt |i LT|4@* ULhhiU|i |@ @?_ |L i@*@|i TL*Uit |@|

@hi @*hi@_) ? igiU| , @4T*it Lu @ttitt4i?| Lu |i |@ uLh T@h|U*@h U@tit @hi tL? W? |t T@Tih |i 4L_i* t @*tL @TT*i_ ^@*|@|i*) |L tii L |i LT|

4@* |@ c @t @ u?U|L? ML| Lu |4i @?_ Lu |i TL**|L? *ii*c _iTi?_t TL? |i _iU@) u?U|L? W| t |ihiuLhi 4TLh|@?| uLh t |L Mi @M*i |L ti }i?ih@* _iU@) u?U|L?t

2 Ai 4L_i*

W? |i t|@?_@h_ |i |MLL! 4L_i* uLh _i|ih4??} ULhhiU|i |@ it |ihi t @? ? ihti _i4@?_ u?U|L? uLh |i ThL_U| %c ' E%c @ Th@|i 4@h}?@* ULt|

u?U|L? hiThiti?|?} tTT*)c  ' E%c @?_ @ tLU@* 4@h}?@* ULt| u?U

|L?c ⁷ ' ⁷E% @h!i| i^*Mh4 t }i? M) E% ' E% Ai tLU@* i*u@hi LT|44 t }i? M) E%^W ' ⁷E%^W At t |i ThL_U|L? *ii*

|@| 4@ 43it |i t4 Lu UL?t4iht< @?_ ThL_Uiht< thT*t ULhhiU|i_ uLh |i _gihi?Ui Mi|ii? Th@|i @?_ tLU@* ULt|t Ei |ih?@*|) Ai LT|4@* ULhhiU|i

|@ c c t }i? L?Ui @?_ uLh @** M) ^W ' E%^W E%^W At t **t|h@|i_

? 6}hi  Wuc Liihc i@U ?| Lu % t @ttLU@|i_ | @ Uih|@? @4L?| Lu

S

TL**|L?c @c @?_ |i TL**|@?| |i?_t |L @UU4*@|ic i @hi u@Ui_ | @ _)?@4U LT|43@|L? ThLM*i4 @?_ t|@|U @?@*)tt t ?L *L?}ih tUi?|

L?t_ih @ tiU|Lh |@| ThL_Uit |i L|T| % |L U |ihi t @ € i_ ^@?||) Lu TL**|L? @ttLU@|i_ | i@U ?| Lu L|T| }i? M) B% Ai @}}hi}@|i *ii*

Lu TL**|L? t _i?L|i_ @c @?_ |i |4i U@?}i ? @ t }i? M) @ ' B% sE@

ihi s t @ }i?ih@*c M| !?L?c _iU@) u?U|L?²

tt4i |@| |i ?ihti UL4Ti?t@|i_ _i4@?_ u?U|L? uLh % U@? Mi @TThL 4@|i_ M)

E@c % ' RfE@ RE@%c R fc 5 ifc j E2

W? |t T@Tih ** @*@)t hiThiti?| |i UL?t4ih ThUi Oi?UiuLh|c |i |ih4 _i4@?_ u?U|L? @?_ _i4@?_ Uhi ** hiuih |L |i u?U|L? ? ,^E2

6h|ihc @tt4i |@| |i Th@|i @?_ tLU@* 4@h}?@* ULt|t Lu ThL_U|L? U@?

Mi @TThL 4@|i_ M)

⁷E@c % ' S7fE@ n S7E@%c S5 fc

E@c % ' S fE@ n S E@%c S fc

E22

@?_  ** @*@)t hiThiti?| |i ThL_Uih ThUi Ai T@h@4i|iht S5c S @?_ R 5Grwv duh xvhg wr ghqrwh wlph ghulydwlyhv1

.

U@? Mi UL4T*i|i*) }i?ih@* u?U|L?t ? @ Ai tLU@* 4@h}?@* ULt|t Lu ThL_U?}

% @hi @tt4i_ }ih |@? |i ULhhitTL?_?} Th@|i ULt|tc ic Srf : SRf @?_

Sr : SR W? L|ih Lh_tc i @hi L?*) _i@*?} | ?i}@|i i |ih?@*|it Lu ThL_U|L? ? |t T@Tih Lt|i i |ih?@*|it U@? Mi @?@*)3i_ @UULh_?}*)

Aihi @hi 4@?) hi@tL?t ) |i T@h@4i|iht ? |i _i4@?_ u?U|L? Lh ?

|i Th@|i Lh tLU@* ULt| u?U|L?t 4@) _iTi?_ TL? |i *ii* Lu t|LU! TL**|L?

Ai _i4@?_ uLh @ ThL_U| _iTi?_t L? 4@?) u@U|Lhtc @*tL Thitthi i ih|i_ M) i?hL?4i?|@*t| }hLTt At Thitthi ** ThLM@M*) u @?)|?} *i@_ |L @ _L?@h_ tu| ? _i4@?_ uLh ThL_U|t @ttLU@|i_ | i4ttL? Lu TL**|L? W|

t @*tL hi@tL?@M*i |L |?! |@| |i UL?Uih? @ML| |i i?hL?4i?| t }hi@|ih |i }ih |i *ii* Lu |i t|LU! TL**|@?|c @?_ |t |i _L?@h_ tu| ? _i4@?_

** Mi }hi@|ih |i 4Lhi TL**|L? |ihi t @*hi@_) AihiuLhi |i UL?t|@?| |ih4

? |i _i4@?_ u?U|L?c Rf ? ,^E2c U@? Mi 4L_i**i_ @t @ _iUhi@t?} u?U|L?

? @

h@|i ULt|t Lu ThL_U|L? 4@) @*tL _iTi?_ TL? |i *ii* Lu TL**|L? At hi*@|L?tT U@? Mi }*}|i_ |hL} @? i @4T*iG Wu U*i@? @|ih t ?ii_i_ ?

|i ThL_U|L? ThLUittc |i? |i ULt| Lu Th€U@|L? 4@) Mi }ih |i }ih |i t|LU! Lu TL**|L? At 4@) @giU| ML| |i t*LTi @?_ TLt|L? Lu |i 4@h}?@* ULt|

H

Uhi Wu @?)|?}c |iti |ih4tc i |i T@h@4i|iht SRf @?_ SR ? ,^E22c **

ThLM@M*) Mi ?Uhi@t?} u?U|L?t ? @ h@|i ULt|t ** ThLM@M*) Mi _iUhi@t?}

@t @ u?U|L? Lu i4ttL?t Lu TL**|L? O}ih i4ttL? *ii*t 4i@? *Lih ULt|t

@t tL4i ULt|t @ttLU@|i_ | Th€U@|L? @hi @L_i_ W| t 4TLh|@?| |L ?L|ic Liihc |@| |t hi}@h_t ULt|t @t @ u?U|L? Lu @ @?_ ?L| @t @ u?U|L? Lu @

Ai tLU@* ULt| u?U|L? t |i ULt| |L tLUi|) Lu ThL_U?} |i ThL_U| i?

i |ih?@* igiU|t @hi |@!i? ?|L @UUL?| Ai _gihi?Ui Mi|ii? |i Th@|i @?_

|i tLU@* ULt| u?U|L?t U@? |ihiuLhi Mi ?|ihThi|i_ @t @ 4i@thi Lu |i i |ih?@*

igiU|t Ai Th@|i ULt|t @hi T@h|*) ?U*_i_ ? |i tLU@* ULt|tc @?_ |iti 4@) _iTi?_ TLt|i*) TL? |i t|LU! Lu TL**|L? W| t hi@tL?@M*i |L Mi*ii |@|

|i i |ih?@* igiU|t Lu TL**|L? ** Mi }ih |i }ih |i *ii* Lu TL**|L?

AihiuLhi | t @tt4i_ ihi |@| |i T@h@4i|iht ? |i tLU@* ULt| u?U|L?c Srf

@?_ Sr ? ,^E22c ** Mi ?Uhi@t?} u?U|L?t ? @ Ai @tt4T|L?t @MLi @hi 4@_i L?*) uLh |i iUL?L4U ?|ihThi|@|L? @?_ @hi ?L| ?iUitt@h) uLh 4@|i4@|U@*

ThTLtit Ai uii_M@U! h*i _ihi_ ? |t T@Tih U@? Mi 4T*i4i?|i_ ?L 4@||ih L |i u?U|L?t ?L*i_ _iTi?_ TL? @

6*L i |ih?@*|) t _i€?i_ ? 4L?i|@h) |ih4t @t |i _gihi?Ui Mi|ii? Th@|i

@?_ tLU@* ULt|t @| @?) TL?| ? |4ic |@| t uLh @ € i_ *ii* Lu @ @?_ % W| t |i

b

i |ih?@*|) @ttLU@|i_ | B%c @?_ | i t|t @*tL i? @ t € i_ @| @ Uih|@? *ii*

@?_ |hi@|i_ @t @ T@h@4i|ih 6Lh @?) }i? *ii* Lu @ @?_ % |i 4@}?|_i Lu |i L i |ih?@*|) t ^r ^R

5|LU! i |ih?@*|) t _i€?i_ @t |i i |ih?@*|) ? |i _)?@4U ti||?} |@|

UL4it ? @__|L? |L |i L i |ih?@*|) W? |t T@Tih (E@ f t ti_ |L _i?L|i |i t|LU! i |ih?@*|)c |@| tc |i _t|*|) Lh _@4@}i @ttLU@|i_ | |i t|LU! TL**|@?| W| t U*i@h uhL4 |iti _i€?|L?t |@| L i |ih?@*|) t @ t|@|U UL?UiT| ihi@t t|LU! i |ih?@*|) t @ _)?@4U UL?UiT| Wu |ihi @hi ?L _)?@4Utc

|ihi t ?L t|LU! i |ih?@*|) @?_ L?*) L i |ih?@*|) i t|t

L| L @?_ t|LU! i |ih?@*|it U@? Mi ?|ih?@*3i_ ? |i _)?@4U ti||?} M) 4T*i4i?|?} @ ULhhiU|i |@ c c hiThiti?|?} |i _gihi?Ui Mi|ii? |i UL?t4ih ThUi @?_ |i ThL_Uih ThUiG

E@c % ' E@c % E@c % E2

At ULhhiU|i |@ i?thit 4@h!i| i^*Mh4 uLh _gihi?| UL4M?@|L?t Lu @ @?_

% Ai ^it|L?c |L U i ** hi|h? ? |i 5iU|L? c t L |L _i|ih4?i

|i LT|4@* ULhhiU|i |@

Ai L4?tUi?|c Mi?iL*i?| }Lih?4i?|<t LMiU|i u?U|L? t |L 4@ 43i

f

|i tLU@* i*u@hi u?U|L? }i? M) |i t4 Lu |i UL?t4iht< thT*tc 7c |i ThL_Uiht< thT*tc 7c @?_ |i }Lih?4i?|<t thT*tc C7 Ai UL?t4iht< th T*t t _i€?i_ @t |i _gihi?Ui Mi|ii? @| |i UL?t4iht @U|@**) T@) E|@ it

?U*_i_ @?_ @| |i) L*_ Mi **?} |L T@) ?_ih |i _i4@?_ Uhi Ai ThL_Uiht< thT*t t _i€?i_ @t |L|@* hii?i uLh |i ThL_Uiht *itt |L|@* Th@|i ULt| Ai }Lih?4i?|<t thT*t |@!i ?|L @UUL?| |@ hii?itc |i _gihi?Ui Mi

|ii? tLU@* @?_ Th@|i ULt|t @?_ @?) _t|*|)c ( Aiti thT*tit @hi uLh4@**) _i€?i_ @tG

7 '^U_f^%E@c 5_5 EE@c % n % E@c % EE@c % n %c 7 ' E@c %% ^U_f^%E@c 5_5 E@c %%  E@c %c

C7 ' (E@ n % ^U_f^%d⁷E@c 5 E@c 5o_5 (E@ n % ^k ⁷E@c %  E@c %^l

E2e

ihi 5 t @? ?|i}h@|L? @h@M*i @?_ @|t @hi ti_ |L _i?L|i ?|i}h@*t @t ? _U@|i_ Ai Mi?iL*i?| }Lih?4i?| tit |L 4@ 43i |i t4 Lu @** |iti thT*tit W? tL _L?} 4@?) Lu |i |ih4t U@?Ui* L| @?_ @| hi4@?t @t |i



tLU@* i*u@hi u?U|L? t

`E@c ' (E@ n E@c %  ⁷E@c % E2D

`i? | UL4it |L Th@U|U@* ti Lu |i 4L_i*c | t 4TLh|@?| |L tTiUu) |i @TThL Th@|i @_iTi?_i?Ui ULhhiU|*) @?_ @L_ _LM*i UL?|?} 6Lh i @4T*ic ?U*tL?

Lu @ ? ^r @?_ ^R L?*) tLt L |i L i |ih?@*|) 4@) Mi ?i?Ui_ M)

@ @?_ 4t| ?L| Mi UL?uti_ | |i t|LU! i |ih?@*|)c (E@

W| t i_i?| uhL4 ,^t E2c E22 @?_ E2 |@| % U@? Mi h||i? @t @ *?i@h u?U|L? ? G

%E@c ' %fE@ %E@ E2S

ihi

%fE@ ' Rf S f

R n S  : fc %E@ ' 

Rn S  : f

,^ E2S _i€?it % @t @ u?U|L? Lu }i? |@| ' c |@| t @*it

|@| hit*| ? 4@h!i| i^*Mh4c tii 6}hi  Ai |ih4 %f U@? Mi ?|ihThi|i_

@t |i 4@h!i| i^*Mh4 |L| @?) TL*U) 4i@thit @Lh _i€?|L?t ? |t

@h|U*ic tU @t |i _i€?|L?t Lu %f @?_ % @MLic @hi t44@h3i_ ? TTi?_ 

`i @hi L?*) ?|ihit|i_ ? ?L??i}@|i *ii*t Lu ThL_U|L?c 4i@??} |@| @t

2

@? TTih ML?_ }i? M) %f*%

Ai _)?@4U LT|43@|L? ThLM*i4 U@? Mi uLh4*@|i_ @t

4@ ^{] "}

f e^3o|` E@c _| E2.

tMiU| |L |i UL?t|h@?|

@ ' B% sE@ E2H

@?_ @ fc % f Ai _tUL?| h@|ic oc t |i tLU@* _tUL?| h@|i Ai U@ti Lu @ 3ihL _tUL?| h@|i t Lu T@h|U*@h ?|ihit| @?_ ** Mi }i? tTiU@* @||i?|L?

W? Lh_ih |L t4T*u) |i uL**L?} U@*U*@|L?t @?_ ?|ihThi|@|L?t | ** Mi Thiuih@M*i |L U@?}i |i tU@*i @*L?} U @ t 4i@thi_ uhL4 T)tU@* ?|t

|L 4L?i|@h) ?|t At t _L?i @t uL**LtG @ t 4i@thi_ M) E@ ihi t

@ !?L?c 4L?L|L?i M| ?L| ?iUitt@h*) *?i@h hitU@*?} u?U|L? ) _i€?|L?

' E@@ @?_ i ULLti |L @i |i ThLTih|) ' *B% : f Aiti |L 4i@thit Lu TL**|L? ** Mi ti_ ?|ihU@?}i@M*) ? |i hit| Lu |i T@Tihc tL

|@| ` U@? Mi @ u?U|L? Lu @ Lh Ai @h@M*i t ?|ihThi|i_ @t TL**|L?

? 4L?i|@h) |ih4t ihi@t @ t |i TL**|L? 4i@thi_ ? T)tU@* ?|t At



4i@?t |@| |i _)?@4U ThLM*i4 U@? Mi hih||i?

4@ ^{] "}

f e^3o|` Ec _| E2b

tMiU| |L

' 8E E2f

ihi 8 ' %f*% s*B% ,^ E2f hiThiti?|t @ |h@?t*@|L? Lu |i _)?@4U UL?t|h@?| ?|L 4L?i|@h) |ih4t tU |@| 8 @?_ @hi UL4T@h@M*i Ai u?U|L?

8 t |i @U|@* ?Uhi@ti ? TL**|L?c c |L| @?) TL*U) 4i@thitc @?_ |t U@? Mi i|ih TLt|i Lh ?i}@|i Ai TL*U) 4i@thic c t ?i}@|i*) hi*@|i_ |L

|i U@?}i ? TL**|L?c @?_ 8 |ihiuLhi hiThiti?|t |i ?i| U@?}i ? TL**|L?

i? TL*U) 4i@thit @hi @TT*i_ At U@? @*tL Mi tii? M) h|?}

8 E ' B%fE@ sE@

B%E@ E2

hi4i4Mih?} |@| @ t @ u?U|L? @E ) UL4T@h?} |i ?4ih@|Lhc B%f sc

| E2H @?_ hiU@**?} |i _i€?|L? Lu %fc | t tii? |@| |i ?4ih@|Lh t |i

@U|@* U@?}i ? TL**|L? ? T)tU@* |ih4t |L| TL*U) 4i@thit #_?}

M) B% i }i| |i @U|@* U@?}i ? TL**|L? ? 4L?i|@h) |ih4t L|i |@| 8

e

@?_ s 4@) @i LTTLt|i t}?tc @?_ t@**) @i Ai ?||L? Mi?_ |t t

|@| s 4i@thit |i @U|@* _iU@) Lu TL**|L? Wu |t _iU@) t *@h}ic | U@**t uLh @ hi*@|i*) t4@** ULhhiU|i |@ MiU@ti L?*) @ 4?Lh hi_U|L? ? L|T| t ?ii_i_

@?_ Ui iht@

6hL4 ,^t E2ec E2D @?_ E2S | t i_i?| |@| @u|ih |i hitU@*?} Lu @ ?|L c ` U@? Mi h||i? @t @ u?U|L? ? @?_ @t uL**LtG

` Ec ' kE n qE E² E22

ihi

k ' ( n 

2%fE%fRn %fSr 2Rfn 2Srfc E2

q ' ESrf SRfERn SR n ERf SRfESr SR

ERn SR² : fc ' ERn Sr

2ERn SR² : f

At ** Mi ti_ ? |i uL**L?} |L _ihi |i LT|4@* ULhhiU|i |@

D

Ai uii_M@U! UL?|hL* *@

Ai LMiU|i Lu |t tiU|L? t |L _ihi |i LT|4@* ULhhiU|i |@ c c @t @ uii_M@U!

UL?|hL* *@( |@| tc @t @? i T*U| u?U|L? Lu |i TL**|L? *ii*c Ai i@tit|

@) |L _L |t t |L }L M) _)?@4U ThL}h@44?}c tii i} k@4i? @?_ 5U@h|3 Ebb `| @ UL?t|@?| tLU@* _tUL?| h@|ic |i ThLM*i4 Lu 4@ 43?} E2b tMiU| |L E2f )i*_t |i @*i u?U|L?

T E|c ' 4@ ^{] A}

| e^3or` Ec _r E

@?_ |i @ttLU@|i_ a@ULMi**4@? i^@|L?

T|n 4@ ^qkkE n qE E^2le^3o|n Td8E o^r' fc E2

wi| t |h) @ tL*|L? Lu |i uLh4

T E|c ' gn`f

o n Ee^3o|c EEAn`f

o ' ge^oAc E ' qE E 2E

6Ym ^CY_Cm=

S

ihi g @?_ `f @hi @hM|h@h) UL?t|@?|t 6h|ihc ti |i uL**L?} hi*@|L?tTt

@?_ _i€?|L?tG

T ' E 2E d^WE Eo c

`f 7E ' E d8 E fEo²c T >E ' 2E d8 E Eo

E

ihi ^W ' ₂^q t |i LT|4@* |@ ? |i t|@|U i^@*i?| Lu |i 4L_i* _ihi_

uhL4 4@ 43?} ` | hitTiU| |L |hi@|?} @t @ UL?t|@?| wi| 7 Mi _i€?i_

@t |i *ii* Lu i*u@hi @ttLU@|i_ | tt|@??} @?) *ii* Lu TL**|L?c |@| tc

7E ` Ec 8E ' kE n qE8E E8E² Ee

@?_ > Mi _i€?i_ @t

>E Y` Ec Y

_{'8 E} ' qE 2E8 E

,UL?L4U@**) > U@? Mi ?|ihThi|i_ @t |i 4@h}?@* ?Uhi@ti ? i*u@hi _i |L @ 4@h}?@* U@?}i ? |i |@ }i? |@| |i Thiti?| *ii* Lu TL**|L? t Thitihi_

Ai |ih4 f t _i€?i_ @t |i LT|4@* ULhhiU|i |@ i? |i _tUL?| h@|i t 3ihLc @?_ `f hiThiti?|t @ Uih|@? |@h}i| @*i i^@*i?| |L |i i*u@hi ? LT|4@*

.

t|i@_) t|@|i |L Mi _ihi_ tLL? W?tih|i_ ?|L |i a@ULMi**4@? i^@|L? E2

|t )i*_t

oE ' E dE fEo dE n fE 28 Eo ED

W? |i tTiU@* U@ti i? i|ih o ' f Lh ' fc

E '

;A AA

? AA A=

fE 28E fE

c fE ' 8E n

yx

xw`f 7E

E ES

W? |i }i?ih@* U@ti | t ?iUitt@h) |L @TT*) Tih|hM@|L? 4i|L_t ? Lh_ih |L _ihi

@?@*)|U@* i ThittL?t uLh |i uii_M@U! UL?|hL* *@c tii TTi?_ 2 Ai uii_M@U!

h*i _ihi_ ? TTi?_ 2 uLh |i U@ti Lu @ TLt|i _tUL?| h@|i t |i uL**L?}

E ' fE n o E n Eo²c E.

E ' fE

2E dfE 8 Eoc _fE ' 2E dfE ^WEo

tL*i_ |L tiUL?_ Lh_ih Ai |ih4 f uhL4 ES t |i LT|4@* |@ | 3ihL _t UL?|?} U ** Mi }i? tTiU@* @||i?|L? ? |i ?i | tiU|L? Ai ULhhiU|L?

H

o ** t@**) Mi t4@** UL4T@hi_ |L f

?i ^it|L? hi4@?tc ?@4i*) @| t |i LT|4@* t|i@_) t|@|i ELh |@h}i|

*ii* Lu |i t|@|i @h@M*i `| @? ?€?|i |4i Lh3L? |t t }i? M) tL*?}

7E ' o>E EH

| hitTiU| |L Ai @*_|) Lu EH U@? Mi tii? uhL4 E @?_ ED M) ?L|?}

|@| ? t|i@_) t|@|i 8 ' tU |@| T ' ' > ,^ ED t @? ?|i}h@|i_

ihtL? Lu EH Ai ?|ihThi|@|L? Lu EH t |@| |i 4@h}?@* Mi?i€| Lu @ ?|

Lu tL*_ ? LT|44 Mi |i t@4i i|ih | t *iu| @*L?i E*iu| @?_ t_i Lh | t |@ i_ @@) Eh}| @?_ t_i

 Ai U@ti Lu 3ihL _tUL?|?}

Ai U@ti Lu @ 3ihL tLU@* _tUL?| h@|i t Lu T@h|U*@h ?|ihit| ? |t UL?|i | Mi U@ti |i? |i tLU@* i*u@hi Lu u|hi }i?ih@|L?t ** ?L| Mi *itt 4TLh|@?| |@?

|i i*u@hi Lu |i Thiti?| }i?ih@|L? 6h|ih4Lhic @** |i 4TLh|@?| ui@|hit Lu

|t @TThL@U @hi U*i@h*) tii? ? |i U@ti Lu 3ihL _tUL?|?} 5i?t||) @?@*)tt

@*tL tLt |@| |i LT|4@* |4i T@| uLh t ?L| ih) ti?t|i |L U@?}it ? |i _tUL?| h@|i ihi@t | t ^|i ti?t|i |L U@?}it ? |i _i}hii Lu ?L?*?i@h|)

b

|hL} U@?}it ?

? @?@*)|U@* i ThittL? uLh |i LT|4@* ULhhiU|i |@ @| @?) TL?| ? |4i t }i? M)

E ' 8 E

yx

xw`f 7E

E Eb

uhL4 ES ihi `f t @ UL?t|@?| `| @? ?€?|i |4i Lh3L?c |i @TThLTh@|i ULUi Lu `f t 4@ 7E Ai UL?t|@?| `f t |i |@h}i| *ii* Lu i*u@hi _ihi_

uhL4 EH i? o ' f W? L|ih Lh_tc |i LT|4@* t|i@_) t|@|i | 3ihL _tUL?|?} t _i|ih4?i_ @t |i }*LM@* 4@ 44 Lu 7c @tt4?} |@| @? ?|ihLh tL*|L? i t|t ) tMt|||L?c | U@? i@t*) Mi UL?€h4i_ |@| |i h*i @TT*i_

ihi UL?uLh4t |L |i L?|h)@}? 4@ 44 Th?UT*i W? ,^ Ebc |i tL*|L?

| |i T*t t}?c 4@!?} ' 8 fc t ULti? ? Eb i? t }ih

|@? |i LT|4@* t|i@_) t|@|i *ii*c @?_ |i tL*|L? | |i 4?t t}? t ULti?

i? t Mi*L |i LT|4@* t|i@_) t|@|i

t ,^Eb hiThiti?|t @ uii_M@U! UL?|hL*c | t @? i@t) |@t! |L ti| |i LT|4@*

ULhhiU|i |@ @| @?) TL?| ? |4i @t @ u?U|L? Lu |i Uhhi?| *ii* Lu TL**|L?

i? |i UL4Ti?t@|i_ _i4@?_ u?U|L? @t i** @t |i Th@|i @?_ tLU@* ULt|

u?U|L?t @?_ |i _iU@) u?U|L? Lu TL**|L? @hi !?L? W? |t 4L_i* t @ UL?|?Lt u?U|L? OL Lu|i? tL*_ Mi T_@|i_ ? Th@U|U@* TL*U) _iTi?_t

2f

L? |i UL?i?|L?t Lu |i €tU@* ?t|||L?t @?_ L? L Lu|i? ?i it|4@|it uLh

|i TL**|L? *ii* @hi @@*@M*i *L?} @? LT|4@* T@| |i |4i U@?}i ? ULhhitTL?_?} |L Eb t }i? M)

'

yx

xw`f 7E

E Ef

,^@|L?t Eb @?_ Ef _itUhMi |i T@ti T*@?i uLh @?) @*i Lu ?L 4@||ih L u@h | t uhL4 |i LT|4@* t|i@_) t|@|i

,^Eb tLt |@| |i ^it|L? i|ih @ U@hML? |@ tL*_ ?Uhi@ti Lh _iUhi@ti Lih |4ic U @t Mii? _tUtti_ M) iU! @?_ AitMih} Ebb2c 5?U*@h Ebb2 @?_ bbe @?_ N*T @?_ N*T Ebbec _iTi?_t |L|@**) L? |i U@h@U|iht|Ut Lu |i _iU@) u?U|L? ? UL4M?@|L? | |i iUL?L4U T@h@4i|iht ? |i 4L_i*

`i ** hi|h? |L |t ^it|L? ? 4Lhi _i|@* ? |i ?i | tiU|L?

Aihi @hi t|** tL4i ?|ihit|?} U@h@U|iht|Ut |L ?L|i @ML| |i t|hU|hi Lu |i 4L_i* L|ic uLh i @4T*ic |@| uLh @?) Uhic 7Ec @ *LU@* 4@ 44 ULhhitTL?_t |L @ t@__*i TL?| t|i@_) t|@|ic @ *LU@* 4?44 ULhhitTL?_t |L @ Ui?|ih @?_ @? ?iU|L? TL?| ULhhitTL?_t |L @ UtT ? |i T@titT@Ui At |i UL4T*i|i |LTL*L}) Lu |i T@titT@Ui t }i? M) |i 7Uhi Wu `ft }i? M) |i }*LM@* 4@ 44 Lu |i 7Uhic @t | t | 3ihL _tUL?|?}c |i? |i t|i@_)

2

t|@|i ULhhitTL?_?} |L |t t @ t@__*i TL?| @?_ |ihiuLhi M) ?@|hi ?t|@M*i At 4@!it |i uii_M@U! h*i ii? 4Lhi tiu* Bi? |@| |i TL**|L? *ii*

ULhhitTL?_?} |L `f t !?L? @?_ |@| |i Uhhi?| *ii* Lu TL**|L? t !?L? M) 4L?|Lh?}c |i? | t @? i@t) |@t! |L ti| |i ULhhiU|i |@ @| |i LT|4@* *ii*

|@| ii?|@**) *i@_t |L |i i*u@hi LT|44

*tL tTLh@_U _t|Lh|L?t @?_ tLU!t MiUL4i *itt 4TLh|@?| | @ uii_M@U!

UL?|hL* , L}i?Lt _t|Lh|L?t ** @|L4@|U@**) Mi |@!i? U@hi Lu ?L 4@||ih i|ih |iti _t|Lh|L?t |@!i T*@Ui u@h uhL4 |i LT|4@* t|i@_) t|@|i Lh *LU@**)

@hL?_ | Ai 4L_i* t t| @t @TT*U@M*i u@h @@) uhL4 t|i@_) t|@|i @t | t

*LU@**)

*|L} | t LMLt |@| |i LT|4@* TL*U) _ihi_ uhL4 t|@|U @?@*)tt t

?L| }*LM@**) LT|4@* i? |i |hi 4L_i* t _)?@4Uc | t Lu|i? Mi*ii_ |@|

@ t|@|U TL*U) t @TThL 4@|i*) ULhhiU| ih) U*Lti |L |i LT|4@* t|i@_) t|@|i N?uLh|?@|i*)c |t t ?L| |i U@ti @t ML| |i LT|4@* T@| @?_ |i LT|4@*

t|i@_) t|@|i @hi _gihi?| ? |i |L @TThL@Uit ^@t_)?@4U TL*U) M@ti_

L? E ' _2E^qEc ihi t |hi@|i_ @t @ T@h@4i|ih |@| t UL?|?Lt*) T_@|i_c

** ?iih *i@_ |L |i t|i@_) t|@|i uL?_ M) _)?@4U LT|43@|L?

22

e "@*|@|i @?@*)ttG Ai |4i T@| Lu |i ULhhiU|i |@

Ai ThTLti Lu |i Thiti?| tiU|L? t |L 4@!i @ UL4T*i|i @?@*)tt Lu |i |4i T@| Lu |i LT|4@* ULhhiU|i |@ c |@| t( @| u@U|Lht _Lit | _iTi?_ L? @?_

L W? T@h|U*@h |i uL**L?} ^it|L? t @t!i_G OL _Lit |i |4i T@| Lu |i LT|4@* |@ *LL!c @?_ L _Lit | _iTi?_ TL? |i ?|@* t|@|L? @?_ |i _iU@) u?U|L? At ^it|L? @t @*tL Mii? h@ti_ M) iU! @?_ AitMih} Ebb2c 5?U*@h Ebb2 @?_ bbe @?_ N*T @?_ N*T Ebbe t?} tL4i@| t4*@h 4L_i*t

t |i LT|4@* ULhhiU|i |@ U@? Mi h||i? @t @ u?U|L? Lu |i TL**|L?

*ii*c Ec |i |4i _ih@|i t

' E

t : f i? i @hi Mi*L |i LT|4@* t|i@_) t|@|i @?_ Ui iht@c | t 4TLh|@?| |L _i|ih4?i |i t}? Lu L? i@U t_i Lu |i LT|4@* t|i@_) t|@|i W?

|i uL**L?} i *LL! @| |i U@ti | 3ihL _tUL?|?}c @?_ ihi ? ,^ E22 _Lit ?L| _iTi?_ TL? |i TL**|L? *ii*c At ULhhitTL?_t |L |i U@ti ihi _iTi?_i?Ui U@? L?*) LUUh |hL} |i _t|*|) |ih4c (c Lh |hL} |i

?|ihUiT|t Lu |i _i4@?_ @?_ 4@h}?@* ULt| Uhit E2 @?_ E22c ?L| |hL}

2

|i t*LTi Lu |iti Uhit Ai _ih@|i U@? |i? Mi h||i? EhiU@** Ef

E ' 8E n 7E

2 Ee

W? |i U@ti Lu 3ihL _tUL?|?} LT|4@* t|i@_) t|@|i t _i|ih4?i_ M) 7 ' fc @?_

`f ' 7E^W ihi ^W t |i LT|4@* t|i@_) t|@|i *ii* Lu TL**|L? Ai |4i _ih@|i Lu t }i? M)

' 8E n 7E

2

Ai t}? Lu _iTi?_t TL? |i t}? Lu |i |hii |ih4t 8c 7 @?_ `i|ih t TLt|i Lh ?i}@|i _iTi?_t L? i|ih i @hi @MLi Lh Mi*L |i LT|4@*

t|i@_) t|@|i *ii* At i @i i}| TLttM*|it |L ?it|}@|i Aiti @hi *t|i_

? |i uL**L?} tUi_*i

2e

 : f

@ 7 : f : 8 : f , : f

K 7 : f : 8 f : `f 7 : 

# 7 28

$₂

, :

f

S 7 f : 8 : f : `f 7 : 

# 7 28

$₂

, : f _ 7 f : 8 f , f

2 f

@ 7 : f : 8 : f : `f 7 : 

# 7 28

$₂

, :

f

K 7 : f : 8 f , : f S 7 f : 8 : f , f

_ 7 f : 8 f : `f 7 : 

# 7 28

$₂

, : f

2D

6hL4 |i tUi_*i @MLi | t tii? |@| |ihi @hi |hii u@U|Lht @giU|?} |i |4i T@| Lu |i ULhhiU|i |@ G |i t}? Lu 7c |i t}? Lu 8 @?_ i|ih |i _gihi?Ui Mi|ii? `f @?_ 7 t }hi@|ih Lh t4@**ih |@? tL4i @*i }i? M) ^ ₂₈⁷

₂

OL

@hi |iti u@U|Lht ?|ihThi|i_q W| t tiu* |L t|@h| M) hiU@**?} |i ?|ihThi|@|L?t Lu 7 @?_ 8 Ai i ThittL? uLh 7 t }i? M) Eec @?_ | t ?|ihThi|i_ @t |i tt|@?@M*i *ii* Lu tLU@* i*u@hi Ai 4@ 44 tt|@?@M*i i*u@hi E5` t

`f Ai tt|@?@M*i i*u@hi U@? Mi ML| ?Uhi@t?} @?_ _iUhi@t?} ? L? i|ih t_i Lu |i LT|4@* t|i@_) t|@|i _i |L |i ?L?*?i@h|)

Ai i ThittL? uLh 8 t }i? M) E2 6hL4 |t | t tii? |@| i|ih 8 t TLt|i Lh ?i}@|i _iTi?_t TL? i|ih B%_f s t TLt|i Lh ?i}@|i +iU@** |@| B%f s t |i @U|@* ?Uhi@ti ? TL**|L? |L| TL*U) 4i@thit @t

%f t |i ThL_U|L? *ii* |L| TL*U) 4i@thit E?_ih 4@h!i| i^*Mh4 AihiuLhi B%f t |i ?Uhi@ti ? TL**|L? _i|ih4?i_ uhL4 |i 4@h!i| i^*Mh4 ThL_U|L? *ii* ihi@t s t |i ?@|h@* _iU@) W? |i |)TU@* U@ti |@| Th@|i ULt|t @hi tu|i_ T@h_ @?_ _i4@?_ t tu|i_ _L?@h_ | |i TL**|L? *ii*c

%_f f W? |t U@ti |ihi @hi |hii uLhUit Lh!?} |L@h_t hi_Ui_ i4ttL?t Lu TL**|L? i? |i *ii* Lu TL**|L? ?Uhi@titc |i 4@h!i|c ?@|hi |ti*u @?_ |i TL*U) 4i@thi Wu s : f |i? 8 f Ai hi^hi4i?| uLh 8 : f t |@|

2S

s f @?_ B%_f : s t %_f |)TU@**) t ?i}@|ic 8 : f hi^hit |@| |i ?@|h@*

_iU@) _iUhi@tit | |i *ii* Lu |i t|LU! TL**|@?| @?_ |@| |i 4@h!i| t *itt ti?t|i |L @ U@?}i ? |i TL**|L? *ii* |@? |i i?hL?4i?| ? i @4T*i Lu TL**|L? | @ _iUhi@t?} _iU@) u?U|L?t t @U_ h@? ihi |i ?@|h@*

Th€U@|L? ThLUitt MiUL4it *itt iUi?| |i }ih |i TL**|L? *ii*

At i?@M*it t |L ?|ihThi| |i _gihi?| U@tit ? |i tUi_*i @MLi @ti @

t ?|ihThi|i_ @t uL**Lt Wu |i ?|@* *ii* Lu TL**|L? t Mi*L |i LT|4@* t|i@_) t|@|ic tt|@?@M*i i*u@hi t ?Uhi@t?} ? |i TL**|L? *ii* @?_ |i uhii 4@h!i|

i4ttL? *ii* t *itt ti?t|i |L U@?}it ? TL**|L? |@? |i i?hL?4i?|c |i ULhhiU|i |@ tL*_ _i€?|i*) Mi ?Uhi@t?} Lih |4i @ti M |i**t t |@| u

|i ?|@* *ii* Lu TL**|L? t Mi*L |i LT|4@* t|i@_) t|@|ic tt|@?@M*i i*u@hi t

?Uhi@t?} ? |i TL**|L? *ii* @?_ |i uhii 4@h!i| i4ttL? *ii* t 4Lhi ti?t|i

|L U@?}it ? TL**|L? |@? |i i?hL?4i?|c |i ULhhiU|i |@ tL*_ L?*) Mi

?Uhi@t?} Lih |4i u |i _gihi?Ui Mi|ii? 5` @?_ |i Thiti?| tt|@?@M*i i*u@hi *ii*c `f 7c t *itt |@? @ Uih|@? @*i At @*i U@? Mi U@*U*@|i_ @t

E₂₈⁷² Ai _t|@?Ui `f 7 U@? Mi ?|ihThi|i_ @t @ 4i@thi Lu L u@h i @hi uhL4 |i LT|44c Lh h@|ih L 4U L?i U@? }@? uhL4 @TThL@U?} LT|44 Ai hi4@??} t U@tit U@? Mi ?|ihThi|i_ @UULh_?}*)

2.

OL _Lit |i ?|ihThi|@|L? Lu |iti U@tit UL?€h4 | ?||L?q L|i |@|

i? 7 }Lit uhL4 ?i}@|i |L TLt|ic iih)|?} i*ti i^@*c |t U@**t uLh @? ? Uhi@ti ? W? L|ih Lh_tc u |i tt|@?@M*i i*u@hi t ?Uhi@t?} ? |i TL**|L?

*ii*c |i LT|4@* |@ tL*_ Mi 4Lhi ?Uhi@t?} Lih |4i |@? ? |i LTTLt|i U@ti At hit*| t h@|ih UL?|ih?||i i | i ?L|i |@| i? 8 }Lit uhL4

?i}@|i |L TLt|ic iih)|?} i*ti i^@*c |t U@**t uLh @? ?Uhi@ti ? i?

|i TL**|L? *ii* t Mi*L |i t|i@_) t|@|i *ii* @?_ @ _iUhi@ti ? i? |i TL**|L? *ii* t @MLi t|i@_) t|@|i W? L|ih Lh_tc i? |i _iU@) _iUhi@tit

| |i *ii* Lu TL**|L?c @?_ t 4Lhi ti?t|i |L |i TL**|L? *ii* |@? |i 4@h!i| tc |i LT|4@* ULhhiU|i |@ tL*_ ?Uhi@ti Lih |4i uLh t4@** TL**|L?

*ii*t @?_ _iUhi@ti Lih |4i uLh } TL**|L? *ii*t At |LL tii4t tL4i@|

UL?|ih?||i

5L4i Lu |i U@tit ? |i tUi_*i @hi 4Lhi hi*i@?| |@? L|ih 6Lh i @4T*ic u 7 t UL?U@ic @t | Uih|@?*) t ? |i ?i}MLhLL_ Lu t|i@_) t|@|ic L?*) |i U@tit

@ @?_ M @?_ 2U @?_ _ @hi hi*i@?| tt4?} |@| 7 t UL?U@ic t |)TU@**) TLt|i Mi*L LT|4@* t|i@_) t|@|i @?_ ?i}@|i @MLi LT|4@* t|i@_) t|@|i Ai L?*) U@tit ? U |i LTTLt|i 4@) @TTi? t ? M @?_ 2_ i? `f 7 :



7 28

₂

c |@| t i? 8 t ?i}@|i @?_ *@h}i ? 4@}?|_i OLiihc |L t@)

2H

|@| 8 t ?i}@|i @?_ *@h}i ? 4@}?|_i t |L t@) |@| i|ih %_ft *@h}i ?i}@|i Lh s t *@h}i TLt|i Wu %_f t *@h}i ?i}@|i | 4i@?t |@| |i Th@|i 4@h!i|

i^*Mh4 |L| TL*U) 4i@thit t ^|i ti?t|i |L |i *ii* Lu TL**|L?(

|@| tc |i i^*Mh4 *ii* Lu ThL_U|L? _iUhi@tit | |i *ii* Lu TL**|L?

_i |L _iUhi@ti_ _i4@?_ Ei?hL?4i?|@* @@hi?itt Lh }ih ThL_U|L? ULt|t Wu s t *@h}i TLt|i | 4i@?t |@| _iU@) ThLUitt t iUi?| L| @hi i @4T*it Lu @ U@ti ? U TL*U) 4i@thit @hi ?L| ih) itti?|@* MiU@ti |i ?i| ?Uhi@ti

? i4ttL?t t hi_Ui_ _i |L 4@h!i| @?_ i?hL?4i?|@* igiU|t W? L|ih Lh_tc

? tL4i ?i}MLhLL_ Lu |i LT|4@* t|i@_) t|@|ic |i L?*) U@ti ? U |i

|@ ** Mi ?Uhi@t?} Lih |4i uLh TL**|L? *ii*t }ih |@? |i LT|4@* L?i

@?_ _iUhi@t?} Lih |4i uLh TL**|L? *ii*t *Lih |@? |i LT|4@* L?ic t i?

|i |@ T*@)t @ 4?Lh hL*i

t4@** TLt|i _tUL?| h@|i ** ?L| U@?}i |i ^@*|@|i UL?U*tL?t ? |t tiU|L? `| _tUL?|?} ' fn o  ihi o  hiThiti?|t @ t4@** Tih|hM@|L?

?*) u f t U*Lti |L 3ihLc ** |i *@t| |ih4 TLttM*) @giU| |i t}? Lu c M| u tLc

|i ULhhiU|i |@ ** Mi 4Lhi Lh *itt UL?t|@?| @?)@) Wuc Liihc t 4@_i _iTi?_i?|c |i |4i T@| Lu |i LT|4@* |@ MiUL4it ii? 4Lhi UL4T*i c @?_

| MiUL4it 4Lhi _U*| |L _h@ }i?ih@* UL?U*tL?t |@? | @ UL?t|@?|

2b

D "@?||@|i @?@*)ttG 5L4i ?4ihU@* i @4T*it

W? |t tiU|L? tL4i i @4T*it M@ti_ L? @ t|)*3i_ ?4ihU@* 4L_i* t }i? uLh

**t|h@|i ThTLtit W? T@h|U*@h i *LL! @| L |i LT|4@* |@ U@?}it @t @ u?U|L? Lu |i TL**|L? *ii*c c | _gihi?| _iU@) u?U|L?t W| t @tt4i_ |@|

f ?|t Lu TL**|L? @hi @ttLU@|i_ | i@U ?| Lu ThL_U|L?c |@| t B ' f

iLT*i @hi 4Lhi UL?Uih?i_ @ML| |i i?hL?4i?| |i }ih |i @}}hi}@|i *ii* Lu TL**|L? tU |@| _i4@?_ uLh |t ThL_U| t tu|i_ _L? @t |i @}}hi}@|i_ *ii*

Lu TL**|L? htit h@|i 4@h}?@* ULt|t @hi tu|i_ T @t |i *ii* Lu TL**|L?

htit 5LU@* 4@h}?@* ULt|t @hi ML| tu|i_ T @?_ MiUL4i t|iiTih @t |i *ii*

Lu TL**|L? htit Ai ?4ihU@* tTiU€U@|L? t }i? M)G

Rf ' @c R ' c SRf ' 

2 n @c SR' 2c S7f '  n @c S7 ' n @

2

`| |iti @tt4T|L?tc Th@|i i^*Mh4 t }i? M) % '  @?_ tLU@* LT|44 M) % ' fH i? @ ' f `i? @ ' fD |iti €}hit @hi % ' fS @?_ % ' fS hitTiU|i*)c @?_ i? @ '  |i) @hi % ' f2 @?_ % ' f Ai |h@?tuLh4@|L? Lu

f

@ ?|L t }i? M) @ ' *2D tU |@| f 2D ULhhitTL?_t |L f @  Ahii _gihi?| TLttM*|it uLh |i u?U|L? sE@ @hi i @4?i_ @?_ |i hit*|t

@hi **t|h@|i_ ? 6}hit 2 e W? 6}hi 2 s t }i? M) @? i^@|L? t4*@h |L

|i ?Lh4@* _t|hM|L?c |@| t

sE@ ' 

fs

2Zj²e^{32E@3>j 2}

ihi > ' fD @?_ j ' f2D Ai LT|4@* ULhhiU|i |@ }i? M) Eb @?_ |i ULhhitTL?_?} ThL_U|L? *ii*c %c @t u?U|L?t Lu @hi **t|h@|i_ Ai LT|4@*

@*ii* t f @?_ 4@ 7 ' 7Ef ' fS L|i |i t@Ti_ uLh4 Lu |i LT|4@*

|@ c @?_ |@| |ihi t ?L ThL_U|L? i? @ t }hi@|ih |@? f.2 E : H t

?i}@|i ThL_U|L? t 4TLttM*ic % ' f uLh @ : f.2 ?) ThLM|i |@ **

_L i? @ : f.2

6}hi **t|h@|it |i LT|4@* |@ @?_ ULhhitTL?_?} ThL_U|L? i? sE@

t *?i@h*) ?Uhi@t?}c s ' fS@ 6Lh |i ThTLti Lu UL4T@h@M*|) @** sUhit i @4?i_ ihi @i @ 4@ 44 Lu fS ? |i h@?}i f @  `| |t ULUi Lu sc |i LT|4@* @*ii* t f2e @?_ 7Ef2e ' fb L|i |@| ? |t U@ti |i LT|4@* ULhhiU|i |@ t 4L?L|L?U@**) _iUhi@t?} ? |i h@?}i f @  @?_

ThL_U|L? t UL!i_ i? @ : fHe E : 2



Ai |h_ U@ti i @4?i_ ihi t |i U@ti Lu @ *L}t|U su?U|L? }i? M) s ' fSe@E @ At U@ti t **t|h@|i_ ? 6}hi e Ai LT|4@* @*ii* t f @?_ 7Ef ' fS W? |t U@ti |i LT|4@* ULhhiU|i |@ t 4L?L|L?U@**)

?Uhi@t?} @?_ @ ThLM|i |@ t ?ii_i_ i? @ : f.D

#iTi?_?} TL? |i t@Ti Lu |i sUhic |i LT|4@* ULhhiU|i |@ 4@) Mi t@Ti_c _iUhi@t?} Lh ?Uhi@t?} ? @ OLiihc ? @** U@tit i @4?i_ ihic

|i ULhhitTL?_?} LT|4@* ThL_U|L? *ii*c %c t @ _iUhi@t?} u?U|L? ? @ **

**t|h@|L?t ihi @hi M@ti_ TL? 3ihL _tUL?|?} Ai LT|4@* |@ t ?L| ih) ti?t|i |L U@?}it ? |i _tUL?| h@|ic @?_ |i TLt|L?t Lu |i Uhit @hi h|@**) ?U@?}i_ uLh hi@tL?@M*i @*it Lu |i tLU@* _tUL?| h@|ic o

S L?U*tL?t

Ai 4L_i* _itUhMi_ ? |t @h|U*i t _it}?i_ |L @?@*)3i |i _)?@4U ThLM*i4 Lu 4@ 43?} tLU@* i*u@hi uhL4 |i ThL_U|L? @?_ UL?t4T|L? Lu @ UL?t4ih }LL_ Lti ThL_U|L? ThLUitt t @ttLU@|i_ | @? i |ih?@*|)c ? |t U@ti i4ttL? Lu TL**|L? 5LU@* i*u@hi t _i€?i_ @t |i t4 Lu |i UL?t4ih @?_

ThL_Uih thT*t uhL4 |i ThL_U|L?c ULhhiU|i_ uLh |i i |ih?@*|) @ttLU@|i_

| |i i4ttL? Lu TL**|L?c |i L i |ih?@*|)c @?_ ULhhiU|i_ uLh @?) uh|ih

2

_t|*|) @ttLU@|i_ | |i t|LU! TL**|@?|c |i t|LU! i |ih?@*|) Ai t|LU!

Lu TL**|L? LMi)t @ _)?@4U ThLUitt M) U |i t|LU! ?Uhi@tit @t @ hit*| Lu ThL_U|L? Lu |i }LL_ @?_ _iUhi@tit _i |L @tt4*@|L? ? |i i?hL?4i?| hiT hiti?|i_ M) @ }i?ih@*c M| !?L?c _iU@) u?U|L? ULhhiU|i |@ t ?|hL_Ui_

|L ?|ih?@*3i |i i |ih?@*|it @?_ hit|Lhi iUi?U) W| t TLttM*i |L _ihi |i LT|4@* ULhhiU|i |@ @t @? i T*U| u?U|L? Euii_M@U! UL?|hL* *@ Lu |i Uhhi?|

t|LU! Lu TL**|L? @?_ |i _tUL?| h@|i

W? T@h|U*@hc | t uL?_ |@| |i ThLTih|it Lu |i LT|4@* ULhhiU|i |@ c ML|

@t @ u?U|L? Lu |4i @?_ @t @ u?U|L? Lu |i TL**|L? *ii*c _iTi?_ Uh|U@**) TL? |i t@Ti Lu |i _iU@) u?U|L? AL t|_) i|ih |ihi t _iU@) Lh ?L|

t ?L| tUi?|c | t |i t@Ti Lu |i _iU@) @t @ u?U|L? Lu |i TL**|L? |@|

UL?|t A)TU@**) |i ULhhiU|i |@ ** Mi @? ?Uhi@t?} u?U|L? Lu |4i uLh TL**|L? *ii*t *itt |@? |i LT|4@* t|i@_) t|@|i @?_ @ _iUhi@t?} u?U|L? Lu

|4i uLh TL**|L? *ii*t }hi@|ih |@? |i LT|4@* t|i@_) t|@|i Ai LTTLt|i **

t@**) L?*) Mi |i U@ti i? TL*U) 4i@thit @hi ?L| }*) hi^hi_ MiU@ti

?i| @UU4*@|L? Lu TL**|L? |L @ *@h}i i |i?| t hi_Ui_ M) ?Uhi@t?} ?@|h@*

_iU@) @?_ M) |i hitTL?ti Lu |i 4@h!i|

. U!?L*i_}4i?|t

Ai @|Lht t |L |@?! i|ih ihU!c w@ht O@@!L?ti?c w@ht @|iti? @?_

k@|h? **LU! uLh tiu* UL44i?|t

H TTi?_  wt| Lu 4@Lh t)4ML*t @?_ _i€?|L?t

At @TTi?_ }it Mhiu _i€?|L?t Lu tL4i Lu |i 4@Lh t)4ML*t 6Lh 4Lhi

|LhL} _i€?|L?tc tii |i |i |

% G 5L4i ThL_U| U@t?} i4ttL?t

@ G Ai t|LU! TL**|@?| 4i@thi_ ? T)tU@* ?|t G ULhhiU|i ET}L@? |@

(E@ G #t|*|) U@ti_ M) |i Thiti?Ui Lu |i t|LU! TL**|@?| E( : f sE@ G Ai _iU@) u?U|L? uLh TL**|L?

G Ai t|LU! TL**|@?| 4i@thi_ ? 4L?i|@h) ?|t EULt| Lu |i t|LU! TL**

|@?|

8 E G U|@* ?Uhi@ti E8 : f Lh _iUhi@ti E8 f ? ? 4L?i|@h) |ih4t E@c % ' RfE@ R% G W?ihti _i4@?_ u?U|L? uLh %

E@c % ' SRfE@ n SRE@% G h@|i ULt| Lu ThL_U?} %

⁷E% ' SrfE@ n SrE@% G 5LU@* ULt| Lu ThL_U?} % e

%E@c ' %fE@ %E@ G Ai 4@h!i| i^*Mh4 | hitTiU| |L % uLh @ }i? ULhhiU|i |@

%f ' ^R_R^f_^3S_nS ^f _ : f

% ' _RnS^ _ : f

` E@c ' kE@ n qE@ E@² G 5LU@* i*u@hi uhL4 |i ThL_U|L? @?_

UL?t4T|L? Lu %

7E ' kE n qE8E E8E² G 5t|@?@M*i i*u@hi

> ' ^Y`_{Y '8 E} ' qE 2E8E k ' ( n ^₂%fE%fRn %fSr 2Rfn 2Srf q ' ^{ESrf3SRfERnS}_ER^R_nS^nER_R^f2^{3SRfESr3SR} : f ' _2ER^ER_^nS_nSR^r2 : f

b TTi?_ 2

W? Lh_ih |L _ihi |i i ThittL? uLh |i LT|4@* uii_M@U! UL?|hL* *@ ? E. | t ?iUitt@h) |L ?|hL_Ui Tih|hM@|L? |iLh)c tiic i}c @)ui Eb. uLh @ 4Lhi

|LhL} ?|hL_U|L? |L |t |iLh) At i?@M*it t |L UL4T@hi |i 4T*U@|L?t Lu @ UL?t|@?| _tUL?| h@|i | 3ihL _tUL?|?} uLh |i ?L?*?i@h 4L_i* @?_ t|**

}i| i T*U| @?@*)|U@* tL*|L?t At | t ?L| ?iUitt@h) |L hitLh| |L ?4ihU@*

D

4i|L_t W? |i uL**L?} |i t@4i t)4ML*t _i?L|i ML| Uhhi?| @*it @?_

Thiti?| @*it 5|h@}|uLh@h_ Tih|hM@|L? )i*_t |i uL**L?} tUi4iG

' f n on o²2n c ' fn on o²2n c

_f

_ > ' 2^tE`f 7c f ' 8 <sup>t`f37</sup>c 2^k__{_}^f >^l__{_}^ ' efc 2 ' ^__{_}^c 2^k__{_}^f >^l__{_}² ' e^k__{_}^l2c 22 ' ^__{_}²c 2^k__{_}^f >^l__{_} ' e2 2^__{_}^__{_}²c 2 ' ^__{_}

Eb

L|i |@| uLh @?) Lh_ih |i ?iUitt@h) ULhhiU|L? t @ttitti_ t?} @| 4Lt| L?i _hiU| ?|i}h@|L? Lu |i tL*|L? |L |i ThiLt Lh_ih L|i @*tL |@| |i @*i u?U|L? _ii*LTi_ ? |i _tUL?| h@|i )i*_t

T E|c ' g n^{k`</sup><sub>o</sub><sup>f</sup> n E<sup>l</sup>e<sup>3o|</sup>' g n<sup>k`}_o^f n E^ld o| n o ' `f| n E n Eo

Ai UL?t|@?| |ih4 t ?U*_i_ ? E AL |i *Lit| Lh_ih |t t _i?|U@* |L

|i @*i u?U|L? uLh |i U@ti | 3ihL _tUL?|?} )i*_?} |i h*i ? ,^Eb

S

Ai }i?ih@* tL*|L? |L Lh_ih |hii t }i? M)

' fn 

2Ef 8

kofn o² o²_^2ln Eoc Eb2

 ' f

2Ef 8c _f ' 2Ef Wc _ ' f

f 8

Nt@**)c Liihc |i _ithi_ Lh_ih t *Lc i *itt |@? |hiic @?_ |ihiuLhi |i tL*|L? |L tiUL?_ Lh_ih t @TT*i_ ? |i |i | ML_)

+iuihi?Uit

do h|Lc #c @?_ W?|h*}@|Lhc  EbH.c 5|LU! , |ih?@*|itc }L@? A@ @

|L? @?_ #)?@4U 5|@M*|)c aLh?@* Lu M*U ,UL?L4Ut G Db.2

d2o _<h}ic +c @?_ kL}!c k Eb.c ,UL?L4U BhL| @?_ |i ,?hL?

4i?|c +ii Lu ,UL?L4U 5|_it efG S..

do 6Lht|ihc Eb.Dc T|4@* L**|L? L?|hL* | @ L?UL?t|@?| , TL

?i?|@* +@|i Lu #iU@)c aLh?@* Lu ,?hL?4i?|@* ,UL?L4Ut @?_ @?@}i4i?|

2G S

.

deo k@4i?c  Wc : 5U@h|3c w Ebbc #)?@4U T|43@|L?G Ai @*

U*t Lu V@h@|L?t @?_ T|4@* L?|hL* ? ,UL?L4Ut @?_ @?@}i4i?|c Lh|OL**@?_c 4t|ih_@4

dDo kii*ihc ,c 5Ti?Uic c @?_ ~iU!@tihc + Eb.c Ai T|4@* L?|hL* Lu L**|L?c aLh?@* Lu ,UL?L4U AiLh) eG be

dSo kLc W#c w@T@?c Oc @?_ 5@?_*ihc A Ebb2c L?|hL**?} 5|LU! , |ih?@*|itG 6*i M*i ihtt W?i M*i }L@? LhhiU|L?tc ,hLTi@? ,UL?L4U +ii SG 2S2.S

d.o @)uic O Eb.c ih|hM@|L? i|L_tc `*i)c i vLh!

dHo Lh_@tc ` # EbH2c OL 6@t| 5L*_ `i Bh@3i |i B*LM@* L44L?tqc 4ihU@? ,UL?L4U +ii @Tiht @?_ hLUii_?}t .2G 2e22eS

dbo Lh_@tc ` # Ebb@c AL 5*L Lh L| |L 5*LG Ai ,UL?L4Ut Lu |i Bhii?Lti ,giU|c Ai ,UL?L4U aLh?@* fG b2fb.

dfo Lh_@tc ` # EbbMc 5!i|U Lu |i ,UL?L4Ut Lu |i Bhii?Lti ,giU|c 4ihU@? ,UL?L4U +ii HG eSDf

H

do iU!c 5 c @?_ AitMih}c A a Ebb2c ,AG L_i* uLh @hML? ,4ttL?t Ah@iU|Lh) ttitt4i?|c Ai ,?ih}) aLh?@* G DD..

d2o 5?U*@hc a Ebb2c O} #Lit L|?} @?_ +t?} Wt `LhtiG @hML?

A@ it 5L*_ kiiT #iU*??} |L | O@h4u* ,4ttL?tc @?Uit|ih 5ULL*

SfG eD2

do 5?U*@hc a Ebbec ? |i T|44 Ahi?_ Lu 6Ltt* 6i* A@ @|L?c uLh_ ,UL?L4U @Tiht eSG HSbH..

deo A@L?i?c c @?_ 5@*Lc 5 EbbSc L?UL?i |it ? T|4@* L**|L? U U4*@|L?c aLh?@* Lu ,?hL?4i?|@* ,UL?L4Ut @?_ @?@}i4i?| G Sf

..

dDo N*Tc c : N*Tc # Ebbec Ai T|4@* A4i @| Lu @ @hML? A@ c uLh_ ,UL?L4U @Tiht eSG HD.HSH

dSo `h*c 6 Ebbe@c B*LM@* `@h4?} @?_ @hML? A@ itG #)?@4U @?_ 5|h@|i}U W?|ih@U|L?t Mi|ii? ,?ih}) L?t4iht @?_ hL_Uihtc aLh?@* Lu L*U)

L_i*?} SG D..DbS

b

d.o `h*c 6 EbbeMc }L@? A@ @|L? Lu ,?ih}) uLh 6*L @?_ 5|LU! , |ih?@*

|it @?_ 5|h@|i}Uc L?UL4Ti||i ,?ih}) hU?}c aLh?@* Lu ,?hL?4i?|@*

,UL?L4Ut @?_ @?@}i4i?| 2SG H

ef

f 6}hi *i}i?_t

6}hi  5|@|U @?@*)ttG Ai LT|4@* ULhhiU|i |@ c ^Wc |i ULhhitTL?_?} ThL _U|L? *ii*c %^Wc @?_ |i 4@h!i| i^*Mh4c %fc uLh @ }i? TL**|L? *ii*c @c i? t ?ihti _i4@?_c  t |i Th@|i 4@h}?@* ULt| u?U|L? @?_ ⁷ t |i tLU@* 4@h}?@* ULt| u?U|L?

6}hi 2 Ai LT|4@* ULhhiU|i |@ @?_ |i ULhhitTL?_?} ThL_U|L? *ii*

@t u?U|L?t Lu i? s t t4*@h |L @ ?Lh4@* _t|hM|L? | > ' fD @?_

j ' f2D __i_ M) |i? ' 2D@

6}hi Ai LT|4@* ULhhiU|i |@ @?_ |i ULhhitTL?_?} ThL_U|L? *ii*

@t u?U|L?t Lu i? s t *?i@h*) ?Uhi@t?}c s ' fS@ ' 2D@

6}hi e Ai LT|4@* ULhhiU|i |@ @?_ |i ULhhitTL?_?} ThL_U|L? *ii* @t u?U|L?t Lu i? s t }i? M) |i *L}t|U u?U|L? s ' fSe@E @ ' 2D@

e