I.

i/! ilrus

[4 Sc,wfrt . *t,e,-ip\a i< e- t-l'.o bu, ^ 4 t e,r.. g

T.L

Js'= >[ax.* ,, ) g

[rz lt -

hos R.5. ltn-clra,r-.o

t " M -) K' u*,fzr' ^(

B./Ll,(t I

', 0 s sar-,fu?,(

A survevtr,' -f<4.H

MClarrrd.

rF vnM

A,-i dI e Jg

Lal l *,* "l*t qY .;.4 €| ,-/

G t,' (O l;t' d,.)Jt ^

(ir=iGu^,h) i

)o ? | lY s-> tR"-A

€tr=..d? =o r.<.cf . Do Crrmo f.zo t

i 1 , +l^t q x Fr"^^ ui awo ?Sia/\.^t lro/r r\rqhic . Az

t,f r; (>.1-'r,.) s. i f r,.rr.+aa;' )t fr

2/7Q\07\* )

i.=l,-.ra

h'+(!"+i+))wrin;^4_

('t(r" -1'?; ))

v*; .?7t -ltrt *r' ) 4 oFtsoZt;z: i(t.**,r*,'l-l\t

\ riIg-1,' t

I

(i ll(r*^r'{. . A,1

Ll+(rf

Itit ) ={4.r u(2,<

,-""W^-!, )

)L

-dsIry, Ve"+-{isaa^tl f4op, nn f uq dna4e' ll Vlhir ai fr,r^e*I %a 1tt^.c"^

gtnt+'9

: ['4

C/n4' E ,

':h(- -o vh; l-1.' t tna

7gcr )trs' T*

hu

Y4

?x

-__+

ta frzf = C,D

4 hol"t,r^gt dZ

'^a2 z,l - oW [c,"'u'Q t

Lo.u Ls tt \J 'i tie. ?*r

Z :

@,-tw

" f oLtt

l-2\

I € c7 n't ;s ^l*^/, q,,r a .

crh-l hol.AJt 3- r\" v.

*tf

:3= lrn lz;,.Lr!

M

t h ,' , ir ,lt-r

;' I-r"r. Vl'7ho[. {- (w*,s.

K,- [n" "

P(*,T;su'w.

M-t

{rrUJ a-

fr). f;^Ao(=

(?\ . L!. f

" 6o*rr t ,"F "

lz / , T; J7h*utc fh( s iS tt^*

q I 1Sl

1-4/t't Plr

o(")/tr(z),5ll +- -a_

r.2

Ky ) ; *oe, 1%,n, .

tt", \ ,< ,"staj ula t.e q ++^4

tr^. G 4+rtr May ;

6r(Lth ) t S\fv-' uAF t 4

tt= ) ;<

5 o (rr -.1

1'v.9 . N,

--/

Sur^^-g : Y" Mq-| t(.t vvrin;^u4( t*o\lt^t. i S o F\)ty,n,Q us-.ry^. crf b ol o . .-r.O .)

t+ fi^r Qo-t*99 fvtr-y L r,5 holcmavphicy ; v.=1 , Nf ., M -J S) is anti_-:::"Y _i"11 , -*[*. fl__"+ ll il au:lt':_ln Vy4 :

. (U.'.-r ;l i5 VCRY eotrj *o r+nSfru^gf n-tin;yn4l S*to*.(er1..;"1\ wL.a..rn M =. Ct dv D }. ; lR"";

iv[tr-+ ; l-?.

;5 l\ +-^^ <

?f', CLc,k thal

Y " M s-r 16) ,i6

Gr[2,3 )

lls6r(r,3) a St

tu1 lv|

) st. lltt)'=o\,7

o( " /r4 --+ 1{

;6tftvbl 5ib4

h ol o .

L 4',

(! r-t'-

t- f **.,s

, 4q

z'Rc I r) ro

vy:.inilv.rI

rz: *J

a

IhiJ>o

4

Vrl - [< F -rr" --tfu3 :

dr'+ o(..'+ o,)' =-

(*, + i,{. ) (o{s * i.{ rz

{,

4r+f4z) 3 : J Uvt^4

r.3o

\-t --

4ta)''aj

nl *,'a( z

io(e ho

f t^^Cl-.Yh AI 5 ,*n2b LV'(

I

o(,

l. d^'W tovnn1

t - 5 w

1") w2') w

W,: "tl +

+ ( x-1 +r.{(( *, - r'o(

1.d ( *,W,{!!

I o1'7

( or

z €L a 3rL=W

= t(t_= I (t*€ ?w

Xa

uJ *iGW A f JT

If2 1'= + I t^5" li f ['* I, I t* 1' l"tf I'r It ftf? iVt'(n I t +ztel'+ torvl )

= | tft'(,*(ol')'Th.'S t- I r t

-) ( u f o 3

6 < us< {"*(

* ,'J"qf .o Jfrzr,s 1v4;".c ?qN e 6e.usS nn.-p .. M S.

(r, -,'9.1 I a Yz -,: ( n,,4,t 47 )*1 -' q- k. 4 x &. [;a ) 'r''= 4i d7

: 'L (',,Qr,4) J r (r,rr",v3 ) hi +r'V

= F,L,,.^ ( o,' G , dt tt , 4,7, )

r{-. J.,{

Yx t1

"r(rlgr *r )rlJl ? Y'o4*, ?tu+, )A -nrrt-|4'i urud N e) = 6

'ta.,r,ta t)t e- W ; 'F \ )U 7. =l J't

'F *.*n .l

/v\) .lo\ J 'ovtt/\^ C ^m^:9.

t yl T ,l rx -/v\ 4 +r,a@qrT '

D I, e t G uzrl 'e D)) s N,A'c

' r+"6r-|-'l 6liTil\J

r)\iz

.( lt{hr() !e.l',i#.\1, tr( t-rt',+"x)

I -- A +.,t h t *z t *t,l tr),t tl ll

t-l6t'b*az'6tlz )

( [re r)( rt6l +r)"tlt

( -?q-"g)'+ (r.,l tl-Dfi .-la.h,-=

1("s *l)( zg-r) ? r'/'|t = "3t, Yht

T ( "ttJ r, ) .t;l + = 'j tr*r \*,'l)*,: t

r a) (..tc] ,.r)"t+t + ;

tt.rc)+r )( r+r)).lll +:

N

,-=I

t.lJ

n viJv

I s (.j*,)i + :("c*,)1J.,*L \ Z- l -' -Utrc*)).(ri

.il,, (r-rg) ' 6\dz'badz)C"lst+r)rt*1 a

v(.I

Iq.b 14 I

e (U ?vv)

4='Ca

(.5

AfPti<z"Vuvw

? ^r A "\^l^"^

tohg; J''1"(,'

f(,tl i,-u{s0.r,n^ro A'04

'-tT se tn,Tlt'f /tis'vtt-Q' o(

;55uu.r. t1/t'c- q-i{*, )rl': z i e ie*

{4f, .

'*J0

&-")

t'€

L **-t Q!-, 1 iI

Ma ('-

(at '

A It uo i r) ( wu ,W ,{,iy",n*u')i q "t

fr1 A(e)= & ; l(*)= *f E, d-Jt \"ao l'1 o\ I y.o*ird, :

J = ^ *sl.-' (+ )

f4^^Tu l,-: -),le[i aiot ( 'r=,i,# r"#:r,*,ltarwohiL h'J u5afl

qe$'tJ. lsneavrno t'toJ-

Irx n,,,^rtAt fu

T)a r.e-

Cb 0:a

at*

I

I

t

I

t

t

I

i

M=G t )= z t

f f p l;ca ho,*o IL '.

(1ra ) 76

Y:t(

e(

t4$ o'^-t SS

s*2

c4

rrl,1,

M

tR) L-w4(-sle vt,itt-

^T a,ul dJ/.,,X +|.-QJ-

rV 4 I* c' 4 Gw.-.*v

M1 c, p {a r'.l.-e.

taV? Y

r(J

)

J,f f (s) Js I,

F

-)?q

F -'rto \ tor,lf r .

*-

qvll v.

)

?

?Q,

1*r ^b o rt,'.Lt d

VA F,

vl = f lZ I

(,'ch loup? &:k Iw/<R5f (, = f-t ij ry.^e c[

t,

,blb

'{

(K 1o' U1 L,'ntvilla bh*r uv1 Cf )le+ wo ( ABR 6s A v)6Y1 -e-'ct'LLe 7f "+ Cf

le;G / l-ef C = cr(L)Qt + r*:*-*G*:.s a J ',wo tqat 83 lih : o lhe'rwi5a {q Wn € ws

g zn -) ?o ( Do , but f'tzo1= f/a. 1+o

wo---

(6ec. 3 haS ho yale-9 r. )it'1 Weresf .- &"f . t /ot'* o

5'C

29

H+o le

f ^J, clitnanh'-l-,oloh o lo , {.,,tr-rclr'o t. 1 -. (, -J 6 ( r

ie- b. Lio,rvilta 'Fh'*,

1--+ c

f,,*::;"-;; ',^:;','ii,;r "'-{ ,. l

S' i-Fo9>i(94 J,r,,ri {Cfi')=?[/^) /

;.$ Lofi^,-T qrllt haue 6 pf. K>'o +

d.. r^ryo& 60,*tt*a o*A, S*t*Q/'lro-7hic

+

rfa:

! i,"rt-,-i(t

Orl c'^,

{ct:

/v\tyt K( ,*ta,S I

t'( t s wvpb-t< 9 u,r 1-*qttgt\.n^/ tcl <

h ot J.a'r^t< C l5 I

(.1

)ltt I

{Jru1 . {'- ) K<}€

Tegu ( E I

;p

s +((tAz )

LJf tett tf I (C

r7 | :lr

fi= F =

fqi oV,.-ite J

tez 4eserma,n

(+ttl'

()\/S

d \n/

3-? i

rt{r)

\ rrrt/q )

t{^-t PI ; vov-,yLteJ O

G -"^*-^^"0{ ,* t'u*r* :t-twf LP f g , vYt t'tzt '

(t ) Frv Y:f"at-t(R*n,)a"'-' l^^t-{ sTt'l I

tf ?(p) ''9 atok 4 p(o-"e' vL\t'rn e\! 6^"s UauT

q- '. M-) (.Yn-' n"p-n'ls c\ l-pu^v<rcr tI hvfu\'lau'

( wln*l d-n U th i5 S+1 ; f q k6o't'+'"al a -, )

(z)

('c r )''fD; (.1;fut)=o

J'9;^cn-r6 : Fo, n(l

B ou.^1,'€zrn'4 ' WR ON 6 hN

tt) . X o v,'tv', Fu iinolo l'L'"*'

t ov Sl,ulo, t4 r. M ov+',il s

{avr'€ , ('t) ' D w, il >. 7

rr1.\ t^r[" o Lg tR'

+ M is ^ hzl .7b^^n

V17z e (

'. M e*-+ /( 3 b*P l- r-t i vr

?/a<c,4 A gs.

f+ S C fb,'a

.r'ft't

f,'*o t

9"^ fa"crpt nf Cr-r:6< J

Rcpa''I9.

W k. ?,(^^ 5'. (

t f f s (o-tv\ [qTh,- F.+ )

Ma,p

oTlt^o(

ukn4^r3..

A S> qv-1 llne p. t{ "* * , '}w . t[.,"-'. ?w S :

TL eo 14-L,,. 4 . ( 7*;sfeucl 6f ISot-h ?ru'tql G6yJr'vr cteg )€ar ^^V blrsr.-,efn'c 5uvfiu (p<rJ5'J , {+

^a.\ytHt l.\e-rc 2a,)15 a tulJLL*Lood 4 qc^(Jn,uole

51r(e,n^ (u, tt,y)) SucL 4\c.t ds'2 )(JN'*J/')(1"* tvt{mit+el SUtotp< Lqit is ia l.S f.x.tS-(L) )

Tt"<- vt...r*r ? . ( U r ; (* ^iz.,f.'o,a TL.nre*, )A"J 5;ny\ qshuec-ted Ric^ou, f-yfa;aun+1 ple* vr-|atat (."td ) iS c.r.,ylex or"\tt*valen,t +-{, ?rC 6f C,vIuJ =5

fl"e,u we ,tz'ut"t ,l- f ,lr,r',\A \sserynae S

T h.e^r'b.v, ( C e..1,t0.{ ^M ge I b er nsl etu T l"e^"e.r^ )Lar t | [4 qr ( J be 4 f*tnev J< J con1le.ra* *ie.-hLQt'vri,a;'-...-l J,""rt'e , lf ?t\9 r>t-a,Q 4 +{* Ga^tg9

^^T trol J-e.r,rS<- / yLAr- t4 ,. 1 1la,*( r*-4 r ( ,tt J.r^ ru|.' n, +n ll'< C4 54 lt = ? ) :

Th^ra^- 4 d Y lol il.,e Sl^^.,t-h^ve + 4-

fr; z ,.u, "n n {,-/bq

-ft^t-vq,- ? + fi , l,l.e q^,lnertal

t^. D , & at J-

r8

(^r/er 4 l\-l

fi+ S'. lrhc^g kco t Ksobuf o^7 L<>tvrlavr Surfu,Z

in 141 LeJ aTc;.'r Jf K> o +<.

or-';lS ^ o(teu JeF + S', WLoq

uLl is a. nbJ 4 v,*(h pote-

( ,'e . 4- &'nh' .o IL

d

_i\d- J.yfi + ( i t{

^ nY a 55,',-,t

A/"f|( is

L? t^ (-^J ?(u)+JYM

lA

Jo fr g D Tlnea^ uJ<NglL^{

- A' .\.If M=C rlhea 7on/ofA

^ LourrlpJ au^{76'. {wworio*t

-i(-- +D fl"t L; on vi t t< &">rr rn6{ aL;vu5t*+ poh ,

A t.u t{*-'c Me l.t^^ A S +a t,u.,. S +t-.-cct M iric,ua.{ S q[ cnnaa; fi lLul'l

AI,"^rft 1f 9tn

M , d; M= Lvl , J f<t*Sor -l *fS (l'f ) sf.

Jf ,Tf M-)TfM st. t?='- f,f 'tf ?-'-JTr*a(n"G.!cr,,^' W Vglq" tf V*6^, lt-L.^ i,V-tV

l''aa Lt- -1. t-v,v..\*, (f J : v-) v StJi-idV fL'tt-'V hcv c, (-w,od-"'Q-e (r.S )

qtr. (o*Lr')'u..= a,t) +LTd )A '. L;a,l^ Wtn'c uu (M'T )

O ;tuvmihc,,^ i? 3(rv, tw) = 3(u,w) b v,w( nt*\s "t4t2,45 , eb. [., (r,w ) ,= 3 (v,- ) -+ $(lv,Tw )(I* V [c tfu Lwi-te'v;t?n 6rtv. t,-rl fo ber. b )

A , VJ e o l (f ?6r^ta)?)rh;5 r'g 04r"-.'rr. +r VuIZW ) = -J 7rN V v/ W

gtu.a-n vu[Jw ) : (rrt )w + T VvWNot"'c, tttul *ti5 i9 trlOf ,. Ivrvi*l Oohd,tiio,.(/-D^^ tf M ;5 <c+ual7r yW mf^ t.

@, I M rT, A ) ,', ,nl&A Kd'hl-r''/ ;( vJ--: p

L

ft l"o ftt gtv I o n'r t

t v,-^ J o,^*t^* ",.1-

,(v,* ) ,=(, ( At(vt ) 5twr(9

F,"* & . T t e").LiLr^.1r, :

IL^o:zYtauJ. ?f -

* Vi<tvt '. d.^/ b,-IL fzvl-^

5(rv,w )(gu, Lawso,4-+@&rft-, )

u) (w'u ): '-6ri-i]r:, !(:li:;:\D r+ (u,r) rs A *^i;*iX )

f,."^ ).. a\ t^: - O

h "2 u? t 9uL ,{Lt* u^ A k A t" Q-v v^t Ar g ^ >f r,.b{*

* Wif,.Y 9 u b .,,o#".i i,u,*

l*o' -h ,rnin;r,ni?x- are& in itS'1,;fi"l[u|V cldsg

,r zrln tr6u,,

ry+sL s ;"ntwt

( A\'Y,)

Oe

)=Je-.tX = IL,/"r-ly =?y Y4;a

( \s

1 ,8

ln ad NJ2.vl wl

I,r

" A)-, 'J5

I +-' WV (x)h2 --rt;Q l),Lig

5,r I r+S xdtt$O t*r1v *\tl-) dW

Ath

^:oyr n e. W

\e7

( r){

-'4'ttu

l-='l q,1v1 12 )

e

,CV

pv

.1q"-- J /,cl/l

;)( ,rl

{t)'! 61/-t\t7

- J=.1

+ -''xr jovrz

( ttCn^/1 +1

.tan/-l f

(t

fu nt kdll c.atv

' ut '"'ll? ; 2 to d-t-, d

><-ry l ry q.r T1rfi y, +w,, A l,r.rr'?

'e ,:A|'t*t ?tqJ/utuuqlol-.r 1 u2

nA e- ( A tuh ) 'a , ,_'A

*.)f A k.-,--- ,) ) R

*alrl1,^c'cr? o?o'l C ),' t,l Y)^ xrtld-rqt /v4

( 't\-) roo)*- 4qw ryw !.rt ,-2 :l-7rt

Wpqtv) s.'w 'Lrz,.-.',*l) ) )1 Il )c*tt> ,r+cwt ) z ty cl2yl w q le 4 y 1^ )Z t

ovtz r?+ i \l .-.r=.r e=(r)fj l r, lZ I =tNTrto+ Qdru,,s ' ,) 2 W 1@ b\

' ^n.1Y.2 o: QY ' l-.V.,-ryn

uhpv uxlo -F .t-'6,_ulrp e Cn

,(.,? = ( Gr,:helg - I !^u,,,,e ) -)

('/"(':h<)g : ( lre'Jtet)g € y lxa, ire J- q.,a,r\)1o' , - < r i \ I

l,)

wt Aa

t,r 1 .'l,

I (x)

he ne*'ts t\

?J

o<

e

,henn^

,1

7J

: .SP''

5 qI'---"'5

, ^-Nn /,r) \,, Y ''^fti /

,Y)f lT - (4',{,{

? ie ydq : JtL/

Ir*e\ed"

t J,r' '/() (, +ll

It Ite'nhe) I (

o he .)

I4 Pp

v-1'/

.vl

dt,sT;n ) ?

t( dur''te)g + [J*e'"*eJ

t Juu .', * J*e / ple .', -'xe

W-t*l Q - -'t- Jn *, ^,i

la

=\- 1/e'rri!-=a

g

f+

( !e,' oell!-, = ( dte t 'os:15.- =i Si( ( d Ae ''re) B'*(i I 6e''rre) ?;:

( Je're ) C

p)L =u] I I_t.

)r?:dnsl"? -,.,, I ,-r,rl 5

11'. fu,4 ne.'5"?

d,

joog

J*-e

tJAe r

It

('^r "

'"'u c )lt

,1A

I I ',( vg!/e) +)g = [ *+ , ,r+\s^,=, \, L

<' g e Jng, e+ q\:*n\ ,l q-<

AI

I\

* " tI

+^j *

dlt e Fir it!, r dir ez3 p J: ! *4zvlr

OltBrTP 3t"g + drt€,.1? d"P( = L? 1-\'1J Nt frr.t> B , u ,v)- ' qy rvl vvrt ) d\1/1 wl+

^'.n) gr + 1 nn'^J B - t A',nl + n ) L'Ga4 .,-.r, t\3 - g 4 -.,^1/<rii l,q

zr{\ In2+ SNyanJ Al,l,n l5 s;\L(

t

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1^'XeoL

n .! * rr{/., Av 5t., -

f c L I l vnrytJ, ) A wy 1^ S:5t? (^nr.11

't-? F

)tf ', 2 s(n,)rv i" e,,rog

.tlp c. i

''X p :='.

t ',)

tLt /toVv 'g )T c lov

'?T LP +

CANcLUSioN ; (.?

(Y,T I r"lu*! Lv ^(&

II ,ryYTM ruae r^o) I arli;.i"J,i;"i'r',"^tn

Lasis f *,',*r;J { tasis f *.}

yl

^{a

il,

\tJavn;n1 : Altttouq^ \.;.n1."'-n. 'i. '.t ''tM,Si'rjrP \ I

Utc,t'r/C;F LHJ ffiTUbuf vtr- ve5 ard" rhetn a) u -trr+zr,,,n^a* ltia- (* J

("cnVniliA,,rn twZfic t ar1 TM1l14t 6-t4l(A^sr'olr f on -TrnA6 , aht,\A2/0 t n't' cf +T T , X i t*zo rlrve- -*tstta 4 '1. he ra; Haa -nshai

uia,, 1.,(v,w):: T(urW'), fry v,We -ffie. hue € f -t*f

dFd N JsF

t\/ Sf" f, i' a"o E.r'{i

*(rr,rf)= J(Tan,ap).-;A(t*,^rfJ=o $oF,\) t,i jf: ) s ,TF::j)_: ,TrF I

r***'+ L g*: _:_uf_l_r:u?r : T inTv 'tan t f,.v,*",* ro*

e5. 6''. r^lE ilnAJ1Jl.J{a

- 'rrli""* t ''.'ni:";'"

I

uB J?d o d*F I___t,_

lL

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ta T-pr4-T 4-

Oat

dtd a dZP

n(,) l?- i.:

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lt't,r tz (W ?l (1

t +[w la ) '

r.q

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.on Yr

t( r 3 U U&(L o( 3o

ud.. f lrl{trn 5t'

Fubini - 5+-LJ nat^'Cfi n I z latfr'-Ht; 'L"a IZl

=g ?; l^X (,*twlFr n/" I

=G t

2a* " ,,. +<*, f u^ J . "t f a,r,r^ r' S

lz l': L.:^ a;V;leo

r\) t-.. 4 (AcV. S 15rtu\'.^

(v", w \

J? [,,,Jwi nafftfft'(r+1w1') )wLT

(^k' He,n^-t- we t*tt-.^A A +v A'(nal a &ttr^ Al'tM)e& a @l*I.h /{',,1 (M\

rl

a,uA I= att b i nr(r) eA?{f)oia a(t ttr )=( &ye 4 _#,:j. ) n or"

5o f= a'=(r*5)*- ?'+ af+7)+''

ie ?'*o = i' 6"^A af c t)

t)r- =[,. ( t,',. ( r+ lwl') - fr' u"/' ) Jwr'A Jfr )'

-rb Lr ( t+lh/l') a t

cw,^ 0n, Lr1 V J-f, -o. *rt1" ds &,Y.*u,ut. I

t I I re

ur)^;G -Fl -'t5,,g Jwdndif5G".- {^^+ X?s:= l*F Jw*ntv'tf "5

<

0,.,u,-d nr'\ pr, ( _r wf s a I' )tf

L4

e y.

( n;nt : 5' -1 5"r*' )tr;

En ft i5 t'et'nYacf '

la*

t4

t e Cl+oi..t ?,,

fu*fu, f r,5

V(t) r- f [+,] Q.

C f; u*t ctw,f

] \u u o1e,r*./W Fg*, ,

IV Of q {,^^. . *t.o r^ o r,1

f; t f(")€o 3 ,.r

t1 hs,aro,

r;weLt *t ,l^"

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?q's frfu1

^ve

Ca.ltP 4 q.

[t n s i f t*i,^"u V c,*-;, tq

**: Pet$nillo"- a( l.,s(. ^c-f.Fw (rl ,ll-;+ (*,7 ) (* ^T 4

f is(r;aL'uo) ["f r,.-,ryh:c i( art"ao$F 1o^ 'n&'

tf "7 es J.c ffUyL-,* lW / A/ d^-e- Op f fif A .

Xo "f rJ 1,./otnwylv+" . (

fh;t i5 e1t-ivtar. )

*rec* cf

ga ; M 4r^/ \o* J,.t6',^^14 r a{ h"{. thwrprtfofr^#4'l u^ A/ K U\ W =) (\A V -i\U4

f{. tf 3,* K,*L,,Lq s*r o\.1 Nl

#-try l-t'q vna"l:ric b [* := dn ] l;',ro

fl*,.J. a Fq,-- ub = *[* q ,[t,^r

etr,:rk.u^A-t, qo Jffe Jttr-l 4 ioJ- E r, lrl,isK,al^Lu n5o Ar.1 r/fix *f d k^$r& Cu, l(^ ^te olq" 6a^t, Igr.

kgj : r' P'" t' d - f "',"- + *; ? Vo{. {,-.*$o ;l fw is LtT2nuy vitrW , tt-,-*-,-,

j*, , cw'), [,.r"1 ,",,-4_ + o h^ huqf M;K" )

2 u?/^ '*f4 rru'iFt br--o b.r^^rr wusl 6e !a6!1 -ywtrer

12'1

z*(",Y)L,

z ) = x *[Y,z\4 ^(r.rd ,. )

-Y-(x,z\ +W rytrPa li' r"

J * ( x, Yr

=LIiJ ;.i "i.^tr^^r;

r

" f<'nn s *

e X o ( r:v,z) - Y 3(r*,7) + z l$:l!,) .. .,

a J [(vr; )v ";ffi: ,'[{'I's 1ri, l:Ei 'i ]

Yr'IYt 1L')

) + X( ?y) :1y,) - b (try7 r t(' )b (1t..y r ); I + 3 (r sz"t,t.)

; X(eryz, K) + ,Lr,ryiL,x\i X (VrzYt X )* , (: vrtlf ,x)

+ ) (N [v,z),x \IFnr) Y,z )

r ,'(rq'l ,v) -w UV+: ,*)vx"t b'-J\ X, Y, L+b h'^-(. d"" Sf

(o,t),**? b ((olr)y,e) + 3((vr,7)zr X) * b((vz.t) f, X) 6&4*Q o{e*

e#c"

fol-io l<v<', b((vot)L,c)= -r(lvoT)',b I fN'V lP*' )o, 0T-o i dd-owr^ \^t^v+\, '|t('nr)rr, Xl

J,^,Ix, ryttz) : I livrf]fv,JL) +'((v'vl)t z' X)

JL* - i4 "* T(pnT)v4 l7^'f J'T +Jo97'J-o

@ vv-T ,+l a*i crtt T" .

,l-[x,Y, LJ Aw ia z 3([?xT) y,z

. N(y ,L\|- J [rY, JA1 -J CY'L7 + lJY',V7 f Lv',TZ1

tfu Nu' 1<^^h,.^.is

t +.',tsc,l/

,t^.9a,..r.f. VJ=0 ff Jul:Q a'utL' N=D

{r is clzor, rtu r'A u?x ^tA, N=o t'h{ t '-ol.ta }Y''

a.^ dr f / 1 eo lq ^-a-!' utt'rr''1"'\ 7aU''=-)lt'

. l'h t*Ata.& [ M,^' l,,^-'*'t - [Virr'r" L*\ ) : PDC -tv''w

{:,,."J ,v?otzt- tJ c o €4 I it ^^ ilat/[Q*' cpY slructrn'-Q*

1r .r-t L lP,^*,

\ltt--ltu.fu,liOw U.I( so u^r, rn. .(i^itt^. A 4+fe_^n+ ) r,8u\rud; o\g/w L lV, Z l = (ty,z I - TCr,z)

+ ry4-zlv:

(i{ is tr"\

N (Yt z

r/z'tr

6,a* \

)

+ rzYIa

t\is nork%S +n s-<

^ lcnior. ( chcta ) ; y ,

)= L(Y,z) + JL(y,tZLo

I

(lfv,zJ = ,,:!-zfv= rty,zJ-(zf)v )\ [Y,,92) = ylz-irv = s(y,z]+(yg)z /so L(fY,z) - rTfytzT - Tt fyrz J

= f t(v,Z)L(Yflz)= (ryr\ZJ -Jr v,?ZJ

= t crytzJ +[(rv)+Jz _, ( ttyz] r (ys)z=, L(Y4 + [Fvlt:= --(yf)F4

L (ar; r)xJ') e D dec. u._!_ I r J aYt' =' - aX l

,t v 64q' u'* [rf 4 L^rLM, vgcfr'vs = o

6hr{ (.synb i na li o n

a" Lut-,' qQ.

u"iLta o^yI'vn^-o K*'f K,at^l<n + L? y't 5 ih b Nq" I q^,, drl-v - A1irc^^ g+-rb J-qh.2

lv\ ib.,It*tal itV L . . YI ur; lnor^onr.cr*]l^-f MY+ \J tp'* 'irtt^tA tdlG\Ltyy-fya dqsis v{ TFM C TrN

€, ,7et /'" €^rT(r- ) (^*r r)(-n, ---" €n,Tgn

9 (ei ,ei ) + B(Te;, te,.) = ( or, (t + v7p, Te; ) "bw 8(,^,fu). (v^tr)t= (tv,.'r)'o J(v^u)M3 JB(u'v) \r'(. g r'5 j-L; Iirwav (via \r1t+rn-++rt2 ) ,rrrtL^h

5o F(",") + B(l\tT,a ): a ie. I ;5 a

(.1

Q;:u.rgiotn: w w^+C rvtin;*r'J )

Wc {-- r^",f *"at\ w-eJ N +b ( e ?^ff:*Fls a^".r1 tt' t

:t

K(*,X,v1 w) e R[",?rtrw)+ ( ${x,?),8{;,w)) - (F(t,w),

Tyl = R(*trX,y,Ty)

t(0 (r,v), 6[rx,,TY)> -(n(x,TY ), s(zx,y))

r[*,rX,Y,]f ) r lt K(r,y)ll )

B(z,t))(1. R(*,TX,yt

t5 ' F (', u

I= F (, .,

+

tf B(q,v) > ( erv J . E l,a,e ) )

(g(J?,v),8(r,Je))

&uras,h I"' 4/,r " ,, %

,e,V ) + & (]r,u, T?-tv )t,e,v) + n(f €,v t7ltv )

c K(e,1,€,v) -r Rbcrn,-Ierv ) -z (B(eru),6(erv)U> ta ,-!t-, S i o ut ,.

P [,nn' l.uva rgq fl *p lr rn S c."wrzJr^,q,Iin q suila(fu t4^",r< - bwf no!

I(ry2tl

( F(,

3 ,h eis:"!

M ihi,^^^q'{..1 It, C"l;bnn*,'or-r1,. to

\ t\d'soA ,4,fnva tu M

J,LV.

lE fr*c ft1 ExLter , TL'e-u t I _

L^,€. oi t'* e4 Tt "P'

I 'uf

i.otd< €+ TpM Cr?fr; ^ upr Sqttyau..-

vx,y(Trfr, - t \r'{=

Pl '.

u,[x,Y)'* ( Tf,r Y )'( [zx l'lYl'* (*l'1 Y l'"=' h.td.4. 49 7X c tY , ;e XrY SF* { ?x t-L"-r

., t g,r'W l a,J 4 Tf fr

M.r urht;Jtv^'o-lrr*, )r\rr.-.Q il is J(e,.,,.,, slr^ z-ftww-,

h*nr ,* uA ^a, + 3 oNr B €, /.- .r e. z,,u* 4 t M bf .

frlo

\

I

-FlTl& a- f*^

ol"at<

\h = ," ( e"4-, ,(rk )

ie, ;f Fr,

'|1.'9il ,)' .\k Ailr< A0 zt1

..-I-, Ai n.---

Jr^, D, tla 6VL

L[-l)')r

k'-1, "'t tnl

&u ltrtla t

,( f<i t ^TrM ,

,t 0 e.m

"6(Jeat,e*)

+i€.

lvft ttJ = (rt

# € ,\1 ...I,* tUf

-(lus, lh lt r'f , "=" l"'(J< (+ l);l=l V*'

by nlotL, € J€rk-, = t^ €rh , ,'4,TtA ; [-;u,tzt,.;orf"

fil9o r"-" hotd4 wi}tna, I I ' I ttgr ocrr*J wt^e^^

ovt'{- hh ar,t 5 xVQ- #^9 $qtr,rl" E?*4 ,t Tl,e.-rsnn TL : nA' "F, + f'A u'\i^ 'K ^ trvr I G {t"'-ttr-Z)

{v" n',-- r,a, vot(r^)= I, + - I^,# € I*, Jv^t = vot(tw'),; ,, 4+ M, also ?X A

iin.^gia.|"

rCAC

t:

!o ,u,t i-ioa.r J* f' lo**a-,,^ i f,oOlc^^^

{K' J *do"^ Lta.*-e.

f" uvr,i l. {4'5 h- | .1.1* J )

A-+K* Pietlwite C'

?' t/r

;r. y is Co

r 6u-,t!ilx- aA tr^.a\ f"',"^e ftS ortna\

Ll uvvp,4 . .( iS C t

For 11

I :aA =S( -)

f ,'s wtulofon-e- ;F Iu

b-l (f ) is uol'\-oureA V P€ f t)

Lowr y et f n5 ctag s t lit,'', J,'lk tu< W' ?rti; 'rhl",ffiXf r= 1 ,f '. A + lR.n st. \ ir pic,auri* Ct t

c^*d' Ylra ' Sl-l f iJ '/va

;n,.1-t;.l 1

fVca t,""^-r-t;,"".r.d F'' z1t z d (z't t3 )

A , Xf \ tR.* ur{rc \ h1

ntt) ,: Jo [** ^ e,1 I ,*&l

( | dlu,", ? wL l*^ '.

Asr,^^r +L* ol io *?, (KrAQ) <to

fi,"J T e Xp st. A(t) - 6ppiruvf 1,4<+4t-A ; t'U"t Lal"^l,r,u, 4 Ve'a*ialtort-a '.

T^t* !^ e Xp er. }iooA(v^) = 67

7 ?. 5 *t" *l*u u6u \-^e.^ T/t ,> Xf

L;C. uo1aLf QLA )

I-^^ 1r'.^t^^!. ho F posl;tk ir"/ {. d-fru^4^ryTb-rv.,.

T tt) A J'u.! a/i E; r( '6 -.,1{ +4",-oa,.. " \rl

Al .". \ ; P^." 'l- 4lrh carl '. 1* JPa; oa. :

?)?

l'L/rD ir,'c.l^LLf tr' feX""i l€ne*la lLosT il J€4.

o(.r) ,= \^ (l*r[r*ty,,l, ) JxJ-., (y-tve,^,aur u*^J-e.t'

"JA.t /\' [ ) , I

tq*,,^r**t Frae,l.r{.

tr"., [vn- (' .-. [vt'(wl'- [v.w I' s ti(1u,r* lwl') J'yr At'r) <ip(v) ,,,^), - ;(f[f*l=tVll a^^A yx.yj :. o

i e , ? : A K" is ^y\ rlr,,,r or r a^ f,r*.,^J ^a,

fScTL: Gf c t Jf , ar:= ;"tJo lor *,1 q € xr t

uF *',.*.=,. ;: Y e xr P(r )

D(k) - Jf € A(g):6f ov_,A y ;r^,A;fu",INoL'o 1,0.'"I ; +e.t ?ln*ta-,,, p,'.^{ a!rr^^ ( ta) scL^*Hor-,tvri*,""^1-l- t

** Let^ L or,'. a, b ;fa0'.1 gat *tn-a 14, :ca.r-t nnur' tv

-, l(*r-- / rt D;ll(a)

^ <- o/r

F^, Y a, L'. i* yna,.ysi a t4 |?l.az:)f gt. fl':.r(,f ,t, *t*,^"-1 irr"*r v-etw,*j

AtJ ,"^r"(r*4 pq/\-r^.,^tfn'u^{-,'* 4 pe., Su,u,rL S,^(",^+MU?fr 61 J+^. uy4a,-,*"-0- W un{ (a)

ix. s (,tt'iLiw tvtt,-"f*"^ e,;u. e =n (- &"u*t* ,u*/ll-l{ L,-( {p

So ;i is "I-voWy h eof,tl=e y whicL., r,niniwizq+L\t Pi r^tct^ (.s l- i r^fr3 r a-Q-

?AcT?" (,,t*y btc(sA,,Rn) , Xt i=f V:{+t*.n f-c, ,*lSo=L)t( db'=r,)',f p(v)(ro , M Jt. yr txb vit; . D(yr).dbLt k !t,,t-t,^ rb lov. (^r, w;A )*ur^1,-. b

+t^f, l; Jrm.lnr +- Vl"AJe +tu-*l"rt q.^^.u,{ {afi€1,.[_qjrrg,svlP.6+.*d.i--.

G ul fi',, t'v.(*v- a/-

i. D(g) stD(f^,e

To "S%j^" {4 L+4ow't^^-l 4f 'L1,lu, L3 ( AA c^^oA t^oz?-t;de(

li e If*xFlvt?h)=la,We S+rll havz )7 : ).,+ D

c( e xr.,

-( h o. Yc/vn ( P^p e ; Lot*o^ f 67 )

Ler 1"4)Jf , *1.-u" y:= lVis e1*Wntihvt^61/14- h dL gJl.

Gr. Avztla- Astotr' I 1 k .71

+ D.*blanttl

(rt) r+( f^(*,,1 )

Jet f o t tninmeYJion,all ta\

= A(fn,r.) = A(f^,t) <

PPL

h *Y a ! t vL.) lt'"^ l- f,

J+.

kt** h->b leF

67,^ i"f A(VI t xr

Jr,=,hf D(t (xr

f iS ^.r'oqnnv^-( . ,'(

[?" {'l vl I Y2<. 'f 1 z o

),

")

r,3/r)

?)

A(u) = J^l<e*av, (J* \p (,c) - I o (fr-l'+ r Yt l)

^ EA(Y\ < D(? ) ';" fcL

z

6p (

?0, )7

{y' itt

f @[

A(f" )

To u{ 4 la c'f

Le.r tP :tntf,40

4 P^* L (La.*'t rv

* Jf ry ,[ea(.

: tJl- l(9")\ 6P

y"Ftu,,v^rln-t* h -fD

f$ ) * i >""0(tr//a

Fact 2

Y"

),

( c'(t'wht

I

J

7r

+.,

A-J

tl

,VJd inm er dio n i

,(n*')

o

*Jh)

I t . (, , f l6.rSU't^ 61'

z, 3 1

, rx/rJ+"( r+

^(n )

er" -uvlud po,:'{< u'

A

k =1,

(q)

lro "(tt| , D(v)<M j

; "r4l , covtt/ - +zr1 ,G 0 ySolwfior+

('vlr

fir {{ )a :

k *f %'t',.'tnn -te

(f Pn,=JA

P,?'l ,^.riX Ct. -----Ll

V o<[<, , v* (ri5t. [(vtcatle s zq

('t,r,. r"* l*r1' ) t xn&rtl

pJviJg

not^A,P(?)gM'

, ?f 'et'f I '

e Ql . ttJ):=J I rO

Jr'JY'o

)e f *-6-'?,M

1,1 (t/t )

-+ v.d-o

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*v

t [rt lt ' t('i r'v' (41 -k ('h]L '^5" (l )

L-, -L qr.ctr 5,r"fif 'qs t?)qx nr

r rr.r- *l,lw o I \I z- [(r |

':' I lt'' o{'lct> - '

)

I ltnt'1^"'u +({'tl*r'\2o I

Yon^'(-

i(. i...= If !.,,*, lu, l')sdr s e(11 < r\4

.thit i, r-snfr' fraln t t , ,, \ dVev.u^i( Yi:c''^LY !u[ (ll ,rl'ttt'lt )fo

-l '- )t r t ' '\ a AheY

J,\ur !,..-v ?. b1 fii1-€a'aal^!-'-t 4 fit,,^'^ -sticJ'on '"h{-'

r€ P ,rrltr'rr'Jt J: 'u'o' t t'4

r 4ry)U n^l t^/7-< 5 u\,',t"^n4 z *

" 1. p

'1-l€ -tAW C *, 4/" qt

J qo

.,?".,{ t" t{ v a.t6 s!\+ 'a)l il ) J Jr '(x3l '1*,

fl Ir*r* {vry

I tz) h - (,>) L I

) t 2l z-'?lf

t trlr\o h1 2 <l 'td- ''4 I

yvw) ll + U c ^g *vvq

.( +., Ja ' .,a C ,,V '2 ?1 ,,! +o u )

2>

l-1, ' t,,r1'., S!')r.,t

7

t)>

h.lwlv,7l,J-d1 /

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I '1"1

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t+

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a,+

g ,,1?

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v+

)" L-*

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7>P>

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su'1

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ol.7

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4s'a

, (v)

,i*.. i *,' *'J|- u^-*t I r; ' ! fl{ "'F* ('r-*r-t 5 *[ *-o *-r't L1

( - (tt..: 'F )

*1 f^1 "o \

+ tl,. l"*It*t'-t(?rl'

t?"'YY 1 - \ + {"r'e- . ?w ?l afea^ 1$-^*l-"'.^,-"

I

o(

.* &.1,

ttrffuieh^-r*

or^ (t;W"'-Q-=t.;

J

Z It-+[tfl--+

x+A

X-+

'Lh

h,[ at'n(Ju" f )\\

o

2

\l

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fl "ol +lt l"|2

is

r+lvfJ'

{ i :- t-t g-

\*-/- ' J

L-+?tf "u-':' :'i.!d&Y jt-

i -".*.:*-

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r+[ "rl'(, lv

e h aj* u/<- o-t','- .> tI rq.^^o.^ Lv/?-. , "'^f "l!t.{,,' q'Fr -*{ fta ,.* i'* *-L W yf rv tn ,;'1-a*q

)'^[*1* *I

tiir i{'Lt :

"i\bvoop.

t/

2;-a/, o "LtenftrlT q,rh'tr'.',.

( o(.0 1"\ -_-----\

-

Jtu { 1*[ol lt

= I l^,rch) -f)n u )

\ k ;)t")A-*t ..'-*

t--u-/ l^ ,' 1 LJ/v uar a\-a-! | et^t'^-^

t2/\."' + wv'eu"'Y [? l" ] '

yi-;,:,rl',tof lL l€:'

{;(

, ln ) = , (U''f lh f *| * *. M r**i '"^'"*{

Vw,*f*-**

*G- r),:^,1

if t'(

n,ttf t

r^J\ft(ut?,;qo"r*o utq7-uL A'( t )v l,wi a f-t on.

a A (F* t,h ) a t+ I r{*tvll',ht'

\JtJL-t' tIv{of ,oh )2

\* Jr@zA"(o) = ( ["4 l' A

-

-//v I\ (r (vf I,

(of,ohL

So Wy V..'^I"** is ,*n'" % sh^b I'4 7 o

L l*C nQ J'*"'vl i u- uw )

"Loto[ 9to6;1if,, " 6{ A'1 ,''ait^ac^l gvLcvati6/t; lt c.y , !-o; *4 " a 6 S sW/<, wtt'u ,' r.r4.vt.A ',

,

JmJ" 3

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fn

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h= 6t I

r, sic.nrt,,;9^:':[u1 o^"1 T )

c..4. {'cv t: A j ( grz_7t^, t+t_Q-

(*.J ) r--r (*,1 , fj(x,y), --.,

( .5r, c Y*.Y, e t+ [Fr lt)( 5rz 3 Yx'?.1 c Fx.Frll\ 5r' = ?y,'tJ =. l+ tFA .|'

6ir' : -! t t+ tfY l' -f-'lJ IJ i -f-'ll {+ lf*l' )

.1 = C,*lf,t ) (t*tfal')- (fr.f;

F=

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A? c 3'lt +

$:,_r_ !{)iF lilfr ?,:t ) t _r,(' _r',_ ).', .

r (,*tf")'J fra I

,i't4 ! .t',1

l'r lirj-

?5

)

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Y, - Y ,

aii ) : o

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:-;,- i-

5')

+

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J.'d.

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\ crkt s,' jpl-Jfi = *hr

A |ik e;3trq 3t,r",i(l (e olto e1h/r.v. {n

= &','v(vl, )= ah

*t ti:1lil+-r,F o,r

J

4a

S ,\ru tt-

=O

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hr

:f =2,

):l

ri ("m t;i tih

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€icEd

vt

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t,itt gh",6r +4n^F

?'t'e,)i [ = o i^f i = o

t&r,d.

( * *\ tr's.*l

5o D1'"

a; I

is ?.

1=lrL

1;, 1

f* z(r,r, ) trl

]L

rJ'

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ef u^^t V. +{

'f "1 tt: ;J, rn -) -r 1.1 ^nC V-r t q:

( ! [ {r] ":r rE }

sl o e

h3 =b

s'b 1

tle ('b

=A )z)

r.J +'r., ) t

?l

Q-]

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\ .t.l )'-tl

+l

fut'Jtn Ji r'?v,) ITJT; +

nrJ.x3 +

r. ll!

ta *,^.- nr,. l; rr. \': '

^(

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tlr r)

n,)

I Je

+

+

('d )

r) )\.

) t .(+.t Jl

lbl+l)

1+.t Jl

,a ("tJlr-r)s.b +(.( .t t'J ) -.r L t? tJl +-.lr

Jl 'r) s'la + (.llt.r-r )

( , (b't) -" I bt.u)

(r

([r , r 'r ! ) , ,'- [-{.d

(t

,lJ

+ lb)L

I

t ,!r' +/ ( Aj-{i)

l; )'r)= 'l /

tJ ''J) z -

h*J. *J Z

I ( A,+. 't)+ I

L thr "-r)j'( Ar''i) . l( =/x1 )+l) Lrl'r''1 z +

,( rl^t) r'') ^*J'*Jz

)

,l\z- I |...a s ' /^J

t,7.hx1 ](

( ,tl,r) tl){1.,'tt

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(,1J1*r) + s IuAA,/ - r , lr!

. C ^hJ.xJ. +.

+)) trtrl'43 .Z +

t, t"r) P(

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