193884424 Solution Manual for Chen

(1)

Solutions Manual for

Linear system Theory and Design

Third edition

Chi-Tsong Chen

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C T Ur€+u

t'

ECE

suN y et te{

gn-{

,t/z'T 0//r4, N Y t t ffr -

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e4y6L

z

2, t kr) .Ltrtza.y (6) _e4 _{g..1 Merr/*rtto-_} 4 (h). { n* ,*Vtut< / = / _ lo . "-, _i.f cfu ,Vr.rrZV /6c;t 7 6 (0. ls|.(fu* xfu P c i ' ( u . i ) _{1 4 / * u c + .} cr, f ( z€) - z'r4) = 4'(o) -/ /t"t (z) f,trr , ₄ A'tc)=g, tfu4* (() * (3) &tz _, $ u, = 4 tr. {i{^e.a n'r/t( a) = _. r,t )tx,t q u(c-i) - q _m) = 4{ (fsr,t/ ,4 4/Ll

o*4

2' Z 8<tn t<- AIH ,t4 d j-*rt2^?6 t< o, d4! ;./e.r/ /-,r-/ _{rtaa ./-Uza,} _4; _)z{

ua,aar' _{e"td raaxor -d< A.-rZr z-,}

4Q4 _baru 2.3 _{,.!+ a /rrnzaa-} , *t+a/ 4+tl Arr,-, ta-y),g _. ( { Thrq. = H qc'' a . a ) = H u _{c - @ , e J} = H Pn il _{c-*. ro)} .4n1^1 = P n H 4 : P n H P n u

(Pu/la)rct

=o

_fu

t>q.

B.ernu.az.

nqt

c >eC tbtaxz-2'4 % ua<a,/. zth.

d r-n.o,

44

E s

2.€ ^f'1ua.pe"2?L

WF

,u<td Ul

/*

du *f?ut ,ud du

";."2-r/

J G&,

4 ,ro) * o. da r;?t4;/ ;6-et ; ( | )

a4( (J) alo nal ,4-€1f _{Tfa2 = Zta) r Z(a)}

* _{7(a) = T0) - z(p)}

, Tfuq ( r) at". G ) au

trtn/ae . ,Jtt (2), a< /tatc )(/") =

q t _{t c t} . - . 4 . i t t l urJ [v) ' t e ) -h * (u,/c/, tL tt))z 4t ( c-t ) ( t - t ) il. (t-i) U t ( t - t ) ? t l ' f t ' l )

7-/'*4 a4/-At4,f {aan )4er L4(

2,7 ,-{- *aAAi;fr, zfs.n

H (tl, to ) : H ( u r 0, .r* r o) .= H (u, xo) r H (o. a)

* d H t 4 o 2 - - o .

{.r _{n {4 ,t Vtutr*} a6f,:a _{- du.n}

11 h u, 27te) = H (e, tr) * // ( u, zo) r'.' - 4(4,.7o) = n H ( u , k a )

a = # ( h 4 r ( - 4 0 ) , n r c - ( - h _{t i l )} = 1 1 ( n u , h t e ) r H ( - n r t , - n t c ) )

H ? n 4 , - r r 7 o ) = - ft (nU, h Irl = -r7 H(a,2t)

-rtu,t _*% _u,'p&^en

H tn4, x ?c)'=

n Hk,4)

t'-

t7

?x-rl"tc rn xzT"zZn* +

{t-f *=* ufu-r-t naa}m ceu -&V't

/-.t u = n'V e,tu't Tr= mXo flit'

H {u, xe) = 2" ll ( I Y") ,.iuoL n7'/,t"

t4 (t/.Xo ) = * H( tr, rc) = H(6 u, i't,)

Caz+rAa

H (ae,ot

_{re) " H (* r, ft ro)}

- h H(iu. i t,)

= L H (u,To) = o1 H (0,2cc)

T/s< 4dZ;tr

4 ry€oo

tl (,f Q, sl 7o) = a H /a,Ac) h ry ,v<5.rr.q(/ 2+u'*-/<a d, ,

(p p, u)ttt att /fu >tznit-o fu

7lr4u _{fu /1q / HP,( tl}

ttx. </o -rteru

( P o t H u ) G ) = (Hpau)G)

(3)

2 . 8 / g z - t t t - " U 7 = t - 2 . r A t z t = ( r - X / ) / z _{a t 4 = = ( x - g ) / 2 ,}

C4x4dr-r-z{(t,t)

=r-t(# ry)

) x _ _

2,ic ,4

,Q{y'aq

4.444.,7

F." ,4,24/) e+*a)totts _/;rr'./ ( t ' t * 2 r - _{l S} i r c t : ( . r - r t i r s t A t r - , f r . , - t k t 5 ' - , d ( r ) = - - _ - - _ _ u 6 ) ( s + 3 s ( s - / )

l r * l ' { - ' t i r t r l

= e - r "

* > c

= /rr4'-A;t-og } Y A X O / X + A r a { t ( :

r y ) - t r y { t

T.ry-th 4z4l6re4-r

TAq lh'")

dr?ct^al/

4 c* t-2. .fu;

aa a4p _{4z -<z.z*tt /?} 4 4= -.2 . d a ' f f t , 2 ) - f ( l - 2 . o )

=^l;

_{f(+-y,+,#)qe +)}

Ax- 0 A x

= h s ( # . 4 ) - t ( F 4 )

_{= o}

d x + o A x 2, t t 4'{

f k) tc ztu a*p*./"t t-zibt?'4t

T/tzi, r

{ ( 4 = J

*; { ( d = o : e < / . t l & r . t 3 t < 2 > ( t < J { t ' ) u t t - c ) c l z ,ry -/-c*< L tJ (t) 4f v a

=

_{J fll4 J r}

0 2 . 7 ( ; ) t < sii) p < f b ) = o o . t : I

2 i 2

f;i'

i,';:,',

i,M=[:;:,':

: :::J;;']

6 a

t =

f:,'

:,';:)' [::,':,

::; ]

{ ( t ( i , , ) I F I 1= t'/t t < t 1 z

2 , 1 3

{ t o = u ( t - t ) , r ( o = t f o

t > o

4 - t : i t ( t ) _{c f ( t ) t y G ) : I i 4 ( t - t )} t 1 ' { ( t t r ) = | + { ( i ) Bzca<- _{/k) " 0} {ltt = / | ,t, =: Q = o . f : t / t ) = o , t ( f l d + 7 G ) ) a t / r t + r ) = o , t ( | r { k ) ) B z e ' u a - . { ( t ) = a h o s t < t ' d l z + + t ( t ) = o , f / * t s i < 2

{ (c) = o.J' 7 t; o,5) = a,7f /* z t t< J ! t t 1 : o . r ( t r a , 7 t ) _{" a , t ? f} _h J s t < +

tu

/*

f*

f -. -. 1 { t t 1 ' J - I t = t t , ; _ 2 x ( * 1 - , ) ' = 1 - ! - . - t ) ' - ( t - t ) z 2 = A = c . 4 4 7 .J = - L - - o . 4 z ! a

t I

( z ' t )

t(+

)

| 1 t , f ) / ( z > q ( r )

z

(4)

-Q : / 9zc rtau<. {t4' I = o = / {(t;,) = | - f (*) / t e 1 = s h a S t < r t * / , a z r / a t < 2 z 3 t < J J * t < 4 /tc;r) = o, € ( r - f cD 7l4z -o < t < / / < r 1 2 /*

h

t t nr! * Fz+ tt *th Bz t t a7 gr'^rl'+u f,'n,/z ₄ T i l ; ( e 2 - 0 , ) - n , l t u p , . . _{= ^ , l r 4}

Al..r- *r=4, .r.- i,

tl =9" ,r**= 4 r (/, rlr) {, u O - n < ' - - v . !

{u) = o

= o , r

- x r -- -5x. _{f 4,q}

n/z

2.ts (4' 4v/,+ ,t/eot&n's y'a^uy ,t+ 4/. 64rf d*f2! a&;LeEh-t1 (zd g - ,g a^a.g = ,xl I i' , D t / t r r < - Lt=g x . = i f t 2 . -| *' '= x\ 4 | ;, = rL dt* x, :V ed'd x, = e , t ( / - e , 5 ' ) = 0 , 2 f _{f ,} z * t < 3 ' o . 5 ( r - p , z r ) = o . , ] 7 s f - , < t < 4 R c = t -t -3 hz? 7z ' ia4, z, * ffi cct zJ au (zJ- zr) I ' A, 'oti z' t/; ( t' -'z' ) 4 i, - zcl , --l c,a xs ), 2 4 : / * * z t i 6 T '

-ft& _{i<t< lar4}

a

x., = t,

Tld ; _{4 Z-rt/u'ta4t>} zyzahz _{.14 9,}to. ,h4 e"'&, + o. z4t+t e

t o

o

o l ( o I

i , l ' l r o y n ) / a , l t

o 4{/n,1,

a l z , l o l,

I o

o d

t l I e I

L o

0 -{il,

o )

l',/n,t,J

rni a a /cicttt?e/. c-fre,<.[*r-,

2 - / 6 o i = J : - { = i , e - l ^ ,

( t ,

t O r t g = ( l , t , l . ) . f r - t , d , ( 2 )

t)e/cn- *t = 4, trti, _{*"= 0, .t , 6 7lutt}

( 2 r ' z z

) t . =

* +

) u r = ' o

I i , = - P "

* .

- ! +

F",L hVet/^.

/<d/-r44 ./"8* Ji e H u*a-// ztlz.n .oa&;e e*t,:t

tu

ft

h

- ? = - 3 T t - r o x 2 + l r . l R/z

/+

R/t

7/w n a zat4ia*

slzZ. etr"&L

J -7ho +64 ty.,v{'*-r. .*crrt -./Ct t/* ,zoty'a,rtz- .

(5)

nft;f du {yt-/,t-t< Arw/rr4* _d (t) a-o.t

(, c44

tT*"f

r ea /;//

'1 s'- i G) > l, tts.t - ,1, i r, t I sfts = (/,. /r.) {rirsl -r(,.trf,r, t f r t ) = ( 2 , ' f ' l - 4 , _{i t l} 6 s + * , 2 ,

ns'ntc,=(

ffi

- a,)irtt

t t J ! . t , ; , = - x , t Q Y3 + i^ = u x J t T t = Z t = { { = t o t c l x 6 t i r t z - { z b s ^ o ' t ( l s + * , t , )

_{* ' l o o - t}

, l - - l C t e l

l x

l o | - t J

, t''

* r ' ,

- t .

-(

| I

,L;J'

z^B

-; u 1' :

_ *

( s * r )

f . s r t

= 8 + | g ^ s S r l . \ _{S s l} T t s t = L , f r t ; ^ ! / Y ) = / t ( i l -v ) . \ t l ( t ) I A , P , s + r 'f"i' rl"*v { t- 1\

f r " l = &

=

i r s )

A r ? r s + |

Tfu 6a.q /.^ -/t-*cfi-t* _/r*' _{4 5 d u}

/ / /

i r i l = i r r r i , r r t = -

L

(ArP,,s'*t)(Arfrs rr)

tu A.*oP

fu".Eo-, l*,

,r G /, /1,

E? ). r ) o&Vzasa/o c,+, n, _{/ &} _az.z,l</

; . I , - l i T t J | -R r r - 4 , R , ) 4 t

"fe;

2.18 i,4rrr*r--f ",f. 4il ,t4//< X t { , = 4 A , c l x , = ( q - { , ) . t t 7 f u t ; . = ' t i

) - t

-

_{f r , ' t}

+

_T

u

l

l { , = i, xt

2 . i 1 rr ri - I

uG)

r-{l-+1

1;tJ-5=_;

s

- < , t i l

faA ; fua.'/*-2t tzu trua-f. __-[ ₂ _+r*fo6

i,a)=

{ftl/ itsl ao o t+nJ lrrul di z4r ,f^au1

, r . A z l

t6t = 8@ frrt)

fot= i2 =

_{tt (S)}

7l- G/.o/-',t

f/ee6dL (*r4 &- <anf,f4

t fu c kz -4)'16 r 4t t+ . )*zrtz .A+;J_{rl ')}

ry

ayzdr.*'(

z4 aA

r-ttj€

a

o

'f/r'ttt t*< 4a.e. 2.2 0 rk -zstGy ctiau & ' q P , ( r t - a . ) rJ e rlet< (,i, . r.J -t/, C'ri. = 4 F'*, Alt at:6+ 4*7. un tLc<q - _Rr*.t _{t 4r} 7/rr4t

x,1 | a -,1c,1

I I

l [ u , l

*'l'l ' o,

_IL',,J

',) li 2l

' (tr - ar) l, , 't,

R,

_{I Iu, 7}

Lut J

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!'' z tto/ ,ry ,/ttn ,a a

/ ' * ' * - , - , 4

e t = o

t; cr,rr7'"tt,

t-nrL^-. {t-nrL^-.U 4+,ztJ az /.t c<l L . . /ts) t l l t ) : - -, I _u,lsl

Cia4/I*

J

J=l-Jl-l

a,d'

'/c's

/"t

_i

['" . f r !i,t

R '

I

R r c L , S

s e c e z a e

_{r = i t , * b i ) ; t}

= C t ,

_{t '}

i , J i ' ! t I

L Y t l I ne 'Up.Ut-Un{e7tA, olg X wlfh ,^-e4.pecf _{to { E.t,irl-* f ; ? i,} haaz/ _{. uq Aaue} R , r 0 , r ! - r t ' L _{e , t} ? L s C . S t t 2 = t ' ^ r ( R r / t t ) s

s'-

_{1@'1r ,}

,

( e, - *)(,"t

f , r F r . r f r , 6 , t , t

"=

_fi

_il[i;J=[:J

Jf- u, = o, a\tl*

.

y'cr,

9,

S c c t t t 4 t f = - l t I t ) i ( r ) : c2 ti r / . J ' f y

o,'i,")

ilTT\

T '

l G )

t _

\(#)"(1,t)i

i) rst - f,o tir' t

du <e7u,a62n d(

t d ' , ? , ] a ; [ - s r . j J '

i o t , U '

-trr(t) _J

( n , s * * ) ( t - * )

: t ' l t lltpzrf ₆

ut 'ts^e

t , ' [i

*, 'otJ/o frr.lrt _{

: lL,:,]

=

[i]

7aJ",41^-t

f ut= f,r',

= L i,r, i,,st I I i':' 1

' l t ' t a J

i J * { . a - d d v W 4

cr$/r+cr+{

fu

erkl-A).

1 1 t c r l l r = _{2 r a f t = g}

t t t , i ( r = J W

ll z,llo - 3 I z-ll , = | f I r | = l, - - 3..7+

/*,*. -/r44 _* t. t/u. /.^Aot 4te,, g rrlla

,4f

_s

u ' r l l , = t 2,)i ut { 4e du >tamzafm_u _t h* a*al zrr ,t4d t:/En/ Az 4. 7tz**

I p ' = ' t r u - fr,(et,)/, -1r(/,g- !) /,

n r X ' = Ar(trc'{) _{/ ^ I} l ^ " 2 / . 0 r / / ^ 1 x , = 0 . z r t d , { = z t d i " ' i 1 4 t ' - t

J ' l

, f z l

t,= ,,/tt x,ll =

J:+

_{I ,. ,|}

'r=

_xr-(fi

_*r,)

t, =

[:J ft t,

=

t r = u r / t t ' t , l l

- -

, , r -

[ 1

,144 Ant _{+, a4/ 7^}

8?'d . ze', /*- t,

rct^+lryA ruc{a< 3 ' 4 1 n ) r 1 , A A ' a * q r , t + t + c < -. + -. t / t 2 r , 4 h = n . q l a , a h - - t,TJ2 A/L( nt/u' -u4( _?. on dttt-t.4 /-.&t = i , a 4 t 0 0 0

i, r't i

7/tt

tr,1

il'

tl

,l rlrt)/ r o 6,tr/t o

l.,lf

It /^,

_{o -1,/r, o}

t l : r a a\ , ^ _{t t s t} l r r l : - = u _{tl (s)} o I o J z

t , e

i

/o se, [n, (1,(,t ,(,lrt)'ir$r]ti l,L /,' - 5

(7)

A u na4//T/a4 . Thtt4 A-t= A' az.( A A'= A A'' - Ir, . Oo ar, orctr/t&. .. /*

7/u ahan .r"^/ t abu _{f, 4} _{f .} i

f.4^o/Azrr, ,l,J, tx lltta . A''- L1', ?"1

, ! . t o I Q A -0 d ' i o ' e r i o - c t ' e 4 t z 0 ' + ' / 6 2 I l ' o , n l s t o , f 7 t 2 o , t r y o l l o , + f d z 4 4 l O a s e a t )

'-f:l

i s

_{f ' ( A , ) = z} _{l u U , { , ( A , ) = J - 2 = f}

P

_{( 4 t ) = g , e i f r}

' ( A r )

_{= 3 - J = 0}

( ( A t S = j

" . r / / ' 4

k t ) = 4 ' ' 3 = |

rs Pvrou

trltf l; ntrq

[iJ

€ x ( t ) - i 2 ) : i t C , - 1 = a e , ' - 4 / t t

q . = t '

( + - t t , ) = ! ( * - j l ' #

-7/yl4 c41 tp-/z,+t^. = II # # # ]'

4r4 du tae&(aal _{2 -h?rt t ,} ( 2 )

n*y

e/boa

trl L:llil;uilra,.H

J . 7 t , . I t l

_{n a u / e f r h , . , g t z * a e . d z}

L I

J

ht',/&E _{q O. At .e^g.Atlir' t4 t4r4flz} q a Szotttta-, [ ;

R*yrryan(

Iiltilftl;

*"c([iJ

t?

- t J 2

3 i 0 , = [ - : ; " I

l - . 1

L , l

B = l i Y t l ' ' - ( ' t - * ) ' * + a ' + ( ' + | = 6 q ' + . L c * r

:,1='

- t

1 f ,

J l = z * f l - . 1

_t _l

l J

_{l - t}

,iB A : t z c + 2 = o .

Ttuo & p./.hz

_{L+ #}

dt tatt&a.f 2-h*+rr t r - t / /

+ t ) ' 4 '

-3'

_{6'p =}

| ; I

it e uLrzrr,, r/u,uLcf

?ac.

I r

)

4 +lonnzd, * uTufrl

u, Pd(ra-t.e,

4 t-t .r

-t oJ'

_{Tt4td d, Sa^d}

art zV+a-Aat 4,u n+t ea.A<A+t,

ft

{ , ( r t t ) ' J,i/ _{,4 *} 4 "/ dil ,tx h oro.h,d

t t r A b

a ' - ' L )

Ot l*att.t*t-Xt<,la,t et /-U K -1arr/ -rat*1 a ( r ) = e l , t - f (s E - A ) = ("-.)J ts -, ) = J { - / , s l - l e J ' - 2 e , s _{t g} fAL,Lt t6 o1z fu p*+.a.tu6.t 1.7 Ftorrt (J.r/ ) . , 1 U x t l ' ' - o r t * ( - + t , s t , + 2 d t ) t * n , t , n ] - S 4 r r * . t r r ' . 4 1 , c 2 - P C , - i 6 t t ; t ( = ' B rt t3 f i = 6 4 t 1 z * < , - I = o * J , ; ( , t J { " ' 4 " o ( t ) + = / o d z ? 4 a , - r l = o *a ^/a,4*-x. .lt l, ia

(8)

T i u A 4 - - i ; - r s ^ c - A - t e A ' _{- 7 A J}

4 6 =

[ u A b tt ' b

t ) b ] l 1 , l

l a l

L o l F * A = t

( ) t - A ) t = l : :

_{: l r = o}

L o e - i l j . t 1 l A D

A L

4 ' L

A '

[ 1 l: 1 I

l-,, I

L 7

J

7-h4/,0

at azf.rzzs"{"ira

_{$ a ,,;/L}

f r { t , A b , 4 ' [ . 4 t 1 ] - ,

i

d o c '-+' I

[ = l r o o , ' o . l

I o

t o - 6

_|

L c o r

, l )

7/rq ,., c/A dL/ 44a/A/4-Gfr-h .{ A

L;//, -t:apu/ 6 { f . aT, A'6. At[ I

o o ' o o l r r = o , t r = l l l

. - f t

o o

1 A r 2 l , r o \

'

_{L o c 2 )}

:

1l

eeryat irr /-* J ; t . r + ) r z A ; ( ^ )

a

+ r l

z o , t l

-ts -zo)

e r ( t r - A , \

( A : . r ) I A t r > A ( A + t ) ( A + t t - t - t I

, * ( t-t

_I

- z s z i

_{) ,}

3 , ,? ) ) +

, I

I

= ) I L

i ) (

A L , - J ) _ t o _e d -t-gi a 0 o - l + t

n , = [ ' : o , , 1

?;ay&.

_Ja

.v@

a^r

l:,11"

8,

t,

l ,

q s -

I

l o t d I

L o o , ) .

- t

; I o i

l o

e |

|

l-z

-+ -s

J

(,,rr-O

_)trlt

G,=li;

_i)

i ; - 4

A,=l!

_il:,1

CAL-A) f4i ts*

t a.,,4,

**f44:

?4tlZq _{2 , Tlaa iAou ct+t Ee} t*d4edt*f hrllr( &a

t , = [ i l t, = l ' , 1

l ^ o J , L o J

F n )-- z

/1c"4 _{. tile. c4tf"'^A}

( t * - ^ r ) ' = f o o

_{i : r \ l :}

I o - L r - 2 o ) L o A+u) = ,rtf (t z - 4*) = I _lS-u)0l r-) rrttzsf = A ( A ' - + r v r + a a ) = ) J ) -- o, o, o ( A r - s Z\ -- 44 4t44 ^.'4 2^e+ _{" ! 1 ' 4} |

Tlru at Jaula'tt /*" A'A'* J'''la4*

:

l : :

: l

A,tr,'=[1

I:I;

(9)

e *

v = ( o

( r t o - t z ) J v = o

. / t o j "ru<rt . L 4 ( 1 o - t t 1

- 1,t

; )

ofu

,-

D

q-,t*,

* r!'

:i,':.^:i

t'

:' ::'

:

^'

_{::i" I}

'

,

t

J

= lT il,-lj ) arr[t't,-)'l(/,,tttA+) UL-4);tLtLl L) x l

i <i:

+

t

n'

;^'

A,-

_o

)r

"i')

=,T1r*t

_{t,-l) {A''l^111'-/)}

_at

[^'''u,u'

^^'

^,"'J

=

,!lrrt't'

-A1

) t't, -l' )('l''-/") (A' -'tt )

: 1 T _{t , l ; - A j )}

''flJ*

J. /4

1r

^"o, orr

*(,t) = atr 0Z - A) =azr |

-'

A

L:

-:

_ , r

_{= 14+4tl}

_{f l}

o o l

arl -, A o

_l,

*l _;

L , - , ; ) L o

O'/otz-Li = (,t+ 4 z)-v =

[[ J

t , = ( A + _ ) E) v = [ * r )

\, = o =

t:l

r/uq ut /,t ,t

rfi i: i I i.=[o,

_{L 0}

- L t

'.',

I

o I

_{[ e d , )}

iil

ltl

r l i < j < + et ^f(

"lX.trr*fu.r2 ow ctu.6nc{ 4% t7u

a'tfe:tzaz.ttaaf _i 4/*l"f /h.*,, t% . f/t4 du t*afrh ; n-"-t)7rrtrr> rrr.d Ar /-r,4

At Ai ) = O ,a fuf, ,*7fu;

af = - o,rt|- - 4),lj - or ); - o(4

h,{ dr; c-7*a6e;, & faru

A

_tii

_l=

_[if

_J=^,fi;

₁

li'J

_t;;

_{I hJ}

fiuo (,1! tj _{4 t )'} _{H a4 t-rfiL+ec6"} _.

[LLLL]\l

fiAu Acxv du _{itt<rta_.e. . /12e_ rtaf} t/ 1 4 = O, ^Alon a Ol) = la n d,At * 1tA', olr)

er4 A =o n ah e.i41"ta-/'tz' , orr zl;

eAt, At uaf,** i ;7"t^^ *"1 )E t+nt'ta,a. d42C h4t ovz4 - o(L a I o l o

J , / 7

A

3. ti

[^i

C A \

l ^ ,

I r I

i

A',

,ti lr' { r i 3 t 1

fr't'r

ti-ri

,lr-A r 0

til li ^i ai'i,

^;

l=

*li,-,; ti-ti

^,

I

I^,'^q

A'-A,

r J _{L 0 0}

^t, 1

,ti I

^,'J

eryac-a/u-t

_{, ,\ . ^, A}

f s ) T , l f ' / , I

( a - 4 r ) = 1 "

o ^ r

I

L o o o )

$ t ? o a * d t T > a - ( l - , t Z ) _{r + q * . * f r 2} aiaLtz*Zz,f -J, i6 _{O.ui+r wA./..af+} _t

8

(10)

-&n<{ *4 J. 7au4 du {q,{,rt, h* * 4 """?* icn/a*, _+ar; _{at ,r*f*t,}

U - t r ) '

( a - , t t S t = o

C L , * Q ,

_{, r = f o o}

f?n{t

(t -,tr)rzr= s

Aol,ur'*

, ,,r: t

L i = ( a - ) z ) ' u =

| ;

₎

\ = ( 4 - , t z )

o =

_{f ) r \}

L o )

b , = t r = [ 1 . l

l ; )

Thqa are +(e.r<

z*4'a'a "{- e+rtV,:Jr..-V a.'tAg- =i _, ruv catVu&.

A a =

[:

^l ^IX^'t'

jrz"1

l , ; ^ l L e

_{: i J}

= [ ^t r' t ,rJZ ^rr2f,

| "

4 ' T

A T I

L o

o

, A

₎

n i = [ ^ : r ' : r : : w

_{: : 1}

L d o , J D o ; l

: i ^ " t

l a ' T 7 t

t t T r l

I o

_{, t r T t t T}

I

l

o

_c

_A

_l

fluat are 4&14Q ag=af _& _e-,Ag=i

t J' ,Lz" r/c.( (A -.t i)'v i a

:l

( r o l t ' = ( l o r * f , A + . . . * f r - , A n ' , )* = (f, t _{F , A + - - . ' f r - , ^ ' ' ' ) ,} = f , t t ) - r

Ttua fut a ,u jarzr-Lrz _{,16 /Al}

J , 2 o A = et g-,

A Q = o / 6 o - ,

f/u4 t<. u*t- aa,u*z _Aal

A a ut. tar{a-,

fu , 4/ a laz -'t/ rct(r^a _324{,rzazz

-aQ.L el * o

f- "tl /;,+4 ,t . T/'14 z.-a l d l L

f t 4 4 = O h * 4 - c , z z o , 7 * n & 2 r

>tqal 1"e n

, cn- A dat o<;tt*n/ttz O a*t7,

zta'ftp(aze _n / v '

Jtr /L =

"tr+ {

A,. ,42,.- J , rAz.*

1 o

= ef I o,o. n!,

t , e l

t z c L A '

4 a J,*-cltzrt 4,h.6 aua,<;fi./ ,rto

@ o, Az4-, u tuu- cE41 ..1r.L _,fu

= [ 2 0 0 0 ^ ' { ' l

J. it A , ( a ) ' = ( A - f , , ) J 1 1 - A z ) \ ( ^ ) = ( A - A t ) 3 ( l - ) r ) = a , ( A ) A r - ( A ) _{= ( A _ A t ) a} Y r { ' 1 1 = ( A - A , ) J A r t a ) = ( A - A , ) 1 1 7 ( ' t ) = ( r l - A , ) ' A o t l ) = I , t - A , ) + f * t , t 7 - - ( , 1 -A , )

a = [ ^ ' { 2 i , : ' ; ]

^'['t,

j

2

( r , + o ) , A f = o

_{f * 4 2}

-'r.l & _{cv-zlu- 4 t*} n ,?'t e+

a*( ra,&uL.ap.

ie',x t/ A

taoa

4 a 4 4 4

/t44 . 7hut

; 2 n a

(11)

-"t

,l

( u t ' e ) t , f ( e t t -o eJ''

l n '

= l ;

f / | o I

o = l : :

; J

+ ( € ) t - e ' )e ' E e 1 i r ' ) t l t A ) = 1 1 " * , 1 , t | + f r r t ^ A = ( _{n i =} i o , i , , i i . . 1 = z e t " = _{i "} . , t l t , , * i , ) : J _{e J " = , , ) r r 3 F r r l l ,} E*r,l fu.a _{, ax} ctztt t'+r.ftLa

8 . = o , f ( e i t - 2 e t ' * e t ) / a t = 4 e ) ' _{- r , r e J t - 2 , f e "} f c = 3 e c + J E t c - e ) i 71ua Bc -/,"4r2

. J 4

qftal.a&Ud _o4 / t t a.+4 C

J,2 /

.v"

_t"il

,t'I

, o 1

o | t p t _ l 5td' d e

0,,

=l: : ,t, 7 ,^ P.*t s' ir

lo

-2r --

_I

a,<

i't*

f , r t o l l o I o l f "

q o

l ' '

A r = l '

_{2 0 ' l l o a t l l , 2 r , I}

I o - t r o ) l t o ' J l , o -r r o J

,0"

=l:

_{:' ll',}

',":l

_f';'

':

_::,"1

l , - t r o ) L , o I J L '

'

" ' ' = :

J

I t q r + ) , , t ' J t t r t L I - | C t i 2 . 6 ; E r d c I l o - ) t t t - L c t J ,ild, f tct 8, = | l n ' t r ) ' f i t ) _{f , ' t}

l " ( c ) , { ? o , 0 r = r ' h

In*

:l

l l

/ J t'^c. d o l l t

2 o l l '

o t ) L p - 4 ' f t 0 J I 'Lr _{ii)) = Fo , F,) n} frA, a/.r( ^*/ f r ^ l = 4'" 3 A t = e : f ( c ) = J i / D : ) F 6 . = c A r = 1 : f t r ) ' ' f i ( r ) : > I = ! 3 , - / ] t f-itl = /''( t) =2 16 t =ili , t,r, ' 1 . = / € z . , , j , = | - i 2 " = - t g r A " t = , i , i t , 3 , A . , 5 r ' A - ' = - / c i A r / 6 2

I i , o l

_{r L , r}

_]

=

_,"rf;

: ,,

_)*

,,,

_l:

,.

_{i )}

= r / / l o : - 1

l e c r I

l e c , J

to./*t^/V, _{t*7 carl}

cl-lcLr-. ( / | q I

A , " , l e

_{e | |}

[ a ' e t )

e A ,

= [ o * e ' - t

* e ' r - e ' r t l

l "

1 € - t

I

[ o e e t )

s l r t = P o t - r , [ ; :

l r ' 4 ( e ) € - e " )

- - l

I o

e ' t

I

l c

o

5,

r ' 2 2

_{t , = [ : i ' : l}

l . o r l

( ; ) a4 ur*/*td n pn/-&* g.

A

=

_e,

_i,n','

_,l:

:' :lt:

e,''i=lt

_{i il[1,'}

_J:i'.]l'

(12)

-e o " '

J 2 j ,( _{n ; tLx tL. lLv /cr,<}

( t l l = , x c ? 4 , 4 + " ' + d n - , 4 o - ' f U ) = F o . r 1 3 , 4 r , . . * / i r n A ' ' t

Lt-c't"oa-c A cannttra ,;{L {atS, t*<

ca.cy'at*L fU)fU)

=7(A)t@

a'"4(,

,t prr*t)z/o-t-. 4 e4t =

"AtA

a m..t<(xt/* O .uo| cltt

c = I 6 e . - '

pfo,1t t u La Iador, _/*rr, "/a4r

{

' r .

2 , 5 22 ; t

s,

r

I t CT , 2 f , f , c ]t t 1 ' -2c ' f , ? ) - 2 t

=fr. I

_{, c} 4 t ) z c f t 2t't a f l 1 f l c

o

7 2 ( g )o t t 4 2 , ,:. .l-a

o

6 t - l t

A*+ P, An

1 l o ,

I * l

o

J ] ,

r t 2 J r 7 t t : l 0-t e

c,r--n?u0-L:'t?

, , : r r )

':

l

l"

l:

- t I S ' l ( s - E ' A t ) = l a I

l a

l ' r , | ( s - r ) ( s G - l 6(s) | 0 I

L

o

nA 'n B) - t-l

. ,, - ts(s)

Y ( s ) = f f i

o

_{, ) _ ,}

r - o

I

o t - r J

- z )

₀

' - t t - , s f

( s - r / s - 2 ) o

I

0 t s - t S , j -t luu 3 , 2 6 A k ) Z = ( Rcsr-, + ... n Rr,-,)(rz_n) tL' s ' n I + 4 t 8 ' ' l / c " ' + u n 7 : R o r ' r ( t t ' R o A ) s n ' t + " ' + R n ' , ( - A )

EtrA?

ttu

"t4/*L;r/

rua'htuo q

&1, ?-l% of r 7.dda dr

+74/'/b4'

uile e.ya6et-a .

obf l; , .i =/, 2,,"', ,L ,, /v du erlztrUodrar_(/

,t A .

D/.,)'-'L' = 'Z A;

t = l ' .

' f t r ] = a A a

-, .-, /* ' lJecautz 4z,t

h U) = h (aA a-t

) = fi, (a''01 )

: f i 6 ) = 2 ) ; " I t

5 a ^ t / 4 . a ( A 4 ) ' L a .

/"tz z.<<4 t& _;Qazri7 l/etfu"5

lrt =

E

^:. 4 =,,2,"'.

-', aigtc i, o: uf3zdatr ,L ( Bc) = A- ( c8) /+<

e r i /

B = A , C = a ( A , € ) s - ,

J , l d A : s ) = ( s - r )' ( s -:> . Ea, retleto

n r l t ( , - L A - t

- ' " ' r ( - , n , ' 4 ' tO ' ' o

tuy fuA _h _{4 = /, 2, - -., ,L . Thu n,+ /tar<}

(13)

{ e =

t / - tr o , ( , L l * t - t .. . , 4 a _ t

_{A , J}

=

/ k, GQI , (, h (Ai-') t,. ?,*-,

riu)l

=

+ & [ A 4 , , ( ,

A t l - t

* ' - ' , + 6 - , 4 ' ]

=

i h I

A 14 6''* t, A14 *.- + (A-,r)J

= / h ( { R o ' , ; .

Tlrl ca7'4-4-ita A. fu rrt./o'

,&al"M{ _{Rn_, ,r"-6} O = r 4 R r - , T 4 n Z '

7.t//a

4 n r 4 r A h - l * _{* i n - r 4 + L n r = Q .}

Tt{44 d du e4.&4 tlai^ta, ats,etz+.

{ q c o e t { t L - A ) = _{n r r I t} - - ' ^ / = u , r * ) ) r 2 l t s r 2 l ' = s L s L S t 2 = ( S t , * j X f r r . _ j ) , J t<ycaa&ua .( A ' -/ .l' _,-r -i tz.Tzutz/rrz c/ B J t

e?*+vztuta a/ cfu {V"Vurrn,

?xe"f.zr-2 * J ' . z _ j

Nc .7t-ta uf4a/a Tlu

/Vapaatn-tfu */Zox /4 )k?r1-{-/af./a* a.4 _/* Qtf

C a -...<-trru ea4z04;- -cri+7s

h t t r S n , = J t t ) ' ' 2 h t - ) i t l > + 3 t l 2 _{= - 1 i l t r n / , = 3} _{( z )} ( r ) - i t S , _{f h , = Q} 4 r = O . . q ) = j 3 3 2 _{t s - r l} d t r ( s i - A ) - o, l , / s t , ) = t (sr2)n I - - r ' * z r f r = ( s * t ) z r/-te,ydq/4 _{t/ A : -/ - -l}

* t ' @ , /

_B

I

W*of

:

tt?/'+ttY z7u<h-d^'

7/r. /fo.f*""u

"f*fu

; 4';N*

A .tiltzneL aitft ₄ _/ c4' 4 /4 d4 4a'f qou,

i a

( 7 f r r r ' , f n ' 1 , = . t S l = r

; , - ; J I , , J -

l n ' ] " ) ' l ; J

- c l

7tt" + )tt, = ) - h t - \ r r > r _{) n .} = - r t / , - H , = 3 = ) D t r + H t = ' J T/cttc 6a cf4f4t-, a,L. u,enau&*f. fAa/tu, _{tu da4L€eL} -r.;4 h C/ % C z = f i - J f i A l , * f u r i b , = 3 ' k , t - D t t = - 3 _{t u h r r h ,} _{= J} 3 , 2

A

:-7

' , J c

(ti =

J,z8

fu d',4't

u4adrtil&)-/.t u=[.n'l

_T4r^

L h r I

,l

q =

I r,

l P ,

t :

L P,,

et

- A ) [ , , n

L

i = t

1 ^ , . I

' J l ' ^ ,

_{l ' *}

I

^,

₎

1 i ^ , P i ;

l / t l ^ , r ,

I

-t

t

l

J

L / r ' 4 1

A ; Q t P . _{a u 4 ^}

' '

= e. (sf -A f'p

l

f , t ,

_{l l f r , i}

l o ; ,

L

J , I " f "

l o '

€ t lt

, A

4

l , A t A,, t P|

P,

₁

P > l

: l

l

P

, ) z

J , 3

_|

[ ' l. -l

:ll::J

.[:"'1,.8]

/ 2

(14)

-l o o

L : ;

I J J

f;

i ;r

[ t o r )

N P "

lo,o,

I

o'0,

lrqt q, 2 - 2 | '2 _f J " [ . . g A

-H

I f 1, H, r 5 - i ) r 6 t l

o l

- t )

q H ,

- 7 A 6)t,t [ ' r o L z - r ,/

)-ftuqi!. y',- 7 ', ,

_{[!,,r,1 i 4}

.<-v u44,

' & e e < t

1 3 il = > - q : _ r

it ; q FGa"1rtLb ji*,

heL _P&14 _{atrxr-trtr!-r4}

;' I

a eu't4' t:,

-:

l' -, . u

z J t, k{ /oa1r&k W,

n*+ pih&

-ar-ct d/r,4

4 t 4 ' 4 r Q s

I f a , l c a , 4 t a r l

Q z d > e z 4 t

l ' |

, - l

4 t Q t q s e t l L a s l 6 d A . d t t a ;

a,,(,.!

_*::fftr;o.=:

I /t. I . 44 "a c*at*F(t , h du Hz t;,. Patl?et" J,t4 , U erir/,uFZuz" 4-t!

*,7arl

a'4 -/- ?o rl . lrt yx'/"

uoArq au 4,ro /6 a'4 ,.7d/6 .

t,36

"lr /*hzo

,tubel*

fu

(r.s?j.

q!

_{V oe}

i la e az,;,/,L/'"'f'

J , 3 +

z )01-,t) - + : A =( ,l

S.',yat*" ya/ua 6 H,' JT , ! , Ae, rur

tt, , *teZzd o/ /ti/1,,

q P ,

"tt (NP) = atr N.cl4P = /2r Q' 4.rP

. s , & f ( A p )

gn &r (sIm-,a g) = ,n, 4tr (' rirt - B A )

8l n =rn, anC A at4 6 az tvd. kxrl, dt"-4 t ^ ( ( s Z n - i 8 ) = 4 d ( r Z r ' B A ) ,

-?,)t "nX*dt- _{At = X, Ua A mrrL eke(} ut*ft _{(A) = n, ,*/L} r-rVd;u _{h > n ,} $ n > lrt -. ,t/r" A'A /4 t xn eu/ "c/Ud.4

7/r.u.,, (Azr4ft or not *F .rr4( fa'nIh'tr

; nof a 6,€.4rtp; . 8t2ru.- ,tA') n,"

a.d n-to)7o'/aa' , .24oAAAV e'(tt+')''dr

)'4 Ax

VJ-/4a { 7a44 e'(4tt')-'{ r '.

U^Lr-Qi- . e/ ,14,n , fu+ lrgA' _"-cly'u'ct'

A A-tq cal aat itL.E-'- _(, $ l,<

'5,-[ ' +

L - c

t :

' 4 0 o

B eZn - G A s h ' B A cb{fl= t(mtn)/z = .e.l e = l d 6 | t l

L 6 u J

I -t L . L

: 1

H:H,

c4u.p4/ "{ /{ll, = ()-r)(^-u) - J / ' : A L - z r A + 6+ z ( A - z z . l o + Z )(rl -z.e? s3 ) f,tlf t /*u y-,e44 "f Hr. ,

l W

= + , 7 c t /

{ f f i

= r . 7 Q / 6

J, l 'f J.l A a egrnr&<,L. aU.-tl'A = A z ,/<.r ). _{/< du} *o, taeca z J

(15)

-4?a

₄

_{) = - t tJ}

{ t A l = C t , , L ( A ) = F n n p , )

I = ' r ' J : errz')* = _{/ 3 r + F , ( - , j )} ^ = -t ,j : p,-r rj)t =

fa+ Ft (t rj )

+ Po- €''oi s _{, /3,}_{, e't 1t ; rr cp r)}

t

{ r t s =

_{r z t 7 J . A k - " { : l , t . a .}

=

f'{ " ""rr-.r*

,r )r'

t

r*-,r-.r, t+a/.c

0 / ' t - t ' i

"J

u- ft-')a (+ -.) ctz : uJ

"

'*ot

u,. (t-z)dz

0

,ti"'"-c)4* (t-z)

_I"

-

J2-,'-')tun

(t-z)

n.

J

C = o o flaa w rb//€ ' ' r - o ' - t t * t \ = _{f { t u ^ r} { f t ) = ' , f I e ' . u ' a ? -€ ' + l r ' t l - ) e ' * L ' - ' ' - - J

e A r - - p o L r r , [ : : ]

- - [ e t ( - u e r e o t )

e ' c ^ t i E

₁

L

- 2 e ' E ' a n n x e ' ' ( u t - * ^ r l )

4 ( 0 = t / * t l a

cla*y e4t ceupe[/ _{cr, P.w4, +. z h- T. r} .

- e4'

=

f:',:::',*

"

_{" ; :: -"^,,1}

= [ o , $ b

I 3 o , 3 o

/ 4

7 l ^ O , e t ? t

- o , / / o S

J

e3rt4/ A n (cf t{ta no /J t

:l

l : e r l & t , ett d . ;

_{I t r}

i = l o i l

-P o J '

= A t

A U ) = . t l f f A ' t 1 , '

I r A J = n

* t .

{rr

iq,t).= id, r i?,,1 f,t,U=

, l = , 1 ' , e n ' t = _{i l a + J ' i ,} A r J e ' . / € = ,,Jo 7'il i ) _ e t t - e - 1 " 'or T- = 'gltt t g r = " i ' - l / r , = u z t e 4 t " u 1 E I ? z r t ; t A = [ n , , - t L - a o ' t ( lt/ld

^ f t ) =

f a c t . + o i c l * u ,

I'*;'t uz t J

1,2 f;i*{ ,'r.rf q _4n1.12 ,/

t : : l z , - [ , , J ,

L z 3 J z 4d

[,,

J

4 , J

B. l

: l

- J - . J

l ' [ i

[ ' : '

0 rs)

d4 ,uf-^ua/c<z

_{), * ry uaz (+, /S) L}

*'"e

Lt , A-' (lo- r) b

=

[:;",::,'J

ftdt41 t _{/,V /"<-.} _A-^1 /-,a

l c r = r e

" [ : , * ' , ' L 2 t l I s t+ 2 5 *2 .fs

----s ' a z ----s r z

i,rt=ir"tirrl'= dFl

' dtft) . f e'ta.n t ,/trd"./ _z _{t/4r7 (+," )} r q - t I , d ( A ) - - r ( < t l ' l = r t + 2 ) r 2 l - 2 4 t z 1 1 4

(16)

-- , = l ' / ' 7 t / l -- t . 7 J / / ' t , 7 r t ?

t

I

'

t ' ? J t f

o

I

I t , + t + z

o

_o

_J

a - t A a i " e " , b u

l - t ' d

_{l r , l t ; " ' l u}

L : ' o

i , 1 f ,, , - , )

c @ f = [ o - q s / ? # o , r o f t J *

I t 1

z + I o l '

I t J

z

'n (ura= t.

_h

t7o). uv

:,1

a l

a'

+,

{ = . P - ' { &

[',

1,

l , t

P = Q

T/rta dq ,/4" urtfr?d _{a-r/* T:r}

h

. l c , g T g J c , . t p f l I

xi'tu1=

l.-o,(i?/

r.';;

;;J*{al

l r A J ' ' L z t l x L ' . j

tr- T = tT, L4v -fet<

) ' t l t r

_{l = f - ' . c ? ) a}

o

1 ,

I o - o . c + . ) 2 J

I r r r t

= 8 2 3 l ^ ( 8 1

o { = { =

u4L qUAqAAB 6 il{4/;

I t l ^ o r = o , t t

_{( r , 1,*r=}

o , f

l x t l * r - t - o t , l T a l ^*r = o, f,2 / c t f , = X , . i r r d , f z z , i , = 2 a i l o o 1

* =

I o o , i o I ,

= P x

l _ o o

{ )

P ' t - f

t o o I

r ' l o z o I

t o o r J

= p A F - ' v + P b u ,

f

-2 o o 1

=

lu:'

L o - 4 - z )

I

x

a r { = ( r - 2 d l r l:* lrt Tfu. a)( 'lt"'. l { ! , , , n = o , r { l i , ! n o z o , r l i r l ^ " , , o , f 2 r , l i t ! o " r ' ' , t L ft* t4 'r"rr/ t<<.f 1...4 nyiLZ. /244 Z(*- (to,/a,:y) = /8,2 E a+vi<.

1 nr*jl

o, ?or tl

o l

'4 7atul

' ' * r ' f :

: i l - , [ : 1 ,

I o - 2 - r ) L , J

! = t t

- t a J t

Canpaat)"

fu

Q = r b

A b

e ' 6 1 =

_u

- :

: " 1

L t - z o J

P : q - t

_{r ' '}

_{= f , '}

I o I

l o ' r e t ' a ' r l

Lo'" o

-4trJ

i - = a - ' A a V

_{* a - ' b u}

=u

i _il.+[:],

! = c 8 1 = [ r - 4 S l ,

frra-e

_fu

6ii41t'z.y'rut _{-, ,j} , -t iJ. , - L

tTuucGa

,f

o

lf :".

q'lo rocti

_ll'znt*i

l -P,

tFl r - on ? rr J I!r? ! 7 + q

f o , ? o T t

1 5 =[-oior,

)

= U.,r,

r,,ry, Il=l : ',lrro

1_-o.r77r -4rl?+ , oa2.ta^62v, _.

(17)

-, 6'aa7k*-,@

y'(r-t1'. rAno.ry

d/1. ll-a -sZr.Zz nf^/t rf , Z u I x r Q_, l ' t C ( s I - l ) ' ' Z ( s ' i - A ) = C s Z : Z A r C t-11/,,f tlu t*r* c/ A ad C , u-Y

let"o-7/* *t cz+>r.ol t7afr+; ar/az -rt aa

' ; T J i l l t s - 6

i ( 2 s r Q

tx A4zr

?]

_{f , - [' il,}

: I t ; , )

'1,1''[i

i],

s Zt t Z ,

4, f a/r*

3x f a,Ld 7: fzt _{zL"' Z" 1 ,, tt,il,r< 7t ;4} V<.V "f e.{con

+ 7 Tutt

,,€,4raL+

+.8 q- *-l

d;lt;,*

h

{<,w -r?a.6

5 Z r - , = Z r - z t Z , = Z r - , F44rr, , c4 4q4

Z r = t 2 , . z , t ' t z r = t ' , = , ,

4.4d, ( f r + n r r " ' r r - . . Tlr('t 4( ia/"r z = - 5 ' " r t _d(s) -t .

t"#

tf .

u t Q . r e d t s t = , , r { , s . r - t n . . . ,

faz .Aaut'+ Aa.tufi t4

G t q =

C ( r i - A ) - ' B : ZB , (2, .r-t j:.1

=

h [ N , s ' ' t " N . 5 ' ' ' + " " ? N n , s ' N ' I 7l,r; caa{p &Ira ./v t<;"r/*'crr-6&

1, | 0 0 ril-r 4a/4.anrct;

W

& {4 e7a-a^r

n dad

*/ 4aK _{r+fu ttte} _{A^(f { e.;tztzJ*a}

Ttu

/<^af /taz tft">Jcza

at4 _{/ , 74t agaat4} _e.puo7.*t"

4 a z € - t ; v / r 1 r 4 / / 4 2 2 a / ' d - r . T f u ,

t 7 '

Eialfri&'e _{zza.fiti n afu+t- aattrt4ot,}

/4'e cer4 *?

A/A.{atr

(,

_,

_",f

_,,

_,:::l

_til

1';* z,

r 1" ) Z, = S''t lri 2. z . zr= *,, t, {r

%

d.k

/an/

^aa./ alz. &rctu 4.

- L t = E t - t

_{- ' l l t l = , * *}

I 1 ( - 1 t

* ) L t t

1 1

[ ' ; '

; : , ] - , [

, , )

,ft

4 . l t f r : r - 3 I G t t S _{= I} t ' 1 ( 5 tt ) ( s t z s _I

I f f * I

: l o

o l * f #

z s - 3 I

:

li tJ*

I #

,,,r::,,,)

: J - 3 . | ' z s - z ₎ Z = : ' q 2 , l = 2 , ,

T,{i i a + -rahatda'^(

*4aI.z,-4,r/ Cti,.dta. {A1 pl ee..tt

t * 1 - r o t ,

L l , j

[ * ] ' l , l " , t

L - t l

- < r Z t _{( . Z t * t t}

(18)

-f : J \ ' J r l - l

|

, t ,, r r t , t ,

I

=

[ j ] .

L ' E

_I

{ , =

_{[ : , : i ] t z , L i J r ,}

-',$rtuV A/41

trd/"

i =

[.:!,,,

-_?_1

r I to

1f

!,1

Lr',,

:1"!:i;J""

I =

_[:,:

_{: i,'J".fi;}

_iJt:l

fli.t _a<4l7tten

lfuu dttaz4e,,/€h- J. attq /zot _d"loo. _t/tt _ete _,; _Pnd,&tn

+. tl

; , ' [ : ] ! : . r , , r - ' z l I u ' 1

l - - 2

c J - ' L + - t 1 r u ' r l

t , ' t t a t z , a E a o i q Se,:ero/ _rt{ :

t # # J = r , r r t t *

= i r , J + - |

"E;;;

[-ts-t

! = [ ' ' 7 = i

'

t - 9 + o :

? [ , ' . ' , [? . - 1

l I u ' ,

I

L U , ) L c c ' r t a J L , ( z J ' L t r J L u r J

7/r4, .r."^/!i6c^ laa clt*,eaaz)ru 4. art a;4

,d,e'a a7a a?ftr u^ Pe4*' 4' / 2 at'd 4z

4a#t lta Al alt t4, P4d6&4 +' / /

i , = ' ^ , + t t - f z I t t - _{l - , l t ,} l v l 7/u -tt-c.e*d q t

- l o l u ,

l t l e4a*.*:

I::

:J

r,

=[":

_{:]., ,l:J}

r,

= G t t -z 'r . t ? L ' -.t-r 'z J

i,.=

_{[:: :J", . [j, :]t:t}

{ r = E t o l r t r r [ . t , 1 t i : J

F,l=

_E

_{/ l t ilr}

:l"F++l

t ::l

x(;)

=

[t!::::"",f

s - t 3 s t z t,t{ tA,uy _dq /4ou.ja. ,ci p+c{4^z J.26, ei ,.i(-i t t S = c ( s - E - A ) - t t = * , [ " p " b r , t - , r < J l , 6 r r - , . r - . - * " R n - r b . j

rtu @,,1. _{d/ frst ,tu ,ftr-uz h e}

t R n - . - , b r o . r R r b = o

l - L i t o , t , . - h . r r - 2 U4/T atz

/arM-* a Pza/4., s z6. /* lzae

o P t b = , : b = a t - R , b = c A h f , t , " 6 = o + c A l = o : e Rn-n, -, b 't O '+ ctl''at 'z S s o t L n - o - , 6 * o + t A n - r r t ' t 6 i o + . / 6 i r = t a t - > _{I r t t ) = x r ( g ) eo.stt}

1 = -*z(o + ltto =(1"uo'" t'or)4ro) ;l,ro)

lr tu):[l], d'* a(t) =

tll

{er

tp)"[f ] tue

Td&, i trlu' r/tcrrtc4G,^( a<art* /.1

, , r , =

l ' J , ' u " t . - ' " " 1

l O n o , s ' c ' ) / ' /

(19)

-X . , f t )

f

u . t t L - t r L c ' t c ' " . 1

e o , t r r L o _, _J - | | - € - o ' 5 t ' J ' " a ' r c t " t 1 = l _o I I a e - o - s t L J

flq statz f<aa4r2; *art* ti

Q ( tr tol = ,y

1t)

,x

'nr,

=l '

' ea't u J."" "

_",r=l

L O e r , , s ( e z - c , i S ) r r f t ) = - } r ( t ) + _{* ^ { t 2 = a-* Z.rb)} Y,tt) ':-xtti) _{', .tt} 4G) =-z't (t) r ? t ZzF)

t,to = e't xrro) ,

J""-('(-c) e. rrlcs dg t

= e't tr, (e) .- xJa) a-, ( "e r. rr.

Jo

= e't z, to) ..r j- arb) "'t (utt

x s o ) : f

_{l l + x b ) =}

_{f u ' ' I}

I . O J L O J r r l f e t 1

7 ( c 1 =

L ; J

+ x f t ) =

_{L ; . - r}

_l

4 /**'(.rrr4tt|rL( Arf,*;< )

f e ' t , " 1

X r t l =

L ;

2 e - t

)

X - ' t t ) = i . f

' u ' t

- e t

;

" - r ,

l - o

e - t

Tlr. Se]4 _Aea4r[.,4 _ato6A

f t''t t, ): X&t X-'trol

= [ " ' t t - b ) l k t u t o - e - c e L o " ' t t ' t ' t Tltut t ts Ine J

,Lr P |to,t) = Xtt) ('x''ro) Ak) = ' f l+, H A(c) r, lg

St"lA'rtrZn

ztaz

_&,rj

_{|t t,l}

"r"Z

] at, Qtqcos

= (f' 9, ) tu*

cika(

*ryL-fi,arprt,

fia4 ,lrf e (4to) ,tetxrou/a-&a, / u// 4) = (Q,,(tt + 1tz('tl a4

l; hrr, te) : f

-i q'( 12

ta ' j' ?''' 4 '" '1

v b [ i r " t t , ' ? c t ], ?u,t,i, J = [ 4 ' , ' " ' 4 , / t ) _{1 [}t , , t t , t z , ) ( , r t ' e , r " , 1 l4r, ttt 4r, (t.t )L ?r, (t,-te ) trr.tg 4l J

f tt t,)

.

1 d . l

J

r r t

= txp | ) (e,,lt)rQ,r(a) Y t o

t f,t+ +l

4rr( 0 to)

= 2 [ €,, t",- t, t,r']

z,(ie-) -(* %)t,,- r,{*t,)

- i ) 4,tl efto.to) = [ n, ( te. cc) L Q, (te,to) ' f t x a , 4 u { r o . e ) = o a * / .].2' ,ft a ) ' t + Q, q,

f,,,

', to, to) L(te,f.a) (te, te1 /+rtt'tt

J=r

J

t')l

fr.4)'f

* + . , ( i i o ) =

E " r , ( 4 c a ) = o- *r, (C ? A z t G )

* f-(t,ta) = o. tr(t,

'7tu

eya&-* 4r(t, t7') = Ar'(tt 4brr(4ro )

urtt _4rrl*o,to) = Z 7 'zi'{a tltt 4tclfu

.t*&c{.e;-

4 Pr"( t, to) . 711 e|a'z''|ze"

+ 4, ,+t, )

-- Azz la y',, |t, ?. )

LaXL fr, l*n,t,) = ct V-/rfa dtt

u"7*'-J-a&.f.-r, 4., G, tc) ? O. cuil' /, ='. dU" \

+*, ttto ) =lt,to f,, (tto ) , A,,(t) . o

? , 1 7

ks

X

i -t( t) +

r-'/t

; x

't)

t X

,X/

.I

J t - r(, (t' 't) 't) ( t (t. (t ; ) ' , t / / t A I A (

A

'to t) ?) C. ' t ) '( (r t ) = Xt

)) =

_i,

l = 0

- x-'fi

- x - / f t

- x - / G

'(t

t)

C tq ,(, L * t ,

d x '

4 r clrt

r(*)

' 1 P ( ,dX 4 ctrl ' f r , ) } C

(v,

Xt

X

4 6{f 4

7E

'H#x,c)

:) Y 7t) - t g = 4,r(tlQr, (c.,ta)

(20)

4 2 0 ; , [ - A / . 1 ^ t o 1 . .

L o - * r l t

t ' 7 , =- _U _{t It:H} . - r 2 F , r D = e * t r r { o ) ' L t ' c t s S 7 r { i l _{F , r 4 ) = p} d l r t c X J o )

r p )

= t

_{: l}

_{x k ) = [}

_{. ^ ' I}

L o J

" '

_{I o}

_J

f e @ x 0 I

= l

' & ^ t l = x r ' ' '

[ o

e '

r

Faan ( +. '/6 ), L4 Lat< tl t O aq<{

pc) =

_{"it x-,kt}

=

[";'" l_J

[:'*.J

Fqalanea" 6/ x,zthia S 't<t ^f,w.4fCz, zna'C7',a q . 2 l X G ) = u A t C " B , . i t r l = A e 4 t c e g t * _{e "} ' A X b ) + r b ) B

t /2 i ,tl= 4, e4,"4ft) e-4,t* _e4o,4to) "'o'(4 * 4 1 1 f t ) - A G ) A t

er (,t t-Ak)) = * (rArc,tI f4, _ ,qtu)

= dtt I un'. (,t r - 4 (o) ) ,a,t J

= 4ef eArt dt f g'Att AU ('t t- A/4) = dil ( t i - A ld ) ( ;"4 e/*11 rl r/ r)

A En4-

_tr

-tza/1'arta^-:

i=o

r{[:':!_1,1u,,,

L e - ) t )

u - r ' A t t e ) t t ' " ) t 1 I I L

-x u) = f i J -

u"fa

X r c l = [ " ( { ) € o 1

L o u'*'J

x ' ' ' ( t ) = 1 " ' - '

o I

L o

e d ' J

Xto) =f 'C c " B ' i g k - e ) t e n l t - z ' ) ' - - ) z z . ) e n - e 4,t J ?./U

1/r+a[.4 n y.><azad ,.r;nu pnli/ T = zn. A ( t ) = [ " c ' > c o _I

I

a u - ^ ' )

\ ' r c t z i r ) =[ "&s k c u T s 1 L o e - p - ( H u i ) J

f t t = { r y c , J =

_{( 5 - ' . l ) t} Q f t . t u ) = x f t ) x - ' ( t o ) r [ n * i ' e t r t _{c o o ' 1} L o e''ti't''a;

co-Tfr {ruruftaa alfan, i til = P[() 7 (t) t"*(

ftau.t /atrr" Q2 *-fittt-Ftei'

/ l / , _ , = 0 ' x c Q # . 2 + i = A 7 i t 3 a

{ =

c x

tr 'fttttt A - Ptt)l p''p)

= [e - r , t A - e ' 4 t r a 1 g a r = o

6 ' P k ) I ' o - 4 * I

[ = c p ' / ( r ) = C " 4 " +,2.f f,iA = c-e)t { t q a = ! ( L - e ) = - - ( t t - 2 t z r = [. n), " e ) , _ / ? _ s J - l ) J " 3 r l ) s ' - 4 J

(21)

A nL - ia rnuorrf *.r/c7 oEzz,

I s t - r , r r

^ 3 1

_f

t

_l

i = l r o o

_{l r , l o}

_{l ,}

l - "

/ o J l ' J

L c

z t x

r,16 /(t,.r:;:r:;

A {/al - r,vr/tta/ ".-Zr/.rfe i _{= o , z + e t e . a t e f t ;} / = A * ; $ e - t y o a e c4/'t'41 _{Sl (t, z ) lah nsd lt erp,ualz/} a4 f k - a)., )( ,nq,zq {q **4 "4

/)d 4 Z*rzo.t- 64Jiz - )a yautz-.t ,f affraEr4,

^ .

_{s ' t - _}

/(sS =-

5 t ! r ' + |

&/ urtl = 4tat , fu

i r s i = i r s t t t s ) =

_#

catd

yfd _{= o.i t gnt t}

q:'fud _{; nc'{ fu,^4bc/ . .tuq}

/a4//'?t4 s; i{ efBO .db/-L

J r

, r : r ' j u

4 r Z o - a / . , _

/ e - t t l = | e - " l l u . " l

_{= e - n t < |}

ft *l t.

q *

_V,u6+,

a SflBO tf&{z.

- c E

r f u r

J ( { f t ) l . *

r t u a

R . s ) 0 ,

, &

lf,rot 1 J t! rctl l e-5'l dr < f*,r1e21ctt

u o v

( c'

5 - 3 , n r F

I t l t n l e = l # . t t

= fi , 1 , . r s l

7k Aa^c/1+/"*rErL fu u 6{ kj a'

ULq6o

5 r7

_o: ??

,; n,{ B i8 Q t6.t1,,

' l n

/ k ) , r ,

7 - ;

i ;

ir't=J tSietT

==fifi.

(22)

9 t t ) - q ( e ' t ) el r(*) = 6rd. zk'-f r r c t = g t * ) = a t ( t - t ) - a ' E t t - z S . n a J d t t - 3 ) - 4 + 6 7 ' x ' 4 ) * ' ' o , @

J

-

, brcsl 4t

'=

Ialtlal' * 1a13

* " '

t @

=H Zlt =|fu q tat

<t

L a 4 ( 4 1 2 . t T/r.4 at _/441)-{'4 df afi.q i BLBO f/u./ du ' a f i / r . ; grT0 af4/4. It u BIB0 4f,a/,4

q B

! r 6 J

= i ( o . s ) r t t ! = o , / . 2 , . . . .

f q t = 7 t s c a 4

= #

W p&, _{Zr) atdz.} _{au ua.f arLd.-.,}

444 41

noQ-- 14 Btg7 Afrz/,4,,.

5'l _{Ifu aro.fui} _{ttod e/f,/i+ua/4&} _{-t aaal /,}

zf44 _d+/

"P /..t nef ,*{ryhhd-,/*

,e6/4 _{)2L ,t4g4} _nfe/&..

,'tO _{ffz *a^Fi} _{/1aa zi)4oua&</} _{-/. o. o ;}

Atd de

* rd 4d ryr7f&e"(

4^G/'4. q d4 -uacafu-f,*

_"

4 4 r'.uf& .Aat a( 44 ,ftr)-.l-^(

P$rrr,'Z ,74,

ta"'/{

/a"htr

"f/er-fu + odt+ -/,

A/+ &

Tfi

a ,f#

A6/'/'- hlc

ccrt"l a.d zl* "+t:.'rt€*/"-5 a'aazu>fA

u;^. A =0 :

' f ' l c

( n - t r ) v = l o o

L 0 0

u*Lt /r/)a ^6co 4

A"W.lr'lf

% ; ; r 4 4 .

f o / o 7 ' " ' 4

c t o t J ' .

'rtul4 taz

_/cda

_fr

al I ;

( - t 1 o o I

i = l-;t_a.!.t_l

L u o i o )

aa4 Au q*afrh;

n*/;ra14

4r../&

€. t / fk balr^p fa4 J.f;t ."4r- -/. o, 4 )

ry

AlzfA&:orp i zat afryry

b6//-d.

dz

_ry&

Al zfea&/

aa*z;ZJ ait( _{) =o '}

( t - / z ) v =

_{[ ' J}

o o

' , 7 ,

= o

L o o a l

ae& 4 *'4 4

F* 4-- /, u,t rlao<

. / l a l < 1 ,

art SoU"art X pd/.L rG) t o - t gtt) _ J I I

fb 4rantr"tttl iyrrf er r)Ea a4 At fp*C

,f,6 irrs=

_#

.'t u(,t) = J

tla4

_7tc)

*

ifr. J __

_d

otr uts) - ui. zt, -dtr*

{rtt *

lirir;l*^

(tt + a ir;t> )

= r.2 g, 4t41 ( tt t /, tt)

t , 7

f r,1

= g-,

t4";'

"-',o

J'' [-;J

= r : ' l 3 1

I T f ] f : l =

, J u = o

+ s r I - 2 t _

Jr 4'4 { a4 /Ltze/ ad4z.az,f

(23)

^ f - t : _o

_ o .

_I

A s l D l , o

t I

L e i o a l

JrAAd

_{aw fu+da,t}

_{64l ^wffir:ft}

*fwcf?r. _{Tto" )6 {etdarr} f_* u

?:P

L' h6r na6*z(

4a//4.

6 , t 4

f i = l _ : -

' , 1

r ,

Y ' 4 t

- r

|

' f d ' & r N = r

f

o - 0 , { l l n , , n, rl (r,, n

| , -t J1',,,,

o,,)*l

n,.r::]Li,,

_{-' l=f}

J:,1

?*a/

ab P,,

jlt* az7:

( t , l ) ; - g , S D t z - q t r r l t = - l 4 > P t r r = I (z,zS , _{hrr- Dtr.ilrtr.-)ttrr=} -l t hrro t,5 ( l , z ) ' ' o , f i l r z l f r t t - H t r = O * , r r n / . 7 f

f r,r'f t I

t l = 1 , , , t l

f r

/ tA-ln /*^+J

ru,r,a'r r.7 f 7 o

. 7 5 1 t . f - l r / > O

M u pe;rt,w clLP,'t/", fhta cLt( rti4.ty,

.f, tS

l::,::l

ir TJL::

i t. t): _{hI.- p.) f nr, -- |} ( t.l1 | -a,, f hl+ + t,,f h,r = o ( l,zS t H.r2 - Drt - Lhr.l - hr"= | fan, _A/d1 / a,v ,pt, ,-/rta*L htL = +,8. ?rltt -- 2.2

, = 1 " r , 1 1

- , '

Lt 6 '; J

Poti4* e'he

7lr4.z ,& _Qdr,rt ///t4 S n laa a7il-6'/t

b4d A&t, /. &t a u1^e4t4, dv 2-/,2'*'ai4d

4 A a',/ 'o,5 to1'o,f, . Bad 1a//' rye

"z-^( prud atd Jst' naTri'te

2a/ -6-a'u /,

7:l[;,,

j,J=

_{[ )}

_i)

Tnrr=

/,6-5.r2 fk naE,.r aea otttuzt*, _{6,, ?, /- 1 ,.}

d.Jt fu &o4ze-&r lnr^{zt a }rer

"VryMr

46t4,

&{a fa*da

i =

_["/j'fl?l

Tlu+r,r a nau{hal/f 4^6/}lr '

ffu n"A^i tlcV 3441 Y'aZrza O,l. t

f ad n _teulaa fnrt, aa i P,t{. f/* au <qla6p,- u *f natytaZQ

";A=

f i:J"'a'a''

) 1 4

^=r':":

_i\

L o : o

a t g = e t 4 , o ,

* r [ ) , : , , l r l

L)'' 'l: A; )

f u , 4

d , i J a/al € , 1 /

a/;/r&, hlrl- % ry ry,?6'14r.

5 ' / 6

_{/ , r A ' [ ! f , t I}

L a o A t J

.'t.t r H4 =

[:,i,'':,:

La,e., (J-et

- Ft'li --' - N

Af ; o&-a* t(al ell -,i,aaua/'zt" / e it'4

ffa6t 'rral F*rs /r/+.1 tt ti

pai/tl-At n'L/4)r.L _{, tltz enpuft} f F I f o ' Q > c l r I I n o | = l A , Q 1 A r 4 t , t . r 4 r l = ' g

[ ;r'J

L^,-n,

't?q,

tot J

= 4,

_{d, o, ao, f ), f,-^, ^1r-^,}

_I

l,'1,'

,t;-"i lr'-'lil

= (, 4r ej (/,-41)0t-At) ur

frr, ;^,]

= 4 , 4 r 4 3 t l ' - A , ) U j ' A , 7 7 t t ' , l r ) 4.t Q h )*nie+? ₄ 4i+ O a.-a't A; *+t di 4"f. Tb4. g l/4 'oa.4 s aa4 kl ,a P&ih* ,L/4.rrl, . ( Mle+y Cs)

A

(24)

--:'

17,,'

f, : J i

d p,o^fri€

d'/"r.&o

'fuut <.t _{t t} A'U / t*4 I dt/t'"t4 _6z-cv-tt<-z ' _{( a , t t d - r} - o , g / + z J tlt ' = - a . o 3lg , .'!4 M{ _/v*Lc-7itu( _ru"rr-tl cr-tz 2 t z ' 4 { t u l - /.?xt ) = gr / _{r . M t} o < t p eoi-Cue de _hd -L*"/ _,

Secorraz-t'ttt* x =

!6,u, * , ,'nj *)

' ; . r ' ( ! { u , ru;'s)*

ax zafl ulleft fu tediZt" e&/4,).Oxzz,

4 u, ? /ry

tu.{nre6*L

ru"'D* _{Ft, :t} _{(Hi, - u.{ ) aat4 44^}

,tzc4 t7"., h. g-x"34 ,*fu

fr

_{, = t ( i:, !1, t i r'J)=}

_[-i,

_{;",' ]}

,l-f 'a n*r _{V H;h.€} o{4;";n &-aazo<-S,to N {t,.5 -- e zltt -tc( " /* t >, C J ' t 7 , " , z t l d c . = s - ) t c l { n u ' t " t , r . = : B r 4 * ^ o , c+ pc )" (Ar,/t)<o. % pn/ht J, /?, ue <Cn,t

'ti (A +7 r) = rli ( A ) +/ rA*.

,12[rt.' tA)]+V't <a 6L Rc ).'(A) < -/

. f ' t f f t u - A r r u l A = f ) N

Pt -(t'0'), (tA)= u

C { - U r O c r - . d lJ > o . d / . .

I ^ ' ( /

n ) I

_"

r l x a I A ; ( A ) | < F o l H Ht^

l=

o

i l

%

,4{

u

f z

L r l

I a.rs"s 1

L'a,

a,'(2 J

to _+o e T t o ( t 1 o , t L , e / z 4 B = o ' " Jt"'d. = i' (on- eto) < | t, fu? tt( t _t{t| _cVO, _{tt< tc/4}

B = d"ft;e'd. , l*u-- u.f eilt

= e-)tk, -

"t")

- (e't- ,)J

L'

= s - L t [ - e ' " - e c o + z i I o Tht'o du aq ehn u I fB 0 ala&(t

- L

t e ( o

'4 &-d-;"{ _P*'-?"/ nio*o t2'L'

O a/4 _{- 0, )S . J'at e,(aQt} _{, *, P}

'' "rt

J

,Lt /,; H*f pft;h).

_W

tuuz<z

i4

fa4 lr?tt*L& o1t 2

/-- "tl to d t v tt rloo at 1a.&" h A , - c ( z r t - 0 . 4 Y ) ' = ' 4 r / o J ' f

BrB 0 fal+ .

1 8 A ' 1 4 + H l I t V H = - N ( A ' * . / I ' ) M r t * 4 (a + V I ) : - N % r r a o t * 4 p t > o , d t 4 4 e l ( e r f i r 4 -,ahra "/ G+,kr) ftc* xra/ild.4.i eal

H r , l '

L /.4 -r

I tr,c) = .+ti t (e-tt-z) S u, e f * *

I , I X r c - z s l r z

= u - ' [ e ' - " ' o ] = t - a - r t - t o ) - t

- ,

J e . t ,

4, - c z = e x L1 1.a. . rt'- t)) = € t S , 2 l 7 = t t z t t l _{, t} , d i . :b 'ea/a _e4rxazit*.

n , r t o ) = - t ' * '

.f, 2 3

(25)

-8 rtrz) = e't' 4 tt, t; ,

- t z - e t ) C o 4 < * - . : t _{e - " ,} U rh/'o _zilt EFa^6cr* t4 ( t _{, ' t}

J l { k , D l c / z = J e - . ' u "

-o _to . i 2 3 , i - t o I

x = L - u - t '

_{o ) r}

_{h t o ) o}

i,rfl: - x(t) '+ x(u = e'+ z,{a) *rct)= - €' t' r,(.r) = - e-1"=,1o)

*

\rr)= o,r. fe-t*- , J z4o.t + t20)

x(o)=

t; L x (t)=

_{[:,-' ,.-u}

r_

_{, )J}

x(o)=

_{L , l}

_{f ? | x(d = f ? I}

L t J

X r U = [ " - ' . -

o 1

I o , t ( e - t " - t ) t J

x-t(t)

=

L".o

,, "-4) i l

a qa) = xb) x-(bo)

.f

t- tt'6)

o 1

L o , r . (u - r , t t o - ; + , , )

fu ro>,6t 4 c V to. */ 4Af 4

f icrr"S ; /fru4&4,,fu a,-2 e/'.h,

d ^"Trh-q dEJL. d ructt'tazV

y

_ft

ti $t4botll +o cta

t+@

n ^dtf *t{

"/,8{

a/rfrae/e ?w,

Tli i ,nf Au _{&,1 , T/ura 44 1r7',',ZA^}

d,rtlt </n'/ry

aEU<.

+ t > - a z ( a f" a/! toq/ ' 6 ' " t S v < e

B zB o 4514

B e u . t < .

_{1 4 t , h ) I = t " t ' , , e}

_a

t + @- k -7p.rrfr*^ d n*t nyq

of,rLl4 .,')t& _rynpfeiaea 4fi/4..

,f, )Z _{F = €}-t',

tt p lt) = e- tt or*, Ftxl=

%

(i,7o), & fu44

t r = f P r c t A o + v p t l P - ' f t )

= f r r " - t ' - 2t e-"-f

"

t ' = o

fAou Al ef)r"ofu e7r-a^fr.U i

= 0 , i ?

= e-'E^* , t

f t t , z ) = c r x l p 6 z ) B ( z ) : l r / x e

rqz- u?'<ez -?ru ,1LlrLa4tud *)a

'%

_at

1,<afat

a' BtAoafaaa,

Tb ;zv

i = 0,2 -;tt *

o, 7Au4

z, or,,aEil

t4 naa64'%,cG/'4

tl a .d

%-f

,A,Z,-4

lfaiQ

7/u f,ara/.ft^a.A,:tu _{? ftl = e'tt} _zo

n{q /y-V-,r-*ryrh

& q a n - p ' / r t l = e t t A { A 4 4 d

Ttu/*

_{,"^Ae'iA? e.'d %ry,e}

- t z

e

u

f = i

- zto e-z

afaaZofiza

(26)

el4/G.L ₆

,

e(C) = l. u*Trollollc

.f

(0) t /. rar "-h"'*aU

o= [:

-,'

f .r

(o) = | 2,or

_"t*"

6,5 fo, d4 st<.G

_n.^6;

n P&lt*6.t.

an nea( .lt'J . ,rt a4 a/nu,q/xl*( ){ra

; lt/i,u( u du 2a4r t.A/,r- t'r*4

4 a r o f f '

_{' r t cf}

J ,

_{I I = f I}

r f 3 n J f

,

_{I oirt,-,}

)

- I (

I .'^") )

d& _{Yt t . (Naa *d} _du aar.f'-1/t/"2;,

a4( tI4r,q7a/.,/4 id-itd *u a*/<;a

A 4t Exr /+ e*-f+U^/'L a/41

% ' Y * )

Fb du .n& "f e6d. n P,v/,44 6,2, W . t q a . ./t=2, /r= |, /=xlrrrf/,,H = Z a o c l P . 3

6 . i

I t o

C = l o d - 1 ,

_I

L o - t r )

( r z I

O =

l - ,

- 2 - l

L / z t 6 , 2

fo anJ=

o | o I .tf 4t'4 ^4+4 _Arr4fel 4.?-,a,

o J' uroZ*ot(a44c P ( 0) =t 4'aotro/4

6 , 3

t A B A ' B - y h B J =

A L t J

A g . e n - ' B f

{ r o y A ' o ' A " e l ) = (( t 6 A B

" A h - '

a l )

"l*'( 4

4 4 n rf*/nl

5,+

!-,+,

_{BI ,**6+qnl4. e>}

Aa-4

la,,-tz

A,' o,1=, P *-{ s (tl

l - A ' , A r r - t i 0 ) V i h t a q 6 , t , V

n a.641

f- **f

W

4A.fb*atat,

4 t a nel an _"rf;'*/t-, d4 (a -tt) lto

,4-*rQ n . Ttuu &t s.6/*ns.r t&k 7^' aueT s, )

s+ [At1 *n--tl _{] *ea N} .1,.ra1, ^44

<'5 t. tr,, A, J u*64f "fu .

l o t 1 I t o t . o L o o : . 2 o t 1

r - t I

- 2 + j ,

u=fi

L o

6 , 1 l i = t _{/ * u l l i} & 4 / t = f

4 ' 8

_{u =}

[ : i J ,

r

f ' ,

] " . { ' t t

' r x

c = [ i i] dt 44e{ ,-' '[l i]

r t u 4 , p = [ _ , , i 1 o , - (

P4

p',

-

_{[" itt; :,1[}

i i]=

[::,1

6 = P B =

_{t l l 6 = c P ' t = i z r l}

/ /tt4

6

f

v :

{ = &/d ta

V = P r ,',rrt( a.*< /-+^

du

%&'

f

j ' 1 r

r f

t 1

L d - r )

l o J '

E z t l f ' r'; _{u'+' /< at&*ct/}

du -f*

i , = J i , , q

I = 2 F , l , = 8 =

i '

u e -r - f I - - l o u - 7, . i r . : - Tz - 7 2 + L t ' l

L: :,J-

+ [:J

,

f a - t J ' z t > u - t 1

o' J . l(c)= |

' 2 r

(27)

6,q Tfu oG,A ,f^"aftA

_{&, Pa^r4&*, e . s}

; ,t eva-/{ n du /Lr,, ,/ G.+o), tiad U caA /4 -+tdtaz-cl 6 ; , - -rt . + tt { = o ' / t r 2 4 Af u ntf d:ga>a-l& . z,/1r14 7 *q /r< /a^4r4 6

6,/l SoAd*,,

ry

I Q, Q ,1 t4 ,rE t 44afrr/t , f = 7 t 1 ,lt/,Lt n nz 4/Zi tva+a/4

6'ro n&, e4-ua? 3.t tz ,q.r,!, u,<

'412 4a/ _{*J n n{ @,} _Lr)€ A , I O O t O_, _t

o A ,

o o i t

d d A 1 l " o I o o o ) i o o o 0 o = [ - o t o x l L 2

z 9

xr

z3

, , , ) ,

v

r/rzt-7 ,15:1a

ta,

o,l

=l';^^:

';,X:,]

g' ff:18=f';,"J

llll',1':;::',)llrlrli'

u; fu enoCe; t 'f h^ 4 qt dl /.,, t, 4 ( 6 +*) aa4 ,aa /q at,lqetal 6

['iJ=L^;

:,]L;Jr[',]'

t l = E t t , [ : , ) fh) lz tz4f.Lr//a,14 aal 82 ztci AAf

Dy'fu

I p,1

_{-- tg, o, I}

-'

L , t

) '

,v^

L;l

l,*,G.'=

_{tiiii ll:l=l:,;}

l

eLA P.. Q, = 0 B.tst^at Qr ,qrri,& _{4 *t!}

I";""4

)4^otoh,r

e*Z/"xe ad tB ftB

.-. _{An't Bf} _{- O} , uc l.ast -p r f j ' = o _{" 4} P z A Q t = o (*rVot- tjt A-ra*-'aZc" 7 =[F:J'

d , = c C Q ,

Q .

l = [ c Q , c o . l

8 eco-rn Prg = o o^tf P' A Q' = O' az

Zre

n b' d/ /**" $ t's"+os

a"1

at1 l* ,u-d44d 6 &t' co*64/"/d

i , = P , A Q , { , * P t $ u

t

= c Q , / , + D u

& r z H

7

-laa./ yza"r^fe;r-t 6 .a.<rfr*t Q.t u,e

P Q , = f : ' ' 1

L o

)

zU /<,taf h, ao>+v *{ P f-tZZ P, -uaJ.latf _dp z t

i,

t, ;, x J (,

TAad efu n'rya6c'- c:att {* '<'cal+ta"l e'

[ : ,

I l ^ ^ , ' ,

o ^

' l [ ' , r

l r 1

l 1 '

l = l

o ^ ' o o

[ [ " '

l - l ' l u

l ? | l o

o A r , l l * v l

l o I

L * , J I o o o ) , l L r r ) 1 , , )

V = [ o I o r J i

%

C-e",t/ 6,8, u.n unol./4. rhr

A1 -<to/t*<z'/ -?fe

n e-,d/a/(

4 C**Au7

6,0& c- F|. t'1. t"4

-11t Aq( 4t a.4 7$ oLt ,-{ e/At"e/'d

tt''e u%

_{fu ef4'rfu-}

'4

t l o a l Y.- /a