193884424 Solution Manual for Chen

Solutions Manual for

Linear system Theory and DesignThird edition

Chi-Tsong Chen

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&tz ,

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q u(c-i) - q

m) = 4{ (fsr,t /

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4/Ll

o*4

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q t t c t . - . 4 . i t t l

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(u,/c/, tL tt))z4t ( c-t ) i l . ( t- i )( t - t )

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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 ?n4, - r r7o) = - f t (nU, h I r l = - r7 H(a,2 t )

-rtu,t *% u,'p&ên

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

(PotHu)G)= (Hpau)G) / * t *a ,

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

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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 ( : ry ) - t ry { t

T.ry-th 4z4l6re4-r

TAq lh'") dr?ctâl/ 4

c* t-2. .fu;

aa a4p 4z -<z.z*tt /? 4

4= -.2 .

da ' f f t , 2 ) - f ( l - 2 . o )

=^l; f(+-y,+,#)qe +)Ax- 0

A x

=hs(#.4) - t (F4) =odx+o

Ax

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

T/tzi,

r{(4 =J

*;

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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 r0

2 . 7 ( ; ) t <

sii) p <

f b ) =oo .

t : I

2 i 2 f;i' i,';:,', i,M=[:;:,': : :::J;;']

6 a t = f:,' :,';:)' [::,':, ::; ]

{ ( t

( i , , )

I

FI

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 yG) : 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 ) z2

= A = c . 4 4 7.J

= - L - - o . 4 z !a

t I( z ' t )

t(+ )| 1 t , f )

/ ( z >

q ( r )

- z -

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 '^r l '+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,t l =9"

,r**= 4

r (/, r lr) {, u

O - n < '- - v . !

{u) = o

= o , r

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n/z

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64rf d*f2! a&;LeEh-

t1 (zd g - ,g aâ.g = ,xl I i'

,Dt/ t r r<- Lt=g x.=i f t2.-

| *' '= 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,

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cct zJ au (zJ- zr)

I' A,

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t o o o l ( o Ii , l ' l royn)/a, l t o 4{ /n,1, a lz, l o l ,

I o o d t l I e IL 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

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) t . = * +) u r = ' oI i , = - P "

* .

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tufth

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R/z

/+

R/t

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- J -

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

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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 l6s + * ,2 ,

ns'ntc,=( f f i

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!. t ,

; , = - x , t Q

Y3 + i^ = u

x J t T t = Z t = {

{ = t o t c l x

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l o | - t J

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v ) . \

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I

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{t- 1\

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i r i l= i r r r i , r r t=-L (ArP,,s'*t)(Arfrs rr)

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

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{ , = 4 A , c l x , = ( q - { , ) . t t

7 f u t ; . = ' t i) - t -

f r , ' t +

T ull { ,= i , x t

2 . i1 r r r i - 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 ,fâu1, r . A z l

t6t = 8@ frrt)

fot= i2 =tt (S)

7l- G/.o/-',t f/ee6dL

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fu c kz -4)'16 r 4t t+ . )*zrtz .A+;Jrl ')

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x,1 | a -,1c,1I I l [ u , l*'l'l ' o, IL',,J' ,) l i 2l

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

R, I Iu, 7Lut J

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

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t; cr,rr7'"tt, 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,tR ' I

R r c L , S

secezae r= i t , * b i ) ; t= C t , i , J i ' ! t It '

L Y t l Ine '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 s' L e , t C .S tt 2

= t ' ^ r ( R r / t t ) s

s'- 1@'1r , ,( e, - *)(,"t

f , rFr . r f r ,6 , t , t

"= fi i l [ i ;J=[:JJf- 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,a*62n* d(td ' ,? , ] a ; [ -s r . j J '

io t ,U ' -trr(t) J

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

: t ' l t

lltpzrf 6

ut 'tsê

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 aJ

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 =JW

l l z, l lo - 3

I z-ll , = | f I r | = l,

- - 3 . .7+

/*,*. -/r44

* t. t/u. /.Âot 4te,,

g rrlla

,4f s u ' r l l , = t

2,)i ut { 4e du >tamzafmu t

h* a*al zrr ,t4d t:/En/ Az 4.

7tz**

Ip ' = ' t ru - f r , (et ,) / , -1r( / ,g- ! ) / ,

nrX'= Ar(trc ' { ) /^ I l^"2/ .

0 r / /^1 x ,= 0 . z r td , { =z t d i " ' i 14t ' - t

J ' l , f z lt,= ,,/tt x,l l =

J:+ I ,. , |' r= xr-(f i *r,) t, =

[:J ft t, =

t r= ur / 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 i7/tt

tr,1

il'

tl,l rlrt)/ r o 6,tr/t ol.,lfIt

/^, o -1,/r, ot l : r a

a\

,^ t tstl r r l : - =u tl (s)

o I o J zt ,e i

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

- 5

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

, ! . t o IQ A -

0 d ' i o ' e r i o - c t ' e 4 t z 0 ' + ' / 6 2

Il ' o , n l s t o , f 7 t 2 o , t r y o

ll 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

((AtS= j " . r / / '4 kt)= 4' '3 = |

rs Pvrou trltf l; n*trq* [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,.HJ .7 t , . I t l n au /e f rh , . , g t z *ae .dz

L I J

ht',/&E q O. At .e^g.Atlir' t4 t4r4flzq a

Szotttta-

, [ ;

R*yrryan( Iiltilftl; *"c([iJ t?

- t

J2

3 i 0 , = [ - : ; " Il - . 1L , l

B = l i Y t l ' ' - ( ' t - * ) ' * + a ' + ( ' + |

= 6 q ' + . L c * r:,1='- t 1 f ,

J l = z * f l - . 1t ll J l - t

, iBA : 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

i t 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/ )

. , 1U 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 t3f 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

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

4 6 = [ u A b t t ' b t ) b ] l 1 , ll a lL o l

F * A = t

( ) t - A ) t = l : : : l r = oL o e - i

lj

. t 1 lA D AL 4 'L A ' [1 l :1 I

l-,, IL 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 . lI 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

oo'oolr r=o, t r= l l l

. - f t o o 1A r 2 l , r o \' L o c 2 ) :

1leeryat irr

/-*

J ; t . r + ) r zA;(^)

a

+ r lz o , t l

-ts -zo)

er ( 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 ,,?

)

) +

, II

= )

I L

i ) (

AL

, - J )

_ t o ed -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 IL o o , ) .- t ; I o i

l o e | |l -z -+ -s J

(,,rr-O )trlt

G,=li; i)i ; - 4A,=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 ' , 1l ^ o J , L o J

Fn )- - z

/1c"4 . tile. c4tf"'Â

( t*-^r) '=foo 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

(Ar-s Z\ -- 44 4t44 ̂ . '4 2ê+ "!1 '4

|

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

: l : : : lA,tr,'=[1

I:I;t, { a4q( 2

e * v = ( o

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

. /t o j

"ru<rt. L

4 (1o- t t1 - 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 li <i: + t

n' ;^'

A,- )ro "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 f l o o l= 14+4tl 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, '. ', IL 0 - L t o I [ e d , )

iill t l

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),l j - or ); - o(4

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

A tii l= [if J=^,fi; 1l i 'J t;; I hJ

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

[LLLL]\lfiAu Acxv du itt<rta_.e. . /12e_ rtaf t/

14 = O, Âlon a Ol) = la n d,At * 1tA' , o l r )

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 , / 7A

3. ti

[îCA\

l ^ ,I rI

i A',,ti lr'

{ r i 3

t 1

fr't'rti-ri,lr-A r

0

til li î 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 IL o o o )

$ t?o a*d t T>a- ( l - , tZ ) r+q * . * f r 2

aiaLtz*Zz,f -

J, i6 O.ui+r wA./..af+ t

- 8 -

&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

CL , *Q , , r= fo 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 . ll ; )

Thqa are +(e.r<

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

A a = [:

^l ̂ IX^'t' jrz"1l , ; ̂ l L e : i J

= [ ̂ t r' t ,rJZ ^rr2f,| " 4 ' T A T IL o o , A )

n i= [^ : r ' : r : :w : :1L d o , J D o ; l

: i ^ " t l a ' T 7 t t t T r lI o , t rT t tT

Il o c A lf luat are 4&14Q ag=af & e-,Ag=i

t J' ,Lz" r/c.(

(A -.t i)'v i a

: l

( ro l t ' = ( l o r * f ,A + . . . * f r - ,An ' , ) *

= ( f , t F,A + - - . ' f r - , ^ ' ' ' ) ,

= f , t t ) - r

Ttua fut a ,u jarzr-Lrz ,16 /AlJ ,2o A = e t 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(râ 324{,rzazz -

aQ.L el * o f- "tl /;,+4 ,t . T/'14 z.-

a ld lL f t

44=O h*4 -c , zzo ,7 *n&2r

>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.*

1o = ef I o,o. n! , t , e l tzcLA'

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

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

= [2000^ ' { ' 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/ Ataoa

4 a 4 4 4/t44 . 7hut

; 2 n a -

- , / -

"t ,l

( u t ' e ) t

, f (e t t -

o

eJ' '

l n '=l;f / | o Io = 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 4qftal.a&Ud o4 / tt a.+4 C

J,2 /

.v" t"il,t'I

, o 1o | t pt _ 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 JL' ' " ' '=: J

I t q r + ) , , t ' J t t r t L

I- |

C t i 2 . 6 ; E r d c Il o - ) t t t - L c t J

,ild, f tct 8, = |

ln ' t r ) ' f i t ) f , ' t

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

In*

:ll l

/ J t'^c.

d o l l t2 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

Ar=1 : f t r ) ' ' f i ( r ) :> I = !3 , - / ] t

f- i t l = / ' '( t) =2 16 t =il i , 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 : - 1l e c r Il e c , J

to./*t^/V, t*7 carl cl-lcLr-

. ( / | q IA , " , 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 ' tIl c o

5,

r ' 2 2 t , = [ : i ' : ll . o r l

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

A = e, i,n', ' , l : : ' : l t :e,''i=lt i il[1,' J:i'.]l'

- l c -

e o" '

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

( t l l = ,xc ? 4 , 4 + " ' + dn - , 4o - '

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,rI 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

o7 2

( g

)o

t

t

4

2 , ,:. .l-

a

o

6 t- l t

A*+ P, An

1 l o ,I * l oJ ] ,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 al ' r

, | ( s - r ) ( sG - l

6(s) | 0IL o

nA 'n B) - t-l

. ,, - ts(s)Y ( s ) = f f i

o , ) _ ,r - o Io t - r J

- z ) 0 ' - t t - , s f

( s - r / s -2 ) o I0 ts - tS, j

-t luu

3 ,26 Ak )Z = ( Rcs r - , + . . . n R r , - , ) ( r z_n )tL'

s 'n I + 4 t8 ' ' l / c " ' + un 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 ) = f i , (a' '01 )

: f i 6 ) = 2 ) ; " I t5 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) /+<

eri /B = A , C = a ( A , € ) s - ,

J, ld A:s) = (s - r ) ' ( s - :> . Ea, ret le to

nr l t ( , -LA- t - ' " ' r ( - ,n , ' 4 ' tO ' ' o

tuy fuA h 4 = /, 2, - -., ,L . Thu n,+ /tar<2 / t s ; = ( - r - t ) ( s - z )

{e= t / - t ro, ( , L l* t - t . . . , 4a_t A, J

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

= + & [ A4 , , ( , 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//a4 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 2l t s r 2 l

' = s L s L S t 2 = ( S t , * j X f r r . _ j )

, Jt<ycaa&ua .( A ' -/ .l' , -r -i

tz.Tzutz/rrz c/ B Jte?*+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 ldtr(s i -A) - o,

l , / st , ) = 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 - ln ' ] " ) ' 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/

% Cz= f i - J f iA 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

Li = t

1 ^ , . I'J l ' ^ , l ' *I ^, )

1 i ^ , P i ;

l / t l ^ , r , I -t t lJ L / r ' 4 1

A ; Q t P . a u 4 ^

' ' = e . (s f -A f 'plf , t , l l f r , i

l o ; ,L

J, I " f "

lo '€ t

lt

, A

4l ,

A t

A,,

t P|

P, 1P > l: l

l

P

,

) z

J , 3 |

[ 'l .

- l :ll::J .[:"'1,.8]- / 2 -

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 -

HI

f

1, H,

r 5

- i )

r 6

t lo l

- t )

qH,- 7 A

6)t,t

[ ' r oL z - r

,/

)-

ftuqi!*. y',- *7 ', , [!,,r,1 i 4

.<-v u44,

' & e e < t 1 3 i l = > - 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 Qs I f a , l c a , 4 t a r l

Qzd> ez 4 t l ' |

, - l4 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, rurtt, , *teZzd o/ /ti/1,,

q P ,

"t t (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 lL 6 u J

I -t

L . L :1H:H,

c4u.p4/ "{ /{ l l ,

= ()-r)(^-u) - J /

' :AL -z rA + 6+

z (A-zz . l o +Z ) ( r l - z .e? s3 )f,tlf t /*u y-,e44

"f Hr. ,

lW = + ,7c t /

{ f f i = r .7Q/6

J, l 'f J.l A a egrnr&<,L. aU.-tl'A = A z

,/<.r ). /< du *o,

taeca

- z J -

4?a 4 ) = - t tJ

{ tA l=Ct , , L (A ) =Fnnp , )

I = ' r ' J : e r rz ' ) * = /3r+ F, ( - , j )^ = -t , j : p,-r r j)t =

fa+ Ft (t r j )

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

t

{ r t s= r z t 7 J .Ak - " { : l , t . a .

= f'{ " ""rr-.r* ,r

)r'

t

r*-,r-.r, t+a/.c0

/ ' t - t ' i

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

" '*ot

u,. (t-z)dz0

,ti"'"-c)4* (t-z) I" - J2-,'-')tun (t-z) n. JC=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,3o /4 7l Ô ,e t? t - o , / / oS 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 ' i l i

) _ e t t - e - 1 "'or

T- = 'gltt t

gr= " i ' - l / r , = uz t

e 4 t " u 1 E I ? z r t ; t A = [ n , ,

- t L-ao' 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 : : lz,- [ , ,J,L z 3 J z

4d[,, J4 , J

B.

l: l

- J

- . J

l ' [ i[ ' : '

0 rs)

d4 ,uf-ûa/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 Is 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 2l - 2 4 t z 1

- 1 4 -

- ,= l ' / ' 7 t / l - t .7J / / ' 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 -qs /?# o , ro f t J *

I t 1z + I o l 'I t J

z

'n (ura= t. h t7o). uv

:,1a l

a'+,

{ = . P - ' { &

[ ' , 1,l , t

P = Q

T/rta dq ,/4" urtfr?d a-r/* T:rh

. lc ,gTgJ c, . tpf l Ixi'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+. )2J

I r r r t = 8 2 3 l ^ ( 8 1

o

{ =

{ =

u4L qUAqAAB 6 il{4/;

I t lôr= o, t t ( r , 1,*r= o, f

lx t l * r - t -o t , l Ta 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 xl _ o o { )

P ' t - f t o o Ir ' 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

xa

r

{ = ( r - 2 d l r

l:* lrt Tfu.

a)( 'lt"'.

l { ! , , , n= o , r { l i , ! no z o , r

l i r l ^ " , , o , f 2 r , l i t ! o" r ' ' , tL

ft* t4 'r"rr/ t<<.f 1...4 nyiLZ.

/244 Z(*- (to,/a,:y) = /8,2 E a+vi<.

1nr*jl

o, ?or tlo l

'4 7atul

' ' * r ' f : : i l - , [ :1 ,I o - 2 - r ) L , J

! = t t - t a J t

Canpaat)" fuQ=rb Ab e '61= u

- : : "1

L t - z o J

P : q - t = f , ' I o Ir ' '

l o ' r e t ' a ' r lLo'" o -4trJ

i - = a - ' A a V * a - ' b u

=u i _il.+[:],! = c 8 1 = [ r - 4 S l ,

frra-e fu6ii41t'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 15 =[-oior,

)= U.,r, r,,ry, Il=l : ',lrro

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

- t6 -

, 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 i ( 2 s r Q' ;TJi l l ts-6

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, i l ,r< 7t ;4

V<.V "f

e.{con

+ 7 Tutt ,,€,4raL+

+.8 q- *-l d;lt;,* h {<,w -r?a.6

5Zr - , = Zr -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 ' " rt d(s) -t

.t"# tf .

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

faz .Aaut'+ Aa.tufi t4

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

h [N , s ' ' t "

N .5 ' ' ' + " "? Nn ,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 /<âf /taz tft">Jcza

at4 / , 74t agaat4 e.puo7.*t"

4az €-t ;v/r1r4/ /4 2 2 a/ 'd -r . Tfu,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/ âa./ alz. &rctu 4.

- L t

= E t - tI 1 ( - 1 t

- ' l l t l = , * ** ) L t t

1 1 [ ' ; ' ; : , ] - , [

, , )

,ft4 . l t f r : r - 3 I

G t t S = I t ' 1 ( 5 t t ) ( s t z s I

I f f * I: l o o l * f # z s - 3 I: l i 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

- / d -

f : J \ ' J rl - 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 !,1Lr',, :1"!:i;J""I = [:,: : i,'J".fi; iJt:lfli.t a<4l7tten lfuu dttaz4e,,/€h- J. attq

/zot d"loo. t/tt ete ,; Pnd,&tn +. tl

; , ' [ : ] ! : . r , , r - ' z l I u ' 1l - - 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 It t - l - , l t ,

l v l

7/u -tt-c.e*d

q t

- l o l u ,l t l

e4a*.*:

I:: :Jr, =[": :]., , 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 ::lx(;) = [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

oPtb = , :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= ta t -> I r t t ) = xr (g) eo.s t t

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 . - ' " "1l O n o , s ' c ' )

/ ' / -

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=lL O e r , , s ( e z - c , i S )

r r f t )= - } r ( t ) + *^{ t2 = a-* Z. rb)

Y,tt) ':-xtti) ', .tt 4G) =-z't (t) r ? t ZzF)

t , to = e't xrro) , J""-( ' (-c) e. rr lcs dgt

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

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

(utt

xso) : f l l + xb)= f u ' ' II . O J L O J

r r l f e t 17(c1= L ; J + x f t ) =

L ; . - r l4

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

f e ' t , " 1X r t l = L ; 2e - 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-

f i ,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

vb [ i r " t t , '?c t ] , ?u, t , i , J

= [4 ' , ' " ' 4 , / t ) 1 [

t , , t t , tz , ) ( , r t 'e , r " ,1

l4r, ttt 4r, (t.t )L ?r, (t,-te ) trr.tg 4l J

f tt t,)

.1

d. lJ

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 xa , 4u { ro .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 io) =E"r, (4ca) = o- *r , (C ? Az tG)

* 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

? , 17ks

X

i-t(

t)

+

r-'/t

; x't)

t X

,X/

.IJt

- r(,

(t'

't)

't)

( t

(t.

(t

; ) ' ,

t /

/ t

A I

A (A

'to

t)

?)C.

' t

)

'(

(r

t )= Xt

)) = i,l = 0

- x- ' f i-x- / f t

- x - /G

'(t

t)

C

tq

,(,

L

* t ,

d x '4 r

clrt

r(*)

' 1P (

,dX

4ctrl' f r ,

)}C

(v,Xt

X

46{f

47E

'H#x,c)

:)

Y 7t)

- t g

= 4,r(t lQr, (c., ta)

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

L o - * r l tt'7 , =- U t I t :H .- r2 F,rD= 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 ) = [ . ^ ' IL 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

[:'*.JFqalanea" 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 e4tcegt* 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 II - L -

x u) = f i J - u"fa

X r c l = [ " ( { ) € o 1L o u'*'J

x' ' ' ( t )=1" ' - ' o IL o e d ' J

Xto) =f 'C

c "B ' ig

k - e ) t e n l t - z ' )

' - - ) zz . ) 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 - ^ ' )

\ ' rctz i r) =[ "&s

kcuTs

1L

o e-p- (Hui )J

f t t= { ryc ,J=( 5 - ' . l ) t

Qf t . t u )=x f t ) x - ' ( t o ) r [ n * i ' e t r t co 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 , tA -e '4 t ra1 gar= o

6 ' Pk ) 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

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

I s t - r , r r ̂3 1 f t

li = l r o o l r , l o l ,l - " / o J l ' JL c

z t xr,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

oa 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 ' + |

&/ urt l = 4tat , fu

i r s i= i rs t t t s )= #catd

yfd = o.i t gnt t

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

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

Jr , r : r ' j u 4 rZo- a / . ,_

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

ft *l t. q * V,u6+,

a SflBO tf&{z.-cE

r fur J({ f t ) l .* r tua

R . s ) 0 ,

, &

lf,rot 1 J t! rctl l e-5'l dr < f*,r1e21ctt ( c'u o v

5 - 3 , n r FI t l t n l e = l

# . t t = f i , 1 , . r s l

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

a'

ULq6o 5

r7 _o: ?? ,; n,{ B i8 Q t6.t1,,

' ln /k), r , 7-; i ;

ir 't=J tSietT ==fifi.

- 2 0

9 t t ) - q (e ' t )

el r(*) = 6rd. zk'-

f r rct = gt*)=at( t - t ) -a 'Ett-zS

.n aJ d t t - 3 ) - 4+ 6 7 'x '4 ) * ' ' o

, @

J - , brcsl 4t '= Ialtlal' * 1a13 * " '

t @

=H Zlt =|fu q tat <tL a 4 ( 4 1 2 . t

T/r.4 at /441)-{'4 df afi.q i BLBO

f/u./ du 'af 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

%; ; r44 . fo / o7 ' " ' 4 c t o t J ' .

'rtul4 taz /cda fr al I ;

( - t 1 o o Ii = 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 afryryb6//-d. dz ry& Al zfea&/aa*z;ZJ ait( ) =o '

( t - / z ) v = [ ' J oo ' , 7 , =o

L o o a l

ae& 4 *'4 4F* 4-- /, u,t rlao<

. / l a l < 1 ,

art SoU"art X pd/.LrG)

t

o- t

gtt) _JII

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 * l irir;l*^ (tt + a ir;t> )

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

t , 7

f r,1 = g-, t4";' "-',o J'' [-;J

=r: ' l31 ITf ] f : l=

, Ju=o

+sr I

- 2 t _

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

^ f - t : _o _o. IA s l D l , o t IL e i o a lJrAAd 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

| ' fd '&r N= r

f o -0, { l l n , , n, r l ( 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. i l r tr .-)t trr= - 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 It l = 1 , , , t lf 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. ?rl t t -- 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 u1ê4t4, 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?lTlu+r,r a nau{hal/f 4^6/}lr '

ffu n"Aî 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 tg = e t4 ,o , * r [ ) , : , , l r lL)'' 'l: A; )

f u , 4

d, i J

a/al

€ , 1 /

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

5' /6 / , r A ' [ ! f , t IL a o A t J

.'t.t r H4 = [:,i,'':,:La,e., (J-et

- Ft'l i --' - 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

II 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-^, Il,'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

- 2 2 -

-:' 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 td-r -o,g/+zJ t l t

' = -a .o 3 lg ,

.'!4 M{ /v*Lc-7itu( ru"rr-tl cr-tz 2

tz '4{ t u l - / .?x t ) = gr / r . Mt 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 dc . = s- ) tc l {nu ' t " t , r . = :B

r4*^ 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)= uC{ -UrO c r - .d l J>o . d / . .

I ^ ' ( / n ) I "r l xa

IA ; (A ) | < F

o l H

Ht^

l= o

i l%

,4{

uf zL r l

I a.rs"s 1L'a, a,'(2 J

to +o

eT to ( t 1o , t L ,e / z4

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 ei l t

= e-)tk, - "t")

- (e't- ,)JL'

= 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 .4Y) '= ' 4 r /oJ ' fBrB 0 fal+ .

1 8 A ' 1 4 + H l I t V H = - N

( A ' * . / I ' ) M r t * 4 ( a + V I ) : - N

%rra o t *4 p t>o, d t44 e l (er f i r4-,ahra

"/ G+,kr) ftc* xra/ild.4.i eal

H r , l 'L /.4 -r

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

f * *

I , IX rc -zs l rz= 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 -

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

- t z- e

t ) C o 4 < * - . : t e - " , U

rh/'o zilt EFa^6cr*

t4

( t , ' tJ l { k ,D l c / z =J e - . ' u "-o to

. i 2 3 , i - t o Ix = 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)= f ? | x(d = f ? IL , l L t J

X r U = [ " - ' . - o 1Io , 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

Lo,r . (u- r , t to-

;+, , )

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 = fPrctAo+vpt lP- ' f t )= f r r " - t ' - 2 t 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 6z ) B ( z ) : l r / xerqz- 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/.ftâ.A,:tu ? ftl = e'tt zo

n{q /y-V-,r-*ryrh&qan- p ' / r t l=et t A {A44d

Ttu/* ,"Âe'iA? e.'d %ry,e

- t ze u

f = i

- zto e-z

afaaZofiza

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 ' J , r f 3 n J f' r t cf I I = f I, 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 . tqa. . / t=2, / r= | , /=x l r r r f / , ,H= Z a o c l P . 3

6 . i I t o

C = l o d - 1 , IL o - t r )

( r z IO =

l - , - 2 - l

L / z t

6 , 2

fo anJ= o I .tf 4t'4 fel 4.?-,a,

o | ^4+4 Arr4o 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

{ roy A 'o ' A " e l )= ( ( t 6 AB " Ah- ' a l )

"l*'( 4 4 4 n *r*f*/nl5,+ !-,+, BI ,**6+qnl4. e>

Aa-4 la,,-tz

A,' o,1=, P *-{ s (t l

l - A ' , Arr - t i 0 ) V ihtaq6, 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 1I t o t . oL o o : . 2

o t 1r - 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 ] d t 44e{ , - ' ' [ l i ]r t u 4 , p = [ _ , , i 1 o , - (

P4 p', - [" i t t ; : ,1[ i i ]= [: : ,16 = P B = t l l 6 = c P ' t = i z r l

/ /tt4

6f

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 '

ue -

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 -

f6o .-u&z<.u/ or,u'zf; u deu.r,uv/4.

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

; , - - r t .+ t t

{ = o ' / t r 2 4

Af u ntf d:ga>a-l& . z,/1r14 7 *q /r<

/a^4r4 66,/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 td d A 1 l " o

I

o o o ) i o

o o 0 o

= [ - o t o

x l

L 2

z 9xr

z3

, , , ) ,

v r/rzt-

7 ,15:1a ta, o,l =l';^^: ';,X:,]

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

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

u; fu enoCe;t

'f h^ 4 qt dl /.,,

t, 4

( 6 +*) aa4 ,aa /qat,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:,; leLA P.. Q, = 0 B.tstât Qr ,qrri,& 4 *t!

I";""4 )4ôtoh,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

&rz H 7-laa./ yza"r^fe;r-t 6 .a.<rfr*t Q.t u,e

P Q , = f : ' ' 1L o )

zU /<,taf

h, ao>+v *{ P f-tZZ P,

-uaJ.latf dp

zt

i,t,

;,

xJ

(,

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

[ : , I l ^ ^ , ' , o ^ ' l [ ' , r l r 1l 1 ' l = l o ̂ ' o o [ [ " ' l - l ' l ul ? | l o o A r , l l * v l l o IL * , 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.- /a

o a l Y

- 2 6 -

Hut,td z : .dtqcv ), <z/ d/

cyant," . Ti/ N

6, p,- 6 n ) au

Ml5:ctu "/

' f l Q , = c t o " a 7 ( p r + a l r 4 r n , )

7ht 'u-an ( .+o>n, fz , ,/ fl , a a. o*-/r.'Ee-

4 f , e , oi (rzcotl't-" ( 1) 6.15 tu;drtu

| ' " CtJ c,s 7

| ' r , c z r , t IL"t ' ct)

"v J

?ru1.7 1- lt rzA^4 atr ctlf ad24{,

t4 aai/7 a+-Aua-r-a. ft* atal+L'

c4.e4. tl at f3 ,

ftuZ ut

tn na{

6, i3 Cea.a34q

x =r4 X' .r B q

f = c z c ' r D u

{or f(O) =nz "U%, * erx>l, "ar"o;?

o/ lr, /n"&flA4a/r^r .tut+v q g .S&,2 O, /^.r, h Q, = lnz , fu Q, h n"z

' a'f4ta

i, = P, AQ,F,+ P, B ta

| = C Q , V , + D u

; S*o -s&/t cV*;,nl*r a tu ryt*a/

€ . / 4 B e a < t * a a n a t { f ? i i l * *L t ' r J

-',aka of t: ", J J * aJ.^+ ,Ji.obfa

dtt "?- a^6* n ce*fud*4, To *

H1 d.r.z u/aeru ef,

[! i i] aA* a1 tu e,r^,,tr,t t{ ti ilwaf 1'<

ry cA,dqartaU.f T/vAup ee/t*tc, au not idtPnl*

dt4lht, & zAu&u a /r; dnt'uailc

pl f 6u lr, I zn"<l /< ry a4+t I a , b+ ' l

L 6t, rtr l

aerl .a-c

ftn n h+f /r&4;/4. fa a< a-h&cAr/.?t- cl/aalat 4

6.'/5 7o & cax&z/4. zu4 zn- -tovo

: f : ' - ? ̂ o o o I f b , IF = l o n " l f , o o o l ; . 1 ; : , r , 1 ,l o o ' ' - i P ' o o I l . , - t t , l 'l "_Lo o o o n, - j f ,J 1a- , t , )

X = U, ?,ril:, t' it, P.,tf, P,'il,lE

J.f n cp+v6il/a/& e btf o; Q* a+ ?; *a, o'=t.2 )

du,W//- Q c, * a; fr. t a t+ fr; f o. .c'z/, 2 .

( Ct'd/.rt;4 6.5 e.!( d.OC )

fU ,f,rarrc lot*rttT '^

t = P zt

W,a/4tf'Lt-E ;,f'

:. in-u,i I [r't, Ix : | ;:e_.,i_,; n, l"-, 1"r,.,* l,t

',-f r tt) L-r?-l

t = l ' , ' ,P, t, i b t '7 *

Tl,u ir n eo*fu4/eLL ?> 6,*0; b;,t zrn'1o n-

6ir. -t/; * O, lt r. r/.r*'z,|rb € Ct * O ;

€ i , = ? r * 0 * C ; z = | 5 i o .

t

t'X = o r - a t

a a a

r z = - 3 x 2 - l 7 |

o , 5 ( s + X t ) r z i t

u;tl"

=

?

i a. - {2 z = i r t

, - J .l z t v , t

6 . t 7 ( ! + r t ) / 2 + ? , 2 :

- 2 7 -

J it f - /u,e.Uera/2 *

tt . orr/ro

du run',al . Tfu; effdtr;-' t) ,4d

u*6c1h-/4 ar'aol 't{ dxz,u'aU-.

s, /8 rfu "f@ n

; = l t o o : 1 - * r " 1 ul o t - t l L o l

[ = t o t o J

f rc) = J

o l- t l , f ( 0 1 = 2-r

I

cr"froAzl Q

xof ilna*z/A

ffu RC. t T ; i ,ar-+-" ,uid Au. <z<-<-lt_+*fqzq

A/A-/.tz tfu zzyatx,<. I u 6 *t ,4ri? M

"tdd 4r iluf 4 Al zzf.,r?r.l , /.rta. g.,

J., )4t

i = [ o . ' l , t [ ' l uL - L - z J

L , J

t = [ . J J ,

,!tr e^/;4-uv/14d .ttr -ltJ TA./ t1r<,uta

,z<et u(4;,a;* qrAeZ;rr* ; ffiTr*

1/,+qZ+A 6 dz *zu6o//;/,A ,o

T + h

a = !m = ) r t f , r ( r / , a . . .trn T = t - du &; a4/4-id zfr*af.a* k+a

enfuhd le Pdltn 4,J e4

Cu pAuL4nd 4 rfuput, 6.r. .f a +6ea/4.-ftat/-'r+. il i olt.zttn-/Q

Fzn A= r7. /4t fuv,, at ce-.t"rrQ/ tn P*6,4,J,

l f i n 1 = l ' o ' o + l z o 1 r t ' t € ( o l. r ' J

I o - o , o * t z l r t h r t L - , . o ( 1 2 J u r a )

l c f i l = ( z t 1 * c { J

&f c*n {u t4a4L+ ua;/<rl A d.

@ * t M a d a*tuue Ltf arUL ltltztta 6',i

6 ' 2 0 i = [ : : ] r * f i J ,

t =

Ti 'xr - T u

i ',Y::1.[IJ,- t - t 1 z

flrr F'n -,t**a&*/ "{"tf^

,/arr.J,€/ l,/ 1 ca>*)q-

du ,L*lrryje

r -z -L|3 1C = l T : : : ' , l , f t c ) = r n s r

l - 1 - J t _

IL z z 2 2 l t - J

o = [; :) e (c)= z o/e'ua//,

ftat u.tc ;rr.Aa/4tt* d, "df"f*

dd ]t cafa4;fr" q dl A.,i^! th^6

t'z,uâJ4 zJ Tfu4 .<tt dae / . =,

A'^4 Z, =-tr -

* i = - i r ' i r =

e.rd

li, l r+ ol i l = l + oL . r J L * o

t = E o o

zz . fl.t*.

_L z,,2- ,

_ [ o , r z g 3 a , J a r t | 1 r . o + v / 1* (hrd'

l-;,'r-r q r - o, /tns Jr tfi '

l-o,,t, J'1t11

{ t 4 1 = E z t i x t * l

o 1 r # 1o l ' * l + , 1 , 'a J L * )t 7 z

{ , { o t l x

tl- l r I

L; il o I

- l o o- L " t

t ' lo-- 6 ' I i J, H,( t1= -Aft tyo,*t r f tHoe)= [ : i l4 [i l'r]= ' d t4'T t. rl'}44 t'tu afrutd,l

4 &LA'lh/4 d upT t / rfua.+t, 4,tz)

N o ( t ) = ( o r 1 , N r ( H = ( o , t 1

"444 [i,:';l J= ̂.,"t t : : ]- tk-c-*a,at Tuauat 6.0/z d a uo/l<.ari.uf

Wo(c,.7, = Ito

mrTT#"wa^.n'orat''|/tz sEA Zaa<.;.ao>, xna.Gl 4 At

t+4 eatTaE-ol * Paa/4.r1 U,/6 a'

ntc, to) = [ | ' eo't t ' l

oo "'t 'L'1

L d e . . r t t r - c o ' ) J

tJ'z .en7>r.6 C * t.. *o ) ., (a e o. t (.t-- ro\

Jaa.l

, f t e - t 1/ vAL ; ; " - ' )= , Per r f t r / , . r2

8u s6rt cyaft* ; a4'4'14"'-'/r4, 6 ryt .

Q)e t*af,tlw Aal ; A/ A4;(-a)pz*v,rcalz , (A,0) - cerk64a/4 4 ,44

4

4 te'., g' ) ;*f

* e-." . ;{ ,a4/f 14 ?r+*d-c/ac( lu

(Atct ,Bk>)) @ al to 4 a44/

% 4 | - A 1 d , a ' t a ) i z @ 4 e rto ,1".- ffi.&o, 6,2z

6,z2 /cf Yk) {+ a- /.'.a/a.,1/a,C/

na.D+x

'/ i = Ak) x . 6L f,Xt"l = AlctXo) .

nh

* r,'t t, x r'D = (# x-It)xtt * f'ra ft xut- ' * ( z ) = o o h u

# r-' o, = =^rrf,:,:::,'.

oLr Xlra &. a @h/ natun 4i tet = - A't+t / Gt & frX, b1 = - A'(tt X, /+t

7a,ht^f i6 fa*'apc*< f^r/"/n

f, xl ,a= - xirtt Ak)

Ttuo ar< 4nr<, X'rc) = X-'1il ,8,'eri'=y/t)

+ lt, z) = X Gt X-'(.)

f , t t ' z ) = X , t t lX , - ' t t )

fi tr,'s ==:,,' ,_ ::,

x', rtt = x k) x''( "'' Q t z r b )

h,^, (AGs, Bo)i cot ffirJ4 ,zr t,

w,(t ,q, =J' E- r l r r e- ' , , n,tc

: l o,- 'o e 'ct ( t r ' to )

II e' t' h- co ) .-2 t,1g,- q)J

M Wr(to, 4) = o f"

4t t, 41.1 fi z tj .7/w'! du efr-f"r, ; het u,rrtd/cir?!{ au{ t,

Qe uaz Tbztatt S,Otz 6 cta4 ilt "rr4/r./,1

N o ( t ) , t t e - t J

N , r t s = [ t e n J [ o o 7 * { f , " - " 7l a - t l

JrA W

aruvT to. flua aq

t .

- e ' c l t L o

-ze-'J

?-,f"- /4 2raf ehz>at-& ef zt*t7

5 . 2 1 t i : ,J^ . [ , * ) ,I t " ' "J *' = [ : u | , r - - , ]

B tzs = [; J,*,,][.!-.J = f:'1

t =Q {c,=

Qtt, r;

' 2 f -

a44 ez4t ZI D

M i a , 4 4 lu s/ao44ra/.ZL

6,23 (-A,il i qn^Mo4c 4 a/4

e,q 4ta ?A)B r-nfa - r-*f

-'al

= I B - 4 8 A ' B - A r B . . t A r - ' B ]

4t-e.t /r.4 @ -sr.6, 6tz*a^<

r .B -Aa A 'B - , a rB

= f B A E 4 ' 6 e t B

( n , , opy

z7u hp,, ap) ttohrt u' u&'i:i*y"-d/q (s ng AzB J " - , t

Q ae A '8 - -7

4a& tl< 'caaz .r.*"4 , a"t( (A,B) ,)

anfuhla ;/ +,^d *( 4 (-A, B)

ti cdrl6r/len& ,Z/tz AaApvQz^, a na7 /-14,q 4rt Zl t*< -

ryry c442. fu "a'r{*.

(AtctrBbD

^ P4or/.(/*rr 5,z/ h d fu

ar oV t. Qa/'&* ('A/a, OftD tu

-Attl=t : : l, t3ttt = [ J'' ]ate '/raa<

f t t . ) = [ : u o , r - ' r J

9 t , , c) I tz) : I u ' , r- . rr-rJ

w"(to,,t,)= Jt' r:._,.Jr, e'

, c , f I e t , ' z z - 1

= [ ' I , r , - ^ t e 2 ( t ' - 2 2 ) J *uro le

=[:::, .!,:i !ii,'r" "^' :; _, ",,)Ar aty to, h'4' a4'r

/-"-( ^ 4 * zta/

W"(4L,) i ,,*t* a"4') GAtct, St't)

/,, u,rn4/1-a/?4 atanl t /ry

(Altt,8@) za n'{,

, t ,w'= J, Qftt .z)g(z) E'(.) { u,, ,2)dz

to

l.t Zan<,ctrTnCte* q' f r t , , z ) = * ( f , . t o )e l t o , z )

a,,e /.I+OG WC A4

wc = f t q.",r[*'* ft" y) B (z) 8.r.1fto

- ')

x {r*o, z) c! ) i'r*,.a)Beuzr-<< Q tq ,ta) zz aateotrtSy+Lt , tzterbz<4a& (Aes,Bre:)

i carZr//a-/4./

"r"l e,$ 4r t

J. Qtto,c) B (e) gi.) e'rq ,z) cf z ( x)4 'to Azn-1/l47pd.A4 . '4At (-,<?4, B'Ot)

to s44z+uaJ4 ;/ .*( 4 4

tr , ,

4t=J, f, ",

to ) E h) Bi,) l, (r, tr)dzto

t4 zana;;u'/"*- ry {rvb):

f {to,,.2 , &e t,.*i6. Wo ad

n E

4o =J P(h,d Btz) 13'ta P'(to.z)c!z

t,"

tolttzl. d A&naa4/ A (x), T/t4d

c.th/.Aror(- dAr (net,Brd) A

l f r 0 o oI o ' t o ol o o r o

L t o o - r .

r l= L e *- z t ' l

J d .

GA'@ grt

' J o -

Ofalr8', 7

7, / f ts l= _s4'

. t ' r 2 s " - g - 2

" l ' z r 2 l [ , , 1t - - l t o o l = r l o l ,l , o t o J L o )

X = f o r - t 1 x

e(O)< J Ncf eAa344/a/'&

f o r - 3 . |C = l t - t , I P r c ) < J

L ' t o z J .

7?n ca+ilJa-/.4

7' 3 toe. uo-c. (6.+aS a; aal a.a 44

laer{ 6 Ae- ,tt-/./"Z;* ; Pazl(c', f. t "

, - l - 2 , 1 i " , 1 l t 1, = l t o 1 i " , 1 " * l 1 l r| :_ t _?-\:) I I -q. IL o o - A i ; ] J l ' ; ' )

? = t o t - t i c r l r

u{r.,,t q. a,nt c4 orz %

flrr4 i et.

ur1 cea,A.#q^/t4 ad uce{q.oyta-/4t

t* . / t+fren +

( t - t ) / (sJ s 2s'- J - 2) .

i,'l = J-'r - ( s ! t ) k + 4 ( s + r ; k ; z S s ' + 3 s t z

i = f - J - L l l r - l' '

L t o ) ' ' L o ) "

{ = f o | 7 x

Tlw n' .L aad

o = [ i , : I

d t r o = - t + i ' 2 = o

,.,0 f+,rar ax f*.*, A/

tArafr4 ,u141-lb+t

f - 2 - , i o o ' , 0 o - J

f - r t , . - 2 - r r O O II e o i - r { ' - 1 - l II I a l r o l _ r , II o o ; t 0 , , L 0 |L o o ' o o 1 1 o J . ?

&le uat ,tAfqB 6 ,uaul'kil" zL,lt/ot,,L,,f

ulualu b ry A /':f,(/. tJz WQ = ( ' z - t z t 1 ) n = E - t t o a 1 ;

s = E d o o ) n o o ) o d O j o n a ; a o d ) . o a n f ;

t g r r T = t r ( s )e/A/, cFudd

f 1 : : . x z z 1 u f t . t t L , d . o o l * r y L

- - | o , L z z F z - I" 1 " o d ; z - z l * f z q ' 6 . i u . a

I i ' - L : L x . | , ' t *ds t , ,0 tD-da , ,n .

L'o , f i i t,

J ,v d'^@{u 1,1-nd',n,

Vu'u aat 6v It^".^+ ;dtfat da"f N c/llffir

aq4 al ry ry ?rtl u; P44 /,t d z.

" o = \ - ; : 0 1 r o l

r a o : ) "L : , ) 'X ' 8 , o o 7 2 c

7 , f z s - t - N o + N r s

+ s ' - l D o t D t E

(+ , t r - l t , s / - t +4s ' ) * (Do+ors) ( - t +zs ) = o

f - t - t : o o l f - _ t t o 1

l l y . ' , , - t - , l l o l - \ = o1 4 o ' , 0 L l l t ; \l o u ' r * o J L D t J

AJAt,t4( D1 ena 2 *t ry con+6nf,

,f A aT+v/rrdr+ E .1ara.uat D, = ! . ti<'

wd = E - 1 o + J 5 n = t ' t 2 o J )

S - E d 0 ; t L a ; 0 d ; o n 7 ' ;

] = u 4 2 ( s t

u l+i* l;/4.

/ : t - a , i o g z o . + o 7 z o a , / t 6 5 J '

Ue xs*ali* dt lada,Crt 6 | q fut/ tr+s

f tu l t t , c-o, f o , f i .e ,Jr ,Tlud up 4n*<.

Z J - l o , f

{ s ' - l s + o , S z s + /4*6;tu "/ io,.

' 3 t -

, . t t O , t ' f t + 2a+.4 l2l'Crr l.rorn -

C t t t - + Z S + O 2

N(s,t (3,s I f),-D ( s l

" r * y r s r ( z

tt/t&

81 s ';.,Ots, Fl-

Tlu &+/iaÂib

o=l ; , : ] , , l ; ) ,

- : , r { l . f t + 4 r s f 4 3

f * ' F r ; o o : o o -

ltf; triltn,)Feie!+ /q, uaz. du r A ,e"

PJ %/ur,t",

6 e/b+u;4^6 ,* ea.6cea if 6

/,r-l/

:11f l il , 2[ -o o

?,7

NQ aul DF)trr*fw t/ ,r/'-, h^// 4

r0 twrr't ^1"/--t(/

L f r o I,

:, t, l= _1,f,,-F..* r,f,f,

o lrt )

l u r o z i o o l

S = l & t P , i " . . n , I

L', or '1'

: ' ldt l ,? = -

"* [ ;

1 = c F , p , I 't4 L4dr44ra/41!

I *ral 4 "/

o = l[,'-r,*, -nr',u,] " mna^7t/a"

ctl'r 0 - - q.Fr 'f: r at 13, f!, = dtrif

ftr44 dl 6rn ccua<Acza. aL. d4 .oa_.

| , - Pt , , o -4tgt , , o - \ ( rg_-,( , f

, ) -

/ lt l ili ; j ::l : ;:: ii: ;i,\I,z i; t ,, i i

n'':n,'' ' l

/ raol (gr i4

r r.-1., % t'

| -9u - : Li t I oi = 1'eaqxz- ct oI i 2 'n ; : ' ! , " o o | # : :u* 'uL, tyx i>rt o o ' c ' , 9 i i J i t e r * r * J

wit+t 4v ccoz{fa-r*-G au alr,L&}Lge4 a"-u t - {ctt-acutd.,i

f (r-rltt/t G/ -, %

t* nta.t<y'v

,4 Z'-,-4 <;,A+oAarcrLd/+

P Lf 6 ^,i4 -4?r au-l-cc:atd O-c*&znn ; /t^.rr++

e-h i5 t*S u A/ML1 at'tq/ Alr2t a4/ ^frrn

ry D*t4*,dln rv- ah-a, ,

4 Ai4 *rycttta{, ;f 4 net Zt"1

4or etl D'u/t*tw au Z"ca^17 '4d?

feaa-nf,/ t/Ir/L t-t{ ,zenru 4trd Zht

lu ry 4 fo, -N E'*#e't

-ttt lz7 ** 4.4-r N' 4d4"a'

/,9 &-'4r/1* N(stO(st

a/"d ,fr ,*2.6c14*14 fu

LelrluG;

, l ' o , ' - 4 1 - < ; l l t lt = l / e o I * * l o l u

l o t d ) l - o J

3 = c f , f , { 3 t J z

Lf. o/<zu^/t/-/'4 7,a"fra ;

l ' o, p, R. 1o= l i ' - t t l , f r s -a ,p t - t t | , \

L-n,,/ .- t , f , i 'nf ,- t , f , -n,,rp, a, f , )-arf , -uri [r '* ,6)

ft'- Ire.tvaf.^ /uz4fa$ o/ uU) U Dpl )

[ : , P t i o p , , o o 1l q * 1 3 . ' d t f J , r D 0 I

J = l : ' ̂ , i o . n " l n , P . , II ' , ' , i , l l f , i } q, II o o ,,'o' t, i,ti l, J _

E4f hN u.ta du / t/^ at Âada4ry- $-t4/ir4"a4 at( c+E<.b a-ftow- { 2*xf ax

tt'.o Ât / (4 & f*ld

-1ir- 6 eZ.a;4tr

aZ( ,a.rEta z-lr*ax lf b /q4/

744/4 &t ausllat<l ,a naU,aTvla't ./

Q//4! 4 4 O i t *r,.*i^trt4.-, &,

4f7'+/lq-4r.flA' , Az aAllaZ*L i ,*/rt*-

)rT&- 4,2,J 4 7 Zts) a,a/ ttk )

aAl- *p.il*.;,t fh44 t, fluttt*tt ?, /,l

V t t/ ' 7 i r g =

* = o , r . - t + { - t - z s ' r r J s - ,v ( s + t ) -

- v - Y

', rA; i a +-o**r.</ an4taih.

? , r z : _ l z t l * * [ , l ut = L o t l L o J ' t = c t z l x

3:;: r 4 1t*o) ur e:z'lt

/ _ - z ^ ? q , f = 7 r (

efr ry /'u^cfi" ta ius=i ' f : , 1 , \ ^ * l ' , 1 u , { = 8 ,

l - t - t ) L z J

2,t -.2

o J x- t t s - n + , f s ' '

T ( r , t = f o l 1 /l . t ' , J f (T t "= ) )=z

T ( t , J ) = [ o ' - ' 1 t r d e d t z ' *

I : , ' : 1 . l = -| , ' !*ru*,,T h e 4 f ( T ( t , l ; ) = 2

L( t) =a. l.t=2 = 1. fA..a,

fa4

( o l uL t )

T/w u -c Au /.r-u,, "/ ('6, y+) tu4 cn'n /'<

z s * L

s t - t - z

Tft' ay;a/ "6,t? 5G.L zTrr-Z-r; "az

lra{ ?ndrlt L4/ A..4'ef.2;4 ; Az'/ e<

h{ "/ftl,^";Û/ aV.*r','4.

't

/+-w-" ry 4f-c/Lt- a4/'uz14r

v

,ra/.z.rd, Ttz P'rf@ /rad

{ r,, J. Au u4t2l I t,- 'J

? ' tJ G, rs ) ' IL t ls+3 r t )

d.. t 6,( t )= # -7f t =o

A , t s ) = s ( s f r ) ( s r i ) r b t = 3

? l

Grtt2 = | G+t)L (sn2(st,2

tI - t - lL

S+ Z (*DUr>) J

42f G,(s) =( s+ t73 ( s t z1

= s + z - ( s . < z , t + r ) -

./v-&/4r4 b

i t z x + u , t = z *

CA zr4t4t* /-^cZa* A aAr irtt= *2 ( s ; t )- - =

( s - z 5 6 s + t ) s ' - zPto cz-drrg fu- a.,e- cat4 tt2'afialv/ v

TAza"utt f,? tr/ 6r;ry2

7 , l O . ( t = 2 , ( z - - l ,

t^ (/. f6 ) / tx

, f o . t 1 r *,

' 1 " E t o - J x

Ttui i 4 cer*nau,irt* - /*t atoQt'at4i

7 . / l T = f o r 1 P - f t - . I' - 1 , - r J . - T = 1 , - r J J

ltlz ttz* A+TrA g . ,rp*

t - E o t ; t - 2 1 ) t t : t t - 2 , i - 2 J J ;

( 4 , s , / I = r r d ( t l ;

", - r6*t k) i

C = { t s t i c = s r t l / t -a t i + * ( 0 ) r t t r * q ( c )

L = t c t r , r ) ; C 0 r ) j

C : f O { 4 r S O ( t . z > J ' r , r 4

i . [::rr1:r" i,;,ii1] J, . [i;,1,1ir, J,{ " f -o , rq% -e , r f q ' / l x

( s + t 5 3 7 s s 2 ) >

A r t s ) = ( s + r ) t l s r z l '

I

( c + t ) ( s r z S 2

L- t - 6 t I-t--

( s + r ) 5 1 t / 2 ) .

. J J -

d,cl, = f

aec'q*+, ry

er'rfv iz. pe/ot *&y'/tt 4t

t"*r, aZZz* e.*t 6,<L , & r{.at<

A r { s 2 t ( s r t ) t ( s r . } ) ' ( s r t ) ( s r g ) ( s , s ) s

1 , + ; . , , [ , r , l - , [ , j - - tc i t s ) = l - . - , I f . E - ) , r ' ; , , , - \ . . . , - i[ - r s J L , J '

o ( t ) \ ( r ) ' - ! j ' ,3? , ,

o r r l = f 1 r l * [ r o l - . ? 1 r ' * f

| " ' ' r o oJ - | . - ; i J ' ' f i t s t ' L ; J . [ t l 'lQ

fltfi dt -tzutTottr ; (f.il

)

Tk k)r n- cil,'^'(b ilj-tq ,2,t -

t@r',th i'd

l/{s d'*t*t -

7fu azM i-dsr.ttt to /@t .

N* tu 'a&i4

7, t-f f* {/u 6 ftl i Puttt*, T. / 4. -1q c.aqoc.

d, d narvur,trt rl"*

-ttaalJa+d aat -(atr4 <î*,(z/ztteQ/.t 4qd L/fS cr'&t*r+ta , //e& ez{ 4//1r, 4

At /4iCF</a,- du .a.etr-' re4 -fe,

r { S + J

Q. f g= I (S+r ) , t+ L, ' ,

! - l- r+rL ( s t J ) ' . t +4

, l

; J

l-', ", oo:,

lI 7 - , - ; \ , ; - a - o 1

l r t " t-)" , t ' , , t t )o , , lo o - t lI O O r a-. ' :

_0_r !I

00

I

I^ 1

I

- / r' - - - 4

o ' o It

o r e 0I r oI, -l I

t - l

Jo

I

N - u l a , * . . r P , 4 a . - h % *

ry dq^(Ln F-ul*o 4,4au

? ,t 6O 4; r . C&.-,7,t'< len

r,16 e ,,, = 11. _/ =

Nts)= [JJ, [ :J ,, "P

N(st D-trs) = 5iL frulzJL ! ( |

D ( 3 ) . 0 + t ' s

[!nT!:rTt3;lb)' ' jf A4v1

4-ehJ I

udr,&f4.(/

t /'c*ft

n *-{ Nz .l

,lt+q.lt pa /11

i .o-: ' ' - 1

I t : o , t

r = 1 ? r ! , i l -t I e l -L o o J

Tt'*' No = tll . N, 'l:l D o" o. D, = |r*7

N I 'ltftt+c{tht.(.'w+

**{ dl P*7 N2 ,I1ru,4/4./-q- u* y'a.-

E o o t o a o l T = o .

ry 4,' P*l Nr dtav*&+e.r 4e*. u't /.t-

( - t o o o t a T T i a

Tl% [- N,) Do l- Nr .D tt = [ ! , :"o

tnYo,,o, oo i

N(s) , t i I Drs) , t " , ;J . I i " , ] ,u t t i : J ' ' t ? l , f , r s t

Nts) =

O-7 A

G ts1

a q ( a V r + r " r * r - f f i ;

t : l . D u ) = o t ! ' , ,

= [: J"-, ,[fJry /'arl-* i t* ry eq+!.rc

9 * [ i l l= * rG^+s)=) z l

r/q f:h

ftar- ,x *f dfu an/f<Z4* ndf-'q

4 atza.utt"/r^6 Pt'414 c/ s t2d

nt't/ ^ttzt ol tn !.rd4 '4 rfuf//r/.+f

eoL*ra,a fu

q 6 A'7k. t/az'r d'L

4L4 it - o&*to,, ri .tzpue*nf eq 76 4lt

ccLaal a'd frat ar< E'a ry

,rZa(s'

/r&&4^r fr- e4ona, T-fu/td rkpttta 7.H1

&t// )ud l&

' J4 -

7an ; ,L *f ,-Vrr-.. re. Nttr

/t* *? t;6+*T zh -r^*tn.E

t4ro.;-

6ot= [: i ]- f i l

4zr e (s) .= >k.2!) - (sttXs.stt) - -t5 + S - + 5 J

A ( r ) = s J o o . e r : s = J .

/air ,r. 1;"t 4 ry *quf,et' a4

Drr,[:,:),fttv rrs =

[ ,_:

]_ fitD ,P

I

I

- - - - - - l

o o ' . t or l

O o ' 2 o t- 1 '

O e ' O t ' 0 O ' , 1 O

V = n t 4 ( s i ) ;

t / JG)t+*-cl / . / / t - t ,r - r ,4 o _a,r lo c, ie,, r ) ', 5 ' z : ( . d l 0 0 0 0 ) J t o c c o ) r r . t 0 c c o ; n 2 c c c c ) . . .

o a c / r o o ) o o c l 2 c o ) o e h r o 4 ; . . .

e o o c d r ; o c o c c ! . 2 ; o a e c d t J t ;

X. nt&.L (szS; /fu(to)ui+r p

' N o

6t- N r

6 i

- l { t

E - e , r ' 4 f ! o

- o , t l - t - t i o . 5 | D a : , 3

xo{ l4r.ret,,t.[:,;] 'ff:: ",','l

o L

'Dto = | |l o

" ,' J-'

TLo; y^.t ; ,iu^fi./

t7z e2uryj oi ntr

44/4 'a cayf,-| X.

d O ' . t Z t O c e a

o 0 , i z t o o ' o I

; - , ' n

o \ , o " ' ,i1 _":' _ 1l _ _

/ o i o o t a a \ t L

{De u'u. 7r ,t<u*tpe4,l:a,, 4

/;4 at

7h44 an ln q

Dk)=[ : , ]^ r l - f : " ; 'Jo " [ " " ;1"= f a ' r s s>+ e ' t r 1

L t - o , - o , f )

N r s ) = f t . t " ' t f , ( o

l ) , r z , s l l o ,

a1'41 ,\

G(g ' NrgD'trs2 ^.r/r .qre

nu bL4.a eay'-/ tdz'./ n4n* 4 D^)

n f o ' . t '

1 at tud t 4 u' , ; t ryWL r o J

E;4e/rla+. Ua ;6*47 'r/tz dztutd

tl DAI a,d, NB) a/'

- ( tLs o,! s o.t s 1 f t 'o,t , t-1

o t t ) = f -o . t , - c . . r ) , * " '= Ura . . r 2 . t J

//e^t Drsl la 4. to&axat 4<At/e f

o'f'44, ttal = fr' : I . L(s) = [':? J

: l ' ,uiJ".r":1"iJ' ,I i ;J",[,:J"

e 0 : i oc e ' z Oe c1 , , o t0 C ' , t L

o ' V : - t ;o - l |P Pt t 2 , c cP c'! p o

' J, = t:: ::,:,1

Wry ,/#atu/z+f &ar.u ao zr':u:tti t t

Uz ^r1Vtd l= io o e o g o t oJ , , 'dz : to o oo o I aaJ;t / L l z E t z e t t o o o J ; n z = [ c e t 2 z g o p J ;

S r , [ d t o o : t f t O 0 ) t L t O O ; n t O a j . . .o a c t l ) o p c l t ) o a 7 - t / o a n t J ' ;

" , tJHq *L' :

_ | t - o , t 1' l o

, J

o : o 1 r r r ,- c . f - 0 , / )

i rl r

tj z - oz{nt

-J5 -

Jl": -1,, -"o,,J=L': :',':':iiJ, o , r : r . , 1t s , f , , f J

- e , l

Ir tl e

*Or= LTl,ul A n*auttl( -têaAV'a,46 ^;=[";' ",,a:1,'1,] ."1::i Ix = [ : i i ; : : J ,

et-fd.u g

! . t ; r l ,l ' l :J, , [ :J,

f i , f r t 7 x

' , 'r '-"irJ,- '[: J'

: i , ' r ' l ,n,- ,+, ] ' " " (4," 4,- 3) s

- ' h , - f f i r + 3

. - t l

L t : lc_, ,+[ :

i i l++ l( + 7 l = t

c = I L A L ] = [ l i J .' l t = { [ c - ' = r r - , 1 1 ' o

r + ; 1 _= c c t t l l

G i ) '

l , t r : f - C

i = i ' - r tL _t-t/e

, r t r I s - LI r ,

[ t t s ) = ( s + r ) ( s 1 2 ; ' = s L t J S t Z

4 r r r 4 r - 3 - 3 e i , t r l 7 , = 6

f i , ' t h r + 3 = z + r 1 , ' r ( , : - |

S'/r*V frl4-- f;/1" i r= t . 4, . I,

8 , t a ' ) = d . c r r t ' L - t 1

I t f , - r J = " ' ' X s - t ) + l

= j t - J s + 3

l = S j r t z - t l = E 6

i - t = l t ' 3 1 e ,' e ' L o t l / -: I

4 r J

F, . t J 'p / ,c r , = [ - : ! r ] . E = r I 1 J

s * 1 < ' < A T - T I : = b 6 . c r ^ -

[: ,, ][7,, ';.:j - I !,: i:jt'; .",J=[: :)

i t r , , . t t t , t t r t r t > t

1 = 1 , I IL - q , t 2 t z ,

- 4 r r J C r r J L , L )

F.<ott du f* 7fte r H 4q a'&

' = f i l r ' ' ' r , ! ; l, 1 [ - t ' 7 ' c +

L r t o )r 7 .

- 3 6 -

4 ' { T - t = c t

"yl.n =l';t ,'l'l^h ue. (5,r3) 6 ear,ffr W

- L J t 3 -

t s , - r ) t l

( r - ) ' lIs - l )

6@ 4, tJe "a,,'f'L4 ( r ) = ( s ' , ) t =

" d - 3 J

' * J , ' ' I

Arts) = (stt)(s rr,r jXs+ r j)

= St f +s .z t 6 S _r +

i = r + - k J ) d - t + - r - , ) l = f 7 r s J

- - ' = l ' " , ' I I u = i : r 1 1l o o ; J , *

l : : i J| | - t - z j ^_ t l r / o lC = l o t 2 - l C - , = l _ t - J z ll - t r t ) - L ; 2 - t J

4 = { C c - ' - - L / 6 + 7 - e J .

€ s '// t e fln4z ae sfrozhza t/ d4

rfrL /a/4"4 d/tf,t- d -2,'),-J-

'4ta" d- ataaaV* /*

/ r t - ,*ka &*l

L'

: Cr-t)lst D J-t9 t - l =' ( ' !+z ) ' ( sn3) (s+z ) (s / ' J ) .

74,, ,oya6+,, ,; BI7O 4"A/4 /pcaz<-tq

F"l ,la4 pila -2 e,4 -J - ,r'4

Vry AU4/4, 4.6/'4 kptat dl

4/14 '2, -2, attôf '3

,

s ' J - 4 , t ' t 4 - r " +

E - 4 4 * / 4 f * f u o n f d ,

t a P ' * ' / e 2 p = f = o , 5

8 e %

/,t4 fr,h* d4, %ea,&/,r<& d az

a'/-,'4 /ad1n44

d/db* "r

/. -2 at4t, -J_

7:%4{42',-

i4aaffih

itrr, = (sq )(s r t) =- ( t - r ) ( s r z ) ( s + 3 )

Tat qoO++ n 0 r(j p {c,/4 , &{ ,o }.14d

e . p f r / - z l f r tx t4+r j = |b t ( , ' ' - L " '

' o

"

J * t h , r

l r ) u ( ( 1

7 t / ? J = [ z o o J t ( 4 ]

A ( t l = & - t ( t t - 4 ) = ( l - t ) t = l t - r l ' . r l - ,

Q) a t<o dU p4q,e-{at uud e; P4.4&rr,

8 ,+ ;

o { l ) = l r = } t * o , l ' - a . l ? o

= ( c - G r ) o - t o - ( - t s l = i t - ) r J

*o.dl-ro, e a+ry' g ''

ur-. du .ea,tu

47n

'u{Try oh/4 -4zu.u'oe a/ V/42,^

,la erfa-va/'/,t4 /

E'7 ' ' l i : , i l . . [ i ] ,t = f t o o J z

[,le ejnf"/f4

, i s - , - t . 1 f h 6 ,(s i -A , - ' = l n s - t - t l = t o *

L o o t - t J l o cT/t* A-

/r*oh- ;

' ^ ' . ( - l : t ' D ' J - 2 s ' z - € s ' + g

f O . = t ( c - - r S t ( s _ r ) sb.r ax LZw44.-?1

i t , p r _ f r ran4" A =[/t t,7 -S J qo cafrhl ; .

?u/-&^ &, + . T/vh dl ^64//4 /.-- /"*, "t-,/ t lo

f * r , 1 6 / H

odtk) - p ,

J^ r-t,r*+ 6

I'uv '<tff"&lz.

/*(o) = t

2Jt - gs r I

-J 7 -

&o t/ac!{r ; Prta/,4*,, 8, +

i = i C C - , = f r , r - 2 . 7

2 : ? , 7 t-5 | =2 .b = -L

t 2

@, t(t l'- .g I * F)

T7tq.: is 4MP

a\-d

Thr 4^6IL /zrzA*44 "/&*

{'zez>,uo

x (Q r t J = (A - b i l x t f r 1 r b u t 41

'(ft'" il tilr'l t ")'*'"[rJ'*

=ft ;,:1"0"[iJ'aH?r4 y* ";,fr,rr eo

t Lrt t , orQ x(t,,,= [:

i, i Jl r,,

tJ. carrr,*6

, i o ' 4A * = l o tJ I

L-t -r

^ t I o en ! = l o aL o o

Tlwo ax 4tu,e

> r t i \ = o

'F'f FL4Gx*^/ P'r-aaa &,7

f , t t - t l ' - c i * ? -( t - t S ' t

!r=v l

, /* ry x[aJ

f u f i > t

o l

: )

f r r6 ,or / r . - - L l tpr t ( ) -E t S z J zcLy,tt& au Za.f /*a$4r $

{ . b

{s t1 s= ft l ' - I , * I

) r

7fu cnnLd^fitu b .f.raa/? ry

*f"

,<*/t t ott ct -4.2-/+!z1a ,;! /

i , r ) : I( Trualt+< S', A 2) . 7/t*a tu< /t C.t z

{os =

f + i 6

l ' r - +

L t *

aq i,e<rr<

a4a+cu4/ ai{fl -/ ae rd (h//ard4.e) a , ,@

*, = t : -i J ", , Il J ,P' '=a=f t :? l ,= [ . ' , i ]Vt=Px , *A Wa-27* .4xa4

i, -- [.r,,,, !, ] r, , [;.J ,Tka, du zr-.ay'^r4a6at

t= [ ! ' i t z ] ,I o - ! P )

rL( t '= o , fu Q>.c,

{ , rg t =

Thza ?f1S= #

,/'r

4

, 3

7 ' t l - /

u*c/' ca,r, lc .t*pau,Jd a4

i r r ,= -ol- - L - -+*-Y ' J - t t t

rfu4

{ c ( J = a - o f , t f t | - + a t E l - z J

l = d { C o l = a - a = o

4 = t { c t 1 = a

r t = z t r t J = a - 4 2 = - J Q

4 Z l t 7 d i = 4 . . [ 1 1

9. re 'T/tr e-gruafu; A 'i /ar-/a.t fu

l-{ a &e+ Aat a4 A.n-rtz,4 -G/a.tAa4aoz&Z4 ,,;{fu

? ra/r.. 2 ,4

a*'d'eile4 drz ZZry /.n-/,atr 4-br"da

- t8 -

u4A .Aa/.4+14" d- ry-a 7-"êr;A'Eljivl'.El ,

, 7 ' t t

c '=*

r 7

t , r /- : f z 1 1 f t l" - - l - , ; J " l t l '

= nx * l t t

1 = 8 1 1 7 * = e . x

J-fi i"'r4*- /a4a6*'h,

t4

i r 4 = s , , t [ t - ' - '

1 ' [ ' 1 - r s - ,L , ' - , 1 LzJ - 'E;

t r - - r - t q t J t , f u

: i r t , 3 s - * i t - vd . G ) ' = ? = = -- { "

F G I ( s . t , ) ( t + z ) r + 3 s + 2

T,'t -Jdreuz.c<t</ {aL .ru Z*ta^b .

n= r::,J ''IlJ (3,X:!:' L X 1 ' L /

[i:T]t: ; J - [.: :]ti :j= [ : : J

( t )

t 3 )

f + - z t , - l

l t 4 t s

l - , - i ' , iL o t l ,

:ll/;[:]

TA. 3 -aztt. q,u.eq.a/ %f.f,^ z.

cerc ftnZy',*4 a//A A1 A.tu

{ t, ,, -,1 e*, e """./;ru, 6 ryu a 4 , e 4 . 7 / u r - M

+t nt ccnMak ; atazp.t- tt/ '

zr)a+raZt. -l qlttof -/- e-taa74a d,rzThtu du aaazaet< 6 du

4a4r

dla . #/J a//.4 tu, Beas-az t/<z

*ercqt.M/o-/4, afu./*r/ -/ A

4,? ia/'-L

@ru -dci.au rt&.+( sra,ê. uAttat<:v

P = - 3 . 1 = l 2

7 = [ t , t t . l

E t t t , l f , . r l - F J ) ( t , t r ) = 1 x f rL - t t )

C s t t - t z t , + c r ' ! = t t r 7 + t , = { t .

, r r = [ * # j7h"4 & u.&e6. ;

I = ' l l + ! u ? f

; = [+ +J-' [:J=['; :,', ]ril< rk -er'g/t*

/'.r.rrt*t- /*, n fi y k)a.t

ecttpufr{ d P.a4a*" 9, // .z,a

i . r r ) = J t - +' t

. t L - 3 S r 2Lnct t<x

Vfqq = r - C + r l 2

6 dt1 A.tv -c*;ua,ee/ z.&rr+b .u,

(z) 4 F"z//1:r, 8, tt.fi /'r/d

( t = r _ c 4 t I [ - , : - , r . r f

l

I r i t t J

= r t ( z l ? S 1 t

Salr<l^luf, A'l- i.-€e ,',5 au^d (z) e'/

O{a a+4t6+L eer" e ccrfurt/ ao

1 t u t r z l [ 0 , . J t o , 1 7 S 6 IT'Lt4 t r , )= Ln,r t72 -n,oa/ /J

htc co*fnc6

r't 'f ',; -','l J " =[:;':,::]

Ttwd Eu la.A;q'ftu L;

i = l- : i , ) t , l l ; ' , ' ,u" ') u' [ :J, (z )i = r ' , l =f : ;

- ' !J Jt

?"n<**, 8, rt yull.

U ** funcE"^ a,

MA TL4 8

J s \ t f l ' r z t J s - z t ) ( 5 ' r ) 2-( t ' + I 5 r > ) ( s r j )

zt E,naZeul ,.J/ >r.tt

firs) =

fl4" €/a

,,//1,il

s t r l s L r l / J ' + t

J . t - 4

j ' * J t r z

' l r r l ' 1 7 i i ' ' ' rt l - L , r , j - t ] l ] ' L ; J "

2 l - l , t , t 1 4 s + t . t i l v l , ( t t |- , ) { t

L - r , c t : t 6 - 2 a , . , t t ) ' ' L o r J '

[ " , 0 - t L 1l-". ,,t, ) "

(u 61211 /*+t-zof aa

' , ' ?, :;, lf 't, l : I '!, '; ,5-''it ,' -i".iit,

lL I J '/ ',:

:::r)c ' . ' r / . c c ' 1 1 ' t c : . ' r t ' l ) L ' e ' s '

I e " t [ ; ]

r o , t r

; . 1 LL ' l

. i-tt = 1 . ,

TtuX ctttt

[ , 1 i zt : l = l ' tl t l l ; -L J T ,

1 : L r

tu- ( -r tu4

+{ttt t .

=r i i lL o ̂ )

1 ' 3 - - r t . j +

c lo I nr lC J

- 4 ?

! / . t J l o | 04 = l o u t

I

f -; i t

l - r / o

)a&4 pei

J'aett( ' + 3 : c c 1 - .

f - = 1 1 - t - ' ! - o . - c I ( , f ' ? r o Il - 2 , - ; ' - i " l L o e a o JJ s r - + - > ' J

L, u,*r/45. qrV4 = L 0 t c o ) € r t / c ) ' l i z 3 t 2 t A o J ;

b = f o o ) o o ) / 2 i o z 1 ;

h b = t t a / o ) c o 4 a l )

t = t - e J C t 0 ; . - ) - 4 o t ' ; e c - t - + ) / ( +

t = % f ( a , - 1 , - b r f r t l

- /? = l<b*1ht (r>

l.i>L"(tv f B z . f , , t 7 . 2 a f r - r , f IK = L c o o o j

{ . k ) ="l

= 3 s - t l= -

i t t J s / 2

'Vu ezrru 4//,rrr'.f td/ {< c!'/{a.rrz./ ,y' ,x

tar du /t*.rf4"|

"V./o'.r-.' m- 'nc{./o." 'n

t /47L8 - q 46 .q 4f / "4 'z / 4

4 b = ( r o e a ; o ( ) / o J ( F , = [ ' n ' o ' , 2 ] )

; = [ : : J ' - t : ] ( r+ r r 7 -6ss )

=[:i ',iJ, - [i,)J, .[:J "' 6 e l . l - r b g ' / 1 / ' 2 - ) -

1

l ' / r , t / r / . 2 t r ' ' l t ' ' )

M ^ftatt4./t- /ua&*r-

c:4q {,c caryu-e./,

ua) ' l t '5Lf f u" /c/ATt+B ct4d

, ) . , , - I s J - 7 . l g / 4 t 7 " 7 - i 7 ) 0 s - J i ' y J 7 /

' l i ' - ' ' , r n 7 r ] . s t . ? l f s ' + 3 / , l t g 6 s t t l . o q (

% "* /tz114o/ €fu nr*q /'<Az 5 r/te hz-

tu64z.la . Fu+'t c.* /tnau/

) - l , t s " 8 5 ' ) z

, f r - 7 r ' t r r r / t ) z s + t l

( r ; r ) ( s r t ) ( 5 - + 4 s ; 8 )

N;a f t ,x ̂ r - f t -u = , - t ; , ' , * ; ; -

Lryu "rlun44aaaa.( cafnraQ- ( l) 4; p1a1,

i , r t

, l : r _ ( + , r l ; _ : , , J t i l = ? r t , t _ i , is'u/"o{A*Ar z[+a ,"rt (r) a,.et 0) /r/Zd

i = ' t r ' f f T r t l ! - d ) ] ) + /

= $ l - # r , t I r * E r

Tfu{ caq i,n anl,a<bar a4

1,1=r: l : ; : l , l t 1 , i : l .I ' J L+ f # )L lJ - l+ ) '? : t t | 4 1 1 ; l

- + c - -

€ta4t ?

? , t D i s l = s t - / , N t s t = . r - 2

EcrctraLl D(Sl etql N1:',/ ek cclyr4t,u-.lr,tl/?*.,+a*tf bv

4 | t t D i s l . f 8 ; 5 ) N ( s ) : 5 - ; 2 5 r 2 - : ; F i s )

L/ , t r ,7 ( / .y) acuf Exat t f /c f t , /uq - lut t r t ,

/-n- "t'7 r4/ 4ar,**{ Q r,

t l l i s t " ! ( s z r 2 s - 2 ) - Q i s 2 ( - s r z . )

B rsl = +

(s rz)7 e", )s rz) + ers) (s"- , )

1) Q 'tc/rc/Znt , h an, Sesl = 7.r. ,(

O, k4 A'u.v A.V B Gl 7 ct7 A{sl *? .A

&r, = &o r &,s' "( df /. t* "Lct'v.

cLX But > ctf 4@ . hr a/ &-r, =fo,

F, t , frt' "/ uf j - aR /uaza ct7 8Ol

f:++niltdz

-ao.h;l-<>L

t44/

citt4"

h'L aq cfaS^

"'. ,Jrrtu lc &//e+//-f a4f q/rtt/"{.

/5 Ntst BU> ,:FB)

P ( t q ) ( / a s t > o )

s ) + + s ' + 1 5 ' ) q

@t

- l rI

t ,t

1 ) t

o l f , t

:f,

i ts I {er-z-+.rta f rt Ia

P Ct i l I ( t ) -o, L

J - p q= zl/..

s ' - + . /

t f C $ 1 { { s 2

, o t s t 4 J ' - o , f -. f - & s . - + , 1

/ + / c S / ) 1 J t - _ c , . /

5 ' 6 J . ; /

- ( z s ? + ) ( s - o . ? )-_, t ' u + r t * 6 , ? s , 4 ;

7/ttt 'ryaZt*^' a .$.A 4ralL . ,jc-urrn-,

<ly At9 Prccz.r*.il P, ttq

tlpL. ,;xi"ttz ,ao

ry Bb,t S drf 46)

€€ru.t/l* Atsl -4o , 4,s - A rt ^ a-d

B rcS = Bo r B, s' r Brt'. T/t*t A; '41 6.'

'tt"14f mzzf

l - r - z i eI d t t - l

l L i , t iL o o t t )

Vva, /* a'4 dt ' f

/t/,fi{4-

IT,IVA ]fll

1 'ftzetua J. 2), jz+ j A, /lr= s>

4 ,( + +.

tluz^ B) * t1 a.d &f B k) > dLf t+ B) . ,4

n = i , d l r A 8 r = o , * / r 8 , i c a t 4 4 , ' c '

Tluo t.,e tt'ttz /La'L< 'Izf SU) 7 <teg A (s) ' h"

cc't.c^/q/.f**r, N 4tza lu a&,La"*1 t'''<ZL

a7 B& < o4 Ars).

Q z . t . . - / r s N u ty ( s ) = = -

, , lr, . u - '=' ";: : ;,: Dti )

fi{St t/t"..r /L1 S'

F t s ) = ( ' s r z ) ( s > * z s r z ) = 4 | 6 r + + s z + s ' J

C A a B e i t , B , J f - o o t o 1 = t o 6 A t l

i - t I o o I

! - ; - i " , 1L c , - t I O J

t" u*r L*B ' '*1 ?r, t = [ . - + c I e ; . - l I o o ; o ' + e / ) a ' t t a l - )

{ = Er/ A + t j i

d ' /a

u /*c/u f *tJ

f A c B o A r B , J = ( - 6 L c 1 ' a 7

Th&a 4q cc++ol*+tzU6L t;I

c/ ' t2= ry = ldt l .x '

*rs t s -6

&44J

3o{t2 =

,/ o .la-*?lt

+ p ' + = - o , 2

' 4 t . -

rhz auynr ,ti// fa-v4 oV q "ay'uzoc,tufuf fo{ 4;fL + t yo e-t-r^?L

d-f cf tS1 = s ruu{ .+aa-2.&-t

A i : s D t i l , s - r $ rs ) N ls , ) = P /s )

]et-n'*t Dtil,s -fuq ctztrt.t*z 3. ru4

h<c'/ L{s.t = r3t 'st - Eo'+B,s r B:s !

tH sl ,+v r A1 s .4rS -

Fn*, dq czr4//L'-J ,/ otg - S = E t -o ,

, i * 4 N 6 ) = t - / = - / . f i r A , ! u , C . S ? t o <

tuIh a,)Ai B,)0, u,Jl!, -:

3 i 1,= ,-l ' " - ; ' ; - i "

- lI c - t 1 c c II

' ' ' i - ; : ' - i i II a a - t r o o J

ftr* dt / tz/-/,",afr aXdaa 4"r, /*- pe

aAdt rk- <-frt: cLoaln tl/'n ,./2, &f

/ = ( s ) = ( s + t ) ( s r l r j i l s ' r l 7 ) ( s ; t ) ^= J t f / c s t . r J f S ) f f 6 s ' r f 8 t r 3 4

Tlv+t /,J< +U+w

F = C l / ? t f 4 J f / o t J

c'-4 ctu t4r+/-j- 4( 4 c B c : 4 | A , . t 4 , B , 1' [ - ' t r - J / ! i d - t m i i i ] 4 J

Ttu+l ltk rtqr_(

C ( t ) = r 1 4 s L + z s z s _ - J l

ctq( z/a

C tsl-4 ts t

fh4 ea?a+a-./* -L.t"/ ,*7r.tz.<. J , Tth*7. +aA)zxJ fir uoHzry/<rsl Az ,4rt+fr/ /ir*24 t/+rrj='1"

L - -

Ntlef /vr/tt.t<' lL +*hUf ,/1*;-tt- ,,-fil.hcf

'.t6a.*,La'"' fu>+{ cn ;"f**"/( t '

C-uar+aq, rid, n = alzl o u ) : 2,

ACs) D is) .* i3 [s) N/s) = ,= 1s)

'ty'- Ct:t . grtt/4ftt u o/ lf / , l-/tz'-

dtt c.+rrT:z*ta"zfu a ,u-7,* . nn'r '-/ /w

tw<>v!a?.az. t-/u ,.*712. 4 C',(s) .6 2, Z{ettt

Ctsl ot tz*nf *rf /sy/ te vt4t /* 44

6 l.L4 4 Cc.t Aqf clprtrczz,ra dt

/atl-

t/s '{er

Cts) = BorB, t *Bl i

4o r r*15 r Ars '

aql o*t*{

Fts) = ( s r z)(r-rLs "

t)(s'r ) )

= i 2 ' - Z \ j . r r & ; ^ r 7 s J - s ' 4

h)e /4'r^!

= f r z z z t g 7 / J

Silrp{on14 a.<4 )uJ o*/re, n& I

#+'<

crtt ft- P4L.z^26+ - ftt Nldrz{,.*

le /.> aa4/ ol ,' [ t (

[ 4 o 8 a 4 , 8 , 4 . 8 r 7

= [ - J o i - t & r c i r r t l r a f t - + i ' t u , o t l .

ed (= J . d1 t4

[ t t , 8c A , B , A , l r J = [a ' t z ; ' z r >z ' : r z l f

a.q/ 4 S L+

;? s. f Z Z& St*r? J- -t 2C t s s = f f ' 6

T*,ocW@"1,a4 * f t

'/t 4-'d aa a-c/"t< -reet*'f '6'4*?

gia4 W

2 /"; te-dC J a4'1p

du @.-pu ,rtt-?t--- '

- q 2 -

h4 nzzo( A ,z&-tkq tr'-L@*otn (f ; /) 6 atLuc-<-.f"44,

-/A'z

4t a,o^c-n -Li dy +ntfoq r:_ d zz, i.r"I,-,/r- r* ifri ./," n/ irst /e.4vt1^€4 i,rr=

qt ( 5 - z , t ) , - '

lt^,r) = ctst:tr:s' r ] croi f t l

= t L z j - + ) ( s _ c , ? )

5 ( s - z , r ) ( s - 1 6 ) r @

t J * ) . f t ' \ + 1 , ? s + J , 6

7t4/, 7a-4+t-

,o gtBO 64 . kz**oz:'

/olcs = Y r, da +7tcL.r"u n Tr// 6ta4' ! . 5 : . /

*7 o6f -t f.-tt^,u

;'rfuf. T/r444 .fru

/.e ft l N(r)c , 5 . - t D h l

) ' r { ( ' r s l = 0k t , .fii , A4 ,r."/.* /A .t"/r'tr/4'<

/u t//Ar/r.r, y'rs) .r*- +n,t . ^ t ( :

.; 4 )

? 7 r

-1t 4 (, t = i 'oi . l .( .s rr a ))

B i s t = t a , B , s ; [ J , r - ' r g , s "

At+J 4411,9r-/ta-

A t s ) D { s ) . r g r ' j ) N ( s ) = F l t ,

- t - 2 5 . 5 - ) ( s - r 4 s . _ f - )

* i .

+ 6 s ' , t i s + j t s t e f

t t +)( s ' . - t ) - [ . E" ' r tJ,s r D- s '+ 8rst1r1

: i rs ' t

t ' 7 + t s 1 - s t ' r r t - 4 s ) r ( s " " 0 r 5 ' & ^ i " B r ! )

: FG)

74zz

*{

f,l ir 's =

Ctr =

J - r- 4 - - . 3

s ( t - : )

8n t B,s-4 c r A r 5

- / + 5o - z s r s 2

[ - , a

a'rf

t z 1 rfuba

2 u - 4 J - /! r r J l 4 - ; ( s - ) )

l %

. 2 2 5 - 4 s - /t t

s - / 6 s B - 2 1

Z.talz- ta

Fts ) = (s rz ) t sz -zs r z )= r t I s r * s r * r r

' z t 1 - [ 4 6 + | Jt o l6 t - t , I_ t , o )

'h'rn dt y'ul|'yt i,

L r s l - z z ; - 4

SrLd

f7r1 : (,r

= S '

A' s (s

,t, =P cr+i,t,r I Crs) j ' ts t

= p , ^ " t ' a o ) ( t - , )

5 5 t + s t * b s t I

1a.^-rn<.< i, t, = p . (@-

= p

f1-4,

7/4o

ry q 4r/a2..e ryd '?a/ frdryd'a6t/+rr- 4 fo*

44r';(zt 'P),

f/- nat:-C y'-t A )t*l h dq fa*.ta--/pr<l

fu r 6 e.. db"r'/nr, PtrT ruts =a.

C+C n l+h, &.drzd. tq h*e

4 , 3t (s1 = 'ffiT, r , * * , s - + s + 3

tT*rtV A* cay'/.r't^z*a

L ' i , B , :B i I , o t l l r r ' : ; - ; ' r _ \

l i - ' o ' - ' 1 Il - , - ; ) - ; ; IL t ; ; , " i v . l

= L a s r a 1 8 6 r J

, $ a t t b - f t z - b t t 2 5 t + t l 7

7lrlra du cz7n{-t*<-zh ?

Ctrl -- 7s'Jrt+s\r J+ s t ')f

s 7 s ' + + )

e4u4aQr t-rft //-a4z d1

t4t' drl 'ue,.yi-rrze( @_ .6,144

- q " l -

*4 ?)14 = t

iTLnr dLl ?1..rf'n A.a-c&o *f o6V ^./rr.r-i'u|tc/ . ffu otd<-/ a ,t, Au

/bz/,,4-/ i

i/'tt

/n 6 ! 7t/'4/car, / /"24v l u

c t J = 4 , n + . / t u r .2

l r Js ( s+ r1

a ' ls f l d : . i . t L *

/ * f . t o ) , ad t 4

4

- -n*{ 142,U{

o/'u 6; t ' z.t u

au4 dlz

a Al

i J - z

I b ) = r - r r -- { r t s - . - L

t ( -- s - 2 ' 5

B f B0 .46/nr

lu A**a/q- /."r*h fu r e Lt 41

, A / - ,

lA r ' .- :

d u , = - _ - _ _

= _ s - L - j _

/ * f t = , * ! ( s + t ) ( s - 2 2

?' f i^ (s) = C (st,irr tufr

tr crslS'tsti t o =

' ' f ( e .

"eo.-' 1 t 6rs,tf,'k2: i ?fen,ts ) t -/' - 2 t t ( t s t t - t s t i f r n r , t ) = ,

, ,

f^,,, .\' r r , * c@, f l . r9=+.

x l t c k t f f t l

J r . l s t ^- ' ' r* Crstfrt ,fonrrt, = 6

;. _ C.ts)Y / . , a

- -' Q ' r i + c r y f t s 1

( ' ; , , , ? , , , ) ) ; r y - ; -l r

I ( t r Cra- ' ) i t - r ) - ' | ( & e>

l - - , - . \c t 4 ) t t e l r o

pa/L /tr,,,

het 4"<d

4 Cf*li1o) t -/, A/.* *T 8,"/;

/".*-[4/r- d ct p*At<-f 4 [,n e+ z,Ltzz-

ry PcZz'..,, 7/+.ta "rA

a*d/ dt -laa&r. Lt /,dZ fAAZrt,c4<r 442 446/4|4- 2t 4t<.2-z /E<tt< .

r )

f ' to i r r l = . (s1-r .)(s-r)

s J t o r s ' r Q r s o a3s - l . 4

fr */r1"4rz/"^C/4

ffij b, i,.-?.6, ()) ,y ra+t-T

s a t21a

( s - z ) 3 '

J - - ,,t_L

( s r t S - )

( s - r ) ( 6 2 s r t t )( s r z ) ^ ( " ' * z s + 2 ) t4,

I

+ xa . HA".64 t z) o+.d ( 3 )f

9 . r t i t r t = 3'G) =

, 5 - l

s ( s - r )

( t ) = 5 ( ' 3 r r t

-

. i t - s + 3

Ir)

v , "p..a&z0a (t)

>r+1a.Oo rz)

1 n J6

- t3 t l

t 4*rt t/t h4{ B IB () .a^G&/A , Th4d d/rt (rst --

ti 4 64a4' 464.

gr(s)A

{ (s)

' 2 s ( s - z )

S ' ' r z S r Z

7fu ry&ru<*6h* q azf 4.6/4/

ffu rtlFaf trrZ( ua'hz'tdr4 4 *7

4r1 *( ea6-ya cf A,lI

ck) = iot') =! ' - - t , i l

l ( t ( , -d"ur )

Bz<wt+r o/ Au /,u4f(44 4 -ij-l? c4a-

cd/"E:o* 4 (s-t2 Cu N

trq. dq ,*gQ^zr+6^dt* ; h4t ei1l v

4f4/4 aa.r/ c&rt tL{ /4 ot tz-{ .o--

p44zCu

;2 ( r - r ) .s t A

- r 7 -

f,rz irr, =

trel/oH ':.41. A d

fot st :

ll ts2

E (s)= -f (s)

, f - i , a

* t ' r ' i " "1 =f f iP,taczdr-t< f, t ,

'rAs.

d q t F ( ) = z < ' 2 r t - r : J

k)e .ec/ar{ fuS= i rJ

L i s ) = - 2 ( ' i r ) )

l r ; l D l s 2 + H t g N / s ) = ( 6 , j ) ( s ' + z s , z )

l t o t ' l o A , H , ] l o - z t f = (6 E 5 t J

l:'- J, e-; ; IL - t t o J

Oq Aî l 'At-r* t4 C-)t -1: / z8 J. Tfuio

A (s ) = s . - z t Mrs ) . = 2p . t - 6 .

VY"/,, dU c'az*y'.ttuah.a ";lrz,

C . t t ) - - g- t - - t - AB t ;_

C t t s )= h r ' g

= ' r - t t

Ao ot n&r W a.4 .ue att.ruf

'ilT*na+t d- ry

',4 tA Eci f 4(d.

iftt = C,rst Fo - C)tst lrst= f C,ut - Crtst il;:;l

C-^*A^

t) "-' - f ->(sril ::+t 'I-

1Ct t l : LT> t r ' - ) l

= [- z -2rJ 'l-:tq- - r8 z 1e J ' [ t - z t s - t t I

= C- z -ze j t * , C-+c - fe2' l

u4rV P'*/12r, 4,/o. 3ae JLlu'1

i = z t z + t - + t - s n z f [ ; l

q : x + t l - r - r t l t ; ]

M.*R/, R'/;tz.

. x R

R c ' l

al

4 5 ' -

, f i J h D t a r r ( s ) =

, \ 4 . ^

f ( r ' { o t s s i r t l = f ,

r (h.< .&< 6

r n ' a Aowtlc 4Q, = {o,t) __.

J r / ^ . l= :,/, ( lru)n) l, *o

46 t

, , 4 4 . , I t( s ) . - - - 4 ? --

5 - < J ' J ' r '

&t p cla "1 i,rss)- l .. s - f ' , { , , r 0 ) o

t s = o

' f;/tc) -ti

t,

4 i,,'t

f , r4 4 " to(s) =

b o

4 elot's

aiyst I =Tls '=o ( . e r 4 1 J ' t " - 4 r ) o ) ^

- ( 0 ' t " r n u n t D ' t ) t l o ' " ' : : " t : J I

- 4 ' b t ' : t t l o

dr'

f l u a i o t o s = t ( * r l 4 o = b or . ) I e , = 5 ,

{"'te) = o

l,rr ftt = Gis)(s-z)'

J r r ) 5 - l

? , , , - 6 , s + b o T c( t )g c ( ! ) =

f r , o d 4

4. Hh.,r,.rr4 r/sa n*c

( b , s + b o ) = 6 , t s . ! l

rc s-z f/4/. tu

h - 6 o : - > b , ,

( D f , r r = ( s - z t ( 4 s + 6 o ) -

t o ' - ' ( s + ) ) ( S - + 2 5 r 2 )

= b , s z + ( b o - z b r ) s - 2 b o

S 3 + + s z * 6 s f t *

6< *p* ru'6/4 ,d/*ta**+4e.& 'u4'f

T 4 > c .

,ru4f e.d44. l&

-Pt - -z

T b 1

d BIA0 i6z/ ,{ , fu o*T p.1,

!u4 ,i.t */t ctu ,yrln /4/t t'// /^' '"^^4

" 4 O a z t ) & '

/'6 foAl ,1tdft4Yu 1Y**

7/u4A b( 4,4t4

drr*)= % {ft) = / ft ' ' #]=folol a , f"rda t

i s r L , s r . ' . r 5 ^ s hrt >. O't

4 c r Q t t r . . r Q n t h

( ( c . . . . , i a t n ) ( 6 , r . ' . t r n l a s D ' t )

,lr i Wnz+v,b&4 fu *? 6r u,/ b"

f., ,nvt-t 5 â-az/2 *V *'F *f*

tR -t-z'1ft*-

- - l b c : * * 6 r : ' 2

b r - - t 6 , = 6 - " b , ' t ( b o - E ) = - +

?, r6

6r '1 = f f r l = [o+t ) ' l , ' ie ' - t ) ) ' tL T ; J t s )

; B l ' r ' , ' ] ' , ) ' , ' ) c ' - J r o ' s ' +

" ) - ' '

= f l tS) D ' , (s tTtna ,i

'a? ar-4'uru 4"'/ D(t) ta

az&.a-/ îl/t ,/t = S (ttz ft,,tu

'n ( f '+z)'

D

N Z

D

N L

Dt v l

N L

0 - t o tt z t 0

,I

/,/

I

daV;atL*f

E

l z i 0 l c e 4 a " * t ' " r

I _ ' - o . , )Q = i o

/ 2 t

O - l I

t

ooaI

0O / o 0 )arytt'&"f

at4 .at*ac"A t& lr*ty *+^/4'f

z+ara ,fu 4 6' 4offarrt , dt clct 4n1

fir "tz.can2.u-rih , fu" dl/.r *"*/ilJ

ffi;:;Z;:,TWt , X / t * , t < , 1 - - 2 r P r . = l a Q P = 2 ,

"/.- tn = P -l = A. VWt Z< ,nfta4rt6- .t

,/ du /er.,",t t

Cft , t = A- 'k t Bts t - - [ . to+ 4, t ] - ' [ .Bo, ,s , f Br ! l !l t > t x l t t 2

trisl i ,{. alqrAll. l

rm -- + cr/^.{ p aty'z<frl' /&)

F r s 2 - - ( s r z \ s ' + L , t z ) ( s r s )

- - J ' l n T s t r t s s t - r r s r t z

=f#@l=r

- y C -

.tiun dtz axyaa'G entt {.< 4*4,.4 {*"

(16 Do, Br r . ) ,A , g , , ' ) f o .I r 2 t c c l -

l " 1 o t c I

| ' ; -- ; ; ,- lL c / 2 t o J

ned, dor.cA< ,o.ecc*+J t/2 .e-av (ol_c.i rc ,/t7a&*t)

i ncf u,uz,/ a-et d1 ce+v<lrztt/.,7r ?t'zt i<+f /< .

A4444qt, 6 /< o. rfu oc&E x "V- tu P*4t f@ H [3 . ; ; t - t ! / J ,s ' - '1 , 7X, , -

e.( ccrr'/rlrtA^h k

C. t r= 4 f t , r s ' r z ' t J =e -Ls i r3 (s t, f r J,t

7hz *<^t/ ry f.tfr*i i

4 i | ( s t t ) ' l t ' € s + t z ' t J

G r t e = f u [ , J( r n a t t , ? . u z ) . -

Q nzztutry et&* ft

6rrtt 6 Z,'a.l a,,,7

q 44r,u1uv u;ff ,b dnf 6rtt l8u /','r)

tad At 4b2 ea TaL. W T'{eq eur7u-t' i7+i't

n Haf /t-' t?'aa nt^-/-'t . At 1rc72n' eno'

? r n

ftlarr1lrz,4Zzrr. ra ,/LaZ 5 P&t'* ?'/l

G ts) = #rf

r str ,1 ' tJ = 6,, ' { , ' , , ' i : t :

e. ] Z{ W. o<)e

f*.4'7 t ' t rf.;I)

Y l y x

asa( .a<rwc4 iA

e*A"4,rut f+*,

r lL ' o t II t ' , o o c l IL o , - t 1 l lt o ' o z d l

l r t e )Y f u f I/"'4/ a^4 t/''*/o4'r'Qt{

Zr/t E'/ufAl 7tun az

f 0 | u "l ' t z t ' oI o r 0 l - tI ' o o ' , ol lL

4u4 /rr = z, ,rgr--m --V,/ =/ Tfua

( / *

Ct, = du)i -t(rs

z x l 2 t / t r t

/ 4/'g/ ./ , z ,{rf

{Zu e+r+ft*rzf* .a

= [';:,it'.',J'''4 ' j'

3r,Z,prt

trt) ' (s t D( s\rzs r z)(sr J)Tlon tfur &+ P.u4/t*tt ?. U- rlu tWr*rrartL

I

(h4 (c. ,*r*pul</ aa

c is l= [ t , t t t /21 ,

l - - L J s + r . r

d {7.r/ 444d4 Aa44/2* /4-06;

4

Qt l= /

= l _

- i ro F ' ts f ts t

s + * 7 s ' - r , p f - * . > s . / / z

. J , , f s ' ) + / ? s ' s z t - f S s t z

t ' n r 7 s ) t / 8 J t * L 2 s r l L

( tr,*t/*rrl ?. u z1 . Eo-.oo<* i)o{o) ' td

7u <X,o6* a^4 .4..,4 "t{

*4 */-',,r2

@ /;fl,c*/ LL6ad-u.V ry /*d-

? t g f r ' - r t 1\ t r ) = / " - t

s - t It * * )

dq s ts), z(s- z) - J ,-( s 1 - t ) ( S - t ; s f i - ' t ) '

A t s ) = s ( j L - 1 ) 1 s - t ) * { 6 t r , ,

/t.--*z/ *

a

5_!5 il

J rs a )c r - rS

4 2 4

o r,1=f '".-" ' J |.r

(t\ t) o 1' '=r,,,[,rs t

f - r ^ - , t J L c t - , )

/3zu.rt<t ltr Dts).= A(s). if d *{ a77ru,'11

D k) q c.*/o*n ,LrtQ4z/ 4xV, cr/aanrt-

,Quz.a ./t, ' ), trr,z !

F.',a^ d41 4ay'{Aztr ,(

^ f o c l . f ' t c l l o o i! t s ) = L r _ , J * L o , ) t , l , o ) '

Nrsl, U,' l , {; : l ' , [ ; i ] 'lfe

/et '̂ C C l - 1 o t . C c " ' / t l

c : t_ ' , .D q ' r ! ! ) t__ . - l

r J

' , [ - 'o:J'

" [ " i J

L 1 \ c C I ' b i -

- |

- .-{- - ' --+.--*-tt . D O t ' l O ' . C

" ' , , C

' , o - , c ) c l , o r ' I "

I t r t \ - t c l t O \ c c

) " r r ' , o e ' , t t ' ,

c c

ad .u ,t'tr-A fi lr"w."/1 1i*'&pztt' '/"'r '+cT14

fu + 6 /4'n-'", u4'i tr'ltra"'fi/r4*l4r

/r""4- ,r/.t -+ava R4.t /.^;4

Thad gtt 'rLa*< 4 = z, ,'tL : 2 ' B eaaat yt ryL

=4. /'tr t/'tz.€ M t'// !t4 ,*ffi

N .aanu t d,/4LP A14' to ;14 '11'?n/ 6

.ota*/y tr,

/r,r )n:D-/;f ' f 'Ld

F t r ) = l 's+ z) (s" u 'zXs+ J) o

1 r /u+,f ll _ e s l t s r s )

l : . (s ' o, l r , , , [ '^ ' ' : . ,1= [ 'o i ] ry" 's 2 q 1 l o s . , l ' - - ' L o , - , )

r u a n f * u d n n ( f u

C tr) = A' '(s) BG) : ( ,+,r, t ,si ' ( 8o', 8,, )

| " : ' - , ' u o -

r ? - : J - - - - - ,a - l d t r - 2 e ! l c t , 4 c i

r r - l - z z t . r l / c l t t ' l

&o, *oty HATIAQ ,,

-+,7 ' t ) , '7 i - , t , I- 2 , d _ z i o

7/r1t c*c. /a<a

A(<)= [s -+ , ' t - d t I l

' L - ) , f s - L j

,4; B; e.4c )r L d 'nn' lc *4<i

I A , ' ,8 ,

tufi.r.<z-

tuC 4o: tJ n

. t a l t t o : z L o ! t * a , / ' 2 : ' u Il D > l

o t ' . "

, i , o t " o c ' , o o )L

- + 7 -

- , r l r O ' , - i t , J + z

o I o t , o ) . t

Bt t ) =

7k; W CB)=,4-,(stgF)

f*.^ .du cd.ne?rr4L4L ixa,fy,yf , r r o q = [ * * 1 - .

| - 2 | erGus=

L d r " t J .

I= lL

7/u)

f - to ,J s - z r '7 4L t ' t z

tI e 2 . t j J

o f z' 4 28

c lr )

t' //

,/ dQ

u,'J1 /1aU.'er( .V&* a, Ftst.

&t,atÛ {/u ^6rvq-.rrrr44r+-,f*, o/ d*

p/t',nf o gc'tt:-t- -fi, d', 44t& 4 ,Lf Nrrt

= z s ' - + f - s 2 + 1 = t ' - + s . t t : ( l ^ J . L t )^ (t - g,2q ), h4*& c<rrrft*a, ).1a CI.

rtuat/.,tt 7A p""4 G "I4rf"r4,aTaltn O za4

ry@ rufizr,cz-

W \rfu.qn^, /..

Au eltat4ri Fks.

/1,i f,,u1 ts(a), [-7, :]

, dtt/t, ia

) 0 1+ ( t ' - + s ' t ) |

( s ' tzs t z ) (sr t ) )

ty& m,*tA/.4 ? a:z cz1ruZ

6'2r,=t-(hx'-D.f * * Is r - 4 s r t I = , - 2 I

L s E ; - ll z r a .= ( r ' * Ls r ) ) ( s s a1 . TAz , t t

| _ , ^ | 8 s ( t ' - t ) - + s t s , - , ) IG i t t G t r ) : l T T t

l + u r t t t s ' r ) r 4 s ( t 1 ) ( t ' z ) lL 6 a ) _

B*tlu d,rr) &/4 6.trr 6.rr, au [>+aLe'L d Bzs|

,4644 , dz4 €"rr, , ,FO**6/4. cDc

pU..t Pr+ udt .tc f .M /

€r,, , N{e s'!5, =f ,'::' :J[t "rt,, ,l,f

r,L

't4 e,,,, .4 ( s ' - l s r t )

s'-4s'+ |s ( s a - r ) ( s - t )

'ulw

t \ r r t r z ) ( 5 r z

0

- (cs ' t ) ( t '+zst$su) o 1r R ) ' L I s ' - u . r ]

e*d o+/H

[Ao,Bo1a,,B,J s' ,f ' ' I : ,, o t ' ,I r z ! t z . t o

Tru /+A.Q?h ;

'+ ,7 - r j , / i - t r . , r - tz

I r' 1 . 3 - 4 . 3 : - o , ) . - , | ,

Tlrt4d IAJ c.+f az<.fov t4

4 ts ) = f s -1 ,7 - ' r J , ' r I

L -J , - r 5 - 4 ' t J

B t s ; , f - t o ' l s - 4 7 + 2 s - " 1

! - o 7 s _ o , ) + S _ t J

Tlt /rr-//.4ri-2,4/ f1'- E rz.ch-<z-t< .fi.'.cb7

t4 t311 1-c ( l . t c )' ( /

P . B' '( i l Frc) N

a.orS--L.w; drtw.f.n . AH 2r//4f 4/.-d

,'t//*u.zr F cs.t {r u ulzar

o l - ) o , J + z

t i ^ o , j +

,t -'(r, citrt = fr;t [-ir,_,,

7 4 - 4 1

- l 6 ^ \ f A

t + # ) = t o

- , l f e ( r ' - q sn ) o ' l

'(s-t) JtT-""'f ')o ' : 7 " : r t lt a o ' c a J

,,,=r:: ,J [,,, :J[:, ,'J''

: l' t f I - + I

L-ro?-t s ast t-:l

=, F'' E rtua a ulr W

/"r;=["': ',1,,,1 ,f;t iJ / '/vt,

€ F = f c x t ' s a o j - r| " a i

tL'e tLe.ut .V, z 3.

Fu44-, f ,r9,

tt,,rQ aaf € f t4 @-;//L cr.lz*r, n a47-t_eu IlV* l r , , J, Th.u, , , i -<

k2= | o"/) aa C*'f'cda{

q = 2 , ! r , 2 i * t o l u = 2 .

- a'4r--nu .1t/*42d

3,rJ a4..t t t41/ '

4 a . 4 d , = , 1 . , ) - !

- rg -

&4t f mL= 2 2 , I

Lts't = EO Errt

ktt .a^Jo< Atsl = tr

, H, s' /tan,- L

A(s) Dts) r Hts

I t t r2Ls .e= l

IL

-i . 7^1" a.-r*72.r.6

=ler" '3) -4rs ' l r I

[-+cs'-rS as (s-tl )

o t4rs r 4zsz Mts) =Llo r f r l rs

) N rs) = prrt Fr, ,

l & s z r ? s | , s 9 a l

o + s / l ' + s ' - s ) )

t o l t ' 2 o t I 0 \ c c \j ' , 1 : l a a t r s ' o o 1

(,,

(Ao 4o :A ,H, : A r i lP l e . A t M , : / r i - l f a d - t o ? c r l o t

, t l O - l r C o l o c l c c I/ I i l : ; - o r ; o j ; z ; l

- , ' / l - r . l , o o , r g l o o ltl',nur | =-.---

t4 ̂y' l l , , i : , i-J t,t i I i "r i' [ ' a ' 7 i i e o i a c

' ' - o l

I f . - - - : _

| ; o 7 , i o , r j ' , i o 1

| ' ' 4 o

o l ' - o ' , 0 o II

" o z ' , , - t o \ o o

L \ o - t l o o \ o e

ttt O

r - - - - - l I' ' , o a ' , - t o t a o ' . 1 o

\ o ' t l o o \ o e ' , o o

- l r z o i z t- 1 . 4 ; a o ; r * o : T o i r o : o a ' l

6 i o 4 i o t i a 6 ' , o o l

hlaf {@ il wv a.u 'Anan rt

dqwcbltf ; dz4r/cr/,ry

" |fusgJ r , te t

tt4,.

/r4{

tlkd,

Nr{e daf a.

6 f'( 4;trz4

- i . l , oo l n ,

+ + z f o o ,o r , s l o t ' , ! i

A(s) Q -yz,l ait/v ,u,-t ,//f.rz4

I et4 2. frfua

dv rq74L ,

A-'(st LB) at<4 A'/kl Hu)

au c14oV/ ad A,z cei+z4fe?4l&./ t(L rrra&f /4

ataytA d f4 o, rfu 4il.,6e, n.ry/t44rLAg,

- / Y ' t 6 1 , - 8 1

J J J

- T , r - + i o

T rt/.d i-< t{4t<.

f . - J !A t s T = | " - J

L -7 , , t

r - e t^t I -L!.- ?

7 l t s 2 : 1 t '

l - c

- r 4 i- ' ls ' + f s - 4 )

+ 4 L t - t 2 1J l

/. ss J

- + 7 -

Al + etiznt, Lz a">rVrz&

Gr&l = lr!(s) F-1, L ts)

= [ ' r , . , > ' ] [ , , - ; r l f , ' , t ) - 4 , , , , , f

l " t t ) ' J l u ' t ) [ ' o u z , s a : ( s ' D )( + ( s ' - 4 s r t )' l 4 o lI

A r - . ' l

L o + (sL-+s r r ) |A J

Tltua.dv ualdf ta cM. fAz Au-+* Lc<t r /

t ry ryeaVadu /od . , ! / - ru< ' .< - a*p+<,tduaz /4* Jiafe\ /. r. t , k4 ,*.4 a4{o_.

Gorss

/,u JdVa,gz

Qr, t= [ ; : ]L :6cf/uL/.4rn e-ruA {4/ezd, u)c //4_/ du ?*,4;o;

C n , = [ : l ; s i r r I ' ' , N ( s ) D . , ( , t, t t J L a s )

F *f*r* - D/s) ; un4',,^.

*&d r-zit, /,, z,7r= I ,

N(s)= l_t, ', J

: N/s, ,..,(Ta N,(u: r

N,''{c)' h [:, -r '

JN'd =

[': :-, ] , 4 ") ' Nt'|kt n1','fl, ,' l

f ( r t ' 0 r s ; i r t s ) f - ' t s t

= l s ' * r t l f t - t l f o , o

l - '- I o 5 J l " - , t J l t o , )

= [ t ' - l ' t t - t 1 i b 1 o

l ' t

L - , "

J L c ̂ , JA/ t* u&{ A, = A, -- /) = S>+ zs r 2.

&un its, to F**f aou/

6 r , r r= f , t r r f , r = [ #L o

': ' J '= l: :lr:' ,' l '

o lJ - t _

'

s ' r s - s r t j

) a z

o' 2 ( s - t )

(sG,

- t )

?rtilf

l - ' z t s

l "t o

)1.(t'1e

€ , , , ,6 = S ' r r g r 2

N'L t t 6 , r r , , * [ :t - t L n

r - z L= l t 6 |

L + + ) ='=: F

-'ft, 'E

(r,,I.r i q{ ctp.tt'}4?-

l , r, i l ' , [ ' ,",J"

" J ' [ ' , : l ' r [ " " J "

oe dt,af ,-{ ,"i( 6a44 oT ofp -"/a/r/ cz

t upa{ . t}e ,ru.

"f

P't'*qduz.- ?.rv// 6 uf&tsar

- , l l + o 1' J l ' c # )

l?; l ' ' [ r ; ]

. rie tat dz c"t//'r""'A

"/

D l r = [ ' r ' ,

N t s t = f , o ,

6 ?

hI 64.//2 P 4 6 4$e"'' 4)c

L t t / , P z = 7 a a t / t t = 2

S, leo f i r , r r l t , s o l Tha tL s t l

Ftt) ' Frr, F,r, = i

r tr j s6, l r i .v.\r-r.Qrrrn

I a a l

."tclq.c/ 7a4/i co4-, n .(awzr f ,,, I o.*{

-1a1r qr-, { t.,t J .

L(s) = frst Erst = f-r,t^rt,

a*4 4{s) =4o+ 4rS oual llts) -- Mca l-{, S ca|

{,4 4rilr"4"( f"-,

AG) Drtr,'ri::r:::;::t, , l

L a . t l r 2 s i z l

e+

I l t . C ) O t , O to o ' . o l \ o o l- - ' t - r -u , { , o

l o o I

TAzt',. u< -llr,<-

z t s r z s l- 2 t

)

Ino nlo; 4r ; nr,d/

-r'

l'1,1 n

d:izLlt t , O O i O O '

I I l ' o 0 | aI o a l a r l o o

' l t ,

N& 44t'

T/14a

n 4 ) = l s + r - / Y

1I e s + + J

. | - 6 t 3 5 +M r s l = y z . - L ,

o : 8 c r . " r o ; t a ' lz ) e 2 i o r i a o J

t / o o a ?

M,, ,fuaefco T/u ,Az-urr/ Cer4"l

+ N l ' r n r ; t3&(4

-+4n) .ucld &//+

-te! d4azat /. It '

4 H, . Ttu N ,>4t*xn ) ;-* 1*'atoez/

du ca++tt7+t"ft N/ -Ltr t4 "ry

ekTendta^r ar'ul 'o t/4fu2/ fu '5

7tu a*/a.6aa ;

f ' t ' t i ' 6 r |

/ o : ' i ' . t J

O 4 ' , L o I o / l : . ' : - 2

r lJ

ru;.e'rybet dtz ry

- r 0 -

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193884424 Solution Manual for Chen