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Sie * Sffitu :l faaL. to4,tece;,A4;a tla*ual
44Yan z
,,1 Na. A ceU & cu.4 An f*;elecatais.
2.2 lo. th ,{n* A c.LcA /Lrr'
*V
fr*orn, pcir "rfl fu fb
4hafrae
u tS adLt . 7a1 ;"t^ft'd''cn)'- c/
At AAu c-ic-eca gu-'U A '
2.3 0r a dv t?fr; e/- 4,e ,ieyc.
ul ;A2, t.d
l.t /rr l. = p; / t , i't.2 ." An t-7 Z'ra'
rv6;a" zr'q*l+zt- u'Oat f;ud ?i
u, La7..to . ,rt, nl'fo';r^f to
lrrrt,),*(t"f,)'+#lf A a .*artti^a/ stprt/,t'> 1x444' M
(htr+ fr,p) u 2tit, +u L6gaa.
YU- ,.* tn r , f|u F 4^r.( a.^fr;t/
zn**/l.u *tz.
! (*r i )=/ ' , ry=gJ /-L* l i \ -1. . t&t t? = -3.v-i ( r ' g o ) - t J o 6 a
tH:,?)=t" '?ln = #*I t i t * {a.rnrrt! {xezu
0t t f i nta 4l tz?
i du'o'iu '
J,t le corr&J a
hcfur. 't/
tt< *re.h V aa
i o , s t / o s t 3 3r t6= (
I d t<o o+4 c>J
2-6 * 0)= o,, r( 4s) = o, )f, x(r) = 4 5rt(4t)
= 6,?f , z(z)= t , r ras) = / ,2r ,7(9)=
r .d. , t (Et ) , 0 .
2 . 9 o . I t t i - t c )- 2 6 ( t - t o \
i'q t' {** f t ft, ott = cz,
"L=: '
-e
rfr/'z. J ano|1t-f le = tdtl. -,- '
6 o tt/tt:O
e
J J - a i t ' f t t - f / > ) d r = o ' k c n u '
' t=fl
ol' $fu n ln'hl a'r r/z od
dt 'W\'ertp* idu'a/
'tta >ocf
-;; fr'o-''' 6"0l' T '
oa, J- t&r! )cn(t - i ldr =o
L o , ) - - - 4 - ; o s f u t ; L,rt/ 4'&t
ef 't/t t
fe o).5'
!-Sr(tt--,t>+/at +t) at
: ' ' = t e - > t ' . + l o t t ' I r = o =
/
o_z+ I = e = |e l -- t = o
e 50 to s,'t dr =0
ot
I io ' ' e2c. { r= o0
Fsrrt'cr&t
2.s t5I
I 1 J 4
3, lA te tJ 1t=76c-T-.)ce = rccsI- d g - c - V = O
. = i l d l = x ( e - J )' t = t - J
{.(4-z\ E(.- t)& = , ,r-rrL-
ro= a ( t - t o )
z,tl Orr; chbc*tlfi.;avo lnI rl4d ,ffi
?naJV &"r*rit+ttt'&it ta ?e'- a),1*
;{ ete{ /";t;e &'b'ry Or
4 "a
/ai,&. tp/t-t "(
d*ca*'**en'
'Ttsa it- a d d+'t"e"tt/ "-o&e' '
2.15
2.t 6 TfoI
- i o- ,
-2
o t 2
x(c+t), X(e 't)
o.rt
3 , ' t f 6
2.12 xrct
q d.;cf uA<rtfiifro'. w cee't t&r Y kc)
oa tfic*trtt, Tfuro tkc) /e/t r(fl fr
*+efre '2*, atifl'ulbqf 6 t=0'o
z.tt t6u c.wta*t = ii = 2,5 . T+et'
l/rt t
x(t, TaA.a +t2,u = lQ at<r"tlo id 'taee
tr tol = '2 qilfo j n 2 itn'rl t 6, fu-3J
2.rry xth- t l
t 2
It 'oj
+ g c ' l
; t t t s d
x ( t ,
z . t & x t n T ) = e e ' + " T
= u - 4 2 n , = b *
** tv b : e 'd ' ''' tzt " 5 a"{t'
7n/ c€t "4 f = - t / 'ea5=- t / r - t
= 1 t a s O , 5 t f = q l t 4 d a a
2 e'o' t ' fn t - ' bo04 l
- l
' , (ort) + X kq )
F r y . ,
2,1( r;
TcAta
q*tu-t
5 x O.aJ
= -l-: 0.83 d4/ , 2
= 4,t! tt'ot*'& E
q o f
, (t)
,t^tl
- 2 -
dv lne b =e 'c ' )1
T,rru cercf = -t /h t = ''y''q)+) ="t'/f 'q{4
: L171 42 = c,tJ ucc"/o
3"1 InL
I
J . 5 ^ j n , 1 t 4 ^ b e t * t t -e = !I - t 4 o n . 4 d
-- 4tdz - (3,f. -1'Fr ft + Fr c. )
fnc&od ove ,lex. rxg)'= *o{'
(!,,., ri*rtI= J [*n,'i'r|'at
{ .1r, G;ur'& =J "'n'"7*2'
J,l rsw n nn */;*4
t,u = f'o i lf; -l,r- ;l=E j ; iJ'"
ttr,'l;:'|Tz:ll= t; * '1"'
Rct
^
J{
Bg nue*uttual
r = f
t , - r2 f "t,
= -12'l ' 7frj - 2 , 2 f i J
A = - 3 - i 4 t f e a t ' '
-3 = t uiI - lood = tae f,ejn
t ! t ; t.1ui'rl t *l' l = t.+d"t*. <t t i lq j ' /h'roi -' to ,t'/t, tai = Po€-
'l -i l : t.**t'i| -t rl t = l','*isr/*
€l ' ll ej'0
J,to xY i ns*P
, , t , =E t 2 " [ i l = , , t , , - ?
= r
"'r = l:y' -f -t7 = f; ,1
'-i-1t ; J I t 1 5 - I J
7a.ett f *
J 1(ft)t1
M re'I rrcle
\r/o
J " J c L = - q e J t
1.1
J-e
"ia€
rt = ! l* oV &f* n oed 6 -
J ' / fe f *=ar jp ,uq tsc o ( *d f ,n t r t / ,
4'A =(ar j F)(ar j f ) =n ' ' /32 +x 'aaf
l A t = , W , 1 A l " n ' * P '
e
* i'u""r,
t*," 11 4.A * lAt'
C d n r o ' o - ( , 4 L r r f = o a $ e A ' A = l A l
3 . 9 x = d , " i p , , { = 4 2 * 4 F z *t -y) t = (n,cr- p, f , n j (d, f , *p,nr)
= c,4t - F,f, - j fu,f , o f ,a\ >
^'{> = (ct - j ,8,) ( a, -J /gr)
t 3 o^Pr,. Xr,at =J; radt'acax
= f,t-ov)
'fi,!t = XF/i)
J. t* No. Bt,ctrq1a fu *r^rne.6itt, -o{
t " 6 + -
s.tg fAcae. u )ra di//+uncz-,
3 tG t)e ";.t".
t - I + I - I ' ? " '
-(5'+) n "- ( + - 4 ) - ( t -
= { - o - o . - o
= (5- 4) - 6-+) + rg-+)
= . : . - ( 4 ' a ) - t r - - r )
= {
- 3
: r xk) = - / ,2 -z 1€'1 ' t '
ut ' t ' ' r ,2j
t"ii'
0rl&A u*h,-oke&t<L.
P = 4 t s .
f =;,* th2 f '
uJ:2tr f=f i -o, f
,')r ̂ ^{ataoclfrA/t;u-
P =+tf s.
c - J - = L l l -J P 4 t ,
u=# =4s d/s
+r(ry3 t.2ui, + gir/z *i". ' t *i i ' / tui4't
| /, {ei49 c
+ /, f e 7'z'8 t
1,3 ai a t + *) t t t4 n{ pt 't'ozt'c
.{x^e*uz. J/t ; x* e *^cEer-,?
*^&+.
Trrat Au rlzre 4z co**aL- ( ,
zn/a, Ttz TLuulczttA'?,
r'' JTr,"tlat .J*ru-a2"d, =t *u4 b o
= * ( o ' r 1 = r t < e
. r ,? x(o = 2ert'tfi
tf'A"t* t4
4, tO' X rro) =!7-ro''st) u4*""
a
= -2 f-u
t-f,:ica)t4it = :;+6o c .
er1r4"l -= )L, (a * t )7e
[ , f .r jat
-c.1'C4
+4 an jt u Trru,ztoc ,& qca.{a.tL
4az<d
fru)d.
lr.r.reo
{ / t 2
zr/g . i.2 t4 p.;a*L il,r4. etq
r ai i i ta Po--'2ry$, '16 /*k-
45 lt o F*qr&, ieaaee, r,l cttr! thft
{arc @t*on /rct;d Po =xr/rr = 2 aae&
* 1-o.r""?t/ 4 o Po ='.,')'d
ru*6/ f-f ? ,, *'a ' tn/Po - 3 '
'6'/..^.baurfr? ft*"7
^ ats
=zrr/po 'v tzJ/s-
Corrt"rrea At+t^t''z (Xc/) (
; a, 'f . rhuo dl
o.7 n$ a4 la
e )
= @ / * ' 4 ' " r
( & ' o ) -
xol= # * -0,o
:o 'o" t 'xus=ftr= #T'o')8":::;,Kki l - f f i =G74- -
z o,zt u ii'r/+ 1a f 1 -h?-b a(e vut*o*'n
xrr*)-fu=@=EEF7"= a ,o2"Jn l> -z teJ t r
rGr rd=. -hr* fu=f f i, o . a 2 e J J r / 2 = d r d Z e i f l z
16 flufuu&<.f '
z, t aa/ 2.8
l-rv,Pilr l - Po=zr/o,7
- 5 -
4,tl Xft) = f,rc>
X r-t = j fa rct I {i' nr.-r * "o r-4,
rn=J 6o).t' 'u'.Jt = dt"*l = !.t t4
fu e - lfa 6e( tt&tf c't
t n , ( np = * I I fta,) l',{ r"t = fr) .) t+' :
@ l o
- - L * ! : * = * ( o - e a t ) s a o
d4 idltreo caead ln 7'tntt''62 )
1*ncfr* J'es*'tf 2r"4a
tt/'b'd
aaa,*J o/ aunf( -
6r*tl-{-.
-- = l yr,otl
jXho) , h'' [t, Ykuflftrt ft'aol
=fu-' f,- 4,,xut1 ttk )rrtll'-4x@'
'7t; qfarf&)fut 742?)' 'fu' &4
Tnotc erttf%uh{ atru 4u P'4 t"
f4t &f,
4,1+ U xe) n 4na.( e*( xr'd=x/6)u
dOro X&> u)' ias u edd (-Aseau'
ara t-u)t -- '/dt r *t ) - Tt"4 ''6
i'?gv'*f,ta'
u+tt(tv (&,e) i dM. "/'4f
h
In Y@) = Q . '17*' XGn') = Fe Xct't) i
-,rrol egd tuuzr) ,
4, rZ-a cl)
Xdrf 1 x(Fte )e!*",(t -Iro-Or"'iuF-eua
= " -rJ +
1 ir, - r", ":t re -8
t t<o
D4* / = t- ts . 7n4 tr ita'
firut=ui*bf 7rFte,iu7o ., "i"o Xt-)
7 = t
"tkiL'ryfulxo,rrl =lu1 u'tollKu>l=
lYtw\
4Xr lwl = f e ' i * to ' r*X@)= 1X@) - uto
4./3 Xf, r(a n l&. ab+
Pe XuO =f'nrtt) eaaarf, dt+
t ' oIn Ytro,) = -J X ttl zi+, at t dt
-&
Sc.aatc uO f-g)t = @ k't, *ry ke
& )((v) =f*rro, cco r+)t dn = k X'/d kq-4,
Eo rw U) f'-ult = - 32r tt'7' & &'
&( rtct n P* itar g{&' n tiea'
i ; * . J r n * i l + 6 r
+.t 5
a , ff) "ts Zla{
, ' * - h u , 4 r = o * " 4 *J ,r"l 'a+a coat '/t =-o
t '-"'^- et<cc< 1tt'
Ttua u< a"u+, tu 713c4'v,
-**8-r,o/rro"f n t*^ n' vv'&b-
,f caWil
h G t t T
:l tx rc. zt tj
'o
' ' 5 -
[t(c -o.s84lf F - zPo
> i;. =2rr/p t rr/fo 7 a/a/2 .
xb)" E E^ ei-Aciln'<r
9 . -1 | f ' . f t ) e ' J 1 , , c " a " o t ?cn= f r " J " x ( t / e
; f c . a -, I f r'-inru!'^4rnr./'rrrt"'4-
v" I Ju rft)e c'tr ?c
'/Lu ,,^- "r<*e1V*S { o, f Xrtu-z) .tt/
t,, 11urz) 16- a., . i f-2,21, e
"/f l') "44tia&/ &'e//'re tr wtd'ql
zat e4&2& / uryh 2s**fu
uq.l eermet de c.a;(t c&)ae /
WaZ|,
O{* i = t' Pa . /fua a"c ,4au-'zPc
.?o
fr*,ea^;'h {rern)"""'7=o
_1ttO"t
'tarat- G'e - &
-,?^4 P. l tnrt I I
( r - C t = f( - t
1 , i e e " l , * & e ' Y
;* -#, t {?n,.'i''6'ntt - 1?o.-i'*:4
> o
1 m n 41r€tr sL rn - zE thttv
; = +" t t'r,r, /' ;"* f; ft) "i' ;;"*J
= i I'io, o
'i'o'" to!" n cF ' c^/z
a
l=Po
t""
J *tleE.o
Beeaua^e-
(i+f) -#
,, ', C.'e/r,
n : c * 4
+, tt x k ) = € , " n e i n u c t
!,tlxp ,4, f lt -t)ntoet
t r?ltv t01, = z rr/Po c'r/ "rt E J*/j"o
dt
ytu) =1"')rot'*''d,
in-- -egf"/z -e)ntoct
o.s lx,tutol
^trJ -/gt
4 X,lu,;1ss
7hcq. .a ,r..) aw*hfr)7
4 a, t 4tcot/o) ad dt
{re "+r..catar/ /4-,'r^A
Zi5I
4X,(rt to)"
{ o.t X,pa"+c)
larn*/ tG-c.t ' l ccnt
rttd<4a44
nfilt
Da*{ tak<Ifufrr*zt {*!t cm=;r'ooy'Pt
x tr)=l*f
"
en.t'niobcl .i ot""
-ft/t
= z ,^ {,ll"i(maao-'t)'ot
a,rlxp ntl)o,rpttu Dl
-1<tt4( xrt-q,r) ea rot.
- 7 -
=T c^ -l .-irru', -utPo/z
lrntuc"trfrlO J ' rmk;- - ; . t ) l t
e
= \i ,a z,La; ftnt,.""'a') P" /z)= lf .2 -L---
I-t -rrt
i t n tal. -- tit )J ', i . -
z n n|&a-^uc> Po/z J
4 , 1 ? L L
X r n)'fr,r.-i'rt IZ +a'in ou' u4'"n
o . L
= f , c t i * i ' n t i s " * n lZ) 1 (nu t r - . ; t t =O
= ; , 4 , . . , . ( e i ' ' * ' " u 1 t - t )- L g ' ( m t d c - ' u ) | -
, t=4,
4,& tfa T*tJ erna77 i
f = #Inlx,ot1'4u,-;h +'#4tt-3
I L
altro &e0Ottt* .of
4,21 X^r4 = o, t I t(fta-*rc) + X (o*a2;f
4 X @'te.) altl l1u rtt" ) do pt at*try-
dt,
I Y*rnt1 a a, r I lfr'a+oil * I Xftrtt 4ul1
a4/ 2(Knrartl ' o,)t[tXu 4)t"* 1Xt"'rqll
661 ryt d xnls tdct
=/;fi,Q l v C c L
t r& ./ . +4y l ( t Xu -htNoto
* I I xrt"'47cr' "';; L )*-e
.Q
-l
* !"lxr"au)l'*)-o
ztz AS./ ctagX (
/4
f .=h fittu,l1>dat'4
aa- \ t '-
/- , "ml \?4 ftQ
Es
1 6 d
o-Lf,rr*rtl'dez f i J
-&
E " = * r r x t x 4 ^ ! = + =
fu ^o*r/4t/ "f
'"*? *a "*fr fut/el d' nWd/ c4,c n Y
-4=#f lXHsu" l 4 'o
.,9
rhq trc fllt'ta
E, = a,ar(E f E) ' o '5 E '
4 ,zz 4 r " t ,NFR = (F . f 1= ( - t r ,11 .
O € 2 t T - 4 f = 6 r r ( * . d 2 f )
7fur d. 24,u. x.(ar) ,/od dt a.sat-
Pf f e dk on/ A.b /"t).r{r"(
fu ,rU ofu*( xhfl:6e1e'n7)=1. /* '*?n
4.zJ 1 ,, o,{., NFR = (*, *J'f-rq, ril
&.caea zt = 6il rrc/ +tr), 4hl o'4
YrhrT /fuu* zttt* WV 2r d/'
\tnf) ,o i pwi^r"4 P
. 77, pa'rV.(
/* 4 xrrnr) q (w efinT'
Bacru<.2 4f l=O ( ' 'd ' f f ) ' Z1lnf l ' t loa
fofr7o *r/A Po>"f{fr.:,'at (d'n T) = / 7C*
aZf n ' 77t+' a* 6'm
4't &et.-f ,ufur" cto . -. '**
Xtu>2
lft)sfj: z
X(q tfit.|
l(r,.)>1i : I
TJ' z " l 0
7k .f"ut *t "/ Trc) ere let to
Xr@t
I
l\t,)l'
, t
J t =z F
tO , l lL
- 8 " -
4/+ T =o,l .. A/ffr = (-ta q. 0"/r j .
\'tnT). i=t.2, J ca. al^a *)nnrl
*7tttactr s/ orz it V.ri,+n? /.tar.
in r'- t,r6 ) oT. Of lao ^A4"'/ ,Ft U' "'a oLt#.
4.26 T'A s NFK = Fz4 zrfl= C6,tq l,4Jv r a * s € ' 7 - ' -
t t . t l _ _ t T / t o/t2c81+-' x(+, *re"n xhT) adt' t ' t'- '
! - - . . \ . 1 v
t l ,ZS X(nT) =, l . t t l?nf
"y T- / . d/r' HFP' ?4 tr i= klrQ J' t*J
gcarytr- ,0 i aa*/;{c ak 'vfr / ?t'
fur{ { tzi ranf i "t€
/o E/4
to = /0 -6,2t = J,'/2 - 6ri l t - l"f/
(f ld 6,29 )
lo z ld - tl..il - - 2, f6 /*d / J,56 )
Ttsl ui rcn7 u;r/t T=a,t A ftg-1. 7!,/_ reg<fu _,- f:_'?_:r'T= 6,3 , NFR=(1 +1 = ftto-4L ta,+/tJ
ee"w to !t- nld. nt' NR- lt'r P.nT'
uiff' T:o,J, ta /4f.
la at/ a t*
fYft
4,27 7' zr/4 t/Fft 'G #, +]'G1 +7
i 0 = / o * - g = z n 4 d A )J 4 = a o - l ' / 2 - & : + t * d I )
rhT)= 2 -!tn tO nT + 4 cds-c, nT
: 2 -tu) znT * a ca +rT ( hnef(/n)
tt ls *l).rl Pf t s,/ + *rt a4
ax g+nel ..u.cry&L nlt) /*ra Xlnf) o&
T -- r/4.
4.1e /=rf/r. NFp=C#, *1.kt, f Ji o = 9 r * d / a >
2e . : /o= O f * td /a )
*(nT)= Z' 3 uA @n / ' * 4 cwJo trT
= 2 - 3 tti O,nT+ + t:t+a 6.rtT
= z -J t ' 7 r4 t l= 5 (P . * "44 / f4 'n )
0r Is {cietl /-*. O ath'ch e;aid*' 'Al
n eu{ /t'"f a. ': cs+'d a'ect**z
:r! i: i:': (::"!1:7= i/to. NF( = pre, tel
2 o = O 1 r d z z )
y hT) = 2 - 3 tt14 pnT't + e zznf
= 2 - 3 l 1 i t o n T + 4 - 6 ' t ' t ' ^ ' O n {c n+*'7{ /tra
)
T=r /a r . NFP r ( - t t 2 f j
x hr)= 2 - }.ti Pn f * /* ccb PnT (n*rriJ/a ' )
Jr l*a na e/t)tt/ Pf ' sl t* c"'
Alcc+ztot tt(t) /rtn XltrT) /*/t'' 7;rf/zf '
4'zr (t 'd F--a." = h
+(r- r ' ) o ( r -- r'l ?l= l - r
H'flyu r* -Atou .Z rn =
h=o
' e n a i - L = /
N = O . L F - = r ' - / - - - ,tr=o / -r
t n ,-.^_ fr-r)(t,t!)N = ( Z r - t t ? r ' - ;
t ' t> O
= t l r
S,rp1re.^t t +t6 ) le /r''
N ct. H
S r t I - r f l ' l'{-
, t t c , I - f
ftata H coti*t' xa I
N l l - , ( s t l
E r n = - Z a " * . n '
( rD- rnr, ) = (pc- f )
3 ) r . . . , ( r t - r ' * ' )
/ - r tJ* ' .T= o,i NF( = G/a 4 rc rrft tt/,+,Ji.+J.
i*/onT, tr.lh T-?./, 4 ,i' 7i*"2'c/
t* ca/ 44 '1laz5 ia '-/L 4Po d
- q *
h = o \ = c
Xrrul= t (o, t)n e-Jc"''=5 (o,Jy''u',
" = O
h l ,
= -/ ' 0 ' J g '
. - , o f
N & . n 4 r l r l = l a ' 3 e " * ' l ' g ' s < (
(+.6v) @rt t'< wVd-l'
pr;da sd *Xd@) s -4zao.
h , a r i t ( z , f / f . t r f i , caa u f i
a t tc l * )1 . tu l=-42tO +rrVeZto
qrl *Xotul * -o.zti + tT . Bnf '7lc
4 *i/( & tit&' * Y;r'iPlaryG r/. 7f1 , ft&o atc <t"tnfur4t ztr 6 fA
4 Xa(es) = -o' 2 co - lf
1,J5 'r*o,2
X4tD= r-_t* i" ' "J" '
r" iu, I u ir f - z ; u 'J 'xt r 1
= e ' i * ' f t 6 rn tdT -z i - ,u t r
t 2 e4t' ( * atf - t )=4 e' ft' docoT)
, a e:)rrtr-n, (, - <zz ,erf)
Eezrttt< t'-4D tc-f V o /- &( at,u" t(rtz
lXar -S l = z ( t ' c 'a te f )
{Xora,) = -br + n ( Ne rL'e( dz /Jta
Pld ,*4f 44 &h;^e/ '6 Gtr''t7)
id * m (Ltt/NT) 'n (ary'lr4', = n(a 'r/l)
o O , r c f / g - e t , 7 2 7 = P i )
(Xrro 1 , o, 1 X"0) = t7 . fleA %ar ag
cenr7*Q* 7r/.4 TXrla) = a PktL
,e,//.+r /<^en zfu ano/V&-;.,/ aza:}t '
6to p,zXr w, d.Aettt;r* ta Zht Jo '
e4'Paaadl .
I X.(tot/s>lt 2 (t - a (#' o' ) =' ft t o's)=3
S Xa(or/s) = - !-!!-ro,a + v = ?"t cr d
, N+l= Z - n r { ' l
1 - f
r - r ( '2? -
l - f
^ t t t t - N+ t p t2 tl ' r + f - f :
=
.tu ft..6 ) ; )<^-/.'/ k eV fd.Etbb * i E-'f n, -2,5 f J , cfr o,z 'i nzsat"'
t'6y+ N-
+,31 x(n72= lo ' -+c ' a n l ct t
,ti lrz{*** 'ttt'<aVcl ed P *ol-
>.r44.
432 xQT) = O,Jo" rVa cd T=a. tCtO Ac 4 . J 1 3 . &
X'rt',) " Z J'o,/tn e"tu"r' 12 k,rge t*r'- 4 i r?o h4
= 3 ,v / - O , f f e J * ' r
*,Jl Xinf)= /, 2. a= O" 2 Lc,/ /= o.2
XrraD= /, z. -* o x tJ- '* , , t" t t- '
* l , 2e lu f 6 . i ' u r * * - ) .u r )
= t,2 ea^f , z c,*4 cv f = z,+ "-"!-r,
lXrrol = lr.+ e4"''. uorurl = a.1l uo cc,Tl
4XrtuS = 4 2,+ * 4 e)t- ' * ) aa ea7
= o - c , t T . r ) O ( c ' < P t o f T oI - v
4 c n d 7 < C
T=42, NFK " (1 f J= Pr4 f,lr j
frL a,' .n l : -J,t t , a,f r t J, &? 42 id ; t
- l l 2 -
lxotu*/t)l = , (, -c+t7q/gt)= tft*es) =3
/ x' ( u''r/s' : : rT'"o l,' "I-;?
. "
J,26 'T' l, uFR a (-rr, n j
X"f4 = 4 4-t'ktr-t ) (r -ee. uT)- 2e=t
&''7D (t - ac co )
lX t r r l l= , ( r - cau)
*XnrO = -eotv
t<) = rn ('a rr/Nr) - n (atr/A)
= o, zrt/g . +r/l ,, sb |! 2
lXrrotl = o, 4 /rk)' o
I Xrer', )l ' z (t' c+z("r/l)' s ( t tqs); 3
9 X"l>rh)=V r 7' = + '- t 'df
I X"rct/g )l : z (,'b (4t/il)= s
4 Xr(ry/g) =' # * o = 3!' ='l?3'
TLtg t+o dt .+anu & ftt&' caf
h P-n/zt-, J,tf.
Alr?fi4 g
f = ,r/rt, dr= 2trh '8 3? AlFR
fA. d&d el,t*q eu A)fzh.y ,/, A rr47
ct4.e & , UettL1 * /.l-ltttr lr;ft
-up-rta xa\/z = tl{, 7.h4e a )r3
6vc't/sllr-{ , //& atz ,t/vcf'u* a/ Txnf)
a et utatb &;nl 27. or/rt{ Le't ' 7tu24r
t4 n4z /* f*^ "X
+hcutt7 or"l ax. ct n E'tt+'eL
Xutt) /*rn X1:d 3r+ 'r"t4.t'Y&L Y(A P
r(nT) *{ cfu ,r&a( '"rrt+7t{ah Ya Plrr).
5, 2 f= fi/tf, a," "zr/7 = JO. nF(
= ( ' r t r r1 .
'ftttz .,+. c**l?ff , 77u au ( at^e{r
dwt7,7*7 t.t/.4
TXrtul = 2'o tr* alt k) t' krr tgJ
7ht4" . P t*n cX *&"t'i' ett I e'x ('eh'
-Y:'r:?-ta .:!!'- -7 : tTr/to , k6 = zn /T : 2^t2. UFR s (-t4 toJ
ttuu , h l*'V ok
? 'x{ a* laassT
Ut,<.ntdv tft, /4^oa XOf) '
- (- 21 24.
t o e J s g c
5.J
lxooq4 JlYt"il- ' - ' , r " l | ru- i \
lXtutt)l un -& e/,6ri'l /r*, lXt,'rsl
,i o{d, arlcc iov +(ero TX4fu) h a i
f,o,+I , r€ et ildi TrQft, t * e s
b4,+Ifa *brrr,, J>, nd .rryb mlf'/-
a1 nctt 4Z-; at 27n;A* "/'/ptc* pu 4
-1xa/co /!'2'e
tT, 4
Xforn,n'), 4 ? 't n/*t ry-,r/c, ttttt,' ,r1.1'aa) *" a4 t*"
d f r z ; ' 7 ' n & a r l P " :
't, nt ptt44 i l^'r/fi e'4"1t' 6 a'Fu*
fXaro't ,^'{'4"'4r *i2/ & 7*tt
cnPLec'ful , d'u -"f* tTtz
4pt*/ /-f*{:4;f'"4a9ry a,,,7t;';^a(. h ?n*fu'7{'l'
ta 2a *af A 4<' d"t"+"/ ;71'74/
' / fur * h/* ah "/H - ry
A-rre&.
t'X@ttS *rr*'t'& o/'Ath"/ P77rr4 -rrnf A- a
6 7 8 .
tXh,) 1@d'
-4fr{EeJd rfa d tafZr{ ai4, r. r/+ +v
,.ff4y 4).rlZrf/f 38, 7"te tn '4futn
a)
TXord = flXt-+mnl,.)h r 4
hrr'nu, X,rre) n f*;*t'L t&d'2*d ot
s',4 x(tt- * f\r*r.tworcs
1a.2uc{ 6 FH T&4+, ft at *i 'dt
NFR: u-4,4) a, /D4r du f;it;t IFR
{4 +1 . )u,,, .fi2 7t+tq 2?*A':--
A.. Asr it> ,a ') f4 i7' rP iaa
T)1rre,2 ' X?) t /P -e) .,
- * ' ' *o ' , u4 'u ' i l 6o
= p - J l { t o ( t + " i t d 1
e 6 , -J . r l ro ( t t aq ' r ) >o ,€ ' - to
i l
*" = f/8I+ NFRI
. - t ' l flnr)
j\:
I
4dc, T . ) ;1 i [ (o -nr l , r / f I
= tu f )11 tQ 2 f , J ' ( c - n7 )
c.-, 14, t r f. -nrt /r 1= > _ x n r ) f f i
,tt Xto), d fr. l.l > ,t^* nd / r< n/"1*,
de, Xte)=o /* lwl > n/r > d'rtat '
, ,'/t r'dt' ) t ( t )=#J Xro)e ctb '
-n/r -iut"T- lux" f r ) z
- n/f n'4
L f "n { alnf l e-r '- - '
er- -
dc'tt l l J H
= T - L)71 izo
? oi rt-af l
uirr -of lai
ln ,&, J'(c-nT)
0eq< an *yie& i e<tt od *
- lz -
rit L )1
o 1 2 r + r'x(o), tft) , Th) x(il. xf*)
7 = { = t
d.6 Fe Ja * O , a I a , a >
't(o) t1tr) r(2,-r) x&lf) 16)
z 1 - . - { = / , 2 !f,-t 4
= l . 2 f x , f = ( 2 f 1 L : f1000 2000 3000 4000
100 1 5 0 200
L = f , s N T : f
L?rF -t -
N - l
d . T N = 62 h = 4 t , 2 , 3 4 . r
_L.46 T
Wy^ry f o, zt/r)
+ 2 n. - ' -J T
" ? ' o , t r 2 :m p , D = O + 7 '
{.to Ya
T : p i / 2 0 0 ; t : 0 : T : 4 ; N : 4 / T ;x : c o s ( 7 0 * t ) ;X : T * f f t ( x ) ;
m p : 0 : N / 2 ; D : 2 * P t / ( N * T ) ;p l o t ( m p * D , a b s ( X ( m p + 1 ) ) )
:i
r,3,Fr o. n/r)
s q u a r e
s q u a r e
,r/r j
: l t / l" l . i io , i - l l
i i r0 . r I I
i l \o'l- I \
i / ' \ l^l
'*-;-o
ro o t n to rao ra rto rE zot
FarTttttrcT ̂ o*t' m.D s O +
[a, )rrh)
9 , 8 N = fU r 2 O r r , 2 . J . 4
t n , P t O e ,
f , . fT : 0 . O O I ; t : O : T : 4 ; N : 4 / T ;
x = c o s ( 7 0 * t ) ;X : T * f f t ( x ) ;
m p = 0 : N / 2 ; D : 2 * p t / ( N * T ) ;
s u b p l o t ( 2 , 7 , I )
p l o t ( m P * D , a b s ( X ( m P + 1 ) ) ) , a x a s
s u b p l o t ( 2 , L , 2 )
p l o t ( m P * D , a b s ( X ( m P + 1 ) ) ) , a x i s
a x r s ( [ 0 2 0 0 0 f . 5 ] )
h. 7 *q€e/, d. Ttacbt l(Fft r fa.s f,O Jffa J
0
- t J -
/at, efu *tcc-46 au t-r/& fit Th., p(+{ k trqt"Lel d{
€, il
L : 5 0 ; N : 1 0 0 0 ; T : L / N ; n : 0 : N - 1 ;x : s i n ( 2 0 * n * T ) * c o s ( 2 I * n * T ) - s i n ( 4 0 * n * T ) ;X : T * f f t ( x , N ) ;m p : 0 : N / 2 ; D : 2 * p t / ( N * T ) ;p l o t ( m p * D , a b s ( X ( m p + 1 ) ) )a x i s ( [ 0 5 0 0 3 0 ] )
at
L : 5 0 ; N : l 0 0 0 ; T : L / N ; n : 0 : N - 1 ;
x : s i n ( 2 0 * n * T ) + c o s ( 2 t * n * T ) - s i n ( 4 0 * n * T ) ;
X : T * f f t ( x r 5 * N ) ;m p : 0 : 5 * N / 2 ; D : 2 * p : - / ( 5 * N * T ) ;p l o t ( m p * D , a b s ( X ( r n P + 1 ) ) )a x i s ( [ O 5 0 0 3 0 ] )
Jt' utt tv-p<;,r FFT u'+ taaa'*
( xrct /'-- €ti':to'^y;**TL*"Jt/re Fti
ntfnrl
4pt+4ta cn t(' 5 2P' 'i' o^/ 'o nt "n7&
rfu tctrv ' 8"dL fl& ; P'a64at 4t(
qld -t rz "* ,i, '*y/'rtr *t"6-
F/
ktt) t* t i fo, f,a)' * Y
tSr*--'-'
r-- ,** rggfuEi-
oeot a
4 "/ezc+ frfv c&sy r/ rrc),c/t"r.v ta du #atf 'ry,
{, t3L : 5 0 ; N : 1 0 0 0 ; T : L / N ; n : 0 : N - 1 , 'x : s i n ( 2 0 * n * T ) . * c o s ( 2 L * n * T ) . * s i n ( 4 0 * n * T ) ;X : T * f f t ( x ) ;m p = 0 : N / 2 ; D : 2 * p t / ( N * T ) ;p l o t ( m p * D , a b s ( X ( m p + 1 ) ) )
1^(t . , /*L>rtan ,'d1; t'1t4
*u,? Lft - 4/rr/P'e = ftry/'r =z'ff
.t;7a , ktwtu, zfrl c"f{*Aa*
; prrl/ra, €, f ,/itd 4otv 4,
qlar ld Enbd "tYtz
'
rtu fn( nyni^aced q *;'h4r uo.vz zl, a4 lo eat te{ 'd/ /uuu'
aa*r, A&ftX 2h Ztr.u /t;/aee
6d'O / c+ -/ , lfu Po4'T
.3nein &//orlhf "*s't c'q L;tlt p= ioa'
N. Soao ?r, ..2"rt t74.4 P+ha '
5.tz
qr& /alr'/4,
cx /u<
' t (1) :o,ef Io , l ts 'aGeJf c
f w t - c3&f t t J
r'd m7irt* qn t7,r--
d c.r./.3?, 4/, or4a( A5: ,o//s .
,f'f*
&rtutt
a = gl laet xcf ,i 4 / !4 rlta
. - t 1 -
'?'t14f-{4 t*ryV %,
rtn r- 4At = 4a5- at fR ,i (-,r/r,
,rkJ = (-62,g, 6t,g), filrt dr
6,1 {d aqvact< ar dt re rqrt
u1-1 Xfrz / 1c <.€f I, flb.t 'A nXc*a
8/ i 4;/A./ ";a4t
d. lelz eo
8/*/At6 =-,qfr,( 4 44,( y'2cuOto n^f
Ttuo 'd- "/h-t,
af ht* +t ; 4'4 6
./.h.," 'rl&
Ar4{ t" f*'4 *4't*Q.rt {"-f, 42 carrfa* ff,;p"cnnZglre^,* ry
d o/r. f;-f q /^62/
4e4.f .rrt| n na&lf 7a"ttil4 f
* layrrrr**a' : f:A,rrotu n;artl^cn/ I "hJua*ct'{tt
ortt( P"-/0a, g' /o ' uJt at "71*+ tt*
aoulrI
Cnttn!,
7.= tf/atn61, -
,l/ ru r lu Pry o'ota|r/
G x z2nk'ei,;^ ; it/ f//
Jf lao lfo ./*f^ af lt -'/, ! /, +' tt / i / *14
; y'4d'
dl* d'icr apt^'LZ'n'
,aar
6.2 {(ct deq rr{ d/?oa/ a qtr
a/ 4t tlorrrtt4J / ** u;4{- 7fq dlafe nt casa^('
(.J lfrJ aaaaA av, utrft|," frfla dt fe
,; "t'{
6,7 n atpznf da7<of {orl {tlr.arla
Y ' a r-'t on ^"t{o^/(
fuaLi - , f /u af#, - t r Iutn-t7 etd 4 A'zi , & /e14 ,tof *tf'J
- ry fu^ru' 'Y' 7114t 4'rfh'
i ex-..C-
art c*taod N
anl an/ 2aaftyan
6,.f 7/tz a/73a" &t6*-/,-/ ^/7
{t) = /,r frrroil'
i *t,*.1r% -r'e*tt f,H 4:4
d{ }n u(x), fr n fi. nua^lca'f
'&c&u a' eatfra* t'r ; "eqoAtr
( c , df i ,a"/-''4+ a'zeta'u' 4
t / *g t .+ l fz ,4b++ z r .
7r*' , ,r-( uo r tt,'ot) = t'f at-ft) + l4o(/t)
+ /,f ,fr'rt) = {rfd
+ {rH + ;ttrtt)$!a)
4 $62 +'{rt*)
€,6 7U- aTeta* "tetc'*da( n'
dlo = (zt sr) utc )
; ,,,-'A?. dri r* ryY 4Pznou
il. c-4|;;"n zx;t) q e /'"''c^6;
4
d t , 4 u=4* / z ' a t *
{ t1-- / zt +t ) / a' ed } (,.Pot) = /' ltt t {'/t)
ea4l (2ttt t d 4/+' = 4 /:Nr) u'(3) = c{&)'
7t4t de qo& n 'hzaa- '
- / 5 -
6,/ ?1u naohtef,r, n/e
{ftt = (* r"r, t) uk)
; u*tt-*tyaet . ,f ;' Z; *VV
&-"aqnz dL eqt/4eut{ catectdt h I
/.","6; / z;:' , ,ty' ugz'l*uz
{tx) c ( cat uot)( ct,rtt* tl'ftt) s/'lct | {'e)
(m ar t ) rl u,(a' ot ( cA bLo) 4ttt| ' * {' (*'
6, tJ
- )TAuo f,tb ,a4ofu a 'htu a+
6,f, tlr,e Dr.<1af+ acu42.( 47
{rot = /.t (uat)z
i ttwnaryrhal, 6t z'tvPw'ual 'drd
dvrqh^tL /e
41 44ltu aza'aa*{ ca
A P-#Z"D, 6.f,.
6.f 7/u DT tTc&n "Aac'-ib/ I
{rnt = (2arD u fo 1
n runeyho.-l*'<vt* /tnl tteV*t& 'n'!7
a7 utrtl df i .b;t ,-Vrt '/*tca6ot zL'
u"//';.tt/ r2tr?r) pt a *tD^ a/ z'1
'A,' ittr , Jt i y'is+ 'tt ri ffra 6'6'
e- 'O
E"a'*, €, -' €-u e'&z itt(
€+t o
6, tO 4 o- /4 ?az. zlz+t
f t n ( t r + ' l r ' , + t = o t u ' r / + ( u " + l ' l
= { r + X / r - / * / , n { ,
Tr.a ttL cTecZJz oo nel ^&oce+ - Crt te<
J.y'i 7'f -, au( 7 - rJ , f,,h lt: tur/
{t<cntt /
= ai , '7la io c /as}u
. ui'- €+ U-, . Vo - e{_ - Yoi , = f . i
- D . , = T = V ,i , + i . - *- = o 8. .ct t . 'c-= o
h( i4. &', = - L',- fr
Rz
Z=- * * zg td - - i r ' t c )Rt fr z
dr p dt ztcnt ca (6'/?) '
Bc'n* t-= O
e = u o ' R tR ' tRz
R' g*s*ol e-t €* =4'
u< &nt< ,..= #
F, cL
L = # . , , 4
aA(,y+q^bu ha ud*reR. il. 4t /R. A=r,2,3*t = -n/R . o,t.rl irrt 4
* f , f . f- f 'o
6.t/ 2/* Va" u(()- uc ar',/ /eOellq -dc
.4 ira ,*to&, .c-v t J4-{H = R iret
7A44 d a 4t<-c Arn --r-u'"-f o7u'2q,t r
' 4 R
6s
+a
-+
'ac'
6.tS rct A
6 , i 6 .
tItt
'lllq uv i<ttC, Zro -:. q, s O, + Al
. - r6
7' | ,h i ,i o.4r"{ J< caatt {rn|a, aroflJ, tira an^h; tzcrts of
ctnfe4; ru ?4at-4t a/ arnsfl 4/
afn-21 . .l!r n fr;. ,z-"ir.rl '&'cmt
t$ ".//r;^"rr^6
.z *r/ ! *te ta cdpete&"f
td ?tte ,
/.2(1') Ce4a./, ^d. ipe.u,'^c# &f
,rarr&i"*y d.ioeu if ,re/aau te,
(2) Catua,/, hi"o,r. 'r/ 6ri. /;tn .a,
( J ) Casre/, /.ita. oql 7t ^'n^'o^f"
/,J ,hv y3ufn|, n > e ae ,1,*<
=,t tn4j -
Senzr< { to+ol '{ful t/fal = {fuf,44 lole d rol 50 .
t f*u r ('4tDI',( fouit {r-ui = a
d.il eyluo
{ r - lu |= - { r tu i = -* { r '7
77rt( eAt',n{,+tI;( bry
h *t Prrir*' o+ x7a'a;< A'A;,"P
,rat/rt+ -
7- f L ro | , 2 | r (n - tJ - +3 , rn -g j
I t a l=o Pe l l n<o6tol = t Ea kt 1 -+ ta t+J
-- o
in7 = r* l-oi '4 A kzi = 2
f r t i = r i t , 1 - 4 4 P r l s o
tu t : z to f zT -+ t " tu ! = -1
i r 4 7 = z f a t t i ' + $ n I = a
l r r | = 6 ' h n = f ' 4 " " ' '
Ttua t* iPt/"t ,utpc'ut a{
{ f o t : 2 4 { s - t l ' ' } ( f n ' 3 l
. Garnl)>P ufa'tJ
=f # 'pgtnl
77r.a * aVn, E;r* ,1222 dl /a"'rtrt',
f*/^-+, ot/ us 4*tt'2t ,1t4,,a
(qalrrlrt-nt)t - # #-rrff i2
(u,orl, g t-at)f,nnt
- ,rfn'tJ
uSaa| t tl, fa't7 ut
Tlq fu 4r'4f't" 'tacl z{ 'no'f
14 Qe rc< !./fot A 4,6 ufal,hro+
4rn7, 4' a . r(rr P * etl: pi,Tca
+".4/37azd/-.;{p tr'ia, t4 &.'4
{ r l a t : 7 / r u / ' f {' / c rg&aFefuq; rAt r 24i t : f ,v. 7aa4 '( foI= tt f YT'r/ f '
uLoI' ttf6t
Jr , r t=, ( t t " l ' i / ru ttir "( = P/ & 4 oq rt"zgt
*Jit^l
tu aaaif P'-fq
rrafiot . 7fu*+#/*t
; f u 1 o z , l t t J = - 4 * t r ( o l = a htt( z t{fr.+ nzn / nna? J ' Jrl FrR
15 f," *i& 4 /tot'z,.rurnJ; l .h7 = 2, i f" rnt = f
?,f , n=oI a n * o
,Jri F t
i'r I E'rl = *' f u rnt, atrtl +u[n-zJ+ "tn'tl
Jra a -t-pai{ ery ^-Ze
t;"14. *ff t /+ =O,af t -
'nOt J .tfr'|"
1 o ,art*.;l-.
ttri FIR
t rqot , {ttuJ 'r{t/"J'f
- l r7 -
Thtrt At taflt/"t *l'dte
.n r - . a t ( n V0
I ' rn i=2x1t ' t ) ' ' l n
lfnl=1 7- tll n <Q, &t'etztt
snlr!(- frrhiQ> ile co*t 24. eg*c,Eh ci
! rn1 = -2 d n-, 7 -26r Io a!'$otnel + 6 $ rn' l1
0e *f& *'wutti'+t, *{ {taPa, h",
n4: {&1=-z{pi-z|t-'1 -$r'zt+ 6$t'fl ;0
b t l ' I i l . -21 toJ'l f"rol ' frt- ' | t 6 f,,t 'sl : 'z
n * z: {tzl ; -z
7 t4' 2 trrt I' $tol + 6 6,,ral "
t-'rkzt
- l = f - t ' J
a= E ! (sl'-zftzl -'z$rzl - fottl+ 6 { tcJ
z(-z)x 3 t 6 ': O
n >+: {t+l = -ri", -tS tEl - $(rt '6 $ftl
= o
n>f ' {hJ z O
I,to tet {5frl = Z &tn-G7 u..te l, ..rtQ - o
v, P"/no ui&, tf or7 -J{tn-rJ = +ufnj'u
{ t l = / , r t ln - rJ +zufnJ
;aa7i&try utnl = {,rnl d4 tutl .{il'q
/.> n <o. u e+rtp*A *czPrltt"f
h:0: dt l = ,, f {krl
,t zEnfol = z
r,: l : {ft l = /,f {fol
+ 2$ftI = 1'ft2 -z
n=2 : f t z l ' / ' 5 t f t f t z57h l 5 2 r7 / ' 5 )
n ' J { t t I = t ' c { t zJ+26o taJ ' t x0 ' r ) J
u t d . f , h 7 : O / . " a 4 h ) + a ^ t l c 2 ? ' , < 0 t
Nt A-d '/ a * r, c'nt
l.rnJ=a P n ,"o trhAt /r//'fu
i ra-(1 = o /'e a4 d z tt ' 71ad tl'
&nA.*r'io6e"' tzt' /'t 'atzfia4at, , ,
{^ t=?*4t ' 'a tut lT
4e<-.tc caalt 4 r?r,f, 1,,0,'"tr'-t'"f rt'6| Fao
{ nt = t pl u rat + t (tl u i"i; : :"'iill,' o'
+ f tfl u tn't|' t A*t u tn'4'
"2:;frY:;*i"rf '
{tn| = 3 t tn| -'u "''J
r 6' ufn4+ f u fa'3J
+O, i t fr , -47 t " ' t O' ' t fA 1
= J a f t r l ' 2 t t tn ' t f + f ,u fn ' |1
Thr, 4 (y',t).
{ tn l 2x ( t . f , )
74.
zt?-
f6'"
$ ufnl = u,Frtl t ztral , /et e4/ n 1a- fu
€trl= 2i in-fr(4rtin u,16)
{ r o \
I , El fa'{l artd7i{'o
ltnt= Zia'ret 1v3 l '+
" Zlrn-61u, fQlry
= {, tnl + |rtnl
/*a lu lttttt/o4 -?w 4 lu '7At
i l{oJ;o, d ttq, 'z ,trzl= 3, *att o /*
0>rJ e td a<o , 9 fP t r - * '
/, I Cau4/cc.,'.3tJ
7' ta l = 7 &f t -4tur41l = o
Ah7,s: ,dxfl
7 ' t t l h t = f l Ln -p lu th t
h t c
,/or urtnT - afn -ar|, tkae o*r afta+-
41{nl=g f*
h€ht, Thte t r t?e'< '
(Hdhl)
l/ u+ til :
(3 it' E't 7 ' dt+
{rr,t = E
t r' -tl| u' tl1
=F Airn-01u,t61
6P
= Z fn'frl Pv,tnll=c
- t'firn? '
=p1,inl (t1)
,l fol= 3, ( nl t '2, Are1'a
- t & -
{ f "1 -Zfr"- f r Iu,reT'1=o
= Zi,rn-ftr urft-nr|fr=nt
O"/* 7= l-n,. 71ua f i=d,t{, el
a0
{,ht = Z7=a
t a - h t ' S t u r e l = { t n - h ' 1
7A4; A.tarr4 A. ycy>I,Z t2 t/ ,f at = /,dea 6*, h
, zo, dl
t,fal=a,trb> nto, zl*t 4fn-#7.1 fr4U i >n . TA.ta s,s ls<,
a , , a-t
{fi1= frlo'olatll =F P'anrs). 'utll
W {"a
7b opaodih fe h a!/ tc atd *<
Wt uuLh't -n't 'E
fanl = t, (1.wtri' ' ut61
- i=o 4-,
narf- e urrlJ
> (reaatsi' \rL'l , o
^f-h&Mf &4 c7+t,o" illfr
lnt = i0loa6:f 'autll
(=o i -n
= Y, ( r, oaa trf 'hu
tll + &eaa/t) u hJ
{oo
: t ,oootr { tntJ + ufnl
'tu;r/,o
{fnt' l 'eaotti { rn' '7 = u fn)
y',tJ 7a fr-$ nnr7 qln-leez cd
? !r, = /(t l+urn',J' "" n'[n-,zt)
g'f A; 4 ,r^art'rt.z44tq q?'-cc ?tqZan
1t nte* lf , ,,t-i aTnlu atfryu t4
f rui = {'/ro trh> n': o : hf
I o / , - r . o a r d n V l a
,,16 c.+t *4.Ad* &a?ezL u9., A
{rat = ̂ Z 4 rn-77 ufeT = a ii 't r( l2=a { = h-t'?
n- * a-:ro'ddul i'aU; 'w ds fffi
r! rU eotaE* 4e ft f"no / ,u-l! n er,./ t'se c1'3 alzlt'
- t /rh-tl + uh'zJ + "'+ ufa-F? 7
{r"',1= 6(+ufn '?al )
Tt44 pe 'lg'v , /- nr7 - ufn-/",
{ta7'l in'tJ = t(o'
-4.
€ ainl r Ut tal 'r u3 A)
Jt a batz*-t sd E;u ;tzlaurztt'+(
9nJ.<>
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o
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n 7'n1
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t s l
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t :l == J '
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t j
r j
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r,{n'rtn
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ItnY.[n
fn+t
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xrtn)'x,tn '
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7, tf, 2.itt
Z /6 /tfnul,tth7 / r-t lEial
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ray a;//'4 fu (r,/8) a*l (/, r?). r20 {En j
Jfi ss epuafiia u Ah 'to';c m zt'
tr< i+ F*lb /, /?-
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u(n<1 utn'27 utn'Z)f,tn7 r2n7 ,.rt^1
utn-+7x*tn1
Eotr-ol z 2 ' t l -*7 ts, daat]
f, t rfirn, "' r
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-&Aanfi, fltn *< 44/4
4h f f t i z ( fn l
Xrfn+t\; xrtnl
Yytnrtl = /'tn )
f*r'n'l : r'fn7
!tn\,4t)(, tol + 42\tn!+a'z
xttnl
fp,rx4ofl * o:2qtn1
7,22 q rr,z "-ry
aaetal a t r.ZiZQ
x/a*ez( ef ac'o. * ry
a+ttltr'c ;f tnl= o
arr/ utnl = a h elf n <o, 7t'4 {''
d
atoJ - t^il*'Ent 'uXt*t*':T
^d/ l',tc*t4 /4 'i It r-tuPN 44ze
Yrlt - 1.eo?/5 t-' Y't| s llQ )
or (t -/,cas tt)' ' ) /rrl -tt(l)
#=fu7,23 {f,"t = ! afa-t 7 - .7 ufnl J.
,95 t@lae .uf"rJ'a€ kra €an7"G/ '*
P.s#at y', f 4e I ftJ's ' I'ttJ = -4 td/
dfn=a /*& n '4fu+ zhtv t a/"f 3 ' //'e
ttq lza<
t t n l ' 2571n- t7 - +5 " ' n ' t J - ,
-t - ' t '3':-4
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: - T
ffii,:i:-m;ItrF.h<a), a* ie"<
'frlt' 2 l'tclrt t - 4lu4tls
=(zJ- , -e l '3) Ul t )
.Hu(nl
! + 0,2 rt tn7
?, lg
[';?,:,trJ" [:,' : :]E^::J. [" J' ̂'! tnl = (-,, s -r,, I yX,ItJ , .u tn7
ukaL 'bf/-:
Y2=U(ttl :#:,1.1i:::
l S a n t f l " t a o
I + a " t J l a e t o
r ' /? drnt--/ ,aso/s: /(a-tJ = afal
0"/.r4 x tnJ = { fa tJ - tAu dhI " Itn+tl
rk^ua t* /rue
X{nt,! = 1,oo?/5 Xtnl -r ufo j
{fal 3 1,c?o/s' Xfnl + uftl
fli trr ss .?ttaE&, y'-a&iauar t -
U 6tj
. - 2 0 "
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i(rmru[n-tJ rufntJ ru7,-rlnttr
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Yw I (rr p { ltrsx i?tov i'u ot . i Uo)
44 HrG) Hlil a'v A/acal f*4
an -tlew Hlil H.fp * HrpHl tt).
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*' r*u:e{ a//'/-""/'Zt ^ fu ''o/rgk'
o?Eu zb. f1/ n'a'o"a" ;'fu niSnl
t f t ) = r i d = ' h r ) + u / t )
utbry ure lee r'4t4t (&'to), 7/"1t n:6 5s
"try*'6i i-tr--;- ; o -4'-l * *, * [oo'1,,r,! * l o - 4 r r o : ' 1 ,
t o )I o " - c " f , o J
{ f t ) = f a e ' t l Y l o * a t t )
ilrt A,er at t'lafr' -7a2'L i ^Az
,ulrs ae 14*), 7At -t'//*f f::
i.apeset-;'.;//M P lE rr)
_ t a l *
frihui* //rQ 4/2 t'/ oul rry
fu4 H,GlHrtt) = / l .QtH'U'- 'Y
/* stS a V&"
k cryt irn'*++te
77n- 6**'u 4 fo"'at*^ cnPcEA '
F*Ur*tO 444fu4'ffi:F*ur*loq?'maare{ ,* Arelta? /
;;-b-.'tu-'"o'tb'' 4
Ht 0) u 2x 2 P'/ '/ H'"/tl h' )^ / '
dr; Hr gl Hr(il n "u/"'uol /"2{
f,r|) Hr4) H hn{/t/"-a
82 F*,Fz],f, I(e), hK&,tff i, '
re/ ZUya ? t-, ccp.+)^{+ a .ti;t|rba ue -&ry.< , ry
(f'tS) '
I = t i t o ) ? , r t $ ' 7 2 / * )= E r -/ OJ trc) + ox uro)/ G4/- ao 7x z d'4 4-{L H&tHtr>
- 2 t -
fAi n 'fu *cfy*f c Vafioi' . 06 4e4
lffr-; h dt "une & r&/*) ct 2*
anl ; P.plh 8, /.
" 'J;. ' , ]L.a,v;, A( w et/tcf at
e.f*;Av w{afu 4,zra, tfi
r*t*ltd er z *t .
tt/ Al idtt*h'
A l l x , = u - ( r ' + z ' ) / z
= - * r t ' * r , * ! "
6 u = r y + 7 J n i t
ry t r ' l t4 td ' i& 4" 2 i '=x '
(b ) + - rF " f t - l
T"{
tI
xt
J
2.J \
'flu wz6fta& it z-St axt&*
i t , t x z . f b
;6 e*ttt+n'f ;
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2.
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ry-lru#I:I,"9 '; .f , '$ui nr lfi
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xt - 5'k2 , Bdf ;Q
-lA )rz
"o44a,+yf ot U"f4 Xt.
, { . 7 2 .
! = xz . 774td 4t atfu'uif a4l w ,u.bd t6 ca+t"af x", Tlh Alo
ntOtr" e,t vrd fu to-o 'rt)t6--
ie-(z u ilsta - 7A2 z-lL"azh' l"et
*qn*q-f ai, + x, eu{ wef tt-7t '
&p ee.htf et w&.ry (*4e* 't,f
eztofAaoa
w &i,v6te , 77t+, dt *walr fetV
etaryl * 2-s 44;rfi'' /; (tt-7t>/z'
AVllft lu KCL ad Mcb A fI'{'
, * , - r y - x z*'Arttl tmp0<za
i , = - * r , ' * x , * t n44.+ry zfu Rlt ^tnX fi' r{-la"t
/.tV N/4-f.r, = /, - to Xz
u'hcl i"f^fu
i r = ! x , ' 2 Y z
lle ret
,lacA^/te'
ita = trc). t t
"1' t /z -t l
'/2 oJ
, c, I
- t- 2
l t v
/ 4 f
frtlrI o' r o
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BeJ lr
'it-/
Pt4 = l - t
II l
r^t 3 f.
dt.,
a
v.1",'lu(t)L , J
+ O 'q f t )trb,Tfu)
8 , 4 a : [ - 0 . 2 5 - 0 . 5 ; 0 . 2 - 2 ) ; b : [ 0 . 2 5 ; O ] ;c : [ 1 - 1 0 ] ; d : 0 ; d o g : s s ( a , b , c , d ) ;t 1 : O : 0 . 0 1 : 3 0 ;u 1 : 1 + e x p ( - 0 . 2 * t 1 ) .y 1 : l s i m ( d o g , u 1 , t 1 )f 1 - n . n n n 1 . ? n .L L - W . V . V W L . J w t
u 2 : I + e x p ( - 0 . 2 * L 2 ) .y 2 : I s i m ( d o g , u 2 , t 2 )p l o t ( t 1 , y l , 1 2 , y 2 , '
( 1 0 * L 2 ) ;
I0
* c i n / i n * j - ' 1 \u r l r \ f v v L L
;
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: t )
,J i*ii;r *^ a "aa6"nje/ Q/
'dx'iIII/t'fl,^n
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20 2t rl
[i:'i' l*: : : ] t:;:J - [ ":'J u "'{(*t= rr -,"1[::,,:J f oxu/t)
-:1. -
Te 7r+t7t'*r, /**A ran V&e-aru *d7v,ef arz e,e/ (.rcL)/ 4A) ead A. .JU
h*t d.ee1 (d&zf Az), rat t3o
St&to aaq*1b. rt*ld d. u"4aAL +a,af a'u14dPnrr7rrl" al *ff-Q1raat 6 ehar 6 At *xaaferq-.
a : [ - 0 . 2 5 - 0 . 5 ; 0 . 2 - 2 1 ; b : [ 0 . 2 5 ; 0 ) ;c : [ 1 - 1 0 ] ; d : 0 ; d o g : s s ( a r b , c , d ) , 's u b p l o t ( 2 , I , L )q ] - o r r / r l n a \
\ s v Y /
s u b p J - o t ( 2 , I , 2 )i m n u l s e { c l o o iv v \ g v Y /
TIL f'r€/Lnayaaa"Qa
,f t C/t t,e ,czf 6 tjznr i daf ot" ,*f
u7*) = 8/c) /-;Z? tl+ar< lfu ,u6a? tfu,6
/*r, z(t)) =O A a/a)= b - olades/. "Au
;f?,rr"*t^ { (g./a) y,;//", l/* € -o,
t
J ,,.t clr = y (s) - t/a)o
/ 6 , t= J 4 ) r z ) d c r J t u r z ) d rt-
: L
- 4 f x , r Q t f c 7
' ' 2 X z { = X , f / O 7 2
Y: = -tFi x; -L#?ir * orJ) Urzt '-o.f, ̂ ; -o,r xr - iJ
i t = o , 5 / r . , { " t ' ,
g,g rtz-l,aie fu4 ,*aga'a' 'o f-atd 4r'rc)
tao J ,r&/ead (e.ol zz*lo 2 tP ory). 2
atle-ox&o (ea ri zs& 2 e? e/41v)- J
2rrl* 4"rrra (eoci tzztda r ? a*V) a't/
J alnTua f* ( 4J "t&
t 'T a/af )'
Tlqa alc *d7"an '*vltza " ut/'/
t ? a-? aafl -
g.ro e-=€* - -o. or z # -
t * ;= #
ir' #
eu+trtr /% /fr zb af>or
,a6 t* .;wtEy Aa,r44" ; c' Tlua av
t b a a 4 E r ' - 9 ! . n C , ; = o# . ; T - R
' v ; - - i ? ( a q r t r y + c \ )
h=425 1a
xt t 42 x ' t
X , t z u
- + 4
| = 1 , ax r l _+J
7 ' 2 9 u
+ 5
x2
z 8 t
1-. 1, J
1 J
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lJ :
X r 1
t +- 2
6 ,
xt
l
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J
o
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x = IL
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(t, tr) ",r/L d = O ( arfYf erc'61 a7
4/t) = ,f H a*d-'x/a) =o ) "f& alc P'o-
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h "41 >) a a*J x/a) = I .)
o l
6r
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- 2 l -
,$ fc= t , d tn g,/3 tu) z A
%s 53
z A
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t ) J:J r zs-+l
V o
t l ts )
Urs)
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t 0
; - = - ( c q r b y z t c l )
F, t I J/ a.v ua.-aa 7/a, aa<:f4zf u -ft(t) dot.o d ' - f /UB)
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dz at+aaaf /h;y fu 4t a,tuf'/ ta"fa
& .arcztV Z*mr)n/ 'i P cikt' 7*4
ar ,tgry
q 4 i ' 4n ' +R R
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i = 4 r ; 1 6 4 . / c r y
8,/2 F-,on, F-f,g,t'7 ae{ rV r& at<<ZA
La P*d-/&rrrr t p a.r/ &, / /, /tr/ /(at<
- , = a , 2 f l t / a , t ( - X - r + o , z f ( - f ' )
f , = - ( a , z ( . - v , ) + 2 r t ) )
t = -( -xr .r o x,)
oL i, = -o,Zi x, - o,5 Xt 7 O' 25- u
i , = o .2 k t ' ' 2xz
{ = Y / - toXz-
an ,litzztz,ad ', P^a{- A,t // a/
6
* ' ( ia ' t t )znnts)=a6
2 s . , '
c v,J
R- C X - 7 O v^rss=#rtt)= /osr+z6.tJ _ g 6,1
. f s r t c ttasl sli * I
J,s.r to i l fsS= -""* /2
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Yo= f f i Voui=; ; f2ost r l5s r /z*
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Ll 6 gru
d-s
1tt
u6)
T4oo *f 4 T*Z-"/ k &e'nd*? & 74? z s r ! = - 2 s
2 5 + ) l - ' 2 5 ^ + |
citz t/t na/lZn F, J lo2 , 'Tluca lu 4
'ry
eiuriy' a A..f rf ".f,&rw.6
Zfu ss - - z x ( * ' z e a ) =L c o ' Z r t n Z e B
cq4aZal uo V*4r?o, ,f,Jk) "'4 k4tt 4
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t*B=
- z ( 8 s " + t )
t 2 s ' t i g s ' t 5 s r I
V ro = Z .o 'U ts )
zns yYtt.vot) =
{r zau ,*
t 2 g '
/ z s ) + # s + 6 s + 1
A t L 2 ( & s 2 + t )- -F ; / z s t * t s z + 6 s + rTIz4 4a-ar' * nr*/ Da/'4 /ry?i
aa st' offzanA uaiyt T -"'"f e)tt"'4 - I^-
T ' S
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r/va at lia's/n /- {7 fu
u 6 /'o,rt&i*{ utt; 7* .onathi/ dt"'/p'' 4
Hr,)=#,'=
r ' 2 5 ' n l r 6 t ' \' ( 3 5 l z s " r r \ /
*>f,zttr& ,
- 2 # -
f f i r ' t 1 / ' j + /
8.t+ .-/ a ,' W_ l,.f"r-fr._z s \ )
fr ,l/r'z?|v-L
z s ' . t
Tt ry.4<ru"P+
7h; Zl;tl -n"4* a.flt*.*fio/ u/n."fq?/
dacruiga {,i/ c.+rx.a/ ia Fa1 f, /+ (6).
g, lg tJt.\= fJ a- 2f ,g
zsL+ t
T e64-czf pryL
8 , t I J " . r f l = / , f , r L + o , f
l ' t r ( s ) = ^ ^ - . _ = - \ ; - (z s ) + 4 s + { J ' r 2 t ' r ) , t
: 7;l,.UJ ,o a , r J x ' r o ' z t
f. is .eV at {aV/'-rz A,e/uf1.* d!*f
W -:*fu e.cr4aafr.ri o. *ris'o 41 t(a'"
s'X/s) = 'a/t5S'rU/s)
/ n ) = & X t s ) + d U t s )
E-r1 ab Vaaf *fi'o/t'', /-4 /4^4
(sra) x4 = t'/ /') Lv xtt=h ttu
T/ttta uq r{ttry
a- (trs) .r d u/s) ,- (* + a)tlrslYr i= # t lu ) ' rdUrs
a^d de r,4r4tf,L- /a"'af"/*t fu u 6zY a
/ /r,s=W = _!_+aLfrsS t'r 4
l / u 2 = # - = " , 1 5 , r . ,tas-.rAfs * /2 d^+ 2,af S * 6,6
rlt ^q Zart, t-//*u4 /farh ez
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sf*;'zhl a4/./ttott/.. d, a-atu frLC
c+.r..t.tf . 74t rurtn/eU 4 uTai^fr+ *J
? -Tu u'tto/ A Aa n/r&z,snZJ'a- ad
k e, // ,tu zL aaeta il'"t'na tfu /att*t'
ttaz4 8 atlafaa d' /t&v utzt ttt'u'U< f<*la
'ftt etct 'au'a'/'(a, o) P'oa/ 'S' J k) a'tz
a'oa*oi^6"f /;'7L /fu "ftz'h
w/{'7rz
ffu m.4c& ctz+'ttilf, 7/" n'on*g d
,fta-fe va+rz/r4n /'t t74; '')74n''z+t'{a/'h
" l o,--1,I a
{ = 7 o
e./6
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def ea 'Irt^. zrtt) = X)r2. rrlt). {nl- 7r/r)=d/c)//
f/It, te t{naua -
i, tt) ={ td = 7, (t)
i , r r= i ' t ts =x, /c)
i,d =ilt= - o'i -ori - aa{ 'L u
t 1 L = ' 4 ' 7 t ' L g X t - o * / ' t l u
oL f f , ru1 f 'a '
'ar 'a*7fx ' rc t f f b l
lu"',7,1= 1 , b o ll *', l* lo lurttL4rctl I o t oJl^r,"J LoJ
* {.ftL =:- | o-
-o r./-o : !:'//?)
t 1 s )
6 -
,z s t* gtn G^r.t I
( t t sr t Ps-n 6s+ / ) Yrs) = / ts 'Uts)
/ , s t ( r r ' ) + & , t 'Y ts )+ /5 ' f f l 'Y ' ) = /2 ( 'UA l
, ( J ) . r t "/ r { ' i l , ,8 j ' , t t + / j r t + d / r ) = 1 t u6 l
4alat*+ rt,r? ze{ i{"aV"'tc"{
- 'Zf , -
,r=i,/* uo ,*/*u x,k;={rD,4@1rZ r"t4=itt)TAa ure 4m
i,txl =!r+S = Tl,1')
irttl-Xto= xtft)
ilA = 7i*) = - q2xJft) - qrtzft) - o+r,k) + b urc)
TA4o at ,(su
/ , t u l l o r o l [ ' , * ' 1 [ 01
l r,trt I= I o o r llx,itt l. lt l"ttL+,, J l-o* -qr -o'JL*''il lt J
{ t *S= f t o t ' 1 { t+S + O ' t t / r )
Y t ' { , aa,l ri'{. 4
6,*C u4/,+
120
DLI"L
7lv.n
Ys)- 7
U(r)
9 , =Ylt)
n< /*t'<
#=# #r= l ' s ' i l ' ' s+ ls (z )
'ab ankda-*'a'L, tt) a4 (z) /'zan'aa
,'"t*) + 4rirr) *arf't1 t 4+rr(c) = utt)
{ft) = l, irtt + 6rtrt1 r b" r/t)
6r* lr, AhL ct4' t34'r na h;r+ rac \2{z
Y r = { r r / ' l = { ,
a4( ,'.,{ryT; "js + J l f , - r s z 7 s r r 6
s t r %
A/< e.Tt'L
4 ( , ) = t * f + f + 6 * O
-,t,r!/-3;'r &/'3) 'l
Q hll ; FJ) 'r) t'J'/
z 1 e o= - ) 7 ' t 4 5 - 2 4 ' * 1
v,ru Q/s) ltt Ftt */ -J ad tr1'/e anl 4tt)
- ^4 r,.t^,..- /c t-z'f&
br t -n .6rs , LJ
J' '* e, st* 4,t t + 4+
g ) + 4 r t t + f r J s n 4 7
Zn
l,elap t
D* t a / i ' : t / , 72= v a t = u , T n e a N
4 * l J + ui , ' i ) ' , = ' Q z x t - 4 " -
i r ' i ' ' / ,
i r = f ' X z
{ = b , r , r l t l t r l t } t
; 7 + 8 s t ot t ' s {
? t ' { 6
- 1 7u ' - [ z ' ) )ort^*or'
n 4 tfi 'u ^'-( nt e /'7af'P6
Tltu4 tP tl'toY
H,u)='ffi=#H, t't 4'+t lcXtu't'
".'::,: rf :7.)*l1uf'o* 4'nL "*tnztttq*n
'r "
ht rx'"'"/ "/&/''Z)t"- : /l'*{
u, r;':J,'l iJ,
c+ o=[": | : '),,u),t t = [ 1 , b , L J l Zi - / r r r l 4 r l { t c
+vlzu- l=fx, )(2 x'J ' Ntu
,r,/).+tpr ro aa*Q *nn/t ry (?'tt;
t', ^ r ''At c, onlrrtfih ''ffi;
o/''tr t's', tat st efar'"a'2
{+ ct*a' at ""i"t|"*'*f
'/n6'cot" a'"
{o, il ett ncf ^f,nq"ehf- 'fectr /4n'
F,ad &, tf . '(
[,=S7 a"/ lt=o,' 4'a' t"e 'ite
_./
ff ts) =
il-rk1 r{4"
s3 = N ' ' 4s ' ]+zs - r DJs )
4e6 4 4 o, )\/o rl.c" r-, aotd
- 2 6 -
et O /rcaat 4lats-t + P, -fAua Nrk) a*/
D2G) au c.Flu'e 44 /lr/9 r/a &ynez.l.
q,u
t c) Ys1= -!/c,'/;ft,0'5u/s)
ll, rs) = o, { ,td/4 nrf c'le+"tZn"7* "-*J/
tfu c*i<Y<J ,
uf.;& t*Tagz 4'.)2t'u i5 aan tfzpe'tt"l"
,,2 du €f ol 't'& O. Az V*iz'arr '
,'v ';r,64^ar ; i;'* ( *y'f;;')/t{)
c&f, o^a '*'^'<-'/a'/n4/ ' 7"4 )/u aaa<tt"
'ta atr ft f'a* a d a 'uy'/e eru /"/
'tf, aryc.at o ; ;
&-/ * ^nifc/*"
b r l
. - r o T ' 1 . - . ' + r - t )t,, JloJ $>v)sr/o
. I - . ). t ' r 2sr /o
2- 2 g ' - s - i 6
s - + l s r / e
s.23 k) y6;= # Llt:2 = o, r L/t:)
J4 fawf,- /+ois2 = ?,J- ltat 'tf- 0 a*{
e *r,e*6r^t *t/ff d'i"'at'- /a )c? eatlf
46'r% t(er*'t lr - 7/ra -At
l't+-<)/c"'
t1
,*';tetr cJaa-cQ'ur* 47 t^6 a'
fu&*it, Yr, =
# t//s) = ct'f //r:)
Hn tg = o, f ,l*ct nir ctl'nac/ct'trs"
cr.Lu14,{
Ileeaatc ala sa,1a{a,er7r
2r&A ; a.4,a6," Ut)'xo
naZ/4 a/ar Z,til k,
l ' - | I r rba ty ' z ,&o*?
fudufu , G f,,ef,t*//*{ ' ;"Ju
u . f-', -': J, r [;J-
t = E l + l Y ' z u r r )
8.a+z t A Z t
Utsl
Qit)zr 1,
(rs1= 6
= f l
- = E J
6 z - A ) a
-tfi
"t[: JJ s r 4 _
zt naa/ c-;Z( nal da(;lt 7fu wf"u ^&;f
' z t ' q 4ca la t i oLa 'u ' / / e+ C * : *
Ac"u? /uacfiir*-
o*/( zo{ cltuo&uf
M6&Zr4 lfu d^cal ' 'f" '2oa'T'Q .'"a-- -'/' - /
2 tct-' h roltt'tl o'ia"J) '-Ahrqo/t/ -4Lf Z,/r)= O (atlt
S * zs 'r/o
"fu tdfepz *'ot'cd4
Dc{a e tt"f B A"fuy
t/k) , Thuo zt o4/'l
afiu4, ta At 2'4'*
/"*rfun- fr- u 'Q f, ^ {' 7/Y4 d z'
c.z+tat*t L at'//o- C ,4ftu at ftaay'*
/o^rt* ,ril/ zl *1u'-"6"'/-
*'/e{/
tfu u-+et'L , A" /t" rt'€" '
'* 'u{a"/'/
&f Z =q2 (qztt ,t*""'l') '
8 '2 r A za
< 2 1 -
" - e ' i t 3 ;-
5 y - r z
; , * x * f ' ,
l = z ; = l r t r * j u
r . - j - ' - - ! '
= s 2 t = ' 5 '
oAB J - , . -L -
- 2+ ls 2 5 z S
- Jls
\u= ff i i l ts)=# =fi iuoty q = # = # u 6 )T/u a.t'4f4' ft'(fu't'
. o -zs/t 3srt) . v(
det za{ cta*6-l'4e{4 T- t tr/tPc ,
ct*c.cif /<'cetat. -rf iot ltr /"
s' 3' 'c4' o 'EnE lLnls/a
dc c'+cv.if -l,qn 6a e&ff *T
q = * , r i r , X r * t i ,
i, ' -!x, - trr* t u
z i t ' x ,
)i, - o'57,
[ ' r '
f+ + 1" ,li| ,L * o J [ o( o t l x
J
zs I - '/.,srz> i) lst
6 s z + . i 2 - s f t - ' '
2s
6 s ' z + 2 s " t
(t) atl rz) /{M- t L '
i , . i - * , = * r , + r i - ; i l= i ' , ' uJ '
Thtro u+ lnuc
, l o h o l l t ' 1 .u ' l o - 2 , l ^ * l o l 'l' -/t o ) L'r' )
{ = i ' : E o - ) t ' l ^
Jr t4 nc{ a tfu sfo'tlea't/ P Taut'e y'
il:.,: ! ":'/!t ' t r rz le A' ) r , ' a1i ' i r ) + tz
F F i , = 4 r , * - * i
(q) 7at u/f.f4"'.1 -u/rt
@,ttVAeta
Xs " X l ' }xz
?7- P/f-tnnl - L'o&/,
4uf<au = * t + l J
i , = ' * , , + f r z r t )( 2 )
v n g - - z a ' 4 , ,T n " a g
5 + a- @ 11ts t
I - t ' 'z
5 z s ) 4 t + l
- ,f'/s-rz) 7t u)Js )s5s + /
9 ,28
7 'l'
* 2 u'> !'t
,&tYtss
frtn lde A, ae 'hw
i , i , , * ,
i , ' * x ' * ! i
{ i ' }
!L-
;' 7 j -
t ;t a
x1
d -l - j' e,fr-/I,rt,,/- /;e laf
z @ ' r , )
( 9 i " ft - J ' J J
(s +z) r ;l'- - l J r 1 t ' 2 5 s l z ._ _ =e 8 - - r ) 2 * + - r ;
fr 2s'+4si l
* r t u - l t ' z X z
ti:J,l:, (:J.,[1"(4'X
= L't '2J 7 + Lt
*I. I T YQ'= ,,/ i i , ;ttut, C * y r l
' t + s r ' i 1 + Ut'i ,td /. dt sfatlod f -
+
Y').=Jr6^* f-f,,n
11/ tS =6 r - + z s . t /
-tat dtg-trt z a'4 dazr r.dafu"t@,
%ee( aL a)a'i/ /*cat4 ab aiaaf
tu
8,21 (4) ,1-;. ;l l t s t n ' X t
t --r ir- l -a-L<
I
L* ' L
u ' x t
f a t Slra'eae e'6r'/',$
- z & _
Y , r ) = * v r r ' # r t t ' )
eJ-.1^a4 lzfrtz 2 4../ /aet rutf c/.eart-^6rftfu fioz4a?+ /z'ncErn ";
l ' ^ , _
c . ! ' + i ' s - r a ' s ' r a ' r 2 f
ry dr at;q;^rr.,tf4 't enz4r{ "hf+hru+il '
Hrq = f f i .s?&3zrf
- + d , / - l {
9."?= f f i r s , o r f
(Ort'+ 4r f a)(S,s ,8o)= 4'8,s- r /Dzlar\], ) s
* ( 48o + Dn\, )s ' , 48n
( u"t'. N, s + Nc)/Att '' ,4)= N'A,s'" 1"1'4onV'4'y
7/"<4 d' ^Cq./t+ ?^{r;^ '.t ata a)zJzt
Hb) =. ,ra
_--J s - * 6 s - r t
s t d ,4t (
f,u Bo.7 /'/., ltu tL Do Bn - No Ao
4 Eo t DnT, = N, Ao'+ Ne At
er D,gn ' NrLo r Oo8'
t , l / n = f e r O a , t 2 3 - J
< l = ( t o l 2 0 , 1 1 J - o . a < t J
;1 e, Ps;:
6 ; ) ( s 'o , ' )
cte.a'ttzt t(f
"!6 /4 ! ' 7/u /&h*'"'/;?"'2-
t/ T/tz
ir .eyafilz- /4 J '' & /Ttttr r{zno aesz'
,, l, 7-/u- dv ss "fo&fu
/t4 4?7nz
drf"ha'rY ( ataad /'e /'&' caTt//d/{"
at+4 oA*-'tla ) oud i n't rtnzJ 't*
r( M,Ar'r NaLr)s t :Uo
O'
,f,rry ot, *t*;*6 of tl'rr' s-o""/
- N o A , ' = o
DrBo + 4 8, t lv24o+ N, /t1
or JtEo - f{'Lo n D' 8i '' N' 4t = O
0.0, = Nz|t c* D'Lt - NtA' =O
D
Ttutz ft. rytf*;* z*r y''z aryPaza'gz{ ur
8. t z , . ( i- { r t t = 1 { t r - z ) 4 ( z ) d z
Az,/rru z = :-z . ^/e6 t74a.r t i f:!
aqc! z i Iu Yo'nn'(4 ' 71tn z=t'z'
cad'( cl 7 = '' d c lht/'4 /44 iot<
o
I t ) = ! "1(e )u rc-z)Gai)7 ' t t
, t I Arq q f f -z)J z=J "t ( 7 )u rc'2)d t =/=:' - '- '- ' '
t=oqJJ /r; {nttl {,c 4t eulwf z'ri64 A7
4/r)= ffa)= / h tVd'
'n/4""t/st<
/ t '
^ . ' - , . ' l
{ * )
drr* l ! n,4. . t Jx 4" f r t )= T€ = 0
aan laqtz+ zlPrrt c'rr/4a
fit y'rtntzd aa i2e4 '
noll*i fu ad
ffl:?tlf|\lf ,Jo
\Xt = xa
' i , = o , f 7 7
4 i r = t t - x t
; . . t = V' J 5
i, -- -0, txJ r 4
q i ( 4 , ' / . * - { t , a a
"(pztntf . 8e-.oo44
' fo o )x :
f . - q f o
L O o
3 = x t = ( a:.1,,F:1,( ) r l x
c.4z tv)tzz,{ i olt"'''-'("t't ftt
L a
Wq cr tTI rVfn'u,
t, ,9a r,on,/r" ?"f""l - i l r l=H,=; ;v
,9.i, ;{-l z. l-r
\1*J+i,;!,f ' t - r jl< -x r1 " r ' | ,
- 2 q -
f . t%a"r_
s- - |tl, ts) =
. l ( s ' r s ' 2 )
- - s f lJ (s rz7
2 s r f - Z P + 2 ' 5 ) -[lrts) =
Wz) -
J g.str )prz)
llrtst ito 61 fN af -)'s' 'z*( 7a4a er
-l at4 .-2 .
. z s /_2s . f {H s l s ) = k + s + t J )
.= (-r-t )zr *
(sro,9[g.4'r fJ
= - (s' ' t r J 'zX'r '- t ' i z)
(s+ P, rS t"*r, I I I f t ' r) ' l - 3 )
- (s a)(s -r '
J (ssz)(s' ' t2
Ai'h 4u=Yl*) = o
, - zs^ - / t , s+ l I =+ .o , f1= A f f i l r . -n - z
f,
f,//,r5i ,lat a, pt 4.f -/ a,/ o /& d -2.g r ) o + l = t r / t 5
+ f t , { " ' ' l t vo
' J q = 4 t - r j €
?.: rk /;'f4hz { /}t't i {''fur';JTfu .{af .1e/par,4z "/. ;gr<1 i ,/''[tttrtl,lJ
= g -'[#tnJ .
7/u; 4,4or^,a dtt aoatarEir* ,
Uri)
/1'4 t(z'<',tf l,u 4uz.
7,4at ar -o'9
I oct/ .tti )
,*af a?t .tt*t
q f r e i z
? . 2 f t k > = f f i ,
Y:) = flb, t = ] i^-/{!-'r,t:'('s rr ) ('s'r t)
= { o . + - *axh /Vn=f ta,)= 2
. o - 2 s 4 1 1 = 2 { ! ! - - t sE t '= Gz l r - , . _ r
, z ; - q o J r t | - 8 + z c t r l = - 2 f( r =
t ' / t l s = - z - ' - z r t
. u f t * l t ' 2 5 c ) + t 3 € - t ' z f e ' " '
ft
,t?rtQa, .' u t t) = Er *) " Ll ts2 ' t
t z o .
JEf : 4(f) = t. 6 Za, tlul=
Yrrl = 11'19 ' /L = 2€ ' -r e'sJ' i' .r /s.rrXstz)
at-., f, , ttt ao ' i . t + t s - ) ' z
to (s-r )
?,4 4V,A'4z-V n .tay'act ^;z.rzVl-'r-'- F*J.,
uu7 (8,+t ) ,
5 Y/, '{k) "t a, aaalYt') =
(s; a, aap t ) Yrs) e f(a)
= 9o
PaYrs) =
' S -2' O'PP?/
q ulcS = o, flil '= fu, {n/'-
ort dtu.t+t /o/ott T"t"t/*
ta
- o .aae/ t
g U i l = ' t u e
drr t, lo fu t"+* fu Xrrd 6 'la^aP t
/a , //-a'{ n,
-\z,ead/f/
7a := 9'7 e
T/21 ae 'r(4t< o) . -o,t J *
' o, Qaa/ tt = h ('/dft
cr i, = / 3+o J a1- zz tta ;2<2 'Jtc'
?,f J E/e 4nrarr'12,
JJ
Yrst=\il:)' -L =(s):tfo) :s -
r ro*/f,(s r a r)J"
t , * - f r - ^ n ' F , = * 4 . * #4r
= Tt ' f i t *16 - .rso,t ' . -$
{ rr l = f , e- ' , 6rt. ' t * {r ' t 'e- ' *(+' 'o ' ' t ' l t '
h t 2o. btiL it- =fl rd= #
1 -7tD .
- J 6 -
?'6 Ytil =N(s)
' -" - 6+t)+( ' . , o.z)(su +js)(sn i i ls
{H=4,"'"* 6rte.'" + SrcL'"* 4*zre-)'
; 4 , * ' F '22 * f i t
" - t * , (a t+ fn ) 'n 4t , ,
/,a> cZa, a'ifft-'
6e=/ l (o)=#=f f i=&' ior '7Y ls)= f f i f f i=#
- / - + ' - l
J g+/
{ r 0 = , - * - : t 7 . o
/t, /& ar +/ ,/ rtot q tutf tv"rtJ
<7 ar" W r, fa.ac,t:'* , al; +V
c( u^rz/?af'n"'' nt^t4r et/o4/"'1 o'n/
,<e4z,t 4 Pts) ''iA & "s''GZ/'
?-F r/,e *ofu,/cA. - naf tuz+fu-a
'fv PQna*"?/4 CT a'{e/'O -
?./l rar.,rr*t * 4os+4, ,q 'ar/ao , gh'i
4 s a + 3 s t + z s ' ' + s t /
t ' t l I s Is* l + z , Eo 1 ,5- o . l r jt.t, l t ' t o,,f, [ o a.s t 1' -
lo ' t | [o -z. j? ' ): lz,.tzrl t l
T dfo/,& 'laanaa a/' dd *f"t'r *n/a'
r J ) : ^ t +
,/++/z.f
z,s/0,8
Nrt C
r r , s+J '
t/e S+ey'r.J s r
rqJ/to,l S ".t
,
t z 3 i T
6 J'2 >o
tt,3 ro,7
Jq , l zo
4trf3 O
t t,3 S'e'il
J a , , I z a j
qBf )
(o
Eo(a
leuttz h *V 4f.zl4 or Pnafa/&
7'A**, kQ ar"r/*'-6to y'o/ "
'fu/*'
ryh / n/*4 rl 4 odo:::paz[* *
"tt;': :*
-/ do 4*4 {tt
e't' ,'/ d",:'4' de*-oi'-)' 'cr {q4
Grrorb )1t1= 4o s' * Q, 5 r Qt ui//' oaT o
s t l 4 a 4 2 -
4,/4/ ; I o" (o 4'1
I | 6 -
4 o,ro, n,i, j'"' o:: r':f#: ;L
ord ar, o , fu*zsat 'Jorg n "'-:' ),n *rrr&4
a*(t d \ors) i cT t'/'q'/'o 'o *1
Dntc) u cT 'or4/'c / */ ^# 4
o''i=o 2'
^" "/ & 'orxt uf '
"tM k4r*,4. *xo'61 q fuoad"(
e'";,
ad a/|zr,n t4t P.44,?,7, 'ftra 'n'*f"*
ry\g- -ha*.{e/ r'rptf uQrcdg- l r
?.? N.t'&r2,. A,,ttt d.4&o "xeff o^z
tib ir^:d' d. e{-ry ;-y'aeo" tu
H h {
? J O , O S i . r 3 " l r 2 5 ' + s * r i n a f c T
trtl4 1^eea44 A'' f"A"' t* I lYff
,,> ia ;;;"i(,- /;,;; ;r',h, o ,ttgzz'u
?,r z
'/a,
.t '+ 4, s-+ Qzs a d3
, ' l / 4 >s ' 1 4 , 4 r f o 4 ,.S l4'4'
-aa
, l r i" 4 J
T a^ t "44 + 4 ,2o ,4 t74
4 i 4 . r - 4 t Z O
* o r r o , 4 r 7 o , 4 , o t
-tt=roT)
o aJ 20 .t'J
a t 7 o
-31 -
-fl,,00 dv 5u,4/4 /ne:n f u'6 g a
4u'=;f f i6 aorcrw'ta'(n't' 'o c:T 'a'ft/4 leu'tzz
fu ,uafi+,>+tc 6 'ta'+( 46/'f Pno'
f'/6 flrst= # C$t .6ez ai*ur&f '; /s.
Ys)=il(s) ! = #* = * -# - h"- #
t {n) = t -i'x- 7.-" - o, f,t'e-t
Yr/a = 4, €-", f.te''t* (rd'e-t'* gotte:ti
n {.e 'a.2t + Qs e'tJn tst + {, )
H tsl a ohi& a'-/ '6 t* eg*lflnr D;
t/o,, = f .r, '7h4/ i/' fafua '15 azcaada
'lrrtr) = /")e
{ t f t )=- ( t ' r r +o' f ' t - )e
ac. ptar l{nrol i du 7'a/'-t'^6r
0.8
zAB J:+ o,o t )' i'g +o,al r i [
_ t +aa l-
+5 ' ' f e ,o4S l I
Y, t1 =ZU' t l ts t
+
Yst
B
,,6 T/r',22 turff'*"fr ::#;%i?.r iS Tfuu H,O a-4t dca
T fIt t;ft'Ja"cz c/zAe
Yl F^"//t( PtszE'h' a/
i s u l r o ; f f i .7/rq aQlftz<'
t o s . t
z = , - r r O E . . = ?b A r t a s T ^ 7 o t 2 - + J t t o'ffi - 4't
&t- t; tr-*L(t ,
- f
7,rrl- /lrg=rffi
A4 4Jorrt1",a P.'*4. ?.{-A 4^q arysatil n
l@= 4, e-t* Al e ' t+ 4""^"-(* t 'o ' '- / A V , , t V O
{r/t) = !* {ro
= -7ro
/r. ltt = {re-+ {rtc-ca 4t tTt r l 'e'Aft
H*l a .&4A vnd iil t'u eatu/*nr P
,/o,t =tQ . TItt, ;f 6'A'q 'rd "u'qrnelt
o 5 1 0 1 5
0#'t4^e t $rC)l = o,tJ5' a'4 l {rrttll = s,e?"6'
7h/4 /v Qaruenf -tzctc'rLld tW
cr' +4 ^,;76 t ?o 4 )6 pn$ '7a1/ta tt+
tuL 6b c*abt4.
?,t7 Can4dtL /-lts; = # ttA a'rf0
0.6
0.4
0.2
0
h Oo a*rctnf a a/<'c caf a4
{c-, dv 25 '-a"'L 4 *a4^'
f. t5 //ri [email protected]
fu alan<t n P+r{ /. e. c,* *fitu
fl!tt=&; {/d = /oc44t
ar4
i ir/z=o, | €
- 3 1 -
iHs'dl
TI
n/,
a 4l lQv)
- t f
'n/t
y'c& fu ,,a7itfr& Azfl" P 4c4/l
atd & /on lafnu a ad/- 'r/' y''tz
aguror*{za r/z 'd' ad Eo"s'dP
?, r8 4 i r=# , / / r4= f t
Ir/,q',sl=1.fu\= #l f t , r t i u t t ' t f r t ' f f i " = J f f ir,lut ee lsc l/4"i*ll= | H'riol 1'au
?.rf Hre :
? , t o / / u ) = ) u - i c r t c i u , | l t u c
I o lal >ut' '
, f "' jors tlz:
f.r') = # J Haol6''-o d, = *l "'-+.i'uta,,,U,tZ' h)=<lo tJ
=fi{'"*r(c-tiudro = ffie'-Uc.
;rc-d>ul
s'tf s r roQ
/18) a 4f,ei6 , in ato/"a' tE *fl$ 7tu'en'L
7,5 , to< *+rn7t'c"6'
' r ( f - 4 )
/* e( r i ('-F),ce), Brnaa t{t0 i x*t
idea^A;tan? Itu /* aA t10, ah ;e4^(
laxtyaa He
; 'Td ca"zof '*{ c24a'{
'{n /*t;tr tt' ^At 4't'? "'-n/a/'
F.2/ ltrst = -5 + re
/|tu) = + , tHtetl: tht/a =: ilnur
-rt-- i ,->=-L, : ; ; frH d o l = f i a = T , r j i . ' t t
= o,le/ ( i /a) P'Jtr/ t
s - o 2
^ t'(t-Go) t'tu 'J (t4) K'.-e - - < € ' -
Tirl'(t -c" )
** f 1s-ro2 rorr l
ttlqe.,l
2.1'4.tn ft-tolru.1
zr j t*- t - l
- o . 2//(p) = ff'
=' ' o,oo 2
i ta - o ;
= Ot tC,2 € t f r
+ j t o - o ' z '
- ' io *ito r /aollQ'to) =Arf +d'lo + ro4
r O. 7 / o - = 1 = / € l
-* 5
d
' 1 ' /ao ' 0 '2 x
H(l'/oo) -- fr;itoo + tao
- t o o t i n ! ' = , o . o I eI o a o d e -
Vru ilL onorlr -sta'& 'v4Pet'u ( /tts I(/
qru'64 4rt 'uf*l
= Z+ ea/at - tta PatI
t4
{ r r / t )= 2x ( -o ,ac 'o) ) '+ | x c ' to ( to t * 0 )
- a ,o / o ta ( / {o t . - fy 'z )
& C & o i o t -
lHgetl = o:loI lfit/ a = o'/?'/ /l 't"r
l / lqwll +O 't4 d n&l l Tq t , / l
' u
- ' ' 4a ' ^ l / i t t l t t l ao / "w , '' rrr& *qrr,ru 7 "'-''Tlrrtrrhk,lnafn'' ' tttrLE , ..., l-,/f ia,
dtto tt lnfaut #G-
I t . ' a.----1OtzQ0
i o/t'
r+vfl> 3'1 B 4a*ntct"/l'
a . 4 o 'o , , Hk ) t c
nd)'l-a'/4 at"{ ea;lV
(s 1q uq'/ oo o
/bll fs; a&en ra&t g^td+ dc o+c/ i.rt - 6 a l q u a r { a t a f -
i. nt k ztVf,c<,tYjra*lf n3;:fuf-rf +inttoct&, frrre. td q /.da/Vaaa
-J3 -
;;7", r*4.tu* a*' /'/7'
?,t2 7t' Aarf+ /a'cfr'a "/ % f.-Ltta) q
/-l, rs) = i/at 's
' ' i + r / 4 t . 5 o , t ^ t + t , t + r o
'l.t ) a/ eL fu u* P..,1. r,21 . 7lu4 Lf
u r'.zspaa ,ut//u J -./8 AA2r..lrt' /a. dc
u"{rrr"6
/ t ,U ' o , t ) = f t r - 4= /
lHrrPt l* Stdt/a 'x o'
t i b ,
fu *t t;* at uJ 4J "/'4f
'/{
pa.fri,t, i;Vat rc*:::"Y,r{ R e_ z
tt,
R, rf,R , = ?P
ll,riroo) = ,#,
T/t4t4 Att "Eadt/'lfa&.(/
x /o : t7, l " - t ' rA
_ J,ILry
4t74f7n'U t4
{rrn, = tui P,/t + o, / ai (tcos -rt/z )
rutu /*)L -t*f'y t''*t"t*o( a ofu"afrl
€r= t- = ous lro = Lf
- uc, - e+ Y" - 9,5Uto
" t = f - = T
_ o , r l b = yR R
{ ' = - i , = - F u ' = - R i: e a t / a ' * = q
ua& ahr tw ttetY uaz'l '-=
' "J r*rl=J
*roru'uoot, ="for"''ti'u'tu
?,23 rtu 6*ay''t /4ao6'o' 4 '.F,! zr (J) a
H^r r1=# , r '= ; f f i - ' #]N
Hr/i*) = ffi x.a./ _dar=o /.trn/z
ilrla) = O, Httb-' ) -'
;ffi - /
. . .i)t' = i- - ti"(iO =o,7 "i*il,+i")= w:,7
/t,g)w)=ff ir:+Ft
Jt i firtpaa^t rir|, J'/B /*1fu| *?
/*fr*,f '' d/' , Ltt4 Yta/'aa'/
t'
Etrt, at), rtu4'6 t'*ol'^{il' i h' 7l'
*-f'r-G.Ca ru'tPn*P tc
{"1"''1" o, t'u/'/t (a, r t +o/') + 'tt}' (pet)
t z -Q l t: 'Q
{?"u-iu*4t* rn Gr,41 Ed ,(0
D z / t u - f ' ' t , n t s u T f u, d
J o ^r.?'*d, 'J'r!- il ei'"'E 1-li)
&@rld,
t = 4 4 .A)
?,24 6e.c.ctto<
It"trri,t l '
Ia,rsuS | '-+
l+- tv 'O
h u,r +a
ryO /'- t"t -- O
l* u: f4i
f* ut + tct
l t ' r ' 'o '1u tft jft
utt a,
= [*x1t) ui';,t{ /it""r "drJ
7=o i 20
'{ fx-, -rt l" =r,,
7,2f 4 X'rs1 ion . .tr?6 7& ar s:o. { (?tr
{< ryp*trled aa
Xr4 = + . fua dtct'fo *ilt-t p"&4
t*ttl" fi, = x'ts,', lr., o
4 e// erle* p&z art 4t<da d' a'ft"q
"'F* eu'i'aar *'f? A'-/ Po4)fu'ZZn
VLrt" z:rn. nepfit4z4 ^Z( tV7>tt*c4 Q q
/ lHq'l I
- 1 1 -
!8, I
l/og- -- ,=1':,;; * #llts)= Vr,6 = -,s
*roo / /
Jr u .&,,wyaa ,ui//o puoZcn,t fa,'1"'J Joz Fud"
?,2 | J"* argnah ct4|t'11 4ee6d ?V ''u'& Q rutJ-
/16'l car, le -aphud at /'- t/"nacn h'ou* 'd z*t
t*u pruradltrt //ri qa W olt'af Att-"884"d{
/0,2 roRt 'w E- = e- = o , i*" o
4ul = A rs) [e* t'l ' fi-FtJ
-#[uo,-VuiJ
6,,f f i )ry,)=#v,ot
: - v i - * = - L' t - R t R t
, ' - W t - = 4 ' ,- z - - t o F r t a R t
-e' - -Ya-
Rt -
rcK1
Tl*u tut /^cc< 4@ = '/o 4' ft) il/
l/otrl= -/o 4rrl - rtraa aIt A*f
't"l-= --:,t,.,o= AH [Ero - E-@f - # Ertst
et, f , r tst=# /ot :1
. t/,;r,t - I",e 4rrl = w.
I*tsya7,(s)= -t ,
$til + Irls1 ' -frfs) = o '" $/t)= -Ir/s)
J!2AJZa - i/atl-Er/t)
Pc'(et ,|Pc aqcfit'e ^t4 fo4'4 '
da, x(A+ 0 ao t*&. fo lfu) eB12
fu ef.-Ea',' "ZU f'{A &zY'znz
-Lit4( /4 ,t<, pc& ( Xtrl d ceauy' s a'd
!m; sX'65= ps+0
Il XG) 4a4 a?u '+ 2424/ &" tn/"
pnfufu .<en? yru.S , tu afz'"6/ P"1'
* t =0.. €rttr* lXt*ll*to ao t +6t '
$ Xrtt fad r4q& pe&t e" 4t i+t 'a^t4'
&^ xft) ca/4/"4*' *tfui"/ dt'&/aftaL
ola-rtxomtb, 4 Xts)= ;rr""
x (o) = c(h ta t , A ez./ta,V/L ks Xb) =a
ttp do 2d ta/e k,xt+s =o" 7h'a L
,4r;rt dz eaa'<f,ottt- ,,4 k'z/f /tt*f
.""1 dl' ya4t4/42{'*d12fu '
uo
o) z' ot .+1-
Rt to Rr
h' /o l/r: /s) - /t1 ErG) = -l,itsl t Erts)
,,... rrGr$2ySg/e VG) = - ;k) r // Etrg = -l'lrqt
7
=t,ut[!# -,J=f r,t/'ffiV,at aP fr&
/Jk)= 4!L = ''l . ta&
,L(t) r / , f +J-t),3-7 *
,PV
Jt> "O ,a fa. raoo ) H k) anol /frts2 ,1rue
- 3 s -
nera^ef "Ze, fri.r-( @3 W P
' o e / o ell (7'u)= ffi
'- # = -/ o = $ti,,:)
fea aa, /t@ corr.n*t & -udz*/ 6 'to ft
% e/,irru/ 4rurttz //rg d l'af da/4 '
ab+ oxa*, dl q 44upaa { tto'
fta* u-&a"t/4; ntfz.aa . f,t ,6/
4/Va?'oz / Hrf"2 o -/o.ha//rvo.7atu
du cA4',/i/ utt*r+{ 4'e att4 la oa Ptt
raRt
4k)=ffi
4
!(tt=/rl/.r'tt
I/orsS = AGt I enrtl - E_ro] o"/L
4rs1 = # . E*a' ll, /<). 5-1q= j ?ot
(s *so, J)yots) = /or 46) -
{ U"S
ol4 :.r z7"t'+z .va/'7L6<;n i
itrt= -'fl t(A + u/c)
{(tl = '?bo tk) + 4a Urz)
Jr u't 4t 'o/'Z'nPt-6/ a'
uaoktl l , 2 = r r f z J ? f 1 44 1r '2 z a; l
2.+, t.,e 4fa* '4t at7?'nd" *'ry= € t = O- ; -
= L z r ^l l e at -aldrtn'
2V ; = P r = p = *
Xtol =/ | !,(c),
oo5 1 . 5aqoo 1f=r r r A K6', ..-
k+ ro .J , /oV, ) 46) > /o ' ( " t '
fl,a At fi,att/+> /*f^ '
ic24 _
H,n=#, ; f f i^ ; f f iJf to..n6& u''t/o Ei" eaahtd '/oo
o.3/ /x/o 'a =/ , / 'P-6. Jra !A*r ' :
7:r':r*;-; te ,)v,i '-'t'/" c:/'41
{q ""rrr+r*ul
a'/ '6 e//"tfi'-4 ff
+en1e . ]c> r--'r'/FF*7 n/'"2 *t '6
l'<,;ttt /nz uu - 7: *"* u'&at+ "of A*
/{'"{ taueb ci 'a7" 1' /lre e*' /'z
-o 2 r,."fi"n"v t,Xol,l
E 'u
Fat mot.pnd 't =z, 4 f = ',2. zi'c't' fu
ay* tu?f r rc7 y ' {ar i * " , -h//X.,L n zfu leywf , tu 'ry a.tt,4.o)'
Qr a .o',,rr'(tt 'i' f/'25' e) ei{eid fu
h=/ , t f : d ,2 ad {= a '6J
oo
5 1 . 5oa0)
o 1o=co 0. i
,.Udtt ,ztl a' | / '
- H s = 4 ? * ' 8 o os r 2 O t f 2 0
. t =o,t
t,4
/d'+ HGI=fu
e 36 ' '
Th& ?va41,g q fiChul /'- "rt=/,( =a.oz aqd zta+."ita f , ,l/ f =42,'v{t
fe,'aA;n-?/uft'T *W 'i dt ,
laf€n, ,hr'i *ry'/ f a,?, a) a"l'J"
a' ,laytzz ZAa4r. f t.sf e) t4&a/ k
t r= / ea , l I to ,2 -
ua6ne catt h u'&,ke, vfutd ird naf( - / - t t L - t j
{"*tr;/" 6" za/r nnVaD'* /*d}-erb
con o{o/,4 q 1i/46ab'
@ aal Hz=#e' t r t r t ,
/q 7 tJ = JL aad /1, = -2 oa a^{a/4 ., , f - s . f l , t d . / o ,
t 1 ' _ _ 6 = S t ' =
l= f f i={zr?2) :+7
= lo = u{ ["i&s - t ? .
T1uu ttu znTa^6u /-OP / f,uo *t:
Jd ctsl= fr a"4 P k) = z/s(.s+ Q, &*- 1 2
Htkt=f f t= , (#0 6
( at" p{e4 { Hy', o" /*o'fi( al'4rtit"
dill ,6 d*ran;oc'G' 'Udtld "{&
(s'r 4 r'/' ))(5 * o, f + J' 2) = 5- 2+ 5 r Ltf
'T/rt4d 4
2( = 4'23- /77' ( t'1't'?f' db4' dl
.*f{ /'//-44 lf'e'r 4* V&d
ar -o'{
!t__t)i dt N* 4 ilfr) au 0'c"'b'/ al'/ y'J'' '
dtla 16 aap*)^.h a/a'Zl etr4
(.rrt -jrX" + t +iz) = 5zr1 t + f,
r'a L Lx/i'6 6' 'tz''Q r'-t 't '- t | = szt 2J 'tt '
fru 4 Cts)=i, a' cffiat^b d a*7no' a '
a* w.umf p/o* dL Vo!'a / 'to' at
_i tJ'2.
to, t t $ CO = #r:,
q dtgrtL,a,wpsn.t-
$ A7"., t. rfu+t'N-st Nc' 2
I t 4 ' 1 = 4 %t r
D , s+2o t6 ' f l )
: 2
H =
- z ( s - Z )'.='" ^t
s'f,t.ilaS ' + J 5 ' f r O
aq dafa/,.&Xu a *
Z (rVt.s; Na )
(qt, 2r,)s (s tr) t z U4s'rNo)= 7 1 .
/o./ r/11 oatgur e ,{ * ?t:*3_o/
arTrf th Ftr. ,o, /J (c) ro ' 4 Rf =R/F '
€ = - # r - ' f i f = ' / o 4 - / o F {
= - t a ( u r p { )
Fntttt %, ro./3 /;;,' '* '(on '4
-/ ='/o'
€ ' - A f u t l s t ) = - l o 1 u + P / ) -
= a. z(/'/' s"f Na )
7t Dr 5t "r (oo+4 )s-n (Dr'tztt, )s *zuo
et A, p{- { H{) oq lnaH cr -z adl
-t l1'z , tl/.L ,'6 /cnot"'ltalat' '/'v'(4N
G+z)k r/ -) z)(srt/ i4 - (r*z)(r"+2s +5)
= . t ? ' f + s ' t ? 5 f / o
Ef't6/? dz wt//i;rt Yu/'/o
4 . / , D n f 4 = + * D o = 3
D n + a N r . ? ' + N t - J ,
z l o : / O + N a = f
Tfu 4 CG,)=#, tlpru
Thq'.fu 7fu, a.ttzl f.;tu
,o,io rrq f.caa/+ /r^fft" / Ef,/4/4 t4f s
, t . C(_t) Pls )i {q=lr- t+ CrrsPtls)
= -t ' - / / , / / , r -
:@
" - ,t-t S'2 (.t-/)(s-z)
/ / t - - T = , , - ' , ' = : : 3 ' / ' : , : 6
- 3 1 -
f / - r r = r e . J L t ' r l s - )t s , t r + s ' + f s f t o
uk ,laa f "dJ 4f -z qrd -r -t12
t/(t)=o,, h t-Za- A{r, du ,*ly/ W"
/ltb)' a ( ne4'13rrL f.5) , Tfuaa a( 4/f4'
HfP)- l ' *=A
=. /
&rt cr.[.,e,v t rwLctt , ttc, d?e/+z,
i ruoz.(e/, Aald
ecfzae/.A. ar|/ aln'7bT L
Mif "/ .*tr M( ,ut/t-t^*zet i77u'r'
8eeo4 I-=O, d/-
-auta ctt.*V,nlt Z pd4;?
dr"r/f z, eal z, *4
- . - - ? o ' / ;L ' z , r z z
Zinq E- ,< f Zt + l/;
= /o ' l / t . 2 .+ 14. = i14 tLzz
l n Z z ' L r I r c
z r + Z -
4 = A ( E r - E - ) = - 4 t r - . = - /
(2 , ; z t )U = - lZ r 4 - / |Z rn
( 2 , + z z * A Z , ) l / , = - A 2 , 4
Thqa /€. .kua,
llht = llrtt =l/; r t)
anA Fzs r4t/(d)o
Becea<" tl*ts) J; dfe/4, V
,r* f*
^42^
Z , ' r z z r A Z ,
l/o tst -n({) z,*2,
= - Z z
z,rzz
A
l . + . = ' AZ ' r Z z
A (2, + Zz) - A Z z
V f Z , + Z ,A 2 , . 7 r+A Z ,
/o. tJ =, = R, Z,= / rz K . . A,= /at-
. , - / o " ' . t O R = - / c 6
H'/') = FraR + rosB :/{'-
= -i2i2T = - ?, ??r?
4 Ar= 2r/or, 'a|z.n
Hrrs; =- 2J /asr/oR
R rtoR 't 2x/o 6 ribizx/of,,\-ZoAoO a O = ' f , ? ? F s2 e o o / l
6- 2 X t O-<
6a 7oa %
,,,/*cJ le/fa b /u
7fu dFr, - dry f,e*zza ,*t/f- 4
lryl$'rrtu .6'*t'* /rtcac-Eaio,
ttu, d.//2, &{
I i l r 'H, | - o ctPe(i .aa6 tn- Q,aa6 f
I+ l =
f f i=o '€Fose - - v '
That r''b ry ft*trfrst t< i,tnufrk
p dt u-^;/Z;n- a/ A '
lo, l f sJ + z,t /+ . t + / + A
r ' 3 | r t
V z r ] | z l r 4r ' l , -A
l z| | i ' e
to r -(r+A)/,1
4frn4 1=> r+A >0
- t < 4 < l
o!.Hr' t=ff iA
4ro=@-5-+zs rs'
Trw Nfn'"t/ ; c:-T
a 'd t ' -A>O <>
A (s '+>s+ f , )o r 4 d = -
g>+zf -+ f + A G'+t )o
'!-t oleaa,r'ta,tfu lza '/ztrt't'u' z.*n/ :
':
ol-o//t 7 *tl n'o, h' " -f,tn1r:f/.Tt ad o/t |fr")' * 2tr"
'+4'u '+I 1<< Altr 'u ' t r l
r/1u rt' /'oct/'-"4 qfffffi^+aa r iz t tPa 4 Hb' b
-L4tr:r;r&.- 4 H r s ) = ; : # t , l t h t t
' , - . A - A ( s ' + 2 s + f ) ' '
/ tSst = f4prs1 -r-+2st{
r A(t4 )
- 3 9 -
' a + H o r s 1 = Wt (zan)s + (fq
m qa&t u u*{ ifalt& '"/
TtLr u-ttp'qe c{ /lrs) cqadd
( R,+ 9rt(RCs + (\>
f t , (pcs*r)-- R,RCs(P ' r f lz1 ' '+ t )2
-
R,(Fcs)'+ 7zR1-Rr)Bcs + B,
,1,6 eon eti,nafaz i tfit, ,.nrn-e .24 de. c*zt-
Ln (ta,*r), Tfu ccz-{.Zatn rt- P9 6 4'"v
p*. a.f tlro= 'i (# ) '* zKt ' f, , nai
Auzff ; ^arz 4.d.nc' a4 d,e axz &tni* "'
,tcdtj* /a,1
tr* r1.i423
Ei. ,o eo ( b)
k cats aa
eri@r|., 7/u
4 >f,, Tlaa
/4 ;f4,
lqtz- -
14/6 t/6)= #'/4 auratu lt-'B) =
# h rcl ada^442
J/ ir ,a ,a7&*rz+,t/ cz ; E/ /a'/4'
v l a A Ak* r )e-" /u ' l : ,#=;t+Afr;
/ f A ' 7 r t
= 4 G+r )( A + r ) s + ( r - z A )
Hrrs) ; ,,er ifal'Q P A ?alf ''*
?
t/.tq^4t o( /1rc5 u*t*r{ & ttaf/e "//''6t/
aa ab f.'-//,a44 @
naftt' A 'uV
Q4 ur FzZ. 1A, /6 .
/ a, / 7 pl/rzrf ^zZ4AZ{'c"
, - RR cs'r t
frCs+l7 -
R '
6 * / * / * e f i E 6 F t l
.1t4 4 a"f ,
A-t + A'm, ,, .. -+ o, .rttt
^,ltd, rn'*')" fi'rR)/Rr aa *-* o',
{X.at ;f, t) t'rztneyett ar'/') olooT 6/4'
,Yn **iL iV&'n"tr*Li;* tl
totta.t4J f
6r* '/i'tttzt/o- Ft'f, td't6'
'7ku 8u 4/fr( dt'i7a'n Aucanz
Rz- z r = n r *
Z+= f t r *
Llet t&.? ,rdzt
Z-= 0., I, = o
Cs
.E-= E, ,zt E+ z4
Jvu
: # n
R, 4 - R,z.t
J'tt frrutok, /*e%b4 '=+zr l ' 4 , " + r - 7 T ; a
(f , ' t) 4=
F-1rr'z+) - R'zt - P , Z I
- ( R,n Fr).=z?R, Z. ' /(t oJ
f**, a' -A(z ,14taf 4d dur a*t cAf urt/ "'
f..r/. /O. ig.
/4/f
&8tF,
4 W-F- #,- 3 ? -
WZ ab S-tra*/ha 6 (?,rtt 7<?.4Ytlt - l'Ytt) = o.o-r [Uttt - |--Urt)
|,-l-' ) Y rls = aa,r(, - l-*) Ult)
7l4a ,rx -t(*<
t t . - . - YZ ^ a,or(r - l -*)
4ttF6 t j-/
" O f h u ' - ' > -= -)-] , t t u _ , )
Neo lr,nr Hre) =ft,(g) #
T/'z/ lntz
4z anq 4t4 4 p/n aa1;z*a *l aaz
/,tL;&/4 fu et*u- .Ju- prod t/,6'.( / '/ t .e
_Ye) = z l \ * rJ+ g _ z -?t - t - t + J l -2
U t P 4 l t + t l n t 4 - r a J - , . t
(+r ) Jn+ l'')Yt2s=12+rl'rtl', tllt)696 d)//e4a4<z eVafzo'z "a
4{rnt n3 d ta-D rxtn-4=;1:::r:utn_t1
r / , f 711 #rql= " ! - , , =:+:)-2J^, 2l r t 2 (r'* 3t a,r)
t ' r Qt+ z)-
( ]ro,g)z + 12,2r
/.rl]+r)
ffir+iar )(l ra,rio,r)
/ /, t Hret=] ttatl = A
p, eaa tr)' J. o
AU
=Z (Lea ' t r l - ' ) ' = In=O A ' /
t - l ,oao/f | - |
t=
J- l , seaE.
/1,2 trl Wfy aA g-6qqa/Lurz- a,
z { t 'nJ ' } g t r t - t J '= l t 'u fn1
ffu "tYgt -jl -'Y6t = 4 t//,)-rlu du tr"e,ra4!e>
?rcEi* ,a
y t t _ 4 _ - _ L - _ z J, t ry : f f i , ,=77=F ' f l r
J% ab4^41 S-fuata/ar- n. At4 *i7t/<-t r&1rht,.t
iAl , 2y (r.-r) n, o ? oZ ZR . Jaar( 'ro /r.a/( 'l t (r), Pta( . t /. ) (z) a Pg +t
/t.J {er {ar7 8d urd 41 Taat* tu,
at S-n/-'*, 6 (/ n) ?r'/4y41 = 4-ar[u rgt ri'h6) +{bo* "' * s'
t I tt rp'l
.=o,af (t*l-/. i-'*.,.*t''t ) t/ry)
7t4 ar tha
//,6 40 olCa "U pee4 ef l'0, 4 4."2a6/
rfu rdt, xt%Vha't7 tr' h'6/ 4
cwV{ta1 fu .gzta o/ ll/ip '/dz/$' /"-/r)
/-/,Afff = oa'r( r +l-'t J -+'r'o'
UlilYrt)
t l t ? t s + . , , + J + )o-ptr /t " / 2'-1- "' ' + I + t 't
l ' ' , l- '
l ' l
zx" f4rfra*r^-,/ l'Lt /'tr 22 n#' fut/
a v d l d t * ' 1 e o t +
l * = , , i h ' o o r l ' e i l " r l o , ' ! t
& a'a d,t6'td ^*A f
; = -f ,lo ; tut "'' "tr"0,nfod tt, 2infi n & r"'l
Ac,Q na zlozot' "47'nf"ndtlo rz/. a+ t7o, tJz'eaaz
414^frt { I =t ,, e-r ) u cn"tLJ lA fu
/ac^b ea) A 4t d/4,t4.444 C /60,
g. I tt rurt 4 7on 2d 4 4 ( Hrltl, A//
b{fu* tf .azt& o/ I'o-t cu- 4tz rc 6 //Jt)
lttQ) rlat au y.n ef -2 oe/ A* 2ah ar
- o,r tja,f,
( z ) H 1 7 t = f f i = #- - ( J ' J ) Q ? z )
l / t+ t1 '
l-t'til fu fto t4 at't atl -z ad /f"tz
p4" et o, -tt d -r ,
llrtl) =i t t l g - t )
- 1t-
oa-d H, @ . Alr' t 7 pr"&n ,,/ /1, e ) c.ut ft, lp
aU /r*u.t ( ef t=O
& = c ' ? e I =rz (trr)(l-r) jn,*=o
f ir=ff ir lr.,=o-
Tlal are /aaz
- Y G ' = _ P . ) - | - - ' I
t . v7? -2 f r t 42 r f
* yt,.=-o,Lrh -, h+.tr h
Vtt'tt AL 4+ 'ut/o>t"u at
{rn'. = 'a,trht)n - z(4&f 'o'2/' hv o
/i,,& l4r1t=#" =fu ,
urnj=rt;t 4tn
lJq= l 'a t t ta . t - -?" f fe f
lt- ,(aoat)g + t -
lt- i,lrl 'r I
_ a.of fg 3 , ,=:' lS -etu'') (l 'e-Ja't)
/r., ){:: rft*:::r74Yr72= llil U6s = -
a,f x a,0 4= € . 2
18x(-o,z)
a ' ? = g ' ) f
z x l , 8I r,7
f/&l = J!I-*-" 'r ' Q+t )/s 'qt)
?i.fl/4e,tafa,lu ufo| = $ tn /, ll (S) - 1
yh)= HraStlQ) = ,
+---o,i- 9 =o,r
i , &
fr /-"! ,X trrrt a2fl:44q *t"il'":"k/'
6 rt Uarq f -/,rar4/bt/?,*
ry=.tlil =orf
Q +D0'4e)
= { , + 0 , h n ( r '
] -o,t
',iL h,- f pS = o
tz,= ft:l ,r"o=fr,= #ls-o*-o
7ha "c lt*c
V_r ' . -# "#&
o{ucl */*
ylt t=-l t h+o'r h
Tfuu dfu u"ry'/u lo
- !ryr -= :",'-1 ll -!:r (o'8 ): n vo
s6f c, t fnl=l ,n>, 4n:F
Ytt=Hrt)UW= %^ t' t - Gtr) t l 'q i l 9- t
lde orp^( YW/l a4
f at=o . Q *
()u) Q -4t)Q -r)
= o " r l , h + r t ^ r t j t f r t,;ifr ho'=f ra,) = Ot - a , ! $ | - _ ' a f - r - a 2 s'(t ( I a?,OG -t ) llrt n ?r!) (-z)
' , ltrl = -a,3'/? ?r,zf )n'2 4u*-ei
Lt+zr1Et't')"
t o, +tu e ir' 4?5,' 't" o")n
'= -4 ?er (lzt)'*q&r ''ro'o ''''f,\ ,';tren'r"r!
: -q) / tL 'z ' f )n + e '9t eq (4lh ' t ' t ' f )
.= -ot t?r //.2t)Q r o, ?t 4'; ( /'/" - /'/-t s nl't)
= -t2, J2.t (/.zr)o + o'?/ 44; k7;/ h 't o'+2)' n to-
Ya - -4Jr'tz *
t J-n"f
J i , l ( y ' t
o,*svrs!"'-u -QE.>-/==+a-luin'' I - e " o ' '
1 #t " - *
- p f ' ,Yrt)4.
&
t t , ? t l es=#
He oppaad f+rA/e 44
-AJEL- -!! l ! b: =-fio r u, /
,d I ( l-P
; - biltbal =kilL ft, = o. Qt ' t-P ll=,
I _ b , t tbc l - hPtbatrz- ] I l+to P
Tktt r.v */alq ^ L. b.-/t^ ,- b a / q r ' 7 +
Hre=v * ' r y t - rarrtil,*y'*
* 4 1 -
t-'tus,I =? {ot * Y r', n)o /t./? arlgr,rt.A(; cT.r6i4 4eA
tl.lo ufnT =lt n7 O, l,l/71 = #
.4qA tlag ayhc ,ra( pa.$ . Jr i A r
6/14 4 a/( n 4aZ 4'4" *trZ*Lat At* t . a 7/X"a""-'( "-i
t' '{tft^tt(
/^ ,,a-rLnL ,,. i , x, * &au .
x t qf D c7 ar/ OT 45'64' ,
x + 2 ; c7 tfr/ft n"r "JOf
o{t7'4'
x -4f 'o 07 rfr44 '*'f *'rCTo6/4'
x -2 D ntCT'ft/4 n^at D7 af"'/4'
Yct = H rD Lltp = J/ l ' *z) +t )
Q -, fb- a r I a t /g - er-jal ),*"ar"f4r,a aye a/,f.Lpdfu ",t+putt4 ;* F&,L /*r, 4t* 4
//. /31t2 f l , t1 t =
Ylt = N(t) I
/1. 4 e:)J (7 - o, r)U', 7' *6) 7
, t* l+o,6t = (J+a.5 t io 'aXlro ' f ' ia 'e )
= ( l - cq f . i z . z r r ( l - o ,7e e i ' ' ' 1 )
7a/4 *,e. (,ate
{nJ , fr6o hl ,1,,G0,, f '4"n (-o,et'4i co'ol
r (r(a,f) 's l"(o, l t)D*t (z.zf n r(t) + lult)"
Tbncryil&etc '/ dt feb 4r 'o'8'jo'6 u
@r=,[ff i-,f f=!.,9f n ,rt !./d doa /, 774/ H'ttl a' z+{
tatd.(L)
HrQ) = l
Bzpntz. dt'nt'a"t't'^h' 3/7'z) *Iz4 Au
4+N /Lo6'r-
a ott *"itn"h" fu le
o/ t l rOl oJ( ' 'o 'z , o i l l47 ( 2 " Y -
p& ). rb ny'ifr& / o'tx;'o'7 Q
Itmrlltat'' ' 7t44 H' n afrnc'
"sH,te)=fu0t144 fr/"l
ar 4 o' ad'o'?J' T-ftt't"'
na{nifuA; *tt fu4 rttd' t ' Tt'&t Ht rc
&l-a&.
'h7dzQ fu z*ATc a4 ,6 y'n*,lrdab
n', /uV-t7, rtaa,/? d-e,( e lil4.aaqu'{
T=| u/i6 /<t
tt,7,t-lVC d ?41f 7. Ae
ft*. o,g *1 o,n = orre tio'tt. 71"d atr'
tM fo / aL "4,tttf>tu a
Trrl"llurn1 t Q,'(/, n {t b,/s)n 'i (o'flfn * 'l+)
/* n as, P&' atf fu H'L4'4 fu ao
dt4 e at,/f./4 ,"L af I't 4 Jtlt6
lfrryWop tS' 46 X I + a,e 1 qa)
/ t , t 4 t r ) g , * F l t + o , ; , z
O z4 t 4 , s 2 / 1 " 2
i + l
q-,( f: b*l= fiot h | ++1,(')n'Lrn(t )ot L ( I - t ) '
fl 't rrr,rtl /*, ; no';( 44'al '6 fr'Q
at ayot u a4 n *n. ,J
ah; 4e' fu
tr)* ,foEot I tr'u/ /*/4/t4'
S r d l e o 7 ' * A o 7 o ,
l * o Z o t d l A o ' t l ( t ) = / a ,
lt 'ti -+ 1O c'-t n +rn
7r2t ttgtt:<.t.V/;un"z '/ f t!'^ A1 '2. 77uq
t +Z A
- 3
a nqafi.e t'aly ryW-Trtu4e
t
fr? o)t/ ^ n^o{ D
: 4fa//2
Itt ) = c. {ft|= 1 /::f-:4::
-4.2 -
f , D - Q ) = 1 3 - r ' - 2 7 - a 7
/ - l 2 - O , a
. - a , ? 2 - / , 4 r . - 4 ?
t .3 O
ors-l frr=r. l/b,s1 = 2,2 f
-D:'!,3y37 *e-,.a) orrs)=21.4+/,e l l , t , fs i '146+J te,32
2 / ,6 t , /2 o ,6 4 o .J2
4 i 2 o , 6 4 l , q z i , 6 2
l,g) r,f i '62 o' tl o
o.l8 t,4z /,-r /,F
1 ,2 r .3 J a
t , 2 t , ?
yg!'td .J t
u)t uzTz"6. // /e/o') -= tlrJ; ' --e '14 '+ 48
a t = o . e t b ' t 4 H r D = f f i = o
ao,, rt/a' el*" 4 ? r4 a. / + H(/4) = 4/rJ'a"J -/
= -r.2,i4? = d./;1ei:f =- o7,'J:^1;:t/.d+jt',7 t,66 6'ta+
u :tr,/z, "iurj
=> //0) = #
= ::#
= / , o f a i t " * o
t()e .a.ez- tirrf -Ln/ ,+n1n dartt',. t4 ))<A'{
"*rrr/A4 , fu "-frtt/
''n&'aa a't t<t'= tf/+'
= O,7& and 4t : rT/2 = /,f,? 4'1'( c</7'14f441
a,ihu lk /f. lhatet'ta. nL ylaa' a/2' tJ =o
ti n/z t , r4z Pb/, ru4 "aa1 le r*Pbou/
an /,*(/./rr/1 , )" .42 uet{ '*mo/( t
t^'rt '{rua
elu >t r l 'h) art l l l iel ia)- ' f f i
= t',o , = I . Tl*a )6 plaat ,a ld n *
/ ,e , i , ' - / . t
ni/z ( ra4 )
.!?ee"J/ r/14f a< tl'a'/a tz'uqap'<l T = I
tincf ht nf f."r /'ttruaf no-f
:' "(-rr/r,'a/f 7= Gn. riJ, Tlat z* &'Y"taf
fuf^t{ /4 f , Frurtn 7/u nhf,n'hil '
'.lzaptmu .dta,*+t,, lerc '4/1 t'/taf A" 'fh
ti a "ari*1.paaa '/ZA
"
t/'/7 F"al drz /s/r'{ t-, P"t'{. tl' /6', k< ca'+L
-t-ead .*r/3 /-/@J' 1= H(r):zQ ' (t't/z
llr e t'4,)l= o."o 6 eJ'' 6 oo{ //leJJ)
= 8. +et "' '
Thu 74'- t6'aQ/';icfr' atfau' t;' uow
flz*ttt, /1, 4 ,
f r , i r \ = 0x z r 0 ,o6 A) (o. ih +/ '6 )
+ g , * / b 4 ( J , t + a , 6 )
d &,q a.n (Jn r o,6 )
a,J& oo,ff6
f ir= a'r?"f
fiX =O,6t
p*= a.l&l
a^"r+ ca{ a rzzTattu eztF";rt rl . )/ '
lowrv-t DT aFe,a(,|, 4<eaaar '?6
tv'*6 a/tt
t o,g aift, neTz<fi"t1d" -(tot 4tr:__
t/. t'r *v 4f ,ra^"'*( l''46+ -l'v 4 il
r /. /6 // i,tt = # . 7/v llA rLA B pta7e*n
n : [ 1 - 1 ] ; d : [ 1 0 . 8 ] ;
w : O : 0 . 0 0 1 : P i ;H : f r e q z ( n , d , w ) ;p l o t ( w , a b s ( H ) , w , a n g l e ( H ) . t \
gat^"rfia
,i p oilaq.r( o:*V,-.fH":eft ui6rc ' T7ut4 D111 n '
1 0
ltrei',l
4 H(d'J t
- | 3 -
Jr r"t4u7rf,L-ftFo.r7 u)ti{ qv'(
aI6n <^a&,, p o fq Z*, frtr*" 7Hr't-- e-,)l(;+a,s) "lao
4 -r, f&
4.f - e,,*
L . =
04 a*I
esre.fa.ttf ot
'= 4r4I
-Tiz V4"n rf'r{'t )o, "/ru 4 fu f&
d/ //rA) , and r+a fu 'z+Pan -/ /2r
rt, cat h rT , Ti44 if i { '4t'utott'{ adl
atL, frf4fr4f P"uo'l& iy'r7'zaet7
Jr ,.,rrl/ hpr 'zc/' Y att/
Th.p*ter-r /1.4 dsed '24/ 4t4/-
1at | < at6.
k , " " lw l ( t t
-g;, ( A,8)
ztwo V ALt" ^*fl+ fh"= a2.+ 'twr/&
fr *ac/, i6t/{ :6t" , ,Pn rafl/ ttraT 't't
lunqaad Z,|c /.cf 7n4f 7.2(t 2p,/'au(
aof i t wpt & an ) t f r7:+,4<'ca4a<' 4te
au ur,6ua^/tz/ t t o/g e*r At{t't't"'('
/r,rg H,(r)=rffi, t#f)=fuTo a'lau lH,ret'"t l'= ll'lrle''usJ ,,
c<'c 'dL'n"r
lia et't!- g l t 1 ee
t'u-'ia I
//.2o /./ rcl-) = Ir:si/4't2c
t't)e-'rl"Qr<'
flr,t = *I"1-1,ui*, e ruort *-fl nlc
t ( u' ' -L L,/u(n'he),.tfr
J (. to'n'e4'a"!a7 -;Ju da'
:d" -crlc
I icr(r,'hd lttc= G76,r* lu,---"
U.itn-n")k|c _ u1/h-ao) t lc,
! ta cro taz s7 /o o: ' g I2rr j (n-no)
I te e a'"' '9 | ' lo (to tcz '{'o -=
;-;--: 2
= I ue c:;0' 4'aazt'io) .orh f (n'no> '" '"1t t )
tle csdtilrt'
l f e / r t - / a l , = 1 " / " o { 8 ' / o t t * ' I
= l*' gt'ro I i rc e-jn'- t I = 1 toe'i'{- r I
: l ra wu) - i ' od ' i " :
- s l
= f f ,a t-+r) 4t ''6t)'* (-ta ati u)
wt ,i l zTorrtb (r ) - ftul Hft) aul Ot':. '
rfe* c/lt 'ttt'tru nr{ uTuc& */T''*:
n*n2^7*'^ u^e $y''u{
/ / /? / l f l l=#
tteu yr& ar l"-l orta/ u '/ am'/A '"t6
ahrtoQ a^Er6 4^14{"44 e-va6/ '47 'o*r a6'nd
ti t$ t/',c f*^ t,6.t
;,;; ' ! , , , ,*to1I oat (o'6n r4Hleioi '
T r / ' t G t ) ' L
- lr (n''na )
a/( n-
r / '22 HqYfu=t+ f f iI tn+ t i = t ,oaa/ {X [aJ + u fn )
{ r f i = / ,oao t { x fuJ t u tn l
f/y .tza<1.1 at alz loarnt-
r r z J H G t = k = f t , r6 ao-r&am+tirna,( a, ntrJ+t,e?'u.o/gito+ t"
l fnn l = o ,8 X tnJ +u0t )
It ' t l = a,t x tq'l + tt (nJ
/ / ,2 / H+)= 1 i i * . r l t l =ow+ l ' * JJn I l ' *2 , /37+a ,s f
= o,r + -a'!7f, 3-! o'* r
l ' , ql ' r l + q2t
[';,';,:','-,J= [- o',"'''' i J[:::'). [: ] "^'
,d iil = (o,er/v d,6 rtT [::';,1rJ
+o'rutnl
- 4 4 -
7" /ad a l-/*+*tazaa^/ .unh7,ahir.
un ,r*n .!O, (
,w F,cQ a corctl G1) o.r{ H 4&4
/+e)=,e ' * ( l -a ' r ) - * ,(l- q s)Q-e,r ,t
= o ' & J - o ' 4 - I /l ' - /,J, + e,+
't4 <ahtr1i"ta; k;
f+rn+ttl=[,, t - a,Y f,?|,4;Juh)
!r,r,*nJ'L / a J[x"hj
I rrl = f o, & -o,1 ,
ft,r;'rJ+ a tn 1
&*: x hl = A.i (l-t)X/t) =oh+o l+t
4 XOI ,let aru aLrtat-f'/- aq/' nV';e
hy'* A&, / e't' ^"?t*1'.4 f& erl=1'7ln
)r(a14 e a. n '>F , J/ X lil Au ufr
uryr&l ,nfte A& 221 4a u";'f*t&'
dt4 xtal arnfet'no aaafrzid aact//af"zn'
eni aU Lff46tu i n{afre ' fu l4 '
//.2 (2) ,4rr&f az S -n'aa/-.''n a
{f"1 ^r t / to', J = '2 .( fit 't J'tt fit 'zi r 6 utu's I
Ylt * tJ-' YG )' -s{' tl/r- / -'u0*ll'rurt)
l/,24 At W ab-rs/.faft > ,4 M, //.r/
oL X,h+tJ = -4/fx,f"l -4zfxrfnl + ufnl
XrtTr+rJ = r,tnl
f rn l =a, t4d 4t r tJ + o.62f xrb l+4dqtn l
//.?d $ X6t ,|ao a e,.ye p& ef /=/, cfcltt {K ryfaaelzd aa
Xfr> : $' + + O-vno otctt 6 e7rtu F%t
;8"4 = l/'v, Xtll'+ = f'h /\'t)X'tl
l - t -
l * ,
4 e( iL,t* tJa. '*!zs noTnifi'{a' /44
d.c4r t. dn A/u+ ^6b anfat?ac't c&(
eflr-raaql JflO do r7 '+c7' . 77144 r,r* lrut
lr-_xfni = l, i tt-,)Xtp- i hrungtn^ + e l + t
4 Xtl, tltt zto 2,4 al l=/ ottl eP&
&H nryt r'G/", ?lu Z'Aaa t , dnt '6 L"t
,ttf+ttttct X[ol+A 64 n'+@. ,.h', azt ca4'
aU ,tV"fto>, ^/.A lf & fuast XA; lct
v,u i6 kwn/f:{:1,-,Y P
- 2 1 ' " t r o t :l/U'ffi =-* 'r',
- t & . - ' t l + J - ' t i
l ' ( r r z t t = ' z i ' ' 3 '
{.$ tnuau< l-Eaa7la"- o' tfu utf>a62 af&b
#ro|'o. t lSJ='4 l l tJ=l 'wo( (rnl=o
{.n ,rU t edt-+' 'rrtam '' 1 a*tl 2 ' 4l{ ta f tR '
t/-
fie ulrc{/ tu zfu <"tnt 'to Poel 7' 8 /2) -
22 J - l + 6
/ t n t l '
xt[nal fn!'PL
- + f -