4 {.1^r -9,*fi1.4.

o

(/nonla. s

T,*öons u{ o? < varlotrl<r. f ,f.*rotiüL

\c prot[g*, urhicJn flcods ,.s to tf,. *.rfi 4 i,rtgrotto, ir t.tt.o:eq ti$"rr,t, ßro.. +te uptinir<,äon pro[k^ urhid sgp,;Ld Ä;l(cterrttanr,u.

ün^:Ua o 9*^,1i- $, Eo,ßJ+rß. 0,.q oi,. ht, \eru*i*rt" +4,r

orca. bE rr.düÄ bu \'h Jre'uts-tol aris !.t*^r..cr,, (o,o) ar.d (s,o1 | {,{nr u.,t\iol. tryt^ttts b*ucr^^ [a,o) and ta , gta)) on .[ü< v',c gra"o\ a,ao[

bctnrr,e^ ( t, o) ov.d. ( r, +(6))

* $a uth<r r auÄ %^nU.' tc Vq 2ah G

4 {.1^r -9,*fi1.4.

(r,{rst)

1" $.ro!-r ü( oli[Q. avrc^us,frr diffi*6.s ir, t'nras*rinf a $ucn oFcA tu^{rr iüc }ro-pß e{ c Su.^..finn i thD t' d anc, g"Jt?ahc{ Lv \,tt y'r'lh

4 Ur elora$".Ntic {*r,fn^^ {, to,rJ +\K + {. "firrol ''.,"r^.tcp:

r i { * e Qrnfo,tl

o g+torwr\a

L

4(*) =

\k Q;.s silu<

9,^ .Ims)

{ania grJl<q 4* ur"g \erot'c( guxfre*l [so - .all"A stg

l\. \.Pi^ih'!,,1 IL lr,trT,ali0+J . ßooi.s

\lc crnsi&r o'nJ ß;* a- eo^po-cr i-t*rvol Ea, {,] , w*i a < & . x n

+& ,t *Ear() 4 oe( f,r*tr-s 4, Eo,,{,.l + K w< sigl< *,t L

sdvt whida u ( sfrdJ oolil *tr g^cfi,n^s.

\€td"ü'rn s.I

\ 9,*t.t {. fa,a1 --at( \s o. *<p f,^ffi. i{4 'l-g'crc is o'

$^rt. S{utrcr T-- to.= \ßo 4.f.r 4... {. xn=C) 4 ..o!. ,ur,,rJcrs s'rcü l1'&

$ i. wnstar.t u^,r l**-,, T,. L f.r, n(A h'--^t"'th ' \lc sa/, +{'"t +&

se4uonuT ts a '

T6. s;; 4 "ll st"f p*.\rs rn ta,{'1 .,.V{ bt Je*üaol +V

s-- \f.a,G] g lR-Eo'ol

F -l

$c .?^t^tl ''ttt 'l'{^tt u"c o*ü' +{t sotr < rt"f $r.s"ü- rr tro.'&]

or.odotÄ io'\\itr '

?g T ts n prÄ\rr. csstcioiJ '*ritt' o.. dh ß*ttt l ' *t"o an9 T<hnehtt r, 4 T ir ofro asstctq,tc,J. *t{ä T.

)+ toru '*.ti\iu^s \ a',d Tr 4 t'o",tl *."";o}'\ orrt^ { are *n.,,,1 +fl"r. is oJ,urogs o ?t;tihiu "'h:ü c?{h'- L*L -l ll^/'^' 2'-t lzle

It^e *nir,n vt %. füirß ir,Tn a,Ä\ a'o\ .-t'l^ld +/ti, {"fu t"t ir'

^scard^n; üJüL ts glf,ol'' 1'1o daairaJ. v.,1"^oft '

Le*otl.* t r

4*rto. T e S to,6? is {tüt"Jtd '

$ o r . * f u 4*ü*s,14cnn 4tt,S* o ' o \ 'iß dtfi*\' L of,t tk'f Je,,'frr"'s '

b

]4

(i'\ L.f {'. to,+] + rK b< o- st+ l'^,^rdln^

be c poäihr. asstc(of,ol "tüt {' To'L euy Ic--

,*.'rlr{. ce \Lr vo'\ut 4 { u^ Jxra-t r xt. L '

thr- \i*r i*gr 4 $ is *4te S"'t< sjb

$ trc,*1) - \ co.. r(=\t---,,\ u \ +tqr4(*.),---r $(rKÄ +{0!.

1t* hr.. ? v.ni,n * 1..fn, C o,*I t'{'. : '^^LY-'P (.t",{']) or< *Ae v'ni'i w"twl r*r 9. l4rc u,r,crl rrrrlnr + + H<r^u + is tfr'^Ärl '

hcs t"Qi"it,0g urnvry

$c :og *tat a 1os\tis^ T' portti* t= [o-=lo ar'\ a"'

o,^d F* t*=xo 4 "' 'x"=$

tr-..rh "{rt ü d't^üt'

(i) Everx dh.- (il T{ $ aÄ

@

(r,) L"t t ,I br iuo gorht,ms d fo,G1 ossYcjqhd o,ilA { oud;

r{/Deg{öur!4. Lrt T t< o" cnarrarr rc{'.nona..t 4 Q a,.r( T. ?t;s

rrtc t^r€( gt tt* U,s.\\c port 1 4- {'t't ,ncao-hv< pof **Ä t{-t Vß<

easy tu sre {'hqf Trr o, gqrhtiM { Ea,<r] assmiohd o,'t{ 1+l r

4 f a,,rÄ -\$ &l"o}. - r"i{a &- . t

\*tnr,. ,b=ßf*,G-J, = \ -P..Eo.,+] ->rrA " $ it tuqn'J"nÄ! ' Th*

S Lr-,oJ g ß ta1t1 a. d r tp Tfrcoro- nt {tt w\i"inttr"' ""d.. }4arintr4, { \ n c s c t e [ o , t 1 = \ g . ' t . ' c ] + t r ( " $ t ' c c ' ' h i , , t ^ r " " ! is o l s s

enfiui"oÄ. in Rtor41 .

\cäniNv' s'j

Lfi $ ,l .. X --a lK !( p.r*firns 0i^ o sif X ' üc &,t'fvnc +'t^{ &'l tr'"i'tr

$u^dli.rs

+ trt , * r.g,.P*, 4-, t+l . *-> K

bb

tr\ Q' u r) [*)* ***\{-(') ' 1(Ö\ '

tr) S r..1) t*\ &Yrtir'\{-(n' 1(*)\ '

Ls) $ ('n) S h^qY* \ S(it ' o\ =G \ 0) (*) '

l,q) $- tr-) ;x! w\aK \ -$(*) 't=G $)u o\ (*) '

rs) \9\ (*) gL \Ttr)\,

ruhqc 0 ")ß -+ lL r\ \aq 'tyfo.tlf O - $''rlrfrnn '

qÄs$lrtq uol"q vq .q .

f,g $ it bo,,rrr-J.tA r .rr€ ca.ta assoc,'of. *fr4 .[ q *.-\ ,ta,r{a6, .rlLd it5 hotn^., +.0

(s'\ \\+\\ g .* \ \et*1\ " xex\

\lvt( +hat {ü,t v'9$fue foff u[ a p"'^'frr^ i\ il-W 'or,7of" '

u-tc st o*lÄ of.t \ccqf iv' ni"Ä {4o,t {4t( nLsolotc uo'h^< t?l vl a S,rrt,. is a l.*ü-,o'\^tf it: nuru'n t\4ll i\ o vntu"hr'

Ex<reis< E r't

?ro* *. l*'ttv,nt6 ossertons :

ti) \{lzro aÄ \g\=o .c*oüfo ,|" ß =0 ' t t i l \+*l\ ä \gl *\g\ oro\ \ßl\ =\+l't.ll

t i i , \ \ g \ = $ * * q - o n o \ . 9 = $ * - f - '

?.e,narlc t'tt

T* .t[ &1 eßE c,G-l urc \"crl(

ti\ \\ 0t\ zro o'uÄ' \\+tl= o i4+ C = o '

tril \\ $ * g\\ e t\ Pt\ *\t1\\ [T'to";l' 5"'1"nfr11) tiil \\>{\\ =\>\'\+t\ $* "o{ >eß '

(w) \\+'l\\ s\\Pt\'\t1\\ '

B

Eracctk

sincr urc haul Sto.,{^l g T5ta,{^) ,ol$ *tr ot*- st"fe,.raü lr/{

o

t"r .t ( {rr^^rf,r. .

@

hreo tdn' {ft ;.tqff {- a frr {*S,,n

Hw üc Crv.fi&r or, =tf &^ff- {, [o,G-]*K qüd tl ,,*p.ehe tt 'pütr

&rca "

,"fl*, t'

it 34oßh G. 1^ gri^oglc ,Sü sf,*l"\ k w'9 sinct ut€

hou< tF alÄ {t"r orrio,s ,1 reüenyln mtg ,

!tv,^xnr,*x 9,*u. tl ,r^l;/cl. tt^ot u^t $,.rl'fi* yirrrz rß< t6 -a'r5

üi(+qra.t prihtrrr^s . u& '",Jf Vu5c{6s pfrß l"vrt 'l'ü^t +l^r a*tifft/

4 or,- + rcta"$r, gstotl^un q' ntrr.^le-r *l'tb'h tlte"'l' s- laa |t*'efi*

srb , ,t ,^rt m an asstsofad 9^r\bi* * ih Ju''a'\ '

t - g t T t < a b E . , A & A u f n - a l , f \ i t r r , o l . * . . % S = i n P I a * o \ b s . t r I .

\.t stt * ls) gI f- s ^' I *I\ +t.h n""[rr 'l4q k'lrt w {4q'

vrncasqq! {-f . ?+

':E = 4 \'ln<^,^ *r< stf, * [r) = 0'

1.-

Lrr vr b< a. äisjsi* .^v,ir,. 4 a pinifq srf, t{ ;'fertoln Tr''-'lE '

T?.c,^ vü( &ät'<

-[*\ +g t-''tai) '

i=\

Hv'^ßvtl , ütr d<tinihr'' J*o rrlulc +'t^r verift'cohm t+ ih

i,^dqeaÄ{r^cl + ${ ree(cscif,-o't''' u{ u^t o'*d l''u Jqtac +ct a's

äiQ{craü ä,\jd.t ,unin^s *+ }'""te0t .^r-,) i'furuo{n.

\t\ [tl\a"t ft-o l't{ 4Jtt*g \t*'nno' '

@

Lw.vno. r-5

(i\ 1( \,-..tq a.^d J,,..., ?s aFc J,l1;"t -p-*,Ya t{ i"trvo0 a u d M = Ü q = Ü J t , l a c n

J : I K : \

-f- F t r-.\

i- tr

ö - ' r

S

Z - r . ^ t ) = ) .

p-- t

Thcr.*oc" , * trt\ i: ,*W%.rssucraftl *l% M auÄ is indepe 'adent o&\,{n. ro..escntö* u[ y\ as 4 disj*tr ,rnion 4 {i^iltfJ v'^cnJ i;htuo&'

(i,\ tä -Q. f.,G] -a K t< u- th{ {,rr^ot''un o*l Tr= (a=ro t'-' ttn=s)' T.-- t a-- goa --. z-yr=a) k trro f*dU.s t{ to.,G] ossst^""tt'l' *tA{'

T o o i--\r--.lh avroL L : [ , " ' r P

av.A.

\* a Jyu" r g,c L - -lf,t

"

\r( sri.F osb,t ari$ pdfr 9i.?x1'-r'to[

*- *tr.) [v*-v*-)

L = {

.= T-\r. vr^ (+ttt',)) ,

ur g\fl

rqLcre-, $= I [Co,af) \s *&( S"]' i*orl '+ ß '

B-.

t . l S i n c r \St\,är g t t l \ $'* tvefg i--t,"'rr rh4r-"r3,*t}*.l/r,t

(ü Ti -- \ n$\ = \ n \. L?.) -= Ü tl et?'.-);

\ tr=\ u--l

tz) ?r= ?r.nA --2ro c\ (. Üq) = Ü t?*nq).

ä'--\

v I

j=l

Si"u \ \r a.u\ i'rtäruo1 q^rA Iln]rr-.. [\n ?s \] o

Y'\

L+(h)

i = \

(ri-\:il -

J'\juf hn;,q

S

Z*tqn?r.).

t a = \

uf i,tcruo0o ,\t )s .?ü49 tD lae U,cl- (r) i*rlito *

"(q)=

?t {*t\v^ns +'t^f,

r s i -

- . F J + - ^ l )

* f t : \ ) ) w . \ l j 0 ) t . f = / .

" ' r * J f -

l - = \ l e - - - ( \

- l c = 4

(t

s

= . Z - * ( 2 r " ) '

E-_f\

r

Z ' " , ( E i o ? r )^{- a )}

rL tr

\1. S sio.ih.e{ {A"t tz) i*pfits * [en) = ä * (q n,r.) .

j = l

T-

[i,) ?+ s..p{icu nb shu,,' +4"t

11

t-{- ( Y;) [*j -F]q) : Z- \]'{'n^ \ $* (*)),

i-- tr sr C\ü.1

erncr VA. .i1Lt üarÄ. stJ( ir indrg "Ä.'t # t*\bnas ' To. ^ qru={ ,{ +l^in elainn {"t *e d' Lü 'rs oUtofr *'r*d

,t ,4 i^d^u, j *i}{ $ \ ,x*,rrxiL = t^r av'Ä *riVt'' \+ (*r)

"[ i.diuo I *.,'V, *(-j) 3 \,].1 . fl.'1,n

9-, t.rr\ -- ?xi{ r xi L u U \xi \ ' l € ? t d 1 e \ c t " r )

{hus, ${|.*l \s o" disjoi'* ,.r.nir". u{ a F,.ih J<,,,^'q ü4- i'"TQntalt d }

vn\ g'\ (.,,\ : äi

|. t'1'.'x;t\ t

\tnux .P.r .nb;eKtu) w. fla,l< läfi l''\;\=t*;,*;t ft a rnc- ule,^o*

r..trvol. aerA m\\ti$o . f,+ h{tt ^ns Urot

',r.h^( qn(-) =\.x. = (v-;-*u) =L*r.(vi-5) iea (v) je? t'r)

? ("r) +f,4

*Ar sef

Z-,-(\xik) = Z- $;-q'),

jer(v) ie?(*)

@

sü

I_*.*(,g-,(,)) = I Z- +th) (*i--,J=Z-+h) (r\',\

ureq urCul {i?(r") -

{:\

siv.u \q,-'.rr\ = u ?t\t') ouÄ 4"s t^r+t'i i*'\lt?s"?kt)=p'

urFur tl

\.t""'tim s' G

Th. *nurJ4r z *.*\ $n t*)\ ßrrn^ Lo,o*a s. r (*truf' c" t,"te+a\-

rxQUl

ä-rt u+ Lrg gor\ön^ osswiolcd *ilt', P\ ls *\\rA {& ''frärqe t{ I anJ,- is urr'r\te. Sf +tA An ur- vrro(c sfttf,- S*f 6ru {rrr'u $4'

" -*o,bJ + K r Q(*') = c- is o' tltviftt gr^firn 1 {/,ea Lepo.&

Sl $ =- c (s-o)'

T.,g,tih m S'?

Lct Sr1. to,cl + fR t<$iT *&^'^fin"s r*ot r€K ' Tl'c'T

r i ) f ( P * r ) - - $ $ + S g r S ( ' l ) - " ' \ S o Ä S t + = r ) = $ { - $ 1 ' ( ü 1 r g $ E t , * * g + . 3 g .

trii) o s. \ S +\ + S \+\ €\\4tt (s-r) .

u

(r) t-€h T : [c=xo z-... .*r.=G) Lc o- got\hior, 4 to-,5? assrer'qFad.

U$tg *i\a. { a-I 3 . Ld \i. Jx)--\ txi I r t'=\t--'tn t<

T?r.^, b Lbuu^a

3rinV.

e"bi\urg

S (+*i =

t - - . \ t - \

(lj)) ,{-\.,,=

- ri-1) :

l + (\il *l ttli) (*i

= $$* 33 '

slc JIf sin^i\ct0y +&-t

trs o e,m4u,tü(c( t

\ t{-l) = S tQ * ( - N : } 1 t 3 t- r ) = s f , - 3 3 '

t.i,\ LÄ T= t = a^o 4.-. 4ßv1= t) a*Ä. \i e ?xi-r'Yi L r \'=t'"' ;r\

be os i" t') ' F-refUin; 4ar\ t-eunrnu s's urt yf

Q p : i +tri) [r; -xr-; . ä e t\i) (*.i- *;") = 33 .

ö t - - p r - I u

d \ n

tl..\\ \4i -\-= to.=*o 4-.., a*nz. !4 a ?*dbir^ uL f o.5] a-ssu.io,t?Ä .r^*h $ orl h e ?f,it 'xit 4"" i--t""rh

h

o e \ I+\ =\ä *(r;[*i-*s.t\'tr te(t;)\ (*i-$'r)=

' \

ö*--il

: s\+\

(xi-x;-r) =

$ S ,

ä

Itry.\

>-

ö : , \ n

L &*l)[1i) (x;-x;-)=

jir

Z- +(\i) (*i-*i-,) |

i=t\

..4 (1i)

^

+ .

Ifr.trosr0i\ -{ &-cfi*91.lf4

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\<{r.r^<

..t^r. t> on ort"ihqrY

osS,r^r<. br t( te'r.uLr\ .

+4( *.t "+ t'hp {orut-.s

+ü( sct tt stp !-u;-ftr,,.it

o e S E o . , t l te S Ea., sl

*,'14

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o

t--

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I

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l I

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a Ut rrlro\ $^"",.frn ' fhcu'

1 \\+t\ (s- n\ ' T}u s t

- \ t - { t t t s - " ) 3 ( + ' T h u s

s w \ S s , s e S + l

, i' ( \ S t , t Q s + q

Sir,cr- *it bh^,"&J. , \\+lt =

-\\+\\ ä *(")

= * \ \ g ( d \ : x G 1 o ' , s l t < * i s h . tl {t\ P" "tt xe to,!') .

I seSg

I

I

Trqo\ö'rn \

lxt 4 -. to, t"1 -l r(- Li\ Fr ony s e .14 ,

q:ß\h.

ti,\ Tor orj tt s q,

<t-\\.

'1.*4

ond

L€t u\ .,^s\J6 l{^t c.mifa,nt S.rlotut t rr Q, Eo.rSJ i te r -c[r) = - \\4\\ r C (r) = \\4t\ ßtc oll re Eatfl '

T \ < , . r , D + & € C r s $ * Q S g o ' d 0 e S + '

(i) Toc au9 se Sg \Ac hcrrt !0'*t s s $ L e' F*au ' Ly ?t'p' s'?(ii),

\ ' . y f U ^ A t 3 s G ! C = \ \ 4 \ \ ( u - o ) . T h ' ^ s , \ S s ' ' s e S 4 \ is o. nrn - or^t\ r "t "+ .^r n,rr lc* u.iJü a- rr,p,"r aü'nL' ns'4ig { & \ . r r r s t t b * r \ b * r e r r i v , u t . H I e w \ 3 s " s e s + \ ' * B h '

(t\ Sivn-fc"O,, . G

,.ffi.ül ---.eK t< o. to.rJÄ T,oifi*. Th<.r^ "w\ss' s*J1l

- , r , ^ I r . - t - \ s . 4 S l + o g + '

\s c^I\od. \{^t f*"t i,intr"t '{ t o*J.. d' *-\ 4 I" + ör I{' k'o,1vp*rtg, ir.( \ s*'I*ß\ i5 c'"\\cü lÄt ufrr i"t(Öf,ol 41

o*o\ t^,tiÄ 4ä Sf + D( S+'

(ii\ h $,.^c\\rr. $r fa,'{^) --+ ß is cAIllA i.te"ra.ül< i', Yl,* gaa is th-trÄ o,to\

* P.csnnn ( or (a;ma,.") tÄVdq) i44 .ß

J $ = T+. ?'n v^'^ (tttt,lht v,u'lcr J P R.i.rrn*n ift4g! -{ $ o*oL it is Jt^tt\ Lp

a T+ is callol +Q<

i'4 1*1r* sr S X+ ü.-

G

s s .

Th( )eo11 + od g(vratrrr i"t,rotr?< Q."^fi*s *: tc,4) + !<

ur(l Lt &,,rihÄ 4ä T=T fo.is) '

&elro.rlß-

Tor o.^e to.rJÄ {-u^fi n , 4'. to,s-J + lK , ! $

tgr^rrlr-

j

Eor( st* {-ur^fir^ il l"ft7nlt. o*l it fic.rr,rn,a,a

ts.,r.uJac *ilt +'{ü M( dtil't^.Ä iv.r s- 6.

: S + .

i,t.7u(

T9.c enÄ\in" "+ i*4AlAt ca^r Lt

*itr.rrrth "ffti*)te criT"si o" u)^a')'t'a '

T\cdrtu^ 5. [L 1 f.ir^r^r,^ Attt"- 1^ t"tatdi&b.\

T.* q l^r^^chr,n 4. f o,G) + 1r( , {4^l {ttt*ritJ stnJf""'It gui"o.l,l^lt '

[i\ $is i"fuill<.

(ti\ Trr tu<xV t>o

s , t € S E o , + 1 3 ' t '

..{or.ulofin\ s} +{'"f ü,^

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g , s s , r r ^ . " { t ^ ' t + i s \ ' f t r y ^ t } ü t Ä A t ! > o ' B e M l 1 1 " i h a a

*lc Cürrodf{riX.fi- Thoqanr^ .$" s'^?cuuA (o"d i"fi'o) l'3o

=te Ja'&o*t s't e s EQ'+1 s't' se $ gt onÄ

,2-

S t r - s ) " ' * ( ' ) - S t - S s

L,f, a7 o k arthra,rT o,^J" s't os i" [il\ ' Th<'r" s r { :t

bn\,.

(it -9 [ii)

5. r^ anÄ

V(<c< ot(

s q -

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tt\ =) t',)

o.r'o\ {,1^c lu^aäeÄrrcss "t tlip p^r^eE un

"+.[. Thq,r Sq and 3J <.*\t anJ

S s s S {

L\*^^.r ,

o €

S\r,.r, t>c

@

i,a. glito, +l^ Lo<rre&J rctl R^( fios

3 Q S l s S t - S s

utts arbitrotg r V{^at^

S ( t - s ) ' 8 .

A t

f = S + a l o

J

S ir i,#r2+"Ll< .

t^d u.s

-[B*

eor.S\&r

{ ,

S + = o r I

+ { ^ r & r r ^ f i " ^ ^ . \

to,r)+hc, Q(*)=f, "f,}:::t"'

$ = [ r sb $ it ,ut i&zr"Jte .

k o" o.jqlr'co'\rm,|, V^l Qicr'un'vr" Qit<rit *t "f

1!orr.^ s' tl3

B

+ & . t S r i s d - u < . s , n u t l c \ < P l " ) <

\ ta,,^r.,obl '

qo$\\i L^ ?* = [o= xo . . *r= s) l

*h..l. b r^tt

E.r.r"tr, vnw.,*.",. f*t^üsn f .. to.,sl + t( tr i"\2roJl< '

\\ . \. v .ä . \u< \,t^T assrtr^t<

r l - 1 s ) l n s o . Q l x e f o ' 1 u 1 , 9 t*i n€ H or,d er^si&r +f'<'

rnhrr-<

Trc -- o. + 14,. t+ I lL-- o,(r.-. rh.

\lt d<t,.t Ste Pr*S*t Srt e SEc,t') o,i}d. u.h,tÄ 1?'r( p.f,l'ihi1n i\

os:tciotcÄ o-s $lxr"s I

s(*) g {-(xr-r\ 1 t t*'\ g 4(**\ 4r xs fag-rlxra f r

s t s ) = t l s \ = { ( u ) .

Si^cr ß is is*-< r vr.( hq,rt< \Ar\ sg .gs\ . Mrr.r'ot,

S (t-r): St- Ss = i p(r.*) (r.y-Ko-r) - *-+(rq<r) (x.-\r,l

t c = t k = l

n h

=- Z- ( +t*t -+(*...f (*.-**.) = =tt("*)-9(**) il

l.--n

h

k=l h

: b;o. I- [Q (**)-.$(x*"f = tq [gtu\ -[t")).

h k - = l ' h

To.

\{^& \s \^> tu-") t+tr) - C(d) . {4,a.^ I tt-s) < g.

€ . '

Iln,^s , wr^Ji\an tiil ,{ vl^( ß^u,,rr'un 0tnaric" il t*t'tt't , te- \A(

eprr a"^J^^Ä 'lt^d C i\ \ff%ük ' -Itc

rAs( uf a,fittn< ln^fr*; t ."ftÄ si.at{afl5.

$*tlrr'ä

(\ 1Fü- o-? o r

? r r . . f , q , t ) + K r 9 * t * ) = : | is i"f,r4^oJfü t" 1roh .'t e Ff o .

t\i\ Tfl,. "Ä.NR,- (*P : t*,{'l) --: rrt N t"t,fa1ß<

Tr"gd,\* r. tq-rr

Let $$,tr , f,o,ol -+ r( b< Lü..{^dr,l l+^cfrus at.d cQK. TLu^

t i \ S $ = - T t - + ) o , d S 4 = - S ( - + ) .

( i ' . ) ! t4+r) z S$* S* ar^Ä T t Q * r ) < T + * A ? { 1 , ! a k

t " f r a Ä , l l e , S * Q + J \ s i; t c 6 o l ? t o * / ' 9 t + * l ) : S f * S { .

( i , , ) )$ tr>,o, i l ^ * !bß)=.. Sß ond Se+t = F - 3 + . ? 4 F a o r

! -NtR^ S (.g) = r. S* auo\ 5t.+) =.. l+. ?f 4 x itea^dt^ t

\4^.r^ "i \s i.teaJ\. o", A S t"g) -- r. I g .

( s ' ) ! [1u61 4 S + \ ! r - . Ä T t g u l ) > , 3 + u q ) f € , t r o r - (

t*go)lc,+4rrr {uJN i"ft7^,tl< arrl. $(+vJ)?9f vQ.

t"t at $rJ ort i'f,ryoil< or^\ Q gt, ü* S+ s 3l . t",\ g \s i'tqro)l< i+ *"ü *,ea * 4 +o"d

4 -qr.

ir,tltoJh-

? * r r ü " f Q A t a t S q = S ( . * _ g g - o - l S t + l = 8 { t * ß + - .

( s r i l \ S * \ r \T1\ r\\e\\ ( s - . ) .

(.r,il ?+ +N ivf?ßlk,!t"^

\ \e\ € S \+\ t\\+\\ (u-")'

ti*\ ,{ ß i, i.qro}le, th* $z it it{4^/\< .

(*) ?g $,t ore i'ihr,ya,\Q , l(* Q-[ \r idh64all( .

B- ( \ -S (-{\ = -i"{ \ S+. +es-+\-- -r"{\ S\'' ti: o. s\ +*^cth

o^^Ät"r-*\ = -:rnt \ $t'. t\s a>t.,1o lutrürtd.a-'P!

@

- -ihp\- S t- +\, t \s a sto l','ü^ u"t4' -++81 =

z -i,^( \ - S s.. s is q. r\ {"c^.f,ü^ ;'llss ß t? =-\'t\- ts' seS+f

+f"ok sv h = -\"t Q*)

(tr\ Sinq \ s*t " sQ Sg

+, sMc^ k wl s'lstf trs r< | vt1 ßov<

6 t e 5 6 \ I \ r ' . r G S f * , \ , * . & f ,

! te-r) = *uo\ ß.. re Sg*1\ >t s"f \ S (s*+) ' reJ4' ''te$;f

= s w \ S s . s e S p ! + s ü r \ S + ' t e S t ! = S 4 * A l .

S , * , \ o r t 5 , \ s t t ' - * e S ß r + e S g \ g \ r " r Q s $ * t l , to

S t g * r ) - - i . R \ S r , . * f " t t < i ' { \ S t s * + ) ' s e s { n + e ' f t f - - \ n t \ S s ' t * s f tr + \ " ' ß \ S + ' t t s l q = R g " T J '

x\ +r l ore .,lrr4Jk, l{ncu J + = 3g *"d S f = SS ?+ -f+tlwus

+ t . r t - - -

S { . \ 3 = ! + - . S t g ! ( a * t \ s S(e*d) g S ' $ + f J = ' S + * S l '

V\<r^or , SQ*t\ =\ t$*l) = S$ t S1 t S'**l \r i'tEoJh o"^"\

S \ g . i l = ! $ * S l .

tit; Trr r?o , \.s'. se \t\= \ +' te S-+\ , \ 's " \Q SSh=\ttn'fl.

Itc,^ SG $\ : s*P \ $t" t e S.r\

E 3 * * \ . ' S s ' - s e s t \ = v ' ' u a \ ! s " s e $ t ! = t ' S + ' rllc Frrr ri*r 0orq +att {tgl =F'Ta.

Tn re-o r bp t) orr( \',(^r t^t +(,af -F2, , u. yt +{'{f

s [.P\

- r

1 .

\ ( " 0 = t r . \

1k e*t {,tri

+.{twl o.s ir^ (l\

( t v \ S \ r . t t \ s u t " s e S 4 n ' \ e S 1 \ lt s't^'^^\osh \{,*

S \+nr) z stP \ \r-' ra SQvl\ >l

e - S 1 " S g '

$st*.1 nbr^I uÄ \ r " tt f

u'\ I

i\ hl\u,r,'r: +'t^S

( t + { l ) - - i ' f \ S ' " r €

--3 + 't Tt'

J ' ' \ Z \ , ^ 4 \ S s .

vsv \ $+.+ejhl

ses+hr i"(\s+.+e$1

T"o \{^. Scwo\ (o$ u( uo( +fu

\eunvr.s tn ".ol vrurubot-s "

lhcts,.^r !4g,o. Lln o-'S rc rl e rL ar^\

{\ne^ tsvl) - tqttc) { }$ Erare-ß< '

Fr:srlHq- V^t S ' t orc \fic6<dh ' hoh'.J Vt^r (^tl,nan^ QÄhrirn '

*.$ d*p l*^'^&** itr t Sl'\ t Stot{'l s'\' s$ L Q tt+ ' E r r l t t l a ' ^ A . o : \ t t * - s g ) ' 3 l ! - t r )

+i.hurJl< \vrqll% ''S t'treao-oiile o,.-'t SG*)=t'f{

g \ . ' . r e S + u l ! t * , (

: w \ S s " " s t !

^ q 4 \ n \ \ , + e s t q ,

\ s ' . s € r I

CIcrao'nn &ikir' tÄ +'^l Htung

a s s u r e { ' ( , c - t . t g ü a ^ Ä c t Ä '

( s - a ) + ( d - . ) .

@

**&-

\ei^"c s-- S+tl S, q'ü' t=tg v\ ' 'Tha^

sf o-rc a't'u t\

s g $uü L\ .uA o !t-s +.ttq-\+)* t\ - sl) L, \(Gur hr"*a ' heelg*l l.n3' u'a , i\ Pol\or'*: \'0^F

o ! 3 ( + - s ' ) 4 - S ( t g - s 1 ) + S t t l - S i l t + + ! = e '

h

$uö

t"l

p^,^cl or$"fi* + va ß,.er,c.r,u^ dntrrim v\{J,{l" \'t^4afr'\ '}+

. Tl.c +^.f l4rn\ [r (+ul) >, 34 " fl 4+tts'^'s i^'"Äiofu['

Si,.cr g6d r {a ft.vt +A.t T vJ = J . Bp ttu\ , tt '9+ltu''r {d'rt

3 l = s ( $ v 3 ) z S { \ 3 1 > , s + '

(i,)

:,;u gpstuuc H'S $ i ' i;ticoAl< ' Slne'r H^t ,^g.rrt-,f 0- ltloiefr*' i: olst it'2cd\<

* I Q + = $ v o , $ - = t - g \ v o r

V0* \,ft{rü,tb 4 qo *A g-'

ßv Fx. s-r [li], rÄ (iti\ w. tö

St= 3.Q*- S Q-r

\e ) Fnss.ura +{^xt t* *A S- or'

$ -- lL l- , \ g\-- $+ * S- ' \\o{- t gqel^'i% tl')

\'ff'b'fiLb\( .

Urqt $ .,,,^\ \P\ lrc i.qrtlk a,"f ' vntcurf'

\\{\-- Sq** I+-'

(ni\ $-\\un 'n^v're1,rt*'Iä Qc* [+'r<"-4 *) ?tv'N (ucfae 'l+'^

6*a$,n.\cn JF ?{^l G-p'rrrarv' i"t''f"I) '

t riit S.ner \ 9\ t \\A\\ r t") v\"tJs

S \{\ : \ \\+l'\ = \Ht\ (s-") '

\\Wustf t

\ßs\ - \ s et er\ :\ s tt- t.+-\ < \st*\-o \s p-\ --

= S Q t * S 0 - = S \ + l 1 r , n c q

3 c +

9 * , $- 7o c'ncl \ b , t r y ( " \ , , 3 C - > t o .

( i * 1 hssur..rr< S r r t t l 4 a f T z o . L c t t > o J x ' " v ' r ' '

s i v r c e ß

\s i"tlrol\< s rrr( c,o.r^ x& Utl üe'rr'aun 0eiterirn tt- f,"Ä

I

stoe &,r.^r$e.s sorb e S to"'t'J 5't' so€ *a \o

SS"-so\ <' *N, rr,rl f',n s.t ür<-

\<{..r< hs't^} s:-- so\o t-f t"--toI\\+tt' Th<g sf '}r

stp {x,.^^ün^s 0,.Ä otso € sg S €t ä +o't\+t\' rrlc $ \v,r'^^odio'tc0'tJ +0't t-s <to-so tto St+-s)sS

(+o-lJ'

\rt*,rrat , sivct sr$tt)tot\t Po{tu^^s +4'ct * e +tttt o""t

\ (ta-*) =. ß t+-.)t*+s) ! s z-u{t\ (r-s) --z\\4(\'s (t-s)

+ z-\\4\\' S(to-So)

Thtrr{+r , ,nd^h*Lir) ü'L v* fiit,r*nr^ &itcÄr'' ir sahrfud o''t,..

tttur 9'\t \tf,tf")k '

Nqu} .t.h $ t( orbitrortl . Si',q P*, $t>,, ...,,<yt +{^,{t (et,.Q).

ort\txnq)k.. ?* si€r') "f g\g?o t it ht\v^lr H"of

*-- \f-g+=8$ "($i"

tN& ,'v^'ti'\ +b 1o^d'fr v^at F i= \"t€artlQ

(*:) hr-h ($ , (t,r) r (tx) o.rl V.'e {^"f l4qt

-!,q

(+-n1 .

ß l =

\ R*r)'-

E

Y ond \.t c Eu,.r3 , to', +l -> lr? g( +14 4 t u , u 1 t

D t \ i 4 x e Curv]

( i = (

L o u{-f^er *}s< ' L.t trr\ e f

chor.ü.rls\r(

L. Th< Grrndq.nin.'ilo-\ Thtor"*n

a , G J r u {

P,^.fi,'.

Q E. ,*J

\le def.',r si*ifo,r% a au,yJ .

ß-ur^ctL +t^& ef,.rvJ I eJ.^,ul ora rto {*c'tits atndl {4.ccrfre,

$^2 &Fe \frcaro,S\c. l+ \s nA',v h sec +{..& If "E*,vJ= SJ ttu,vJ'

?1 -9. forbJ +K is itcrf,Je., *l..* oEu,ul{ is i"h'nnAk 42

ltnr s. lQ - 5. ls. (*) . Nvt^r ulc &P''"(

Sl + *g Sf " En,,-)4.

Lcr,,r.ot{..

- n u . ^ +

Ja - f ..,u1 $ =- 3^ " rn,ra {' Trlt+

[1crc\< . Tttoo,hrn 2-

B

t4t {, fa,t"] ---:t( L. ifi13-r\t - 1,1^r^ .P.r a',9 me fa ,{) ,

S*+ -- sJ+ * 9,1 +

l"*lt

L.f ue ta,al.

Sit

rrlc rcs^'rl. Plcst

o e ( ^ +

{r"t a

fo,r. * "l^,al = (' -f'etn

o....,o.)+ = S: "ro,*J{ .3: _{c f}

1n,b')

= s;{ + S: +

Re*atL

,rt +a.t Sl + -- o

-9, X + Y. -ß is c^llzd

( o((*,v) <- s -) f (+tä, Pf')) 's)

'E

t5 t&.r; vrt:'d i" *tnc Ärc 1rry'"itio' o'

},e*4 [ l'.o'\vsio a 'T'fior;o!' rs)

\e{i',i\ion

r \ l

l-ü tx,Ä) r tv,il t( " äf.'' JPcata oho u^[or*h enffiv,ururr iQ

(vt'o) (a [ >o\ Lv *'v eA

\hewe,rn

-

L (*,.\) ' (:, t) tt t^^tN" vo'(t' o'"{

Q- cr"ilrnutd/r a*t( X ontgad

{ , X + J . f h e a

ä + *lfnotY "o#"uü'r'

T,-do*..fr \ thcn * vf \i(4-eri''hiol o-".J T';f'l 0'1c"'1"'

\X.U:Y)

L"\ C, to.,t1 -r K- tt c ffinuu'r'r 4*chr"' (i) I ',s i-fieydle.

t',n Tt^. 9,.*Ar"

T o : I o , t ' 1 + K , T " ( * l 4 S I +

\s a.,,r o;\&riuofiv< 't { , %d is ! is J{q'r-,ft'.,lh anlTo\=$' tiii\ Rt anä o""tiüoriuöv< T 4 $ ' +& +Jts.*"' t^'LL

Sl + -- T tu\- Ttö .

b*.

ti) Sin cr ß is er".Nrumra sr.'(.trt"\5 ts.'hnutu'r'

thcre$r. 0tr lvrfg

(r\ \*_y\. t :)

Il ?=(a--xo 1 "'z' x"-- +) b{ ü"ä qo-rtrti- v+ tc1{'1 s't'

\\l\\ g rnü* \ r" - xi-\ " i--\'-"r"\ a 8'

{hcn $o ot'g i=\,"';n t

.rrrv G tt\-r,r',1 =) \ x-v\ € xi-xi-r ä

[r\\ <! -) \'T(*) -ttv)\' h:'

(e)

t*rilti"I {a. {h..ct r^ * tt. v\''inin^*n ^*Ä \la*i vYtil' tt *(t or''hvtutotr"

-l,, r.JK* + rn *l',. clm?o* i,'ttwo{ f xi+ti'l t \:\r.''lh ' *? / *hot +{or< "rlfi wri--- v^\n * t t xr+rr'1) t si= vv\cx T(f*i-tt*;il onoL '

rn {4e o*tod "ttrvol f o" Gl ' $ is

!-2o Vfunc .*i.h $>o st'4|n''Ql{rvQ[c,{rJ

\ .( (*)-ltY)\ . f* '

y ^ t f c * ; - , i l n a n e a F a u i r y i e f x i - t , { , 1 r r r i { ü { - l u i \ = t r T i , Q(vi)=}4i.

\* t ". nüAr

s$. ta,{"J - tß b

s[r) : vv'i l t(*) -- Ri

stt\ --\tu)= +tb\ '

ha *g fr-i* 1*'' L , \:\1"'1h

i = \

e t+-") -- L '

= v

b-'L

H*n^u r $4 e^^' qfb V^r (^o*olnn'

r-l*.

x * t - a

\f e "lrryo\lim u's t Vh.re .*u\: 5?o st'

tq) s '\*-xo\ a[

Ixi tro. Si"u + tr

*.. oQl rsfo,d) r

1kö\

N $ > 0

Qrft,nor -tt e^tl"/., +I'ot

\,J( h ov< t$ sh u"r +{'"lt Tot [*") = Q (x") '

ti',) L ä f , o € f o ' S '

\h-t \:

(.)

-0^Yr, a tn -T"9-- P(*"\'

x - ) ( o

(r) is a2oiv"'{d *i% erenn; +4^t fot oll ato 4.. o& re f *'{'l

--) \ T'(iS(d -

\ 1 - E o

ernhvturrra "t Eo t {'f"rcc

:) \ + t*\ -+ (*n\ < L.

L

1 t .

t") \x-*"\ t $

s . t .

? n +'k Sjfd \tr< pr$< +4*L L.i x e fa,+1 b< sudr T&t

E ( x o - x \ - L L L .

+

Nv\uH*r

?.^ g\o-cr "t F [q -F to-)

tt\ is so.\ s ftYJ..

o < \ x - t ' o \ a 8 .

*,v w s.

J'l'r.r, o-fc til e o$O :

\ f l

t) [ {-xo. lheä

X o

xo -x

r) X>xo' ulr RrÜß sl*'&'89 +A.d

\T"t*\ -T'(*"r - +(.')\ --\ q - g(*o)\ t t

\ x - F o \ \ x - x o

Th-, ]ti' diq4'rc-tio}\c 'tt' '' tr r"'(.,.n,: *Tt-:;" Krefq'$l

rpro-s orL\hürr) r i+ |J\t^rs {a.t E ir ä''l4'rÄJh aul Tt= ß '

(üi) Lc\ T 5r cn or\da.ivöu. ,+ $ . sre\lini tan'f,in' q'L(\ ' it piltv'n

\A"I Vur< rr\st: ee L sf ' T--T"+ c ' "[ta'

Ttn -Ftc) = ( r"ts)* i - ts' ta)*t\ =T'tul -="tc) --

- - Si'q- 3 J t

n

ü4< o.[o' u.rrifa F\t e'r Ft-)

\:

\ - r \ ' a r o

I[ugnrhm ö ' qs

L-€t 4 ,. U t \o) -- ta b< a- +,-c\^ ö\.r. Ll a tlr^Ier ä'{n?

$ta = oo +Qt x*-" t o'^* +-" - ä- A'nf '

Vt= o

u^hiuf, ho.: Yk r"l,,^v, 4 annv.f,gaa ?.

Thcr, {'lnt ?0{r." lcrre , t b- ; $toincd b lerwt- ux(

\r=\

lassoXt to o.,hdc"ivoltu.r ernv'Tra Äst.1."fü" r4 t)e (") aul { d<li"o a {,rr efi* F ' Uqto) + K sucL \ü"t TI- {

ar, ror\\*lo, 8* a< lr tv, üq |..o\ w( hcrl< tJ+ = F (s) -t(a\ . Trn'L

lts \n {'l^c n*4 ü 1^crcts \'s rl"', lüüarL3'tq(iii) \r( }* {'t^ot t{'

?bry(tr )eft€a t-T xh

h = \ a h = 0 n * \

r*,\ir.*r 4 srnvct;a'r'u ! os * anJ'

.€

Ha^u T- on" )cn ern\ardra Äsü'fr''t"5 rn Ut f c) a"-l lh'ut

; r \ ^ r ^ r , " ; ; ; ' u q ( o ) - r t < , F ( * ) = ? g * n = a g J ]

.

' t t ' 7 r ' \ |

h = \

r \

h = o h + l

Si.cr (t'o*)t-- 0.-xh 4." "lJ n?o , q,c4iU T|,crcer.^ q.r,l

\.n lh? ){\rt.hdü\ 4 Ptnrtr srrYo r *. ü fhat TL- 4.

T\r Qo"\ Jol* {tlts.rrs iv'nr,ncJ^ ,Irh +4"".. Vh( E,urdc* e.f,*l.

Thoct rr^ (i',\ .

7. ß,,,\.s tg f'QrÄo^

Th. 1i"Äar*.rr,to[ J(cru* <stotrtrrha o. e,.r.f^yr brturerrr .tt9^1;r" ,^^{

ä({aü^hfir . -f[N

c.r.*c$y,, sg]z,t tcthri1,,at -8. i'f,<2,r"fr,r" "rhirü FuA

prollnl tr e.rirarf te*,",itr^ra &\ Ai{+.N^ffi- sud'. os *4e o{'o'ir' rut

^nü tt^c dblr.ot r,,h.

-|rnt

.F{b,","1 "r,^lh .e*idof< +l^in er,.fi- ,tÄ fl*, o- .ij",f-

c"dr to\c.

Xu tJü Sgd ,,x tttß Ntho$,r"

11 s <o iv, K- 0-[ {. E stq'l -+ K is i"t<7rÄk , $^

tl{ s - six'