ry tt/ '1 - University Of Illinois · xJ . ~. ~. ~~ ~ ~~ ~

L€.A/tV-VVV L .

Vvv~i4vl~_qf. ~t~~

~: lf Ol, b c 2 .. at= o, we s~ -thM a J~;Jes b / ~-teet ry tt/ b,

'1 b ::;: t\. c c.hO{ c G. 2

~ dw~'f»'s of b 2-1 Dw (_ b) == f a 6:2 / o.. 4 o .. a..f h } .

&-)\_ Dw (LtJ== {I, J.,4, -/_, -l.,-4]. Dw (o)=== 2.- {o}.

~- lf bfo ~ afb, ~ (A-Jsh. ~, PwCbJ 0 f~He.

I eli 0

Q#.. fur a, b €. 2 / -f;t.g, ~ olwl-5.,-,..s 1 ~ ~ b 2-1 [)w (O.,b):: r ~~z afa,d{ h J.

f)c. DV'II l 4-, 6 J ==- f :tL :±.1. L

~- L-et D, b 6 ~ s.t. aA- leo.&+ DW2- of a .. b zs nonzero.

~ jed (O.,bJ :== ~ I>v11 (Or, b) , -h .-:1~ CoH1~ olwL&or _of 0t akO( b

~- jool ( o,, b) ~s ~~.&- Om.£;{ 2f o,,bf o, mW. /lOt-/, /bl J ~Joe/ (o.,hJ'l/.

Eo.vt- _ lf c e t/.,v (tJ.,b}, ~ er/ Jc4 (O"b).

~- We SC7J ~ a CJ..tJ b ~ ~. pv~ zt v yccl (O.,bJ = f .

~ ~~e.r p t;z ~ a.. pv-~ 2f ?~ l. ~ D.:-v ( PJ =: [ :t.f, -:tp}.

~ ( ~ ~ of k!A-Ame-+k).

LeA a~)._ _, a. 6. 2 , ~ ] Ot. !A.4t-t.e r~~z.tvfl.n

P oL, c)...l. otic:

a.== ' PJ. --- PI< ~ p,, --., rk ~ o{;,s-ti+wf p~--~.

j_

~- LA- o..,.b G. 2 ,. b=fo _. l ! ~~ r ~ 2 , s..+. Ot= ~ b+ r

~ o~ V' ~ 1 b/ . 1 zo ~u~ -& _juot~+ ~ r ~ ~ ~a.~c1et-.

~- r=- o zff b[ Ot .

~ /_M o~h 6 z, h ~ o. L« Ot= Zh-+ r, ~-r t-2 . ---ctua, Jed (Dr,bJ:::Jcol ( b_.t).

,kt~/ Dw (4,. hJ = Dw Cb" r) .

'Bas.e.el t7h ~ t~ " vv.e MN~ -k &Jtz.ei.~"' A~ or bUt., .

~1-

-~ ~~ -bWt fu;l~ lr'J tn-Vfh~~;r. lf a,bc.2 / o.:Fo~ b=/=o, ~ _i x,!j6"£, s~-t . .jed (CL,hJ= XCl-+ tjb.

~-4 /57

jed (a,hJ ~ a. l~e4r (~~er) ~b~ '1 a. CV1d b.

~- W- Jll~/ ba- ~~ - f-m- Q7btZ , we WY'bt.e u ~ b (moJ. n) /

{5)r- a :'S:h b I '-1- h { Ot-b 1 i.e. vf 0t . o,_,{ b /w.w.. ~ ~4~de.1-- wheh

dwidMl bj n .

~~- :z.fnz = [ co..J~/ tt~2} / ; .. ~. ~ ~ue.v~-~ of o.U ~IA~o.l~ce

~lAI clas~e.s of ~t~ M YJ iTYJ 2.

~e vzu...,ber of e/OtA,~ W. ¥2 u 11 , vn~ /

:zj,z 2 { [oJh, [IJ,, -·- / [»-il. J .

Le{,~ .3 .

r::p-osrA~ _ ~ p ~..l b.e, a. pl'~e / ~ p { Qb / -tl,ey. p { Cl oY- pI b / o. J b 6 ~ .

~ we de{~ ~ upua~ -f-, · 01-1 2~ 2 ao

--:f&nlzt [~J,_.-+ [hJ~~ [tt-thl, ~ led,_, Lbl"' = [pbJ,_.

P~+~ 1 -t , · en, ~ z . ,

rl> [o..Jh-+ ( [l,l, ~ [cJ~) ==- ( UU~-~t U,J~)-+ [cJ~

C1-> [a.]., -+ [oJ., = loJ"' -t [a], ~ [Cl].,

(,$) [a]"'+ [-ol ;> [-o.J,.,-t r~J.,:::: [o].,

~) tal, + [_ bJ"" = lbJ,-~'- laJ~

~> [ cq"" · ( [bl;( CJ"') = ( c.a]H· Lb]~) · ~ [CJ~,

c&J La]"' ·liJ., :;:, [ ll,- [Q]~, ":> [a]"'

CD l.o.Jh (cbJh -t ccJ.,.)= caJ~.tbJ 11 f caJ.,CcJ..,

cs) l Oij;, [ b J"" = c 6 ] "' . [ r1~ .

~ • ~ ~~ / , ~<M ~ ~~ ~-' j X t 2 .>:t. CA.X Sn / Zff jcJ (CLh)=: {.

5'~w.~ ~ [al, LXJ., .

( ~ ~ ~)X :::: { [ Cl.]"' { 3 be;£. s.-t. [~]"' [bJn.:: [ /J 11 J

~ =: { [a]. 1 a <'Z ~ s c4 (a, n) ~ 1 1 . ~. {?"2/= f~1J1. ,[;J,. ,[7~., L/ JJ,~ } .

tb:t£ . rb [ol\11 ~ (zjn2 )x

(.l-) l-f h?J.- ~ ~ I(~ 2)~ / = ~-[ VfT Y7 ~ 4 pr~-€- .

c~J If fCtJ~ £ ( "4/n -z)x ~ p6;i. 0 ~ ~+ [CJ"' LbJ~ ::flJ~r

~~ b def~:A-~; [h]~ t. f2(n2J X

L~4 Gh7t-tp Th~_

?W i A h~N1~ 1t4" t>f.e¥{J;{l.t>n * (a, b).:::. a* b . oy

Da.f . A b~Q~ ~~ * S rHJ ~ agoci.a.-ttv.e

(o..~b)7tc ~ CA~ (J,* c) .

t:~ ( !R / +) ~ ( ll< / . ) o.wv Qg5"Vcia4we . ~·

t!>~ De.f~e- * C1Yl 112.. b_y X * -!j == X+ .3(j . 74e, -Pt7~ * a no-t C-~ocd?-tWe •.

t;X_ Xf f, defi--.e r(X,XJ-~ f -f-/-t:X~xJ. ~UJI~ (F(X,XJ/ o revk.p~vt~J) /

~ . fe-y ( <;; / "* J , a..£, el.eAM~ e e- S u a.. ~eM fA-o,{ el~ for- -x- vf 'r/OtcS., D<*e=e*a=a.

~ */ ~~ ~ == e-.l-.

~ 0~~Vf

~ C /111 ""'~ l~J, · ) , e= 1., . ~ ( F (X ,X J 1 o ) , e= ..u..e Ue.rt-~ H-to,p , I)f

~ ( 1<--L -t) / w~ d.cnff ho..ve e.-

J2:!1.. Le;;t * he a. bwtor~ ~~ ~ ~ ~:t . .:1 Qe:s ~ *. w~ ~ -fu..i aeS'

£.& ~vevti--ble- Vf 3 b ~ ~ t:t. Cdfh =- b* tt ;;:>. e , ~ b ~ CAIA-eJ

cu, ~~se of a_ .

~MA ~ (S~~J be- a.~~e~ att..e( e ~g ~ ~ , ~ &(- Ot e~ Ot i& fA.t~~ ~ tl /

-tJ.e ~V~e of Q. Z!, IA..hlf,Lte / d.~c>tee/ 0. -{. ~ver-H-b[.l(_

p~.. S~e- b / L1 at-e -br.vo tMv~.s of a/ ~

b ::::. h*~ = b* (b1*a) = b4t (a-*b1) == (b*Cift b'::::: e-»b

1 == 1/.

~ o b ~ ~e IA-"til~.t.e-- ~v~~ of 0..

&£... r (fcx,~o, 0) I f ~ f(X,X) ~ atV~ivl;~ Vff f is Cl bye«c.o,., I tvtJ tA-5 cA-tv~a.

l& f -/ .

PQf.

M.

~ (z/nz/ ·) , "'~.2- . e::::. [ IJ,., . J,v~le ~f! [C{]~, ~ sud. -UtoA-

3c~ (Q,V1):::.( ~ ~oJ~ (Z~2) X •

~ ~ ( ;vr., ( ~J, • ) , e:: k, A ~~ ;Mv~-tiAJ/e Uff dtM C/1) =f 0.

~ ( 4~ ·) ~ trn~ :t-1 a-ve &t#~tz,b/ e .

pr ( Mn (2)~ •) , ~/\ltv~ del A:::: ±{ ~ W,~f~{e .. ( d~(ABJ:::. )' o-f 4 tA7tffuiM1 ole-kcA) cW- tB) ·

A

A

~()_)

P'l

(~)

-G

(o..*h) "* c ~ {A-¥ ( h*-c-J \IO.,h, c 6 ~ .

]eeS s.-t. ~~e-=e*Ot=e lfcl.

v a.~s / ] b s:l. ~b=- WtO..== e- .

;} rl~o.l .e.{~

UV! i-11 ~cvf -t;, ve-H-;A, A .::J . 5

~ . ( 4/.2/ ~ 4 0 -r .. ;.H, • &~ (C ::?/.. :zf / ) ~ 4 J"'"f .

( 'R /-t) ~ a J~ . ~ ( ~/-+) _, ( cQ /-t)_, ( C_, -t-)t\o.~-e ~'1~. ( 2/112, +) .

(~ ... ~;- r kM. ciiJI el&ftA!fo] , • ) ~ a :~-., ~ ~L= j~( liAtt~ <J~ .

( F (X7XJ _, o) [-f. 4 Jroc..p Z1f X .:, hM ~ 01e d~ /

bwf u~ vwf a (/h:nAf oit,.er'Nige,-

J. f X:/:. 1/ Ssw, (XJ = { f:: x~x /-P u. a. bije-eu~~'~} ~

( £jw, (XJ / 0) 0 CAUe€/ ~ 4~w,~ J_~ ~ X.

:Lf Sn:. ~ ~ ~ h ; gJW! ( { L .)_ J , • • _, n J) .

LecA:tMr0 z;; . CCAU~ ~ s~~ liM~ 8~ uf d.f'J~ ~ ~ 1(

? -.£t-.. ~ L ( 11, JR) == [ A ~ M n (/<.) { de-i ( 4J.::-l } ~ tt JI'Vwp wi.-4-h • { ~wl-IZpllc~-/e'.;n} •

SL(YJ/£)a{~M.,~)~ de.t(AJ:::.ie/1l1 A (2.)

r~ r1 J~!_ L~ c G),~) b0 CL 8~'f .

cj) ( Cl_, )-l = c.l VZ~6 <q

( ~J ( e _,) -J == .G

(3) \Jh~l\[ _, a,,-·· _,l4, c cq _, M{ po;sl/bk VVO.jt; of ~petifj~ ~ S6(4~ of 4{"f~'J

* iA-, ~I-* C\l--..\!- --. *t:Ln p~~ ~ StiW!t? n::gt,Jf -' i.~ -t/,e f"t>c/ltre>(; '1 a,* --7e ~ G4 ~cl~~ c.y ~ err-c~~ of 1-11""ltvpl~ _

7'1co a, cc,tleJ, ~ _J.eNJ~o.(ize1 Orssocf.MWe {Aw.

ctt; V £A,h 6 G, _, (a.~ J _, = b -~a_ -1 )W-e (cw b)~ U, -~~Ot ~) = o.~ ( b~"* 1:,-1 J ~ a-t::: Dt ~ e"* 0t-1

= Cl.*Cl-t =e.. <;'w._;fcu"J_, (b-t"*q~)-* (o.ff*hJ=e.

( t1r<-~r,) -1;::. a, -i.;f- -· -* ~ -1

6

(~) ( Le.{t /vfJM- ~~ ~~)

lf a .,l( X = b ~ X / ~~ ~ == b

Lf X*(l.::=X-*b / ~ a=b .

( ~"l+tp~ X -I -to ~ rfj~f 17f &n-h (Zrk,)

(- ~--~ ·-·-·· L&(t-~-).

L-0W!VII14 L~ ( C,_, *) be a ~ _, x G Q . Tk1~

Y'x: Q ~ G / r)C (0.) = a.,\' X / an4

lx: ~~ ~ _, Lx co.)= x~ ~

-p,~ rx o..-ui Lx ~ b~je.v~wn.s / i.e- p~J<;\wf~ of Q/[-B4-t~ of ~ .

pvovf: Fj k CO.~~ {~ws__, Y'x ~ t:x a~ ~--bo-~.

\1 b G. ~ _, ch.me t\. = b ~ x--1 / ~~ V.>q {0.)== b~ )C1~ X= b

So r~ 24 OJ.-rfo s:-~;;{(J.I'!J / Lx u on+o ov&D.

~u _, Y';c Mel L~ ~~ /x;H, bj'e.vHve,

M01--~ _, Cr-x)-1 = Y'x-1 ~ tLx)-t ~ ~x-l

M. Mwttpl~+~n~ uhf~ ;- ~ ( GJ ~ fu,vte-) j, ja- -~-

UstAA~ _, [€71- 8,: e- . ·Jn'

gl [q,-*J, !],.~g).. Jt!Jil jl.. '8 .. ~1, JJ.~J~- ~t1 ...

! I

3~ ~.,-'~j, jVI--'Ijl- ~h~j,

l2=i_. LeA; (Gt/ *) k Cl Jvo1 o..-4 Q.6 G .

c /) If l111 ~I_, o._ ~~r :P e _, ~ / Dt{ = oo .

c,._, If 3 VI ~I /.>.-t 0<. ~:: e / p~AA {o./ := W1W.. { 1-l?tf ct.,~e-J .

o..-~=(a_,J~== Ot_,* ---*a_, '-----v---'

V1 -t !M,-€.!

~ ~ > le\~1

/

7

f): b,::: ( ft< \ f 0 L . ) I en-~ ( --1) =:" _)_ / orJ. (~).:::. OJ

G= ( /P. I -1- ) / ~ ( I)=CXJ / m-4 (o)= {

g. G, ~ ( s!f ... fJ, 13 L o ) , lef u- = ( l i lJ .

~,

CJ =- :fe. .l.. ( I .L. s) 3 I .2...

s t? c:n-d ( () ) == 3

p~~ & en-4~

cb -e- tlVI-f't\-1 ( 11)...., - ~11'* ____ * Ct..., -= 0.. -~

)">-- -t-.;....-"'S

(CLI1)WI == 0t_I-1WI

(~} or~ (e) ~ I

't!Ot/e ~~ .} --fiWu, ord {o.) > / S'~ c Lf' J [a.{ =-I ~.:> 4 = e .

£5) Lf 6-Nl.(o..J= ~ <ro, -el..~ 0c/c=.., = e V ~ 62 ~

(t) lf CJw/ (cl) =-VI <c;b / a..fe, ft1 7 / 1 4·~ Ct Ot.J../ --· _, ll1rl Oke o.U tk-t~d.

\lij ~ 2/ -bt,~ ai-= o..J iff l=nJ .

prev f 0 f CG r (j) SfA.pp"'S.tl. l 0~ L-~j ~ Yl-j / ~.-t. 0..:, = Qi .

~ I = oJ-i anO/ J-v '70 /so ~ (ct) ~ j-i < n 1 ~du~.

8

L~6

:: -ttr.e )~ of o.tf ~;,»~~~ of tt r~u{cvv V!-jdh ;,.,. -lk

pi ~~ / ltV. Jr. t Cowrpo5:A-i..:n-t .

- ( tMt/ b~ ~icn 1 ( /, l-, ~ · / Yl } -to iM~Lf vvdh M-~c/ -tv

r-!J~ ~i-oltl <1 -t~Nz- pLDMe / 0 ) .

P4: ~ j ~ f I,--·) 1+1} I ~ Cit~ v~VM0C o.rljc.e~ -to J ) I.A-"1/ik..etf -to tl -'>!j""-~ f'f AA VI-J011 .

~ It-") j -' we. h~ Y1 ~ cl,o~s _. --e4en ~ l +--'> t_ 1

we. have

~ ~ D.lM 0. ~ ~etA>~ ~ ~ t~ -e~t, o t~.~ -fJ..e v~ 1 .

t 6 v~ ~ ~ 6LocAc~e- ~~ , ~ .

De m,t-e ~ LJ&.+ca ~ ~ 1 _

p~r-"~:

( l-) r f. I / r h =- I/ I r I == VI . ( I , y- I • - > }"' '-H ) are oM d~~ .

o J S" s r, . - , s r 1-1-f Ave 4J!!I olMc..sf~ ~ Vu.

l4J r~ f Sf'j _, ~ o~Z.~J-=5n-f.

5'-v f I, t-, · - · __. r v.--1 _. s _,sr:- · > r h--1 J ~ Ovl/ o{~-t~ .

C7J ~r1=r-i-s

~ f'~S==Sr-i.-~ Un.sefh4ei2: (c;~i.-)~ sri-sri= ~s,._-l-,._+~

= s.' = I -=a.) /sr~l= .2. vo~ir~"'i 1

fy-.ee B""'i>s x 1- r : ~ se:t ( -M1~+ of ~ ~ o.lpka.~« ) /'.

>< == X u X -1 I X --J -= f _x-l I X~ X } J; ~ wf~~ C}lp~ Ire*

We s(J --Mr.M- tt ~,var-d w ov-er X '1. H ved ue~ if llriie (1\1 h~ ~ o

~(Ahw~s vf -bf..e fo...-Wr XX1 <-'Y' )f"1X w~ X6X.

E;<J_ x::: r o.J b J / w= a.Otb o.._, b..., o.. z.o t--~e!J ~ __, 1/J.::. Otbh-1 o..cx-1 u ~+- r-e!J ~f4etl..

"' ~ fee jli01Af Vlt X = F(XJ;;: r w/ w l1 4 M ve4~ lN~ uv~ X t . We sOtj ~ ~rt:J. ~d E. ~ F C>O .

}AwlVlp1~f->~ ~ f(X J ~

s-'tf x:=: r ~7h 1 , Dtbb I b4 b-' b-1 {A e: F ex)/

erbb-b_,b_,h-~a.~ C{M;JrJYfi-to.. =~b_,a..

Et~ee.~ free Jr~IA.&fion on A. ~ IN :: r~ov"J ~ subworJ ""( ~ fur-1M

><ncf C)y >r X I w~~ )I] G; X.

Mr-. ui-bti-ec:+Gm-t rwf ~ {jl;t fcXJ. '-' .,.... r vr J,vl , wl. G r lX} I

-to """ 11ffJ w, · w-'" , t.ve ~ c.""'""'- w, .. w~ Ow/ -et..., o.p;7 J -&f.-.e e1. e-w, ~4111 ~ veo{"'-ttfc:,.n., . !4-e, ~ h• , •. Af

v ~, VV,·I.VJ...t:.FOO.

/o

V.t.vifj : d) MsocUt-1-Wu-:J : sov+ of h~4 . ( Wl-lj ? )

(.).j E. ;; ~ ~~ ~&1~.

(h ,b' ,.,-1)-l ~ /l.b-fb-1 1_J ( ~) ~~ie,c.,~ i ~~~ .' '-" O<A. Vl ilt-(!) I .

M.:n,.Q. Je.M.evo.~ 7 z+ W6 f(X} _, IN::. )(, t.. x:L ~- ~~ I ")C~6-x / fj,= iL _/J -1 -£.. -f..:~. - ~ --v"'.U, w : = ~ ~ ---· xl. -x r 6 p oo .

~-evriicrr · If X = ? o., ,_- / ak J ~ "t~ ~e 0v~ 1-t h~ _, ltV'€- wrote t1.--

fO\J ~: F ( o.,,-- ct~cJ .

L&C?f;uv.e 1. 50~~~~

M. ~ "'I G 1"1 ' ~ k '~ (ss ... ( I p,--' "l)' o) / c..A * de.-.~ £#e. pe-«tMu...s ~

of f I J ~ ---/ ~ • ~Jw.~~ j""'f "f ~der / ~ J1 .

I .--'} c- "' J a- ' .:l-~"> Cf"{l-J

' l h ~ rTOt)

(I ..l.. ~-· "YI )

(} = t:rU) (rl.)..J • • • t:rC tJ) •

~ -· 0 ;:2. (3' .l.. 3) ~ .l-J 6- 3·

II

():::: ( I J.-

3 I 3 L{- )

5 .

~- 0 = ( a,' tl;_/ -'" / a.,) 6 5:"" ~ -#u- rrWlwf-MlA>"'l g .t.

~ o- zo co.~ AA ~- c:t_c1~ . ,

B. V1~ q. / (/.::: ( l 4 3 ) :::: + ( 1' 3 I ) ~ ( 3 l lf) -

~.e- Je~.~M:!J / 0 = { tl, , ---/ CJ~ = (a._,- ,D"'t, Ct~)

17) 6:$7 .

01,~ 0..1.

o- , a.~. 1 '> ~ ' ' .

a"'-~ ---"> t1 ~ a_,.., t---::.tt,

i ~ 1,

111-~ ft,---, 1-1}- fc..,.--~ a~]

~. Vvt (};: (a,,--/~ .... )~ S' V1 ~e OJt1 ~- Cjo[e. / T. = ( b,, -·/ h~) 6._$..., b.a ~

L-c:yvle , ~ W€- s~ rr ~ -c tJw.e ol!fl-owvt vf (4,~--~ cu... J (l/ b,,"/ b,)=T .

( u~, l-11~)., ~2.)

E:i r;,..- (}~~VI/ -Ute su~ of (J / .s'ifpov-t ( ()) = { i 6 r L .l,--- ;~J - (7(~)= v J u /

;,-e. { ~ { oaJ-=fi}. ~lApp co)

~ vv~ s~ ~ ~- '?: 6~~ , (} M L th·e _ d~jo'i,..rl; Zf >0pp (a-; 11 swpp ( 1::' J-::::: ¢>.

~' If )1,?.2.-, ~ rr (D.,,~/ O.v..) e- ~hi ~ ~urr(v).::: ( 0..,,-- /a~) .

~ ? If o-, 1::: e:.S 1-1 ~ ckj-u~M+ I ~ (T 'L ~ ?:: o- .

~-wt S'V) 2--5 vwn-orW~ V n-? 3> .

\1 o- 6 SV! , .3 1).. o/u..""'~ iAVt>Vl (J=. (Jj -- • lYk. _, wh~ Oi, --/ (}l< Ct.1--e of~ou.A-J,

CjcAe-.! . ~; 8vle ~ ~ -fi,u alecowrosl?tt&-, ~o ~ po.~wu~

~ $lAWI vf ~ l~ 1 ~ ~ Oj, ~-, Oj, / ~ YJ, 0.~

~ .hV.e;J n~be-r [, -- __, Vl Cf>pe.a.+:5 Ut--t o;,-" (7k -eM~ ulflc..Q..

s;~ a- 1().htor~ ..:( o- u ccMeb{ 0t. eo~r.lete f~f-i;z.Nf~.

( 1-t'~ (;u,ine__ V-J-, -eo ..S-o~ ~~ Vf 0';,~/0k).

~- .4, S7,

(I .)_ 1){7 !;)(I 2..)(4 7 J clQg I q 6

~) ~ ~e {)Jt~ cJA ~ ,

== ( I ..L ~ 5 ~

7 .2.. S" 3 6

- ( I 7 .:.r 5 r 6 ) c.2.) ~

e. LeA cr = ( ~, --__, t{...,) 6.$ Yl / ~ 1 er /.:::: 11-1 .

/he{ o--' == (a,_, ) a~-11 .... , --· _, t\1) .

&~~ w cr-c-~v. ~ t:: 0 Ct c:Jde ) r = (Ot,, -· _, CA~)E. ~~.

f~ o 7:: () _, / rT --4 'L: () . { CT io OcrbiA-~)

L~ D ~ F / ~ Lt-~ / Conj~~ k, sh ) .

,, I =- I / /-I I= .2.

/} I :t v/ = I :t3 l = /:t k I =-1 .

~. (J( 8 = f ±II -± i- I :t-j J :±.k 1 .

I {9./ = 8 . { &g , . ) w~ ~wtt1'1~~. t-5 a J ~r -

~- w ~I tJw;( GL. k J~~ . A ~uarn lf:: ~I ---3> cL. 2o cetUeof a_

(JvowpJ hok-lo~inifhi&WI &f Vt~,h6a, 1 1 tp(Q.·b)== 'f(CI)· 1/)(h)

~ 6) ~ ;, C[/(1 +) -7 ( R~, • ) X \------7 e~ . €btp ~ tt W,~ph~-&~ .

GJL.e+ l-1~.162/ tp~ 2->2~2 / tf(O..J::-[0.]"' 1 ~~~u -+.

tf i-s 0.. hcw.17111 ~i-s VI-, .

& de:t : G,L (.)_, ~) ~(K<! 1 ·) U tt ho~1J~t,~ . ( daf LAS.}-= olet ( AJ ckf (8}) .

~~:t;S · Uvt tf~ 611 ~ G~ k- 0.. ho""ok-W~i&w. / ~

t1 ) c.p ( ee:., J :: e~.l. .

e~, = ~,-eq, -) '-P{~,J=- Cf{~·e;,,_)-=- ~ (.e~~J tfJ(EJ;,,), Cll~~ ~-o tf(~,)-= .e~h.

U-) lf ( a -I ) ::: [ cp ( 0.) j -1 1/ A 6 ~ I .

{3 ~ tf ( C(4) . I-f ( Q;) = ~ ( 0.-1 0..) :2 \{J ( e ChI)

~. I...A7t tf: ~I-;:> G.). k ~ hoWI~h/Jwl I ~.e k~~ _of tp z.s

/<.er ( ~) == t a.~ G, I { tp ({:() = e~.:l. 1 .

prop. W f:: ~-~ H be. a. h-o~~.r.ph~'M J ~ tf 0 ;;..,Je.«we 2f{-

k-er (tfJ= re~J.

H ~ ( ~) cSbvi<>'t&.

( ~ ) s~ c,/b 6 G, o.wl c.p co.J ~ cp c hJ

7'1&-7 >(> (aJ ~ftt,.;J -4 - e44 bJ (>)

tp ( o.b-1) = tp(Q.) ~ { b-1) == 'f(O.} (~(b))-(

'fra; & ( e.;J _, 0 <2.f.l

~~ l3J lf(Oth}::: [CflQ)]"~. CfY!etl, ?J GJ

&4> Jf Otn= e~" ~ [~c~!'- ~ .

-= ~ tl,; ( tp U>)-t := e u . So ab-t = e G,

=) Ct= b. =-> Cf u uye.awe

(S) If /il.J = VI, ~ / tp(Dr.> / olw~~ J-1 1 1". e. {'fell->/{ h

{ 6) lf tf ~ G -~ ~ Z4 aJ1 ~evf-i;v.e, ~ll,~m; ~ ~

I b /_ t ~tw~~c)}-/)~(,& ~ (1) lf 'f :- ~ -/ H ~ '"f ::- t-.d _..., f'. ~ ~91••Atl I /

~ tf " \.(? ~ G, ~ [< Z;s o.4-v a_ h-tJ•wo~h i!.m .

~- ~ G 1 JJ ~ J4S · A wtOcf f ~ ~-:V H 0, W, Uomo""f-hi,st.M 21 tp 0 a bj·eerfwe hoPkOK,.:Jrphi&wr _, ~ w~ S'tf -MtM ~ ~ l1 ~

~o~:et,u 1 ~eo{ G) ~ H q ~ eMU~ C1vJ ~ot-f\rrr-pl-.i&m c.p:: ~ -7 H.

~Yic · ·r/,v\:) ~Mcr-rhu ctt-vups AAv€/ ~ 5D~ afrhHJ.L-c ~ w. ~.-t

J~ o~lm-1~__. So ~ a~ ~ s~ 1/Jo.:} ~ u sa"-le 'I (}h:>up.

15

Jd1-. CD B><l P :l {I(_, -+ J -=;:> ( IR-+ ., · ) u. t>.v? ts o ~-wvr-p irlis n, .

@ 'f~ ( (1,-1 L ·) -> ( 2(:J,.z .~+) _. If ( 1 >= [o].t- _, t.p H>= [I],~... 'f z.o ~ V5o~pl-dw-..

® Gr= (f:2-'''{ne.£:j,. ·) _. ~~ (2_.-t) -> (G,,-) 1,J--~ ~"" ~~~Wt. V1 ~.2."'

l~ > .1 ~ .. ~ __.:;;. G w ~ lw-Aj .s cu., u~v .... phi.rs ~ .

(~) lf ~:: <'3r-/H ~ +~ N-)1< ~ ~JMofh~~.~ ~

lfo 4J ::- &;~ k ld als-o at, u~~~i&~ .

l4J ~rvGy lb~ t:vJ).

r I) l <Lt'Jt>Jtb) w~;:;;-"',.1~ ~.::: rt J ~ H~ ~ tbj (SJ lf ~) . ih o~"OYf*'U W1 l6

'1 ) ~.{-(;on s 0.~ j~ . (b) lf ~V!t-J, !i~k/ ~ (h~/<. L (3> .

(1) Lf- ~~ ~ .I ~ I~ l =I HI . cp~ 4---o,_ h~·~~).

C8) If 'P~ ~-/~ i&~ ?$o'*4~ ~~ ~6~--~ I a.f = /tf(Ot>/ .

~~) 1f f~ G~k\ '-6 ilJ-1 ~o~M~4~""~ ~ -v ·~ 'i; ~ tlvt~N/

lf = { tX t G, I 1 ~ 1~ n 1 -3> ~ b6H [lh/~ "'j 0 O.V7 uOM~pt-.i!W1.

L. P4•i-IM4•, I I 4 G G./ I"''~" l /=I { btrl/ I •I~" J/ II h ""~ .

ll o) If (lq .0. H 1 ~ G) && abe{~ iTt H 26 abeA~ .

( gv C1 -Mo s~ tAle ~wt Clb-01~ L ~-~kiLO.~ at~ ~-1-htte / -tltfj Wl~-4- W1f J,.e_ 0t>Wifl-phz.e 1 j.e _9 no ~o~f'h b.e:-fw~ ~)

tb

?::?~ ~~ ~. A ghl~ (1 <A s~LA1 w b~ 5:Jo1ic Lf ...u,~ ;s a c ~ , s:t.

~ ::. r Ch,~ I ~ 6 & 1 ~ ~-t~ ~ = < a. 7 ·

tft. ( £/q. 2 / -+ ) = < Cllt / / ( "Z /-+) = <I/ c:n-- <-1 / .

S~::: {1//l~l-}J = < {Ll}/.

Pn!f· ~ Z6 CJol~ 0 G to ~ltAYJ.

~· ~t q ~ H ) ~ ~ ~ Cjdi-e- Z{f H ~ CjCI/le, .

.L, ftwt / if ~= <o.// ~ H == ~ c.p £01)/ / ~ tf~ G-~ ti ~ %

~- (2 / -4-) :p (&, +) J J,

Cj tA ~ hPf- ~d~ .

7.?1 A 3~ Ch 'J CAU~ f:t±:& s~~ 'l{- -~~ &)j~4; (),__ ~ike

.94~ SS:~ >-t IIJGty / ;z tl ~~ J=S 1£'--· s:: ,w-4~ !)~€ s;, ~~=-±/. We wrue 0f.::: <g>.

~ . (2, -1>) =: < {IJ / / ( d X 2 1 -t) =:: ~ < { (./, 0) ~ (OJ I) 1 '/ .

F (o.,b; =- < f(),b J >.

((Q,+J ~ (R,-t) ~ ~ ft-.~Jet,~. d ~ n .:rt- C.O~~< "'~Ue

-ti-t~ O.~"wt- d~o""e~ ~v:J prv-~.

If ~ C'6 -r~ 3~~ , ~ <9, £(5 Cowrl-a!le, .

£'\{ppooJ..e. '1 = < s > . j:r l-1? 1/ pk4- 8n= { J e G. { J.: ~,£, ___ s~ 4, / St,cS__. £-i.:;!! :t.1J.

~~ /B"I ~ flM~ fur 1/11?1. ~ 9.::: '() Bn / A Cot\c-d-Q~b W1~V. Of ~k~-!~l,k (~lA-e) Se.4s / 9o ~ to CXJ~~le. ~P·I

17

pro2, ~f ~ ~ t-l / ~ ~ 0 ~*1 J~ -0-f H ~ f~~ Jer.~rn4e4.

pwf, s~pf"Se G, == < ~ '/ _.. ~ H -= < ~ (~J /. t.p .. G-/li (J,J, 21v~cnrh~&M.

EX. (ZxZ,-t) #- ((Q/-t)

f"'~ ~ .. ~ J f"'~ j ... .-1-eel.

Gro~ Aaron

~. Lei Q k- a. J~ ~ X ~ C\ set. bt aeAicn of Q 0n X

(& tl 4 C1 X X ~ X / r~'*-f~ .. {J.-X)~ :r· X/ s.-t.

l b e~ · X = X V x aX .

(.l.J a.· (b·X)= (o.b).X If ~b6a .~ 'rh<6X .

EM. rl} G= ( Sj~ (X) ___ o) / x:~?. ( J /><) ~ 3w 2& "'- 84 M+~.

~~~ G , a.1 ""f / x- Cl / ['J;"J ,__..,. j x to a :1 -p tuA,:,., . ( L--~+ll<-l~lo.+z..,) (~J ~: a J/) )(::. ~/ {J .~X)~ 8Xj1 u a,_ (j~ ~. ( Cohj\jori06n Ct.~

[Lt;C, ~ GL (.2-/ Q<.) / x-1¢. Gi'xX -/X .I (A I c;~l) -~ A[;~] t:~2 •

lh0. 16 0.. 8~ o..u~ .

L~V-~ [o

f:i ~ ~- r! ~ gwi>s: ~ H1X -> t-J ~ tt N ~Wn ~ r ~ ~-:Y H

/_. .,J .. :L "'7'1 ~ del~a- AA a.M.L.on .-d. G (Jh XI a&' u tth YI'Qk1oh...o,.r • .:~ 141 . till ( ~1

c:::c; =qfz > -c:; ;z ---7 2~2 ~ -c (AJ= faJ... . -rt,~o 1.6 "" ~w~~n-p~.

~ ~ A-t.1 ~~~ 2 >4 X ~ X 1- ..,...

G7 4(..2.

(a/ LhJ.,Y ____, ( (IIJ~, ul.J ~> ([o.->bl.) <;?:> (a, Uil..) _______.., ( [atbl") .

~ e,,. ~x ~ x k- ~ c.tAU~n , &vt a. e6 7 ~ [c,.: x -> x ~ lA ()q)-= o.-x __ ~Gx~

~ ta 2<> tl b~ewi"la-t . .1-t fcvt 1 ~ ~ =- Lo._, .

M. ~ ~ >t 'A -7 X ha Ct. ~ (lef~ . Th /<er~ q -t:t,~ ~~ u

{ a E G I ~o..= ldx } = faG~ I 0.-)4~x for eflet:J ~Gx]. (.ea, u ~ ;;...~ it-€4-'-1-e-1 Df ~17 Ot.£A:~).

f!tJ.. tz,r ~ c&ov.e ~0.4Jl.e I ~ (ct, IbJk) ~ c [CHtJh)/ ~ ~n&f L& r /<VJ11c:E2 J.

fl?-. Gzl (.).1 f-) -J. (R.l. -~ lf-2-, (A,[;!.])~> A· f;~j ~ ke.-~ c.,nrufJ of o~ j ~..l..

~ o.et~ ~.,X -Y X ~ ~fJ[ec{ f0~-H trr eft~ t1- -fAe I<~ a. f e B,j.

~. ~ G~xr-},X' k CM-t ~. D~ f: ~ ~ %""0~) hj f (a.J: = lo.. , ae6].

~~ f U tt ~~o-rp'h~l1rl o.~ CA~eo{ -Mte ~~c<A-feeJ ~Ot'o\o-rph~wt {w- -tJ,~

Q.,dZol-1.

lk+-ttf ~ t.Ne-- ~ to t~ bl~,h GGt, p co.bJ= peN pch) ~'> pcmt pcttb)= Lo. ·{ b

~'> L ~ ~ lo. · ~b . f:l.x6 X/ [a, VvJ.:: abx = o. Ch~J = ~. Lb c:xJ = l£A. Lb (xJ . ~. ~. 1ile ~~ q ~ ~~ G)IX-))( ~ ~c.ef!j ~~CfJ/ ~ k~ ri- ~

tH'5\)~ ~t..tsh-t ~ -tt,~.:s CuA~ . 19

M). Le:t. p:1 a~ s~rxJ k tt h01-1~~ . T:k1~ G)(x~>< lj

( J I X) ~ ( p (g)) (X) c: !1· X .

-dre.. -eht& U 4. J~"'::> CU7{~ ~~ f1%D~1e4 ~~ hiok1 £:5. ~ p.

C/> e._~ 6 l-J -vh op~~ on ~. ,4r) e.- J~

C.2.-; H i& dcs.e4 ~ rn.J!q>1~~ ~ iMV€J">e.

--re,~ ~ v-es-evu.A-tcn ~ ~ ~ or~ c7f a, h H / st~rj

(~, ~ )/ H ' be-~ 4- flew 04 .

(.l1 GJ = ( t~ / ·) 1 H :z ( f<;>o, ·) · ~ f1~ ~ ·

8) 3L (.l,JR) ..-:= G,L (~ IR) I SL (.2/1?.) ~ ~L (~ IR). £1- (}

do+( J =-1 c(~ c J :fo

CAJ ~~ (/ ~=- [2,-+)1 H= ~d I ~ ~ 8,.

l~) ~ zo 4 :]~ I o.e:G h 0.~ ~ / o(~.e H=c:::Ot.>= f Cl~ I k ~2} ~ G,.

~ H ~ ~ · Cire& S14bs~ ~ ~ ~ $}0;/i£. g~JvoupJeJt~ ~ a_ .

(6J Uo+ Ga, £4 ~ <J'45_.. tf~ G,~ ~ ~ C\- ~~151Vll ke)- ( tf>J =- {4~e.l ~tt:\)=e-~.1].

-y"h.e,., ~( tf) ~ q . (7) ~ f~ a-:;> fi be a. ~~h~~ / ft t= C{J(C.)= { tp(C\) I A 6 G.}~ H- .

ltren H I ~ H- .

~~11

f~ . :f#: LeA: D. E G / G ~ ~kW(.., I l-1: =- I a./ . Ttret-t ( ~)U£W2, ~ /{) . ....:----

l b If V\ < oo " -tJ,~ ().,I<=- I iff &~~{/< , I< e~ .

(~ (X_J::, ~ {).~J. / 7ft ~I =:. /11 ~~

t?> < ~ / == fLo._,~--, a"'_.} ~ {<:tA.7l == Vl .

(t.t, lt ltl::.QO , ~ 0,. ~ =-tli::L- L.1f [<:.1 ;:::.~l. I f<'t- 6 ~ .

~ <~'7= { LO.r··, a, k, --} A~ {<:D~/[=- /a[ -::::Cow-tAb~ Mil~ ·

~*J,- {A ~G)/ ~

cb l7f /o..l=-1 , ~ &-,= {e} ~ [<Dr,l:::.l

ll--) Zf' 1<-ID.._I <V1, ~ <(Ot 7 Q:' 2j1-1 z

(~> q- {ct(=oo , ~ <£l') /V 2 .

~. ('I u A. 11 F b ( I Jh4W ~~ v 3 G (~, ) S'.+ jt e ' j -:::. ro.

B<. Lct ~ ~ Ot J~ ~ s~~-, ~--be < S /:= { Sr~ --- 5:v.

2"/ h?--0, S-z,G ~ "1,

~ <.S:-;. ~ Q ~ 0 CG.U~ -tita S1AbJ.-o1Af> ~~~ ~ S . £ ~ = ±J

"' ..

0 f §

~- L-vf- c, ~ o.- Clrcrtf ~ tt.c= ~ /

c~ (0..) : = f bG G/ bet= o..b } J C4Me4 ~ ~ liz.e.r vf £1 ~ ~

~.. < ~ / E:. Cq (C.) ;::; G, .

P~· N? eGI t!. c~ r.c.J ) ak ~ ~ (Q>

(.:1-} l b h c ~ h{h.l-- Ct_ =- b! abl..-::;:. t~tblbL ~) b~bL 6 ~ (Q) f r) }. e ~ ctl),

0) lf b €. ~ (A) J ·~ h~=-tl. b ~) b = o.b £), __, ~) b=t Qh tt-

b -1 = ctb a. -t = b b ~ ( Ct) .

Ct ::. C I .)_ J t£ Slf ~ ~ Cs~ c ~) = f I) C1 )... > _, c 3 4 ) , U .l.. 5 4-) J_

~. Lf H~ ~ / OteG, 1 ~ a ftOt--i:: = { tthOz--i / h e-H] / cctf~ tD a. I o.-1 ~1

1;t.e ~jujOv+e "£ ~ bJ tl . L)f /.].. ,.._..... IIH"--1 ~< 12 Q) a,k,o.-1.a_l, .. CI.-I -i v IJf ~ V\. V\. - L/1 =- £th,h ... 0.1 6"lie.

~ ctHCI-t ~ ~ _cq. ( tt£101--i ~ o. .sw1.~L). @ (o..hO._,J 4 ==--~-1 ~Q-16-o.~

~. Le,t H ~ 6J / -~Jt.4, N~ ct-tJ := {a Gs, { aH~-i == H J , ls ~u~

~ hOrW~o./iz.er v{- [-/ ~ ~.

H ~ Nr;, u-v Uf

LeA- ~,c H. ~

&,·~ tll E H ~ 3 h c tJ ~ •.

11 I =. h 0 ( h 0~ h I h 0 ) h 0--1 ~ ~ € H .

~. tb If HJ, H.~. !f ~I ~ rtt !1 Hl- ~ ~ .

f"ke- ctM-e- fur ~ f C::... U"e or !Mfa. v4-.e ~~~,un h k 6'~

(J.-) lf { l-J ~ l ~<=I 5 Gt / ~ fl H ~ ~ ~ . l<:>.I

Le~ /.2.- _ -M. LM- e, k a. J~') , ~ oowtey cf r;, ~

Z ( G) ) ::::: { a e: 6z f ~b = h o.. v h s 61 }

.=: 11 G:r (b)

bE:; br

&D~ . !IJ ~~ 1:1 be-G., ~ Lh) ~G)/ s~ z (a) ::: 9 D1 lf Gl 2& tllbeA i-At-, , ~ Z ( ~) = fl .

~. rb Z (~VI) :::: f I J , 1-1 ~ 3

(:l-J z CD>+.)=- 5 f 1, r ~ t , 1 ( I } 1

'&i.. Lf tf~ ~__, H ~ 0t ~~t,~~J ~~

~ ( ~) ~ a, ' aW21 tp ( Gf) ~ H .

~ q X X ~ X 1e A. 8~ ~ . -rka ll%-&c~ftlel &,<M-to~IT·-p~f6~ : p;: Cl ~ s~-o<.) ( j, XJ 1->JX . j __., ~j .

ke...cp) = { l1~~{ D.x~x 11'xcX] ~ 67 .

~. V x eX_, ~ ~ 4 J~ , -#.e s+ehJ;2.4- cf x vf.-7 9 2s

S'~s, (X>=- G)( : = l J ~~ /3·X-=->< ] .

__r:t g~~ (X) ~ ~ •

P1. tl) I· X =)( -=) I e; ~-feJJ~ CX).

(~) D/ b t s~~ ()(} I ( Ot. b). X= Ot· (b·X)::: Ct ·X=- X =) Deb G $-~erb Q, (X) .

(3J Ct 6 S'~c, c~J , > o o.-~X =-> Ot-t· a.x = o.-'. x ='> X= cr~x =) o. -1 ~ $'-fcl:,61

()() ~

~. uJ Ca.,c[J,) ::> f hG~/ bo.=.o.6 J ~ f b t:~l bt.th_,:::: ~} .

Sv vf ~ [e;t ~ ~okkn, '' • '' be ~j~t~.+~ m, q / -tl..tu, ( !ft+ 'X== ('o,})

Csr ( cu = 9-te,bG, {Or) .

f?-) f-1 ~ G I "'ecAtl N~ (H) . /p dt X:= f L{ L!! ~ } / cJefcwz -4e Q/Pfiov. ~ G) onx -to b~ : ( g I L) t----) J LJ -I ~ =: j. L . ~ / 3 LJ ~ ::; G, .

~ ~ H <eX / Ne, CH) = S+c.be,( H).

~ G ~X -> ~ X: ~z.e_ Q J~ ~~.

~ ~ orbA- 6f >< / V>~'6-A1, Ox:: :z { J·xfSe~ J

Le,t j = j • X' 6 ~ o,q I ~# ~G) tx) ~ <g.te;bc. ltJ).

1-f aE~~Q txJ, ~~ ._Jttj-f, sx=-jx

C{A'IM. · ({· ~~br;, cxJj_, = q+er~c, l~J , MrJft . .!J=S·X

E.:.L W Gx)(->X be ~ Q&ftm,, X<f:.X / 3eG,, !J~j·X.

~ ~--&o.h ~ (!j) -=: j S7-tl1ba, (X) J _, .

~~ clJ lf t\~j~ub61 {.)eJj=' · ~ e ~-1-el,a c><J, ~

!1 tt J -i · J-;q = S ~ · c ~-1-J J. x =- J· t1 · )Q =-J · (D.·XJ)== :Ix . --:> !J Ot1i ~ :;~b~ ( J~) .

~ o J ~-u.b~ (')(} 3 --1 ~ s~~G. c 3J. )_4

(~)If he:~~bc, (jx). ~ ~=j_,bj _, s-~f. b===j·Ot·5 1 .

tL 7h~ Otx= S...,·b·J-X.::: j-4_ (b·jx)= j-t.jX=- X/ s..,. fJ~~.Jebo, ex>.

S'o b ~ j S.feb ~ CX) j -t =-~ g -!M,G7 ( bx) ~ J S+tJ, Ch 0.) J-i .

j=j,X' 3( <;'-/-8<1, ( ~) = 3 ,5'...,{, <X) j -l

X ~ c>4>

fut. .lf H~~ / 4~~ ~ ~ H ~ ttHa.-f .

r4- t cp ~ H -> Ot.~ _, ~ ~ tp ( ~>= at, t:t-1 ~ tt A "'~ """'fe-.~~. hUed w-e-

~. Lu a,: ~~-~ _, X~ ~ 1 , ~ ~ , "' } , ~.., 'A X -> x ~ ( tT _, ~) ~ (} ( "J ; fT- L- .

w.- ~~.2. ~ ~s1..Jer s-~ G) (n). b det / 9f.e.t~ ~~) = r cr e £'., I tr'(11}::.-n 1

-= l ere~ ... / cr = ( I J.. --~ 1-1-1 : ) ' { l1t,'.- _, ~} 0.. 4 f~ 6-f #- { /, -~~ ~-q } . I a, '~ .1. • - • • a11-1 • , -

-=-) ~~G, (11) (\.. ~1-1-1 .

Jt l{J ,• ~ ~ ~ffib~ ()<.)

o- ( (i,):; f <J'"( ~) / {~ i~~<~-f

., / 1::::-h

L-. -fA..0 fPQOttMple / 0"' = X~ tl ~~x / ~+e.b_q01 (~J IV ~"', •

( ~~£.-, {l,) V.S &r~6<jMe -brJ g~b~ (~) /\..- $'c.,-;) .

~. L-eA G=SL (.2/2] / X= Zx£. I axx~x I ( A/L~J)~> AL~J.

LeA- X= [~] I ~pMe_ 4 / ~ ~~hG (X).

)

LecA:ure I~

~Df~ _3. rowps

~- A S-f G; u ~ Uf ;J a 66 s.-t. G, = <a::> = {a!"/ ~«z]

(3) 4 I a..j.:::.h~ J I :5 Vi<:().:)'

11\.:z-j ~., c.()> = f I }. L ,.-fJ .. 1 ~ 1\ ~-"'-~ 7H ' l Vt~..L e<'> cO.>= { {, Q ,a. 1--' 4 , ~ ~ V1 ~ Vll L- EnJ .

<f; \jll6G,.) I~A//= /ttl. (S) 1+ "'(:&1 II h bG~.) /o.{ =-I hi J ~

({,) 1f c,, c~ Q.A..t2 ~de-e.~

~ c, (\/ c~ zff lcd=-/C:~-1 . (bj (bJ).

OJ l-f- A'~ l o,f; CX) I ~ c:::Ct / ~(2,+) ~ I cJr j,.( = ()0 vf ~f 0 .

~<$ ~/ (o..l=l-1<:::~.1 ~ <0.) ~(¥2,--+) I

tlj&2/ fo}/ = vr Jcol (j, h) .

(Cf) /~.VJ<=OO, ~ C ~ Djv/U ~ IC/=-Vl.

~ C u 0~C7Yfl.~ w ().tr ~olu, ~ f urd~ n -'

P~-- c ~ (¥2,-+).

({p) 11~~ / ~ c .;,s esoiU. ~ /c1= vo J

~ c ~ (2 / +) .

~ t-o+ G) I ~ k j~~ ~ lM ~ /( H = {C~bJ [ ~~- bG 11 1 . ~~= (D,b).(c;ol).= (~c, bG!).

w (a,b) 6 Gl 14 ~ / ~ ~ / ( a,b){ ?

SUe (O,h/:: (o. 11Jb):::: (/~, lwJ vtf o!'=lo.,.. b11=1t4.

5\ tf (o..I~(AJ.~ &r ~17j;oo1 -&/,ec., / (a;bJ/-= 0o.

If [a._J LOO l I bl~ I 1(4.1~ ~I I I b I= ~.).. ~ { (O,hJ I::::- L~ (/<-, I k:L) .

&< La-t r / 1 ~ 1 / r~ ~ 6 ;z / J uA (_ t/ ~) == t

~ q= ~/p2. X Z/a, 2 ~ .zfrtt z T4· c.m&~.er j=- ( C!Jp, (11i> 6 rq , I ttlrl=-p, Jcutl~ ~-

> ~ I 3 1 =:-laM-, u,. ~ ) = pee, .

NO\N <J> ~ ~ ~ SZ1.eQ. [<3~1-==-/G,I-=>fi&-f~ /so <8>= ~ .

~-a ~:a 2/pZ ~ ~~<?t: ~ '4p.£..

If C i-5 4 c:Jd~ (J~ ~ ~:5 C _, ~ H 2:s D&o C!jc/~ .

r~ I /AJie._ ~~ ~ Cf).$-e ~ c= ~A.,__ 1 Ovt== CKJ •

~ H~ Gt.

d> If W=fd, ~-

(P) 1-t N 1 fd / l ~ ~~L hJJ. ~ H~ c / ;I h71J. s.+. a-tt' H .

Lu A -==- r "' t "' &2 / h ~ , , lt ~~ <==111 :~ r ~ above. .

85 LVe-bl-ord~1 ~~1>k / A hao 0.. $H&..Uett ~ / ~ Vlo

~ ciA~ H ~ <. a"'o> .

s~ o..,ho el4 / S-o <0.~> ~ H, s~ <O,Ho~ l? 4 si:J}O~·

Ms-o, ~~~~1-11 l,=-a~-~ frrs~ h S~e c~.c.A>.

~~ h= ~ho-I> r / <£, r c2 / 0~ r<:!~ ~ r=J: 0 I i~• ~~,..~-~ • I I" A -q 11

Till .e... t' .::: £1-1, 11.-b =) tt .::: {).., ~ . (a 1110 ;- ( / s C:W<-e- 0."' 6,.- b1 / ~ "'-> G li ..... ) (a"") e-n>

5 D ot e H / s 0 r 6 A ~ r< 11 0 / Ot ~~tor, wifh ow-

do~ ~ Vlo.

fj-ec.~ 0.::::0 -) V'J-:::~11.-o ...... ) ~=C\11 ~ <CA~>-2 :z-) /i~<c:t~>.

)...l

~ &~ f~u~ JBn~ >uhJ~up 4 (~/-+) hs CJdk.

Vf · Uvt ~ ( Q _, ~) , S ~ l:l / ~ f~vte.

tb 1+ (-{;. ( 0 l ' ~ (J.-> lf H==f {oJ / s~ ~~ (~,)--/ 5~) =- ( J:

1 -~ / ~) / P~~ i1- 6 d..

'L7 ~ a~.e. ~ .9 Pz.:fo ~ P~ fO~ I:IC=-1,·-J k. M~~-- D.&s~ P~ :?O, ~v>D.

H = < S > ::: {VI'~ ~--- -+ Y1k ~~ } st.-.e.e C aQ,-+) Z:s c.be-1 ~-n~~2.

6 <t,rl---~

/ ~ "J -k ~~~ -d,~ /

~ ~ s11own tQ. = ~VI iA's f~i-f-ef.J J€1.~ .s~nnp U <jete· -;;) (/)_ ~ fJ..x Q.

~ ~ ft<.?C ([). t "2. X 2 !6 ~ ~ Q. bwt 2x2 lA h£711- c:rAu.

Lai?Are /If

~j~~-1_~-e.-~ ~ (A ~w~s~

LeA- s ~ 9 I ( s / : = [ ~ /' -- . ~,/ ~ I Yt ~0 / 5" b ~ / £" = ± I 1 ~ q .

~~2·

Lf S ~ f~itk>.J < ~~ Zd c.M~ J~- J.~ .

~. f (~,b> :::: < {a, h J >

2 X 2 :::! <: f t I, 0) I ( 0 J I) J > .

~ = < Gr ) / ~P 1~ ~vfe Jr-ot.:p ~ Ot~ f~~ j-t+.. .ere. +e;J. .

~- G=- F ra,b) I .S= f a,b~J.

Ghow fcll,b) =- ~ = < 5/.

~~ h-= ba. Dt 4 0,~ a ~ $ ~ FrA,b)~<fa .. f:.b / So fcCl .. hJ ~ < S>.

~. LeA ~~~/ G ~s~, ~ <~>=: () H ~SIJ

7/w:+ !.:s _, < S > ~ -f),.(!_ ~"'-ta.bfes+ .9~4 of q H~ ~ C,./1\+e.u.s~ s; .

PJ. i'Joie ~ ~e.t f H { S s. f-L H:s ~] =/. cf ,s~c.e.- ~ 0 ~ Of-.

'f)~+e- Ho : =- n H I ~ ~ l6 4 Svo~I'V'f D.~ s ~ H 0

ss.H~H

LN'~ t-o ShoJV < ~ > == H 0 cks~ u~ p~tk cwf ~

U ~~I II ~~ gs_fio Q...J /h ~ 0. 8W~ v+.s-elf_, $1 .... S.., <==Ro,- ~o <~>G.Ho.

>o 1-J.o S S.

~u/ <~'"?:::: Ho.

~. ~ L ( .l-, IR) := < { ( b ~) I ( l ~) I ( ~ ~) I ( b ~) / ( b ~) I ~t ~I f t ~} >. (Pf)

f;:4, ~.21 $"1'1 . w A= { U,j) ( {~i>~-j~l-lJ

CPf) ~~ $'~ = < A > .

k:J. c:q : 5'/,~ -thM- 4~ w,- CJcle (Ot~,-~, a~) ~ be- ~se.J. as tl fK>~

of ~f)$;,+~. ~ ~, ~ C.Jek w1-M ~~ -hvc.? .eleH,~ :0 c.c.~eG{ a. --tft:fl,sposvf\,0'1.

~- lf G ~ tl f~~ j~ Jvo1Af, ~ ~ u ~~le.

~ GL (~ lR) ~ l-Vl~bl.e ( blc lRJ / £:0 zA& 1-1-o+ f;..,~ J~er-4.fei.

ht1f- +· J. H~~ o, v~~ ?

L-e+ 6) b-e iL 8vovp ~-+· ~ 0t ol,a~ uf sWjhnf~ 14 17 :5: G s.-t . 00

H, ~ Hl. ~ --- '¥" J.J~ ¥ H~ ~ -- ~ 61~ ~ H'-1 I ~ ~ h ~t f. J .

flO

c;::::. u 1111.:;) v ~=1,-·· I "'-1, ;} ~~~~ 9 I, s .. +. ~t E 1-J~,~ . C..::>j

r~ V1-= W10.X 1 ~~~~~---~Vl..., 1 , -HtP1 1-!J.s.Hj-+l ) ~~H~~ q .=>'"><S> ~kl~.

Bwt < S'/= a, I ~ ~ ~-+1 , $1:> ~ ¥ J.t~o~-tl / hu+ G ~ Ul-l.., I $,;, ~4~. ~

I oo -:e [tJ = V H~-~ . 5., 1=0 ~----

p,~ - - -

L{U~ t;; ~~ ~ ~;.e4- aw~~

~(..gje,... Gl: 4 J~r

H:5G,

( fvt.:rH-vo.f:.U,.,' G::. ( £/ -t) I H = < h > = h ? ( 1.1~.l} 2/,2 :=. { [_O.]v, J~t:2} , z:.tU..,=-{0.-+ [<n I ~eZJ ) .

~- La;t 1-i"'~l fsr ll69 1 ~ lef-t Co-S-et vf H ~~.....cA~ ..b, a.

Z& ~ ~'-"'H - ~111w4.f~ do.s~ of 0..,~+0/

-bho-.s~ { ah / ~e: H J =: ttH ( = [<AJ~ J-1 ) .

M. ~I H :::: G/ tvH = { a,HI C\c.GJ. ( ~~W)f~ s~) .

~ dJ ~ a,b ~ G1 I -e~e.- AH ::. hH \))- o.H n htd = r. ( vf ll rv14 h) U;(- Ct f 11 b)

( foikc.v.$ ~...... M~t ~

of ~"wc.l~ vias~~ ) .

l ).-) It; H = H . ho H = H fw- "l1., ~ H .

P-f, {a,H.::{/<;Jhlt-tt:HJ=I-·L

JiM~ ho:;;./ ') ho / S-o J,., r--1-4 f <; 1 &j tb 1 /a, H = H =- h., li ·

~- ~ H ~ ~ / ~ ~~ u-f H ~ ~ I

L ~ : H J :::.: I G/ H I = ~ (~/H)

~- f'b ~= -z I H= < 3 > ::. 3 £ I ~

G,/'r\= ~ 7. I s.. [.~: HJ = 3 .

A« ~~ : [0]3 I [1]3 / [ J.]-3 •

().} G, :2 f ( Q I b) / H :: ~ Dt > ~ ~ .

bH = f ht-.{~t!t:H l::: l bo..n( ~tzj 1

a.hH = { aJo.h/1'16-aJ

We. se.e h H, il1ib 1-L th'"l-t ---, ett h H , -- · oJA oiZ$+i:wvf V=- o, 1, 2, --· .

-=-) \ f (Or,b) : < 0.., I = 00 I WI~ 9f=ui'i<. / c,oW1fo)-k. 00 3/

l H ~ t I ).. ) 11 ::=- H ;:: { I J ( I .l-)} == ( I ~) ~

pl. G H 00 r (f 3) 1 , ( I 3) tl , ) 1 = r ( I 3), l 1 ,_ ~) 1 ;:: ( I ,. ,) H (,o~~ t ~

(.l-J3) H :;:;- r (J- 3 >, c ~ !>) u .l- >1=- r (.l- 3)~ o -3 1.) 1 ;:: ( 1 ~ }._) H

~ 0 I ~~ I H I ::: 3 .

7h~.~~ ~ Q, ~ tJ. fiv!Ae ff/ , H ~ Gt .

-rM~ IC11 ::: [~ ~ H]. I HI ( = {G/t-J[ ·/til) .

L~IYZA c::.- - ..

LM H~G,, ~ fo- tl!~ tte ~/ [o.H I= I HI .

f!. ~:al~ f -' hJ -> ctfi , ft>o= a.';<, X'6 H / ~ f i6

-f l!> s 1.\~--je-vr;.ve h:J cJ2f Df ai-J . f 14 /--to-/ _s~ CW ==4j =-) X=!j.

a. bj'~~.

c! So Ja.J-H =-[HI .

Pf of ~ a; H == { J ~ H;: a, !1/ Oo-H J t\Jl·L -~ / a fh H J I ~~ ~ =- I G; = H { = I ~/H I ,

7k 4b~ t~Wt.tl ~pi~ -tU.-t / avl-1 /=-1 ~f \i ~::ol, ~-/ ~ ·

~~ ~/H u -i4e c{~owi- V\1'\~ vf av+-J I £.-e. I G./l~= "~ D<vl~ .

~ [GJ/t-11 = rv1) I ~~111 = /I~ I ~ ( ~1 = 11-1· t !.JI / ~[A;~ {~I =- { G?· H{ ·I H{ =- I ~/H ,., HI .

~. ~y 7hw, ~~~ / -p,v. _J~:+e- J~ G1 / ~ H.::;~_,

~ /HI//G,/. ~)

If G1 u {). fw.~ [/~ J ~ {).. ~ Gr /

I o..f /t ~ l .

Pf S~c.e- <t~o.~ ~ ~7 (t~.-{ =<a> / ~ aU 2s r~Ae-/ kJ LAJ~.e- Th~,

I< {A/ 1/1 c;, I =-> t ~ t/ I 6 t .

[ ~: k.] ? /611 / = ({J ( C\) . Th~ f ~ w~-~~ oH.OiJ:ie{,t~lle-_

v~ ~ -f ~ w~-def~~. ~~.S-l<- VV<e-~ o..b / (!, c t o./<, :.e.

b/ c t:= /< :::-k.e,y. ("f)/ -fit~ -f ( 0. KJ t:-1 s.J.Uil J ~fe -vtJ.~erl .

v~~ ~t f ~ 0.. h;_ju,t;.,.,. ~~ 'f t,s twrf-b ~ ~ ~ Ot e (h,

~,v.e ~ f~ ak s.-f. f(o.k)= VJ(O.)/ So f u ~.

~ ~~p~.s.e.. f< A/<)=- f-cbk) / -t/.v-, ~({).)::= '{J(b) -=-) 'P {D.)[ y; (bJ]-1 = /~,J :::-) ~(()..)C{Jtb~J=/u =>) ¥J(Otb_,J=/u -'> o..b-~~ k -) D..k;:,.f,k. .,~ . .a. o.~cb.

~~lb ( 5'o-....,e.t>~ .J ().N£2. -H.a- ~ t.#~~ q PM>{. ktqw~) .

~- .Lf &; ~ ()._ JYOVf / A hor-~ sW;;J~ N ~ a Swb.pof s~+.

q- n6N 0..~ f]6G, ..J-i,.~.HJ 8 h(/-1 0, c.&o ~ N.

~( If ~ Zo ~~~/ ~ o.{!f s~~ of G, ate vwr-n-rM .

Q ~f tp: GI-!:.>H ~ "'-~~h:.Sh-1, ~~ k=~~('{J)J ~ K u tt h~ ~~bjwup ~ ~ .

G l¥eM 11 :5 ~ 1 ltV~ h.a,Ne ~~ CA-H 1 b ti 1 ~ we wwt +o ~tlfly ~~ ~ c? ~ lAH · bH := o-.hH

Tl) cAae.W: ~4 -e-tt~ ~ w.e-lll-~~ .>~If~ cd-i= o.'rt bH-:::> h1 H1 ~ O..==a.'h, /

b~h't1 1. ~ s~~ h11 h.~.-6 H, ~ Ovh= ~ 0.1

nr!lh:l.

~ ~.v~ o.ko ~.!l~ ~ kf~e_ ~11-&S~.!: "f Cvse-h v-..no{~ ~ ~o.+~~ ~e.. 6:>~ ~s~

~~YVI ().. d~- ( rJ..q_ 2dM~ ~ I~ / (~11}-1 = 4-' H) .

33

L~ I]

H ~ ~ I G I fi = f CJ./1 I Ott:: g, 1 . I;Vawf -t-v clef~ • 81'1 ~~ N ~ et.H · b 1-:J ::: ~b H

1 w ..ftt10 t-s ~~ o.lw~s

~vve-IA- clef~ . ltowe.t~, f ~ ~pos-e -#..at H ~ ~~--moil 1 dan~ H _:::! ~,

; • .Q.. H ...6 t1 norwtA!f s:tJ;.J~-V"'r v.f G, I ~ ~.-ve.n so.fe.

7h~ :;, bece.we o..[-t = a. 11 1 ~ h 11 ::: b, H / ( 4 e 4~__, b,::::. bh) , h, h

1

e}(

>f 1-J .($ kor-Wrtl1 "i-..e · 1-j ~ G, · == ttbb-f?,hli.:::; o.,bH.

~ ~ at.~ tJtbf-l =- a, hdJ . ~,'~t~

{).., b, H =- ad:t M h~' H ==- a_t, b H '---v-"

=H ill.. J.f H ~ ~

7 • ~eJ On G/H ~ daf~ 45 ttH- hi~~:::: abH,

~ ( G,/H 1 ·) u a 8rDrf , C4U~ ~ _j£«>1-i~ J~ of ~ bj H.

7~ ;;cle..rt~ ~ (a, 1-I;;:. HI ~ l ~ J-f ::::. Ot-' H.

~ [M H~ G, I cJ~ n: G, ---7 GJ/H 7 n {OtJ=- ~1-1 / Or69 , ~

-rc ~ an ~ hoW,oWrt"~*YJ OtiUJ( ~<~ uo= H . n t--5 ~ 1JWfi~t n-,o.p .

Ef. n 14 ~ b def. iff { o.b)= a6 H I?IJ ~ ~. h H :.. 1( (A) 7{ Cb) =) h o~o"""'thl&~.

fin- a~ c;, 0t ~ ~ ( ~J lff- 7l tAJ = H 77ff ttH == H ¥1 ae: H . ( ~f-1==-1 a, tJ *f Ct= la.h,~t!--1).

~- L124 H -1 -

Csr_ LeA- 1-l ~ ~~ ~ H 4 G 2{f ;~ ~= G -~ k 7 s.--t-. ~ u. o. ho~01'~ort,i$W1 , k

::0 s OH-112 (/1-()r. f / Otn;;/ ke~- ( Cf) ~ H .

Pf. (~) oJ~er4J ~OWh.

c )) if H ~ a, , {_,f '-P= Tt.. , -ete '1~.~~-t.~+ ~r.

~- H ~ ~ <-~ • "l-1 G,/H k.f~ a.,g AH · h H ~ 4~/-j u ~vebt ~~.

C--tv:J -M ~ <? ) .

~ p t-v p ; ~ s ~ 3. I , D 2< F .

~I ol.e.f~ H trh ~ {lg ~ ~ b z+( b= J,a. ~· S'D~ h~H . <?-':> h 4-lc.l-t .

14~ Hr'\/ u o~v o.~ ~wal~eli? rdA-t&:>v, OJ.-t ~ • ( V.e#~ ! )

~ f* ~<£~, -ftr.e {'"" - ~V.!tvt>.l~ ck.4~ q 4 Ls

H D. ::::. { ~ / h .G H } / ~ }:_fJM ~e:f ef f1 hJ 4 .

~ ~ H \ G, = f H 4 / Ae Gc J / "'- 'fB.ri il1 ~ t7 ~ . ( H I~ =- b-U .

~- ~ H.sG;, /1-l\Gj =/~/HI.

H. w~ a };~e-Pf-Wn fwn-. fJ \ ~ -bo 9,/ H . -f : 1-J \ G, ~> G/ H .

Def~ -f ( H-b) = b-1 H

-f u ~-ek..f-Vw24 : s~ l+h= JJh 1 1 ~ -{-ciJ--b> = b_,lt =- b,-'H==- -f-dJb,J. 0-

h,:::hh/t,Cft,

~ b~kl=~ (t,bJ-1/1 = b-lt,_,H = b---~H. 5o LA-e/1-def~. -to sh6i'V .____

'1.1- Vf :0 4 b~;ecf-:,_. ' rl_._t -1 (~ v VI'C-'1 ~ J: ~/H -) M \ ~ / j {t:tt-i):::. Ho. . j ~ weM-de;f·:u.e.( ~ ~u..., vfA,.. Y'24 ~Oh { :..k e f .

~ CJ"f) ( f~b> = J ( ftH-hJj ~ J t b-1 HJ::: H lh-lf1 == 1-lh /

C-f- .. j) ( a.t-U ~ f (Jc~~J) = f (1-t~,J = (cx;y;H =-aH.

s \) -f- ~ c. bj euf ~ . ( -f -l = j ).

M. ~ H .:::1 ~ I ~ ~ .(W~ ae:G/ Cl/-{ ~HOt. ~

='=lt;P > LeA H~ ~/ ~ H ~ G bff a.~:::: Hc:t tiCiGG, . ---· s~..tce. H~G tf. C-=->) s'i>~ H ~ G , ~ a~61 . ~ h6l-l / a/,=o..het-~a == h,Ot ---.,_.......--

~~0Arl. / h o.. = a_ 01. -t h a. s~C-Q.- H~ c.; J ----..-- .:::: (),_ h J.. = ')

h.l.~H

h, e-H HC\ s. ctl--f

So tl-1--/::::.Ho...

=> aH ~ Htt.

(~) lf o..H::: Ha., VOtebJ /~ Vo.~~, ~~~~/~h,~l1 s.f. o.h=-h,o._

=-> c;._t-J cc' ::::.t,, ~ H => v~ 6Gr/ a. H 0t-1 ~ 11. 1/ ~ e- H / Clh ~ D-H .:= H 4 _, S\J 3 ~I c t1 ~-+. ~t,:::. h,o. =') :8; h = Cl.-f hi a._

=) l1::::: a_-f 0 I (o_-ly-f ..:>) v A~Gr, H ~ AN c.-1.

S,o \iCtc6J" H = a~o.-J ~'> H ::! q .

LaA- H .sG,/ [~:: 1-lJ=..l ~ ~ H ~ G, .

~~ H ~ Q t,Nikt, [~:1.-JJ ==-1.. = I Cl/ H /. ~ L;== { H,a/<4) ~~ a. 6 9 Scwe I C:,/ H I= I H\G,j " s-o I W\GJ ~~. "'"'-'~ a¢ H . ( t5 U

( G,= H u etJ.l) < Jl . -~0 G= { ft H(, J / furs~ beG,/ bfi-L Gr li u H-J,. ~ ~j oiMf LN-'1 vOV1 .

~o cd:J = H &_ . hJ a# fJ =:?> H a :=.f-1 b _. s~ 1-1-a. lz It i

S-o Gr:::. H u o.H == ld u Ha. -> aJ{= HCL

N4v leA- 8 e. G 62- o.rb:.+ra!1 / vf 3 e f-L ~ 1-lJ== H = CJ J.J . J=f d 1-H /

-it-Rt, .. G c; H. J 6 a H ) <'o VQ 0. h fro.- smte.e h 6 H j lf 8 4 H " ~ 1 H :1/-L ff3FI-l ~ s~ G,=- H ua.~ == lfu Ha."

s~ j H ==a. H / HJ = /i 4/ So JH = H.J b!J p~v~ P""P •

~o V a<£G" a.H =I-I a ~ H <4 ~ .

~ . ( fih-s.f lso~~hl&w! ~)

LeA t{J: ~ ~ /< be 4 SUjeM-We howwn.o?rphUh1. 7h8+J G/l<er (tf) rv K .

'e:f. ~ f: G,jt<4 {'f) --7 k t.J f ( o..k-2+-t~J J,-== ~ cctJ.

cV~ ~- def~s ~ f · 0. /cR.r(tfJ::: a, k~f'f) / ~ 4:: a,J,, h~kerti{JJ.

'f ;-s t,o,_, f (ctk~~)= Cf(O.).:. C(J(O,,f,l)= t{J(O,,)<flh}::::. ~(0,,) ~-- h6/r:~('(JJ.

-= fr4, k~(tpJ). Sv f d. f.N.tb{;f- de-f~ _

~ ~ f U. Ot ho111o. V' .:.& /,o~

~ oUf/ -f (a,kerrf)· h/<.~('fJ) == t (ab f..:.~r'f;) === tp(~b) = r.p(O,J'f(b)

.:::: f ( Ork~Jr(YJJ) f ( b ke.. ( VJJ) /

5-o f i6 a hoi'>10.

G) ~ ~ f Zs. bye-vtwe- .

S~ tp ~ a~~ .>v tl 1< 6-f<_ / ~=- tp(O.) fr so""'~ Ct 6 tl - T~ t (c.k-e..-(I.{J,)= ~(4-J~k _.

S<> f ~ also o k+o .

To s'hm-.' f 2o ~-«?t-~Q _, On!J ~ ~ &how k.-e.--Cf> = / 9/k-e.-t'fJ = K&( y>).

k-er (-f> == { o.{<-eNI'PJ / fta.t<-e.-L'f))= / 1<.} = f o.k~rwf CpiOtJ={t.:}

= r o.. k.e.s.- r '(>) I k~ r ¥> 1 ~a. 1 .,... ! a k.e+- ( tf > 1 a "' ~~ c 'f) J = /<.er('P).

~ ([), ty, (M4}. @ , f ts """ kw•ry h;,"" . S:. G, / k"'l 'f J "-' k .

~- 1f N ~ Gr ~ ~ N Zo rwHVlA/ Vf llj eQ, _, (! N J-1 = N / deh.-tea/ N ~ 61.

~~ ~~wo.l.e.wf- olq / N ~ ~ 21- V 11 <G N _, ti J e: ~ _, J hJ_, 6 N .

-~~ 18 ~pl~fkm: 1 I >-'~ 1-~ o ~p~»-r -n-w~-,

EX. U) ~L(r-,,f12.) I ~L (n, TR) rv ?

LeA t.p ~ ~ ~ Q,L (111,/R)

~ bt-e- <.f = SL (1-1,~),

{.)._) G :;:! ( c y. J • ) I H == $ I / H ~ b1 ( G ~ c,be/uu,).

G/H == t3)1./s' ~ ?

leA tfJ·· (?><-~(JR.~·), '-{>(ZJ=/z/.

~ ~e.. c.p = g I .

f')l/ I ...} s v Q., I ~'"' = ( R", . ) == ( IR+ I • )

( 3) ~.:: (/RI -t) I H = lZ I-+). H ~ G; .

6/H = R/z l/1 ?

LM- c.p: U<. ~ ~ , ~ ~ t x) = ~ ( .).~)( ) + ~ ~~ (~J = e ~~ .

~ k-ev.t.p = z. ~ TP--/2 V1 l '£ I / • ) .

~ (Lf') G; I H 8nnr~ / a x M I N ~ r ( J / , u) 1 J t: c. 1 / N ~ G ~ H .

~xHjN~?

w cf: G X H ---7> H I 'P ~ -#..Q, Oo~~ """¥ ~ tp { (~,!,))::;:: h .

~ /<er c.p == N .

~u ~)C HjN v, H.

Ccr ~ G / k k ( fw.,(l(-e) ~~s 4tJ1 Cf: 61 -Y k be. ~ c::»rl-o hox.ofl:Jurp~w,.

~ [ ~ : k~ tp] ::: [ k J .

f¥ · ~ l'f ]$o rh~/ G,/k~ '-P V\ k ) [~: k~cpJ=-/ ~~~~~~ = /k/. -/i.e ~o;.., : f ( C; ~ ~) =- ~(D.)

L-Le.A. f.- G-)~ ~ OtV! owfb ~~ ::z_) ~I~¥ v, k. . LA ~ ~ 61 . t,.tk; ~

~ ~IM>fj,Q...,.-1 ~P 1t = G-:v ~~~<f ~ ""fl(C.>= 0t t<~<f. ~ '1lt/-b= I t-,k~~/ht:~J~o/F&f. ·.!

-The., 7{ £1{l /V i- ( 7i t H)) ~ I 'i' th) I " ~H l ~ 'i' ( H ) . . . . :,' ' /:} : ; . .. . ' • ; ' ·y //

r, I

.'-., .· ''f ,··

~ · 1f tf: Q -=> k l0 4<.. ~ h~ Oht, H.:::: Gt , ~ -rr c H) VJ tf c H J .

7t : G -) r;, I kfW ~ I ' 1{ ( Cit) = 0. ke.- f .

P.! . r' ee- 0. bov-e .

LrM- N :::1 G , Tt .. ~ G -/ G 1 N / ~ ~~A-o-ft~ 3 14n r. ~ _ ~ t~7L==N.

LaA- H ~ ~ . ~ 7t I H : H ~ c.,/ N '-6 ok~ a ho~ .

~ / s+ 1-son-, · -,1,~/ H / (<Gf.. ( 1i.-/11) ~ 7t / H (H) = 7f ll-l)

4 cJCtH-> = r~e-HJ hN=, N 1 = fV,6H 1 h6-NJ ::z Hf\N.

~ 7=l, d+ J = r tdf 1 h ~~ 1. t,N

~ ~ GJ J N $. G => H N == { hn/ h~~t 1-1cN J ~ ~ tv~~ [ )

S:o -r1: tH) = ~IN ::: HN/ N. (vQ.A-~ J) ~M. L-eA H ~ k k 5~1-Q~r '7t~. _ _I_ - HI/~ H I of (A_ &4 o.v.J de1~ vr~/ f\ N ~ N N . H K:: ~ { ~~\ ht-rL ~b\(j .

~ c s~ Jgo~hlo~ -a~J

W N ~ G, J H :f 61 J ~ H / Hn N IV H N IN .

tf. CD skw ftN .:s ~ 4~ N ~ H N . /

~ J-J,h,n,= J,-,h,h,-lhh,n, = hLY1l.h 1 =hJ..~~f-IN.

(h h) -I= v,-1 /,-I = h-I h.,-; J, -f ;:. I, -1 11~ t: ttN.1.

"'

~ ~ J l.-1 N N

~ 5"~ /a, 6 H / /a, 6. N/ So /4 fc,=- { C, ~ ?JN- ~ HN ~~

>~ N~ [ h, )1 J .... c,NJ ~ HN /so N~HN.

1~ V1eN ~ hn,tHN/ ~ (hnj_n(hi1:Jl-f = hn,nh,l-7-i= hr~l-J,~ J.

~~ I ., N ::! (1 ·~ "N ~ H-N ., -='> '1 N ~ H N ~ . N

(;' 5k l--!f\N ~ H . '6!1 d-ef ) 1-l (\ N ~ H . 7k ~ ~-f N .1 Q, =/ H 1\ N ~ ~ ..,..., ~~~ N ~ H .

G) f;h-v -#,.Q it, 'D"'-'JI-ph~w. ( ~0"'->~hl&w.J

Peftne ~: HN -~ H/HnN bJ YJ(~hh)= h l-InN.

tb we4/l-ti~~>= S'"'Pf""'JS1-- hv.::: h,n, / 'fCh~--t)= h HflN, "Pcl-J,h,J=- h,/-JnN. s ~ h h ~""hI / s 0 h,-l h = ~I h -1 E N -::::-:> h ,--1 h 6 H 11 N .

Th..~U? s~ h, h ~HAN J h H 1\ N == h, f.lf\N => Y:.ChhJ; r.p ch,n,) .

L~ 11 (.).-) Cf' Z6 D. hoJWo~I-U~. '-P{ (hh)ll-t,hr))= "i11~,1<1 1 J../A~J t_p(l-,hh 1 V11)

= c_p ( h h 1 h 1 -f ~ l-t 1 11 1 ) = '-P { 1-! h ' n l- L1 1 ) hj !.e.! h h 1 1-111 N b !I _cLt2-l t-, f..J /1 N · h rl·l /1 N == tp { h 11) t.p l h 1 11,) . N

t3J 'f w S'j~e ~e.e- -for ~ t-.~~ Atw/ h MI\N ~ H/HilN, J,~HN o.ttP/ \fJthJ=hNnN.

(4) ¥ La ;,'J.6bli'.16- t-~t}J fi) F~ /<-er y; . J,., I-ll\ N = I· !-!/IN

/<e.- 'f = f hn I 'f'th~l= /.._rflfJ "' 1 hn 1 "~~= ~ .. ~11~ J = {hn/ h.; ~~~N} . ~ /· ft(JN

s~ N !E:. f h ~-~ 1 ~-r c If H (\ N J c 1 ~ 1<1~1 N > __ ~0 N s. ~ tt .

A-lso ke~- "{J ==- { hh /he Hll N 1 ~ -fJ 14 N N sk,£e. 11 G~!-df\N ~ N ~ L1cN.

So ~-e¥ 'f = N ~c.e-" 'f :- H N -~ H /1-411 N i.& o.. SIMje.cA'We ho~o~orphl&~ /

().1-r-o{ k~ tp = N / $1:> b:J Is+ uoh-1orphun-. 7hk-1/ H-N IN~ H/r4'1t'.

E1: L.e-4 Xf..~ , Fe>{) -h ~ firoUf en-. X 1 ~ ~ ~ ~wv.p G ~ 0.~ ~~ -f ~ X-:> G, 1 B} [-,~vi':OH-1 tp ~ FOO -'> ~ s-+. tp ~)= ~J Vxe;X.

tf. Det~ lf~ fDO -) G, M tp ( x,~. -- xt'/-) .·= fcx,) E.,--· flx.,) th .

4 a,~.~ w~ ove..- X. ~ W»i{y "f ~ 0. h0/1-,o,.v.-pJ.,~.,s,._, / 1

. --:.)

o.n4 c/t~ IA"?Jf 11-e- •

Y.. } (Q,J,) 0.~ 2.., 2 ::-) vv>4-h -+

f: ;a,h)-/ 2){2 : f{~J= (/,o), {cbJ.= to.~l).

~ Cf' F(Cl,bJ~;l)f~ S'-1- ~(O..).=U,o), <.p(bJ=(o)l)

£4-e... <f ( Ctb-2-tA:. -t b)= ~ -2.¥<-b)- ~-+ ¥ Ch) = - '(It b)-= ( o,--1).

~lA-W! ~ ~r"~ iM a/,-J. Q-1 b F Ot I b I ~~~'

exp fur ct = CJ , ~ f'>- b= - J / _;-.., ~ ( Oth -Lo.~ h) :a- tzt" ( o~-1) .

h .~. ~ fA~ WE F(Ot,l:,) / ~(_WJ= ( 0Q (w), o-b (\.\1))

J; ~ exr~ 311 "-1 €), rn.e,.A- J'VI ""

of Ot ~ w. -o-f b en w.

Lf-o

~. L-et ~ L G / ck~ < < s :>) G, ;:: h c l ( s) {

£1 -r ~ -II n~o / St.-<:::~ J = J,S, :], --· j,S,., 3,., z:i.-=±1 ~ j~,6r; .

h d ( S) ~ ~ -the- ~k-lAI dos~ of ~ iM cq . ~ ovfco ~owl-\ fM. ~ ~~~M-e v/;o!;Wr0 &t g ;;.., 9

(;;y <<~-,)~ == (l { N/ S~N~f,}.

J¥ · l/) V /;v~s .

(\ f N I S s. N ::E Gt J ~ << 5 :>) c;; . ~ 4 o~ d~~, tux N >-f · g~ N:::! ~,.

we- sl?ovv < s I c N ~ '" 6 s~ --1 b. -1 N <. '> ~ - , .... -> , ~ or ' Jr --- .g,.,s... j, .£::.. •

(i. £- S.· s·~ <;.sN_. £i,~N . ~i+re.4V N.!:!.~ ... VJ~. .. JvS-vl.,-1 eN. Tf,-01. S~u. N

2-6 a. j~p7 ~ pa--oh..e1- 4 c.t/ .j-:s/;,3;,-~ / h4~,. ~ .J~s,~,_, --- J.,.Sh£j., -t c N _

t4e.... v€- ... << s -;.)a, s. N .

M. LeA- X#f" [<~ f.CX). -rtr~ <X I R > ::: F(X) I<< R>/t=tX).

~ ~ /s-1 LM>rn17"1'phtsk-, -#,fN!/ (~ 1 b/ O.bO.-Ib~) Vl 2.}(2_ ~ .

7L. c R> =- 1... (~~ i t.vrl~ (]~).

bj' ol.ef , e>t~& Fco.,b>j << ~bc.--t b_, >> Fco.,b).

vJ,~ k-e.- ~ = << o.b ~-~ h ~ "">/ p (O..bJ.

CD ~ k~ t.f = { w l:: fu~.b) / ODr ( W) = llbcwJ = o J . ~ f'n-- o.h o.-1 h -1, uo. = 01: = o . ~ ~ 0.'1 w 6 ~< o.hC. -t b -t>) F-tC~. b) , oq CwJ :d~( wJ=-o.

~:o << o.ba.-1 h -1 ?) F-lAb> c,. k.e...lf . L't I

k.Rh \IV~ -bv S~ -ti,lj 26 -t;x; /1\o-fu.e -£:h9,4 J~ CAhO. {-t <=- k~ 'f / ~ k-e.-- ~ ~ h<rr~ 1 C!~ << a.bo.-t _b-1 77/ V ~ sW!i),t1~+ (M}r-Ut.a{ 8)1()lf

~-f-AW.~ c.ho.-t b-t) ~ ~ << o.hD.--4 b -t /) c. ker 1 .

~ N()l,v I I~ IN 6 k~- e.p g.-f. Cia. (W):::::. t1b tW) =- i).

Le.ok M- 7[: F c4,b> -;> pca.bJ j << oJ,cl~b-t>/.

7h~ 71 tOrJ 7tthJ n ( a~J 7L th'l = 1

~) 7'[ ( 0.) 1[l bJ 7t lOrJ -1 7i-U,) -1 :;;_ 1

7\. ( (),bo.-f b-1):::::. l-"> i4, -#..Q 1tttJ1t~

Jl-t77·

~) 7[(~)1ilb) =- 7l(b)1i.{Cl) -=) f£4,b)/<<ctbo..-lb-t::>) 0 D.be/i.Al-J.

~ S~ 0"4 tw)~ ObCIN)={) o,t-..ef -f;/...rl -f4t+ ~ /{(D)/ -a tb) C-o""'""'w+t! /

we s~ Ftc vvJ = ~ =') W c << O.bt2._, h -J '"?/.

th~. ( ~ Thwd, lso~-v~:rhuw, ~).

LeA N f::. H c G, q,.~ . N ~ ~ a~ H -$ G, .

-rf,e.. G, !H ~ ~ /N I 1-1/ N . 1-f G,/N= G,' H/N~ 11' 11M z. a,/J.J "'G, /H. E!. ciJ v~~ -HtM- 1--+/N -1. G, 1 N. Ch--se h N ~ 1-t!N J !iN~ G./N / t, 6~L j 1:: 9 .

(JN)(hN){jN)_,::. (.JN)(/-,NJlj-fNJ=- gi-Jj-1 N e= H/N s~a .j/-,f{1 e:N

( N S ~) . (J-) Sh(fll\/ ~/J.d '::::(6/N) /U-t(N) . 7kf~ lf: rl,jN -~ G/1-/ ~ JN t-----!;1 J H . (j) l;t;eM-def~ ~ S..pp0312 jN=J,N_, ~ '(J(jN)=JI-1 / '(l(j,NJ= J, H.

J N::: J IN =-) j ,_,j EN~ ~H =-) J,-'J '"=H =) 3 H = j, 1-t -;».) \{> (.j NJ::: 'f(J, N)'

0 <f 0 ~""ti e.vtw-e . V 8 H ~ G / l{, 1 j tY ~ (), IN s, + · y> l J N J-= S H . {j) f ;o ~ hom~huw.. ~ !iN/ J, N 6 ~/N__, -tt..u..

'P{.JN9,NJ= l.f (JJ,NJ:::: JJ1 H.:: .Jf-Jj,f-J = tprJNJ ~ (J,NJ.

(§) ke.- Cf = HI N . ~ ~ = { j N / J ~ G, I ~ CJN)== l·kJ } =: { 8N I J H -==-1·1-l j = (3N/JcH] ti.j ~/N.

~ ~j /sf k01-ryh~w. Th~/ G/H ~ ( G./N) / ( /1/N) ,

21. ~ <: cA I b I ~bo.-lh4 / Ct >.

~ bj 3 h»/ ls.o~,f,~w, -rtwn/

~ ~VI / gJl" (CJ):::: E. (CI) 6 {±/} J ()6 SV~. h~.2

~ .6.., := fl O<v--Xj) / Xi, Xj ().;e_ k...,~ va.~l.%~. /S~<j.s. h

a- ( ..6. VI) '= 7T (X(}( :u - )( O"'l,}J) ~~~~<h

, or

, ~ cr ( lln> = ~.d., I Zf (T(.C,h) = -..:::111

£ ('ItT) = z. ('L) t ( tJ).

!J. w "'?2-. cr-(6h) - n lXo-c"->- Xo-tjJ) l<"<.'<h r'l-- j-

(-c: o-)( 6 V1) = TT ( x )( . \ 1.:·<·.:: "CCit~> - rcrcj)/ -~j-~ .

~ Z:. C6 H.,wf-ftph~

k: = # vf y4.,_~ ~~~ ~ ~, ~A. CT'( ~) > & lj). ~ 2. cr::rJ= (-/)~

• I , I t.- > J .

>, (-l)t< ("!:IT) {.6-n) = '7: (..!>11)

(J::.'> Z:. ( o-) ( -r; ())(.6 "'' ==- -c (.dv.)

<!-> tr:rr) <~ .. v.) = t <t:r> -c (LJ.h) . £1h

~- tb ~ A';j ():: t.:.,j) ~ 5'~--t / Vl-3-..}../ £ (rl)= -I

<>-J A,., ~ == ke-t- E = { rr e s;,_, / E..c75J= I } . ~ l-1 ~ ()/(..£-<RHHAl~J_J-1)~_:_

Thtvt A~-~ ~ s,., I 4~ [;;h ~ A .. ] = ..2...

:!1- ~ s~ z: ( 1> :z. t z: c c ~~i '> ~ -L £= s11 -~ 1-.t.l I 2.1 oz-r+o.

~ /s-1- •. ho~~hl,.._,. s..,; ,4-,., '-1 f-=t-1} --> Js~<~/ ~t ::l .2. .

(4) Fr:n-- be.~~/ wv~ ~ [<- Cj~ as

( t\, DJ... -- · Ott<) = (a., ~) (a., ~{c:--1) • • • ( o.., Ot3J (tit ct.)

z. ( (ct,J- ~>) ~ e>Jo/ ~ L-1)

E ( (O,,--C4J) 0 ev~ -7 (I)

(b) ftn- J1?t2. / v' ()6511 CQ....., be. rer~~ t..s (5":::a ~ -- r:-#'Vl w{,~ -c~,

4s a. -br{)t.,& ~we.{)-,., .

( 7) L, l6)J if I'Y1 ~ -evet--t ( oofal) .~ £ (rr) u odt;{ {~).

C8) If o ~ s~.7 ~ o =- ol, ell. • - ol)t., - 4 C<mtf~ ra~i,~r~ of () ~ of<4Jo w.+ CCfo-lU .

~~ £ ( (T ) = ( _ 1) n-W~

~- A-1::::. fr}. Al. :::-. r ' t . A~= r 1 • r 1 .l. 5) .~ r 3 .l.. ') J L1 ~.s .

4zt = {I} (p.)(3 4J, ( 13> (J..q) .I ( 14) (.l 3)., {( l. 5)/( I 3 .2-), ( l.J.lf)l( I 4 l-)7 (/, 4-)

~ kl~!Nt 4-j~4> ~ ( I 4 .)J _, (l. 3 4-) .~ t 1. '-t 3) j

L-) v~ { /_, (l:l.J(34), (/.3JP.4J, (/q)(l-3>} ~Aq I V""' ~J...xz.:J... ~) So~~J cc.tW.e< Vq..

ru. A 8~ G1 h ~p/.Q_ ¥ wJ.,~e-c,.e- N ~ G, / ~ N:::! {I l ~ N=- Gt .

Jhwt. Ah u o.. s¥ 8i'1>t..p fur V n~ ~ o.k.O{ Y1=#Lf . ( Azt ho.J Ot nC1k-+r:..VJl.l1

Ylot+~~rl .s-fA.hJWlf', ~~ v~ J .

Co~~~ iA., s,. __ . r_ gc/Ok s~ cr.~) .

Cl> Lf cr6 s,. .~ ( a, - - ·. ~J ~s,.., u t~t. /<- c:Jde 1 ~

cr ( Q, --· Otr<) o-- 1 = ( (){llr) (]"{0.)..) -·· u-tOt~c.J).

Is) Lf o-~g...,, -rr1= (0. b --··){co(---) (-e f -·) o/t.&joM F~ .:Jf <(!Ide&_

o- rr 1

o _, = ( (}'" (a, J v l b) - . ) ( ~:rc c > crt of J ~ ) ( r:r ( eJ t:r( f J _ _ ) •

~o c::r' ~ o-C/'r:r-' ~ h >~ c.Joi2 s~.

f!K. o-~~~ tr 1=- ( I ~ J (~ {"" 6 ) ( 7 g > (l..).

{4)

C)CJ"7c:J-J ~ {crtrJ o-n)) (crC4) O"fS> r:rc6J) (CYC7J crc8J) (a-(J..>).

7~ ,, 11 ~ 1" U / e- ~ $C».t..e Cjcb.. ~ _, ~ B o-~S,__, s.+.

rr rr I o- -1 z cr 'I .

L, r-w~ _&_' CT II= ( 4 6 ) (/ $ £) ( .l. 7) ( ~) .

o-= { I 3 4 b

4 s 6

3 r 7 8 l...)

a = (I Lf J (:J. 8 7) (3 6 5) .L 7 0 .

4S

t£_, ~ V tr6 S:q. / ~ (I 1-) C) ~)6"_, = (o-u> CJ'(J..)) ( O"C3) ~(4>) ~ V

S~M..ilfA,_ ~ C/3)(2..'-tJ t~~ Cl ~t)(.l.. ~)_

G, YO'j?_ f:UA~ S

,Jn twf~ rq xX-? X M~.,c.,:.a,+~ wo-U, [a_.. X__, X / [o._ tj > = AJ ~ L> bj.uA-~ , fA -1 =-{o.---1 -

Th'Wf ( ~ ~) Lwf G he a._ f~lke- .gvowp, ~ /~I= VI < oo _, ~ (';, U

Z5ow.~hte -to a swb3 vof Df :; n _

rtf_· X=-~-- GxX ~x / J·x;;>.Jt< 'rJJ,><t.X

ai-w,: f: ~ ~~42-- / i . .e . k~ ~ = f 1.1. La-+ a 6 /l(&- s I ~C> Lo.. == LJ X = Lt 9 =0 t~ {i!::::1.~

=) a.-1. = 1. (:;) 6;

=) a.= 1.a,

'il x~x, ~ orb :A vf x w. X / Dx = f a.~ { o.~ ~ } - ~ · >< -

~. G=- ~3 / X=- {I,J-, ~1 , ~><X _:;,X / rr. ~ = cr(i).

%r x~J / Ox.._1 =X -' ~-te.h~ (X:=.IJ ~ f 1.." (J. sd.

-yt,,_, . ( OJ.-ht+s- ~-+e.b:A~2.erl ~~o.) ~ ~ x X ~ )( ~ 0.. J~ tUAUsr, .

~ II ><eX , [ G, = >+e.b~ lX> J = / Ox [ .

~ " -()t,t.5 yt,,.. app /te.g io oo CA$€., ~"'~ ~ s<..o/~ r:1 -1.4:& e.ttrc.lvf:J ,.a

ow-e of ~ s~~ -t:Jpe o.f iMf~UJ .

e£ : ~ a. b!J~ f, 6j / s~~ t~) ----3> Ox / ~ ~b~ t~>= H .

~ f(ct.{.J) =OtX, liOt~G,. O.!X<=~. S'o flo,~.}).•=. D.>c ~Ch.

~ v.AU1-~ = Vf ac.I..J ~ h H , ~ b= 0th , ht~.J.

f- ( ~>H>,. b·.>f :::. o.h->q == o.. ct-.x/'~1-1 o..x ::: f taHJ. v

c,hu,k f '--5 oVJ?tv ' ~ .!1 ~ o~ ' -f:t.-., -:1 = o..x ~ son.v:z_ a. / s 0 3. 0. H ~A-. f ( 0. H ) :::: A. X :::. !1 . v---

~ f ~ ~-tv-~= 21 fto..H) = fcb?·P , -tk.e- o.x=bx

~> b-l a.x =>1 =) b -1 o. ~ H ~> ~ b H = 4 4 . v

~/ f 24. ~ Ct bj.a..ct<..n,, So [ q: ~~t~ C"<) J = / Dx I.

47

[X]a, =: oM ~u~ = l t~,j> / J£_t-<t-j~~-t] => / C><]fir} = ( ~).

C (X) { . (' I <Y (. IJ ::::./ J cr- ( .l.y::. l. } G1 ;::,.. O"c.>J-, ~ ~ CTCJnJ..., ~(.l-J=/ .

_, [G; ' Ca.,.,) ~ I D•lG, I ~> I~ Vi Cq '"/ ~ I [~J .. / ~> "'lo. ()<]/ ~ # (";!_~

---> I c~ (>()I :::= _2_. ( h-~) J

{t,w, L.e.t H ~~I /< ~ G, 5·+· WI);:! [ C,: l-lJ < 00) /11:=. [ G,: KJ < ()0 / ~~

[a ~ ( H/) kJ J ~ 7Vth .

.fi. ><=(G./~) x (Gr/kJ = {co.H,hkJfa.,h6G,J.

I X I = YJ;] h . De+~ AA o,_vl-U, "t G 01-1 X .. GJ 1( X_, X/

j · ( o.J-L b K ) ;::: ( J ~ 1-J I 3 b k ) ( d.e-vt< -t?,k<, 2-s a.~-~ a <>f-CAn, _,) .

~"" (X) = i s .:= G I s . (..&> IJ ~ ~ Jq - X /. ~ )I~ ( 1 H ' 1/<) .

~ ~~b61 (>o = f J6:~ jfJ. t1U, 1k) =z c 1.J4, 1 }<)] J

~ t1H,1k) ~ { j ~ I j l-J = rL sk==-1< 1 ~ {86-G./ j e 1-L 36 k 1 ::: H (\ 1<.

Ox~ X =I {ChJ~/xl =~M-

~ [ &, : <;~·b G, (,~) J ::; 1 ~I ~ J1;t ~ I /r.v1 [G.: ~.fe.b~ WJ J =: [ ~ 2 'H f"J K]

7?1) [ ~:: c H 11 k > J -5 fh n .

2». ~- a 14 · X= { H / H ~ G,}.

G, X X -')X ' l H = j' H 3 -I .

~w ~ ( H) = r j ~ ~ I 8 !+j -i == H i = N ar ( H)

OH ~ (~JJG; = l3Hj-t / 3~&1}.

=) [ q ' N"! (1-l) 1 = I 01-j I = I [/.JJ~;/ ~) [ ~ ' N,;, { 1-1!] ,,[1-J 1 Gr I ~. ~ = s L c J-, z J ~ )(=:: 2. '1-L. &; xX -> X ~ A· [ ~ J = A[~] .

Le-t X= [ ~] e. X. l,vr~ ~b G, oo/ Ox .

A~[~ ~J ' O."" / [~ ~][_~} / ~.b,c,o(«~} - / [ ~] /a,c.o:e:)-

s~~~!XJ= n: JJ I [~] ~ [bJ ' M,d6;ll ~ l ~ ~]I u .. £].

~of O!Ybk

cb xt:Ox ().-) lj~,je-X '-€;~ cJx nQ, ='? 'VI-' Ox:::;.C} {vf !3=-3r fvv ~"~ jEC,)

I JJ ~ s-e-+ o.f o.IA c:7Ybik ~ ~ ~ ~vtiri-WY. of -t4 MW~e+-So.1 31'17~.

()p- of k o~bv+- ~M~hz-er -rhVh , .Lf 1 ~ l:;t c:::oo _, ~ ~ ~~#-h 24 ~ -r-o.pp~ LAJ~ Th~ .

{Oxl= ja,l { 5-to.ba, vof

~.CD A f~L+e 3 k>"f ~

Q Lf G,-a 8~,

/HI==- p,., r?-J.

~ ct>.Ue&i{ Cl p- Jvvwp ( P7J-/ pr/r,-e) q I~ I= p r ' -ft>r So~ r3/. ..--

H~ <~L ~ ~ ~-t H z:s ()._ p-s~~ of ~ . z(-

~. rp 61 ~ 24 2 >< 2/J-2 -x ~ Z ' ~ {& I:;; ~ -:::7 ~ kS ~ .). - f1 ~ •

(v} G] ~ ~~ o ' < ,. ', () l'!..L.. r >> v;) 2.-<7v·0~_, ~r> ~a 0-s~vVWf>,

Th»~ . ( f~t ~low ~)

LB-1- ~ b~ ()_ ru Jl'f)-,;p ~ j> ~.2. b-e ~ rpr~ ~ k3-/ $.+. p I S2. / .9 . ~ ==" !J g ~ f 9.s) s 6 ~ f . l vvifj -thu 2s. tt (f ru~ Abflvn)

~ ~ tS2 / ~ s.s.~ ~ I>/=- pte. P'uA< a~S:.

Pef~ f= S'""*GJ (~) -) cq , f( 3) = J· a.. . ~ -f l6. Zj~e (V~ ! ) .

(/-lAMe» tAo I f kl -4 ~b { g.f4J,~(S)/.:5 { f, I = p"' . [) jvl~> f, S't4~~ { &)-'> s Z-1 0.... b:r·e-v~-~,..,

J . / G./ = ~ f<+r WJ ___.:::::> ~

pk.(J~)-=--') (G-,):::. 'f~-tr;', r~O-- P{;, ~{~o/(P,~J=/.

P"'-1 w.pk- j - yv,~ ... 71 rp/<_,

J=-1 I J

(~p~"')( l'l-4pl<~:_l)--, (V~-~pk-tr -PI': -+1)

1 · ..1.. s --. _ ( pr _, J p k

~) ') p (/52./)= r. ( ,ke rw-w~ p~ -fm- ckf or ? ) . We- ~ ....Q= o~, 1.) o!;J._ u ~ uO~-t / ~-o l..nl = -± {Ds- I .•

r,'f:::-1 ~

7h.rw. l~~.s;;;.n_ 5'·-+· Jp ( fOtvl)~ r l~w~ ~pci.JL/)::>v-).

9-o / q .. / == P~ v , g~ r > P~ v. 11

l ~I 1 o~..,l =

5o

~. w ~~I= p". ~ ) tdt~ P3-;L lj ~ p~ / VI~ I / Jol ( p/ 111-1}~ /.

L -M,ts CAJe. / ~ StA~VOkf p ~ bl IN~ I p / =- p n ~ ca.~ a...

f ~L~~.. ..,~01-ow p-~~~ 6f ~.

Cor_. Le;t Vp ( / ~ IJ ::: Vl3-/ ; p~l ~ a. p~-~ I -t£uu,

d) 3 evf l.e.a..s+ an..e.- !Jh:.-..v p- swbj~') of 6 .

!1. c.b /tv>pj /rt- %~ ThV>-1 ~ l<=h

(~ ;}ppb / s..f ~j~ -rf,._ ~ /<~1 / -t~ 3 H~p Svf· I H I~ p / Cl pt-~Q .

Ch:J ~e) s:'o H ?.!. c:Jd~. LeA H == < Dt> / ~ {~I~ p.

....A> ' p!-.l- pr~e. LV'MW!a_ P- r p- :tro~-·'-~. w. ~ k o.. -fw,v+-.e ~y()¥ / w Q ~x -) x k a. tJro.r ~ ~ w~-,~

X ~ tt {;,.,<4€ S0f. Pwt Xo = F~( ~) = f,q6,X/ j·X~x Vjc ~ J.

~ /XI 5-r IXol .

!i,. x~DxiLJ···UOX-t. '4 X~fXo7~ [Oxv/~)_/Qo 1 ~ 1 'l..L

f>-+DJ>G, CXtJ{

2-/ P ( I Oxvl .

.Lf ><~Xo >"> Oe fx J.

~ /XI ~ {Xol -+ .2:: I O>t.vl fo)f.J~l..

6N( ~ IOxvl I p => [X/-IXol/ e /cJxv/?L

3'"1

~r~ )..~

~>~-p+-C4J-l, G, Ot f~ike3vvwr / p~;l.. pr~l fc,l-:::rncz,, 11?1, sco!cp/q)~t.

II /-51<~ VJ/ 3 H ~ G; s:t. IHI = pk.

)t.ck T~~ ( S~ SJ~w) W. p~ Gr be c. ~~w p-"§~'f of G1 ( ; . .e · J rf~ P'1) .

Le-t H~l; I IH-1= r k I hd<~VI, -U,.e..., d 86 c; s.+. BH3-; ~ p.

n. w x == { j r 1 j 6 G, 1 = Gr 1 p . ~ 1 ~ -'~ ~ r = .1;* =- ~ • LeA- H aPt e-l-1 X hJ Le,f-1- ""'...-1-t;pt~ I b:; l~mA ~ Prl,

I Xol ~p lxl f. f0 . ( lXI::~ I r-eLOtHNV;j r~~Q._ ~;vHi, p).

~) Xo -:F f. Xc~ f~ X (1-\) ·

p ~ j p (£:; X 0 J ~ If h ~ H I h j p == g p ='/ !f1 h 9 p = p :::) s -i h j <f,_ p .

-) J H J-1 ~ p .

Cm: . lf p, ~ p.).. ~ SJ~tow p-tl-1'-J~'~ of GL -Ui.eN1 3 j6G, s-t. :r' p 2. 3 = p, .

~o "'M po.ws. Of SJJ~w p- ~sps ~ CO"jja.-+e ,

~ . np == # { P/ p ll. !jkw p- .st."J~'f ~t 611 . ,= # of SJ L-p ( G,J.

-~ ( Th~ fJlow) As$"'~ M ~11/2,{ / ~ MY ~

C/) hp I ~

{J.-) VI p s. p I

E£ . dJ C:rn5Wier ~ o,pti:,n of G, on X= 5!1 ~ p ( G,) hJ Co~'j ev42oJ-t I

lef p .o ;;~ lr ! G, J , ~ 9P ~ X""' ~~~ P ! G,) b1 ~ a~w... en.- . (11.-b;A

~ /></::: hp.

~~b G7 ( p) = ( j e <q I j-' p j -= p J = rJ G, ( p) .

r0

P~t > Vlp = I Op I= [_~: g-t-othG, LPJ 1 =:

{ 7'1 Gr { p )/ .

s;o

-=)

P11 t - q I

{NG,(P)I -

Mp I t . II G,

LA X= <;~Lp (Q,) / p ~X / C4z-.~l.J-er- ~ Ce?f:2cJh a( p OJ, X t:J Co~jj4+AA-r .

/XI==- np/'t / $0 fx/f.p 0. Reca,IA /x/2p /Xo/ I t8> Xo= F~ (~) X tt

p -') X 0 * f. p 6Xo . ~ ex t:X D -) 'g' X6 p / xc><x-'-= Q. (b'J CS<e)(l>)

s;o 6J...= p.

S., )( o ={P} --) /x / =- p /Xo) ~/u.g {xf =- p I

=)

pn,e_. Ltv+ H 4 ~/ ~ ~ G; I S'.J. G1=- < /-L I<> ~ Hl\k = { 1.].

~01V!Hxk.

~nJ'4~ (App/c..e..4,~) of S:r~ thw-/s

CD s~ ~ 2f rn ~ 0.. 8w1' .>.-t. /G, I = 77 I ~ ~ k:l. 2/77 2 .

-rw~/ ~ ~ C!Jd~.

L.w4 P1 -5 G; / I f>1/ =:: 7 , 11-r = I ~ P1 ~ Gl .

n,, 17, VI,,=.,, I -=) vr,,:::.[ . .So 0- Pn ~~~ I Pill= ~I, Vln=./ -:>) p,, ~ ~ .

~·~ 7, l/ ~ p,..~ / so P1, YIJ a~ ~d:..v -=--;> P, ~ ~ 2/ l/Jr VJ 2;j,4 .

5vppo;e. hb p11 nP1 /~ [r.,l{ll //nf/7 =) [h)=l -=)/,=1... c;]o p,()?1:::(1].

Th.e.-, Ozfp!J ~ o.bo~ P~P ;;? (t-te.eel -1-u V€+bfti G, = < P1 / P117 . ) ~-3

Lh+ L =. < P7~ Pti/J ~ p1 ~ L/ p/1 ~ L -=:> 7/1 LL tt/ ( Ll /

-=' { 7 I I L \ =) I ~ I II Ll --) [41 ~ IL/ / b~+ L ~ 6] /

So c; = L ~ < P1/ p,,>.

-=> aba.-1 h _, = :L -) ~b ==btL.

~ ==- < /-L k>.::: { 4b I 46/-L b~ k ) ~ Ctb=b~ II Ot~i.t h~k. ~

~ y;. t-t ~ k ---3) G, cu <f {CL b) :=-CAb / a~I-L b~ k .

'f u. ~ . 'f ~ Ot.. hvm~ or-ph~ n, / s~ cp { ( 011/ b1). ( 4 J__pd)

( a,b=l.4

=t.f (Cl,O..L-/ b,bl-J) == tLa.~.-b,bL = (a-,b,)(CJ:...hJ= c.p((o11_,b,))· "P(a...._,b.)

<f 0 D~e--h;;>-~ · /....a+ L~-b)c:; ker lf =.) ~b ~ 1.. ~::> Ot.=.b--1

3 ~~ 0..-::S- J-1 .~ b -1 c k _, H /l k == 11} ~ lls.sh,.. p+-ib~, s-o ~-== 1.=bt

So I<~ 'f = {u/u} _, -trwt.a./. ~ a.~b-==-1..

f:+a-e-e ~ Cr t-, H X I<

51.

( :3J Cd_ b c ) == (a,/,) C

A r-~ R u IAk1 iltO. ~J- vf 3 J_61< , s.-t-. 1. . Cl -=- 0. . ~ ::: a. ~ 1 Zf«~/ II o, lf 1< { <A'..s W!ZJjl/1-€- ).

A ~-~ rR_ 2-5 01. dw-~;,o,.., r' q 'R Zs iM,VfO.~ / 1.!-0 / ~ ~- Vat:R.\/oJ :Jb

~- d./ (/;{ / U<, C t-v;A-t, i-tS£14( -+; • , ~ a.~l /AVJ~ Cc-,..,~y....fM-1#€. r~s.

({)., ; fR / (0 are feel ol.s •

(/V/).xl-1 -f,.) z.o 0.. n.o11eo~~ ~AYril+~j' f'i4j' / ~,vV/t, 1.= I.L

7 ~ trf.ls ~~to+

?l (,(WtoWh ~ ( S~IA{.a...- ~r~) . ~~ r~

ex. #-1 iM ~ ~k / {)._ ~~IA-!I+l~We dwi6Zvv! r~.

4 r.x]-= s ~Dkx~<, £-t?o, ark € &- J I 1'-::o-o

_io_b-~'~<>,._.CA.f H~-

J< o UO ::: { -fc lR()qJ }-fc b)= o } _,

" J( [.X]

&x w R= Cl {)OWl~~ w,LAD.v:J ~ / Gr=- ~ 8VI7"f .

RG, :::: { 3:-~ C.J. j I s~Gt / c.J e R 1 - { c, j,-f c~jJ- +- -· -+ C~:J~ I j '- eG,, C._(;R}

{3!CJ:fo] fi4-t~ I • ~1 o/o~:-. _,.} k d~-tr~b ~iAr.t , [ 1' I ..-. -r 2.& d.e1~ ~ Cor1-1POl-7-eMT!.ui.&e-- . VJ ~,~ "'J v 11[_~

~ . Lhl ( 7< , -t , · ) le- t1 r~ ~ -l:h.u. D · Ot = a · o = 0 t1 t:U R .

~- 0-= a-to -> D • Cl = ( o-+ OJ tA ~u o~..,. o. a_

0·0..:::{)

ol;s b~ a.hove P-f. (:-1 )·0.-+ 0t = H)-0.-t t·a. _ (-/4/)A. = cJ.£X = 0 ='> (-j).Q.=.- -a...

~ . R [ cxu ~ == { ! a Y1 x ~ f Ot., ~ 1R J

-t , ( ?. a., x~ ) -t ( :2: b..,~<~ ) == 2: ( Otn -t ~ J X h

. .

.

VI C.,= L: t:At- bn-;,

~;.-(/

Jf< [){/ x-1 J =:. ]R [X/+ j ~ =. { -i.O..J< Xk , l,5j / ;:.,j ~ ~ j . .,., o.Uow rn?jD-1~ row~~-~== i,

~. 1<-~ ,.~, X,,--·, )(~o:_ - ~~ ~~~ 1/0...IA~ &=-'7 X;,Xj = XjXt.

(<r_x,,-- ... XkJ - -po~,.,o~~ w~ ~i.dewts LA-, R i;vt V41-ZA4~ XJ,~.J)(I<..

t;b

P#-. L0f V< b.Q_ A- r' J' A s~set S c: R .4 0.. >~r~ ?f

d) s ~ A. swh8.-o~ of ( R,-+) tJ~iXm' s.::; R - swh~-~

(.l) s Z0 dv~~ ~er 1"1/N{tfl;CA+~

lS) <:hL (~JR) ~ ti12.,2.. UR) u t-w+ a s.Jh,.~ ~ b~-e GU2-.i2J ~ wo+ ck.seYf w.J.~ a.afdb4-0>v, Vt-t MJ..l.- en<..) .

C7) g == i ·-fvo £d' [.'/Qj j -fco J.= o j :: / l1o -1- Cl,~ -t · -- -f O,,.X' 11 J V1~f) , tiv~ ~ / Cto=-U} ~ dtZ:X).

2.6 c.. sv.br~ .

( 8) T::: { o,x / a6. 2 J s;; p[XJ , ~-1- o.. ~..Ar-~.

JfZ.J-OJ?e-.-+~-- U+ ~ Ire ~ riMj :

ely Lf S z;_ fi< 20 t't s~~-~ vf 12 _, I c 5 ld tt s ~t.:J v.f S / -#uu, T.c:. 1( ~ a s ~ r~

"f 1<..

4 s;o( s R ONe St-~bl-~_s ~ o<.G/J,, ~ () s;O( £. R to a_ ~LNhr-~ de/4 v

(.2-)

(sJ Two -#wi .. ~.A &~r~~ : 'R ~ { o} .

+I ;6

~ R be a_ Y~ / Y C R A .>wb>d / C-onsi:.ef~EW < Y ::> _, DMcircJ 01-<::5

-tA? StAbJ_ro~S J~ '?J g~~~ . --

(?,> <Y/ - /I S ~ .:-s a. s v.t .. ~ or- R y~ $

/

<;;., ~ 13)~ <Y> ~ ~ "'slt-1.4t~t-" s~~--'71 ~+4~~ r/ o.rzP~ '* Z--:s ~

-t~ subr.t;:;_ "-{- R ge-v,ed~ b~ y .

~. L-eA- R ~~ S ~ r-~s . A rno.p tf: 12.~~ 5 ?-s c.aJ{eJ. tL-

_!':tJ hoVf'10I'r,c7)rfhtsn, if 4/ ~A, 6. R /

Cf ( Ot+ b).:::! y; (CtJ-+ 'f Lb) ~ ~(Orb) =- C(J{Or) tf (b)

~ A ,..~ h~~t,~,._, p~~ -+ e.,hS>{ • of --fhR.- do14-za~ ~ _

~, Lf 'P· R-:> s w t:t ~ h~~~ ~ <f: (R .. -tJ-'l~~-+) t& ~ h .. tt-.on.~..,

~ -two c:vb.e4:..a.n ~ / ~ c._p ( DR.) = 05 ~ ~ 2 , 1-1?.2. _, '{J(O.)-::: [aJ 11 , 4 CL ~ ho~v.

oJ) {[a. b]) = [ [(:(],_., [b]'-1] ~ Ot r~ ~o-T C of [C]~, [o/j,_. V

b. lf: ~ [ ~] -~F. ~ <.p r f) ==- fr .fl:J , -f = ~.,..,.a,~--~----+ et...x"' 6 -a [>tJ ~ -fr·.G.-J , P~ .;.... ~ .

~ 'f Z-d 0. ~---~ ~ .

ex. L-e.-+ ~ £R h-e ~ ~z-,1,,..~, o. <E= 'if< c.;-.bv+ra~ / def~

Z6 tt r~ h<O IWJ.

CfOl : g [X]~ R / <fo{ (fr:: f ( oO;

r! po'JHo'-(..4,& 4 x11

vvl4-l,

~~-{-row. s -t/ 57

Le:ot c.p, rr2_ ~ s be a rru ~WK; / def~ ~ k~ :?f cp /

f<e-r <-f = { O&~ R / <f(D.) =: Os } .

Th.u. dJ k~ tp :::; R ~ a s,br-~

l~ V C\ ~ k4- 'f / be: R / ab ~ k&- tp / b t:t ~ k-eA- t..p . ~/ ke.v- 'f .::3 !<. .

Pf of r ~ J ~~~ 0. b k.er1 / b e R , ~ t.p ( q J =: Os .

~ Cf (abJ = ~LW· ~CbJ = Os · l.fJ cb; = Os

S b cJ., E k~ Cf .

s~i~ / bo. ~~e. y. Fw~ c l-J, i7f!s o1,v~ ~ ke- tf u cios-e4. ~er. n.wif;,pl~+ior, ,

(/; ~.$ (R.,-t)

(~J V o. ~ 1 , b ~ R / err6 ~ I / b 0t 6 I .

~of4+~ I ~ ~ R ti

~c.~ q- hN~I >"'-t.:.,t~Mfs.

tJ1:rl-e , (..>..-) 0 S~e-..- ~,_, Y"-e.Jt~A"l+-~ L -«; k- ~ w...c~~ ~-1-tplto..-l~n/ J.,-.e-e_

L es o. ~ubr~ of 1< .

J!:1. L-eft r]2. ~ S k r~s / okf~ R.x S ~~ / (C./b)/ ~~R ,_ b~ S J _

w-e. Ce..£.. cJ.e..f ~ • , -1- c1Y> R, S p-o~~..Q_ ..

(Ct /b)-+ (C/ c/) = (CJ,.fC/ b-fo() / (0.~, b)· (c/o()-:: (QC/ bc4J.

Thu. ( R X s / -+ ' . ) ~ Ot. ~"'7/

&-:X w R b a. eo)l..~~w.e_ ~~~y "~ / et t:: R

0e1~ -Mte- pr~c~pcd z._deA/ J~~ bJ fl.~

( a):==- ( b o./ b~ R j ~ R

~, ( a ) <d ~ Sh-UJ.,~+ z.dae;{ ~a~~ a .

~p~ OJ.., -8f...e_ etf4e,.._ s ;.ole_ rp~-e :

rb 2 2 ~ 2 / 2.2 = ( ~) ().) f f ~ -;]l)q] I ftoJ=-0 J Q ?. l.X]

'' (X).

~ ( &_.o-0~ r~2 Lei r<. ""-' A- '""j, _L..::! R . W !1<./ 1 , +) = ({It-t I I a" I?. L -t )

b.e ~ tk"~~ JWt.p t'f ( R~-t-) . ~ • ~ R/L :=. I 0.-tl{ a. 'R] cl5

( a.+l). ( b-+~) := a.-b +l

~ • 20 ~~VeM-def~ 0.~ ( R/ ~ / -+ I • ) Zo 4 ,.~ ew..d ~ CClU.eo{

~ _JIM1t~ r-~- 0f R bJ L .

Pf. • u vv~-olef~: *W?.- -t-o ~ if (l-t-1:. ~1-+1 1 b-tl:::. 1/-tl/ ~

(~-tl). (b-tL)= (Q/-+l)· tb'-1'l) <?-> ~.},..,.I:::. O/·h'-+L .

t3wf ~ ~ a/- a.+x .,. '>)c-L o....J b1

:::::. h-t .!:J / 'JGl/

5o Ot 1' b I==. (0.--t-)(').(_ /:rt !:J) = Dt-b + O.!j-t X b -t XU !,vi:#, L ro. ••. oo v ~ / X '.h 'X~ e: I .... ~ ..1 24 ti.A--1. ZPle-4[. ~v o/-b/ = O.b-+ c ~ c~l =.., 7 tt· b-~> I = a.'!:/-+ I .

C/</1,-t,·) Z5

J<~k: c-IJ 7k .. 0 .. iM R/I ~ OR.-+ L

{.J-1 Lf- R U:, C-oh-tWI ~~ / ~ R/l ::& e,.ow,w.~+W<e- .

(3} If R Z4 kJ.7 i+e.0 _, ~ R/L i4 ~i:+S,J wPI-t, iR.~I = j_o/z .

~. L-f ~: R. -> S ~ 4. ,...~ hd'M.>'-.:n-phu""") -tt,~ /<~ tf u O.e.. ~~ .

Coh'v~~ / i"f L ~ 'I< ~ O.h ~~ w. R 1 ~-e.., I ~ ~ ~.et-~ of So~ ~ ~ol4-ov>-pl-ttsn..> <{J: R-') S: .

~ ~: R --7:; be- 4 s~evtWe- r~ h~huw. / ~

f</k.e.-<f ~ S j a1>w.~hk M r~S.

¢1 , bet~ f ~ R../k~ ~ -3> s I -f- ( CJt~ ke..tp )::::: cp (CJt) .

(J) f 41 V<--0lll - b{-~ . Lp 0t -+ k.e..-c..f -:: ~ / + k.e .. r.f / ~ o.!:::. a-+ X_, X~ k.Qf. 'f.

1 I.{JOO""Os

~ c.p (D.).:::: <(>{CJ..+X) =:: Y>fO.J+ 'flOC) = tp{O.)

s'J~w-e- s~ y u SfAIV~W--

c£J T l-6. ~ 1-~ ho1no~f,~w, • -f ( (0,-t l<~'f)-+ U:,-t~'f)):;::: t ( o.-th-t k.fM-lf)

.:::: cp ( Ortb) = 'P l Q) -t VJ (h) =. f ( 0.-t ".er ~) -t f ( b-t ~.e+- tf).

f ( (C\-+k~¥)· C b-+/cM-I..{JJ} 2 f ( o,.h-+ k4-l.{>) ~ tp (Or·bJ~ ~(0.)· <fCb)

== f ( 0.-t t<~ ~) . -f ( h-t k~ tp)

u~/ f l& Cl rtJ 0,o~t.~~ ~~ /2. /k.e..c.fl :: s .

lf: ~ [ ><J -;> e / wtr.Q,.. f* ~) 6 R Lx] / ~ tf> ( + J , = +( u .

~h tf 4s 4 r~ ho~<Aorpt,:-s,W!. ~ {<e,.. Cf .

Obs.~ ~ 'f cx.z.-t 1)::: 1 ~I :::.o ? s.o )q .~..~I G 1::-e.- <f.

Pf. (J) (Xl-+1) S- k~ tp. lf +~> ~(X~I), ~ f= qoo·C>f-+{) ~> ¥(fJ= 0

-> f G k~ tf.

(i) ~-e,.. tf £:. Cxl--t 1 J · LeA fz>4J ~ ~* tf " ~ fvo .:: 1 (>9) cx.l... -t IJ -1- reX) - qw0icn bj cxJ.. -1- /) / ~ ~I t'C: k. [:x] /

~ crJ~ ~~ r: 0..~-4-b .

--.-) +i->== ~(Lr} cll_,_,)-f rf"-J } ~u -t~ ~-b-~ ~ fri.-J=-0

c-) 0 = 0 i + b C=> a -= b ::::..-0 <'b) r a 0 (?) -P-vc;= ?,ex){;( l.-+ I)

C=-') f ()C> e O<J.-+ I) .

~~ t.f> L5 owf-o ~ ~ ~ CA,.h~RJ 'f (0.>4.~h) = 0.~-t b 6 C,.

9-o ~ 1..s-f lso~~""' ~m/ R l.>4] / (X2+1) '-" C .

~ . ( ~ R.~ ls~h&.,.., ~)

&u 12... he- a ~--~ / A ::5 R / B ~ R I ~ A ..,. 8 : = r Ot-th J 0, ~A / he B j ~ R.

t>M.Of B~ A-+8. ~)

(A-+BJ/B v, A/ A/\5 .

Pf · s~ ~-+13) /e ~ A( AA B. ~~ -n, ~ ~ r<l B , r.: <XJ: x-+ 13 .. ~I<.

~~ y; : = n I A=:t::S : A .fS -~ r<./ B . ~ 7{ ,. ~ 4+te- ~---~ ~h-u:> . A

k~ n.:::f> . ~e... t.p =- AllB . A-n..t ~ ~ of tf l6 A-t 13/

.So t.p/• ~ ,4 ~ A-tB/B U ~ ~ k'{J/ = AIYB

~;v~ <f/ = tp~, 01-~J ~'J ~ ~ s~ .

'tJ { s+ 1-sv · !~'WI > A/ A /1 B (,., fH B / B .

~~ v ~ Lso,...u_:p__h~u-. T~ ~a. -·

LeJr R b...a.- A ,..~ I 1 ~ R / J ~ R I .> :+. I c. J ~ 12..

~ JjL ~ R/L w R/J ~ (R/L)/(J/L).

Pf. fte+~ <p: R/1 ~ ~/J / c.p ( CJt..} L) = a-+ J . ~ 0 4 ez..-11> r~ ~

I<~ <f == Jj~ . ~ /~ ho~o~~ 7h14/ CP-/LJjrijL) ~ R/J .

~. h o.. r~ 1< 1 ~ ~ vf ~ ~eA Bf 2-G/eefs .& s-t£,1( tu, Ldeowf.

J1 4 .:o o.. y.,v~~ "f a r~ i< _, 3 a Sk-t9ot1ert ;_dee;// ( AJ / Ccrr-rf-ol+.!:J 4

~~ tAJ= !li 1 l~R . .h.~~~ A=faL LAJ=-(aJ~ ~ A;=L

1:- ca.t1ee{ ~ p1-~ta.1 UeJ. ~ Zo/etJJ[ ~~~ A ~1.

_b!J A .

7~ ~ 2 I o.;l1 i..GI~ ~ P'"~:pa-1 .

1i . 3-p I -= d. " 1 = ( I) , ~ p~~~~ ·

~""1~~ 1_ ~ >~ crt~,.- uie.t2if. L.et- n ~ ~ >~t fo51Aw~ ~-'~CM<-b-er- ~ 1.

Lf m ~ l / ~ Yl1=: ~h-+ r ~ ~ O!f r< h.

W7 6: I / 1-.v. C:: ~ bJ d.ef / s 0 r <5:]_ . 8._.--t r-< Y1 0,~ kJ ole.{- of h_.~ r = D .

~"0 m == ~ n --> W1 ~ ( h) =/ 1 ::::- ( n) .

-p.wt . )1~~ ~w I< Z6 C( r':J l;vtft, j_ / ~ AA zdeaA 1 1..5 r-~ Z{f- :L J L

~. LoA- 1< be a ev~~ r~ ~~vlfi, 1. . ~ 12.. ~ a. ~ UfJ

~ m-rb iA.e.e.l' VIII l< ~ R ~ ( 0) .

r£, [2 .:0 Q fiA.J ~-:> R. Co a. Cck-.~~1-l.-<.- v'-'1 wl<h, .1 !i.-4-. q 0,.~ o / 46- R/

;I tA -1 $ ,-f . Ot Ot -1 = 0.. -j ~ = 1.. .

( ¢z) ~ ~ ~ L.d.e.A,~ 4t--e ~ M (o) 0 ~1A>~ ~ fh..cfOr/ ~

(~) 1 o.-f0 1 ~ ({).)::=7<. _, ~o i.<!f: (oJ=- { bo../ h&12.J , ] b~ svt. b4~l

~> b -= a. -1 """"> R 0 a. f~ 0

( =-)J s,...r~ rr.< Z-s o. f?eb! DM.O/ -ea.k.R.. o.~ ~ Lo/eQ,/ L ~ K 0

..J. -t b.J oboue 71, w, L.f I~ (o) 1 ;I O.:fo 1 CJ,t::-1. 1 ~ tt Ou:;:l =) 1.6] -~ I:::: R. a 63

~. A Wl!hX~ Zft(~ / ;1/1 / ~ {). ~'-Vvtj R L& a Me-r zdeo1 {s-o M~ R)

s.-t. ~ ~ no Z£iee.l .L ~ 72. wbl-t, /11 ~I ~ 1<. 7W 0._, ~ ~ ~

~ ~nip~ zol~ S*~ ~~~ M.

if< I I u Ot f ~ Lff ~ u ~ tl ~~ z.ei.efJ1{ •

Ef-· (~) S~ 1. t& a_ M.a-X~{ J;/.ea.) ~ ~k M 1</.L/ ~

~ rj_ vv;,fl-. r~ R. ~ Lef.eA.Is Vl-1 7</1 ~k.. L ~ ~~

~ CJ).~ o-.!J ~ p_ t7r ~ / C¥ko/ .L u ~ -fh.e_ ., 0., ~

12-/ L / tkol Q ~ ~ WZ.,.:.k- R/ ~ _, ~ ~ ~ww~ Th-rn __, P/l 0 a fi.aJ4.

( ~)) 4 rr<../ ~ Zo ().. f?-eUJ/ / ~ ~ o-»!J ZPUuJ s; ~ R./ 1 ~

t4l ~ ''o'' = 1 .. ~ ~ ld ~~ ,

Lv--twv..er J.-8

rp..olp~~ ~ ~ . k ~ ~~ r~ 7<. ~Nv+h 1

c(J l.f ~ ~ V<. , J .1 'R. / ~ .1.-+ J ~== { a-16 J tt~L, b<G:J J -:E R , '-:> ~ sw- of 2- 'i.td-'2..4)J

12--J 1-f s~R, ~ <<5.>>:= { 1:\,:xl-1'···-+ C\k~t<J 1<~1/ .xL,e.g, c.~6-R) ~R ...

~ << S::>/ 26 ~ ;_plea_( J.e...~ 9!1 g · << S >) u ~ sr-.-,.Ait1-e.&i-....

1 4 f2-, J~R

(3) v/ I ·J ~::. f 0.1 h, -1---- -t Clt<bk / k~l, ~-vel-, L-:> ~ p-.oolk-Vf-- q- ..)... zaie41-S

~- f-or 11 ~.). / VI£ ~ £. L5 t\. Wtt!.>t~{ z_o/~ E?> Yl l.s tl f>H4M-e--- •

/JU"\)1

DtM JJ.~ 4{ ~ ewe prihe:r~ , 7'4~ fo~ ~ ~ c:W( sv.b(J~

"f a ~ ~c1~.

Ex. (X,Ij J ::1 (Z[X ... ~J no+ pr~ cq>cvf .

~. ( ..l, XJ ~ Z LxJ ~ p~vpoA. (.)..7'>\J:=- {.)..·~J-t ~·jcxJjf ... 8 6 ~L>O J

( ::>.-, ><J) ~ J< l.>qJ 2..o p~e~{ <S~e..e.-- I .:=. -1)1.:>_ ~ (2-, X) .

Ntn-v.. R u ~WI~ VJ/?1--h 1.1:0.

cJ) R. t4 4 fCAdd Off ~ Ol'IJ ~eek ~ 7< ~ R ~ f o} .

fi, C --> > Lf rf< 2-& a ~ / ~ zA.eo./ eon#~ 1 2f hvf- £ u j .

( 0.) == 1< 7 s 0 1 6 ( Q)

~. ,4-r, ~-t_"'Jrcd domOr~ Z& a. Coh->wt~~t-to.-twe r~ wH-/., 1.=f0 s.-t. \la~bc-R;

~ f. 0/ b=f o , -U.e+-J CA. b :f. D . ( fr'TQ..Q,~ , o..., /M~~ f don-ta~ hAs h-o 2:~ olwuCl--s.).

~. 7k -p~w~~ ~ o..~f Cf-..~ro,{ ckn-ta.~ ..

-a: / Q / JR J cC I 2 L~J J IR ~] '

?:».. a/6z u hv-( ~ ~"1-fJrll( cion-tl:<vfJ / ~~~ [2.1. [~J..:::: 0 .

~. R >< If<. z.o ~ ~ ~t~rt~.f oioWt D. lA-. / .s~ c f, o) . { o _, u = r._ o _, o J .

!J?:T. l.f ~::1 rJ< lo mAx~{) ~ 1 ~ py-~.e__ . But ~ e-on~ l:s f4l~~.

Pf. 2>t{o1 ~2~Z ~ 0. t-ok¥\+..ey~a.1)l.e.. ef ~ Ccn~,

~ u., f</L ( a-tL) · (b-tl):::: ab+l = 0-tL CJ.b El . / s~

f3u+ Ot-t-1 t- 0-t~ J b-tl 4 0-tl / f).v ~4t; ~~ d t1.d.,5 0>--~ •

~/ .s~ R /..& ~· I k/L ~ a. f~, P--/2 ~ ~/ so h.::>

66

~. LM 1 .::1 f?..' ~=! R. / ~ 1 ~ pr~.e 2{-f R/.1 ~ 4h U.f-<Jro./ d~. pt. (.¢z.) S"'~~ QS ~ ~~ 'P~.

(=)) S't..p~ l 2.1. ~ / W Ci-fl=iO-tl. ? b-tl=:Ao-tl /

~ {),, b<!f~ / So c..bfl s~ 1 u p~r~.

~ (a.-tl) · (b-tL) =. a.b-t l =f. 0-t I s~ ~hfl

9o R/ ~ to a-,., i-h~f do~ .

~ · cb ~ R ize C{m-.""'~ tr~ v..-Vft, ~ =¢ o . L-et 1 ~ R , L =I- 12. /

~ ~ ~.i.vts c., ~o.)tJ~I eoleo.i( J ~ R / 5,+. :r ~ J .

02.~.. -bi,0 ~ ~ en Zcn-e-/~ {~tn.J)..

c lAS.~ e.,.. ;:it' ~ ~

0,"7 ~-kcJ Y4l cW ...-ul k.t

hwl- ~vt ().. +~

r!;z ,~ f ~ / ~1 hc'2, hiD] ~ U. fX. vv12.- ~~wl2.-

\:y --ehA-4 WI ::: ~ ~> w.v/-:::1-1""'/ /0.1--1 /\../ ~<l+Ul,, ().. fudA V1 y,/

N -+~,~o ~~~ +a,_, 2 ~ cQ ~ ~ J~~ -tv ~-u-vt-<A- fudds

~ X:=:, f (~,b) J ~/b6R_, b=t-oJ / ~ a reW.+INh rv ~ >4 ~ ~

( o., IV "'-/ ( o/1 !/ J ~ D~b1 = bo/ ~ 12. .

~ . 11 R iO o.~ ~~ro;l domtlkt ~ X c..r..d rv ~ d.~~eJ OtJ Otbwe / ~

/'-./ i0 AA et}!I\W a[~ ;-e;/ O.t~ .

pt. ~ lo 61~ ~.»e ~ fjw.~Zc-. ol,~ -e+-4fv.s?1w~ .

)VI~ (a, b)--- (a', h1) _, {a1

/ b) ~ ( o..'/_, b') ~ ~ ~ cU1 ~X

'1'\ AJ/f V (, -'G. • 1..-\10 - b ~ = 0 .

s~ a.b/- bo/ = 0 1 ct/bl/- bj0../1 = 0

==--> o.. '' (A b/- btl;==-o , 0t l o/ I/' - b' a,11J =- 0

:::::>-) lA Q ~ b - o/ c.'' h =-o 1 0, 0, I hI/ - 0,0, t, h' =-(}

~) ao/hf?-D./c.."'h=o

:...-) o./ ( a. I:/' - CA..'' h ) = o

Cas.e j_ . c,'=. 0 Cvbl::::. b/ o..'' 'C 0 / s 0

~ o.b II- Q!l b =-o • ~)

o/ -t-o. 7/vx.. c4 ''- D." b =-o . (~.

D

~ '·. ,,

7hnr LrJ4 f:- b..e- W1 c;,.,~rtV! clo~, -&t,;u,

u) ( ~ ( 1?->1 -+) . ) ~ 0.. f~~

( b, b.1-:f.o s~ b,.Jo/

b;;,.:Jo/ R 1<3 tl'"1 ~~1 dv'/'h.a/...,).

()..-) rwr~ <f: J<-3> ~c_({L), t..p(a)>;: ~ I~~ f 0 4h ~'U--tWe v-4 ho~OI>1~~H-J.

fl.. cJ?

(>)

f~, d,ed-:_ ~ ( frtt<- U2..), -t, ·) l6 a_y-~

~ t..-e-- h.4ve "'{' ~

~ "' 0" ::z 0

I

~ ~o,':J.d~

~ a =f ,. " ~ b 0,

tp (o.,-t a).-J =

'f (a, Cll.-)..::::.

,, ,, _jL PC--(/<.J, i.e. 1= [cLUJ"= ,

1M w... J-"Y~!RJ h 4~ L/ ~ ~:pi!Ze4+iAJJ- ~v~.

a_ =f 0 ) bf=. 0 11--- ~ k ~~ I

c.2:.. ) -i - __b_ h - (A .

~ ~er tf = f tl,_<f=f<-{_!f:. = ~ J ::: / ~~ P-/ Or::: a} = f of . ~-o <f Zo Uje<-t~ . U.

~ -u.~ ~~ ~, 0-v.f~ doh-tfJh-. R 0 ~w~ Vl.. a.. fi4I.DI / h4H-.~ / '--) cnr Ql.t-. b~

Frow ( R.) .

BJ Thw./ ~ ~(7)'\., <f::. F ~ ~ LF-) Z-s C,j~.

~ LeA- -} 6 ~1_), ~ ~ t:vb-1 e: F D.ki>{ <.p (D.b-'J ~ o.;-1 : f >v 'f ~ c::>vrt-o =-) cp LA h0Q.M-~ =-) ~ cp) ~ F .

~. Lf- 'R. l.d Clh M7J Y'OI{ ~~ ) ~ R (){] 4 au.. "?M~NJ.I/ clcll1o. lh .

~ Fr-O-£- L Rt::xJ) = { J~ / ivo, J ex)~ RDtJ-' j.:f.o J / ~ R: = FrlU- c R()qJ; to ~tle.e( ~ __1~ '1- rcriwh44 ~~ .

'/5wf .evu. »"~ / ~~ 2 ~ ~ 2 ~ 2/W!, 7: a..~ r~s . ( Ql,~ e- R.e--hV).~)

-rtn-11 . Le-4- R. bB 0t ~ ""~ r-~ ~--vbfl, 1 -:1 o , tL g ~ 1<. g.+. A -+ B = R .

~ lf:: f< --7 r</ A X WB , 'fCXJ= ( ><-+ 4-' x-+ 8 ) Z5 a._ sw:jee--1~

v-wy tt~~1htc.n, wvih I<~ Cf :=; 4 /1 8 =- A · B ~ ~ /

h:J 1 <;.J- Jr~ 0.o~t,~h-J ~~-' ~ ~ -(}(e_ {r>~ !:}fJ how,o~phL&w,/

R/ 4/)B :::. R/.4 ·B ~ R/A X 1<e;t !1~B-' sA. *+!j= 1.

~ Cfl>qJ== (o)l)-= (o-f A, 1-t BJ" <fi(IJJ-== c1,DJ= (1-tAL o-+ BJ.

~ ( r-, -t A, r~ -1 P,) {; 'P-/ A )'I r< / !3 h..e- {J,y-bVfraj /

~ lf ( n. X -+ Y't !j) == lf ( r-~ X) -+ "P ( ~"'t tj) = Cf C Y..J-) ~ CX) -+ Cf L ~"'t) '-P c ~J

~ <.p C Y..l-) • ( o1 I) -+ 'f C r-,) · ( I J o)

=:: ( r-, -+ A/ r.l. -+ 6) /

'-I u. sv.":]~ .

7k-e- d€f <>f c..p Vw,p liJJ-8 -M.a.+ k.e.-. tp = A 11 B .

7twn A · B c. A-11 6 _, s ~ ,4 .:1 R / B s. R .

~ c ~ A n B J c. PP ~ 1 =- :xr-r !J / tMe J..e4 c ·l == c c ~ J <?> c = Ck-+ Cj /

~ ~ of A · B / ~-e s~ ~+ c. E: A · B .

0

lfX lf jcoltWl,n)=-/, ~~..l, ¥1~..lJ A=.w.2? B=n2 /~ .4-+B~ 2

A-1$1) J A 11 B = J-1-1)., 2 == A · B .

s;,., b:J ~ ct,~ ~ Thh-1/

Mi.. 1/~ ~ / I D( ~.f.]/ P 0 a Sf~- ~ ~ U.e.. ~ ~ 1-v0 Y1~.l s.t-. h)._/ D).

62. [ ,fP J -= ~ .., (.IV) ~=- { C)-f UD I a, b 6 4;< J ( 9o 6( [,/DJ l i< (.JD)) ~ ~ jie-1~).

T~D==-1/~

d)_ [ v] = r Q-+bv/ ~I h~~ j / -k GAk.!1&lAh ~.~.s .

2 t,f() J = 1 ~-+bID 1 0r /be -z. 1 ~ ~ r JD 1 / -a c.roJ zs t-o .. + a. f.·eW~ .

1-f- -R P~ I (~ 4-) , ~ z [ '-+~] == I o.~ b ·('i{?) / tLb~z J::: gz [JDJ]

~o~ d [ t-t{£7J 0 Cl, f:ek/ ( Skc.rv D::: I l-M~ q)) .

'Q.#_, @ = f3 ~ = { d Li¥3 J / 2+ l).;j I (I'M) r;{ 4) -d.~ 8 u C~J,;t{€,#( &[FoJ /

£ [ 1-t{D] / 'Lf D3_J (~ Lf) -#,~ r~t.!:fJJ_~ 4 Vqi;...e_ N.- Q [ -fr5 J -7 tJ. , ~ f~ "'~ ~ ~ t.!D 1 == & ( Ji5).

N ( a-+ hJD ) : = (Dr-+ biD) { o.- b.fD) === a l.__ D b .J / a , bb {)_ .

.If a.. ~-d/ ~ o" ~ Ot-t b fr) .:1 o / ~ 1'1 ( Cl.-t h$; I o .

~~ Of N . ( D~ I/ s1~ -~ ~) .

ciJ N {O..-+b-JOJ=O bff ac~b=o ". (~) Lf a/b62." -u~ Nfo.-+bfi5J~Z.

C3J f'l (r:X~j =-N(rJ.>N((3}

£4J Lf D~ I c~ 4) ,

eX., f ~ ~ [./D J .

\7' q? b ~ ~ / N ( 4-t b '1!>) E 2 .

r~. ~ D:P I ke. 0.. ~1~~ Wt~) w & = 8f><UDJ --bC..tz r~ 1- ;,.,+~~ of aL L-/DJ / ~ -M..e- i4.~-rv~:>Le_ Si-vb5e4 / Y = { 0-G::. oj N (~J= :± I } .

.X I <3> f 1 ££ CD w d. 6; e -"> 0( = ol,-1 e.e , N (I)= N (d-o._,)::: N (d.) N td.:J,

~ 'N {I) == I / s:~ N ( o() = :t. I.

(i) Le+ d.ttJ•/ sA--. N (ol.J= -t-/ / at= Ot-+bw~ W=~ Z1 -pJ- 1 l ~ It) lA;;z J-t~ q- 1)3-/ (~ Lf) w 1N' = 1--ID

./

~

7/

N ( d.) == ~ ( 0.-+ b W J ( 0. ~ b W ) ~ ~ Ms4+-w-., N C cJ- ) ::: ± J ,

_=) t (0.-tbw)-i c ± (t~+hW) .:. 8

{))4 == { ±.I / -;t. X" -t. X l. J / X= 1-+ ,-B ..}._ .

~ ~ D = -I / () -= 2 [i-] , 8)4 = { .± 17 ±tj

G) If D < o / D ::f-1 / 1):; - 3 " --u..o., & =- { 7!-l } .

@ Lf- D>o, ~ ftJ~f"==loo. ~1< a.+ a.. ~t-J.f'Le ~ ~u.)

..1-f /)= l / () : {) IXL.JIJ -== 2 WI] ~ ( H.f.L) 6 ()Y- -U..tu, ~ pow~

'T ( rtf.i:.) / .·,.a . ( 1+5 )1-1 / u ~ 014 / ,_.,.,~~ 0-+.JL/1c. t)~ . ~ :1 ~f;....,·~

~~ vt~-v~ ( 1-t-5;"' . c;-.> JO J- oo J lJ..tjj:J - .

~j)o'Jhoh·,~U) .

~ J2. ~ o.. ~...._~ r~ vvvtt, 1 / ft)qJ" ;tvo G: Q[){].

~ ol~ D.-= D , d~ -f :~ mO.X { zija J o.._:;.o J 21 ~J: ~ av.>q~ / ~Ji 0. L.-=-o

fA~ . (/) ~ {f+ j) _::; MAX ( d€5 f / cJ.aj j) .

{:l.) oll?j (f· !J) :5 d~ -f. + oJ.ea J . ( b~~ ~are_ ~J b-e Z.et-v olwZ&or-J).

(3) lf R. lo 0..h ~+~ra,[ ckwtO.~/ f =I 0/ j.::l- 0 / ~

d~ (-f. 3J = ~ f -+ d~ J.

& . LM- R- 12.e.- o.. ov,""'wt-o.~ r~ wlA-i, 1 'l w.~" $-t,.ep~ R 0 ()t-,

£n~~ra.1 oto~~) / f.tpf +~) / J CJO ~ 1< [X] S>+. ckJ J ? I / ~

J l>o = Ci o-+ a, x -+ , - - -+ t\,X h wh.A,.Q_ h = ol~ .J , Oth c:: R. X l~+<-M-e J ~

~ 3 1/thl.cf~~~..e- Cf;oo / rf~) ce:: l< [XJ / s.t. -f-oo = ~ex)· J oo -+ roo ~ RrxJ

~~r<deJJ. 7~

Let,~ 3/ ID ,-.. A.v. w..f.eq.,.A-f dowtA'i-v,, w O..oo/ bLxJ6 RCfiJ g.t. JtJj b?/

~. ~ppo>- f'. ...... u

~ ~ ler>td~ c-oe(fw~+ of b ~ w. ~ ( c. V~kti>'t). Then ~Nl ~i&f3

~tt"'1~ ct(XJ J rt~J e. (<L)(J s.t. £A.= <f;b-t- r ~ 1<-[)q] Wu1( d~ r ~ ~ b.

1i. !() fJ)uf~: ~oltte+L-on or, J~ Ot. . 1f c(Rj C\< ~ b / ~ 1 =--0 ~ Y':;. C\. .

-If ~ Ot ~ ~ b / SCI~ ~ 4. = 11 ~ WI=~ "'- ~I.

L..cvt Ot uo = a. .. x ., --~- · -. -+ a. o " hw J ::;. b,..., 'X "" -f - - -t h o .

I - ' I -A l") b -1 11--*' ~ <t('f}- ~ -f = a.- cxJ · a,.., h,., x / -u...u..

App~ ~ ~~~ h!:Jpo-f~~~ -t.<> f .

(.)..-) J!."'Uj~S . S"'11'vs..e- Ot:::.. 1~b-t r~ I (,::>-1,.1./ d~ r~ < d~ b .

~ (1, 1- '1 .... ) h= r~- r 1 ~ ~~ h.o.v12- ~ O·"l- -r,J < ~ b _,

~ s~ f<QqJ .A Cln ~~1'"41 domo.IA-,/ ~ (~, q,).., o q- 1, -1~-j:o_,

d~ ( 9, -'i ... ) h ~ kJ C b) ... eohfr~. go ~~- 'i1. = 0 / 6.~ So V'J-.- r 1 :: 0 .

~ / ~~= ~.J.. / r-, = r..J.. / ~ ~ ~ ~M'~Cf"~·

~ rb ,4 f~ F Z6 a..lw~.s tt ~t_4e.a,,__, do"Wl-Wt . O,e "'or""" on F CAl.-, l,_e_

N (O..)= o v o..GF.

7)

h. ~ G~~LB,e., M~_, 2'ti,J, Z$ {l¥1 ~i4~"' doWtO.~.

ei. ~ a::: a-t hi / a.,hcy, w N Ld..J = tt~h l.. = fa-fl... ~(ov $2)

~ N(ct~J= {'/(d..)Nl(3J. f;;:;C-td~. d.,p~-;zc1tJ. Le1 fio.

h, <SJ .::!..=.. 0.-+hi.- = (0. 4hU(c-ch) ac-th~ hc-ao{ , P Cfe{v (..2--fc(L- - C2.-t-dL -l'"i,CJ..-+o(l- _:~ r-+Si.

W Pt2 '~·IP-~k:l, ~.,-z ,>~. /'l-s./:;.:1_ 1'-d<aHJ. 1 r~ =- o<- c P-+~v) p ~ $-v d.::: (p-+~nf-+1 ~ -tA,f:$ w~.

l/V~ fA.5..l2.

~ p,~~+--1 ~ ~~ -to OsfW~

r, s .

C{o.Vt, "r::.O / or N( )') -5} N((S) < N(f3J. -----..

fM e= Cr-P)+ (s-1Ji: ?) fe=r. 5~ J. - r-+ -.Sv, (3-

th'11.. . /_e4- J< he..- a ~u:l~ doH.-oaW. ~ ~ eN.I2NJ t.D/IJ4./ ~ f< ~ pr"H,c;.,po.( •

~. S'wpp~ I~ R.

(!) .Lf I:::foJ, ~ 1::: (0)

~ 1-f 1.:/: 1 o} , C>.M..o{ we Mve 0.. VJV~'-1-"'1 N : 1(.-> fg 90 or. ~.

w fV1 ~= }7.-J~ { N (D.; / 0t cl, o.~o 1 / a.h.o/ ckcou_ a/61 .. di o s.+. N (~)=: W~.

o/o.1.1-. ~ I= (oJ) · Lt'.5 ~~t, bt> .>l-tCl'V 1. S tol]. W t}~0 1 O.c-1 /

~ Ci. = ~ c{-+ r ~ r-=- o trr N l r; < N ( G/) . Fu+ N l rJ<-1'1 (of) 26 w-rp~~vl.;l.e-.

£o r=o. ~o a::.~cl --> 0!"' cotJ =-) 1 ~ cci.J. H~ ... l=CoiJ.

f:;X · Rec~~ ~ ( .1., X) ~ '2 Z:.>q) / 4t..J 1-v-e.- ~ p"l't}wa.el -M.tlt ( 2, )<) 2.5 ~ pt-~c~1'o.( S.: 0 2 [)q] ~ Vz.o4 E"' e/ • d-'2#1

I •

L~ 3.L

.fl. rp == 2 [rHJ == o ~ c-K-J ( = {a-+ bfi} ~~ b~2-}) ts hot ~~ bf71~h '~Wj.

/2-eP.$~: l ~ [ 3 ~ .1.-+ +5) ~ I>-"Mc:-1;-o.f ·

_t:£. ~ 1:: (3 __ 2..-tK) = ( a--1 h.Fs) · (o~~b,~)

~-

a.

So 3 == d. (CHhR)" 2-tFs = f ta-+hEJ ~s-o~ o<,~6 R.

~ j = N (o<J N (G-tb-Fl) s~ N (;)::: 9 ( N ( C,-t bH) "= CJ, L+ Sb')

= N l rJ..) • ( o. )._-+ s-b)-)

u.~l-. ().~~b).. =1 . ~ /'l(ci.J=/ / g<l c:X== ±1.

$;o a-+b-i:s=-t.3 / .So b=o a~ Cl=:tj

LA s.-e. ..}_. /\. ).. _. r1 .).. _..., I I b VI --. 0 0 - => 0. = ± / = 0. _>\, (>, -t b-f-S = "± I .

A -WI

tiJ

{i)

(3)

f3t4 ~ l = ( 0.-t b.{:S) := (-:t.. /) = 'R. / .> 0 1 e: 1 ~ (3, .)_-t-Ff;) .

s 0 I= s, + (:l...-t.,f-S) s ~ £~ Y, 8 6: 1<

pr~~a;f i:.elea.{

2 -FS .::: 3 o .. -&) r -+ ~ s = 3 [ CL-./I) r-+ 3S]

::: 3 (o/-t!f-H)

do Mo.{,.. ~ AA ~~ro.;f dow. a~

(<. ~ ~~-~Cfovf. ~l-ed bJ P.I.D.

A b-tc!~r, dow.(),ik, Z5 4. P.L. /). ( ~, F Lx'] / J..~w:( -f;

R

2--

2 r--RJ u t-w..f- ti. 'PLD. 2[XJ u z,of- A_ PL.D,.

9-+· ~~

7-LiJ).

w/etJ./

~ [ t-tf9 J 2& Ot P,LD 6+ y,.,J- ~ Ml.e/02.h do~L-t, r~ D»-Y.::).

75

-(a dw~~ b) ¥ b=- C\G .for s:o~ G~R. ~O<te Vw LhJ-== fa~R../ aJb}.

fm- 01 1 h <G R , ~te ~ 0>7nm0>1 qiN~~ Cf 0, ~ b ~

DIN {a~ bJ == I d6 R.j dJo._ a~ 4 J b } .

~- ~ R ~ A~-1 ~ro.1 ck»W.h.-. ~ {), J b 6 R. h1J-f bof-1-, 0. ~~~~+

rAe. R ~ tt JCGI 1 ()._ ~b 1 ol/ 0.. / d/ b (~e. o(~ Dw (4,bJ) /

0!4 v d 16 Dw (o., b J / we. ~ cf/o{.

~. Le>t 12- b-e tt P.I.'U. I ~ (), 7 b €:: 7<. nv-1- ho#, 0. ~~

(/) Lf {a, bJ = (o() --~ o( ~ c.. JcrA (Or} b)

t)_> ~ d.; <;;K ... ~ ~ ha-~ pew+

cf:::: ex d ~ .}~ IX t~ ( w,vfs) 4h12/ cie dJ~ q 1 Zs a Jed ( 0., b) &1-f

s:'"' 1M -M41 s~, JCG/ ( 0.; b)

Ei' cb ~~ ( QJ hJ =(Ch 1 ~ ~ a 1 b 0.t-.e- bofh /1--oCAf.ftple5 of ~ o{ j $0

de D2-v (a/ b). Con~ , d-=z o.x-+ h:J ft-r ~ x ;j 6]< .

S'"'f~ cfe Dv-- (O,_b) ~ ~ ~ Ot:::: Ot, cV 1 b= b, o/ 1 fo.- S~:>~ o.1

, b,.

s{} d= CAtXoV+ h,jo( = (O,,X-t b,!J) cA 1 => oJI/ o{

c;.o oi;:;:Jeo/ (O.,b).

(.}.-) S'"'P~ d I I aiL- 0.~ ~~ Ja>f { 0. I b) I ~ d,f c) L- ~ ~I cA I •

~" oL. = o.o{ 1 / cl, =- p d2.- ~ s~ o1.,~ bR.

~ ol.1. = d..f~~ s~ cL. 6: 7<. D\.~-t cA-.--t-~yQ,I ~~ Clhof d,.l.=jo s~ fA; b

:=) ex~ = I = > (}, , f5 ~ R. x L VW1 ~ J . ·~mrlbo#, 0.

Co~~ I g~e~ d = 3 ~ot r a,b) c-.t-wl c1::: ~o{ w~ ~pz.-/ , d.,~~ o.

(j<~t1 ~ (IV~ ~

~tMtA/ ZP(e.a,/ ~ prt-..e ~et>./ bvd- ~ ~ c.,.,~~

Z-k gbJ.,~ r~c . B ~~o+ i-t.,

p.l.D. / ~ do hAve..

~. (~) ~-

(~) 5'e.p~ .I k,. p1-m-e c.,.J v--~ h9.ve 1=- (p) ~ P~l / p=lo s~C--4-

R k! 4- P.LV CM..J l u pr-~. 5~e I .s J :::J 'R / ~u~ J ==- ( wtJ .

7het-. p <f- ( »1; so p =- rh-1 .

glw<-e rw.:::. p e:- c p J ~ 1 p .. ~ / e;,ft,Br r 6- c p) i'rr }1-1 6fJ.

If n-t~:(PJ/ ~ <PJ= (~J / ~ 0 l=-J .

lf P= rh-7= sph-1 ~ .s 0 r ;a> C,rh::J =.) 'f> (/-S-w-.):=: v -s~~ Pi 0

>v .s:~= / . ~ o ,A_ DX J 0 ,~, b. ,......, -=) -= ( ~) =- F. s~ J ~a.~ 1 .

t~, ~ ~+-~~~I.

~ ~ R:::. £riJ ~ fa-t-hi-} ct7b&.2} t,..t-Ai, 1-1~.n--n., N(·J ~ 1\t(o.-+b~)::::. o/-+-bl..

F~ J~ (- 8 -+ ~ ) .2..-+ 1 ~ > ~ 7L Li,J b;f bM1ut~ c;.;'J-vt-i-1-4~ .

- ~-+ i. = i ( ..:L-t 1 ~) -t ( 1- ;, )

~ .2..-f 9 ~ =- { - 4-+!:,~;) Ll- ~)-+ I <?--->

77

~- La-.+ ~ k At-, *'~ rCr f Jonu;. ~ 1 r c 1< / r =1- o J r <f R.>e . VV ~ st.~(! -e0.t

r u ~rY.e.Jvtc 'vbk ~ R ~ ;_f r CAJ,Y>O/- ~ wriAt.t.U-t 46

~- w rf< ~ C\n M-~ro!f dv~Wt ~ W p~Q/ P=l-o / p~ R.x a4 ? ~ pr-Vn-,~.

~ p 0 0rr..ePf"le-i.-4:Jl-e

tf-, p u

/yl

pr~ -.:/ (p) :=1. f2_ U 01.. ~ uieo./ · t:}, 6 ( pJ _ +

P= 4b / q, b ~'[<.. s~ oh :=;. p 6: LP) So ~ ~ o.ap> !)}- b 6 cfJ .

/;vLBtq , ~s.s ~ a C: C fJ / £u tl = p X /vv- J ~ Xe f2_..

~ p = p X b =>/ p (/-X h) = 0 .J·~ f¥ 0-' 1<. u M U-tf~ ~I do~t...

-=:.J 1-xh=-o =? xb=/ ~) b6 R! . ~ P ~ i:kr-e./~1-.e,

Ex. f<. = '£ [,[-$] . ~ 3 Zo VYY·e~t-te~·Me l,wt 3 0 Vwf- pv~.

s~ 9;;:. 3J. o.~ 9-= r .2.-+-f=S) (.l.-g > . -5} .2 ::tE w. J< .

So ~ 6: ( 3) ~ ?= (.2.-.-tA-$) (.1-~-8) bvtf .2..-:t..fi f ( 3) /

~-o ( J) 0 vw+ a p1-~ Lc{eA{ / >v 3 i4 ~ a. ~..e. ~ f<,

7J

p Z-<5 ckY~~C-Vb~ 2ff

tf-~ (_~) ~-( -:=/) 9t-tp~42-- p ~ l-YY'~ne4>/.e.._

s~ R ~ p.r.p'> ~=- ( h-l) fv~'" ...\~ 1'Y!e.l<. /

s-o cp > .£ C n-,) .::1 R . go p ~ ( n, J =) p :::z r rn 1m-- ~ r~

s~ p i& WY.eA~u4- / e~ Y'e.~ / 0>-- WlcR._>C.

If h167<>d / ~ M= t n.,) = R .

.If r E R ~ ~ ( p ) = c n,) = M

~ c p J ;;c. tt ~/ t.ef~t ~ lf2. / ~ cp) e& t._ p).w,.,e t4eA/ _.

s-o p ~ pr~ z,..., R .

A W'/~ 11-e ~'i~YI do1'1-to.i-h ( lA. F. i)_) u C#-. ~rorl ckn,c..~ f<

5-i. ~ eA~ r 6 V<. / r.;. 0 >' V' ~'{<.X / ~ {{> Uot.v~ ho[P{,

d> :;] ~~1,~--~-~ r =. p, pl--. Pn wlt~ h~ I I Pi- 6 R i-0 wred£1cvbl.e .

~ r = Cf_, ~J.._ ~-· ~n-, ~ ~er- S't«J., f~·~~, ~~ J'VI=h ~ ~ 0t.

pv55i-hl..e- ~Y1#1-fA+k>n v-f q, 1 , • -, ttn vv~ ~ -+t,p;.t p ~ o.t..4 'ti 0t1-e- CtS.Soe-i.B.iwe

~ R, ;.e-. q,~:: c"P~ vv~~ c'v~r<:

P.1TJ u tA-1-- D.

b.. ~f R :s A Vi. f. 'D. ~ re=R / r-=1 o, r~ 7<! ,~

l5 pr~ ' r W1 R lff r 2-s wr.e-9/t-tc-l.-bl.e.- .

.Pi-. c ~)) ~ .

(e) 1M- p~i2, p.:!o, p¢1<.:' , o.wA p Z-5 wr.eJ~Ie. WZ:$ rp 25 pr~l ; . .e_ •

( P) =:! ~ ~.s tL pr~ l..o/.12.0,{ '

~ a7b6R Cwu>l ol-;6 cpJ / ~ Otb=. pc ~ ~~ c.~w...

~$~ ~,b1 c :f o ~ C.b, c ¢ ry<'~< { ~~5€ W> e.45;-ev).

s ~ rR 0 4_ vt.]:. U ·1 !Me.- ~ Wt-V'i--e_

tt-.::2- p, ·-· P~ 1 b:::: f~o-,+1 --· Ps 1 ~~ 1 2-t-v&;~~U;,te_s 1

~ C = tr -- ~-t ~ .S~ ~ £Ne ~-vv f 4:. ~f Q._ 'U-r.e-d·"~c;,!;J-e.

~ p,- -- p,.., p,...,_,., ... Ps .:::: 't,- ·- ~-t P ~ ~ -+lte- w-,'7~~ ~

~~~" W, (A.~j) / p ~ ~ ~~o~/A-4-Vve ~;At, f ;_ -(or J oH-e- {.$ ;:,_~ S .

..1-f ~~~~/lvr, ~ P/Ct./ so a6.Cf). 4 ,..,-tl~~~s, ~ rlh,so b6CfJ.

~.e.,..c...c.. LPJ 0 4. rp~ 'i...e/e~4, So p z..s pr-~.

~ LeA rg k o,_ IA-"F.V._.. 'ft-R, p:;;J.o' p.¢~ p ~ Vlrv~U.,k R~ / /IYI

~ P[a, ---al< r.vt,~ Ot,, --· 1 o..k 6:R /

~e.-. P/ Ot 1-- -F $~ /:f~~F-.

~-:> Or, (ti.l.-- Ork) ~ CpJ Clk.o'l ~~e-e- c_p) <:J p-4-ne, ~ Dr 1 6:Cp) ~ CJJ.--...fAt< cCPJ

s~ e*.er P/ a r o-r- r;p I 4.).-~ ~ v..., --u.ts CA~-€- O.pp':f -+ltR_. inel~ Zvn ~ p.,-4J.r~t.s -

~~ ~ R 4 o.. pr..:v/ ~ ~ ~ 0'0+ e-?qu+ ru, ~~lA-e- cha.~ ef

~e.e.ls L :1 R- s.-l. I.v. f L,-t/ II h 'l { .

'f· S....~-e 9~ o.. ch.A;,.., ( s-e.y~J e1(~f> 1 ~ ~ ~

/

)~ R. ~ CL p.l.D/ It' h / Ih = ( cL,) for .s~ ~Gf(. 0<)

4 S411~

Let ],= UI.n ~ h==--f

1 .s. R . 7itu, 1 = (d) ~ f>Q~ o!6 R .

/

~ vf ~ r-e4 j::l thiYt '

9~ 7< l6 c.v fj).LD / r~R 1 r.::l- o _ r6:r<!.

r u irre.4t-u~k / gry . r hoi- IA-r~/hl.e., :..e. V>eo/~-W:1Jle J -M.8..., r::. r, Y'l.. / Y':.-4 0/ r. 4:. P!

v

BJ rep~ -+t.l<J P~/ ~ ~ r ~ a,~ .9-f- W¥~.

~~ ~ r mM+ shps ~ -f-....vt-efy ~ .s-eeps.

~~ (4 Y'J ~MM L-fw.~) t!J1 ;.e. do vwt ~~.

~ vve ~-+ ~ o..~ ~v+tv+--.e ~ i..... ~ ~e.a.~ s.+-. h. ¥ L.-+1 /

~ ?J ~ kM~, --eJ?t.s u i#.pr1~ih/-e. Clht:s. ~ wh-ew p.J.{) c..e»nes ;;...-tv plCj' 1)

P1 ~~ P"' = r- =- ~ ·-- 1-n-t

1;1$e ~~ ~ WlA')( r n,mj ~ s~ ~t -1JJ~.e- ~v ~l/2-4~ ~

~ .cC~ up -1---'V pet"-~f-t..4Wr, ~ DC~o-c..-LA~.

L ee-ilMr~ ~~

LeA R be a- t-1. FD_ W rA,b t:. R / tL b ~ 0 / ~b j'l<! .

wa..,+ +o f~ $uJ. (~,b) .

P 0<1 p ()(,..

Ot== 1 ••• n / p; ~ ik~.eol~~t£~bl.e. , o( ~ ? 1 , o!U{ Vf ~t j ~ p ~ a...J FJ ~ hcf OrS>oci£dwe... _ 2: eX

b:::. p/1 .... :pr/"'?!7'---f~,._, / p,/ ... ,,Bvr?O / fn+,,-~,(5V>"~/ .

• 1-1. /1 h 0 ....... - ~ 1 •• N (Ci...J.h;~) =: /l ~I 2..-We-~ d: [.i,] Z:s 0., E..V. I.A"Vl"l VL "rr f'l 1 v !.A ? /

So Z [:i-J ~ D.~-o a. f-J.ID./ ~ a, {.;{.F. D.

R~ c~r.iJ)x-== {:tl,:t-tj . w~ +t> fwv4 oAA l#.,..e.J~ u., 2-L~J.

fo.ot- ,' w P&-e) p ~-..2.. I p 0 a r~~ . ~ p = c/+ b 1.. fm-- J-o~ Cc.b c z

ThW~ L~~wbk .e1~ ~ 2 [£,] ~.e ~~ -ih.e-- -foUm.v~ tAp w ~vc4-f~ .. ll) / -+ i (~) ~ odol prlwle Z-»+~er p ?-3 s.+. p =: :3 l mvq 4 ) .

(3> .1J rp~3 ~ pr~ ~~ s.-L f3../ (n.wd 4') tMtPf ? =-c/L-tb'-- / o,,bel"'

~ 01± bi ~ ~ved~e-

~ dtU-e.As ) ->~ V ~ r: .

~ . lj2__:: F I X] / F if, tl ft~.

~ f< 2$ a... .ft.td<4~ v~ / ~ o R. 19 ~o A. />.1./) ~ lA·~.

~- 11 {1,>qJ t:. Foo / ~ cf)7! i / ~ -fcXJJ u ?Ar~tteiA:).e- ~ FL><l.

a~~ rt<x = F \ {oj . '-'* t G f[]qj .>·t. ~(f)=:./ ~ f= O,t><) b().<)/

~ cbcr (rAJ~ I ~ ~ 1 b>.:=..J c.>w! ~ 1~-t ~ .>f 0t / b 2-s c:x:f ~~ 4' 0 /

1 . .e- _ 2.-s wY'e.O/Vt-C-i4;L.e- . b-o f ~& Zkr--e.J ~t-e .

~. .Lf -r'<) c FtxJ / aly rfJ 9/ _, ct ~ F / ~ (x-o<J/ fuv ~ fvo {;ff f(ci.J= o. [;z">) O~v~. (~) Bj c{w~(N-Yl c.f:j~·~!W\/ W>-vf-€- fcxF- ttt:x) rx-o.;-+ Y'IP<I) s.+. ~ (r; < {

>-<> r vv:2- r 6 F . ~ D= frc:J.>-= r ~> ~J= 1txJ rx-a.J ;:,_) (_X-OtJ / ftx;. ~

~ t:L,) ---) Ao e..([?. / 0.~-, .fO . 7J..e., ~ ~4 .>-r_, --- ) .Av. 6 C ~.+-.

-fr.>O= lA11 (X-AI)--· (X-An).

--· EE. Le:.& fx> t fDqJ 9.-t. cWjtf> <!f. [2-/ ~ j / ~ -f lJ w~le- u, rDa

&If -P h1J5 wo ~s v.- r . ( =)) t)~v~ . (<!?:.) s .. p~ f h£?.8 h-o Yrl17'IT w, r b~ -f 0. ~Le_ ;,.., :P[;qJ.

~ wrvre f e>o..:: f, m f)-!><) >4-. dfJ ( 1tJ ~ / " ~ l ~J--J-3-/ . ~ cl.fJ (-fJ=: ~ (~l)+dfj(~l-J.

s ~ d2J l-f) :=. 2 en- 5 -' S-o ,at l~€t- f7hR._ rr.f olrtJ ( ~I) o.w:/ olfj { Z)-) k I . 5-o M i.eA->+ cn-..e_ ef tj, I u-v- r ~..- l-1. ut ---/ih.e f-rn-. Or)(-t b _, ~ -o 2A- tv« 4

~~ A = - Ct -I b / s; 0 A u c. H:7r7f of f iA., F / Un-,.fl,-o_t;;/Uf~ .

Th!!t. Uu f uo ~ Rv~.J ~ .4. dq_j cfJ 3-/ _, ~ .p z-s w~1.e.- w, .JR.uJ Off

~ ~ c-f) =:!-/ / JY d.tj tf)::::.2 ~ T ho.~ t-.o ~ ~ '12..

~: c~) v~. (=-::>) 9u-p~ fwJ&f<,U] ~- rlfj (f)~ 3" +~J2 ~,.;ql-1_.,,. -t 0,,)1-t llo / Gl~G~y O,.,:f.p

~~ ~ CA ... ~ ...... ' r~J:: a .. (X-AJ) --· {X- .Al-1) h., ecx] ~ F.T. O.A.

Lf ~ -"v 6 ~ / ~ ft>--iJ= o ~:> f 0 recluUbLe- .:+.. iJ<DJJ .

I-f ~11 .At- 6 C \ lR / ~ -f C N ~ 0 ~> f tJ:-.J=: o . _>. 1 =/-A2-.

9wp~ >-r= t:l+ b~ (h~} I~ Otf-£:r-.~ 'l\J_:::: CA,::::. tt-bi- / ~,-:;...). hv-h of fc~). ~ (X- a- b1.) ~ [X- Dr:+b~) ~ ?A-r.eci~le- z.... Cf_XJ cv..A -+~/re- e,...o'f

0-"ocic-~v..e.

(_X->") (X- }..l-) ( f.>o <?> (X- Ot -b n t><- O.+b l.) t-r~) 6--> (X-{),/ + b ~I ~) . { iN1 cSc.xJ).

f5w. s~ ftxJ a..vA (X- o./..f J/- a~ D.&o ~ i]Rc.x] / ~ ko.v...f?.,

(x-~/-+ bLj T>o ~ fRrxJ. <;.o ft)f.) 0 Yl€J~M-Lhk- s~ ~ tfJ~:3> / On..JK?.o/ic-1-~.

S'"'ff'~ -f-oo eiJ<I:xJ s.~. ~ c fJ <. :S ~ ~ ~ ~w>14 ..-~~ '111 y Zf ~ cf1 -=-} /

-f U wre.-1~/;k. ; t,f ~ tfJ =- .l.. / f' u Wr-~ncvbu t.f -f ho..£ no h71rts ~ ~

F = F~ ( F ) ~-:> '/<.DG " F [X]

~- C ve4LWt~ Wt-Of) 0 / P6a / p-72. ;?

'-"<:Tlv>"~t,i..sn.. Cto-+tt,x-+--·-ta....x"' f--.../ ~<> -t Q,;>< --1---- -t a.., X"' / Di--e:~_, O.v E 2t/pl.

t!_oiort~ ~< ... ~ R ~J v we- t...&e. (A J "'"' o. &; -t-o ~ ~ ?"'~tpa'( u-1~/ J.e;,. ~ 4.-.

~> t.ve w~o-~e ( 0..) = ~ o.l<. .

L~,-, Y1-tA Uut R b.e O..h ~rl:V( ~~~ Ls'R./ w c.p ~ J2[><J--:?> ( 7</L) ~J k

~ y~~ hUlvl~hl&WJ . ~ k(b. tp ::: 1 [~] . ~/ OJ~ 1 ~ r7:J kD 1o-o0-pk:s h-)

-ehm, £Me. hAv-e f<[X] I I. LX] ('\..- ( 1</.I.) ~] . l ~ S0e. 7J.s<F ).

~ .h, ~ ~ s:A-r.ta+~ I ~ rov~ RuJ wlU, d-eJ ( fJ ~...l. .J s.;.+-. p(}(J:;: A(}q) 13uo)

vv~ A vcJ) Bu<J> e=. F~J ' J~ (-fy "?/ / ~ 0!3)-3-/ . ~ 3 r ro) sf. o / v.. 72 7 -+.

Ct (XJ = r Ao<) c I< ex] , ho<) = s Bc~J e- Rr:.)qJ / ~ P(XJ = & uo boo ~ !<G<J.

~o.vk , -rt,0. {MP 0 e.eUee( ~ 4AAss1 ~ .

..ff. A-z>o, ~oq) 6 prxJ == p,.uC{<) . ~ -t.ak-~ 0>,..,~ cknow.~~~ / J of/o G.R, ~

0\; c h) 1

J/ f'V ,:. R l.><J / >.>f. ~ . p oo = c/ oo b' oo , ~ rJ2 r>cJ .

tJ 4 cfe:~ / pt~J:::!_ J-1 o.'r>o b1 (~) ~.

Vf.f. D. /

tp;;)-= k Pi-'R ~ R , ~~ Pv ~ 0-v~~Wt-bk a~ Vt- Dt CA+.v, P.."' u c.,~.,

p1r~. Sv P..(p;, 7<. ~ 0\.Vt ;:,...{~r4-l ~-w.iM/ >o ~ (;~f.,R/ ( f</p1 R) r.xl .

o~,~,.~D ..lucxJ:::: o..'r~Jt:/C>tJ) ~.:;~6( ?, ~ l<c>eJ. -> o =--4/~. b~x) / ~ tk,u. (~ ~~]2.) 1..6 44-o ~--- q r, - . 7 ,, i-wt~~/ ck..a.J. 5o Wf- 0 _.~ 11 f 0. ~pss.e CY CxJ =- o ~ (R/pf<.) ~>4] ;:;a.) o.IA ~~ of o./ O.ve dw16A;l.e b!J P1 ~ R. . So o/ov -= p,cJ/'cx)/ c/'o~J tS RW ·

f:"b d pr~J::z. p, PJ. ~-· P~ ?(xJ::: p, o.''ovJ/oo -=) f!.--· p, poo = o.''cx>b'c~)

Leh-tw0 3].

~- LGzAIM>1 ~~~) Le-t i< l>e- IN u. 'F .D:I F':: ~ { R) , p lX) 0 R [XJ I d~ p ~ 2. >.+.

pt)() = A {X, B (X) / w~,~ A (>fJ, 13 ex> 6 r r.xJ , d~ A~,, df!J s ~, , 71,~ 3 Otoo, boo ~ ~[Xl / ~ r J s ~ F J r:j.o j s:j;.o I c;~+.

r A vc>:;, o. "'o 1 s: B ex)=- 6 oo , ~ ptk) = CllXJ boo ~ R ~J .

~. L~ f< b-e- tt LA-t-·V · ~ F::: ff4c-(1<J ~ fV<) 6 RrxJ , d~ P~l /

s:t. Jco/ 1<. (of eee+(U1ew1s zr.f P)= / 1 ~ Pt>o ~ ~r.ee/h?<bfe ~ !<.De]

Z{f pvo ~ wr~ ~--te#61e- ~ "F r..x] .

'e:! ' J" ft>r) u c;ry..~~ ~ FD(J b~ roo~ ~ R.~J I ~-e-t..

pcx> = Ot · Prl>O / w~ Ci-6. 'R, a.4 rp!, t\ ¥0 1 c.. k> a tMtu- t-... fU><;J ..

ll~ p 1 (x) tf 7<. C~]. ~ z+ 1-olton..J ~+ 0.. o/w~ o,t;f tJD.e-ftt.-c.~-13 of

p ~ 'I< I ~~M'~ -64.e h:J~.e-s~ -bf.A.f Jcsi ~ 4 ~efti+i&.+s cf- f ~ I .

.If p~J u f?ed,.e.Vhf.e_ w. F QrJ , -ti.e.-. p t)o 1-1 re-d"'-e.vb/e. ,;.., R.W P:J

Go.Ms' ~~-

~. Le-t rf<. b.e tV! ~ro.A dow. aiM , -tt,~ 1?. ~ Q. {;1. F u. Zff 'R r.~J u tL u-F. D.

&en. If R 0 c.. Vi:f:'."D V n? I 1 -t~.~ 12. r.x, ~- 1 x 11] 2.$ a. u. f?.D. ~

Ji_.n- c-. ~;,.:.~ : f<l:Xr,X:d; (f<l:)q,J)Z:.~l.J Rrxr,Xl.,-~·,X"~J ~cl-ef S'.ee vJ< F

~ ~ o.. rp,:r..:O./ s~ (Xr, X2..) ~ ~ L,;x;,,~ ... J ~ ~ P"'~c-~D.if / how.ev-" b_!j

-M?Zd 7~ a,h.P( lA-s ~,.. 1 2+1S ti. t1. f:'.D.

{ ..-,)) >wrfM-€- e. 4 4 t-1. F . D. LeA- F =. 'PH«.. ( P.) . Le+ p ()V <f: R [>q) !1-':,f/.,

~ P ~I . L« ol :::: .J~ R ( ~~;-e¢-S "f pt~,)

~ pc.x; = d p, C>() 1 p,c~; 6: /<l-x] / [Jes/R.. ( ~~-&..~ of p, lxJ):::: I.

&7,.._~ F l.:s a f~' Pxl~ Ot- 'Evtd:.clee~-t ot~~ c~--~) / h~ a. p. L 7) I t-f, F. D)

}<> ~ ca... fotA-rrr r~~) M 0. ~~ "=f Zrresike~bf.e! "" Fc.xJ. 7h.e., 1/t~~ Gta."''5/ l~ma. , £.ve CA"' wvl-t.e.- di7!Nh o. fa~~ ~ p, oo 4.< a.. ~d....4

vf z,y~,.e~&l~s 0--. ]<c:.>qJ . 1-t adc/:1-kn,, d CC.t-J o.l$-o /,.Q. r~:'leef 2atv 'Vvv-e..o/~1~

(k. '{2. , c.l~, CA1'1 /,e s~ 44 ~ R.z:'l4J . ~"' we- J~ a. ~"ao.-H.9., of pvv

~ wred~.dM .. e~ iA.. T< LX]

~ J,e ~ *' "D&F .

(A,... LeA poo t; ,ll>GJ h4 J.1.tonte wvf-h ck:J ? ~ 1 , ~IM-1 ptxJ ~ wr.e.ol~LR- ~ 2 Oq_J

C::.='/ prx> u ~~itz- i:t-, lt2l><J .

~lf!IVIt l_.eA- ~) ~ d. L>cJ be n...o11u v--:+t. de;j f ~ 1 . L~ p ~.l. b.e. a. pr~ ~7Jer .

Le-+ f CX) ~ (Z/Pd:: } l:xJ k -fl4e- r.e4~ ~ of f Yk~ p . -,;t,~ Z7"

-fLxJ zo re.,G{ueUJI-e WI 2 IxJ 1 ~~ f z;>qJ u f'leolt-ta.lAJ~ ~ (2/ P 2:) r..xJ .

Cn.,S4 t-t e.-.+I::J / &f f CX J u w~ ~ ~ ( ~ p 2) Cx]_, -#t,.e,._, f (>(; .:.S

lrr-~ ~ "'"' 1 t~J , h~ -ftx; ~ al!:o Zr~~iL U., r£2 ~:X] .

et ·. Pef~ eX: a ~J ~~ {a/p£ J z:.)tJ / ~ reg{~ h OVI.., o ~ phi& 1-J.o1 •

lf foo u reef~ (.e. ~ al>fJ, ~~ fuo ::: a l>o b (X) VI. '"&~) OAJ

d~ Ct ' dl2;J b ~I/ boftt a £.)f) o.k..Ol boo 4¥-.e- ~u.... $'-o f ~) ~ <X ( f~))

= d {allfJ)d.. (bC)(J) = 0. Cx)· f lX) wJA-t., ~ dl2j ~ .1 ~ b 3--/ _,.

s-o f (MJ ~ f'1e.GI ~ &z.-- ~ rz I P~) "L'X] -

&. fvo =. ~3 +]X-+ I tf: Ll)q] / Vf P-== .l' -&l,e41 f (>O;:t x3-+ x-+1 e: c~/)..2) l,)¢].

9~~ f ( 0 ) =: 0 3 4 0 -+ 7 .::.. T rf. 0 / -P ( l) .:! 73 _,. I +I ~ I =I 0 ~

-f'oo ~$ ~ ~ ~ ?Ljl-£. s~ £/2.-(L u ~ fuU:l. ~ ol~ -f:z3 /

~ ~ pww~ ~ui/-/ f l:s ~ t..e4k ~ (&/:L£) E-x] .

~e-e, f u Z¥red~t.e ~ a C:X] / ~ £~e.JV f ~ n,o.,Le.. /

f ~ ckv 0--~hd/,/..e..- ~ /l.. DX].

~ . ( b c:s~~~-~/s Cr~~,.J L~ 1/<. b0 a,.,. ~tiJH~o[ ~/Nt / p ~ R be a. p~.e.-- ~€2. t.

L~ -A~} ;::. X VI -+ a~-~ -1 X _, -t • .. + Ou '>< -+ a. 0 G R [')(] 1 ,~ I / >-.;1-.

~-

{<.e. caM ovt1 ~~ tw-e- ~ ? / so 4f+~ --{;lz..e f'!e.dw c+un. ~~htsk-. u,

moe/ p / ~~ f (X)::: X h ::: t\ (XJ b CX) ~ C~/p) [XJ. ,...,..,

1.+ fo~ -lrl..A-f ~ Cor.'~ -ter~.s cry

..A.,>O

L I" ~ ,_,_, f =-.x -+ ~-~X -+ --- -t a.,x-+ ?to 6

s-+- pI a~ / i.::.o, --· J n-1 / M

~ £LX) 1

1-J.e-..-~ oA~o Z.V~IItC-4/e- h.,

- c. h-e{ W-e~ - ~.;p / Ot h 0 ..1) u..

""£ r.~ J , ~-'~? I " P ~ .2.. zo a. prt...-,-e ~ ~ /

Pl. J' Ct. o , -#,.et, f()o 26 i-Yt--.e..e-l Lt c;,b 1-e

d2.~J .

~- fx)= ~ b-+ 3X,r- 6x J._..,. /::l. ~ 2rxJ ' p.::. :S / -&It~ b?J CDr / fw) u t¥,.e_..11A.cU>l-e

j;, "dtx] MJ ~~J .

L~~ 38

f2_ - tA.F.'().

~k/~ -th.M -P-zxJ ~ tL h7T1f

~ _(){a~ . P/ O.o h., R

~)-:=. 4~-~~"'-t t(ll-1 X'11

-l-+- •.. -t tf,X'-t tt~ ~ /([.xJ I VIP./ /

.>.t. Otof;O/ .jc..aJ.R.(ct'1,Cl."--l, ---,Cj,,C(o) .. { _

r6: F, ~ r= -f, p, ttc=R, p,~f-o, Bcd(P/'l)-=/.

0.~ ~ I tiv, iM R .

'fin- tto ~ a" rt 1-1-1 := - ( ~"1 p ~-+ . -. -f Q I f't ~1-1) o/iMui4JL.e- ~ p ~ f2.J15 /

.!'" P 1 tt o •

fn-- tlh ; t(, r"' = - ( t;), p~rt~ -1>---t tloce,h-1) c/iNutb~ ~ f ~ r-445/

so ~fa.,.

87

~- -Ptx>-== ;<5 -+ bx + .i e ~DQJ

7ke- ~ ~ pv-eN~ o/o.W..,. ¥ -f-a<; ~s a.. ~ 0, tl~ r >:>. ~ , ~ v/ J.. ~ q, Jr --""> ~::=:-/ ~ P= :e../, :1:..1... ~0 r"" ~-~, :t.2.. ~?t.cs ~ r==--±1,-t.L /

WR 5f 1o6 z,._, 6< ~ r ... for; ~ 1-ro ~ u. iJ. w·.

S ~ l2. =-s a -f t.e1.d / derJ f = 3 / fr~) ~ ikr-.e.9{ ~:{ l-e- ~ ~Of] _ o. l.t..O/

~ Gams l~~ , ~} ~ 4&-o ~i.e. ~ 2Dil .

~ ~ rJ2. k a. ]>.l.TJ. / tw>l !AM de R ~ ~ #O ~ ~~R)( , d. ~ zYr-e-1~~

~ ( ~ ) 4 1<.. ~ W!Dt)(i-~ •

~- R ~ a.. 'P.I.v =/ R ~s tt U'f'.7) _, o~ d 2-s i¥v~t--.~le_

_/ o[ ?. "'-""~'AAI'I{ r·,':.~~- h01-1'2:e4-o a.~ z..al.on.{" =') V1 0 pr~ Z1, rJ<. ~') ( ) <l R ..., ''lY''\'VVY'-"'1 um.....- r· "---t:;( ...

c;.v.Q.. ~~ v, a. p.z.-o . .

~ 1f F Zrs a. -f~, ~ ..iF fvo 6- FVcJ / ~ -f ~I , -fe'>f, u t,vve£lr...e);~fe ~ 'Fi:xJ.

~ r{) cJ/(-r) l.s a fre/J,

.h ~~ ca&e, n.: FtxJ ---7 FrxJ/tf> , Gh)C) 1---7 Q,cm-+ cf>. ~ n/p ~~~We,.

71, 26 14 ~~ ke..- {70 = c-{'J , ~} /1 F ~ { o} , .s (.) i:..a... (rt /pJ ==- { o} ~"/ nip ~ ~~ .

~. ft~>-.::: X'l.oo~ l 6: £/3£. VcJ .

'P~ -._, .X= :1., :2, 0 , ft>C) hP.-s ""-' ""'""~ U. ~ "';3. ~ / $G f '/4 Wr.e.JJU,M,u_ ;... ~&;<J.

s~ ~/~lL u a fi~, bs ~ / ~ ~ (2/:32 t:xJ)/cf; ~ 4 fi-elo/.

~ c.brn.A- /(a/~~ DvJ)/ c-f> j = ?

~ dwM. ;...:n., of ~ 0t l~) 6. ajsl [>e] hj ft')c) : f)_t}qJ-:z ~ ClCJ (XL-tl) -t r~;~) /

~ -~ r .5- I . h r-~ ;~ 7L ~J) If-f> :z { t:io-+ a_, X-+ CfJ ~ Dto, Or,~ 2/321 /

~~ /zhl/:2 :S ~ ~ ~ 1~132 [>q] 1(-r) 1:: 3l. = r .

~- Le--t 72 k Q)1 w~~ ckMJJ.~ / f'l(> 6 l<r>~J ~ ~ f ~ 1 .

~ 3 a -fi elPI F ~a~~ R.. ~ a stJ,~~ s-1-. f oo ItA~ o__

h704 ~ F . ( ~jo ~ h7if13 ) . ( a{g% J-4 k- dos fM'le)

1!. fz~) ~ F c~J.

~ ~ wvVf..e -fc>< J ~ P• C>O "frt'<J __ piN'l C'!4) / p;_ (A-~~w,~ ;,., Ft>q] _,

~ p._ ? I .

L.J2-t p : = F [~] j(f,uJJ) . s~ p; l>q ~ 0-. p ['Jc] _, ( p, <!1,) <1 Fct1J

~ ~~I ~ F h Q fi-12{4 .

7't: ' F UJJ -:::> F u ~ i~ANfl~- ~~huW~ / ~ we.- ~vl-V Tt./F ~ ~j~-

LeA A::: 7[ l~) = ~-+ ( Ptt'dJ ) 6 F . ~ ck."w... : p, (.,~\) = 0 i-t-, p . .A

it-. f l..><] ( l~f]) /

~ .,!1 11 -+ -·- -t Cb..!f-{' 4o -f.. (p, no) ~ Pil~>-1- {PtCij>) ::2. 0.

6-f~ / -f c .A-) ~ 0 ~ p

L~~ 3]. ft/lt>~:{~iAl- u-f ~ a~ ~ = B~ ~Xj'p"'J -bt,~ 74w. -f"i+,:A.e& wu:.,vef ~~/ w.a-

~ t~ o.. -f~ol /< s.t. flx> = a,, ex- ~Jq) lx-ct~.-> -- ()(-0-.YJ) ~ KCxJ -for

So~ o<.,, - .. , cXh c:S K .

on:ler ~ ( R./-+)

~- dew ( ~) = 0 .

d ~... ( 2/4-£.) = 4 . ct.a..- ( 2/ 1')1 2) = Wl . ( ""'3-2.} .

~~---lc . We.- ~'>V\~ -el,£+ ~ r~ R. ~ ""=>+ Or ~ 1-~ , So 1.. -f. 0/

h~ chctv CR..) -1 I VI< .

La4 (<.. ~ tV-1 ~fe(Jvq / do~v~tJ..l#. s. i- · Gtrc.t~r [{!.) 'f. 0 1

-#teh

CJ,a.,_ ( }<.) ~ &. P~ U-vf"Uer.

~ ( /-t - .. -+ I ) ( I+--·-+ I) - I_,.--. -+ I ::::: o . ~~ ~

p '[, Ptt=-rn

do~vtai-+,1 cw- l~s-1-- on...e.. af p = t-+~--t/ ahil/ .._._,____ ~ ~ /-+--------+I / .Q. f~AA/s 0 .

p ~.. d~J..- ( 1<.) 6 p tn- ?, < }"V] / c,-,...~u+~ '

,____,____ ct

-· 'fiow, ~ p~2. 4 tl P~ / ~ ~ ~ l)o~s~te.. f~;,;f.e- f~c{~ o-f ~ (Fr=:: f ?

w~ ~IN -bkM ~1 p2 ka.s ChtJ. .. ::: p . Wt>.+~. fr == 2jp2. ( ~eA.;:!:~ ~~ fiel~ ~ v~

l(e.04t1 ~ claf;...*~ ~ 0t veeA-v-r sp~Ga.- 1 !Mi~ ~i t.v.Q C.C.t1 d.ef~ Ve.<-b- r.pcu~

ever a f;;.a,Lol t=' / Cw..o/ a-~1 ~ cb-1~~ ~ Lu,~ Ot-{jebro.. ,

tl> /Fp = { D/ ( / /-+/; ---/ [~/} ~ J< 0-6 4 Swbf~o{. P-1

~ W-e. CAA vle.IN k a-6 a ~ <Spa.(!..Q.- vve-v f.p . .If I< 1.-5 f;,.., vf.e.. I

~ /<. :.S Ot.. fu,.,V4-e.- olvw.~si.ornh 1 V~ .s pt~ e-Q- ove,.- f p . LeA J~ ( k.J::::. VI J

t:)y~ e, ~ .el-/ --· I -€-y, h-a Cl_ bo.sL.& ()f k. I -d,r24-, ~ -el~ of k ~ ~ fM.r '-f '-' ~ %f lr-e.Is~ QJ 0t: { if-reAv ~b~UJ, : d. 1 e., -t - -. -t ol..h -e~

(o

Thwt Le;t p ~~ , rp 0. t2. PY~ , h~ I 2.& ~~ / ~.e-v. 3 a. -p~zA-e ..

-t~~cl. k ~~v~ Cho.¥ t k) := p a~ 1 k 1 == p n .

s:.-r. ftxJ=CX-d..l) -·-cX-cX.pn) W! Fc.>c]

~ ~ f:M f ~a~ lFp

1m- ~VII.u2 0( I .I - , <X r • v.. F) ~~ Cha...(lfp)::::p &!-1M k =fall,-·_, cXpn].

eww( fpb ~' OtP.v( KJ~ P ·

h

'/Me /( = I ol6. p ~ fcot>;: 0 t ::::. { ol. ~ F ~ cl p ::::: eX } . 1-f o( b /(I -fh-41 -t:>~..~Js v c/,;r,.e.ol k't-c/ey " If

Sa o ~ /< , j_ 6 k ~ /< Zs ~-eo/ v..nokr rnt.o.t/-tpl~~ . i.e. do!.~ (.M.c;{e . ...- ~k~ J-o,£-\,l+~l~~ U.v~-e..s

,4-uo ' M ol. 6-k, ~ ol.-1 c /< ~ ~o ;;.., ~e.- ~ ve,.,l1j ~+ K 0 4 fz.eJol,

~ 1-1ee-el -b-o s'-'~JW -etrA.ot ~ u ~s.e.J. ~-4 ad4iAWY, .

;;"upp173~ Dl., P (f; I< .~ ;, e. o~. P,.,;:! eX. , p P""' == (3 , ~

( c).-+f?) ph b~o~ TJ,,_., ~l fh + pill p~'~-1 p 11 ph-I r ~ { I ) ol. f + -~. -t ( I ) f ol. +

I Ph

q t1 .2-evos , i"> ( ) s~ r }<. /

~4 ~ cltA.r ( K)= P .

~ ~ Lo ~ ~ 4.ch/v/-~ .

~?,n, ' k 2.6 4 gwb{telc/ e:f F .

Thw, · .Lf {< ~ C. fu,;-t-e fieJJ vf c»d et ph ~ cho.v ( k > = P .

n~ ( k >< / • ) Z6 Cj 0 i.-e of trr~ ( p "'- I ) .

~I

L~ 4o r[<eview -(err FWt~ll

r~ I v~.s I 8~ '1 ~eA-t I MidtevWJ p~t}~ ( ~ C1t"">fJB6V' ttJC1W, ! )

EJX. NJ 53 t,vt.tl{

J-hOhCJ.!~~~

en (..8?., -t) o.~ ( :IR)o _, ·)

V1 hJ ~ta.1 ~

{5) UR. J -+) ~ ( 2 _, -t J ~· ~

V'ro+ Cti cA u 01 clZ-c-

~

lv) a X 2 aw..e1 R ~ ~

~~a;h 19 fMU..o k.Wf-C/b/Q

l4J ( jg_)4' • ) ~ ( {_X-' • )

rt I ~ V!o ovc{ev 4 el~t [ ~ I~ I::: Cf

( 6J ( (/)_I -+) ~ ( d X "l_, -t ) .y d--

;:1:;~ ~~~ j~cvfe,.f ?J ( L//o)_, {o-' Uj_

3 f~u-~ j~~ £.uhff~ {a~~-' -t) W4~ L.s hvt Cjc1U

_,.:;:; )1oh- ~(M)tt~ J'vr>1J . ~- 7L ['A.J / ( x-5J ~ ~ v.-~ Cf ~ :ar:~J ~ 2 I <f (-f)= -fcsJ , ~ ./2NO;~"C:oh tiV>'nV~ph<-5~

") [ "v,.., .. eiJ -~II. ~ +o V-€4-LfJ :> Y'ef~ I e&p~ t:J r-..~ I

]'0+-0. s~ c X-5) l-5 "YV~onk) we ~ Dtf/f}j ciw-uc:..on t>{JoHi~"VVl fcr (X~ 3) .

( .1.. I l-a [ i] 1/V/.IH.. ~I?YWJ (f;-td~"' r~) .· N et_. hv) = Ci -+o .

ex. o<= 3-+~i I p =- ..L-- 1r.

~ -s-+~~ U.-tin3.-+1~) -3-~>J.-f-v ~ 7t = ~- c =- (..l..--4> v J c 2- .t) =- - 5 - = - s -+ f!- ~ -=::> - I -+- Lf i-

Cs-+ 1 ~) ~ c~- -c,) (-1--~-4~) o-+ 1 ~) 9 f-l.- -tlf) + 1 i.

s-t r ~ = c-J-+ 4 iJ ( l-- b) +I o;!, ~

~...,. r" ex f5

Documents

ry tt/ '1 - University Of Illinois · xJ . ~. ~. ~~ ~ ~~ ~