View of Some remarks on means

t"

"i1;)';ì1 ^rrìr\

-

trf '1¡ ¡; ¡¡

J,'.in rt.\si,r *, *,r11.""'¿'¡1")"';t"l'"'l'ì)lii:'ì';',;\i,'ì:irìr()t'''

;1f.1.Îl

iì.li.d' ¡,.r

,r'¡r,r-¡r¡i,åì

f)¡ì

f,._q¡u¡,

;rr¡r¡rr,

ji). _ld".

_j

_{_.J.}

ti);it^

¡16r...rr,,_,i,j.n,ü \t.{¡.1.,,{(}.r*

SOI\4Iì

REM¿\IìI(S

_Oìr,

il[ÌANS

(ìlt.:t.oAl)lj[ì

((lluj-r\a¡oca)

"' ,,,1'*r'r,'ï{rjj:|ìïiì' # riir':(H rìîrì,åïï,;Jî.,,fî\;,ìr.:ïibe,is)

is

,rofi,u,cr

(rì

_rnirr

(a,,

lt) < lr1r,3/)

_{_< rn,rx}

(r, tt), yrr, !/ >

0.

r\'insr;

of

úrre usrrar,1cÍì,'s ìravo

acltrili.rrar

¡rr'.¡r.r,tics

likc

s¡,.rnrc1;r,.1'

,t)

ironrog.encity ^i),t@,

y) : rt(!/, x),

^yt;,

_!/ ) o;

¡

l.r.¡f orcler one):

(.rt

Jl[(tø,

ty)

₌₌

tilI(r, r), ^yt,trt _{!/ ), 0;}

cll: .r¡Lonotorr¡.:

the trean

_,,1[

is

ìncreasing.

if

;

(4)

_Mçn,

y) { i[(n,,,.!J,) iI?;,

_{_( 11),}

¿rrtl

t¡ 4

^t1,.

l,\'c, rlrus t

ltt

i r¿tt,lc r'' or' (,\iùrìrt)in,

,1,,,'l]:',1,1Jrc

Ìrlaûion (l)

coun

t"r}ai;,r.

_JI

_i,:Î1,*

tcan ^{tt:' l'} _/r,

-,iäiiíd¿'iii

^{ir n pì"1'} x ¡.y ¡

_{kintl ol'ttr,nr}

tony lrri.s

il¡c ,,*rpe.t¡, ,

(''1(n:,

'¡) :

_l."z

I

^y")

_{I k, -,,}

_lt)

0(tls,t)

_--,

_c(t

12, 1) _{_... il(ì.}

i,ïTiÏ'l,ilìï

,'?r',tT

ì1,'¿ll:

ro

c'listribution

,,;i"li,'lliï,i:i'ilnn': ^{otrrc.s. r,} 7 ( ,j0,,

^{*n,,,,, or}

"rjìli

*iii"ìlh1l ffå|",ì:ì

l liJ

e-

\lsr.r. f¿¡J¡i¡¡¡!,1(l),

. t,

_{li(l) 1'/. \\}

_r'

,q'r'l

lttl (,\l)olì(,ltlirrl l'tra,

(ib, li-oaclc¡ _:ì

So ¡1r, I í,rìi¿t _{I J\ s} olt llla);til\

lllllell

rvt-' slllìlllrz,l'iz(l 1,htt uulirL l'(ìlâ,1;ioJìN

br:tl'cclr

llrrì¿rus

a,lrl

ir,lllll,t.

(bcll

1.1:.tl:1.:r::llì_,1,1 *.I,r,?uer'1,,1, oI horroiìcricil,.1,

rlorc s",ì"iãr

ì]tren 1ll;. ti.jrL:r,rrr, r\-(r qlr'(r I't'stt[1s

otl

tloull]t-' ,\iequonc(ìs

lelatcr[ io iho

a,r.it.Irrntrtic-g't,rlrel_ri,, ìrr(ì'.ì,rI

ol

^tìa,llsri.

if

hc

pàPe]' r,rott1,¿ljìts s()ruo ll(,r\¡ r'csrLIi

s ltul

i1

s

rrr..ì,ilr a,i¡n

is to

_lroir.r 1,

ottt

1

hc

lesull

s ol

1,ìte

tlltlllrtt' l'hich

ha,r'e ¿r.llì-roal'ctì

in plc¡l.in1s ol il

voll¡¡¡.¡.1," u il

lr

lcss r.il.r.ill:rtiti¡r.

2,

{lotsf ¡,utq{io¡r r¡l n¡(!it!ts. ll.lt<,rlr¡ 1.rr,o rììor,(Ì gt¡llcr,r¡l nrc[ ìtrlrls ir)r, ctrrÌ-

stlllctioll tlf'ltlt¡Íl,tls'

_Sotr¡

e oli

f,hcrn usr, algcbr'¿¡ii, n-tc-tii,,ci*. or' l,urrrrl.iorr¡ì [3.f)

l.

^{Ohhcr'¡ rì,r.c,} llr,St:cl r¡lr

llltr

tlclr,rL rnto,s'mls (sec _|

12l,

_I

:j01,

_l2lÌ

l,

i ft i

i,,iÌi I

i

lli,ll' ïlll,,: i};ü,.11î:]i.ï'

_l,,lll1' ,'ni,ìrruorrs l'nnr,1,iorr rvrrich tro.s rrtir,

,lil:ilJl

,,!iì,1r,å1,/,n1,ì,',J'ìiìlìi",lilîì,îi];ï

zo.o o* a,,r'

i,l,r¡r,t'a,1, [,lr.rr

*

r¡

rlal'i.a i¡

ìrrc,r,r,

¡i,

_o

li\,

:

l:;(,i',

.t¡) ((,,

I

),,, (.t/

I

)i,,,,1a,,

_{\,,)

rr jtìr,l¡ lì<,rrrar,ì.:irr¡¡.

nr.

ilt,lìnrrl,

llrrrf il

_i.Jì(j al,', _{/ :r¡¡rl}

,,*ì ,,ì,

strlrlit,ri lriso

,,,

rr,,, ,,1,,,,1._ì,,,;,,,,,_

i¡¡

_{/2g ¡.} ,r,r,

rl, llri,

lir,,rrr

ll,.¡,,..;¡¡ ( tttt.tl

.1,r,,.,.r11 tr

\

/,r t, t

I

_!/,( ,l,.tt)

j rrltr.i,r,/.

_lr,r,tl

,,¡¡1,.¡,,ì.1'',,,"T,1,f' lLl'tr llolìlrrg¿'¡¡11;¡¡

'r'

1,1¡¡11liri,,"i' 'iìli";ì,,,1"i1,1]j",,,ì_;1,,

iil,r,l.,,;; _tr)t[o11 i, .Ì,,,¡r){,{,rir

t,rr

,

¡¡¡.r.i,,rl,ttr

¡,1,,r, ;

,i/,ç.t,.

.r11

^(:t..t/,

|

.i¡tr,,) ;i (1t,,

¡ .tt,)

^(lìrr.

lì,sliri.i1z

_rrr.,r¡)

,' , ,1,;,;];,;1,1,-,,''l'' i tt') _'Q'" t ;/'))"t'' (ilre (li,i

,,rt'¿r,i,)

1,,., ,

^{(t lrt,}

lJcclicnlti¡,t,lt l,t,lrlli,l.

_ltrcln,l

('

1r,,, (i,lrt, t,oir{,¡,1¡llll,r,rrrolit.

lr¡r,il,l).

lì'or. _r,

,,

.s,"

lilt,

^(,l

irrj

rrrcl¡rr ìs ¡-t,ivt,tr

irr

_{/.:? J} 1t,1. _;

l',.,(',', .l) ., r'r¡r

((,,,,, loe,

,¡, i

_,t1, Io¡¿,

.tt) (;t i

lt,))

,.i,

^{l,sirrg I} l¡r, strruc irl.rr, _\\ r, ll:l.r ¿,

,i

lÌt'rrtìr'¡ i'ir':¡lrrr.rrr'lrrrrrit.rr(,irrrli. ,,,,,l1l..'.'1.'1

,,

irr..i

ilr

_{J srrr}

'rlr'rr('¡':rlir,,r¡,,i,*",,1 ,.r.

(i .rrr ,. ' 'ì{'r'i',t,','rr.,ll'i;;,,,riìì;'l';,,11;llllii,"í;ll,ï;'r-

tI,(:t,.t¡)

_1,,.

ì (l t)!t. (i,(,t,,,t/)

_{,¡,,.t/, ,,}

ß,(,t',

.r1)

^{, ,:i..r¡} _¡ ^(.1 _.r¡ ^,,

(l

1)r¿,) iirr, 1 e.. /(ì, I _I

)i ,

1,,,,t

{,

Iil,r,r)r,s¡

(t

_iùn(l

ll: '"''"rl ^Iho

^l'ol.lr)u

irr¡¡ (s,irillìì(,llir,

_0r,

rrol)

gt,rit,rllji.zrLl i<¡l¡il rr

(i,,.,,1,.,',,,1¡ (u,r..t

, (l (t

_l)).t,!l

i

lt1¡:Stt.t,l)

_<¿¿. ^i.r -^< I

Il,, _{,, , ,,.(,,,, .U) ..(u:¡,2}

i (:

_I

(t ,

lt).t,.u.¡ lt.tt2)!(.tt, ,¡ tlry). ()</1 <(., ⁰

çá ç, ll i ^lilt,

^lirre¿¡1, r,orr¡/ri

lìi,,;ì,,,. \\.o ^(1¿ìlil coll-

ilt' :

llollN'\'lllllì(ì1'l'i(i

l:l'"(:t'

,

,r¡)

. ₍

l,l

(t,.

"t1¡

i

_Jl¡t1

,

;, ¡1,2

0f)

t' , ,,1,,,,

1t) , ₍

\

(.t(t) q(tt <v I ^¿

t(

^,,) , ,,)"

l

\\rc

clt,tr ollt;i¡ill olr

lllis

^N¿ù1. sorrìc ol, f ht¡ ustr:ì,ì rrr<l¿ùrrs

ljlic

:

,9,,"('r,, y)

.

((,r¡r,)

(,r,,'

_!/,')

l(¡,, .tl'))tt,,,) (exl;.trrl.tl

r't,zr,trs)

i.tl t C.l

1,,(,r, _1¡)

-.

,(, _,,(,rr,

.i7)

^(r.

r(rr,,

_7,)

_/

_(log^

_;i.,

_.

_ìou

7))r/, (gc.,nclaìizcrl Io{l'ru,i(,1I ur ic).

1l'.

gcl tllcll uo rrse:,/(l) - l,'":rrrrl !(t) ^{-.1" r,}

^u,i1,h

s,-0 iu llle

^s.rurrrcli

r,¿ì,sc.. .,\ri s¡tccìit,l (r2ì,¡i(ìs \\,(r lrlt,r,r, :

,1",.,,(t: , .r¡)

-

1,,(t', _.ty)

. ((,,,' i lt')l2li,

^(t,ltei 1rorr.cr. nrcirrr)

-'I(t,, 1¡),. l',(t', ¡¡) ^(,i,

^,,

!t)lJ ^(tlrt,

ar,i1l,rrrt,1,i. t't:¿r,rr)

(l(;t',

_.t1)

,.

I'r(,,t',

.r¡) . (rq)tit

(1lte gconrtrtr.ic

rlcill)

II(:r, ¡) I' ,(.,t',.t¡)

^2.t,.r1

_i(:t: ¡ ,tl) ^(tìtt:

hal.rlouir_i rrcrrrr)

l,(,i', 1¡)

^L,(,,',

!/) (e,

;i¡)¡(

l.u,r, l'¡¡ 17)

(t,he lrq.ar.i1ìr'ri.'r.rr,r¡.

ñ,(r,, _.l)

,.

/S¡,r(:t', _,r1)

-

(l'-

i1rr,, .r¡,)i(,t.

.,/)),i,,

,, ((h.

(ìalr..¡rri _rrrtrrrr)

IQ.,

_{.r¡) ...} iS¡(;r,, _,i7)

, t,

t(tt:,,t;t¡u)tirt

tt) _(llto

itìcrrt,rìt, rneatr)

1.,(t:, ^,u) ,,- t\,,,(,,'t

,U) _)t,(;t:,.

,.r¡,) (gencra,lizcrl

itltlrt¡ic

rrrrll¡,tr),

1')() (ìh. ^'I'oarlr:r

Alsrl, Ior

¿ì,

giyut. Ììtoal,

_''11

l,c

ca,rì consl:aler

iis

inr.cr'¡ic

;lli clcliltt'tl !tr':

tl[t(r,

u) ^{.'., ,rry} I i]I (e:, _U) ot' ii,s corrrltlerrrcrrl

rll" tìeliiletl

Lr¡ :

-ll-''(,t:,

r¡)'--

r) -1,

lt - ^tll(t:,

^y).

.l¡ol in¡it¿ncc, tJrt-r itrvc't.,¡tr

ol l,'

is ^(?, thai: oll

.Á is t.t

anrl

oll L ^js [, _,.

^il.ht,

oornpìclnenl, ol' -r'[

i;l

.,1

anrl

rll]

// is

0,

(ìiYclll

tho tllttittl

-ill ¿r,nr.l

the

Llijecl,iorL./,

x'e

c¿.r,rr <.ltflirro ¿t lì(ì1ìrì ,l/(./,)

b¡' :

J:t(.f) qt:, a) ^...

fr][(J'eù,,l(tù.

ilhi;; lllat

rnel-bo(.1

flo:n t,lte :tlitluriel,ic lrc¿rn

lytls st,uciie,tl lio:'cxarrrlrle w.r c:¡rr

ìr¡'

17iu1,r,,0 ol¡[,¿.r,i.n,

it.' firt,

_l':¿6 ir¿unoiric ineir,¡

l.

^It;

^is

^{e¿sr' {,o ¡rrtt-r}

li

lrsirìg' .ï.(.u).-.1

i,r:,.the gcomcfic

_nro&n G using,/in,) -,,

log ø, Ilro

¡triu,t,r, tnciì.,1r

I',,

rrsittg'

/ir:) .: _{trl tncl}

^-lcl

_{cl¡. ;\ìs¡¡,}

_in ^"iZú

_I \.ç

1r..t,.,.ç r,r,rrri¡rJçr,rì 1lr¿1 :

(5)

_/.,j ,,=., if(cxp).

lrr

u'll¿t, J'ollori,s ri'cr ¡;ìrall ¿lr,io trso l,rro rno¿r,.ns oltt¿lj norl t,Jrjs

u¿t.:

1i ^{,. ,} -/,(o>; ¡t) ^{r¡ncl .l¡Ì, ,,,.,} 1,,(cxlt).

\tr'r¡ rkurott, rllrio

:

-fi ^{, .} .I1,.

(,iit't'tl

_{[,tv<¡ tno¿ìtts}

_rll

_{¿lrrtl ik]}

'

u,c ^ci¡,n ¿tl¡io cloljne 1he

rriclrrrj

,)l

'¡ ,ll'

¿r,rLrl .lt

^

)lI

'

ìr-\':

),1

\/

^)'l[

,e:,

_{r7) ., ,,}

rr a,x ( lll

(t:,

^.1¡), ,\l ^' (t

,

¹¹⁾⁾

trrrilttrc i

il

eì.t' :

l[ A.JI'(:t)1

ll).,, tnjn (:V(t:,.¡), ,i,1,(r,

r¡)¡.

lllircil

rrre¿,niirr¡'u,iìl !lc utt)l,o

cjrìar,in tlio

lirl[ori.itr¡¡ ltnlzl¡¡i,lr,¡tlr.

,

^{.'\ìso, ¡¡ivorr l} lrreo nlclì1..s þ!-t ^j14', .ìi!'" st't: dcÍrbre

llrs ¡rea,¡

)l(.:tt

,,

_{ll ",:}

b"_v :

,ll ( M ^'

.

^it,l

")

^(,t:,

!t) . ^H(XI'

^{(:r:, y)}

,

lI,,(,"r', _ry)).

lllllrl

lrto¿¡rls crì,lt

llc (lvttr Itro

i.ilsl,

cll

l,ht-¡ scconrl lllo,irrctjorrs ^.qi\ er¡ irr::

["'(t:,

'y)

:..

:p, ft'?(,7; ,

g) ,.

'lt .

lllhis uLet,tlocl rvir,s usorl _,

for l'll ^j,

l,ltì ] or' 11.i

l.

^{],l rrirrrs} ol.rirr,ir-

cd bv

thjs

rlr¡thorl

a,r'e

¿ulso i:¡l iio'il

^¡i<

¡. ir

f's 1

;t ^js

stuctjr,ri

lhc ^problsll 0l cou¡ol'va,ti ition oi *

^'g.i ,uur'class

oi

lìr(,rr,rr.

Jr'ril r',xrì,m¡tle,

l,ìretr P"(l).,

Íìr J)o\volt nro¿ll ^,?

\\it

sa¡' th¿¡1, ilf

"

is sylr¡illetl.i<:

to iú'

l,ela,1,jr.c

1o it[

^{jl' :}

ìU ( _'1'[ ^'

)

_^U'

^')

^{.. ,, ;l[ .}

S<,ltlc I(,¡ttarlts <llI Ìlìoans

I ^(,1

lllhe stnlrrref

ll,

l,el;r,1,

,rf

iltr'jr,orììi

i,l0l. iìi

I hc'

corlllle,rl.,,i,

_oI

ls

1,he illvcr,¡¡o oli ,Jf

lvrr _liucl l1¡

, Jl' .l

js

is

r.ollsirlr,rr;(1. si.rurrroll,ir.

itt, ti,

l:.1j,ì,1.,1,t,1¿uLerI

.¡¡',,,¿ilir.ì lrr.[

lr) srr¡trtl

¡¡.

_r.r,srrlIs¹¹

,,i¡

;l

^{rr,rrrl .11,}

^is

¡r.rrrrrr,1r.ir,

r,i ,,,;';;i;;;ì,, t, (; it rj,,

Anolht,r, urcl'hotl oll <rollsir.lcI jolt

pal&gl,rùlÌ[].

^u(r

^t'r

^(1olìNf

l'llctloìl

rll'rtlea,llsi

n'jll bc gi'crr i' _the

ìa,s

1,

¡ll*,ísttlt (¡¡, !!t(ùlurbi,

,,,., _{lllt,rrr. 'l'lrc}

lrr,l-lirrrrÍtr

-ilt'r

_neAn jìì(ì(ììtrr,lii.¡,, ri,ìl th¿Ll, tìrc nt<.¿r,ns ,,li

.ll(t,

.r¡) -.-- ,ll'(;.i:

t

.t¡) |ot, iì)

*

^tt.

,t\s i1,

is

ìirlrlu

lt

(sec _{i,l.S ]) :}

I),

^-.1

_l)" il,

l, ^.,._ s.

ru-trir'Ir

fì(ìlì,'jììizos

_{t he}

l-ìir,r,.

r,crrriorr<,rr ill.tlrr¿t,ri1,.r., _:

{l

_'-,

(i

.:- _-1.

li[]olr,ltslt, iir

_¡,lrt I

I

¡,.rulrl

tlr¡¡f ,{

i¡

?ì.s tn)l)t,rr\/(,rl

ltv

lì.

\.(ì(Ìr) Jìr.¿.rìs o.",,,,,ì,,,1).]1,]l,,Tli,.,r,

.r.,,,_

,it1

r.rs.r,

f

r,o'r 1:i

1 ,

'ì.;,:

_:,;,il' ^,;ì.-

"lf

. _'.1.

[',

rutrrl r'.,

. 11, l) lcu I i

^Ir¡1.

^¡,

^rol

t

7

^\\

r' _lt,i\'(, ,,í

tìr

itr

(,;,. _ll-1. ^, 1l' ':,).1

/

ttrrì,r

(lÌ, i'r) ¡¡''i, ^:'i¡.

^, _I¡

3. l/! ol I

lrer.¿t.t¡st, _:

'9' "'

_"1

'"'

^l11,

lrl,r .-

l'¡12, _,g

.t ,. (ì:.,,

^.l)..

l'<u' 1,

, 0

tvtr Ìtill,e :

(6)

_1,,

. (i

--,. .!, ^.:_.

[,,,,

rvìrich

\ì;ìs

r)l'o\¡('(r ^r11' l7i¡¡

i¡¡

_f r r

/. ^rror

^r,

^.,. f thclo

ii rsrl Í.ilrrou,s _:

(i I

_!',r,:,

_.r

_/-

_<:

1)r,,,r.

:,r.

ll].,;']l,lTìil.lïlì'iì ,!],ì.,ì.':''l:ì,'!;¿,rirr _'r'1a,,'.

sr,,¡,,r,, u,,,1,

is,r, ^j.:

,e,r,

f'tt11ìtt,g

irr ({i) llrrrl (',) t,...

¿r,. ¿r,rì(l

.t1.. ¡:tl\.(j

eï,1 ;

(; '<

^1,,'-,1

I),i,t

,1, P,¿,/:t,-.:

[, .< I,,tu:z: l, :,

ll,

or'

_'D

: D" -- {(t:.

^{,rr) :}

cornpalabilil,.y _ìrìc'

llaí;

1,^ií,,Tî!;ìHl,k,'J

Go,t,

1G,r',tt'+

IL

]

cL', ¿/

<

^ú,

Go.u

I Á,' èc _{ç rnin ¡lu,} I - ltl¡

1Io..,,",,,

1t!" ^<>e _{ç min} (ufc,

(ct

_l

_¿t

_ _b)lþ + ^d),

^I_.|)ld,).

fllhey

ale

irnmecliate

the lbllorving

eqnivalences _:

l'[ _< f,[' + IIi {

^M¡

+ ]Ii 1.t}[" e Jl[\/ l[, : ]1, å

+r.

ltAnf, : n¡ +,lf _<. l[,, (][)

^jl1,)

< ]l[,,

^V-,V,,.

\,Ve also have :

jl,I(p', M,) < ^jJ[,

^z,nrL

i]I(fuI,, f),,)>

f,y,.

It'irraìÌ1,,

ìte

I,ern¿ì,r,lc

flrat ilÌ I,c

denol,e

ì:y:

Ð(M):

_{(,¿,

_{u); )I(n,} y):

il-

f,i$.,]1r"""

^{is nn}

r

suctr

flrat (r,

y) e

DeI) l.hile (r,

u,) e_Ð(rV,),

ilren

^.w,e

lrnt ^>'!l'

^rT

^{M < M'}

!/

):, 1¡'

fot r ¡ ¹

and _U

<!1,

^for,

ø q j jf _M <

^ilil.,.

4' l[o*ro1¡.lroiry ¡l.lrperlies" rìernarìri'g _trrat,

'ot ^arl

^{1,he srrrtrie'}

nleâ,Ìrs

ale

tromogeneou,s oi.

logarjt¡riil, : 1r;"*;i.,il: _tha¡

_{is :}

Jl[(e.t,

f) : ]llt(rt

r7)

for _{ü¡ !/¡} t >

⁰

itr f'o

_i28 rncan

j

_\\'tr

/1 rla'c is carred;;;üh",;,;;ääî, rroti'ctr r,ire .oto*,i*s

g.rre'alizir,tion (l-rog-subriornoseneor$)

: f'r.

er

givc' ir:

r, ->0

ÌlI(l,e:,

tu) 4 ^tM@,1t)

(r.espccl;ivel¡, jl,¡1¡t,

.1,)

( Ilt(r;,

y)).

Ìf the i

l'es¡re<;l;i

^'sctl

^,

^ülte ttt"etùtt

is

"a.lla9, -superJroruugeneous.

¡t ii lii

gc[eotr;(.

of

coulstr,

it'lu

s

iåìrhh;;;;g;;ì;;il;

1l.e have

flre

fclllorvjng lesuìts.

Sorne rerna¡i<s otl meaÌ1s

I cl3

10:.1 Cìh. -foarlcr

IrL

[36] l'e

l-r¿lve pt'ot'ecl thal, ^:

Ð s ^A : P,

a'lltl

thai,

Z'is not

corn¡ta,t'able

l'ith

?,.

jot,i'> _{5/3. \\'e}

_.h¿-r,r,e corrjectulecl tlrzr,l, 1/

)

^I?utr.

In

l'28

| ^using

^thcr

lc,nark (5) anrt puttìng in (./) n : stt,

^,!

:

eu

¿nd

logat'ithmal,ing,

we

^{get; ;}

1lrr, { Il

^q.R.r,r2.

Âlso, fi'oru ((i) and (7), ri'c have G

<

^.1,

< 7

^u'hich

^siì'cs,

^{¿l,s ¿ùbovc:}

(8)

¿1 .::

I; <

^lL

.[ìel¿r,tittlrs ltotrveor generalizotl aritluneticr, gcornetlic

anrl

.halnrlrnic ìrl{i¿ì,ns

hal'c

btrcn

givcn irr _lÍ37j.

Urs le..tnincl sorne olì 1;hem:

Gu,tt

{(}n'.r,'

^.'>Q'

-- (' - ll'-

^D

>

⁰

I:1o,t,,,,,¿{ 17 u',¡',"'.,t'

*:";.:,

:: ;r::,;",r, ::'},,rrr'-

al

^b)lQ

+d) :

-

Gn,t,

{;1.<+fi-¡ll-f a1,r::=

⁽¹

f ^o -

^It)12

f:[ u.,,.".¿t

1 ^A" ë

_{ulc 1-} ^lrld,

<

^{L, e}

:

(u

-- ^lt f

^{tl)l@ -]- d).}

'llhclc

a,r'c ¿l,lso inecluzr,lities

of

-tni-xctl ^{,.1.pe,

u'ìrich inlolve

rror'(ì rìrr¡rìrìs. So,

in

_[12] J-ì. C. Callson plovecì

t]rat

^:

G'

.l'1¡2

1L2.

llllris rva,s ìrrrlrtovetl b5'

II, Alzel in

_{[.1] as} ^:

(,].[..',f,2

'ryltr¡ _¿llso ¡l'ov-tit1

iii

_I'lì

| that

^:

tl ^'G <L'T.

Ilsìrrg

hherrr, rve li¿u\'o tleril'ecl

it:'

_{l'27 )}

the

in,eqtalities :

rt _-l- /l -

^/'-

< ll _<2t¡ - ^A

rvhich

cz¡,lr l.¡r-' cor-n¡rarecl rvi1,ìr (8).

I'ol norrsyrlulctric

mearìs,

in

_[29.]

atttl

_[1

6] was

uscd ^¿ìr colììpar?ì-

biliLv on a

subsel;. 'llho means

-il[ anù .il['

are

in

relal;ion

lI 1o ^trL' il:

M@,

1¡)

4 il'(r, ^y)

^1'or

_1r,

u) ^e

I)

ß

( iir 'l oarlr.l

ã\ i.[ if

i,t I Lor¡-nrltlr()ntollot(oux) l,ltcn

tjl.¡

^,t'n- | ^:l ort_,:it ¡ttrlto_

ll

Sttrìri-' _{¡¡,;,r ¿t rlr-s r)Jì} iÌt(\¿l]ts

l,rì\t \l \

ttti)tJ('ttc0tí.r. ^()t

)t) i,l .ll

'ix t-sttlùtotìto(tc)t(ous)

lli(tt ll, il;

lsul)r).ìtonto(l(,n(,ou:i,

c) f,l :ll ¿s

!stibitottt()tl('t¿(ot('i,

tlt(n ,ll'i:¡

tt

.so

l-sttl¡lto¡tpít4t('otts,

., jll. !/. ^'rlt. )l', ,l[,"

_{1rr' .r} (r'o¡¡)-!rtr)rtotnotJ('tteotrs (rn(r

.]Í

^,í:; itttt'r'u,s,i,,tri¡,

lltt'n .tlt(il', ,ll")

^,í,x L (l t,g) sttltltonto¡¡t,t?,(,ous.

\\'t' l'clllltl'li 1lttlt'

tltt¡.ltl¡rLrrir, inr¡roscs ¿rrotlierr, tr'¿t,l-

ol

ol.¡t¿r,ilinH^ ¿t

i\,\'r)ìlìl(ì1I'i(r

tlt{'iìIì

i't','¡¡¡ ^,r,

i.ïiy¡lr 9¡rt,¡llit,ìt

lll.cii(,t,\-(!s

tìie /

l¡¡¡_lriLltlroir';¡_

{.i(ìni'jl,\'.

'l'llis

r:il,lr lre rlciinr.rl

lri,:

;¡¡rr (.t' t .t1)

.

G ( )l

(t',

u)

,

^.tt(,¡1

,

^t')).

itl

_l2fi

i

tt'tr ltll\''(ì ì'ernrìt'ìicrl

1haÍ

f,hir rncarrs

1,,

iùl,o I, l9g srtll¡9rrr¡- Íl('tr('()rrri

l't¡r' I ¡ 1

^{aLrtl -r¡',. iì,r't¡} /-sçllhonrrlrl(ìÌrcoirs _fìrr,

/

-__

ì. ..,\ls,l

w(, ì.tlt Vt' ¡lt'tlt'tlrl ^l

ltai

^{/ti^ is} _l-sulrlìorìì.o.!,e rìcor¡s

r¡rirl r ;s

t,to3'-suì.rìrorrroggrrsg1Ls 1,":.

/ :

^{'ì ,/ìo'g ,\}

'

^{0.f)61 . '}

,

[-,rsìn'tì 1[u' ¡i¿lrriu rriollrot'l ìr.,, r,,r,,' }r'or-tr llrc I'ollori'ing, rrot,(' Iìctìel'¿t,l I'oirrIt, :

'l'rìi,t,lìi:rr i. [.l

tlit:,tttcrr

tt ,\,t

^yriJries llt

e

tlottl¡l,a t,t:Iut.io,:

!1)

1,,,

<. )l

^{.:_ l',,}

ht,tt t'.1. t:s

7tfry

l.og-suliltotttog?tl.toulJ.

I't'oo.;f

. flllte

incrirL¿r,lj1,r' (f))

ltì*¡rìs

1,h¿11 :

((,t,,'

,

ryr)p\t;n

<

^,1/(e,, .r¡) -1 ^((¡.:r

!

,Ít)f2)tt,t.

['ttt,iitrg i¡t

[,htr l'il,,qt, ìl¿tL,t c,D

- ^t(

Ít,tì(l ],//)=-

t, l.o

l¡trl.:

(¡¿

I

^'¿')i2

.1

ill.t'('rrLtn, ,r.titt¡.

ÀlsL,. l't'oln

illtr

setlolltì

1;ali, ^lirt'

^.)),t --,ìt7 _.tltt .-,¿.) \\.(ì h¿t-o:

t1'['1 (ttttq

,

'¿'l/")

<

^{(¿¿ .}

I Ì)

^2.

'lia.l<ìrrg,

in tIt'

r'esultirrg iricr¡rrrr,lit,,r,,

rr

^-.,¡¿tu, ¿lrrt[

á -.

1;t/t,, j1. lol¡rrvs:

.llQ(t,l't, brl¡t)

<

,1¡r,/,t(rr

,

^b),

/\triÌl{)rqou¡il\', \\'(ì ^()¿ùtì _l)l'ovrì :

'l'll,:ol: _t,t.rt

2.

-I./ ^:

ll,, .:- ill

^{.-- lÌ,,}

lltr:rt

:l'I,i,t; _¡t fq,:;tr lthontoqr:trr:ott:;.

lit¡tlhltr 5,{!{llietlc{t¡i. (lir.crti _{t \\'o} lrì{lltr)¡i ,Jl

antl

,lJ.' ottt: rrit,¡

r[gfili.

l¡

rloribltr s{Ì(f ucttcr(}

(ol ll

lrirtirrrclrsjorra,l i1,cl,a,1

ioit

¿lgolit, lrnr) slat,iirrg, l,rorir i;n-o llosi{

iyt'

nr¡rrrllel,ii u,o

itlrtl

^'r7,,, itL

tl ^o

ⁿ

t\.s

:

(l()ì

)',,.,,--,1,[(t',,,t7,,),

ll,

t-.,i|[,(,t,,,1,!1,,)

(l i ) _;7',, , , ,ll(t,,, _.r¡,,)t !/, t . i!,(rt,,,: t, ,,/,).

r,(ìl:ùi^(l _1L) ílì(, lrill:iillt., t,gir {il :[ {.r)tlilrrrr¡¡ ji¡¡¡,¡.

/ ^I I

i ^t,). ti /;,,

_,,;,;i

iì'¡ _: 1 ^., .

.Ì.lt¿ t ,t/ ¡t : t- .t,,,

[ìt i,s,.1¡¡¡ \'r,Ì,g.(,j¡(,{.

r i,,, ,,,,j,,,ì,

,,;: i:;i;,,1;;lì

_,,;;,jl ,,,;;ï,,,,,,,,

,;.¡,,11:,,,f :;,,r,r,r1,¡¡ 1,¡¡r,,¡.

;r)o¡.t/at

¡e

rrerLri. ,,,i,')11,,1.1i',f,]]"],:.

::

('oirl,:,11

tt;i;i'ir;ì';,ili

{r{'ìrìtiilil¡1¡"" _¡¡' a

gorìr ,, (,u) ;,,;;"ì,i:lìïì:ilïl;;,:î,,1lil':-i,;::,llli

1,ìli,,itf:]ri;

:;ì;;i'ì,ï _l'ii,;; ,j','l"r)',."r'j(r

^rr

^.,r,rr). ir rlis 1,,, ^,,,,.

^.ttii'l

,¡'!tt,) ,rrisi,\

,\(l

,

^r,

,

_Ll

I/ i,

^,,,,

"" ^{tt' ill'('}

li-('('llr¡"''itJl,''1 ,','*,,.,.,i,',/r

i:

-r.t:rrrrrr.sirrrur).

-l-("r,,i,,,*ir,i,l ìi ì'rilì "i;iìl:",l,ll'';,,lli,::,;'r.rri¡¡¡¡r¡¡¡'*

"r,ì,';ì,,,r.i,.r¡¡,,¡¡¡¡,i .,,c

( l'; ^¡

\ '^ ,/ _{,il (:t:,}

.y) ^:__ ,1r :-> ,, r _.ti"

Itt fllÌ/.',il lrrr\.(ì l)r,()\(¡(l llrt,s:ùlutl _r,,, Itì(ì¿üll:i. ll¡ l.:ll I u,

,,J't:rtri,,t,s.'''¡"ì"'""ti'i,''ìì ,,iI,,"'ti,::tlll,,';li,','it'll,,lì1",,,i.,

',|ìt',ìi,'],,lil;1,;),,l,li

,(,ns

_ill tt.t¿tl

lV, ís

cor¿,[it¿ttotts uutl Ir3)

)l(.t,,

_1¡)

-

^. .U =>

,r,

_,,/.

tnen

tltl.sl;tf ,

_enists.

10ti Gh. Toader ¹⁰

Proof

.

n'rorn (1) follorvs

that the

sequences (u,,) ancl ^(t¡,,) (10) Iie in

the

closetl

interval l

tlebermineil

by

ru ^ã,nc1 _3ro.

By

the

$reiersl,rass thcorem, there is ^¿ù sequence _Qr¡,.) and

the points

ø, strch l,hal,:

iinr

ccr,

:

¡ur

lirn

_U,,r

: !/¡

^{lir:t't {ütq¿+t}

- fit)

Iitl-r yr,.r'

: y'

,li+æ ft+æ d+æ å+æ

llhen r:

^{y. fncleecl,}

^if

^{ure sttppose}

^n1u¡

^{as ï),t;it}

:

-l[(nrr,7¡n¡,) ancl !ftt¡,]t

:

=.

tr!['(ü,,,r, lln:J) ilj follorvs

that

^:

n<n'4.ut0<!l'<y.

\Ye pror.e ^{1,h¿11, :}

(14) ^ß' : ü

oY

n' :

_?1.

Il r<n'<y'{y, ^rve

^choorie

0<r'.--(n''-n)i2

^{trIC1

1l==f1,.

such

that:

lfrnt;+,

- ^{n'I < I}

and lYnrt,

- ^{!/'I <1'.}

So;

rrrr7,.-rr

) ^ff' -

^{,l' ;>.}

^(u'

^{-l- n)12}

¡¡,ntl

!Jn¡,+t

)'t/t

^-

^t' > ^(n' +

^fi)12.

ft,

^{follo-n's :}

r,, ) ^(û' !

r)12 ;>

r,

Vn,

> I(

which is inconsistent wif;h the hypothesis [,]rat:

\frr"r,: n. If r { U' < r' < y rve obtain a similat' contrad,iotion b).

^{choosi¡g ¡}

0 <

^?'

<(y -

^n')12.

Arralogou-sly

we

can.

prove that

^:

(15) !l' : n or

_Y'

:

'11

holcl.

It

¹⁴ saiisfies (12) anct (13),

from

(14) ancl

the continuity

of ',41 rve geb :

æ

: l[(n¡ y) at y : M(t:,

^y)

tlrtLs a; :=

y.If il{'

satisfies (12) ancl (13) rve use (15).

The hypobhesis

r ;'

37 gives analogously

r: _!J.IIence

^:

lim

ø,,,

: lim

_lJrr

:

fr

À+æ fr-+æ

'¡vhich lea¿ls

to

l::\*":1;y2u":

^n'

Rem,rtrfl:. lhoso results pertnil,

to

cornpose even cliscon.i,inuous rrt€Al1s

ìihe:

M@, uJ: ^min

^{(rr, q)}

^il

ⁿ

⁴

^a

nra.i(ø,

q) iÎ

n;> u.

- , ^.\s

(1(Ðtecr,rts

tlto

:r,st¡lf, lesrll[s. il]lre trrosü knorvn

is

üit

of

_.ühe corrrpoxif,iol

e

¿¿rirrhnÀtli"-'c=åili' rvo

rL''rnind

lele

so¡r'ur

;r'lc tnean

of

{ì¿lrrss _: .)1T/2

_Jl

!/o)

^,,.

^'!

('¿i troszl _-J-

.7Ë sirr'?t)

-'t, _dl.

0

ft ^js also plor.erl

_(sec

[.13])

^1;hat

kt'å

-

^r!¡trz

fi at<t r:os(uofuo)

(n?,

-

^ltâ

^)'t'

arch (n,,f _¡¡o

In [32] l.c ll,ovccl that:

¿17-l¿': it,, c,,ltila,

-.-

G,, ,,!zilu,:,, _*,jLtr r: pql(r _

^,p

_lpq)

hoJrl _ancl

¿,li.l'tr: _{-{", n,,l!,.f}

,,, =,(,,", tt,r--g

¡Iro ^=.= }f

,t ^wJre'*

s _{=_}

It is

eas¡.

to

,sttc

that:

^- -'--i-- 'l¡:--

rI, r

^{wìtet'rl .s} =-

ql1 _--

^,p

+

^g)

,1,,!gltt, ,..(i

anil in _f?] it is

also rern¿tlkecl

that

:

t:,fglr

_{_,}

: ti.

Generallr _iú is

difticult to

fincl i;ìre corrrlrou¡¿

r.ean.

_{li_or}

-'ïffiï"un;;

.J

. \\¡jnrp itt

_{l4Z l.}

As

cotlcclrrs

lltc

l,el¿l,tiolr _ltel,u,eer

lcsull :

^{I l,Jtc} cornporllrd _nrc,ùns,

rvc

¡¿ve

_ûbe Irrlt\{ì{;\.

I,f

^{jl,t q,t¿d,}

il,

cc),e ,1,7xçy¿qsrtrtyJ,

l;hert, _:

il|gf,M' -.' trl-altvr"

n,""nJt'å,"iî,1'1'il,,i',,1;,,uîÍ;::i¿fili,i#ì,,i,i;li* ,r,, ¡¡|¡sy6

_{1,airs o¡}

(Tr¡, ro prove jr clirecuy,rl''n <

_'qra''|G'

_

^{'l'he r.ate}

^of

^co

arso

srurricãõ,:;-,i,r,ìT,"r'"",iii;i,,fiîÌ:iï;liîîî,'î,rrJ1o

",,,,,non rirnjr

rvas

II Sonre .i ctn arks 'olt _ìllearì¡i

given

by Ilolzano-

?/¡

fr'¡

_!/',

107

l

't

^{t)(I G(øo,}

clc _<1 '!/o

!/ o) _?

lc

A

) '

^fru

^);'

^t¡o

ìll

i:

I 1

Gh. Tr.¡¿tcler

IìI.]IIIiIìLÌN(]IIS

12

l I I

1 t)ri

i;l Sonc rl:t.narks on IìroaÌlS

109

l. .\ .l I rr s i a , ^(i. , liLt tttrtt r:1¿¿ssc 11i rrlgot iIttti iLcrLttioi bíditttr:ti:tiitttaii, Iìt'lld. fjcrlr' lI:it. Ullìv 'l otiuo, P$ (l9ûç) 70)' 269-29ti.

.j ^{J\ j I} n i ⁱ u ,' (,., itrtu rtrtttctttli:zct:ione dcllu tlisur;uttl\(LIì:(L di Liapottttoll, ì'ìcrrrl- ^Sicnl. l\'Íai.

ì lrir,. i't¡lilcch. 1'olitto, 3;l (197't--7ã) , 2ll'l ^'222.

ij. .\- lz- c r', ^lì-. , t,Ingleit:l.un¡1ctì ¡úr ÀtiLiatt,tctlc, -A'cit. ìlal-¡., '{? (1986), ¡i22 _-'1jlli'

.1. ,\ ^L 2., ¡, Lì. ,'fuin i,rrr1lutiitíqi lor nrcutts, (1. iì. llaLh. lìcp. Àcatì. Sci. (ìarratln, IX ⁽¹ 98?)'

lt 1(i.

l) À¡(l r.c¡Ii, (,,, ,\lttlic ^{a lot} o ^processi ítcra!ioi, Cio¡'¡alc lll¿r[cnt. Illtltngtili" ^{(5), Bì;}

(19o'l), oiì ^79.

ti ììau'cr, [iI., ^{-,! ¿./r¿s¡j r:!} nrcrLn: rutrL t¡:lr¿ittl itrcquilÌlics, llatlltr;cr'ì¡lta,llaLh,.55 ^(1986),

199--2112.

7 flor.rrt'ill,,I. ^1.I., llol.uciÌt, l). ll,, 7'1rc ti,rty t'l'ttl itncrLtts, Àll;cl . -\Ialh. r\'lonl"hly, 9? (19¡j7), i'l 9 - ^522.

¿t Il L'ì' n ,r .: . , ^.I. i,., lt _{er -r,} ^s, lf. F,., Sonu: rc¡trotlttcirt¡: ld¡rl/ill¿s _for fittttilics ol ntcan ttctlu-ct;, -\c11turt. i\1:11.11. , iÌil ^{(1 rJ87), -t 00} - ^{1 1 il.}

fl,ltrilìclt,l).S..\liLLi¡¡r,itt,l).S., \usió.ì'.ll.,,ì/rttris<uttltÌttirirt.ttclttctlitits, f). tìcidct l'ubl. {lotlr1.r., Dor'.lttrch[, 19tj8.

ig, llrrr'r'oì\'s,Ii. ^L., îalìro l,Iì. l¡.. ^{ll'hic/¿ nteatt tLo} IJILLnÌ(etl?, t¡1. .I. llat-h. Educ, Scì.'l'ccìl:oì., l? (1980), 275-'-2tl'l.

ll, ^{(ì ¿rL.} lso¡, 13.(,.,,41¡1,,r'iitt,nsittu6.Luingurill¡utclit:tttttlrtt't¡¡t¿lticlrlc.¿/ìò-,Älìlt'1 .ÀIath'XlonLhly'

i'3 (i971),,{96 ^l-r05'

l12 (ì a ^L. l,;,r-u,lì. C., |l-lrc lrt¡¡rtritlunic rrrnr,Àtr.rcL. l'l¡.Lh.Ifonl"ìr1¡" ?fl (1972)' tì15--613.

lll ^(ì Lrr'ìson,ll. ^{O., G Lrs Latsr} ou,.I. L,,'J-olaLposilioity ol tttctutDulLLcsu¡tdlillpergconrc-

lrit l'nttt:lioits, Sl,\Àt .J. l.l¡.|.h. An'.rl'' l'i ^{(1983), 389-395'}

l,l. t,'oitcr', I). ^ù1. ll., L)Jrillips, ^Cì. lI., A ¡tcutrolirallou olllrc:\rcltitttatl¿tt¡t dotbLc se- r¡tLr:ntr', J. rlhth. ^{¡\nal. Àp¡rl.,} l$t ^(19t14)' 575 581.

1... i',stor',1). ll.,tj.,f,¡iliips,G.ÀJ.,7-û¿ urilinnelic-lru¡nottit:tntrtt, ],I¿rlh.otCorup.'

¿ri! (l9ii1), 165' iii3 191.

'| {j. tf o,sf .,i-,p.ìI. Iì.. ì,¡il1ips, ^(ì .,ìI.,Octrcrc!rntnpuLtu! ^rncrtrrs, [ì.cl;.Nolcs]ltth., ^131]

(19[J5), ãíj"'6t-r.

1Ì ì.ostcr',1). lt. Ii.,lrhillipr;, (i. ùI., Doul¡lcnuttt /ìro.¿ss¿.s)'l'lrt'lrtr;l"itulc oi]{atìl'

¡rrrl iLs '\ppì., ilil ^{(19fìrl), 170-173.}

Llì IIa'rl)','t;. ll., f,ìl'l'it \r,ootl ,.:J. It.,l)olr,:r , (\., ttrcqunli1lcs, (lanrlllitìge, L934'

lir. L;ìil ,,oi,gc, ^.J. -- l,.,,Sul ^uttc ¡to,-ror:!!t ntiitr.¡tlc rl: calcul irtlcgrul ,l'iclrl. ^{Ì';\cacl' Roy.}

Sci. ^'i'Luin. , 2 ^(l-/84 -1785), trtl\¡res ^. t. 2, Palis, 18(i8.

i2ir. I.cac¡,iì. ll..Slrulalirt cr',1I.(-)., li.tlenclcc!tneattualucs 1/, J. llailr. Anal.Âppl.,

t¡¡¿ (r9¡ì3), 20i ^:12:i.

2 f . l, ^j ; , 'l'. 1,. , ')'1rc poutcr tnccut ttnd tle lo¡ltu iiltttic ;nacn, AtncL. lf rrtlì. ìIonlht¡', flf $974),

liTu ^8R3.

2'l ^r\,f a l- ^s , ^{i\,I. 1Ì,.,} I;ttttcliotts tulticlt plt unrcl.rizc tnccLns, Ä¡icr', llatlt. ^lfouLhìy, 90 (1983)'

l) I / uù.t.

2:i Àfil-rinovió,D.S.,PeðlrIió,J.fi.,firetlnjeDrcditoslittntaLentutici,Nart<In¿rl{njiga' Iìcoglatt, f .i)8{).

it I lI o,-s li <l v i I t , l)., ,ltt alignntcnt t:lnr! for ^uoriorts rrtctttts, Àrtler. ]IaLìt' llouthly, ^4l]

(1933),592--59t1.

2f . i{ yr.'Á

" '' g, lr. J., S¿¡r' ¡¿n¿ ¡1en(:rrtliscttiott clc l.o nrcgenne u'ítlmtLirlttc-¡¡lott'rót.riquc tlc ^Gauss, (1. lì. r\catl. So. Paris,:?46 (19ã8),3201-3204.

2il. pioL1a, G., I)i tuur _formulrt per iIcalcolo ^rlelle nttlic contbirrrLloríc, AtLn. Soc' Pt'og'

Sci., 2? (:939), 5, :lB--45. _ì

2i. ^I> j Llen gc r', À. O., IneqLtctLìttes bcluectL uritlt¡ncllc u'tillogarillntric ltTccttts, L-niv. lloograrì.

Pub[. lflektro. Iìak., 678-?IÌi ^{(1980)' 15-18.}

2g, Sárrrlor., ,Ì., Ioaclcr, Gh,, Ofl sonTe erpcneltliul rrcttns, "Babcg-Bolyai" univ.'

Prept'int ? ^{(1990), (35-40).}

l2fr. S c lr o o n lt ^c r.g-, I. J., A,Icttltct¡tt/ticaL linte exposttrc.s, 'Iìlc llath. Assoc. oi ^Arntllicn,

1982.

30. StolalsI;.y,I(. I).,Gcnrrtili:rtllonsctl ilt:lorlltilhnit: ^rirt'nn, lllllt'\fngazirlc,¿*'U ^(19'1'c),

at o,

Íì1. ll'oatlcr, (ì¡¡.,(i¡t'Lpic:;gr:ttcrtLliz.ed r1e(t)r.\, I' ils t lr{at, S¡'rrrp. "Iìcal!zãr'i ¡ipcls;;ci:ti\e îrr clt llrcnirti lratlttcIollclol", Chrj, I986, lll, _'lti'-49.

tblc sequen-es, Sl_urlì¿ t,,¡rir,.,,llaitcs-lJoh.ai,,, of dortblc s,equcttccr;,,,tìlbcl_13ol¡,ni., tiriv.,

s, _¿\lal. Nurnér.. .i.hcor,,,\p¡l,o;i.,

ffj ^(1gBZ),

rcans, N:rt. Cont. r\ppl. l\Iailr. ùfcchan., Clni- es_Iì^o.t¡,ai,,,IJn eiric ancl l.un-nonic i v., Prepirr ;narzns,,,13al)e;;_tìolyai,,t ? ^{(1. ggB),} õ 1 _ _¡j4.

alqorithnts, .,Baìrcç-Rol¡,¿i,, l,Tltiv,, plcprinL e scquerúes, Secoud NaL. Cont. Âppl. ÀInilr.

ari d¿Ile lrc classicltc nviie , AtLi r\cc. lici.

,lìlìli.l':l;,l,i-;itç;ì,|rlÍr#,,1#,_::{i:.i,.t,,¡tet!'a¡tutisiit,tttericrt, oonoc¡1rtol,r/ci.rr.,:\ccatr.

ut),]"."r',1,;,,'],'rJJ:'íii¡l]';iîì'ttttt itc¡{¿tio, at¡'oritttitis,lrcrir. s.¡'. -\r:ri. r'rir.. l'orircc. r.o.iro lìcccirtd _1.X.1990

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