Content-Type: multipart/mixed; boundary="-------------0301021407111" This is a multi-part message in MIME format. ---------------0301021407111 Content-Type: text/plain; name="03-3.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="03-3.keywords" Fractals, Astrophysics ---------------0301021407111 Content-Type: application/postscript; name="universe.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="universe.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: universe.dvi %%Pages: 4 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: Times-Roman %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -D 600 -Z -f universe %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2003.01.02:1523 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: 8r.enc % @@psencodingfile@{ % author = "S. 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Fr(in)f(the)g(apparen)n(t)f(dimension)h(for)2042 116 y(smaller)c(scales.)56 b(W)-7 b(e)35 b(suggest)e(that)h(this)h (increase)e(ma)n(y)g(v)n(ery)2042 216 y(w)n(ell)21 b(p)r(oin)n(t)h(to)f (the)h(true)f(answ)n(er,)g(namely)-7 b(,)23 b(that)e(the)h(dimension) 2042 315 y(of)32 b(the)h(set)g(of)g(galaxies)e(is)h(considerably)f (larger)g(than)i(2,)g(and)2042 415 y(ma)n(yb)r(e)27 b(ev)n(en)h (3-dimensional)f(in)h(agreemen)n(t)f(with)h(the)h(exp)r(ec-)2042 515 y(tations)e(expressed)f(in)i([7].)2125 621 y(This)39 b(w)n(ork)g(w)n(as)f(supp)r(orted)i(in)g(part)f(b)n(y)g(the)h(F)-7 b(onds)40 b(Na-)2042 720 y(tional)46 b(Suisse,)k(the)d(Minerv)-5 b(a)45 b(F)-7 b(oundation,)51 b(Munic)n(h,)g(Ger-)2042 820 y(man)n(y)-7 b(,)43 b(the)d(Europ)r(ean)f(Commission)h(under)g(a)g (TMR)g(gran)n(t)2042 919 y("Con)n(trol,)33 b(Sync)n(hronization)f(and)h (Characterization)e(of)i(spa-)2042 1019 y(tially)c(Extended)g (Nonlinear)f(System")h(and)g(the)h(Academ)n(y)e(of)2042 1119 y(Finland)g(\(pro)5 b(jects)27 b(46208)e(and)i(48557\).)p 2764 1337 598 5 v 2839 1338 449 7 v 2914 1339 299 9 v 2988 1340 150 11 v 2080 1579 a Fn([1])34 b(Y.)45 b(Baryshev)f(and)g(P) -6 b(.)44 b(T)-6 b(eerik)n(orpi,)50 b Fo(Disc)l(overy)c(of)e(Cosmic) 2194 1667 y(F)-6 b(r)l(actals)28 b Fn(\(W)-6 b(orld)25 b(Scien)n(ti\014c,)h(2002\).)2080 1754 y([2])34 b(P)-6 b(.)33 b(Coleman)f(and)g(L.)g(Pietronero:)49 b("The)33 b(F)-6 b(ractal)33 b(Structure)2194 1841 y(of)27 b(the)e(Univ)n(erse",) h(Ph)n(ys.)g(Rep.)f Fb(213)p Fn(,)i(311)f(\(1992\).)2080 1928 y([3])34 b(F.)28 b(Sylos)g(Labini,)h(M.)f(Mon)n(tuori)g(and)g(L.)f (Pietronero:)40 b("Scale)2194 2015 y(In)n(v)l(ariance)h(of)h(Galaxy)f (Clustering")h(Ph)n(ys.)f(Rep.)g Fb(293)p Fn(,)k(61)2194 2103 y(\(1998\))2080 2190 y([4])34 b(L.)48 b(Pietronero,)54 b(M.)48 b(Bottaccio,)55 b(M.)48 b(Mon)n(tuori,)53 b(F.)48 b(Sylos)2194 2277 y(Labini,)24 b(\\Scaling)f(in)f(cosmic)h (structures",)g(F)-6 b(ractals,)24 b(in)e(press.)2080 2364 y([5])34 b(E.)41 b(J\177)-38 b(arv)n(enp\177)g(a\177)g(a,)44 b(M.)d(J\177)-38 b(arv)n(enp\177)g(a\177)g(a,)45 b(P)-6 b(.)40 b(MacMan)n(us)h(and)f(T.C.)2194 2451 y(O'Neil,)47 b(\\Visible)42 b(P)n(arts)h(and)e(Dimensions")h(preprin)n(t)f(258,)2194 2538 y(Univ)n(ersit)n(y)25 b(of)i(Jyv\177)-38 b(askyl\177)g(a)25 b(\(2002\).)2080 2626 y([6])34 b(In)k(fact,)k(there)37 b(are)i(really)f(t)n(w)n(o)h(p)r(ossibilities)h(of)f(whic)n(h)e(the) 2194 2713 y(second)25 b(is)g(ev)n(en)e(more)h(dramatic)g(for)h(an)n(y)f (measuremen)n(t)f(than)2194 2800 y(the)e(\014rst:)31 b(Either)21 b(the)g(part)f Fm(F)3076 2808 y Fa(V)3150 2800 y Fn(that)g(is)h(visible)h(to)e(an)h(observ)n(er)2194 2887 y(at)32 b Fm(P)43 b Fn(can)32 b(in)f(general)i(not)f(ha)n(v)n(e)f (a)h(dimension)f(greater)i(than)2194 2974 y(2)g(or)g(it)g(ma)n(y)e (happ)r(en)h(that)g(the)g(dimension)g(of)i Fm(F)3727 2982 y Fa(V)3813 2974 y Fn(dep)r(ends)2194 3061 y(in)d(an)f(essen)n (tial)h(w)n(a)n(y)f(on)h(the)e(observ)l(ation)i(p)r(oin)n(t)f Fm(P)11 b Fn(.)30 b(All)g(the)2194 3149 y(kno)n(wn)c(examples)f(b)r (elong)h(to)g(the)f(\014rst)h(class.)2080 3236 y([7])34 b(J.P)-6 b(.E.)32 b(P)n(eebles:)43 b(\\The)30 b(Standard)f (Cosmological)k(mo)r(del")d(In)2194 3323 y Fo(les)k(R)l(enc)l(ontr)l (es)j(de)d(Physique)g(de)g(la)g(V)-6 b(al)t(l)n(\023)-37 b(ee)33 b(d'A)l(osta)h Fn(\(1998\))2194 3410 y(ed.)26 b(M.)h(Greco)2080 3497 y([8])34 b(P)-6 b(.)20 b(Grassb)r(erger)i(and)d (I.)h(Pro)r(caccia,)j(Ph)n(ys.)d(Rev.)f(Lett.)g Fb(50)p Fn(,)j(346)2194 3584 y(\(1983\).)2080 3672 y([9])34 b(H.G.E.)41 b(Hen)n(tsc)n(hel)d(and)h(I.)g(Pro)r(caccia,)45 b(Ph)n(ysica)39 b(D)g Fb(8)p Fn(,)k(435)2194 3759 y(\(1983\).)2042 3846 y([10])34 b(J.-P)-6 b(.)30 b(Ec)n(kmann)e(and)g(D.)h(Ruelle,)i(Rev.)d (Mo)r(d.)i(Ph)n(ys.)f(57,)i(617)2194 3933 y(\(1985\).)2042 4020 y([11])j(P)-6 b(.)22 b(Mattila,)i(Ann.)c(Acad.)i(Sci.)f(F)-6 b(enn.)21 b(Math.)h(A)e Fb(1)p Fn(,)j(227)f(\(1975\).)2042 4108 y([12])34 b(K.J.)24 b(F)-6 b(alconer,)24 b Fo(The)h(Ge)l(ometry)i (of)d(F)-6 b(r)l(actal)26 b(Sets)e Fn(\(Cam)n(bridge)2194 4195 y(1985\))k(Theorem)d(6.9b,)i(p.)e(83.)2042 4282 y([13])34 b(B.)27 b(Hun)n(t,)d(Pro)r(c.)j(Amer.)e(Math.)h(So)r(c.)g Fb(126)p Fn(,)h(791{800)h(\(1998\).)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF ---------------0301021407111--