%PDF-1.3
%뢠 rules
4 0 obj<>stream
1 0 0 1 72 720 cm 0 g BT 1 0 0 1 64.54 -62.46 Tm/F8 9.96 Tf(c)
Tj/F14 9.96 Tf -2.77 -0.3 TD(\015)Tj/F8 9.96 Tf 13.28 0 Td[(2013)
-333(Heldermann)-333(V)83(erlag)]TJ -13.28 -11.96 TD[(Journal)
-333(of)-333(Con)28(v)28(ex)-333(Analysis)-333(20)-333(\(2013\))
-333(483\010493)]TJ ET 1 0 0 rg BT 1 0 0 1 61.77 -98.63 Tm
/F15 9.96 Tf[(A.)-383(Zac)32(hos)]TJ ET 0 g BT 1 0 0 1 61.77
-109.09 Tm/F16 7.97 Tf[(Dept.)-472(of)-354(Mathematics,)-354(Univ)
30(ersit)30(y)-354(of)-354(P)30(atras,)-354(26500)-354(Rion,)
-354(Greece)]TJ/F17 7.97 Tf 0 -8.97 TD(azachos@gmail.com)Tj ET
1 0 0 rg BT 1 0 0 1 61.77 -138.98 Tm/F15 9.96 Tf[(G.)-383(Zouzoulas)]
TJ ET 0 g BT 1 0 0 1 61.77 -149.44 Tm/F16 7.97 Tf[(G.)-354(Zouzoulas)
-354(Ltd,)-354(Mein)30(tani)-354(25,)-354(117-41)-354(A)30(thens,)
-354(Greece)]TJ/F17 7.97 Tf 0 -8.97 TD(pantarei@zouzoulas.gr)
Tj ET 1 0 0 rg BT 1 0 0 1 61.77 -184.31 Tm/F15 9.96 Tf[(An)-383(Ev)
32(olutionary)-383(Structure)-383(of)-383(Con)32(v)32(ex)-383(Quadrilaterals.)
-511(P)32(art)-383(I)-32(I)]TJ ET 0 g BT 1 0 0 1 61.77
-210.21 Tm/F8 9.96 Tf[([F)83(or)-472(P)28(art)-472(I)-472(see)
-472(the)-472(authors,)-507()]TJ 0 -13.95 TD[(J.)-421(Con)28(v)28(ex)-421(Analysis)
-421(15)-421(\(2008\))-421(411-426.])-707(
)-421(W)
83(e)-421(solv)28(e)-421(explicitly)]TJ T*
[(the)-301(generalized)-301(Gauss)-301(problem)-301(for)-301(con)
28(v)28(ex)-301(quadrilaterals)-301(in)-301(the)-301(t)28(w)28(o)
-301(dimensional)]TJ T*
[(Euclidean)-333(Space.)-444(By)-333(in)28(tro)-28(ducing)-333(the)
-333(v)56(ariable)]TJ/F11 9.96 Tf 61.66 -38.07 TD(c)Tj/F8
9.96 Tf 7.08 0 Td(=)Tj/F11 9.96 Tf 10.52 0 Td(c)Tj/F10 6.97 Tf
4.31 -1.49 TD(G)Tj/F8 9.96 Tf 8.91 1.49 TD(+)Tj/F14 9.96 Tf
11.16 6.74 TD(j)Tj/F11 9.96 Tf 2.77 0 Td(B)Tj/F7 6.97 Tf
7.56 -1.49 TD(1)Tj/F14 9.96 Tf 6.68 1.49 TD(\000)Tj/F11 9.96 Tf
9.96 0 Td(B)Tj/F7 6.97 Tf 7.56 -1.49 TD(4)Tj/F14 9.96 Tf
4.47 1.49 TD(j)Tj/F8 9.96 Tf 4.98 0 Td(+)Tj/F14 9.96 Tf 9.96 0
Td(j)Tj/F11 9.96 Tf 2.77 0 Td(B)Tj/F7 6.97 Tf 7.56 -1.49 TD(2)
Tj/F14 9.96 Tf 6.68 1.49 TD(\000)Tj/F11 9.96 Tf 9.96 0 Td(B)Tj
/F7 6.97 Tf 7.56 -1.49 TD(3)Tj/F14 9.96 Tf 4.47 1.49 TD(j)Tj ET
0 G 1 i 10 M 0.4 w 0 J 0 j[]0 d n 165.41 -287.63 m 261.11
-287.63 l s BT 1 0 0 1 210.77 -296.96 Tm/F8 9.96 Tf(2)Tj/F11
9.96 Tf 51.54 6.83 TD(;)Tj/F8 9.96 Tf 14.39 0 Td(where)Tj
/F11 9.96 Tf 35.45 0 Td(c)Tj/F10 6.97 Tf 4.31 -1.49 TD(G)Tj
/F8 9.96 Tf 9.47 1.49 TD(=)Tj 11.71 6.74 TD(1)Tj ET n 337.64
-287.63 m 342.62 -287.63 l s BT 1 0 0 1 337.64 -296.96 Tm(2)Tj
-275.87 -31.42 TD[(is)-289(the)-289(Gauss)-289(constan)28(t)-289(and)]
TJ/F11 9.96 Tf 114.02 0 Td(B)Tj/F10 6.97 Tf 7.56 -1.49 TD(i)Tj
/F8 9.96 Tf 6.19 1.49 TD[(are)-289(p)-28(ositiv)28(e)-289(real)
-289(v)56(ariables,)-298(suc)28(h)-289(that)]TJ/F1 9.96 Tf
158.45 7.47 TD(P)Tj/F7 6.97 Tf 10.52 -2.46 TD(4)Tj/F10 6.97 Tf
0 -8 TD(i)Tj/F7 6.97 Tf 2.82 0 Td(=1)Tj/F11 9.96 Tf 12.25
2.99 TD(B)Tj/F10 6.97 Tf 7.56 -1.49 TD(i)Tj/F8 9.96 Tf 6.08
1.49 TD[(=)-278(1)]TJ/F11 9.96 Tf 15.5 0 Td(;)Tj/F8 9.96 Tf
-340.94 -13.95 TD[(w)28(e)-460(deriv)28(e)-460(some)-460(new)
-460(ev)28(olutionary)-460(structures)-460(of)-460(con)28(v)28(ex)
-460(quadrilaterals)-460(and)-460(w)28(e)]TJ T*
[(giv)28(e)-475(the)-475(de\014nition)-475(of)-475(the)-475(degree)
-475(of)-475(plasticit)28(y)-475(of)-475(con)28(v)28(ex)-475(quadrilaterals)
-475(whic)28(h)]TJ T*
[(could)-394(b)-28(e)-394(extended)-394(to)-394(the)-394(degree)
-394(of)-394(plasticit)28(y)-394(of)-394(con)28(v)28(ex)-394(p)
-28(olygons)-394(with)-394(resp)-28(ect)]TJ T*
[(to)-364(the)-364(top)-28(ology)-364(of)-364(w)28(eigh)28(ted)
-364(Steiner)-364(minimal)-364(trees.)-537(Finally)83(,)-372(the)
-364(solution)-364(of)-364(the)]TJ T*
[(w)28(eigh)28(ted)-279(Steiner)-279(tree)-279(problem)-279(for)
-279(con)28(v)28(ex)-279(quadrilaterals)-279(giv)28(es)-279(a)
-279(second)-279(prop)-28(ert)28(y)83(,)]TJ T*
[(whic)28(h)-333(is)-333(the)-333(translation)-333(b)-28(et)28(w)
28(een)-333(the)-333(t)28(w)28(o)-333(F)83(ermat-T)83(orricelli)
-333(p)-28(oin)28(ts.)]TJ/F15 9.96 Tf 0 -25.9 TD[(Keyw)32(ords)]
TJ/F8 9.96 Tf 49.57 0 Td[(:)-444(W)83(eigh)28(ted)-332(F)83(ermat-T)
83(orricelli)-332(problem,)-333(Steiner)-332(minimal)-332(tree,)
-333(con)28(v)28(ex)]TJ -49.57 -13.95 TD(quadrilaterals.)Tj
/F15 9.96 Tf 0 -25.9 TD(MSC)Tj/F8 9.96 Tf 25.52 0 Td[(:)-333(51E12,)
-333(52A10,)-333(52A55,)-333(51E10)]TJ 143.85 -152.82 TD(1)Tj
ET endstream
endobj
1 0 obj<>endobj
3 0 obj<>
endobj
2 0 obj<>>>endobj
5 0 obj<>endobj
16 0 obj<>endobj
17 0 obj<>endobj
18 0 obj<<>>endobj
19 0 obj/
endobj
6 0 obj<>endobj
21 0 obj<>endobj
20 0 obj<>stream
%!PS-AdobeFont-1.0: mvr10 001.000
%%CreationDate: Fri Mar 12 17:02:53 1999
%%VMusage: 120000 150000
11 dict begin
/FontInfo 14 dict dup begin
/version (001.000) readonly def
/Notice (Copyright (c) 1997-1999 MicroPress Inc. All Rights Reserved.) readonly def
/FullName (mvr10) readonly def
/FamilyName (mvr10) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -17 def
/UnderlineThickness 3 def
/Weight (Medium) readonly def
end readonly def
/FontName /AGBTJN+mvr10 def
/Encoding 256 array
0 1 255 { 1 index exch /.notdef put } for
dup 8 /endash put
dup 12 /fi put
dup 34 /quotedbl put
dup 40 /parenleft put
dup 41 /parenright put
dup 43 /plus put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 47 /slash put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 56 /eight put
dup 57 /nine put
dup 58 /colon put
dup 60 /less put
dup 61 /equal put
dup 62 /greater put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 74 /J put
dup 80 /P put
dup 83 /S put
dup 84 /T put
dup 86 /V put
dup 87 /W put
dup 91 /bracketleft put
dup 93 /bracketright put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
readonly def
/PaintType 0 def
/FontType 1 def
/FontMatrix [ 0.00100 0 0 0.00100 0 0 ] readonly def
/UniqueID 4011610 def
/FontBBox { -40 -250 1009 758 } readonly def
currentdict end
currentfile eexec
arqռ0ʄv!$&`W_RԨZqΎ[&},;mS6b~b,RmJBDڙ6D+Ip
+dЈdgB^Y$!@+ ?^loE/ҮS%_Mmn,UInhƞu37ӄsb*{im@e /bn
X976(
Eˠxh$LI|OB9=҄@?[ZbW
Lҳ)&Z(QEt74Vlmz|aPշ "e;"֦keZ=a] ~T"+%rmdhEIݭz
8Hٹ;lQ~_ =n?sFL|xEl:f`e0