%!PS-Adobe-2.0
%%Creator: dvips(k) 5.92b Copyright 2002 Radical Eye Software
%%Title: spodarev.dvi
%%Pages: 12
%%PageOrder: Ascend
%%BoundingBox: 0 0 596 842
%%DocumentFonts: Times-Bold Times-Roman CMR8 Times-Italic Helvetica
%%+ CMMI9 CMR9 CMMI10 MSAM10 CMR10 CMSY10 MSBM10 CMMI8 CMEX10 CMSY8 CMR6
%%+ CMMI6 CMSY6 MSBM7 CMBX12 CMBX10 TeX-cmex9 CMR5 CMSY5 CMSY9 TeX-cmex7
%%DocumentPaperSizes: a4
%%EndComments
%DVIPSWebPage: (www.radicaleye.com)
%DVIPSCommandLine: dvips spodarev.dvi
%DVIPSParameters: dpi=600, compressed
%DVIPSSource:  TeX output 2005.01.04:1244
%%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
% File  8r.enc as of 2002-03-12 for PSNFSS 9
%
% This is the encoding vector for Type1 and TrueType fonts to be used
% with TeX.  This file is part of the PSNFSS bundle, version 9
% 
% Authors: S. Rahtz, P. MacKay, Alan Jeffrey, B. Horn, K. Berry, W. Schmidt
%
% Idea is to have all the characters normally included in Type 1 fonts
% available for typesetting. This is effectively the characters in Adobe
% Standard Encoding + ISO Latin 1 + extra characters from Lucida + Euro.
% 
% Character code assignments were made as follows:
% 
% (1) the Windows ANSI characters are almost all in their Windows ANSI
% positions, because some Windows users cannot easily reencode the
% fonts, and it makes no difference on other systems. The only Windows
% ANSI characters not available are those that make no sense for
% typesetting -- rubout (127 decimal), nobreakspace (160), softhyphen
% (173). quotesingle and grave are moved just because it's such an
% irritation not having them in TeX positions.
% 
% (2) Remaining characters are assigned arbitrarily to the lower part
% of the range, avoiding 0, 10 and 13 in case we meet dumb software.
% 
% (3) Y&Y Lucida Bright includes some extra text characters; in the
% hopes that other PostScript fonts, perhaps created for public
% consumption, will include them, they are included starting at 0x12.
% 
% (4) Remaining positions left undefined are for use in (hopefully)
% upward-compatible revisions, if someday more characters are generally
% available.
% 
% (5) hyphen appears twice for compatibility with both ASCII and Windows.
%
% (6) /Euro is assigned to 128, as in Windows ANSI
% 
/TeXBase1Encoding [
% 0x00 (encoded characters from Adobe Standard not in Windows 3.1)
  /.notdef /dotaccent /fi /fl
  /fraction /hungarumlaut /Lslash /lslash
  /ogonek /ring /.notdef
  /breve /minus /.notdef 
% These are the only two remaining unencoded characters, so may as
% well include them.
  /Zcaron /zcaron 
% 0x10
 /caron /dotlessi 
% (unusual TeX characters available in, e.g., Lucida Bright)
 /dotlessj /ff /ffi /ffl 
 /.notdef /.notdef /.notdef /.notdef
 /.notdef /.notdef /.notdef /.notdef
 % very contentious; it's so painful not having quoteleft and quoteright
 % at 96 and 145 that we move the things normally found there down to here.
 /grave /quotesingle 
% 0x20 (ASCII begins)
 /space /exclam /quotedbl /numbersign
 /dollar /percent /ampersand /quoteright
 /parenleft /parenright /asterisk /plus /comma /hyphen /period /slash
% 0x30
 /zero /one /two /three /four /five /six /seven
 /eight /nine /colon /semicolon /less /equal /greater /question
% 0x40
 /at /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O
% 0x50
 /P /Q /R /S /T /U /V /W
 /X /Y /Z /bracketleft /backslash /bracketright /asciicircum /underscore
% 0x60
 /quoteleft /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o
% 0x70
 /p /q /r /s /t /u /v /w
 /x /y /z /braceleft /bar /braceright /asciitilde
 /.notdef % rubout; ASCII ends
% 0x80
 /Euro /.notdef /quotesinglbase /florin
 /quotedblbase /ellipsis /dagger /daggerdbl
 /circumflex /perthousand /Scaron /guilsinglleft
 /OE /.notdef /.notdef /.notdef
% 0x90
 /.notdef /.notdef /.notdef /quotedblleft
 /quotedblright /bullet /endash /emdash
 /tilde /trademark /scaron /guilsinglright
 /oe /.notdef /.notdef /Ydieresis
% 0xA0
 /.notdef % nobreakspace
 /exclamdown /cent /sterling
 /currency /yen /brokenbar /section
 /dieresis /copyright /ordfeminine /guillemotleft
 /logicalnot
 /hyphen % Y&Y (also at 45); Windows' softhyphen
 /registered
 /macron
% 0xD0
 /degree /plusminus /twosuperior /threesuperior
 /acute /mu /paragraph /periodcentered
 /cedilla /onesuperior /ordmasculine /guillemotright
 /onequarter /onehalf /threequarters /questiondown
% 0xC0
 /Agrave /Aacute /Acircumflex /Atilde /Adieresis /Aring /AE /Ccedilla
 /Egrave /Eacute /Ecircumflex /Edieresis
 /Igrave /Iacute /Icircumflex /Idieresis
% 0xD0
 /Eth /Ntilde /Ograve /Oacute
 /Ocircumflex /Otilde /Odieresis /multiply
 /Oslash /Ugrave /Uacute /Ucircumflex
 /Udieresis /Yacute /Thorn /germandbls
% 0xE0
 /agrave /aacute /acircumflex /atilde
 /adieresis /aring /ae /ccedilla
 /egrave /eacute /ecircumflex /edieresis
 /igrave /iacute /icircumflex /idieresis
% 0xF0
 /eth /ntilde /ograve /oacute
 /ocircumflex /otilde /odieresis /divide
 /oslash /ugrave /uacute /ucircumflex
 /udieresis /yacute /thorn /ydieresis
] def

%%EndProcSet
%%BeginProcSet: f7b6d320.enc
% Thomas Esser, Dec 2002. public domain
%
% Encoding for:
%     cmb10 cmbx10 cmbx12 cmbx5 cmbx6 cmbx7 cmbx8 cmbx9 cmbxsl10
%     cmdunh10 cmr10 cmr12 cmr17cmr6 cmr7 cmr8 cmr9 cmsl10 cmsl12 cmsl8
%     cmsl9 cmss10cmss12 cmss17 cmss8 cmss9 cmssbx10 cmssdc10 cmssi10
%     cmssi12 cmssi17 cmssi8cmssi9 cmssq8 cmssqi8 cmvtt10
%
/TeXf7b6d320Encoding [
/Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /Omega
/ff /fi /fl /ffi /ffl /dotlessi /dotlessj /grave /acute /caron /breve
/macron /ring /cedilla /germandbls /ae /oe /oslash /AE /OE /Oslash
/suppress /exclam /quotedblright /numbersign /dollar /percent /ampersand
/quoteright /parenleft /parenright /asterisk /plus /comma /hyphen
/period /slash /zero /one /two /three /four /five /six /seven /eight
/nine /colon /semicolon /exclamdown /equal /questiondown /question /at
/A /B /C /D /E /F /G /H /I /J /K /L /M /N /O /P /Q /R /S /T /U /V /W /X
/Y /Z /bracketleft /quotedblleft /bracketright /circumflex /dotaccent
/quoteleft /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p /q /r /s /t /u
/v /w /x /y /z /endash /emdash /hungarumlaut /tilde /dieresis /suppress
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /space
/Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /.notdef
/.notdef /Omega /ff /fi /fl /ffi /ffl /dotlessi /dotlessj /grave /acute
/caron /breve /macron /ring /cedilla /germandbls /ae /oe /oslash /AE
/OE /Oslash /suppress /dieresis /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
] def

%%EndProcSet
%%BeginProcSet: aae443f0.enc
% Thomas Esser, Dec 2002. public domain
%
% Encoding for:
%     cmmi10 cmmi12 cmmi5 cmmi6 cmmi7 cmmi8 cmmi9 cmmib10
%
/TeXaae443f0Encoding [
/Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /Omega
/alpha /beta /gamma /delta /epsilon1 /zeta /eta /theta /iota /kappa
/lambda /mu /nu /xi /pi /rho /sigma /tau /upsilon /phi /chi /psi
/omega /epsilon /theta1 /pi1 /rho1 /sigma1 /phi1 /arrowlefttophalf
/arrowleftbothalf /arrowrighttophalf /arrowrightbothalf /arrowhookleft
/arrowhookright /triangleright /triangleleft /zerooldstyle /oneoldstyle
/twooldstyle /threeoldstyle /fouroldstyle /fiveoldstyle /sixoldstyle
/sevenoldstyle /eightoldstyle /nineoldstyle /period /comma /less /slash
/greater /star /partialdiff /A /B /C /D /E /F /G /H /I /J /K /L /M /N
/O /P /Q /R /S /T /U /V /W /X /Y /Z /flat /natural /sharp /slurbelow
/slurabove /lscript /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p
/q /r /s /t /u /v /w /x /y /z /dotlessi /dotlessj /weierstrass /vector
/tie /psi /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/space /Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi
/.notdef /.notdef /Omega /alpha /beta /gamma /delta /epsilon1 /zeta /eta
/theta /iota /kappa /lambda /mu /nu /xi /pi /rho /sigma /tau /upsilon
/phi /chi /psi /tie /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef
] def

%%EndProcSet
%%BeginProcSet: bbad153f.enc
% Thomas Esser, Dec 2002. public domain
%
% Encoding for:
%     cmsy10 cmsy5 cmsy6 cmsy7 cmsy8 cmsy9
%
/TeXbbad153fEncoding [
/minus /periodcentered /multiply /asteriskmath /divide /diamondmath
/plusminus /minusplus /circleplus /circleminus /circlemultiply
/circledivide /circledot /circlecopyrt /openbullet /bullet
/equivasymptotic /equivalence /reflexsubset /reflexsuperset /lessequal
/greaterequal /precedesequal /followsequal /similar /approxequal
/propersubset /propersuperset /lessmuch /greatermuch /precedes /follows
/arrowleft /arrowright /arrowup /arrowdown /arrowboth /arrownortheast
/arrowsoutheast /similarequal /arrowdblleft /arrowdblright /arrowdblup
/arrowdbldown /arrowdblboth /arrownorthwest /arrowsouthwest /proportional
/prime /infinity /element /owner /triangle /triangleinv /negationslash
/mapsto /universal /existential /logicalnot /emptyset /Rfractur /Ifractur
/latticetop /perpendicular /aleph /A /B /C /D /E /F /G /H /I /J /K
/L /M /N /O /P /Q /R /S /T /U /V /W /X /Y /Z /union /intersection
/unionmulti /logicaland /logicalor /turnstileleft /turnstileright
/floorleft /floorright /ceilingleft /ceilingright /braceleft /braceright
/angbracketleft /angbracketright /bar /bardbl /arrowbothv /arrowdblbothv
/backslash /wreathproduct /radical /coproduct /nabla /integral
/unionsq /intersectionsq /subsetsqequal /supersetsqequal /section
/dagger /daggerdbl /paragraph /club /diamond /heart /spade /arrowleft
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/minus /periodcentered /multiply /asteriskmath /divide /diamondmath
/plusminus /minusplus /circleplus /circleminus /.notdef /.notdef
/circlemultiply /circledivide /circledot /circlecopyrt /openbullet
/bullet /equivasymptotic /equivalence /reflexsubset /reflexsuperset
/lessequal /greaterequal /precedesequal /followsequal /similar
/approxequal /propersubset /propersuperset /lessmuch /greatermuch
/precedes /follows /arrowleft /spade /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
] def

%%EndProcSet
%%BeginProcSet: 0ef0afca.enc
% Thomas Esser, Dec 2002. public domain
%
% Encoding for:
%     cmr5
%
/TeX0ef0afcaEncoding [
/Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /Omega
/arrowup /arrowdown /quotesingle /exclamdown /questiondown /dotlessi
/dotlessj /grave /acute /caron /breve /macron /ring /cedilla /germandbls
/ae /oe /oslash /AE /OE /Oslash /suppress /exclam /quotedblright
/numbersign /dollar /percent /ampersand /quoteright /parenleft
/parenright /asterisk /plus /comma /hyphen /period /slash /zero /one
/two /three /four /five /six /seven /eight /nine /colon /semicolon
/less /equal /greater /question /at /A /B /C /D /E /F /G /H /I /J /K
/L /M /N /O /P /Q /R /S /T /U /V /W /X /Y /Z /bracketleft /quotedblleft
/bracketright /circumflex /dotaccent /quoteleft /a /b /c /d /e /f /g /h
/i /j /k /l /m /n /o /p /q /r /s /t /u /v /w /x /y /z /endash /emdash
/hungarumlaut /tilde /dieresis /suppress /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /space /Gamma /Delta /Theta /Lambda
/Xi /Pi /Sigma /Upsilon /Phi /Psi /.notdef /.notdef /Omega /arrowup
/arrowdown /quotesingle /exclamdown /questiondown /dotlessi /dotlessj
/grave /acute /caron /breve /macron /ring /cedilla /germandbls /ae /oe
/oslash /AE /OE /Oslash /suppress /dieresis /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
] def

%%EndProcSet
%%BeginProcSet: texps.pro
%!
TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2
index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll
exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]FontType 0
ne{/Metrics exch def dict begin Encoding{exch dup type/integertype ne{
pop pop 1 sub dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get
div def}ifelse}forall Metrics/Metrics currentdict end def}{{1 index type
/nametype eq{exit}if exch pop}loop}ifelse[2 index currentdict end
definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{dup
sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1 roll
mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def dup[
exch{dup CharStrings exch known not{pop/.notdef/Encoding true def}if}
forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def}def
end

%%EndProcSet
%%BeginFont: TeX-cmex7
%!PS-AdobeFont-1.0: TeX-cmex7 001.001
% Filtered by type1fix.pl 0.05
%%EndComments
13 dict dup begin
/FontInfo 16 dict dup begin
/Copyright (see\040copyright\040of\040original\040TeX\040font) def
/FamilyName (TeX\040cmex7) def
/FullName (TeX\040cmex7\040Regular) def
/ItalicAngle 0 def
/Notice (converted\040after\040April\0402001) def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
/Weight (Regular) def
/isFixedPitch false def
/version (001.001) def
end readonly def
/FontName /TeX-cmex7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 101 /e put
readonly def
/FontBBox {-14 -2954 1627 771} readonly def
/UniqueID 4314415 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMSY9
%!PS-AdobeFont-1.1: CMSY9 1.0
%%CreationDate: 1991 Aug 15 07:22:27
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY9) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY9 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-30 -958 1146 777}readonly def
/UniqueID 5000819 def
currentdict end
currentfile eexec
D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964
7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4
A213ACB58AA0A658908035BF2ED8531779838A960DFE2B27EA49C37156989C85
E21B3ABF72E39A89232CD9F4237FC80C9E64E8425AA3BEF7DED60B122A52922A
221A37D9A807DD01161779DDE7D31FF2B87F97C73D63EECDDA4C49501773468A
27D1663E0B62F461F6E40A5D6676D0037D33F24E2FAC2B0009AD3C8350CDF8CC
65BCA87979C36D14CB552E9A985E48BE4E88ECA16DF418749AF04FDD2B0E1380
D281BB2476BB45FF30946B247DFD7F57305FA87E50CA338121C71CDFDF927A9C
77FF14CB4A1D6D80356FB1171ED38C37702350497B44E42CE31DB2F493807DAA
15B887C671199A54C4C1294BC520F5538C15556BC43C9F62342B121C6DCD6C5F
491DA47FF360201EE21C08A781ED0589A6DF91B99FE118B9B29E4F068672E52F
1A06C514D91C4C937D4E642503392B1CD1BF5AF0BCA28EBD840AD76CC39AD7AA
CF2C057D436A245217829DB786A3D592C0F5A073E44D137405B0D44F7D7356F1
DFE3D933072E0CA836B5B72B1DDEB8FF86D5F9A2AFDEC789B2FBDAC307F2DBF7
2B5BE20870A423F851473AB54C112C1D08AD8BFCCC7B6FF4FC0A1570B977EA3C
C020589CD924CA88A25AC7E806C25D26CD8E08D43C2B3E84F88D9B91E8743B1E
6BFCC0776C0E1A8B855DE55AB87AFCA973D87CD1ACA5625081BF578BAD5D179C
BF230EA1FE372E07C6CE86081A5CBCA161C70A024D8E07115C940BAF4CEA50A2
8D4CF5FFB87DB25E80F3949D1825B2C55FF4E75FCA951403A73B7750167F398B
300511EFE0FC5744A2EBC78FBF00C87031B4D275014123DFB4B4830B052CFAB3
3C4F63FFF8C52ED74946B7D6FC786C99B4084E6BACB791FE0090410D3C587A08
5B2FDACA4B6FAD0BDF572C17845893206E1D5C01193EB86889485AF2AF547579
084D72478254C35FE4AD63E939A6256207301DC8D473ED05EB3BAC0CA2BBFA06
42ACCD9F940B0A2C
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMSY5
%!PS-AdobeFont-1.1: CMSY5 1.0
%%CreationDate: 1991 Aug 15 07:21:16
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY5) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY5 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{21 -944 1448 791}readonly def
/UniqueID 5000815 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMR5
%!PS-AdobeFont-1.1: CMR5 1.00B
%%CreationDate: 1992 Feb 19 19:55:02
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR5) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR5 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-341 -250 1304 965}readonly def
/UniqueID 5000788 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: TeX-cmex9
%!PS-AdobeFont-1.0: TeX-cmex9 001.001
% Filtered by type1fix.pl 0.05
%%EndComments
13 dict dup begin
/FontInfo 16 dict dup begin
/Copyright (see\040copyright\040of\040original\040TeX\040font) def
/FamilyName (TeX\040cmex9) def
/FullName (TeX\040cmex9\040Regular) def
/ItalicAngle 0 def
/Notice (converted\040after\040April\0402001) def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
/Weight (Regular) def
/isFixedPitch false def
/version (001.001) def
end readonly def
/FontName /TeX-cmex9 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 101 /e put
readonly def
/FontBBox {-26 -2961 1503 773} readonly def
/UniqueID 4314405 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMBX10
%!PS-AdobeFont-1.1: CMBX10 1.00B
%%CreationDate: 1992 Feb 19 19:54:06
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMBX10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMBX10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-301 -250 1164 946}readonly def
/UniqueID 5000768 def
currentdict end
currentfile eexec
D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891
016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171
9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F
D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758
469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8
2BDBF16FBC7512FAA308A093FE5F00F963068B8B731A88D7740B0DDAED1B3F82
7DB9DFB4372D3935C286E39EE7AC9FB6A9B5CE4D2FAE1BC0E55AE02BFC464378
77B9F65C23E3BAB41EFAE344DDC9AB1B3CCBC0618290D83DC756F9D5BEFECB18
2DB0E39997F264D408BD076F65A50E7E94C9C88D849AB2E92005CFA316ACCD91
FF524AAD7262B10351C50EBAD08FB4CD55D2E369F6E836C82C591606E1E5C73F
DE3FA3CAD272C67C6CBF43B66FE4B8677DAFEEA19288428D07FEB1F4001BAA68
7AAD6DDBE432714E799CFA49D8A1A128F32E8B280524BC8041F1E64ECE4053C4
9F0AEC699A75B827002E9F95826DB3F643338F858011008E338A899020962176
CF66A62E3AEF046D91C88C87DEB03CE6CCDF4FB651990F0E86D17409F121773D
6877DF0085DFB269A3C07AA6660419BD0F0EF3C53DA2318BA1860AB34E28BAC6
E82DDB1C43E5203AC9DF9277098F2E42C0F7BD03C6D90B629DE97730245B8E8E
8903B9225098079C55A37E4E59AE2A9E36B6349FA2C09BB1F5F4433E4EEFC75E
3F9830EB085E7E6FBE2666AC5A398C2DF228062ACF9FCA5656390A15837C4A99
EC3740D873CFEF2E248B44CA134693A782594DD0692B4DBF1F16C4CDECA692C4
0E44FDBEF704101118BC53575BF22731E7F7717934AD715AC33B5D3679B784C9
4046E6CD3C0AD80ED1F65626B14E33CFDA6EB2825DC444FA620E40822E15C2AB
8BF88EF4FF68D9C81564F0AC5495C426E3ED091CF4AEAD7696C3B00A0D6FB6CE
60547AD516EC9CC7B904D6617F81D2AC5086C30E40057B3C8854C4893D3B1D82
2D61C4414046FFBFDCD7AD22EE19016B50905C92287F9946F2DBA4CB1B18E118
FD01CB5EB39E77C77A4BE276258F7EF35269272729704F2A26BDE6159C77034B
5492340010118D673DD5EA0631B64A0EE2906E1321C368BA259627B5CE07FDDE
370FAEB2899539198B07BE6F24470C1E01F4A8D3E62984EF9664D474691EC320
28DA9A0CBD11491F728A478893BC17794E74D3E2424ACF51BA3F6072286F6BEC
1A62D46F106741754359040396E550FFC0F8233A93E9CCF0781C10D85D307F58
749BEB8FADABBDFB390AE058D999DD3603A9672973B7D614155767FF32453295
DEA1CE13BC01DEB6A6F083A4B0B35956BF1299E8839AA67145A78FD0AA9AE98E
58131D5920429D516B1DC74BEED8C5CEC2BE44A972D113F4A73C3FEE0C3A41EE
E29067EF5DBE3B981C0335F840ED03174225CBD9E6E76A168950
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMBX12
%!PS-AdobeFont-1.1: CMBX12 1.0
%%CreationDate: 1991 Aug 20 16:34:54
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMBX12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMBX12 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-53 -251 1139 750}readonly def
/UniqueID 5000769 def
currentdict end
currentfile eexec
D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891
016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171
9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F
D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758
469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8
2BDBF16FBC7512FAA308A093FE5F0364CD5660F74BEE96790DE35AFA90CCF712
B1805DA88AE375A04D99598EADFC625BDC1F9C315B6CF28C9BD427F32C745C99
AEBE70DAAED49EA45AF94F081934AA47894A370D698ABABDA4215500B190AF26
7FCFB7DDA2BC68605A4EF61ECCA3D61C684B47FFB5887A3BEDE0B4D30E8EBABF
20980C23312618EB0EAF289B2924FF4A334B85D98FD68545FDADB47F991E7390
B10EE86A46A5AF8866C010225024D5E5862D49DEB5D8ECCB95D94283C50A363D
68A49071445610F03CE3600945118A6BC0B3AA4593104E727261C68C4A47F809
D77E4CF27B3681F6B6F3AC498E45361BF9E01FAF5527F5E3CC790D3084674B3E
26296F3E03321B5C555D2458578A89E72D3166A3C5D740B3ABB127CF420C316D
F957873DA04CF0DB25A73574A4DE2E4F2D5D4E8E0B430654CF7F341A1BDB3E26
77C194764EAD58C585F49EF10843FE020F9FDFD9008D660DE50B9BD7A2A87299
BC319E66D781101BB956E30643A19B93C8967E1AE4719F300BFE5866F0D6DA5E
C55E171A24D3B707EFA325D47F473764E99BC8B1108D815CF2ACADFA6C4663E8
30855D673CE98AB78F5F829F7FA226AB57F07B3E7D4E7CE30ED3B7EB0D3035C5
148DA8D9FA34483414FDA8E3DC9E6C479E3EEE9A11A0547FC9085FA4631AD19C
E936E0598E3197207FA7BB6E55CFD5EF72AEC12D9A9675241C7B00AD58FAF645
1297991B5D01701E82228D0313FC7C66B263BC79ACDDF9AAC48A3CBF42B96E38
583E1D059953076D68148DC8B6C9527B3A74CE7DEF788A11531F44120BDF0F61
0B2F3ED94EEBCDE4ACD23834C242AA4314B9EF98E4BE72DB76EBDD0A028CEA9D
B4C38C1F2D24B8FDE686832FE96204552C820E45B6BAF0C3308742AE290D69BA
D6C478E571C9E7625F22D7236D13D480F65273A6AE8A067CC2A53444FE5FE5CF
008AFBB3CA068F275E3D33F7C8ABDEFAD7D014AC8A78873C385F412141A58CBC
7582EE7AEBB90F568091278DB5A8E9BD7376B13BC271A4D11D3043BB109526DC
8B5393488FDAF60E1B5F5AF9B8637AE31872F32B87E438D467022423871A6CC9
EB25C8D776F14C9CBF09392ED2888254A3FF22C77B279DA71350C088A0E46380
9E8E5420BDADDDF04B1429028D6DD8884656501C454C3554CF091DA3448A8C50
C4304FCB7C07F2F4ADA83563AE2FE869626B52318134CD16A13D72B6AD61B061
58CF8A3793BC1084DFA20B66D021DA602CC809BC09A292B889D9436F2AC805AF
75C0A15A299F7F7F13DB990FD52EE0EB1FD9D42A875FE49B4E7213E7BDE37FC4
A52C2DFB25AD24664328D67DE769F9E8CEA752E4BB5D3793DA4F26025A4DA829
B65C16319FE325D74FCC1B62DA436BC886C73C55316A6014EE2361D7DDA0BACC
0BACD75B29
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: MSBM7
%!PS-AdobeFont-1.1: MSBM7 2.1
%%CreationDate: 1992 Oct 17 08:30:50
% Math Symbol fonts were designed by the American Mathematical Society.
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (2.1) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (MSBM7) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /MSBM7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 82 /R put
readonly def
/FontBBox{0 -504 2615 1004}readonly def
/UniqueID 5032014 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMSY6
%!PS-AdobeFont-1.1: CMSY6 1.0
%%CreationDate: 1991 Aug 15 07:21:34
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY6 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-4 -948 1329 786}readonly def
/UniqueID 5000816 def
currentdict end
currentfile eexec
D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964
7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4
A213ACB58AA0A658908035BF2ED8531779838A960DFE2B27EA49C37156989C85
E21B3ABF72E39A89232CD9F4237FC80C9E64E8425AA3BEF7DED60B122A52922A
221A37D9A807DD01161779DDE7D5FC1B2109839E5B52DFB7605D7BA557CC35D6
49F6EB651B83771034BA0C39DB8D426A24543EF4529E2D939125B5157482688E
9045C2242F4AFA4C489D975C029177CD6497EACD181FF151A45F521A4C4043C2
1F3E76EF5B3291A941583E27DFC68B9211105827590393ABFB8AA4D1623D1761
6AC0DF1D3154B0277BE821712BE7B33385E7A4105E8F3370F981B8FE9E3CF3E0
007B8C9F2D934F24D591C330487DDF179CECEC5258C47E4B32538F948AB00673
F9D549C971B0822056B339600FC1E3A5E51844CC8A75B857F15E7276260ED115
C5FD550F53CE5583743B50B0F9B7C4F836DEF6BA1ABE5F0F80D96571277EAF86
A3AAFCE3693728E396048C32573DAA11E6D2F036BD9756F1F0A5877DD15DC64A
A9C2E20B570464B31E783692E6D10101828C4F6DF30A155808A7697D24C5854D
DD1D111B4B4FE343E045A0FD3B2F13E69E86DAEDA05BD3652EB89D54EA09F1AD
21AFFD14905002BAB1B4B6255AF7CE887AA2E890ECF359AA2CB6CBDA8EBECA5B
E356F639EF564863B33DCA632F664832A6605DD1D7B53D95BE9F104DA7DD1507
BE1F98BA5FF17CDBE936BE543CA34D3B6D1D27202FE54CAA00CE69DF26821959
85B05A247E013BD4FC806C6FC6A6C798A8D9C7461FB261DFF6C979652A2D97FA
35F2DCA13001B99659AA4F0442A87881830B9E59B20C82D245B3CBC50A24F8D7
D8C2F7E0BE7BB2D32C681F87840C252564E10A85B5BD0E46F59D740B9C6B849A
1ABBD853156290ECFE523D22786C0709821B06A1B893385F3FB5AB12DC67425E
1B7340AE67CE5C75BBA5B359408F5D566BC8A3B6776B73C347F88E01BD66DADB
441D96FB208C35E0016AC8AF5135C45800DC4F62175B74CB6C94C2410BDB8B28
A119156022E19F5DB1BF948427A07D75C2E7DF2FBEBC477EC33F702B885D7794
1C1019
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMMI6
%!PS-AdobeFont-1.1: CMMI6 1.100
%%CreationDate: 1996 Jul 23 07:53:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI6 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{11 -250 1241 750}readonly def
/UniqueID 5087381 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMR6
%!PS-AdobeFont-1.1: CMR6 1.0
%%CreationDate: 1991 Aug 20 16:39:02
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR6 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-20 -250 1193 750}readonly def
/UniqueID 5000789 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMSY8
%!PS-AdobeFont-1.1: CMSY8 1.0
%%CreationDate: 1991 Aug 15 07:22:10
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-30 -955 1185 779}readonly def
/UniqueID 5000818 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMEX10
%!PS-AdobeFont-1.1: CMEX10 1.00
%%CreationDate: 1992 Jul 23 21:22:48
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMEX10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMEX10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /parenleftbig put
dup 1 /parenrightbig put
dup 12 /vextendsingle put
dup 14 /slashbig put
dup 16 /parenleftBig put
dup 17 /parenrightBig put
dup 48 /parenlefttp put
dup 49 /parenrighttp put
dup 64 /parenleftbt put
dup 65 /parenrightbt put
dup 66 /parenleftex put
dup 67 /parenrightex put
dup 80 /summationtext put
dup 82 /integraltext put
dup 83 /uniontext put
dup 88 /summationdisplay put
dup 90 /integraldisplay put
dup 98 /hatwide put
dup 101 /tildewide put
dup 112 /radicalbig put
readonly def
/FontBBox{-24 -2960 1454 772}readonly def
/UniqueID 5000774 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMMI8
%!PS-AdobeFont-1.1: CMMI8 1.100
%%CreationDate: 1996 Jul 23 07:53:54
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-24 -250 1110 750}readonly def
/UniqueID 5087383 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: MSBM10
%!PS-AdobeFont-1.1: MSBM10 2.1
%%CreationDate: 1993 Sep 17 11:10:37
% Math Symbol fonts were designed by the American Mathematical Society.
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (2.1) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (MSBM10) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /MSBM10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 78 /N put
dup 82 /R put
readonly def
/FontBBox{-55 -420 2343 920}readonly def
/UniqueID 5031982 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMSY10
%!PS-AdobeFont-1.1: CMSY10 1.0
%%CreationDate: 1991 Aug 15 07:20:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-29 -960 1116 775}readonly def
/UniqueID 5000820 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMR10
%!PS-AdobeFont-1.1: CMR10 1.00B
%%CreationDate: 1992 Feb 19 19:54:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-251 -250 1009 969}readonly def
/UniqueID 5000793 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: MSAM10
%!PS-AdobeFont-1.1: MSAM10 2.1
%%CreationDate: 1993 Sep 17 09:05:00
% Math Symbol fonts were designed by the American Mathematical Society.
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (2.1) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (MSAM10) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /MSAM10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 54 /lessorequalslant put
dup 62 /greaterorequalslant put
readonly def
/FontBBox{8 -463 1331 1003}readonly def
/UniqueID 5031981 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMMI10
%!PS-AdobeFont-1.1: CMMI10 1.100
%%CreationDate: 1996 Jul 23 07:53:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-32 -250 1048 750}readonly def
/UniqueID 5087385 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMR9
%!PS-AdobeFont-1.1: CMR9 1.0
%%CreationDate: 1991 Aug 20 16:39:59
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR9) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR9 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-39 -250 1036 750}readonly def
/UniqueID 5000792 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMMI9
%!PS-AdobeFont-1.1: CMMI9 1.100
%%CreationDate: 1996 Jul 23 07:53:55
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI9) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI9 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-29 -250 1075 750}readonly def
/UniqueID 5087384 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMR8
%!PS-AdobeFont-1.1: CMR8 1.0
%%CreationDate: 1991 Aug 20 16:39:40
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-36 -250 1070 750}readonly def
/UniqueID 5000791 def
currentdict end
currentfile eexec
D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891
016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171
9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F
D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758
469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8
2BDBF16FBC7512FAA308A093FE5CF4E9D2405B169CD5365D6ECED5D768D66D6C
68618B8C482B341F8CA38E9BB9BAFCFAAD9C2F3FD033B62690986ED43D9C9361
3645B82392D5CAE11A7CB49D7E2E82DCD485CBA1772CE422BB1D7283AD675B65
48A7EA0069A883EC1DAA3E1F9ECE7586D6CF0A128CD557C7E5D7AA3EA97EBAD3
9619D1BFCF4A6D64768741EDEA0A5B0EFBBF347CDCBE2E03D756967A16B613DB
0FC45FA2A3312E0C46A5FD0466AB097C58FFEEC40601B8395E52775D0AFCD7DB
8AB317333110531E5C44A4CB4B5ACD571A1A60960B15E450948A5EEA14DD330F
EA209265DB8E1A1FC80DCD3860323FD26C113B041A88C88A21655878680A4466
FA10403D24BB97152A49B842C180E4D258C9D48F21D057782D90623116830BA3
9902B3C5F2F2DD01433B0D7099C07DBDE268D0FFED5169BCD03D48B2F058AD62
D8678C626DC7A3F352152C99BA963EF95F8AD11DB8B0D351210A17E4C2C55AD8
9EB64172935D3C20A398F3EEEEC31551966A7438EF3FEE422C6D4E05337620D5
ACC7B52BED984BFAAD36EF9D20748B05D07BE4414A63975125D272FAD83F76E6
10FFF8363014BE526D580873C5A42B70FA911EC7B86905F13AFE55EB0273F582
83158793B8CC296B8DE1DCCF1250FD57CB0E035C7EDA3B0092ED940D37A05493
2EC54E09B984FCA4AB7D2EA182BCF1263AA244B07EC0EA901C077A059F709F30
4384CB5FA748F2054FAD9A7A43D4EA427918BD414F766531136B60C3477C6632
BEFE3897B58C19276A301926C2AEF2756B367319772C9B201C49B4D935A8267B
041D6F1783B6AEA4DAC4F5B3507D7032AA640AAB12E343A4E9BDCF419C04A721
3888B25AF4E293AACED9A6BDC78E61DA1C424C6503CC1885F762BADE1E60F381
8ABB3D45547347BCA2454D6E5C5265D023668E944CB74ACA86238A6EA8B7D99E
6F60C8DD3D15D671E83E5B64A7D435081BF0069181030D2C2D95CBC302A40975
C8084A73ECC57539E1A2C8FAA02F63AB62FA6907EE921AF3C3FF392FB0E7E5D0
329FD77A06342948EB94FE96FEDE167E2D834B5CD4BE37BB7963856462286E5F
2A5E720DE1FBBA6BD8E1ED22F10609E47F654AA4428AE2CBFB99B61E54B1A24E
48DA5A773E13D2CC3634C099D19234BD8EB37D1066FFA6E1CA82BD4810913CF7
CEC46532008D8CC66DB41481DBDE91B10E38D77A69364071E66204D4CF4B8070
71BE9FE233D9C73765EC825758CEA72012C2C6EE4EB911977DD52E3B2E2C7623
90D6BED9A439CDE232C268EE331F4A542A56F3BE354AC1720C455D3445AF778D
D02BB7A4F8FC2677189C452F5E5A7E356FEE1834A18BDCD3D45D45DED14E0808
04B33C39847F499376DEE22A6044280DDF273C1B58053499E1DD0B98069356EA
14C8A3E82374A93DE714B42D3CB1FB057BE0F5667BDDF3BCC0A278A741A362B7
212F23D532D5B654864BAA75A1D76E1B4EF1F60FC1468739C997CC887875F5EC
AB243B1A93E083E05C1608B4796FBFB9722447641CDD9CD425B2A81F40BB2972
A4282CAE2F8B4A8AD6EAD74A95A84F462501F8A6BAE961E478849F244085A2FA
E6B7AAF6F3F01E9BE41DE90DDA5BF2FB46A84A835350403CF01E1DAFE999F20F
19F0DE731F5EC666CF03B655BDD234D004CD30B0319C20154D34C1FD33B78CFF
5C1F1CEE7BBCC9A3421B35868139D60FF1F2E56EA0951B326361702BB4B00567
803F8AA252FCDCACD132F4745600D2A0A6AEDEC5BB6EAAE9FCA07BB472669B19
024F55BBDD2CB02F58DB93C3E1171CB2DB7F62792EEA6FE6792B630663526418
8AE2B08E453EC3262BB916533FBBCFA1EB4BB671C284474A374DA5902EB3B8C7
D4EB273CC521A69C268C2CF37FA103B423CA317CE5AC09FD6EB68B3B6EC84EA8
6F3C0AFE50EBB20D4D35D9516A8D887E2CEF425E0570AFB57E0353D4A82718C5
C36E2CC816B09439DF54AE331F8C0476F0965AE3F2BB57C194F3BA1C40AB4A18
625A96D9A925C01DD986EC11B42D5C3CEBEEDC7B39FEE08C15A0DF04D6FCC07E
675DDD3BF014605EEE13C49DACE67D7AEDACE395C70525E620C287871F17E5BB
611FC0865A6A4009E858A46BCA697D8185E50B2107153E91CE1F2D02C0421FFF
27C6B2B397E54ED5A501CBCD332FA9B0769FF45FD8D4F7532F3D3F3512A8A254
F84306B4CED14A1FFBD810B8789FB4D6517004A4A5ADF059EEAF78126909F98E
63DEC14C3411E31DA29A8A997CFE1F6B917B9FBD30322FABB31995BDE7650C3C
69CCCC943A7D03B75F96106B058FBBAF106E570C8E93F3D5F590EEFFE01D6C78
3DC5EE9ACC6C0B4462A97F0ED94E0138538EFA70E60109309AB89C2AD929840E
0BC8596A5E6BB3F7BBB46722E36211A0CA703D4EF7404FE7D581987B56CC411C
A3A2F1EF0BB3EE4891A2FA4808C16382150CDA7727066950FE1B2DF57F41531A
1865FF6533BDA22A6EAB3569282E6BF5659E8DA638FCB9AB13F9362B170883D0
2ECF45C41ABA991984D6082292CB19E1F929B9545686AE6A7E80EE4D581A32DC
503C4E3B9D491203C0EB2D28107C3CA7E818145561E19B250CE1829D2C043D8C
03162625D73F336B6E93481E019E0099CBFF40B400F2EF127FA64CB2B3326087
CBE17A51AC157E41D41E36088EDBB1AB9EB2658DF687A5A0C4432B9386439FA6
E1ECA2ABBDDEE82E552D443A910593D6DC439787B07FD5980B323AB0E52E18DD
0088D731FE892D32DD7AB415D27B0FE7472514629BE1D2361673D53DCE380750
279C9EC03763FB6BF71999D955E9A33C9C0199EF33FDE262A73388C4AD16BBF4
9A8FC4F57F290AE2F09BF7D9FBDC8A94969B89A23A5339BCDED6DAB889427E08
3B6496E41784C779FC55C8420165B4275753CA96F14B657739ED7785F69BDB28
F976DCB7CC7E7253621326277E996ED67CFE6699A6F7711C151243D9992CB863
4369B9D323908BD3EE31C92AE101EF073605E4068DD1F5DBD8D74AC664A035AA
425E99B4E92BDE3E9A7B54D798F72A934C9ED08A14293F5B0C
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
TeXDict begin 39158280 55380996 1000 600 600 (spodarev.dvi)
@start /Fa 154[32 101[{}1 49.8132 /TeX-cmex7 rf /Fb 253[60
1[60{ TeXbbad153fEncoding ReEncodeFont }2 74.7198 /CMSY9
rf /Fc 252[31 3[{ TeXbbad153fEncoding ReEncodeFont }1
41.511 /CMSY5 rf /Fd 205[28 28 28 48[{
 TeX0ef0afcaEncoding ReEncodeFont }3 41.511 /CMR5 rf
/Fe 154[43 101[{}1 74.7198 /TeX-cmex9 rf /Ff 206[52 49[{
 TeXf7b6d320Encoding ReEncodeFont }1 90.9091 /CMBX10
rf /Fg 139[30 35 40 1[51 45 51 4[25 24[56 28[45 1[45
2[23 46[{ TeXBase1Encoding ReEncodeFont }11 90.9091 /Times-Bold
rf /Fh 154[51 81[56 19[{ TeXf7b6d320Encoding ReEncodeFont }2
99.6264 /CMBX12 rf /Fi 173[48 82[{}1 66.4176 /MSBM7 rf
/Fj 252[32 2[48{ TeXbbad153fEncoding ReEncodeFont }2
49.8132 /CMSY6 rf /Fk 137[31 2[29 29 3[38 2[33 25 22
4[32 13[36 26[19 59[{ TeXaae443f0Encoding ReEncodeFont }10
49.8132 /CMMI6 rf /Fl 203[30 1[30 30 30 4[47 41[50 1[{
 TeXf7b6d320Encoding ReEncodeFont }6 49.8132 /CMR6 rf
/Fm 145[35 3[20 13[47 11[49 17[55 7[0 3[47 71 19 12[35
1[71 23[55 55 4[35 2[55{ TeXbbad153fEncoding ReEncodeFont }15
66.4176 /CMSY8 rf /Fn 143[91 10[51 2[51 7[51 1[131 4[76
43 1[96 12[80 80 80 80 14[80 80 30[54 54 1[53 1[30 10[42
42{}20 90.9091 /CMEX10 rf /Fo 135[40 4[33 32 32 1[34
43 62 1[37 29 24 4[36 12[67 8[56 2[60 8[53 53 37 3[55
20 20 23[33 11[42 7[31 14[{ TeXaae443f0Encoding ReEncodeFont }23
66.4176 /CMMI8 rf /Fp 173[66 3[66 78[{}2 90.9091 /MSBM10
rf /Fq 145[45 2[45 25 2[45 45 9[61 61 7[55 77 1[63 4[69
15[45 4[0 3[61 91 14[45 91 6[71 71 15[71 71 6[25 71{
 TeXbbad153fEncoding ReEncodeFont }23 90.9091 /CMSY10
rf /Fr 135[48 3[35 5[51 76 25 2[25 3[40 3[45 3[25 1[25
29[71 1[25 25 45 45 2[45 45 45 45 45 45 4[71 1[35 35
2[76 3[25 13[45 14[61 2[76 57{ TeXf7b6d320Encoding ReEncodeFont }30
90.9091 /CMR10 rf /Fs 193[71 7[71 54[{}2 90.9091 /MSAM10
rf /Ft 134[45 52 65 44 2[43 41 41 46 44 55 80 1[47 37
31 52 43 45 42 47 39 1[48 6[62 53 75 86 53 3[69 72 2[73
1[62 77 50 4[67 1[65 69 68 2[71 45 71 25 25 30[52 4[55
53 52 5[40 47 13[{ TeXaae443f0Encoding ReEncodeFont }47
90.9091 /CMMI10 rf /Fu 134[37 37 1[37 42 23 32 32 1[42
42 42 60 23 2[23 42 42 23 37 42 37 42 42 13[42 3[60 55
8[51 1[55 64[42 2[{ TeXBase1Encoding ReEncodeFont }27
83.022 /Times-Italic rf /Fv 105[45 27[35 40 40 61 40
45 25 35 35 45 45 45 45 66 25 40 1[25 45 45 25 40 45
40 45 45 13[45 2[56 2[76 6[56 56 2[56 19[23 30 23 4[30
36[45 2[{ TeXBase1Encoding ReEncodeFont }37 90.9091 /Times-Italic
rf /Fw 105[45 1[40 40 24[40 45 45 66 45 45 25 35 30 45
45 45 45 71 25 45 25 25 45 45 30 40 45 40 45 40 3[30
1[30 3[86 1[66 56 51 61 1[51 66 66 81 56 66 35 30 66
66 51 56 1[61 61 66 5[25 25 45 45 45 45 45 45 45 45 45
45 1[23 30 23 2[30 30 30 35[51 51 2[{ TeXBase1Encoding ReEncodeFont }71
90.9091 /Times-Roman rf /Fx 105[54 28[54 54 78 54 60
36 42 48 60 60 54 60 90 30 60 1[30 60 54 36 48 60 48
1[54 13[60 78 1[66 1[78 102 72 2[42 3[72 78 78 72 78
10[54 54 54 54 54 54 2[27 43[60 2[{ TeXBase1Encoding ReEncodeFont }44
107.929 /Times-Bold rf /Fy 154[34 43[38 38 38 38 38 38
38 38 38 38 6[30 30 2[64 17[38 14[51 4[{
 TeXf7b6d320Encoding ReEncodeFont }16 74.7198 /CMR9 rf
/Fz 137[37 17[40 13[45 26[21 21 43[34 14[{
 TeXaae443f0Encoding ReEncodeFont }6 74.7198 /CMMI9 rf
/FA 3[37 101[37 17[33 9[33 37 37 54 37 37 21 29 25 37
37 37 37 58 21 37 1[21 37 37 25 33 37 33 37 33 3[25 1[25
46 54 1[71 54 54 46 42 50 1[42 54 54 66 46 54 29 25 54
54 42 46 54 50 50 54 5[21 21 37 37 37 37 37 37 37 37
37 37 1[19 25 19 2[25 25 1[58 62 33[42 42 2[{
 TeXBase1Encoding ReEncodeFont }75 74.7198 /Times-Roman
rf /FB 134[37 1[54 2[25 29 33 2[37 9[33 42 33 42 37 21[58
9[54 6[25 58[{ TeXBase1Encoding ReEncodeFont }14 74.7198
/Times-Bold rf /FC 137[33 37 18 33 22 1[37 37 37 55 15
33 1[15 37 2[37 37 33 1[37 32[67 17[18 22 18 44[{
 TeXBase1Encoding ReEncodeFont }21 66.4176 /Helvetica
rf /FD 27[37 77[37 28[33 33 50 33 37 21 29 29 1[37 37
37 54 21 33 1[21 37 37 21 33 37 33 37 37 11[54 42 37
46 1[46 54 50 62 3[25 1[54 46 1[54 50 46 46 6[25 37 37
1[37 4[37 37 1[19 25 19 44[{ TeXBase1Encoding ReEncodeFont }49
74.7198 /Times-Italic rf /FE 162[20 1[20 29[55 10[35
35 35 4[55 1[27 27 35[47 2[59 1[{ TeXf7b6d320Encoding ReEncodeFont }11
66.4176 /CMR8 rf /FF 137[46 46 25 1[30 1[46 46 46 71
25 46 1[25 46 46 1[41 46 41 1[41 10[66 2[51 13[56 11[46
46 46 46 46 46 46 46 46 46 3[23 44[{ TeXBase1Encoding ReEncodeFont }31
91.3242 /Times-Roman rf /FG 166[90 2[90 90 83 69 90 2[97
90 118 83 2[48 97 1[76 83 90 90 83 90 65[{
 TeXBase1Encoding ReEncodeFont }18 124.533 /Times-Bold
rf end
%%EndProlog
%%BeginSetup
%%Feature: *Resolution 600dpi
TeXDict begin
%%BeginPaperSize: a4
a4
%%EndPaperSize
 end
%%EndSetup
%%Page: 1 1
TeXDict begin 1 0 bop 598 1241 a FG(ON)47 b(THE)h(LOCAL)f(CONNECTIVITY)
h(NUMBER)f(OF)598 1383 y(ST)-11 b(A)f(TION)n(AR)l(Y)30
b(RANDOM)g(CLOSED)i(SETS)598 1691 y FF(Evgueni)21 b(Spodare)n(v)-6
b(,)1287 1658 y FE(1)1347 1691 y FF(and)21 b(V)-12 b(olk)o(er)23
b(Schmidt)2070 1658 y FE(1)598 1812 y(1)637 1845 y FD(Univer)o
(sit\344t)c(Ulm)598 1936 y(Abteilung)g(Stoc)o(hastik)598
2028 y(D-89069)h(Ulm,)e(Germany)598 2136 y FC(spodare)n
(v@mathematik.uni-ulm.de)o(,)j(schmidt@mathematik.uni-ulm.de)598
2426 y FB(Abstract)178 b FA(Random)23 b(closed)g(sets)f(\(RA)m(CS\))e
(in)i(the)g Fz(d)p FA(\226dimensional)h(Euclidean)g(space)f(are)g
(consid-)1054 2517 y(ered,)i(whose)f(realizations)g(belong)h(to)e(the)h
(e)o(xtended)h(con)m(v)o(e)o(x)g(ring.)34 b(A)23 b(f)o(amily)g(of)f
(non-)1054 2609 y(parametric)d(estimators)g(is)f(in)m(v)o(estigated)h
(for)g(the)g(simultaneous)g(estimation)g(of)g(the)g(v)o(ec-)1054
2700 y(tor)j(of)g(all)f(speci\002c)h(Mink)o(o)n(wski)i(functionals)e
(\(or)m(,)g(equi)n(v)n(alently)-5 b(,)24 b(the)e(speci\002c)g
(intrinsic)1054 2791 y(v)o(olumes\))g(of)g(stationary)g(RA)m(CS.)e(The)
i(construction)h(of)e(these)h(estimators)g(is)f(based)h(on)1054
2883 y(a)g(representation)i(formula)e(for)g(the)h(e)o(xpected)g(local)f
(connecti)n(vity)i(number)f(of)f(station-)1054 2974 y(ary)k(RA)m(CS)e
(intersected)h(with)g(spheres,)i(whose)f(radii)f(are)g(small)g(in)g
(comparison)h(with)1054 3065 y(the)19 b(size)f(of)g(the)h(whole)g
(sampling)g(windo)n(w)-5 b(.)23 b(Asymptotic)c(properties)g(of)g(the)f
(estimators)1054 3157 y(are)i(gi)n(v)o(en)h(for)e(unboundedly)k
(increasing)e(sampling)f(windo)n(ws.)26 b(Numerical)20
b(results)g(are)1054 3248 y(pro)o(vided)h(as)d(well.)598
3449 y FB(K)n(eyw)o(ords:)111 b FA(Mathematical)26 b(morphology;)k
(random)25 b(closed)h(sets;)h(stationarity;)h(Mink)o(o)n(wski)e(func-)
1054 3540 y(tionals;)17 b(intrinsic)e(v)o(olumes;)i(nonparametric)f
(estimation;)h(local)e(Euler)o(\226Poincar)p Fy(\023)-36
b(e)28 b FA(char)o(-)1054 3632 y(acteristic;)19 b(principal)g
(kinematic)g(formula;)g(Boolean)h(model)598 3847 y Fx(Intr)n(oduction)
697 4005 y Fw(The)35 b(theory)h(of)f(random)g(closed)i(sets)e(\(RA)l
(CS\))e(and)i(its)g(morphological)k(aspects)598 4113
y(with)31 b(emphasis)h(on)f(applications)k(to)30 b(image)i(analysis)h
(ha)n(v)o(e)e(been)h(de)n(v)o(eloped)h(in)e(the)598 4221
y(second)e(half)e(of)g(the)h(20th)g(century)-6 b(.)41
b(This)27 b(scienti\002c)i(process)g(has)f(been)g(signi\002cantly)598
4329 y(in\003uenced)d(by)f(the)f(pioneering)k(monographs)f(of)d(G.)f
(Matheron)j([6])f(and)g(J.)f(Serra)g([15,)598 4437 y(16].)28
b(It)19 b(turned)j(out)e(that)g Fv(Mink)o(owski)i(functionals)h
Fw(or)l(,)d(equi)n(v)n(alently)-6 b(,)24 b Fv(intrinsic)e(volumes)598
4545 y Fw(are)37 b(important)h(characteristics)k(in)36
b(order)i(to)f(describe)i(binary)f(images,)j(since)d(the)o(y)598
4653 y(pro)o(vide)30 b(useful)h(information)h(about)e(the)f
(morphological)k(structure)f(of)d(the)g(underly-)598
4761 y(ing)e(RA)l(CS.)e(In)h(particular)l(,)31 b(the)c(so\226called)i
Fv(speci\002c)g(intrinsic)g(volumes)f Fw(of)f(stationary)598
4869 y(RA)l(CS)19 b(ha)n(v)o(e)j(been)g(intensi)n(v)o(ely)i(studied)g
(for)d(v)n(arious)i(models)f(from)g(stochastic)i(geom-)598
4977 y(etry)-6 b(.)697 5085 y(There)31 b(e)o(xist)h(se)n(v)o(eral)g
(approaches)i(to)c(the)i(construction)i(of)d(statistical)i(estimators)
598 5192 y(for)c(particular)k(speci\002c)d(intrinsic)i(v)n(olumes)f(of)
e(stationary)j(RA)l(CS)c(in)h(tw)o(o)g(and)h(three)p
eop end
%%Page: 2 2
TeXDict begin 2 1 bop 548 550 a FF(2)588 b Fu(On)20 b(the)g(local)g
(connectivity)f(number)g(of)i(stationary)e(r)o(andom)g(closed)h(sets)
548 744 y Fw(dimensions.)70 b(Ho)n(we)n(v)o(er)l(,)40
b(in)c(man)o(y)g(cases,)41 b(only)c(little)h(is)e(kno)n(wn)h(about)h
(goodness)548 852 y(properties)26 b(of)d(these)i(estimators,)g(lik)o(e)
f(unbiasedness,)j(consistenc)o(y)-6 b(,)26 b(or)d(distrib)n(utional)548
960 y(properties.)35 b(Furthermore,)26 b(an)f(e)o(xtra)g(algorithm)h
(has)g(to)e(be)h(designed)i(for)e(the)g(estima-)548 1068
y(tion)f(of)g(each)g(speci\002c)g(intrinsic)i(v)n(olume)f(separately)-6
b(.)648 1176 y(In)23 b(contrast)i(to)e(this)g(situation,)j(the)d
(method)h(of)f(moments)h(proposed)h(in)e(the)h(present)548
1284 y(paper)i(pro)o(vides)g(a)e(uni\002ed)h(theoretical)j(and)d
(algorithmic)h(frame)n(w)o(ork)g(for)e(simultane-)548
1392 y(ous)k(nonparametric)j(estimation)e(of)f(all)f(speci\002c)i
(intrinsic)h(v)n(olumes,)f(in)f(an)f(arbitrary)548 1500
y(dimension)c Ft(d)i Fs(>)g Fr(2)p Fw(.)j(The)20 b(construction)k
(principle)f(of)e(these)g(estimators,)i(which)e(is)g(sim-)548
1608 y(ilar)g(to)f(the)h(approach)i(considered)g(in)e([11],)g(is)g
(based)g(on)g(a)f(representation)25 b(formula)c(for)548
1715 y(the)26 b(\(e)o(xpected\))h(local)g(connecti)n(vity)h(number)f
(of)e(stationary)j(RA)l(CS)23 b(intersected)29 b(with)548
1823 y(spheres,)g(whose)f(radii)g(are)f(small)g(in)g(comparison)j(with)
d(the)g(size)h(of)f(the)g(whole)h(sam-)548 1931 y(pling)35
b(windo)n(w)-6 b(.)61 b(It)33 b(can)i(be)f(considered)j(as)d(a)g
(statistical)j(counterpart)g(to)d(a)g(method)548 2039
y(for)g(the)f(simultaneous)k(computation)f(of)d(all)h(intrinsic)h(v)n
(olumes)g(of)f(a)f(deterministic)548 2147 y(polycon)l(v)o(e)o(x)26
b(set)e(based)h(on)f(the)f(principal)j(kinematic)g(formula.)648
2255 y(Our)k(estimators)k(are)d(unbiased)j(by)d(de\002nition.)54
b(Moreo)o(v)o(er)l(,)34 b(under)e(suitable)i(inte-)548
2363 y(grability)29 b(and)e(mixing)g(conditions,)j(the)o(y)d(are)g
(mean\226square)i(consistent)h(and)d(asymp-)548 2471
y(totically)h(normal)e(distrib)n(uted.)39 b(This)25 b(can)h(be)g(used)g
(in)g(order)h(to)e(establish)j(asymptotic)548 2579 y(tests)c(for)g(the)
g(v)o(ector)g(of)g(speci\002c)g(intrinsic)i(v)n(olumes.)648
2687 y(Notice)37 b(that)g(the)g(method)h(of)f(moments)g(\(which)h(is)e
(also)i(called)g(the)f(method)h(of)548 2795 y(intensities)c(by)e(some)f
(authors\))j(has)e(been)g(used)g(in)f(the)h(analysis)i(of)d(v)n(arious)
i(further)548 2903 y(statistical)24 b(aspects)g(of)d(models)i(from)f
(stochastic)i(geometry)-6 b(,)24 b(for)e(e)o(xample,)g(in)g(order)h(to)
548 3011 y(estimate)g(the)g(intensity)h(of)e(germs)g(and)h(other)g
(characteristics)j(of)c(the)h(Boolean)g(model;)548 3119
y(see)h(e.g.)k([7],)c(and)g(Sections)g(5.3\2265.4)h(in)e([13].)648
3226 y(The)e(present)j(paper)e(is)g(or)n(ganized)j(as)c(follo)n(ws.)29
b(Some)21 b(necessary)k(preliminaries)f(on)548 3334 y(Mink)o(o)n(wski)
32 b(functionals)i(and)d(intrinsic)i(v)n(olumes,)g(respecti)n(v)o(ely)
-6 b(,)35 b(are)c(gi)n(v)o(en)g(in)g(Sec-)548 3442 y(tion)36
b(1.)65 b(In)36 b(Section)h(2,)h(the)e(computation)i(of)e(intrinsic)i
(v)n(olumes)f(of)f(deterministic)548 3550 y(polycon)l(v)o(e)o(x)26
b(sets)d(is)g(brie\003y)g(discussed.)31 b(The)22 b(abo)o(v)o
(e\226mentioned)27 b(representation)g(for)n(-)548 3658
y(mula)20 b(for)h(the)g(\(e)o(xpected\))i(local)e(connecti)n(vity)j
(number)d(of)f(stationary)k(RA)l(CS)18 b(is)i(stated)548
3766 y(in)h(Section)h(3;)g(see)g(Proposition)h(3.1.)28
b(W)-7 b(e)21 b(gi)n(v)o(e)g(an)g(alternati)n(v)o(e)j(proof)e(of)f
(this)h(represen-)548 3874 y(tation)30 b(formula)g(which)f(mak)o(es)g
(use)h(of)e(an)h(e)o(xplicit)h(e)o(xtension)i(of)c(Steiner')-5
b(s)30 b(formula)548 3982 y(for)22 b(con)l(v)o(e)o(x)h(bodies)g(to)e
(the)h(con)l(v)o(e)o(x)h(ring.)28 b(The)22 b(result)g(of)g(Proposition)
i(3.1)d(is)g(then)i(used)548 4090 y(in)j(Section)i(4)e(in)h(order)g(to)
g(construct)i(a)d(f)o(amily)i(of)e(nonparametric)k(estimators)f(for)d
(all)548 4198 y Ft(d)i Fr(+)g(1)33 b Fw(speci\002c)i(intrinsic)h(v)n
(olumes)f(simultaneously)-6 b(.)63 b(The)34 b(construction)j(principle)
548 4306 y(of)26 b(these)h(estimators)h(is)d(described)k(and)d(their)h
(asymptotic)h(properties)h(are)d(discussed.)548 4414
y(A)h(related)i(f)o(amily)g(of)f(least\226squares)j(estimators)f(is)e
(also)g(pro)o(vided)i(in)e(Section)h(4.)42 b(In)548 4522
y(Section)32 b(5,)h(some)f(aspects)h(of)e(v)n(ariance)j(reduction)g
(using)e Fv(kriging)i(of)d(the)h(mean)f Fw(are)548 4630
y(touched)e(upon.)41 b(Finally)-6 b(,)28 b(in)f(Section)h(6)f
(numerical)i(results)f(are)g(gi)n(v)o(en)f(for)h(the)f(planar)548
4737 y(Boolean)h(model)g(with)f(spherical)j(primary)e(grains.)42
b(The)o(y)27 b(are)g(compared)i(with)e(those)548 4845
y(obtained)j(by)d(another)j(method)e(described)i(in)e([10])g(for)g(the)
g(computation)i(of)e(speci\002c)548 4953 y(intrinsic)e(v)n(olumes.)p
eop end
%%Page: 3 3
TeXDict begin 3 2 bop 598 550 a Fu(Computation)18 b(of)i(intrinsic)h
(volumes)f(of)g(a)g(polycon)m(ve)n(x)f(set)1034 b FF(3)598
757 y Fx(1.)216 b(Mink)n(o)o(wski)27 b(functionals)f(and)h(intrinsic)g
(v)o(olumes)697 915 y Fw(Let)d Ft(d)i Fs(>)g Fr(2)d Fw(be)h(an)g
(arbitrary)i(\002x)o(ed)e(inte)o(ger)h(and)g(let)f Fq(K)g
Fw(be)g(the)h(f)o(amily)f(of)g(all)g Fv(con)l(ve)n(x)598
1022 y(bodies)p Fw(,)g(i.e.,)f(compact)h(con)l(v)o(e)o(x)h(sets)f(in)f
Fp(R)1964 990 y Fo(d)2004 1022 y Fw(.)28 b(The)23 b Fv(con)l(ve)n(x)i
(ring)f Fq(R)f Fw(in)g Fp(R)2921 990 y Fo(d)2984 1022
y Fw(is)g(the)h(f)o(amily)598 1130 y(of)f(all)g(\002nite)g(unions)1283
1062 y Fn(S)1358 1089 y Fo(m)1358 1157 y(i)p FE(=1)1492
1130 y Ft(K)1569 1144 y Fo(i)1620 1130 y Fw(of)f(con)l(v)o(e)o(x)j
(bodies)f Ft(K)2332 1144 y FE(1)2372 1130 y Ft(;)15 b(:)g(:)g(:)i(;)e
(K)2651 1144 y Fo(m)2743 1130 y Fq(2)25 b(K)q Fw(.)j(The)23
b(elements)598 1238 y(of)29 b Fq(R)g Fw(are)h(called)h
Fv(polycon)l(ve)n(x)i(sets)p Fw(.)48 b(Furthermore,)33
b(the)c Fv(e)n(xtended)k(con)l(ve)n(x)e(ring)g Fq(S)k
Fw(is)598 1346 y(the)f(f)o(amily)h(of)f(all)g(subsets)i
Ft(A)45 b Fq(\032)f Fp(R)1835 1313 y Fo(d)1909 1346 y
Fw(such)35 b(that)f Ft(A)29 b Fq(\\)e Ft(K)52 b Fq(2)44
b(R)33 b Fw(for)i(an)o(y)f Ft(K)51 b Fq(2)45 b(K)q Fw(.)598
1454 y(F)o(or)35 b Ft(A;)15 b(B)53 b Fq(\032)c Fp(R)1174
1421 y Fo(d)1214 1454 y Fw(,)38 b(the)e Fv(Mink)o(owski)h(sum)f
Ft(A)30 b Fq(\010)f Ft(B)40 b Fw(and)c(the)g Fv(Mink)o(owski)i(dif)n
(fer)m(ence)598 1562 y Ft(A)26 b Fq(\011)f Ft(B)35 b
Fw(are)c(de\002ned)h(by)f Ft(A)26 b Fq(\010)g Ft(B)43
b Fr(=)c Fq(f)p Ft(x)26 b Fr(+)g Ft(y)42 b Fr(:)54 b
Ft(x)39 b Fq(2)g Ft(A;)31 b(y)42 b Fq(2)d Ft(B)5 b Fq(g)30
b Fw(and)h Ft(A)26 b Fq(\011)g Ft(B)43 b Fr(=)598 1670
y Fq(f)p Ft(x)e Fq(2)f Fp(R)903 1637 y Fo(d)984 1670
y Fr(:)h Ft(B)30 b Fr(+)d Ft(x)40 b Fq(\032)g Ft(A)p
Fq(g)p Fw(,)34 b(respecti)n(v)o(ely)-6 b(.)56 b(F)o(or)31
b(an)o(y)h(Borel)g(set)g Ft(B)45 b Fq(\032)c Fp(R)3099
1637 y Fo(d)3139 1670 y Fw(,)33 b(denote)598 1778 y(by)25
b Ft(V)766 1793 y Fo(d)807 1778 y Fr(\()p Ft(B)5 b Fr(\))25
b Fw(its)g(Lebesgue)i(measure.)36 b(It)25 b(is)h(well)f(kno)n(wn)h
(that)g(there)g(e)o(xist)g(nonne)o(gati)n(v)o(e)598 1886
y(functionals)d Ft(V)1074 1900 y Fo(j)1136 1886 y Fr(:)i
Fq(K)i(!)e Fr([0)p Ft(;)15 b Fq(1)p Fr(\))p Fw(,)21 b
Ft(j)31 b Fr(=)25 b(0)p Ft(;)15 b(:)g(:)g(:)i(;)e(d)k
Fw(such)i(that)f(for)g(each)h Ft(r)28 b(>)d Fr(0)19 b
Fw(the)h(v)n(olume)598 1994 y Ft(V)651 2009 y Fo(d)691
1994 y Fr(\()p Ft(K)32 b Fq(\010)23 b Ft(B)998 2008 y
Fo(r)1036 1994 y Fr(\()p Ft(o)p Fr(\)\))30 b Fw(of)e(the)i
(so\226called)h Fv(par)o(allel)g(body)f Ft(K)g Fq(\010)24
b Ft(B)2620 2008 y Fo(r)2658 1994 y Fr(\()p Ft(o)p Fr(\))29
b Fw(of)g(an)o(y)g Ft(K)42 b Fq(2)35 b(K)29 b Fw(is)598
2102 y(gi)n(v)o(en)24 b(by)f Fv(Steiner')l(s)k(formula)1275
2351 y Ft(V)1328 2366 y Fo(d)1369 2351 y Fr(\()p Ft(K)g
Fq(\010)20 b Ft(B)1668 2365 y Fo(r)1706 2351 y Fr(\()p
Ft(o)p Fr(\)\))26 b(=)2025 2237 y Fo(d)1977 2264 y Fn(X)1982
2460 y Fo(j)t FE(=0)2124 2351 y Ft(r)2168 2313 y Fo(d)p
Fm(\000)p Fo(j)2295 2351 y Ft(\024)2347 2366 y Fo(d)p
Fm(\000)p Fo(j)2475 2351 y Ft(V)2528 2365 y Fo(j)2565
2351 y Fr(\()p Ft(K)7 b Fr(\))15 b Ft(;)572 b Fw(\(1\))598
2621 y(where)19 b Ft(o)25 b Fq(2)g Fp(R)1059 2588 y Fo(d)1118
2621 y Fw(denotes)c(the)e(origin,)i Ft(B)1871 2635 y
Fo(r)1909 2621 y Fr(\()p Ft(x)p Fr(\))26 b(=)f Fq(f)p
Ft(y)k Fq(2)24 b Fp(R)2423 2588 y Fo(d)2489 2621 y Fr(:)h
Fq(j)p Ft(y)7 b Fq(\000)t Ft(x)p Fq(j)25 b Fs(6)g Ft(r)s
Fq(g)19 b Fw(is)f(the)i(closed)598 2729 y(ball)h(with)g(midpoint)i
Ft(x)i Fq(2)g Fp(R)1514 2696 y Fo(d)1575 2729 y Fw(and)c(radius)i
Ft(r)s Fw(,)d(and)h Ft(\024)2259 2743 y Fo(j)2317 2729
y Fw(is)g(the)g(v)n(olume)h(of)f(the)h(unit)g(ball)f(in)598
2837 y Fp(R)664 2804 y Fo(j)700 2837 y Fw(.)41 b(The)27
b(functionals)k Ft(V)1416 2851 y Fo(j)1480 2837 y Fw(are)d(called)h
Fv(intrinsic)i(volumes)p Fw(.)42 b(The)o(y)28 b(are)g(closely)i
(related)598 2945 y(to)22 b(the)g(widely)h(kno)n(wn)g
Fv(quermassinte)l(gr)o(als)k Fw(or)22 b Fv(Mink)o(owski)h(functionals)j
Ft(W)3069 2959 y Fo(j)3126 2945 y Fw(gi)n(v)o(en)d(by)598
3066 y Ft(W)684 3080 y Fo(j)720 3066 y Fr(\()p Ft(K)7
b Fr(\))27 b(=)g Ft(V)1052 3081 y Fo(d)p Fm(\000)p Fo(j)1179
3066 y Fr(\()p Ft(K)7 b Fr(\))15 b Ft(\024)1400 3080
y Fo(j)1438 2993 y Fn(\016)o(\000)1532 3026 y Fo(d)1534
3097 y(j)1568 2993 y Fn(\001)1610 3066 y Fw(,)23 b Ft(K)34
b Fq(2)26 b(K)q Fw(.)31 b(There)24 b(e)o(xists)h(a)f(unique)i(additi)n
(v)o(e)g(e)o(xtension)598 3174 y(of)32 b(the)g(functionals)k
Ft(V)1336 3188 y Fo(j)1404 3174 y Fw(to)c(the)g(con)l(v)o(e)o(x)i(ring)
f Fq(R)e Fw(gi)n(v)o(en)i(by)f(the)h Fv(inclusion\226e)n(xclusio)q(n)
598 3282 y(formula)831 3512 y Ft(V)884 3526 y Fo(j)921
3512 y Fr(\()p Ft(K)1033 3526 y FE(1)1093 3512 y Fq([)20
b Ft(:)15 b(:)g(:)21 b Fq([)f Ft(K)1458 3526 y Fo(m)1525
3512 y Fr(\))25 b(=)1716 3399 y Fo(m)1681 3426 y Fn(X)1683
3623 y Fo(k)r FE(=1)1813 3512 y Fr(\()p Fq(\000)p Fr(1\))1999
3475 y Fo(k)r Fm(\000)p FE(1)2226 3426 y Fn(X)2147 3621
y Fo(i)2171 3630 y Fl(1)2206 3621 y Fo(<:::)o(<i)2399
3633 y Fk(k)2452 3512 y Ft(V)2505 3526 y Fo(j)2541 3512
y Fr(\()p Ft(K)2653 3526 y Fo(i)2677 3535 y Fl(1)2737
3512 y Fq(\\)20 b Ft(:)15 b(:)g(:)21 b Fq(\\)f Ft(K)3102
3526 y Fo(i)3126 3538 y Fk(k)3168 3512 y Fr(\))128 b
Fw(\(2\))598 3771 y(for)24 b(an)o(y)f Ft(K)956 3785 y
FE(1)996 3771 y Ft(;)15 b(:)g(:)g(:)i(;)e(K)1275 3785
y Fo(m)1367 3771 y Fq(2)25 b(K)q Fw(.)k(The)23 b(intrinsic)j(v)n
(olumes)f Ft(V)2442 3785 y Fo(j)2479 3771 y Fr(\()p Ft(K)7
b Fr(\))p Fw(,)23 b Ft(j)31 b Fr(=)25 b(0)p Ft(;)15 b(:)g(:)g(:)i(;)e
(d)24 b Fw(pro)o(vide)598 3878 y(information)29 b(about)f(the)g
(morphological)i(structure)f(of)e(the)h(polycon)l(v)o(e)o(x)i(set)d
Ft(K)38 b Fq(2)31 b(R)p Fw(.)598 3986 y(F)o(or)e(e)o(xample,)j
Ft(V)1165 4001 y Fo(d)1206 3986 y Fr(\()p Ft(K)7 b Fr(\))30
b Fw(is)g(the)g(usual)i(v)n(olume,)g Fr(2)p Ft(V)2264
4001 y Fo(d)p Fm(\000)p FE(1)2395 3986 y Fr(\()p Ft(K)7
b Fr(\))30 b Fw(is)g(the)h(surf)o(ace)h(area,)g(and)598
4094 y(the)g Fv(Euler)n(\226P)-7 b(oincar)s Fr(\023)-48
b Ft(e)36 b Fv(c)o(har)o(acteristic)f Ft(V)1932 4108
y FE(0)1972 4094 y Fr(\()p Ft(K)7 b Fr(\))32 b Fw(re\003ects)h(the)g
(connecti)n(vity)j(properties)598 4202 y(of)e Ft(K)7
b Fw(.)59 b(Notice)35 b(that)f(in)g(the)h(planar)g(case,)i(that)e(is)f
Ft(d)45 b Fr(=)g(2)p Fw(,)36 b Ft(V)2671 4216 y FE(0)2710
4202 y Fr(\()p Ft(K)7 b Fr(\))34 b Fw(is)g(equal)h(to)f(the)598
4310 y(number)25 b(of)g(\224clumps\223)h(minus)f(the)g(number)g(of)g
(\224holes\223)h(of)f Ft(K)34 b Fq(2)27 b(R)p Fw(,)d(i.e.,)f(the)i
(number)598 4418 y(of)h(connected)j(outer)e(boundary)i(components)g(of)
e Ft(K)32 b Fw(minus)27 b(the)f(number)i(of)e(its)g(inner)598
4526 y(boundary)h(components.)34 b(In)25 b(particular)l(,)j
Ft(V)2003 4540 y FE(0)2042 4526 y Fr(\()p Ft(K)7 b Fr(\))28
b(=)f(1)d Fw(for)h(an)o(y)f(con)l(v)o(e)o(x)i(body)g
Ft(K)34 b Fq(6)p Fr(=)27 b Fq(;)p Fw(.)598 4634 y(Furthermore,)40
b(for)c(an)o(y)f Ft(K)55 b Fq(2)47 b(R)35 b Fw(and)h
Ft(q)s(;)15 b(x)48 b Fq(2)g Fp(R)2295 4601 y Fo(d)2335
4634 y Fw(,)37 b Ft(q)51 b Fq(6)p Fr(=)c Ft(x)p Fw(,)38
b(the)e(so\226called)i Fv(inde)n(x)598 4742 y Ft(J)9
b Fr(\()p Ft(K)q(;)15 b(q)s(;)g(x)p Fr(\))25 b Fw(of)e
Ft(K)30 b Fw(is)23 b(gi)n(v)o(en)h(by)902 4902 y Ft(J)9
b Fr(\()p Ft(K)q(;)15 b(q)s(;)g(x)p Fr(\))28 b(=)d(1)20
b Fq(\000)54 b Fr(lim)1565 4963 y Fo(\016)r Fm(!)p FE(+0)1808
4902 y Fr(lim)1775 4960 y Fo(")p Fm(!)p FE(+0)1983 4902
y Ft(V)2036 4916 y FE(0)2091 4828 y Fn(\000)2133 4902
y Ft(K)27 b Fq(\\)19 b Ft(B)2386 4920 y Fm(j)p Fo(x)p
Fm(\000)p Fo(q)r Fm(j\000)p Fo(")2646 4902 y Fr(\()p
Ft(x)p Fr(\))i Fq(\\)e Ft(B)2938 4917 y Fo(\016)2976
4902 y Fr(\()p Ft(q)s Fr(\))3090 4828 y Fn(\001)3331
4902 y Fw(\(3\))598 5108 y(for)k Ft(q)28 b Fq(2)d Ft(K)7
b Fw(.)28 b(F)o(or)22 b(all)i Ft(q)k Fq(62)d Ft(K)7 b
Fw(,)21 b(we)i(put)h Ft(J)9 b Fr(\()p Ft(K)q(;)15 b(q)s(;)g(x)p
Fr(\))27 b(=)e(0)p Fw(.)j(In)c(particular)l(,)i Ft(J)9
b Fr(\()p Fq(;)p Ft(;)15 b(q)s(;)g(x)p Fr(\))27 b(=)e(0)598
5215 y Fw(for)e(arbitrary)j Ft(q)s(;)15 b(x)26 b Fq(2)f
Fp(R)1376 5182 y Fo(d)1416 5215 y Fw(.)p eop end
%%Page: 4 4
TeXDict begin 4 3 bop 548 550 a FF(4)588 b Fu(On)20 b(the)g(local)g
(connectivity)f(number)g(of)i(stationary)e(r)o(andom)g(closed)h(sets)
548 757 y Fx(2.)216 b(Computation)26 b(of)h(intrinsic)g(v)o(olumes)g
(of)g(a)f(polycon)l(v)o(ex)h(set)648 915 y Fw(Gi)n(v)o(en)f(a)g
(polycon)l(v)o(e)o(x)k(set)c Ft(K)38 b Fq(\032)31 b Fp(R)1811
882 y Fo(d)1851 915 y Fw(,)26 b(apply)i(the)f(principal)i(kinematic)f
(formula)g(of)548 1022 y(inte)o(gral)i(geometry)f(\(cf.)43
b(formula)29 b(\(4.5.3\))g(in)f([12]\))h(to)f(the)g(Euler)n
(\226Poincar)p Fr(\023)-43 b(e)47 b Fw(charac-)548 1130
y(teristic)26 b(of)f(the)g(intersection)j(of)c Ft(K)31
b Fw(with)24 b(an)h(arbitrary)i(translation)g(of)e(the)g(ball)g
Ft(B)3212 1144 y Fo(r)3250 1130 y Fr(\()p Ft(o)p Fr(\))p
Fw(.)548 1238 y(This)e(yields)987 1393 y Fn(Z)1038 1600
y Fo(K)5 b Fm(\010)p Fo(B)1211 1608 y Fk(r)1245 1600
y FE(\()p Fo(o)p FE(\))1353 1517 y Ft(V)1406 1531 y FE(0)1445
1517 y Fr(\()p Ft(K)28 b Fq(\\)19 b Ft(B)1734 1531 y
Fo(r)1772 1517 y Fr(\()p Ft(x)p Fr(\)\))c Ft(dx)27 b
Fr(=)2213 1403 y Fo(d)2166 1431 y Fn(X)2170 1626 y Fo(j)t
FE(=0)2312 1517 y Ft(r)2356 1480 y Fo(d)p Fm(\000)p Fo(j)2484
1517 y Ft(\024)2536 1532 y Fo(d)p Fm(\000)p Fo(j)2664
1517 y Ft(V)2717 1531 y Fo(j)2753 1517 y Fr(\()p Ft(K)7
b Fr(\))15 b Ft(;)334 b Fw(\(4\))548 1807 y(where)34
b(the)f(inte)o(gration)k(domain)d(is)f Ft(K)h Fq(\010)28
b Ft(B)2049 1821 y Fo(r)2086 1807 y Fr(\()p Ft(o)p Fr(\))34
b Fw(since)g Ft(V)2506 1821 y FE(0)2546 1807 y Fr(\()p
Ft(K)g Fq(\\)27 b Ft(B)2849 1821 y Fo(r)2887 1807 y Fr(\()p
Ft(x)p Fr(\)\))45 b(=)e(0)33 b Fw(for)548 1915 y Ft(x)25
b Fq(62)g Ft(K)i Fq(\010)20 b Ft(B)975 1929 y Fo(r)1013
1915 y Fr(\()p Ft(o)p Fr(\))p Fw(.)28 b(Introduce)f(the)c(notation)j
Ft(R)2073 1929 y Fo(r)2136 1915 y Fr(=)2232 1841 y Fn(R)2275
1946 y Fo(K)5 b Fm(\010)p Fo(B)2448 1954 y Fk(r)2482
1946 y FE(\()p Fo(o)p FE(\))2590 1915 y Ft(V)2643 1929
y FE(0)2683 1915 y Fr(\()p Ft(K)27 b Fq(\\)20 b Ft(B)2972
1929 y Fo(r)3010 1915 y Fr(\()p Ft(x)p Fr(\)\))15 b Ft(dx)p
Fw(.)648 2034 y(Writing)26 b(equation)i(\(4\))e(for)f
Ft(d)d Fr(+)g(1)j Fw(pairwise)i(dif)n(ferent)g(radii)g
Ft(r)2687 2048 y FE(0)2726 2034 y Ft(;)15 b(:)g(:)g(:)i(;)e(r)2969
2049 y Fo(d)3034 2034 y Fw(yields)27 b(the)548 2142 y(follo)n(wing)e
(system)f(of)g Ft(d)c Fr(+)g(1)j Fw(linear)i(equations:)1675
2332 y Ft(A)1743 2346 y Fo(r)1775 2355 y Fl(0)1810 2346
y Fo(:::)n(r)1900 2358 y Fk(d)1956 2332 y Ft(V)45 b Fr(=)25
b Ft(R)16 b(;)1021 b Fw(\(5\))548 2545 y(where)24 b Ft(V)45
b Fr(=)987 2471 y Fn(\000)1029 2545 y Ft(V)1082 2559
y FE(0)1121 2545 y Fr(\()p Ft(K)7 b Fr(\))p Ft(;)15 b(:)g(:)g(:)i(;)e
(V)1530 2560 y Fo(d)1571 2545 y Fr(\()p Ft(K)7 b Fr(\))1725
2471 y Fn(\001)1767 2494 y Fm(>)1826 2545 y Fw(,)23 b
Ft(R)j Fr(=)f(\()p Ft(R)2167 2559 y Fo(r)2199 2568 y
Fl(0)2238 2545 y Ft(;)15 b(:)g(:)g(:)h(;)f(R)2508 2559
y Fo(r)2540 2571 y Fk(d)2581 2545 y Fr(\))2616 2503 y
Fm(>)2698 2545 y Fw(and)899 2919 y Ft(A)967 2933 y Fo(r)999
2942 y Fl(0)1033 2933 y Fo(:::)o(r)1124 2945 y Fk(d)1189
2919 y Fr(=)1285 2682 y Fn(0)1285 2842 y(B)1285 2896
y(B)1285 2954 y(@)1406 2751 y Ft(r)1450 2718 y Fo(d)1447
2776 y FE(0)1490 2751 y Ft(\024)1542 2766 y Fo(d)1666
2751 y Ft(r)1710 2713 y Fo(d)p Fm(\000)p FE(1)1707 2777
y(0)1840 2751 y Ft(\024)1892 2766 y Fo(d)p Fm(\000)p
FE(1)2106 2751 y Ft(:)g(:)g(:)85 b(r)2340 2718 y FE(2)2337
2776 y(0)2378 2751 y Ft(\024)2430 2765 y FE(2)2554 2751
y Ft(r)2595 2765 y FE(0)2634 2751 y Ft(\024)2686 2765
y FE(1)2840 2751 y Fr(1)1406 2868 y Ft(r)1450 2835 y
Fo(d)1447 2892 y FE(1)1490 2868 y Ft(\024)1542 2883 y
Fo(d)1666 2868 y Ft(r)1710 2830 y Fo(d)p Fm(\000)p FE(1)1707
2894 y(1)1840 2868 y Ft(\024)1892 2883 y Fo(d)p Fm(\000)p
FE(1)2106 2868 y Ft(:)15 b(:)g(:)85 b(r)2340 2835 y FE(2)2337
2892 y(1)2378 2868 y Ft(\024)2430 2882 y FE(2)2554 2868
y Ft(r)2595 2882 y FE(1)2634 2868 y Ft(\024)2686 2882
y FE(1)2840 2868 y Fr(1)1442 2976 y Ft(:)15 b(:)g(:)245
b(:)15 b(:)g(:)209 b(:)15 b(:)g(:)119 b(:)15 b(:)g(:)152
b(:)15 b(:)g(:)118 b(:)15 b(:)g(:)1406 3093 y(r)1450
3060 y Fo(d)1447 3120 y(d)1490 3093 y Ft(\024)1542 3108
y Fo(d)1666 3093 y Ft(r)1710 3055 y Fo(d)p Fm(\000)p
FE(1)1707 3122 y Fo(d)1840 3093 y Ft(\024)1892 3108 y
Fo(d)p Fm(\000)p FE(1)2106 3093 y Ft(:)g(:)g(:)85 b(r)2340
3060 y FE(2)2337 3120 y Fo(d)2378 3093 y Ft(\024)2430
3107 y FE(2)2553 3093 y Ft(r)2594 3108 y Fo(d)2635 3093
y Ft(\024)2687 3107 y FE(1)2840 3093 y Fr(1)2957 2682
y Fn(1)2957 2842 y(C)2957 2896 y(C)2957 2954 y(A)3281
2919 y Fw(\(6\))548 3291 y(is)30 b(a)h(re)o(gular)g(matrix.)51
b(Then,)32 b Ft(V)59 b Fr(=)38 b Ft(A)1834 3258 y Fm(\000)p
FE(1)1834 3314 y Fo(r)1866 3323 y Fl(0)1900 3314 y Fo(:::)o(r)1991
3326 y Fk(d)2031 3291 y Ft(R)31 b Fw(is)f(the)h(unique)h(solution)h(of)
e(\(5\).)50 b(The)548 3399 y(inte)o(grals)25 b Ft(R)951
3413 y Fo(r)983 3423 y Fk(i)1036 3399 y Fw(can)f(be)g(approximated)j
(by)1389 3641 y Fn(b)1372 3664 y Ft(R)1441 3678 y Fo(r)1473
3688 y Fk(i)1529 3664 y Fr(=)e(\001)1701 3627 y Fo(d)1791
3551 y(m)1756 3578 y Fn(X)1757 3776 y Fo(k)r FE(=1)1903
3664 y Ft(V)1956 3678 y FE(0)1995 3664 y Fr(\()p Ft(K)i
Fq(\\)20 b Ft(B)2284 3678 y Fo(r)2322 3664 y Fr(\()p
Ft(x)2409 3679 y Fo(k)2452 3664 y Fr(\)\))15 b Ft(;)719
b Fw(\(7\))548 3938 y(where)20 b(the)f(points)i Ft(x)1211
3952 y FE(1)1250 3938 y Ft(;)15 b(:)g(:)g(:)i(;)e(x)1504
3952 y Fo(m)1589 3938 y Fw(belong)21 b(to)f(a)e Ft(d)p
Fw(\226dimensional)23 b(cubic)e(lattice)f(with)f(mesh)548
4046 y(size)24 b Fr(\001)p Fw(.)k(Thus,)23 b(the)h(v)o(ector)g
Ft(V)43 b Fw(can)24 b(be)g(computed)h(numerically)h(as)1683
4245 y Ft(V)45 b Fq(\031)25 b Ft(A)1945 4207 y Fm(\000)p
FE(1)1945 4267 y Fo(r)1977 4276 y Fl(0)2012 4267 y Fo(:::)n(r)2102
4279 y Fk(d)2160 4222 y Fn(b)2143 4245 y Ft(R)15 b(;)1029
b Fw(\(8\))548 4458 y(where)816 4435 y Fn(b)799 4458
y Ft(R)30 b Fw(is)f(the)h(v)o(ector)h Fr(\()1435 4435
y Fn(b)1417 4458 y Ft(R)1486 4472 y Fo(r)1518 4481 y
Fl(0)1557 4458 y Ft(;)15 b(:)g(:)g(:)i(;)1776 4435 y
Fn(b)1759 4458 y Ft(R)1828 4472 y Fo(r)1860 4484 y Fk(d)1900
4458 y Fr(\))1935 4425 y Fm(>)2024 4458 y Fw(of)29 b(approximations)34
b(gi)n(v)o(en)c(in)g(\(7\).)48 b(This)548 4566 y(numerical)21
b(solution)h(hea)n(vily)g(depends)f(on)f(the)g(choice)h(of)f(radii)g
Ft(r)2660 4580 y FE(0)2699 4566 y Ft(;)15 b(:)g(:)g(:)i(;)e(r)2942
4581 y Fo(d)2983 4566 y Fw(.)27 b(T)-7 b(o)18 b(reduce)548
4673 y(this)27 b(dependence,)k(a)26 b(least\226squares)31
b(method)c(can)g(be)g(used;)i(see)e(also)h([5].)38 b(Instead)29
b(of)548 4790 y(\(5\),)23 b(consider)i(the)e(\(o)o(v)o(erdetermined\))j
(system)d(of)g(linear)h(equations)2800 4767 y Fn(b)2783
4790 y Ft(R)i Fr(=)f Ft(A)3042 4804 y Fo(r)3074 4813
y Fl(0)3109 4804 y Fo(:::)o(r)3200 4816 y Fk(k)q Fj(\000)p
Fl(1)3335 4790 y Ft(x)548 4910 y Fw(for)c Ft(k)28 b(>)d(d)10
b Fr(+)g(1)21 b Fw(pairwise)h(dif)n(ferent)h(radii)e
Ft(r)1935 4924 y FE(0)1975 4910 y Ft(;)15 b(:)g(:)g(:)h(;)f(r)2217
4925 y Fo(k)r Fm(\000)p FE(1)2371 4910 y Fw(where)21
b Ft(x)k Fr(=)g(\()p Ft(x)2873 4924 y FE(0)2913 4910
y Ft(;)15 b(:)g(:)g(:)h(;)f(x)3166 4925 y Fo(d)3207 4910
y Fr(\))3242 4877 y Fm(>)3327 4910 y Fq(2)548 5018 y
Fp(R)614 4985 y Fo(d)p FE(+1)744 5018 y Fw(.)28 b(It)23
b(is)h(well)f(kno)n(wn)h(that)g(the)g(v)o(ector)1221
5208 y Ft(v)1268 5170 y Fm(\003)1333 5208 y Fr(=)1429
5134 y Fn(\000)1471 5208 y Ft(A)1539 5170 y Fm(>)1539
5230 y Fo(r)1571 5239 y Fl(0)1605 5230 y Fo(:::)o(r)1696
5242 y Fk(k)q Fj(\000)p Fl(1)1817 5208 y Ft(A)1885 5222
y Fo(r)1917 5231 y Fl(0)1951 5222 y Fo(:::)o(r)2042 5234
y Fk(k)q Fj(\000)p Fl(1)2163 5134 y Fn(\001)2204 5157
y Fm(\000)p FE(1)2299 5208 y Ft(A)2367 5170 y Fm(>)2367
5230 y Fo(r)2399 5239 y Fl(0)2433 5230 y Fo(:::)o(r)2524
5242 y Fk(k)q Fj(\000)p Fl(1)2662 5185 y Fn(b)2644 5208
y Ft(R)568 b Fw(\(9\))p eop end
%%Page: 5 5
TeXDict begin 5 4 bop 598 550 a Fu(Stationary)18 b(r)o(andom)h(closed)h
(sets)1792 b FF(5)598 744 y Fw(is)23 b(the)h(unique)h(solution)h(of)d
(the)h Fv(least\226squar)m(es)j(minimization)f Fw(problem)1133
955 y Fq(j)1191 932 y Fn(b)1173 955 y Ft(R)c Fq(\000)d
Ft(A)1422 969 y Fo(r)1454 978 y Fl(0)1489 969 y Fo(:::)o(r)1580
981 y Fk(k)q Fj(\000)p Fl(1)1716 955 y Ft(v)1763 917
y Fm(\003)1817 955 y Fq(j)26 b Fr(=)73 b(min)1964 1023
y Fo(x)p Fm(2)p Fi(R)2099 1004 y Fk(d)p Fl(+1)2227 955
y Fq(j)2285 932 y Fn(b)2267 955 y Ft(R)21 b Fq(\000)f
Ft(A)2516 969 y Fo(r)2548 978 y Fl(0)2583 969 y Fo(:::)o(r)2674
981 y Fk(k)q Fj(\000)p Fl(1)2809 955 y Ft(x)15 b Fq(j)598
1201 y Fw(and,)21 b(therefore,)j(can)d(be)f(re)o(garded)i(as)f(an)g
(approximation)j(to)d(the)g(v)o(ector)g Ft(V)40 b Fw(of)21
b(intrinsic)598 1309 y(v)n(olumes)30 b(of)e Ft(K)7 b
Fw(.)43 b(F)o(or)28 b(a)g(discussion)j(of)e(the)f(practical)j(choice)f
(of)f(radii)g Ft(r)2999 1323 y FE(0)3039 1309 y Ft(;)15
b(:)g(:)g(:)h(;)f(r)3281 1324 y Fo(k)r Fm(\000)p FE(1)3414
1309 y Fw(,)598 1417 y(see)24 b([4,)f(5].)697 1525 y(In)37
b(general,)42 b(the)37 b(numerical)h(solutions)h(\(8\))e(and)h(\(9\))f
(of)f(\(5\))h(do)g(not)g(necessarily)598 1633 y(preserv)o(e)j(the)e
(positi)n(vity)j(property)f(of)e(the)h(v)n(olume)g Ft(V)2437
1648 y Fo(d)2478 1633 y Fr(\()p Ft(K)7 b Fr(\))38 b Fw(and)g(the)h
(surf)o(ace)h(area)598 1741 y Fr(2)p Ft(V)696 1756 y
Fo(d)p Fm(\000)p FE(1)827 1741 y Fr(\()p Ft(K)7 b Fr(\))p
Fw(.)28 b(Practically)e(one)d(can)h(cope)g(with)g(this)g(problem)g(by)g
(changing)h(the)f(v)n(alues)598 1848 y(and)29 b(the)g(number)g(of)g
(radii)h Ft(r)1541 1862 y Fo(i)1597 1848 y Fw(as)e(well)h(as)f
(distances)j(between)f(them.)44 b(F)o(or)28 b(a)g(detailed)598
1956 y(discussion,)e(see)e([4].)598 2172 y Fx(3.)216
b(Stationary)26 b(random)h(closed)g(sets)697 2330 y Fw(Let)i
Fr(\004)f Fw(be)h(a)g(stationary)i(random)f(closed)h(set)e(\(RA)l(CS\))
f(in)h Fp(R)2689 2297 y Fo(d)2757 2330 y Fw(whose)h(realizations)598
2438 y(belong)25 b(to)f(the)g(e)o(xtended)h(con)l(v)o(e)o(x)g(ring)g
Fq(S)k Fw(with)24 b(probability)j Fr(1)p Fw(.)h(Recall)c(that)h
(stationar)n(-)598 2546 y(ity)f(of)g Fr(\004)f Fw(means)h(the)h(in)l(v)
n(ariance)i(of)d(its)g(distrib)n(ution)j(with)d(respect)i(to)e
(arbitrary)i(trans-)598 2654 y(lations)i(in)e Fp(R)1028
2621 y Fo(d)1068 2654 y Fw(.)36 b(More)26 b(details)i(on)f(stationary)i
(RA)l(CS)24 b(can)j(be)f(found)h(in)g(man)o(y)f(books;)598
2762 y(see)e(e.g.)k([6,)23 b(7,)g(13,)g(15,)h(16,)f(18].)598
2978 y Fx(Speci\002c)k(intrinsic)f(v)o(olumes)697 3135
y Fw(F)o(or)k(an)o(y)h Ft(K)45 b Fq(2)38 b(R)p Fw(,)32
b(let)f Ft(N)10 b Fr(\()p Ft(K)d Fr(\))38 b(=)h(min)o
Fq(f)p Ft(m)g Fq(2)f Fp(N)g Fr(:)h Ft(K)45 b Fr(=)2684
3067 y Fn(S)2760 3093 y Fo(m)2760 3162 y(i)p FE(=1)2894
3135 y Ft(K)2971 3149 y Fo(i)2999 3135 y Ft(;)54 b(K)3155
3149 y Fo(i)3222 3135 y Fq(2)38 b(K)q(g)598 3243 y Fw(denote)25
b(the)f(minimal)f(number)i(of)e(con)l(v)o(e)o(x)i(components)h(of)e
(the)g(set)f Ft(K)7 b Fw(,)22 b(where)i(we)f(put)598
3351 y Ft(N)10 b Fr(\()p Ft(K)d Fr(\))25 b(=)g(0)f Fw(if)f
Ft(K)32 b Fr(=)25 b Fq(;)p Fw(.)j(Assume)c(that)1634
3572 y Ft(E)c Fr(2)1766 3534 y Fo(N)7 b FE(\(\004)p Fm(\\)p
FE([0)p Fo(;)p FE(1])2080 3511 y Fk(d)2117 3534 y FE(\))2174
3572 y Ft(<)25 b Fq(1)15 b Ft(:)885 b Fw(\(10\))598 3774
y(Then,)34 b(for)f(an)o(y)f(sequence)j Fq(f)p Ft(W)1636
3788 y Fo(n)1683 3774 y Fq(g)d Fw(of)g(compact)i(and)f(con)l(v)o(e)o(x)
h(observ)n(ation)h(windo)n(ws)598 3881 y Ft(W)684 3895
y Fo(n)771 3881 y Fr(=)40 b Ft(nW)j Fw(with)31 b Ft(W)53
b Fq(2)40 b(K)33 b Fw(such)f(that)g Ft(V)2017 3896 y
Fo(d)2058 3881 y Fr(\()p Ft(W)13 b Fr(\))41 b Ft(>)f
Fr(0)31 b Fw(and)h Ft(o)41 b Fq(2)e Fw(int)q Fr(\()p
Ft(W)13 b Fr(\))p Fw(,)33 b(the)f(limit)p 598 3916 74
4 v 598 3989 a Ft(V)671 4003 y Fo(j)708 3989 y Fr(\(\004\))d(=)g(lim)
1094 4003 y Fo(n)p Fm(!1)1327 3989 y Ft(E)20 b(V)1467
4003 y Fo(j)1504 3989 y Fr(\(\004)h Fq(\\)h Ft(W)1790
4003 y Fo(n)1837 3989 y Fr(\))1872 3916 y Fn(\016)1925
3989 y Ft(V)1978 4004 y Fo(d)2018 3989 y Fr(\()p Ft(W)2139
4003 y Fo(n)2186 3989 y Fr(\))j Fw(e)o(xists)i(for)f(each)g
Ft(j)35 b Fr(=)29 b(0)p Ft(;)15 b(:)g(:)g(:)i(;)e(d)26
b Fw(\(see)598 4097 y([13],)e(Theorem)g(5.1.3\))f(and)h(is)g(called)h
(the)e Ft(j)5 b Fw(th)24 b Fv(speci\002c)i(intrinsic)g(volume)e
Fw(of)f Fr(\004)p Fw(.)598 4313 y Fx(Local)k(Euler)l(\226P)n(oincar)p
Fh(\023)-54 b(e)44 b Fx(characteristic)697 4471 y Fw(The)31
b(e)o(xpectation)j Ft(E)20 b(V)1457 4485 y FE(0)1512
4471 y Fr(\(\004)g Fq(\\)g Ft(B)1778 4485 y Fo(r)1816
4471 y Fr(\()p Ft(x)p Fr(\)\))31 b Fw(is)f(called)j Fv(local)e(Euler)n
(\226P)-7 b(oincar)s Fr(\023)-48 b Ft(e)34 b Fv(c)o(har)o(ac-)598
4579 y(teristic)g Fw(or)l(,)h(equi)n(v)n(alently)-6 b(,)39
b Fv(local)33 b(connectivity)k(number)c Fw(of)g Fr(\004)p
Fw(,)h(where)f Ft(r)45 b(>)d Fr(0)33 b Fw(is)f(an)598
4687 y(arbitrary)h(\002x)o(ed)e(number)-5 b(.)52 b(F)o(or)30
b Ft(r)41 b Fr(=)e(1)p Fw(,)32 b(the)f(follo)n(wing)i(representation)i
(formula)d(for)598 4795 y Ft(E)20 b(V)738 4809 y FE(0)793
4795 y Fr(\(\004)g Fq(\\)g Ft(B)1059 4809 y FE(1)1098
4795 y Fr(\()p Ft(x)p Fr(\)\))29 b Fw(can)g(be)f(found)i(e.g.)44
b(in)28 b([13],)i(Corollary)g(5.3.2,)g(where)f(its)f(proof)598
4903 y(is)f(based)i(on)f(the)f(principal)j(kinematic)g(formula.)41
b(In)28 b(the)g(present)h(paper)l(,)h(we)d(gi)n(v)o(e)g(an)598
5011 y(alternati)n(v)o(e)k(proof)g(for)e(an)o(y)g Ft(r)39
b(>)c Fr(0)p Fw(,)30 b(which)g(mak)o(es)f(use)h(of)f(an)g(e)o(xplicit)i
(e)o(xtension)g(of)598 5118 y(Steiner')-5 b(s)25 b(formula)f(\(1\))g
(to)f(the)h(con)l(v)o(e)o(x)h(ring;)g(see)e([12].)p eop
end
%%Page: 6 6
TeXDict begin 6 5 bop 548 550 a FF(6)588 b Fu(On)20 b(the)g(local)g
(connectivity)f(number)g(of)i(stationary)e(r)o(andom)g(closed)h(sets)
548 762 y Fg(Pr)n(oposition)25 b(3.1.)41 b Fv(F)-10 b(or)24
b(any)g Ft(r)k Fs(>)d Fr(0)e Fv(and)h Ft(x)h Fq(2)g Fp(R)2121
729 y Fo(d)2161 762 y Fv(,)e(it)g(holds)1189 1045 y Ft(E)d(V)1329
1059 y FE(0)1384 1045 y Fr(\(\004)g Fq(\\)g Ft(B)1650
1059 y Fo(r)1688 1045 y Fr(\()p Ft(x)p Fr(\)\))26 b(=)2015
931 y Fo(d)1967 959 y Fn(X)1971 1154 y Fo(j)t FE(=0)2114
1045 y Ft(r)2158 1008 y Fo(d)p Fm(\000)p Fo(j)2285 1045
y Ft(\024)2337 1060 y Fo(d)p Fm(\000)p Fo(j)p 2465 972
74 4 v 2465 1045 a Ft(V)2538 1059 y Fo(j)2575 1045 y
Fr(\(\004\))15 b Ft(:)490 b Fw(\(11\))548 1351 y Fv(Pr)l(oof)o(.)46
b Fw(Consider)25 b(the)f(stationary)i(random)e(\002eld)g
Fq(f)p Ft(Z)2276 1365 y Fo(r)2314 1351 y Fr(\()p Ft(x)p
Fr(\))p Ft(;)31 b(x)26 b Fq(2)e Fp(R)2721 1318 y Fo(d)2762
1351 y Fq(g)p Fw(,)e(where)1121 1566 y Ft(Z)1183 1580
y Fo(r)1221 1566 y Fr(\()p Ft(x)p Fr(\))k(=)1682 1479
y Fn(X)1465 1680 y Fo(q)r Fm(2)p Fo(@)t FE(\004)p Fm(\\)p
Fo(B)1734 1688 y Fk(r)1769 1680 y FE(\()p Fo(x)p FE(\))p
Fo(;)19 b(q)r Fm(6)p FE(=)p Fo(x)2076 1566 y Ft(J)9 b
Fr(\(\004)21 b Fq(\\)f Ft(B)2402 1580 y Fo(r)2439 1566
y Fr(\()p Ft(x)p Fr(\))p Ft(;)15 b(q)s(;)g(x)p Fr(\))g
Ft(:)548 1879 y Fw(and)29 b Ft(J)766 1806 y Fn(\000)808
1879 y Fr(\004)24 b Fq(\\)g Ft(B)1047 1893 y Fo(r)1085
1879 y Fr(\()p Ft(x)p Fr(\))p Ft(;)15 b(q)s(;)g(x)1383
1806 y Fn(\001)1454 1879 y Fw(is)29 b(gi)n(v)o(en)g(by)g(\(3\).)45
b(In)29 b([11],)i(we)d(sho)n(wed)i(that)f Ft(E)21 b(Z)3121
1893 y Fo(r)3159 1879 y Fr(\()p Ft(x)p Fr(\))36 b(=)548
1939 y Fn(P)644 1966 y Fo(d)p Fm(\000)p FE(1)644 2035
y Fo(j)t FE(=0)790 2008 y Ft(r)834 1975 y Fo(d)p Fm(\000)p
Fo(j)961 2008 y Ft(\024)1013 2023 y Fo(d)p Fm(\000)p
Fo(j)p 1141 1935 V 1141 2008 a Ft(V)1214 2022 y Fo(j)1251
2008 y Fr(\(\004\))29 b Fw(holds)j(for)e(an)o(y)g Ft(x)38
b Fq(2)f Fp(R)2186 1975 y Fo(d)2226 2008 y Fw(.)48 b(Thus,)32
b(it)d(suf)n(\002ces)i(to)f(pro)o(v)o(e)h(that)548 2136
y Ft(E)20 b(V)688 2150 y FE(0)743 2136 y Fr(\(\004)g
Fq(\\)g Ft(B)1009 2150 y Fo(r)1047 2136 y Fr(\()p Ft(x)p
Fr(\)\))52 b(=)f Ft(E)20 b(Z)1527 2150 y Fo(r)1565 2136
y Fr(\()p Ft(x)p Fr(\))32 b(+)p 1820 2063 V 30 w Ft(V)1893
2151 y Fo(d)1933 2136 y Fr(\(\004\))p Fw(.)70 b(Notice)39
b(that)f(the)f(function)j Ft(f)10 b Fr(\()p Ft(r)s Fr(\))51
b(=)548 2244 y Ft(E)20 b(Z)697 2258 y Fo(r)735 2244 y
Fr(\()p Ft(x)p Fr(\))35 b Fw(is)f(continuously)k(dif)n(ferentiable)g
(as)c(a)g(polynomial)j(in)d Ft(r)s Fw(,)h(where)g Ft(f)10
b Fr(\()p Ft(r)s Fr(\))45 b(=)548 2279 y Fn(R)609 2305
y Fo(r)591 2384 y FE(0)662 2352 y Ft(f)717 2319 y FE(\(1\))810
2352 y Fr(\()p Ft(s)p Fr(\))15 b Ft(ds)23 b Fw(since)i
Ft(f)10 b Fr(\(0\))26 b(=)f(0)p Fw(.)j(Furthermore,)d(for)f(an)o(y)f
Ft(s)i(>)g Fr(0)p Fw(,)e(we)g(ha)n(v)o(e)1381 2604 y
Ft(f)1436 2567 y FE(\(1\))1529 2604 y Fr(\()p Ft(s)p
Fr(\))j(=)1795 2543 y Ft(d)p 1774 2584 90 4 v 1774 2667
a(ds)1874 2604 y(E)20 b(V)2014 2618 y FE(0)2054 2604
y Fr(\(\004)g Fq(\\)g Ft(B)2320 2618 y Fo(s)2356 2604
y Fr(\()p Ft(x)p Fr(\)\))15 b Ft(;)683 b Fw(\(12\))548
2825 y(where)29 b(the)f(deri)n(v)n(ati)n(v)o(e)i(on)f(the)g
(right\226hand)i(side)e(does)h(not)e(depend)j(on)d Ft(x)g
Fw(by)g(the)h(sta-)548 2932 y(tionarity)g(of)d Fr(\004)p
Fw(.)36 b(In)26 b(order)h(to)f(sho)n(w)h(\(12\),)g(let)f
Ft(A)2117 2946 y Fo(o)2181 2932 y Fw(be)h(a)f(suf)n(\002ciently)i
(small)e(open)i(cube)548 3040 y(with)f(diagonals)j(crossing)g(at)d(the)
g(origin)i Ft(o)e Fw(such)h(that)g Ft(A)2409 3054 y Fo(o)2479
3040 y Fq(\032)k Fr(in)m(t)q(\()p Ft(B)2795 3054 y Fo(s)2832
3040 y Fr(\()p Ft(o)p Fr(\)\))p Fw(.)40 b(Then,)28 b(for)548
3148 y(an)o(y)c Fr(\001)p Ft(s)g(>)h Fr(0)p Fw(,)e(we)g(ha)n(v)o(e)589
3341 y Ft(Z)651 3355 y Fo(s)p FE(+\001)p Fo(s)835 3341
y Fr(\()p Ft(o)p Fr(\))e Fq(\000)f Ft(Z)1123 3355 y Fo(s)1159
3341 y Fr(\()p Ft(o)p Fr(\))84 b(=)1854 3273 y Fn(P)1511
3429 y Fo(q)r Fm(2)p Fo(@)t FE(\004)p Fm(\\)p FE(\()p
Fo(B)1807 3440 y Fk(s)p Fl(+\001)p Fk(s)1966 3429 y FE(\()p
Fo(o)p FE(\))p Fm(n)p Fo(B)2142 3437 y Fk(s)2177 3429
y FE(\()p Fo(o)p FE(\)\))2339 3341 y Ft(J)2398 3268 y
Fn(\000)2440 3341 y Fr(\004)20 b Fq(\\)g Ft(B)2671 3355
y Fo(s)p FE(+\001)p Fo(s)2854 3341 y Fr(\()p Ft(o)p Fr(\))p
Ft(;)15 b(q)s(;)g(o)3136 3268 y Fn(\001)1357 3533 y Fr(=)1854
3465 y Fn(P)1511 3621 y Fo(q)r Fm(2)p Fo(@)t FE(\004)p
Fm(\\)p FE(\()p Fo(B)1807 3632 y Fk(s)p Fl(+\001)p Fk(s)1966
3621 y FE(\()p Fo(o)p FE(\))p Fm(n)p Fo(B)2142 3629 y
Fk(s)2177 3621 y FE(\()p Fo(o)p FE(\)\))2339 3533 y Ft(J)2398
3460 y Fn(\000)2440 3533 y Fr(\(\004)20 b Fq(n)h Ft(A)2690
3547 y Fo(o)2728 3533 y Fr(\))g Fq(\\)f Ft(B)2934 3547
y Fo(s)p FE(+\001)p Fo(s)3117 3533 y Fr(\()p Ft(o)p Fr(\))p
Ft(;)15 b(q)s(;)g(o)3399 3460 y Fn(\001)1357 3724 y Fr(=)83
b Ft(V)1564 3738 y FE(0)1603 3724 y Fr(\(\(\004)21 b
Fq(n)g Ft(A)1889 3738 y Fo(o)1927 3724 y Fr(\))g Fq(\\)e
Ft(B)2132 3738 y Fo(s)p FE(+\001)p Fo(s)2315 3724 y Fr(\()p
Ft(o)p Fr(\)\))j Fq(\000)e Ft(V)2630 3738 y FE(0)2669
3724 y Fr(\(\(\004)h Fq(n)f Ft(A)2954 3738 y Fo(o)2993
3724 y Fr(\))g Fq(\\)g Ft(B)3198 3738 y Fo(s)3235 3724
y Fr(\()p Ft(o)p Fr(\)\))1357 3907 y(=)83 b Ft(V)1564
3921 y FE(0)1603 3907 y Fr(\(\004)21 b Fq(\\)e Ft(B)1869
3921 y Fo(s)p FE(+\001)p Fo(s)2052 3907 y Fr(\()p Ft(o)p
Fr(\)\))j Fq(\000)e Ft(V)2367 3921 y FE(0)2406 3907 y
Fr(\(\004)g Fq(\\)g Ft(B)2672 3921 y Fo(s)2709 3907 y
Fr(\()p Ft(o)p Fr(\)\))15 b Ft(;)548 4097 y Fw(where)24
b(the)g(third)g(equality)i(follo)n(ws)e(from)f(the)h(f)o(act)g(that)934
4221 y Fn(X)800 4423 y Fo(q)r Fm(2)p Fo(@)t(A)p Fm(\\)p
Fo(B)1075 4431 y Fk(r)1110 4423 y FE(\()p Fo(o)p FE(\))1244
4308 y Ft(J)9 b Fr(\(\()p Ft(A)22 b Fq(n)e Ft(A)1596
4322 y Fo(o)1635 4308 y Fr(\))g Fq(\\)g Ft(B)1840 4322
y Fo(r)1878 4308 y Fr(\()p Ft(o)p Fr(\))p Ft(;)15 b(q)s(;)g(o)p
Fr(\))27 b(=)e Ft(V)2371 4322 y FE(0)2411 4308 y Fr(\(\()p
Ft(A)c Fq(n)f Ft(A)2703 4322 y Fo(o)2742 4308 y Fr(\))g
Fq(\\)g Ft(B)2947 4322 y Fo(r)2985 4308 y Fr(\()p Ft(o)p
Fr(\)\))548 4613 y Fw(for)k(each)g Ft(A)h Fq(2)g(S)30
b Fw(and)24 b(for)g(an)o(y)f Ft(r)28 b(>)d Fr(0)e Fw(such)h(that)h
Ft(A)2215 4627 y Fo(o)2278 4613 y Fq(\032)g Fr(in)m(t)q(\()p
Ft(B)2587 4627 y Fo(r)2625 4613 y Fr(\()p Ft(o)p Fr(\)\))p
Fw(.)k(This)23 b(gi)n(v)o(es)631 4886 y Ft(f)686 4848
y FE(\(1\))780 4886 y Fr(\()p Ft(s)p Fr(\))i(=)43 b(lim)1014
4947 y FE(\001)p Fo(s)p Fm(#)p FE(0)1191 4886 y Ft(E)1289
4825 y(Z)1351 4839 y Fo(s)p FE(+\001)p Fo(s)1534 4825
y Fr(\()p Ft(o)p Fr(\))21 b Fq(\000)f Ft(Z)1822 4839
y Fo(s)1859 4825 y Fr(\()p Ft(o)p Fr(\))p 1289 4865 685
4 v 1572 4948 a(\001)p Ft(s)671 5132 y Fr(=)43 b(lim)767
5193 y FE(\001)p Fo(s)p Fm(#)p FE(0)945 5132 y Ft(E)1042
5071 y(V)1095 5085 y FE(0)1134 5071 y Fr(\(\004)21 b
Fq(\\)e Ft(B)1400 5085 y Fo(s)p FE(+\001)p Fo(s)1584
5071 y Fr(\()p Ft(o)p Fr(\)\))i Fq(\000)f Ft(V)1898 5085
y FE(0)1937 5071 y Fr(\(\004)g Fq(\\)g Ft(B)2203 5085
y Fo(s)2240 5071 y Fr(\()p Ft(o)p Fr(\)\))p 1042 5111
1349 4 v 1657 5195 a(\001)p Ft(s)2425 5132 y Fr(=)2552
5071 y Ft(d)p 2531 5111 90 4 v 2531 5195 a(ds)2631 5132
y(E)h(V)2772 5146 y FE(0)2811 5132 y Fr(\(\004)f Fq(\\)g
Ft(B)3077 5146 y Fo(s)3114 5132 y Fr(\()p Ft(o)p Fr(\)\))15
b Ft(:)p eop end
%%Page: 7 7
TeXDict begin 7 6 bop 598 550 a Fu(Estimation)19 b(of)i(speci\002c)e
(intrinsic)i(volumes)1487 b FF(7)598 751 y Fw(No)n(w)-6
b(,)22 b(using)i(\(12\),)g Ft(f)10 b Fr(\()p Ft(r)s Fr(\))23
b Fw(can)h(be)f(re)n(written)i(as)639 938 y Ft(f)10 b
Fr(\()p Ft(r)s Fr(\))83 b(=)1045 865 y Fn(R)1105 892
y Fo(r)1087 970 y FE(0)1185 903 y Fo(d)p 1168 918 69
4 v 1168 970 a(ds)1247 938 y Ft(E)21 b(V)1388 952 y FE(0)1427
938 y Fr(\(\004)f Fq(\\)g Ft(B)1693 952 y Fo(s)1730 938
y Fr(\()p Ft(o)p Fr(\)\))15 b Ft(ds)26 b Fr(=)f Ft(E)c(V)2247
952 y FE(0)2286 938 y Fr(\(\004)f Fq(\\)g Ft(B)2552 952
y Fo(r)2590 938 y Fr(\()p Ft(o)p Fr(\)\))h Fq(\000)f
Ft(E)h(V)2992 952 y FE(0)3031 938 y Fr(\(\004)f Fq(\\)g(f)p
Ft(o)p Fq(g)p Fr(\))891 1126 y(=)83 b Ft(E)20 b(V)1185
1140 y FE(0)1225 1126 y Fr(\(\004)g Fq(\\)f Ft(B)1490
1140 y Fo(r)1528 1126 y Fr(\()p Ft(o)p Fr(\)\))j Fq(\000)e
Ft(E)g Ff(1)1929 1140 y FE(\004)1981 1126 y Fr(\()p Ft(o)p
Fr(\))26 b(=)f Ft(E)20 b(V)2357 1140 y FE(0)2397 1126
y Fr(\(\004)g Fq(\\)g Ft(B)2663 1140 y Fo(r)2700 1126
y Fr(\()p Ft(o)p Fr(\)\))i Fq(\000)p 2962 1053 74 4 v
20 w Ft(V)3035 1141 y Fo(d)3075 1126 y Fr(\(\004\))15
b Ft(;)598 1304 y Fw(where)24 b Ff(1)895 1318 y FE(\004)969
1304 y Fw(denotes)h(the)f(indicator)i(of)d Fr(\004)p
Fw(.)p 3371 1304 4 62 v 3375 1246 55 4 v 3375 1304 V
3429 1304 4 62 v 697 1476 a(It)k(is)g(well)g(kno)n(wn)h(that)g(the)f
(Mink)o(o)n(wski)i(functionals)h(of)e(polycon)l(v)o(e)o(x)i(sets)e(can)
f(be)598 1584 y(de\002ned)e(through)i(the)e(Euler)n(\226Poincar)p
Fr(\023)-43 b(e)43 b Fw(characteristics)28 b(of)d(their)g(lo)n(wer)g
(dimensional)598 1692 y(sections)36 b(by)e(means)g(of)g(Crofton')-5
b(s)36 b(formula;)k(see)35 b(e.g.)59 b([13,)35 b(18].)60
b(Proposition)36 b(3.1)598 1800 y(immediately)25 b(implies)f(that)p
1010 1974 74 4 v 1010 2047 a Ft(V)1083 2061 y Fo(j)1119
2047 y Fr(\(\004\))i(=)1605 1986 y(1)p 1382 2026 493
4 v 1382 2110 a(\()p Ft(d)21 b Fq(\000)f Ft(j)5 b Fr(\)!)15
b Ft(\024)1745 2125 y Fo(d)p Fm(\000)p Fo(j)1904 2047
y Fq(\001)1960 1986 y Ft(d)2007 1953 y FE(\()p Fo(d)p
Fm(\000)p Fo(j)t FE(\))2190 1986 y Ft(E)20 b(V)2330 2000
y FE(0)2370 1986 y Fr(\(\004)g Fq(\\)g Ft(B)2636 2000
y Fo(r)2674 1986 y Fr(\()p Ft(x)p Fr(\)\))p 1960 2026
872 4 v 2259 2114 a Ft(dr)2350 2087 y FE(\()p Fo(d)p
Fm(\000)p Fo(j)t FE(\))2867 1943 y Fn(\014)2867 1997
y(\014)2867 2052 y(\014)2897 2111 y Fo(r)r FE(=0)598
2300 y Fw(for)i(an)o(y)f Ft(j)31 b Fr(=)25 b(0)p Ft(;)15
b(:)g(:)g(:)i(;)e(d)e Fq(\000)g Fr(1)22 b Fw(and)g Ft(x)j
Fq(2)g Fp(R)1878 2267 y Fo(d)1918 2300 y Fw(.)j(Thus,)21
b(similarly)i(to)f(Crofton')-5 b(s)23 b(formula,)g(the)598
2408 y(speci\002c)k(intrinsic)i(v)n(olumes)g(of)d(stationary)k(RA)l(CS)
25 b(can)i(be)g(e)o(xpressed)i(by)e(their)g(local)598
2516 y(Euler)n(\226Poincar)p Fr(\023)-43 b(e)42 b Fw(characteristics.)
598 2731 y Fx(4.)216 b(Estimation)26 b(of)h(speci\002c)g(intrinsic)g(v)
o(olumes)697 2889 y Fw(In)33 b(this)g(section,)k(similar)c(to)f(the)h
(approach)i(considered)h(in)d([11],)i(the)e(method)g(of)598
2997 y(moments)g(is)f(used)h(to)f(construct)j(joint)e(nonparametric)i
(estimators)f(for)f(the)f(speci\002c)598 3105 y(intrinsic)25
b(v)n(olumes)p 1247 3032 74 4 v 25 w Ft(V)1321 3119 y
Fo(j)1357 3105 y Fr(\(\004\))p Fw(,)e Ft(j)31 b Fr(=)25
b(0)p Ft(;)15 b(:)g(:)g(:)i(;)e(d)p Fw(.)598 3321 y Fx(Indir)n(ect)26
b(estimation)h(via)g(local)g(Euler)l(\226P)n(oincar)p
Fh(\023)-54 b(e)45 b Fx(characteristics)697 3479 y Fw(F)o(or)23
b(an)o(y)h Ft(d)c Fr(+)g(1)j Fw(positi)n(v)o(e)i(pairwise)g(dif)n
(ferent)g(radii)g Ft(r)2426 3493 y Fo(j)2462 3479 y Fw(,)e(Proposition)
j(3.1)d(yields)i(the)598 3587 y(follo)n(wing)e(system)f(of)f
Ft(d)12 b Fr(+)g(1)21 b Fw(linear)i(equations)h(with)d(respect)i(to)e
(the)h(v)n(ariables)p 3173 3514 V 23 w Ft(V)3247 3601
y Fo(j)3283 3587 y Fr(\(\004\))p Fw(,)598 3694 y Ft(j)31
b Fr(=)25 b(0)p Ft(;)15 b(:)g(:)g(:)i(;)e(d)p Fw(:)1761
3802 y Ft(A)1829 3816 y Fo(r)1861 3825 y Fl(0)1895 3816
y Fo(:::)o(r)1986 3828 y Fk(d)2041 3802 y Ft(v)29 b Fr(=)c
Ft(c;)1012 b Fw(\(13\))598 3955 y(where)26 b Ft(A)913
3969 y Fo(r)945 3978 y Fl(0)979 3969 y Fo(:::)o(r)1070
3981 y Fk(d)1135 3955 y Fw(is)g(the)g(matrix)g(introduced)j(in)d
(\(6\),)g Ft(v)33 b Fr(=)c(\()p 2495 3882 V Ft(V)2569
3969 y FE(0)2608 3955 y Fr(\(\004\))p Ft(;)15 b(:)g(:)g(:)i(;)p
2941 3882 V 15 w(V)3015 3970 y Fo(d)3055 3955 y Fr(\(\004\)\))3221
3922 y Fm(>)3306 3955 y Fw(and)598 4063 y Ft(c)39 b Fr(=)f(\()p
Ft(E)21 b(V)961 4077 y FE(0)1000 4063 y Fr(\(\004)k Fq(\\)h
Ft(B)1277 4077 y Fo(r)1309 4086 y Fl(0)1347 4063 y Fr(\()p
Ft(o)p Fr(\)\))p Ft(;)15 b(:)g(:)g(:)j(;)d(E)21 b(V)1840
4077 y FE(0)1879 4063 y Fr(\(\004)26 b Fq(\\)f Ft(B)2156
4077 y Fo(r)2188 4089 y Fk(d)2228 4063 y Fr(\()p Ft(o)p
Fr(\)\)\))2412 4030 y Fm(>)2472 4063 y Fw(.)50 b(Similar)30
b(to)h(the)g(determin-)598 4171 y(istic)d(case)g(of)g(Section)g(2,)g
(choose)h(an)f(appropriate)i(estimator)f Fn(b)-51 b Ft(c)27
b Fw(for)h Ft(c)f Fw(and)h(de\002ne)g(the)598 4279 y(estimator)e
Fn(b)-52 b Ft(v)26 b Fw(for)e Ft(v)i Fw(by)1782 4387
y Fn(b)-52 b Ft(v)28 b Fr(=)d Ft(A)2017 4349 y Fm(\000)p
FE(1)2017 4409 y Fo(r)2049 4418 y Fl(0)2084 4409 y Fo(:::)o(r)2175
4421 y Fk(d)2214 4387 y Fn(b)-50 b Ft(c)1032 b Fw(\(14\))598
4540 y(in)24 b(order)h(to)f(estimate)h(the)g(v)o(ector)g
Ft(v)h Fw(of)e(speci\002c)h(intrinsic)i(v)n(olumes)e(from)f(a)g(single)
h(re-)598 4648 y(alization)i(of)f Fr(\004)e Fw(observ)o(ed)j(in)f(a)f
(certain)i(windo)n(w)e Ft(W)41 b Fq(2)29 b(K)q Fw(.)34
b(F)o(or)24 b(an)o(y)i Ft(r)31 b(>)d Fr(0)e Fw(such)g(that)598
4756 y Ft(V)651 4771 y Fo(d)691 4756 y Fr(\()p Ft(W)37
b Fq(\011)23 b Ft(B)1012 4770 y Fo(r)1050 4756 y Fr(\()p
Ft(o)p Fr(\)\))35 b Ft(>)f Fr(0)p Fw(,)29 b(consider)h(the)f
(stationary)i(random)e(\002eld)f Fq(f)p Ft(Y)2888 4770
y Fo(r)2927 4756 y Fr(\()p Ft(x)p Fr(\))p Ft(;)j(x)j
Fq(2)g Fp(R)3352 4723 y Fo(d)3392 4756 y Fq(g)598 4864
y Fw(with)e Ft(Y)844 4878 y Fo(r)882 4864 y Fr(\()p Ft(x)p
Fr(\))43 b(=)f Ft(V)1213 4878 y FE(0)1267 4864 y Fr(\()q(\004)20
b Fq(\\)f Ft(B)1533 4878 y Fo(r)1571 4864 y Fr(\()p Ft(x)p
Fr(\)\))q Fw(.)56 b(An)32 b(unbiased)j(estimator)f(for)f
Ft(y)2859 4878 y Fo(r)2939 4864 y Fr(=)42 b Ft(E)20 b(Y)3192
4878 y Fo(r)3230 4864 y Fr(\()p Ft(o)p Fr(\))32 b Fw(is)598
4972 y(gi)n(v)o(en)21 b(by)k Fn(b)-54 b Ft(y)973 4986
y Fo(r)1035 4972 y Fr(=)1131 4898 y Fn(R)1174 5004 y
Fo(W)10 b Fm(\011)p Fo(B)1359 5012 y Fk(r)1393 5004 y
FE(\()p Fo(o)p FE(\))1502 4972 y Ft(Y)1555 4986 y Fo(r)1592
4972 y Fr(\()p Ft(x)p Fr(\))15 b Ft(\026)p Fr(\()p Ft(dx)p
Fr(\))p Fw(,)22 b(where)g Ft(\026)e Fw(is)h(an)g(arbitrary)i
(probability)h(mea-)598 5108 y(sure)f(concentrated)j(on)d
Ft(W)30 b Fq(\011)17 b Ft(B)1643 5122 y Fo(r)1680 5108
y Fr(\()p Ft(o)p Fr(\))27 b Fq(\032)d Fp(R)1982 5075
y Fo(d)2023 5108 y Fw(.)j(F)o(or)22 b(instance,)j Ft(\026)c
Fw(can)i(be)g(the)g(normalized)598 5215 y(Lebesgue)f(measure)g
Ft(\026)p Fr(\()p Fq(\001)p Fr(\))k(=)f Ft(V)1614 5230
y Fo(d)1654 5215 y Fr(\()p Fq(\001)g(\\)9 b Ft(W)22 b
Fq(\011)9 b Ft(B)2066 5229 y Fo(r)2104 5215 y Fr(\()p
Ft(o)p Fr(\)\))p Ft(=V)2351 5230 y Fo(d)2394 5215 y Fr(\()p
Ft(W)22 b Fq(\011)9 b Ft(B)2686 5229 y Fo(r)2724 5215
y Fr(\()p Ft(o)p Fr(\)\))21 b Fw(on)g Ft(W)h Fq(\011)9
b Ft(B)3262 5229 y Fo(r)3300 5215 y Fr(\()p Ft(o)p Fr(\))p
Fw(,)p eop end
%%Page: 8 8
TeXDict begin 8 7 bop 548 550 a FF(8)588 b Fu(On)20 b(the)g(local)g
(connectivity)f(number)g(of)i(stationary)e(r)o(andom)g(closed)h(sets)
548 753 y Fw(or)30 b(a)g(discrete)i(measure)g Ft(\026)p
Fr(\()p Fq(\001)p Fr(\))38 b(=)1664 685 y Fn(P)1760 711
y Fo(m)1760 780 y(i)p FE(=1)1894 753 y Ft(w)1959 767
y Fo(i)1987 753 y Ft(\016)2027 767 y Fo(x)2067 777 y
Fk(i)2098 753 y Fr(\()p Fq(\001)p Fr(\))30 b Fw(with)g(measurements)j
(at)d(locations)548 861 y Ft(x)600 875 y FE(1)639 861
y Ft(;)15 b(:)g(:)g(:)i(;)e(x)893 875 y Fo(m)987 861
y Fq(2)26 b Ft(W)33 b Fq(\011)21 b Ft(B)1354 875 y Fo(r)1392
861 y Fr(\()p Ft(o)p Fr(\))j Fw(and)h(weights)g Ft(w)2056
875 y Fo(i)2111 861 y Ft(>)i Fr(0)d Fw(such)h(that)g
Ft(w)2693 875 y FE(1)2753 861 y Fr(+)c Ft(:)15 b(:)g(:)22
b Fr(+)e Ft(w)3128 875 y Fo(m)3222 861 y Fr(=)26 b(1)p
Fw(.)548 969 y(Notice)i(that)h(inte)o(gration)i(is)d(performed)h(o)o(v)
o(er)f(the)h(reduced)h(windo)n(w)d Ft(W)36 b Fq(\011)24
b Ft(B)3137 983 y Fo(r)3175 969 y Fr(\()p Ft(o)p Fr(\))k
Fw(to)548 1077 y(a)n(v)n(oid)33 b(edge)g(ef)n(fects,)h(since)f(the)f
(computation)i(of)e Ft(V)2280 1091 y FE(0)2334 1077 y
Fr(\()q(\004)20 b Fq(\\)f Ft(B)2600 1091 y Fo(r)2638
1077 y Fr(\()p Ft(x)p Fr(\)\))32 b Fw(for)g Ft(x)40 b
Fq(2)g Ft(W)j Fw(re-)548 1185 y(quires)21 b(the)e(kno)n(wledge)i(of)e
Fr(\004)f Fw(in)h(the)h Ft(r)s Fw(\226neighborhood)j(of)d
Ft(x)e Fw(while)h Fr(\004)f Fw(is)h(observ)o(ed)j(only)548
1293 y(within)28 b Ft(W)13 b Fw(.)38 b(Thus,)27 b(assuming)i(that)f
Ft(V)1784 1308 y Fo(d)1824 1293 y Fr(\()p Ft(W)36 b Fq(\011)22
b Ft(B)2143 1307 y Fo(r)2175 1317 y Fk(j)2212 1293 y
Fr(\()p Ft(o)p Fr(\)\))33 b Ft(>)e Fr(0)c Fw(for)g(each)h
Ft(j)37 b Fr(=)32 b(0)p Ft(;)15 b(:)g(:)g(:)i(;)e(d)p
Fw(,)548 1401 y(an)23 b(unbiased)j(estimator)f Fn(b)-51
b Ft(c)24 b Fw(for)f Ft(c)g Fw(is)h(gi)n(v)o(en)g(by)768
1612 y Fn(b)-50 b Ft(c)25 b Fr(=)929 1511 y Fn(\020)984
1488 y(Z)1034 1694 y Fo(W)10 b Fm(\011)p Fo(B)1219 1702
y Fk(r)1248 1717 y Fl(0)1286 1694 y FE(\()p Fo(o)p FE(\))1395
1612 y Ft(Y)1448 1626 y Fo(r)1480 1635 y Fl(0)1518 1612
y Fr(\()p Ft(x)p Fr(\))15 b Ft(\026)p Fr(\()p Ft(dx)p
Fr(\))g Ft(;)g(:)g(:)g(:)j(;)2113 1488 y Fn(Z)2163 1694
y Fo(W)10 b Fm(\011)p Fo(B)2348 1702 y Fk(r)2377 1720
y(d)2417 1694 y FE(\()p Fo(o)p FE(\))2525 1612 y Ft(Y)2578
1626 y Fo(r)2610 1638 y Fk(d)2650 1612 y Fr(\()p Ft(x)p
Fr(\))15 b Ft(\026)p Fr(\()p Ft(dx)p Fr(\))3011 1511
y Fn(\021)3067 1533 y Fm(>)3141 1612 y Ft(:)548 1902
y Fx(Mean\226squar)n(e)27 b(consistency)f(and)h(asymptotic)g(normality)
648 2060 y Fw(F)o(or)22 b Ft(\026)p Fr(\()p Fq(\001)p
Fr(\))k(=)f Ft(V)1120 2075 y Fo(d)1161 2060 y Fr(\()p
Fq(\001)36 b(\\)19 b Ft(W)33 b Fq(\011)20 b Ft(B)1616
2074 y Fo(r)1654 2060 y Fr(\()p Ft(o)p Fr(\)\))p Ft(=V)1901
2075 y Fo(d)1943 2060 y Fr(\()p Ft(W)33 b Fq(\011)20
b Ft(B)2257 2074 y Fo(r)2295 2060 y Fr(\()p Ft(o)p Fr(\)\))p
Fw(,)j(the)h(inte)o(gral)1454 2273 y Fn(b)-55 b Ft(y)1495
2287 y Fo(r)1558 2273 y Fr(=)1654 2149 y Fn(Z)1704 2356
y Fo(W)10 b Fm(\011)p Fo(B)1889 2364 y Fk(r)1924 2356
y FE(\()p Fo(o)p FE(\))2032 2273 y Ft(Y)2085 2287 y Fo(r)2123
2273 y Fr(\()p Ft(x)p Fr(\))15 b Ft(\026)p Fr(\()p Ft(dx)p
Fr(\))548 2502 y Fw(is)24 b(the)h(least\226squares)j(estimator)e(for)f
Ft(y)1812 2516 y Fo(r)1850 2502 y Fw(,)e(which)i(is)f(mean\226square)k
(consistent)f(as)d Ft(W)40 b Fq(")548 2610 y Fp(R)614
2577 y Fo(d)672 2610 y Fw(pro)o(vided)20 b(that)f(some)g(inte)o
(grability)j(conditions)f(are)e(satis\002ed;)i(see)e(e.g.)27
b([3],)19 b(p.)f(131.)548 2718 y(This)35 b(means)i(that)f(for)g(a)f
(sequence)j Fq(f)p Ft(W)1898 2732 y Fo(n)1945 2718 y
Fq(g)d Fw(of)h(unboundedly)j(increasing)g(sampling)548
2826 y(windo)n(ws)30 b(with)g Ft(W)1180 2840 y Fo(n)1264
2826 y Fr(=)38 b Ft(nW)13 b Fw(,)29 b(we)h(ha)n(v)o(e)g
Ft(E)21 b Fr(\()t Fn(b)-55 b Ft(y)2080 2840 y Fo(r)n(;n)2201
2826 y Fq(\000)25 b Ft(y)2342 2840 y Fo(r)2380 2826 y
Fr(\))2415 2793 y FE(2)2492 2826 y Fq(!)37 b Fr(0)30
b Fw(as)g Ft(n)37 b Fq(!)h(1)p Fw(,)30 b(where)552 2934
y Fn(b)-55 b Ft(y)593 2948 y Fo(r)n(;n)714 2934 y Fr(=)810
2861 y Fn(R)853 2966 y Fo(W)920 2974 y Fk(n)962 2966
y Fm(\011)p Fo(B)1070 2974 y Fk(r)1105 2966 y FE(\()p
Fo(o)p FE(\))1213 2934 y Ft(Y)1266 2948 y Fo(r)1304 2934
y Fr(\()p Ft(x)p Fr(\))15 b Ft(\026)1496 2948 y Fo(n)1544
2934 y Fr(\()p Ft(dx)p Fr(\))23 b Fw(and)1065 3118 y
Ft(\026)1120 3132 y Fo(n)1166 3118 y Fr(\()p Fq(\001)p
Fr(\))k(=)e Ft(V)1437 3133 y Fo(d)1477 3118 y Fr(\()p
Fq(\001)36 b(\\)20 b Ft(W)1740 3132 y Fo(n)1807 3118
y Fq(\011)g Ft(B)1967 3132 y Fo(r)2005 3118 y Fr(\()p
Ft(o)p Fr(\)\))p Ft(=V)2252 3133 y Fo(d)2294 3118 y Fr(\()p
Ft(W)2415 3132 y Fo(n)2482 3118 y Fq(\011)g Ft(B)2642
3132 y Fo(r)2680 3118 y Fr(\()p Ft(o)p Fr(\)\))15 b(;)548
3298 y Fw(see)32 b(also)h([11].)56 b(Assuming)33 b(that)g
Ft(E)20 b Fr(4)1802 3265 y Fo(N)7 b FE(\(\004)p Fm(\\)p
FE([0)p Fo(;)p FE(1])2116 3242 y Fk(d)2153 3265 y FE(\))2226
3298 y Ft(<)41 b Fq(1)p Fw(,)33 b(it)f(can)h(be)f(sho)n(wn)g(that)h
(the)548 3406 y Fv(co)o(variance)d(functions)f Ft(C)1401
3420 y Fo(r)1433 3430 y Fk(i)1459 3420 y Fo(r)1491 3430
y Fk(j)1527 3406 y Fr(\()p Ft(x)p Fr(\))j(=)e Ft(E)21
b Fr(\()p Ft(Y)1958 3420 y Fo(r)1990 3430 y Fk(i)2020
3406 y Fr(\()p Ft(o)p Fr(\))p Ft(Y)2187 3420 y Fo(r)2219
3430 y Fk(j)2256 3406 y Fr(\()p Ft(x)p Fr(\)\))j Fq(\000)e
Ft(y)2575 3420 y Fo(r)2607 3430 y Fk(i)2637 3406 y Ft(y)2682
3420 y Fo(r)2714 3430 y Fk(j)2775 3406 y Fw(are)27 b(well)f(de\002ned;)
548 3514 y Ft(i;)15 b(j)42 b Fr(=)35 b(0)p Ft(;)15 b(:)g(:)g(:)i(;)e(d)
p Fw(.)46 b(Furthermore,)32 b(under)e(suitable)h(mixing)f(conditions)i
(on)e Fr(\004)e Fw(and)h(as-)548 3622 y(suming)24 b(that)997
3549 y Fn(R)1040 3654 y Fi(R)1088 3635 y Fk(d)1144 3622
y Fq(j)p Ft(C)1234 3636 y Fo(r)1266 3646 y Fk(i)1292
3636 y Fo(r)1324 3646 y Fk(j)1361 3622 y Fr(\()p Ft(x)p
Fr(\))p Fq(j)15 b Ft(dx)26 b(<)f Fq(1)p Fw(,)e(the)h(random)g(v)o
(ector)1059 3730 y Fn(p)p 1150 3730 630 4 v 82 x Ft(V)1203
3827 y Fo(d)1244 3812 y Fr(\()p Ft(W)1365 3826 y Fo(n)1432
3812 y Fq(\011)c Ft(B)1592 3826 y Fo(r)1630 3812 y Fr(\()p
Ft(o)p Fr(\)\))1780 3738 y Fn(\000)1825 3812 y(b)-54
b Ft(y)1867 3826 y Fo(r)1899 3835 y Fl(0)1933 3826 y
Fo(;n)2019 3812 y Fq(\000)20 b Ft(y)2155 3826 y Fo(r)2187
3835 y Fl(0)2225 3812 y Ft(;)15 b(:)g(:)g(:)i(;)i Fn(b)-55
b Ft(y)2472 3826 y Fo(r)2504 3838 y Fk(d)2540 3826 y
Fo(;n)2627 3812 y Fq(\000)20 b Ft(y)2763 3826 y Fo(r)2795
3838 y Fk(d)2834 3738 y Fn(\001)548 3978 y Fw(is)27 b(asymptotically)32
b(normal)c(distrib)n(uted,)k(where)c(the)g(asymptotic)i(co)o(v)n
(ariance)g(matrix)548 4086 y(is)e(gi)n(v)o(en)h(by)f
Fr(\()1015 4013 y Fn(R)1059 4118 y Fi(R)1107 4099 y Fk(d)1162
4086 y Ft(C)1227 4100 y Fo(r)1259 4110 y Fk(i)1285 4100
y Fo(r)1317 4110 y Fk(j)1354 4086 y Fr(\()p Ft(x)p Fr(\))15
b Ft(dx)p Fr(\))1625 4053 y Fo(d)1625 4112 y(i;j)t FE(=0)1824
4086 y Fw(and)29 b(can)f(be)h(consistently)i(estimated;)i(see)c([3],)
548 4194 y(Section)23 b(3.1,)e(and)h([11].)29 b(Notice)23
b(that)f(the)g(inte)o(grability)j(and)d(mixing)h(conditions)h(men-)548
4302 y(tioned)i(abo)o(v)o(e)f(are)g(ful\002lled,)g(for)g(e)o(xample,)g
(for)g(rapidly)h(mixing)g(germ\226grain)h(models)548
4410 y(including)35 b(the)d(well\226kno)n(wn)65 b Fv(Boolean)34
b(model)p Fw(;)j(see)c(e.g.)54 b([6,)34 b(7,)g(14].)55
b(W)-7 b(e)32 b(also)g(re-)548 4518 y(mark)26 b(that)g(the)g(estimator)
i Fn(b)-52 b Ft(v)1464 4532 y Fo(n)1540 4518 y Fr(=)29
b Ft(A)1708 4485 y Fm(\000)p FE(1)1708 4541 y Fo(r)1740
4550 y Fl(0)1775 4541 y Fo(:::)o(r)1866 4553 y Fk(d)1906
4518 y Fr(\()t Fn(b)-55 b Ft(y)1986 4532 y Fo(r)2018
4541 y Fl(0)2052 4532 y Fo(;n)2119 4518 y Ft(;)15 b(:)g(:)g(:)h(;)j
Fn(b)-55 b Ft(y)2365 4532 y Fo(r)2397 4544 y Fk(d)2433
4532 y Fo(;n)2500 4518 y Fr(\))2535 4485 y Fm(>)2619
4518 y Fw(for)26 b Ft(v)i Fw(is)e(mean\226square)548
4626 y(consistent)33 b(and)d(asymptotically)j(normal)e(distrib)n(uted,)
j(pro)o(vided)e(that)f(the)f(estimator)548 4734 y Fr(\()t
Fn(b)-55 b Ft(y)628 4748 y Fo(r)660 4757 y Fl(0)694 4748
y Fo(;n)761 4734 y Ft(;)15 b(:)g(:)g(:)h(;)k Fn(b)-56
b Ft(y)1007 4748 y Fo(r)1039 4760 y Fk(d)1075 4748 y
Fo(;n)1142 4734 y Fr(\))1177 4701 y Fm(>)1259 4734 y
Fw(for)24 b Ft(c)f Fw(possesses)j(these)f(properties.)548
4950 y Fx(Least\226squar)n(es)i(estimator)648 5108 y
Fw(The)18 b(least-squares)k(approach)f(of)d(Section)i(2)e(also)h
(applies)h(\(with)f(minor)g(changes\))i(to)548 5215 y(the)e(case)g(of)f
(stationary)j(RA)l(CS.)c(F)o(or)g Ft(k)29 b(>)c(d)q Fr(+)q(1)19
b Fw(pairwise)g(dif)n(ferent)i(radii)e Ft(r)2972 5229
y FE(0)3011 5215 y Ft(;)c(:)g(:)g(:)i(;)e(r)3254 5230
y Fo(k)r Fm(\000)p FE(1)p eop end
%%Page: 9 9
TeXDict begin 9 8 bop 598 550 a Fu(Estimation)19 b(variance)h(and)f
(spatial)h(sampling)f(designs)1134 b FF(9)598 751 y Fw(such)20
b(that)h Ft(V)992 766 y Fo(d)1032 751 y Fr(\()p Ft(W)e
Fq(\011)6 b Ft(B)1318 765 y Fo(r)1350 775 y Fk(j)1387
751 y Fr(\()p Ft(o)p Fr(\)\))26 b Ft(>)f Fr(0)p Fw(,)20
b Ft(j)31 b Fr(=)25 b(0)p Ft(;)15 b(:)g(:)g(:)i(;)e(k)s
Fw(,)20 b(the)g(corresponding)k(solution)e(of)e(the)598
872 y(least)f(squares)h(minimization)g(problem)f(is)f
Ft(v)2019 839 y Fm(\003)2084 872 y Fr(=)25 b(\()p Ft(A)2283
839 y Fm(>)2283 894 y Fo(r)2315 903 y Fl(0)2350 894 y
Fo(:::)o(r)2441 906 y Fk(k)q Fj(\000)p Fl(1)2561 872
y Ft(A)2629 886 y Fo(r)2661 895 y Fl(0)2696 886 y Fo(:::)o(r)2787
898 y Fk(k)q Fj(\000)p Fl(1)2907 872 y Fr(\))2942 839
y Fm(\000)p FE(1)3037 872 y Ft(A)3105 839 y Fm(>)3105
894 y Fo(r)3137 903 y Fl(0)3171 894 y Fo(:::)o(r)3262
906 y Fk(k)q Fj(\000)p Fl(1)3386 872 y Fn(b)-54 b Ft(y)s(;)598
1000 y Fw(where)27 b Fn(b)-54 b Ft(y)28 b Fr(=)d(\()t
Fn(b)-55 b Ft(y)1092 1014 y Fo(r)1124 1023 y Fl(0)1163
1000 y Ft(;)15 b(:)g(:)g(:)i(;)i Fn(b)-55 b Ft(y)1410
1014 y Fo(r)1442 1026 y Fk(k)q Fj(\000)p Fl(1)1562 1000
y Fr(\))1597 967 y Fm(>)1679 1000 y Fw(with)28 b Fn(b)-55
b Ft(y)1909 1014 y Fo(r)1941 1024 y Fk(j)2003 1000 y
Fr(=)2099 927 y Fn(R)2142 1032 y Fo(W)10 b Fm(\011)p
Fo(B)2327 1040 y Fk(r)2356 1056 y(j)2392 1032 y FE(\()p
Fo(o)p FE(\))2500 1000 y Ft(Y)2553 1014 y Fo(r)2585 1024
y Fk(j)2621 1000 y Fr(\()p Ft(x)p Fr(\))15 b Ft(\026)p
Fr(\()p Ft(dx)p Fr(\))p Fw(.)30 b(Notice)25 b(that)598
1154 y(the)f(estimator)i Ft(v)1141 1121 y Fm(\003)1207
1154 y Fr(=)g(\()p Ft(v)1386 1121 y Fm(\003)1383 1179
y FE(0)1427 1154 y Ft(;)15 b(:)g(:)g(:)h(;)f(v)1675 1121
y Fm(\003)1672 1182 y Fo(d)1715 1154 y Fr(\))1750 1121
y Fm(>)1833 1154 y Fw(for)25 b(the)f(v)o(ector)h Ft(v)30
b Fr(=)c(\()p 2552 1081 74 4 v Ft(V)2626 1168 y FE(0)2665
1154 y Fr(\(\004\))p Ft(;)15 b(:)g(:)g(:)i(;)p 2998 1081
V 15 w(V)3072 1169 y Fo(d)3112 1154 y Fr(\(\004\)\))3278
1121 y Fm(>)3361 1154 y Fw(of)598 1262 y(speci\002c)25
b(intrinsic)i(v)n(olumes)f(of)e Fr(\004)g Fw(is)g(much)h(more)f(rob)n
(ust)i(with)f(respect)h(to)e(the)h(choice)598 1370 y(of)e(radii)i
Ft(r)927 1384 y FE(0)966 1370 y Ft(;)15 b(:)g(:)g(:)i(;)e(r)1209
1385 y Fo(k)r Fm(\000)p FE(1)1365 1370 y Fw(than)24 b(the)g(estimator)i
Fn(b)-52 b Ft(v)26 b Fw(gi)n(v)o(en)e(in)f(\(14\).)598
1586 y Fx(5.)216 b(Estimation)26 b(v)o(ariance)h(and)g(spatial)g
(sampling)f(designs)697 1744 y Fw(Besides)33 b(unbiasedness,)38
b(another)c(important)g(criterion)g(for)e(goodness)j(of)d(the)g(es-)598
1852 y(timator)37 b Fn(b)-52 b Ft(v)38 b Fw(gi)n(v)o(en)e(in)f(\(14\))h
(is)f(related)i(to)f(its)f(v)n(ariance)i(properties,)k(where)36
b(the)f(radii)598 1960 y Ft(r)639 1974 y FE(0)678 1960
y Ft(;)15 b(:)g(:)g(:)i(;)e(r)921 1975 y Fo(d)984 1960
y Fw(and)23 b(the)g(a)n(v)o(eraging)i(probability)h(measure)e
Ft(\026)d Fw(should)k(be)d(chosen)j(in)d(such)i(a)598
2068 y(w)o(ay)d(that)i(the)f Fv(estimation)i(variance)h
Ft(\033)1854 2035 y FE(2)1918 2068 y Fr(=)g Ft(V)c(ar)s
Fr(\()q Fn(b)-52 b Ft(v)s Fr(\))25 b(=)g Ft(E)c Fq(j)q
Fn(b)-52 b Ft(v)18 b Fq(\000)c Ft(v)s Fq(j)2750 2035
y FE(2)2811 2068 y Fw(is)22 b(possibly)i(small.)598 2283
y Fx(Bound)j(on)g(the)g(estimation)f(v)o(ariance)697
2441 y Fw(Unfortunately)-6 b(,)35 b(it)30 b(seems)h(to)f(be)g
(impossible)j(to)d(determine)i(the)e(estimation)j(v)n(ari-)598
2549 y(ance)24 b Ft(\033)842 2516 y FE(2)907 2549 y Fr(=)h
Ft(V)c(ar)s Fr(\()q Fn(b)-52 b Ft(v)s Fr(\))26 b(=)f
Ft(E)20 b Fq(j)p Ft(A)1588 2516 y Fm(\000)p FE(1)1588
2572 y Fo(r)1620 2581 y Fl(0)1655 2572 y Fo(:::)o(r)1746
2584 y Fk(d)1786 2549 y Fr(\()o Fn(b)-50 b Ft(c)21 b
Fq(\000)f Ft(c)p Fr(\))p Fq(j)2071 2516 y FE(2)2135 2549
y Fw(e)o(xplicitly)-6 b(.)31 b(Ho)n(we)n(v)o(er)l(,)23
b(it)h(is)f(easy)h(to)g(get)598 2667 y(an)f(upper)i(bound)g(for)f
Ft(\033)1370 2634 y FE(2)1409 2667 y Fw(.)k(Namely)-6
b(,)24 b(\(14\))g(implies)g(that)994 2913 y Ft(\033)1049
2875 y FE(2)1114 2913 y Fs(6)h Fq(k)p Ft(A)1323 2875
y Fm(\000)p FE(1)1323 2935 y Fo(r)1355 2944 y Fl(0)1390
2935 y Fo(:::)o(r)1481 2947 y Fk(d)1521 2913 y Fq(k)1566
2875 y FE(2)1606 2913 y Ft(E)20 b Fq(j)o Fn(b)-50 b Ft(c)21
b Fq(\000)f Ft(c)p Fq(j)1933 2875 y FE(2)1998 2913 y
Fr(=)25 b Fq(k)p Ft(A)2207 2875 y Fm(\000)p FE(1)2207
2935 y Fo(r)2239 2944 y Fl(0)2274 2935 y Fo(:::)o(r)2365
2947 y Fk(d)2405 2913 y Fq(k)2450 2875 y FE(2)2553 2799
y Fo(d)2505 2827 y Fn(X)2510 3022 y Fo(j)t FE(=0)2652
2913 y Ft(V)20 b(ar)s Fr(\()t Fn(b)-55 b Ft(y)2897 2927
y Fo(r)2929 2937 y Fk(j)2965 2913 y Fr(\))15 b Ft(;)246
b Fw(\(15\))598 3163 y(where)653 3341 y Fq(k)p Ft(A)766
3303 y Fm(\000)p FE(1)766 3363 y Fo(r)798 3372 y Fl(0)833
3363 y Fo(:::)o(r)924 3375 y Fk(d)964 3341 y Fq(k)1009
3303 y FE(2)1074 3341 y Fr(=)65 b(max)1170 3402 y Fo(i)p
FE(=0)p Fo(;:::)n(;d)1434 3341 y Ft(\025)1487 3355 y
Fo(i)1515 3267 y Fn(\000)1556 3341 y Fr(\()p Ft(A)1659
3355 y Fo(r)1691 3364 y Fl(0)1726 3355 y Fo(:::)o(r)1817
3367 y Fk(d)1857 3341 y Ft(A)1925 3303 y Fm(>)1925 3363
y Fo(r)1957 3372 y Fl(0)1992 3363 y Fo(:::)o(r)2083 3375
y Fk(d)2123 3341 y Fr(\))2158 3303 y Fm(\000)p FE(1)2253
3267 y Fn(\001)2320 3341 y Fr(=)2876 3279 y(1)p 2425
3320 947 4 v 2474 3403 a(min)2425 3464 y Fo(i)p FE(=0)p
Fo(;:::)o(;d)2689 3403 y Ft(\025)2742 3417 y Fo(i)2770
3403 y Fr(\()p Ft(A)2873 3417 y Fo(r)2905 3426 y Fl(0)2940
3417 y Fo(:::)o(r)3031 3429 y Fk(d)3071 3403 y Ft(A)3139
3377 y Fm(>)3139 3426 y Fo(r)3171 3435 y Fl(0)3206 3426
y Fo(:::)o(r)3297 3438 y Fk(d)3337 3403 y Fr(\))598 3619
y Fw(is)30 b(the)h(squared)h(matrix)f(norm)f(of)h Ft(A)1803
3586 y Fm(\000)p FE(1)1803 3642 y Fo(r)1835 3651 y Fl(0)1869
3642 y Fo(:::)o(r)1960 3654 y Fk(d)2030 3619 y Fw(and)g
Ft(\025)2244 3633 y Fo(i)2272 3619 y Fr(\()p Ft(A)p Fr(\))g
Fw(is)f(the)h Ft(i)p Fw(th)f(eigen)l(v)n(alue)k(of)c(the)598
3737 y(matrix)36 b Ft(A)p Fw(.)64 b(Notice)36 b(that)g
Fq(k)p Ft(A)1586 3704 y Fm(\000)p FE(1)1586 3760 y Fo(r)1618
3769 y Fl(0)1653 3760 y Fo(:::)o(r)1744 3772 y Fk(d)1784
3737 y Fq(k)f Fw(is)g(\002nite.)65 b(Thus,)38 b(it)e(is)f(reasonable)j
(to)e(choose)598 3845 y Ft(r)639 3859 y FE(0)678 3845
y Ft(;)15 b(:)g(:)g(:)i(;)e(r)921 3860 y Fo(d)997 3845
y Fw(and)36 b Ft(\026)e Fw(such)j(that)f(the)g(bound)h(in)f(\(15\))g
(becomes)h(small.)66 b(Consider)37 b(the)598 3953 y(v)n(ariance)30
b Ft(V)20 b(ar)s Fr(\()t Fn(b)-55 b Ft(y)1176 3967 y
Fo(r)1208 3977 y Fk(j)1244 3953 y Fr(\))34 b(=)f Ft(E)5
b Fr(\()t Fn(b)-55 b Ft(y)1569 3967 y Fo(r)1601 3977
y Fk(j)1662 3953 y Fq(\000)23 b Ft(y)1801 3967 y Fo(r)1833
3977 y Fk(j)1869 3953 y Fr(\))1904 3920 y FE(2)1971 3953
y Fw(appearing)31 b(in)d(\(15\).)42 b(F)o(or)28 b(an)o(y)g(\002x)o(ed)f
Ft(r)37 b(>)c Fr(0)p Fw(,)598 4061 y(let)26 b Fq(P)32
b Fw(denote)c(the)e(f)o(amily)g(of)g(all)g(probability)j(measures)e(on)
f Ft(W)35 b Fq(\011)21 b Ft(B)2876 4075 y Fo(r)2914 4061
y Fr(\()p Ft(o)p Fr(\))26 b Fw(and)g(let)g(the)598 4169
y(function)g Ft(L)g Fr(:)h Fq(P)34 b(!)26 b Fr(\(0)p
Ft(;)15 b Fq(1)p Fr(\))25 b Fw(be)f(de\002ned)h(by)f
Ft(L)p Fr(\()p Ft(\026)p Fr(\))j(=)f Ft(E)5 b Fr(\()t
Fn(b)-55 b Ft(y)2526 4183 y Fo(r)2585 4169 y Fq(\000)20
b Ft(y)2721 4183 y Fo(r)2758 4169 y Fr(\))2793 4136 y
FE(2)2857 4169 y Fw(for)k(each)h Ft(\026)h Fq(2)g(P)7
b Fw(.)598 4277 y(By)23 b(Fubini')-5 b(s)24 b(theorem,)h(we)d(can)i
(write)787 4478 y Ft(E)5 b Fr(\()t Fn(b)-55 b Ft(y)939
4492 y Fo(r)997 4478 y Fq(\000)20 b Ft(y)1133 4492 y
Fo(r)1171 4478 y Fr(\))1206 4440 y FE(2)1271 4478 y Fr(=)1367
4354 y Fn(Z)1417 4560 y Fo(W)10 b Fm(\011)p Fo(B)1602
4568 y Fk(r)1636 4560 y FE(\()p Fo(o)p FE(\))1745 4354
y Fn(Z)1795 4560 y Fo(W)g Fm(\011)p Fo(B)1980 4568 y
Fk(r)2014 4560 y FE(\()p Fo(o)p FE(\))2123 4478 y Ft(C)2188
4492 y Fo(r)r(r)2259 4478 y Fr(\()p Ft(x)21 b Fq(\000)f
Ft(x)2510 4440 y Fm(0)2533 4478 y Fr(\))15 b Ft(\026)p
Fr(\()p Ft(dx)p Fr(\))p Ft(\026)p Fr(\()p Ft(dx)2996
4440 y Fm(0)3021 4478 y Fr(\))g Ft(:)190 b Fw(\(16\))598
4702 y(Suppose)26 b(that)f Ft(L)p Fr(\()p Ft(\026)1242
4716 y FE(0)1282 4702 y Fr(\))i(=)h(min)1594 4716 y Fo(\026)p
Fm(2P)1758 4702 y Ft(L)p Fr(\()p Ft(\026)p Fr(\))c Fw(holds)i(for)f
(some)g Ft(\026)2591 4716 y FE(0)2658 4702 y Fq(2)i(P)7
b Fw(.)32 b(Then,)25 b(using)h(the)598 4810 y(methods)h(of)f(v)n
(ariational)j(analysis)f(de)n(v)o(eloped)g(e.g.)36 b(in)26
b([8])g(\(see)g(also)h([17]\),)g(it)f(can)g(be)598 4918
y(sho)n(wn)g(that)h(the)f(function)j Ft(g)s Fr(\()p Ft(x)p
Fr(\))i(=)1785 4844 y Fn(R)1827 4950 y Fo(W)10 b Fm(\011)p
Fo(B)2012 4958 y Fk(r)2047 4950 y FE(\()p Fo(o)p FE(\))2155
4918 y Ft(C)2220 4932 y Fo(r)r(r)2292 4918 y Fr(\()p
Ft(x)22 b Fq(\000)g Ft(h)p Fr(\))15 b Ft(\026)2651 4932
y FE(0)2691 4918 y Fr(\()p Ft(dh)p Fr(\))27 b Fw(necessarily)i(has)598
5036 y(the)24 b(follo)n(wing)h(properties:)730 5193 y
Ft(g)s Fr(\()p Ft(x)p Fr(\))i(=)e Ft(L)p Fr(\()p Ft(\026)1173
5207 y FE(0)1212 5193 y Fr(\))91 b Ft(\026)1393 5207
y FE(0)1433 5193 y Fw(\226a.e.)205 b(and)h Ft(g)s Fr(\()p
Ft(x)p Fr(\))26 b Fs(>)f Ft(L)p Fr(\()p Ft(\026)2587
5207 y FE(0)2626 5193 y Fr(\))92 b Fw(for)23 b(all)h
Ft(x)h Fq(2)g Fp(R)3224 5155 y Fo(d)3279 5193 y Ft(:)p
eop end
%%Page: 10 10
TeXDict begin 10 9 bop 548 550 a FF(10)542 b Fu(On)20
b(the)g(local)g(connectivity)f(number)g(of)i(stationary)e(r)o(andom)g
(closed)h(sets)548 757 y Fx(Discr)n(ete)27 b(sampling)f(designs)648
915 y Fw(Suppose)e(no)n(w)f(that)h Ft(L)p Fr(\()p Ft(\026)1466
929 y FE(0)1505 915 y Fr(\))i(=)f(min)1813 929 y Fo(\026)p
Fm(2P)1977 915 y Ft(L)p Fr(\()p Ft(\026)p Fr(\))e Fw(holds)h(for)g
(some)f(discrete)i(probabil-)548 1022 y(ity)e(measure)i
Ft(\026)1047 1036 y FE(0)1111 1022 y Fq(2)g(P)30 b Fw(such)25
b(that)e Ft(\026)1693 1036 y FE(0)1733 1022 y Fr(\()p
Fq(\001)p Fr(\))j(=)1950 954 y Fn(P)2046 981 y Fo(m)2046
1049 y(i)p FE(=1)2179 1022 y Ft(w)2244 1036 y Fo(i)2272
1022 y Ft(\016)2312 1036 y Fo(x)2352 1046 y Fk(i)2383
1022 y Fr(\()p Fq(\001)p Fr(\))e Fw(for)f(some)g(inte)o(ger)i
Ft(m)g Fs(>)g Fr(1)p Fw(,)548 1130 y(where)20 b Ft(x)841
1144 y FE(1)880 1130 y Ft(;)15 b(:)g(:)g(:)i(;)e(x)1134
1144 y Fo(m)1226 1130 y Fq(2)25 b Ft(W)19 b Fq(\011)6
b Ft(B)1563 1144 y Fo(r)1601 1130 y Fr(\()p Ft(o)p Fr(\))19
b Fw(and)i Ft(w)1950 1144 y FE(1)1989 1130 y Ft(;)15
b(:)g(:)g(:)i(;)e(w)2256 1144 y Fo(m)2348 1130 y Ft(>)25
b Fr(0)20 b Fw(with)f Ft(w)2754 1144 y FE(1)2800 1130
y Fr(+)6 b Ft(:)15 b(:)g(:)7 b Fr(+)f Ft(w)3131 1144
y Fo(m)3223 1130 y Fr(=)25 b(1)p Fw(.)548 1255 y(Then,)32
b(it)e(can)g(be)g(sho)n(wn)h(that)g Ft(L)p Fr(\()p Ft(\026)1722
1269 y FE(0)1761 1255 y Fr(\))38 b(=)g(\()p Ft(e)2020
1222 y Fm(>)2079 1255 y Ft(Q)2151 1222 y Fm(\000)p FE(1)2151
1278 y Fo(r)2246 1255 y Ft(e)p Fr(\))2323 1222 y Fm(\000)p
FE(1)2455 1255 y Fr(=)2564 1182 y Fn(\000)2605 1187 y(P)2701
1213 y Fo(n)2701 1282 y(i;j)t FE(=1)2887 1255 y Ft(q)2931
1217 y Fm(\000)p FE(1)2928 1282 y Fo(ij)3025 1182 y Fn(\001)3067
1204 y Fm(\000)p FE(1)3190 1255 y Fw(holds)548 1363 y(pro)o(vided)c
(that)f(the)f(number)i(of)e(atoms)g Ft(m)g Fw(and)g(the)h(atoms)f
Ft(x)2593 1377 y FE(1)2633 1363 y Ft(;)15 b(:)g(:)g(:)h(;)f(x)2886
1377 y Fo(m)2985 1363 y Fw(themselv)o(es)548 1471 y(satisfy)25
b(the)f(condition)1321 1650 y Ft(q)1365 1613 y Fm(>)1362
1673 y Fo(r)1423 1650 y Fr(\()p Ft(x)p Fr(\))p Ft(Q)1617
1613 y Fm(\000)p FE(1)1617 1673 y Fo(r)1712 1650 y Ft(e)i
Fs(>)f Fr(1)182 b Fw(for)24 b(all)f Ft(x)j Fq(2)f Fp(R)2575
1617 y Fo(d)3236 1650 y Fw(\(17\))548 1829 y(and)34 b(the)f(co)o(v)n
(ariance)i(matrix)f Ft(Q)1619 1843 y Fo(r)1700 1829 y
Fr(=)43 b(\()p Ft(C)1914 1843 y Fo(r)r(r)1986 1829 y
Fr(\()p Ft(x)2073 1843 y Fo(i)2121 1829 y Fq(\000)20
b Ft(x)2264 1843 y Fo(j)2301 1829 y Fr(\)\))2371 1787
y Fo(m)2371 1860 y(i;j)t FE(=1)2574 1829 y Fw(is)33 b(re)o(gular)l(,)k
(where)c Ft(e)44 b Fr(=)548 1962 y(\(1)p Ft(;)15 b(:)g(:)g(:)i(;)e
Fr(1\))910 1929 y Fm(>)971 1962 y Fw(,)23 b Ft(Q)1089
1929 y Fm(\000)p FE(1)1089 1984 y Fo(r)1210 1962 y Fr(=)1308
1888 y Fn(\000)1349 1962 y Ft(q)1393 1924 y Fm(\000)p
FE(1)1390 1989 y Fo(ij)1487 1888 y Fn(\001)1529 1911
y Fo(m)1529 1998 y(i;j)t FE(=1)1723 1962 y Fw(denotes)j(the)f(in)l(v)o
(erse)h(matrix)f(of)f Ft(Q)2872 1976 y Fo(r)2934 1962
y Fw(and)h Ft(q)3130 1976 y Fo(r)3167 1962 y Fr(\()p
Ft(x)p Fr(\))j(=)548 2098 y(\()p Ft(C)648 2112 y Fo(r)r(r)720
2098 y Fr(\()p Ft(x)20 b Fq(\000)e Ft(x)968 2112 y FE(1)1008
2098 y Fr(\))p Ft(;)d(:)g(:)g(:)i(;)e(C)1310 2112 y Fo(r)r(r)1382
2098 y Fr(\()p Ft(x)k Fq(\000)g Ft(x)1630 2112 y Fo(n)1677
2098 y Fr(\)\))1747 2065 y Fm(>)1829 2098 y Fw(for)24
b(an)o(y)f Ft(x)i Fq(2)g Fp(R)2339 2065 y Fo(d)2379 2098
y Fw(.)j(Moreo)o(v)o(er)l(,)d(in)e(this)h(case,)f(the)548
2206 y(v)o(ector)h(of)g(weights)g Ft(w)k Fr(=)d(\()p
Ft(w)1489 2220 y FE(1)1529 2206 y Ft(;)15 b(:)g(:)g(:)i(;)e(w)1796
2220 y Fo(m)1863 2206 y Fr(\))1898 2173 y Fm(>)1980 2206
y Fw(is)23 b(gi)n(v)o(en)h(by)1635 2385 y Ft(w)k Fr(=)d
Ft(L)p Fr(\()p Ft(\026)1976 2399 y FE(0)2016 2385 y Fr(\))p
Ft(Q)2123 2348 y Fm(\000)p FE(1)2123 2408 y Fo(r)2217
2385 y Ft(e)15 b(:)937 b Fw(\(18\))548 2564 y(Notice)23
b(that,)g(for)g(\002x)o(ed)f(sampling)i(points)g Ft(x)1974
2578 y FE(1)2013 2564 y Ft(;)15 b(:)g(:)g(:)i(;)e(x)2267
2578 y Fo(m)2334 2564 y Fw(,)21 b(formula)j(\(18\))f(coincides)i(with)
548 2672 y(the)k Fv(kriging)h(of)f(the)g(mean)p Fw(;)i(see)e([19].)45
b(In)28 b(this)h(case,)i(the)e(estimator)k Fn(b)-54 b
Ft(y)2850 2686 y Fo(r)2915 2672 y Fw(with)28 b(weights)548
2780 y(gi)n(v)o(en)h(by)f(\(18\))h(is)g(also)g(kno)n(wn)f(as)h(the)f
(generalized)k(least\226squares)g(estimator)e(of)e(the)548
2888 y(trend;)23 b(see)f([9],)g(p.)e(11.)28 b(On)21 b(the)h(other)g
(hand,)g(the)g(locations)i Ft(x)2521 2902 y FE(1)2560
2888 y Ft(;)15 b(:)g(:)g(:)i(;)e(x)2814 2902 y Fo(n)2882
2888 y Fw(can)21 b(be)h(chosen)548 2996 y(iterati)n(v)o(ely)k(using)e
(gradient)i(algorithms)g(described)g(e.g.)i(in)c([9].)648
3104 y(An)o(yho)n(w)-6 b(,)28 b(the)f(choice)i(of)f(an)f(appropriate)k
(number)e Ft(m)d Fw(of)i(sampling)h(points,)h(loca-)548
3212 y(tions)25 b Ft(x)800 3226 y FE(1)839 3212 y Ft(;)15
b(:)g(:)g(:)i(;)e(x)1093 3226 y Fo(m)1182 3212 y Fw(and)24
b(weights)h Ft(w)1707 3226 y FE(1)1747 3212 y Ft(;)15
b(:)g(:)g(:)h(;)f(w)2013 3226 y Fo(m)2103 3212 y Fw(depends)26
b(on)d(the)h(co)o(v)n(ariance)i(function)548 3320 y Ft(C)613
3334 y Fo(r)r(r)728 3320 y Fr(:)44 b Fp(R)863 3287 y
Fo(d)947 3320 y Fq(!)f Fp(R)32 b Fw(which)i(is)f(unkno)n(wn)i(in)e
(general.)60 b(Therefore,)38 b Ft(C)2829 3334 y Fo(r)r(r)2900
3320 y Fr(\()p Ft(h)p Fr(\))p Fw(,)e Ft(h)44 b Fq(2)f
Fp(R)3347 3287 y Fo(d)548 3428 y Fw(has)29 b(to)f(be)g(estimated)i
(from)e(data.)44 b(Sometimes)29 b(it)f(is)g(preferable)j(to)d(consider)
j(the)d Fv(va-)548 3535 y(riogr)o(am)34 b(function)h
Ft(\015)1254 3549 y Fo(r)1334 3535 y Fr(:)43 b Fp(R)1468
3502 y Fo(d)1551 3535 y Fq(!)f Fp(R)32 b Fw(with)h Ft(\015)2023
3549 y Fo(r)2061 3535 y Fr(\()p Ft(h)p Fr(\))44 b(=)2350
3500 y FE(1)p 2350 3515 36 4 v 2350 3567 a(2)2438 3535
y Ft(E)20 b Fr(\()p Ft(Y)2613 3549 y Fo(r)2651 3535 y
Fr(\()p Ft(x)p Fr(\))28 b Fq(\000)f Ft(Y)2952 3549 y
Fo(r)2990 3535 y Fr(\()p Ft(x)g Fr(+)g Ft(h)p Fr(\)\))3324
3502 y FE(2)3365 3535 y Fw(,)548 3654 y Ft(h;)15 b(x)49
b Fq(2)f Fp(R)916 3621 y Fo(d)956 3654 y Fw(,)38 b(instead)g(of)e
Ft(C)1486 3668 y Fo(r)r(r)1593 3654 y Fw(since)h(it)e(can)i(be)f
(estimated)h(more)f(easily)-6 b(.)68 b(F)o(or)35 b(cor)n(-)548
3762 y(responding)g(estimation)f(techniques)i(and)c(algorithms,)k(see)d
(e.g.)54 b([1,)34 b(2,)f(19].)55 b(Since)548 3870 y Ft(\015)595
3884 y Fo(r)633 3870 y Fr(\()p Ft(h)p Fr(\))26 b(=)f
Ft(C)942 3884 y Fo(r)r(r)1014 3870 y Fr(\()p Ft(o)p Fr(\))12
b Fq(\000)g Ft(C)1288 3884 y Fo(r)r(r)1361 3870 y Fr(\()p
Ft(h)p Fr(\))21 b Fw(holds)i(for)f(an)o(y)f Ft(h)26 b
Fq(2)e Fp(R)2228 3837 y Fo(d)2269 3870 y Fw(,)c(\(17\))i(and)g(\(18\))g
(can)g(be)f(re)n(written)548 3978 y(as)1327 4086 y Ft(p)1373
4048 y Fm(>)1373 4108 y Fo(r)1432 4086 y Fr(\()p Ft(x)p
Fr(\)\000)1611 4048 y Fm(\000)p FE(1)1611 4108 y Fo(r)1706
4086 y Ft(e)k Fs(6)g Fr(1)183 b Fw(for)23 b(all)h Ft(x)h
Fq(2)g Fp(R)2568 4053 y Fo(d)3236 4086 y Fw(\(19\))548
4236 y(and)1713 4344 y Ft(w)j Fr(=)d Ft(\015)1949 4358
y FE(0)1988 4344 y Fr(\000)2045 4307 y Fm(\000)p FE(1)2045
4367 y Fo(r)2139 4344 y Ft(e)15 b(;)1015 b Fw(\(20\))548
4495 y(respecti)n(v)o(ely)-6 b(,)29 b(where)d Fr(\000)1330
4509 y Fo(r)1398 4495 y Fr(=)j(\()p Ft(\015)1580 4509
y Fo(r)1618 4495 y Fr(\()p Ft(x)1705 4509 y Fo(i)1754
4495 y Fq(\000)20 b Ft(x)1897 4509 y Fo(j)1933 4495 y
Fr(\)\))2004 4453 y Fo(m)2004 4526 y(i;j)t FE(=1)2174
4495 y Fw(,)26 b Ft(\015)2270 4509 y FE(0)2339 4495 y
Fr(=)j(\()p Ft(e)2516 4462 y Fm(>)2576 4495 y Fr(\000)2633
4462 y Fm(\000)p FE(1)2633 4517 y Fo(r)2727 4495 y Ft(e)p
Fr(\))2804 4462 y Fm(\000)p FE(1)2924 4495 y Fw(and)e
Ft(p)3127 4509 y Fo(r)3164 4495 y Fr(\()p Ft(x)p Fr(\))k(=)548
4626 y(\()p Ft(\015)630 4640 y Fo(r)668 4626 y Fr(\()p
Ft(x)21 b Fq(\000)f Ft(x)919 4640 y FE(1)958 4626 y Fr(\))p
Ft(;)15 b(:)g(:)g(:)i(;)e(\015)1242 4640 y Fo(r)1281
4626 y Fr(\()p Ft(x)20 b Fq(\000)g Ft(x)1531 4640 y Fo(m)1597
4626 y Fr(\)\))1667 4593 y Fm(>)1727 4626 y Fw(.)548
4842 y Fx(6.)216 b(Numerical)26 b(r)n(esults)648 5000
y Fw(T)-7 b(o)21 b(test)j(the)f(performance)i(of)e(the)g(abo)o(v)o(e)h
(estimation)g(method,)g Fr(200)f Fw(realizations)k(of)548
5108 y(a)g(planar)i(Boolean)f(model)g Fr(\004)e Fw(\()p
Ft(d)33 b Fr(=)f(2)p Fw(\))c(with)f(circular)i(grains)g(were)e
(generated)j(in)d(the)548 5215 y(observ)n(ation)k(windo)n(w)c
Ft(W)45 b Fr(=)33 b([0)p Ft(;)15 b Fr(1000])1864 5182
y FE(2)1907 5215 y Fw(.)40 b(Let)27 b Ft(\025)g Fw(be)g(the)h
(intensity)i(of)e(the)g(stationary)p eop end
%%Page: 11 11
TeXDict begin 11 10 bop 598 550 a Fu(Numerical)20 b(r)m(esults)2159
b FF(11)598 751 y Fw(Poisson)21 b(point)f(process)i Ft(X)33
b Fr(=)24 b Fq(f)p Ft(X)1720 765 y Fo(i)1749 751 y Fq(g)c
Fw(of)f(germs)h(and)h(let)e(the)h(grains)h Fr(\004)2841
765 y Fo(i)2888 751 y Fw(be)f(independent)598 859 y(circles)31
b(with)e(radii)h(that)g(are)f(uniformly)i(distrib)n(uted)i(on)c
Fr([20)p Ft(;)15 b Fr(40])p Fw(.)48 b(Then,)31 b Fr(\004)d
Fw(is)h(gi)n(v)o(en)598 967 y(by)22 b Fr(\004)j(=)892
898 y Fn(S)967 925 y Fm(1)967 993 y Fo(i)p FE(=1)1086
967 y Fr(\(\004)1182 981 y Fo(i)1225 967 y Fr(+)15 b
Ft(X)1386 981 y Fo(i)1413 967 y Fr(\))p Fw(.)28 b(The)22
b(intensity)i Ft(\025)d Fw(w)o(as)h(chosen)i(to)e(\002t)f(the)h(v)n
(olume)h(fractions)p 598 1001 74 4 v 598 1074 a Ft(V)671
1088 y FE(2)710 1074 y Fr(\(\004\))50 b(=)f(0)p Ft(:)p
Fr(2)p Ft(;)37 b Fr(0)p Ft(:)p Fr(5)p Fw(,)i Fr(0)p Ft(:)p
Fr(8)p Fw(,)h(respecti)n(v)o(ely)-6 b(.)70 b(F)o(or)36
b(each)h(realization,)42 b(the)37 b(v)o(ector)g Ft(v)i
Fw(of)598 1182 y(speci\002c)26 b(intrinsic)i(v)n(olumes)f(of)f
Fr(\004)f Fw(w)o(as)g(estimated)i(using)g(the)f(radii)h
Ft(r)2870 1196 y FE(0)2939 1182 y Fr(=)i(10)p Fw(,)d
Ft(r)3219 1196 y Fo(i)p FE(+1)3366 1182 y Fr(=)598 1290
y Ft(r)639 1304 y Fo(i)672 1290 y Fr(+)5 b(1)p Ft(:)p
Fr(3)p Fw(,)19 b Ft(i)26 b Fr(=)f(0)p Ft(;)15 b(:)g(:)g(:)i(;)e
Fr(49)20 b Fw(in)f(the)h(least\226squares)j(method.)28
b(In)19 b(the)h(estimation,)i(sampling)598 1398 y(w)o(as)31
b(performed)j(on)d(the)h(re)o(gular)h(square)g(lattice)g(of)f(points)h
Ft(x)2662 1412 y FE(1)2701 1398 y Ft(;)15 b(:)g(:)g(:)i(;)e(x)2955
1412 y Fo(m)3053 1398 y Fw(with)31 b(mesh)598 1506 y(size)f
Fr(\001)37 b(=)f(5)p Fw(.)47 b(Finally)-6 b(,)32 b(v)o(ector)p
1663 1456 48 4 v 31 w Ft(v)1710 1473 y Fm(\003)1786 1506
y Fr(=)37 b(\()p 1929 1456 V Ft(v)1976 1473 y Fm(\003)1976
1531 y FE(0)2016 1506 y Ft(;)p 2056 1456 V 15 w(v)2103
1473 y Fm(\003)2103 1531 y FE(1)2143 1506 y Ft(;)p 2183
1456 V 15 w(v)2231 1473 y Fm(\003)2231 1531 y FE(2)2270
1506 y Fr(\))29 b Fw(w)o(as)h(b)n(uilt)h(being)f(the)g(arithmetic)598
1614 y(mean)j(o)o(v)o(er)h(the)g(results)h(of)e Fr(200)h
Fw(realizations.)62 b(Its)34 b(v)n(alues)h(are)e(compared)j(with)d(the)
598 1722 y(theoretical)26 b(counterparts)g Ft(v)j Fr(=)c(\()p
1679 1649 74 4 v Ft(V)1752 1736 y FE(0)1792 1722 y Fr(\(\004\))p
Ft(;)p 1963 1649 V 15 w(V)2037 1736 y FE(1)2076 1722
y Fr(\(\004\))p Ft(;)p 2247 1649 V 15 w(V)2321 1736 y
FE(2)2361 1722 y Fr(\(\004\)\))e Fw(in)g(T)-7 b(able)22
b(1.)29 b(Additionally)-6 b(,)598 1830 y(the)26 b(speci\002c)h
(intrinsic)h(v)n(olumes)f(were)f(estimated)h(by)f(the)h(method)f
(described)j(in)d([10])598 1938 y(from)d(the)h(same)g
Fr(200)h Fw(realizations)i(of)c Fr(\004)p Fw(.)29 b(The)23
b(resulting)j(arithmetic)g(means)f Fn(e)-52 b Ft(v)3150
1952 y FE(0)3189 1938 y Ft(;)17 b Fn(e)-53 b Ft(v)3273
1952 y FE(1)3313 1938 y Ft(;)17 b Fn(e)-53 b Ft(v)3397
1952 y FE(2)598 2046 y Fw(are)22 b(also)h(presented)i(in)d(T)-7
b(able)22 b(1.)27 b(T)-7 b(o)22 b(compare)h(the)f(precision)j(of)d
(both)h(algorithms,)h(the)598 2154 y(relati)n(v)o(e)j(error)g
Ft(\016)1134 2168 y Fo(A;B)1297 2154 y Fr(=)1408 2118
y Fo(B)s Fm(\000)p Fo(A)p 1408 2133 165 4 v 1464 2185
a(A)1604 2154 y Fq(\001)c Fr(100\045)j Fw(of)g(an)g(estimated)i
(quantity)g Ft(B)i Fw(with)c(respect)h(to)598 2262 y(the)21
b(theoretical)i(v)n(alue)e Ft(A)f Fw(is)g(gi)n(v)o(en.)29
b(It)20 b(is)g(clear)i(from)e(T)-7 b(able)20 b(1)h(that)g(the)f
(performance)j(of)598 2504 y FD(T)-7 b(able)19 b(1.)75
b FA(Theoretical)18 b(and)i(estimated)f(v)n(alues)h(of)f(speci\002c)g
(intrinsic)f(v)o(olumes)p 598 2623 2840 4 v 598 2655
62 4 v 598 2715 a Fz(V)660 2723 y Fl(2)694 2715 y Fy(\(\004\))768
b(0)p Fz(:)p Fy(2)679 b(0)p Fz(:)p Fy(5)729 b(0)p Fz(:)p
Fy(8)p 598 2771 2840 4 v 598 2818 40 4 v 598 2859 a Fz(v)638
2828 y Fj(\003)638 2873 y Fl(2)1477 2859 y Fy(0)p Fz(:)p
Fy(194299)489 b(0)p Fz(:)p Fy(490611)539 b(0)p Fz(:)p
Fy(793328)599 2951 y Fe(e)-44 b Fz(v)635 2959 y Fl(2)1477
2951 y Fy(0)p Fz(:)p Fy(199362)489 b(0)p Fz(:)p Fy(498217)539
b(0)p Fz(:)p Fy(798085)598 3042 y Fz(\016)p 632 3021
50 3 v 21 x Fk(V)681 3072 y Fd(2)713 3063 y Fk(;)p 732
3034 33 3 v(v)765 3045 y Fc(\003)765 3082 y Fd(2)804
3042 y FA(,)19 b Fy(\045)618 b Fb(\000)p Fy(2)p Fz(:)p
Fy(85)581 b Fb(\000)p Fy(1)p Fz(:)p Fy(88)631 b Fb(\000)p
Fy(0)p Fz(:)p Fy(83)598 3146 y Fz(\016)p 632 3125 50
3 v 20 x Fk(V)681 3176 y Fd(2)713 3166 y Fk(;)r Fa(e)-34
b Fk(v)763 3176 y Fd(2)800 3146 y Fz(;)p FA(\045)641
b Fb(\000)p Fy(0)p Fz(:)p Fy(32)581 b Fb(\000)p Fy(0)p
Fz(:)p Fy(36)631 b Fb(\000)p Fy(0)p Fz(:)p Fy(24)p 598
3204 2840 4 v 598 3296 a(2)p 636 3235 62 4 v Fz(V)698
3304 y Fl(1)733 3296 y Fy(\(\004\))i(0)p Fz(:)p Fy(011476)509
b(0)p Fz(:)p Fy(02228)557 b(0)p Fz(:)p Fy(020693)p 598
3351 2840 4 v 598 3440 a(2)p 636 3399 40 4 v Fz(v)676
3409 y Fj(\003)676 3453 y Fl(1)1477 3440 y Fy(0)p Fz(:)p
Fy(012123)489 b(0)p Fz(:)p Fy(023402)539 b(0)p Fz(:)p
Fy(021547)598 3532 y(2)q Fe(e)-44 b Fz(v)673 3540 y Fl(1)1477
3532 y Fy(0)p Fz(:)p Fy(011361)489 b(0)p Fz(:)p Fy(021947)558
b(0)p Fz(:)p Fy(02022)598 3623 y Fz(\016)p 632 3602 50
3 v 20 x Fk(V)681 3653 y Fd(1)713 3643 y Fk(;)p 732 3615
33 3 v(v)765 3626 y Fc(\003)765 3663 y Fd(1)804 3623
y FA(,)19 b Fy(\045)648 b(5)p Fz(:)p Fy(64)641 b(5)p
Fz(:)p Fy(04)691 b(4)p Fz(:)p Fy(13)598 3726 y Fz(\016)p
632 3706 50 3 v 21 x Fk(V)681 3756 y Fd(1)713 3747 y
Fk(;)r Fa(e)-34 b Fk(v)763 3757 y Fd(1)800 3726 y FA(,)18
b Fy(\045)642 b Fb(\000)p Fy(1)p Fz(:)p Fy(0)620 b Fb(\000)p
Fy(1)p Fz(:)p Fy(5)649 b Fb(\000)p Fy(2)p Fz(:)p Fy(29)p
598 3785 2840 4 v 598 3816 62 4 v 598 3877 a Fz(V)660
3885 y Fl(0)694 3877 y Fy(\(\004\))17 b Fb(\002)g Fy(10)975
3845 y Fl(4)1458 3877 y Fy(0)p Fz(:)p Fy(4778163)451
b(0)p Fz(:)p Fy(3919529)471 b Fb(\000)p Fy(0)p Fz(:)p
Fy(6059316)p 598 3932 2840 4 v 598 3979 40 4 v 598 4021
a Fz(v)638 3989 y Fj(\003)638 4034 y Fl(0)691 4021 y
Fb(\002)17 b Fy(10)844 3989 y Fl(4)1458 4021 y Fy(0)p
Fz(:)p Fy(4348681)451 b(0)p Fz(:)p Fy(1555031)g Fb(\000)p
Fy(0)p Fz(:)p Fy(10798772)599 4112 y Fe(e)-44 b Fz(v)635
4120 y Fl(0)687 4112 y Fb(\002)17 b Fy(10)840 4081 y
Fl(4)1458 4112 y Fy(0)p Fz(:)p Fy(4312496)451 b(0)p Fz(:)p
Fy(1595565)g Fb(\000)p Fy(0)p Fz(:)p Fy(10672334)598
4204 y Fz(\016)p 632 4183 50 3 v 20 x Fk(V)681 4234 y
Fd(0)713 4224 y Fk(;)p 732 4195 33 3 v(v)765 4207 y Fc(\003)765
4243 y Fd(0)804 4204 y FA(,)19 b Fy(\045)618 b Fb(\000)p
Fy(8)p Fz(:)p Fy(99)562 b Fb(\000)p Fy(60)p Fz(:)p Fy(33)622
b(78)p Fz(:)p Fy(22)598 4307 y Fz(\016)p 632 4286 50
3 v 21 x Fk(V)681 4337 y Fd(0)713 4328 y Fk(;)r Fa(e)-34
b Fk(v)763 4338 y Fd(0)800 4307 y FA(,)18 b Fy(\045)623
b Fb(\000)p Fy(9)p Fz(:)p Fy(75)562 b Fb(\000)p Fy(59)p
Fz(:)p Fy(29)622 b(76)p Fz(:)p Fy(13)p 598 4366 2840
4 v 598 4568 a Fw(our)23 b(algorithm)i(is)e(comparable)i(to)e(that)h
(of)f(the)g(method)h(described)i(in)d([10].)29 b(Ho)o(v)o(e)n(wer)l(,)
598 4676 y(the)c(abo)o(v)o(e)g(results)h(can)e(be)h(impro)o(v)o(ed)g
(by)g(taking)h(e.g.)31 b Fr(\001)c(=)g(1)p Fw(.)k(In)24
b(f)o(act,)h(the)g(precision)598 4784 y(of)36 b(our)h(computations)i
(can)e(be)f(controlled)j(by)d(changing)j(the)e(sampling)h(design)f(as)
598 4892 y(well)21 b(as)h(the)g(number)g(and)h(v)n(alues)g(of)e
(dilation)j(radii.)29 b(The)21 b(increase)j(of)d(the)h(numbers)h(of)598
5000 y(radii)g(and)g(sampling)h(points)g(results)g(in)e(a)g(higher)i
(precision.)31 b(This)23 b(implies)g(longer)h(run)598
5108 y(times.)40 b(Hence,)28 b(the)g(parameters)h(of)e(the)h(algorithm)
h(should)f(be)g(tuned)g(in)f(accordance)598 5215 y(with)c(the)h(needs)h
(of)e(speci\002c)i(applications;)i(see)d([4])f(for)h(an)g(e)o(xtensi)n
(v)o(e)h(discussion.)p eop end
%%Page: 12 12
TeXDict begin 12 11 bop 548 550 a FF(12)542 b Fu(On)20
b(the)g(local)g(connectivity)f(number)g(of)i(stationary)e(r)o(andom)g
(closed)h(sets)548 757 y Fx(Ackno)o(wledgments)648 915
y Fw(The)k(authors)i(are)f(v)o(ery)g(grateful)i(to)e(Simone)g(Klenk)g
(and)g(Johannes)i(Mayer)e(for)g(the)548 1022 y(implementation)k(of)e
(the)g(algorithm)h(in)f(Ja)n(v)n(a)g(and)g(numerical)h(e)o(xperiments.)
40 b(Further)n(-)548 1130 y(more,)28 b(the)o(y)g(w)o(ould)g(lik)o(e)f
(to)h(thank)g(the)g(referees)h(for)e(their)i(comments)f(that)g(helped)h
(to)548 1238 y(impro)o(v)o(e)24 b(the)g(paper)-5 b(.)548
1454 y Fx(Refer)n(ences)612 1607 y FA([1])46 b(J.-P)-8
b(.)23 b(Chil)1023 1606 y(\204)1023 1607 y(es)i(and)h(P)-8
b(.)24 b(Del\002ner)l(.)46 b FD(Geostatistics:)25 b(Modelling)h
(Spatial)g(Uncertainty)p FA(.)47 b(J.)25 b(W)m(ile)o(y)f(&)745
1698 y(Sons,)19 b(Ne)n(w)f(Y)-8 b(ork,)19 b(1999.)612
1809 y([2])46 b(N.)22 b(A.)f(C.)h(Cressie.)37 b FD(Statistics)22
b(for)h(Spatial)g(Data)p FA(.)38 b(J.)21 b(W)m(ile)o(y)h(&)g(Sons,)g
(Ne)n(w)h(Y)-8 b(ork,)22 b(2nd)h(edition,)745 1900 y(1993.)612
2011 y([3])46 b(A.)20 b(V)-10 b(.)21 b(Iv)n(ano)o(v)h(and)f(N.)f(N.)g
(Leonenk)o(o.)35 b FD(Statistical)20 b(Analysis)h(of)g(Random)g(F)m
(ields)p FA(.)32 b(Kluwer)m(,)21 b(Dor)o(-)745 2102 y(drecht,)e(1989.)
612 2213 y([4])46 b(S.)26 b(Klenk,)g(J.)h(Mayer)m(,)g(V)-10
b(.)27 b(Schmidt,)f(and)h(E.)f(Spodare)n(v)-5 b(.)53
b(Algorithms)27 b(for)g(the)g(computation)h(of)745 2305
y(Mink)o(o)n(wski)20 b(functionals)g(of)f(deterministic)g(and)g(random)
h(polycon)m(v)o(e)o(x)h(sets.)27 b(Preprint,)18 b(2005.)612
2415 y([5])46 b(S.)17 b(Klenk,)h(V)-10 b(.)17 b(Schmidt,)h(and)g(E.)f
(Spodare)n(v)-5 b(.)26 b(A)18 b(ne)n(w)g(algorithmic)g(approach)i(for)e
(the)g(computation)745 2507 y(of)h(Mink)o(o)n(wski)h(functionals)g(of)f
(polycon)m(v)o(e)o(x)i(sets.)27 b(Preprint,)18 b(2004.)28
b(Submitted.)612 2618 y([6])46 b(G.)18 b(Matheron.)28
b FD(Random)20 b(Sets)f(and)h(Inte)m(gr)o(al)f(Geometry)p
FA(.)27 b(J.)19 b(W)m(ile)o(y)f(&)h(Sons,)f(Ne)n(w)h(Y)-8
b(ork,)19 b(1975.)612 2728 y([7])46 b(I.)20 b(S.)f(Molchano)o(v)-5
b(.)34 b FD(Statistics)20 b(of)h(the)f(Boolean)h(Model)h(for)e(Pr)o
(actitioner)o(s)h(and)g(Mathematicians)p FA(.)745 2820
y(J.)d(W)m(ile)o(y)g(&)h(Sons,)g(Chichester)m(,)g(1997.)612
2931 y([8])46 b(I.)15 b(S.)g(Molchano)o(v)j(and)e(S.)f(A.)g(Zuye)n(v)-5
b(.)21 b(V)-8 b(ariational)15 b(analysis)i(of)e(functionals)i(of)f(a)f
(Poisson)i(process.)745 3022 y FD(Mathematics)j(of)e(Oper)o(ations)i
(Resear)m(c)o(h)p FA(,)g(25:485\226508,)h(2000.)612 3133
y([9])46 b(W)-7 b(.)18 b(G.)g(M\374ller)l(.)27 b FD(Collecting)19
b(Spatial)h(Data)p FA(.)27 b(Physica\226V)-8 b(erlag,)18
b(Heidelber)o(g,)h(2001.)575 3244 y([10])46 b(J.)22 b(Ohser)i(and)f(F)
-6 b(.)22 b(M\374cklich.)41 b FD(Statistical)23 b(Analysis)g(of)g(Micr)
m(ostructur)m(es)h(in)f(Materials)g(Science)p FA(.)745
3335 y(J.)18 b(W)m(ile)o(y)g(&)h(Sons,)g(Chichester)m(,)g(2000.)575
3446 y([11])46 b(V)-10 b(.)16 b(Schmidt)h(and)h(E.)e(Spodare)n(v)-5
b(.)23 b(Joint)17 b(estimators)g(for)g(the)g(speci\002c)f(intrinsic)h
(v)o(olumes)g(of)g(station-)745 3537 y(ary)e(random)h(sets.)i
(Preprint,)c(2004.)19 b(T)-6 b(o)15 b(appear)h(in)f(Stochastic)f
(Processes)i(and)f(their)g(Applications.)575 3648 y([12])46
b(R.)28 b(Schneider)l(.)58 b FD(Con)m(ve)o(x)28 b(Bodies.)h(The)f
(Brunn\226Mink)o(owski)j(Theory)p FA(.)58 b(Cambridge)29
b(Uni)n(v)o(ersity)745 3739 y(Press,)18 b(Cambridge,)h(1993.)575
3850 y([13])46 b(R.)21 b(Schneider)i(and)f(W)-7 b(.)21
b(W)-6 b(eil.)36 b FD(Stoc)o(hastisc)o(he)23 b(Geometrie)p
FA(.)37 b(T)-5 b(eubner)23 b(Skripten)f(zur)g(Mathemati-)745
3942 y(schen)e(Stochastik.)e(T)-5 b(eubner)m(,)19 b(Stuttgart,)f(2000.)
575 4053 y([14])46 b(J.)14 b(Serra.)j(The)d(Boolean)i(model)f(and)g
(random)h(sets.)h FD(Computer)f(Gr)o(aphics)f(and)g(Ima)o(g)o(e)h(Pr)m
(ocessing)p FA(,)745 4144 y(12:99\226126,)21 b(1980.)575
4255 y([15])46 b(J.)15 b(Serra.)20 b FD(Ima)o(g)o(e)d(Analysis)f(and)h
(Mathematical)g(Morpholo)o(gy)p FA(.)23 b(Academic)16
b(Press,)f(London,)i(1982.)575 4366 y([16])46 b(J.)29
b(Serra.)60 b FD(Ima)o(g)o(e)30 b(Analysis)f(and)h(Mathematical)h
(Morpholo)o(gy:)g(Theor)m(etical)f(Advances)p FA(,)g(v)o(ol-)745
4457 y(ume)19 b(2.)27 b(Academic)20 b(Press,)e(London,)i(1988.)575
4568 y([17])46 b(E.)22 b(Spodare)n(v)-5 b(.)41 b(Isoperimetric)23
b(problems)h(and)f(roses)h(of)f(neighborhood)i(for)e(stationary)h
(\003at)e(pro-)745 4659 y(cesses.)27 b FD(Mathematisc)o(he)20
b(Nac)o(hric)o(hten)p FA(,)g(251\(4\):88\226100,)h(2003.)575
4770 y([18])46 b(D.)29 b(Sto)o(yan,)i(W)-7 b(.)29 b(S.)g(K)n(endall,)h
(and)h(J.)f(Meck)o(e.)64 b FD(Stoc)o(hastic)31 b(Geometry)f(and)h(its)f
(Applications)p FA(.)745 4861 y(J.)18 b(W)m(ile)o(y)g(&)h(Sons,)g
(Chichester)m(,)g(2nd)h(edition,)f(1995.)575 4972 y([19])46
b(H.)18 b(W)-6 b(ack)o(ernagel.)28 b FD(Multivariate)19
b(Geostatistics)p FA(.)27 b(Springer)m(,)19 b(Berlin,)f(2nd)i(edition,)
f(1998.)p eop end
%%Trailer

userdict /end-hook known{end-hook}if
%%EOF