Content-Type: multipart/mixed; boundary="-------------9908230506225" This is a multi-part message in MIME format. ---------------9908230506225 Content-Type: text/plain; name="99-306.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="99-306.keywords" Interacting particle and spin systems; Kac potential; hydrodynamic limits; phase segregation. ---------------9908230506225 Content-Type: application/postscript; name="mmsped.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="mmsped.ps" %!PS-Adobe-3.0 %%Title: (mm?.tex) %%Creator: (Textures\250: LaserWriter 8 8.2.3) %%CreationDate: (21:22 Mercoled\223, 12 maggio 1999) %%For: (Raffaele Esposito) %%Pages: 50 %%DocumentFonts: CMBX10 CMR10 CMR7 CMBX8 CMR8 CMMI8 CMSY8 CMMI6 CMR6 CMSY6 CMMI10 CMMI7 CMSY10 CMEX10 CMSY7 CMMI5 CMR5 CMTI10 CMSY5 Helvetica CMSL10 %%DocumentNeededFonts: CMBX10 CMR10 CMR7 CMBX8 CMR8 CMMI8 CMSY8 CMMI6 CMR6 CMSY6 CMMI10 CMMI7 CMSY10 CMEX10 CMSY7 CMMI5 CMR5 CMTI10 CMSY5 Helvetica CMSL10 %%DocumentSuppliedFonts: %%DocumentData: Clean7Bit %%PageOrder: Ascend %%Orientation: Portrait %%DocumentMedia: Default 612 792 0 () () %ADO_ImageableArea: 14 12 597 780 %%EndComments userdict begin/dscInfo 5 dict dup begin /Title(mm?.tex)def /Creator(Textures\250: LaserWriter 8 8.2.3)def /CreationDate(21:22 Mercoled\223, 12 maggio 1999)def /For(Raffaele Esposito)def /Pages 1 def end def end /featurecleanup{stopped cleartomark countdictstack exch sub dup 0 gt{{end}repeat}{pop}ifelse}bind def countdictstack[{ currentsystemparams /CurInputDevice get (%Fax) anchorsearch {pop pop 1 dict dup/Policies 1 dict dup/PageSize 3 put put setpagedevice} {pop}ifelse}featurecleanup /md 213 dict def md begin/currentpacking where {pop /sc_oldpacking currentpacking def true setpacking}if %%BeginFile: adobe_psp_basic %%Copyright: Copyright 1990-1993 Adobe Systems Incorporated. All Rights Reserved. /bd{bind def}bind def /xdf{exch def}bd /xs{exch store}bd /ld{load def}bd /Z{0 def}bd /T/true /F/false /:L/lineto /lw/setlinewidth /:M/moveto /rl/rlineto /rm/rmoveto /:C/curveto /:T/translate /:K/closepath /:mf/makefont /gS/gsave /gR/grestore /np/newpath 14{ld}repeat /$m matrix def /av 81 def /por true def /normland false def /psb-nosave{}bd /pse-nosave{}bd /us Z /psb{/us save store}bd /pse{us restore}bd /level2 /languagelevel where { pop languagelevel 2 ge }{ false }ifelse def /featurecleanup { stopped cleartomark countdictstack exch sub dup 0 gt { {end}repeat }{ pop }ifelse }bd /noload Z /startnoload { {/noload save store}if }bd /endnoload { {noload restore}if }bd level2 startnoload /setjob { statusdict/jobname 3 -1 roll put }bd /setcopies { userdict/#copies 3 -1 roll put }bd level2 endnoload level2 not startnoload /setjob { 1 dict begin/JobName xdf currentdict end setuserparams }bd /setcopies { 1 dict begin/NumCopies xdf currentdict end setpagedevice }bd level2 not endnoload /pm Z /mT Z /sD Z /realshowpage Z /initializepage { /pm save store mT concat }bd /endp { pm restore showpage }def /$c/DeviceRGB def /rectclip where { pop/rC/rectclip ld }{ /rC { np 4 2 roll :M 1 index 0 rl 0 exch rl neg 0 rl :K clip np }bd }ifelse /rectfill where { pop/rF/rectfill ld }{ /rF { gS np 4 2 roll :M 1 index 0 rl 0 exch rl neg 0 rl fill gR }bd }ifelse /rectstroke where { pop/rS/rectstroke ld }{ /rS { gS np 4 2 roll :M 1 index 0 rl 0 exch rl neg 0 rl :K stroke gR }bd }ifelse %%EndFile %%BeginFile: adobe_psp_colorspace_level1 %%Copyright: Copyright 1991-1993 Adobe Systems Incorporated. All Rights Reserved. /G/setgray ld /:F/setrgbcolor ld %%EndFile level2 startnoload %%BeginFile: adobe_psp_level1_basicimages %%Copyright: Copyright 1990-1993 Adobe Systems Incorporated. All Rights Reserved. /$i false def /flipinvert statusdict begin version cvr 47.0 lt end def /iw Z /ih Z /im_save Z /setupimageproc Z /polarity Z /smoothflag Z /$z Z /bpc Z /smooth_moredata Z /datatype Z /:f { /im_save save store /datatype xs $i flipinvert and xor /polarity xs /smoothflag xs :T scale /$z exch string store /bpc xs /ih xs /iw xs /smoothflag smoothflag bpc 1 eq and smoothflag and userdict/sc_smooth known and vmstatus pop exch pop iw 3 mul sub 1000 gt and iw 4 mul 7 add 8 idiv 4 mul 65535 le and store smoothflag{ iw ih $z iw 7 add 8 idiv 4 mul string iw 4 mul 7 add 8 idiv 4 mul string true false sc_initsmooth /iw iw 4 mul store /ih ih 4 mul store }if /setupimageproc datatype 0 eq datatype 1 eq or{ smoothflag{ { [ /smooth_moredata cvx[ currentfile $z {readstring readhexstring}datatype get /pop cvx ]cvx[ $z ]cvx/ifelse cvx /sc_smooth cvx /smooth_moredata/exch cvx/store cvx ]cvx bind /smooth_moredata true store dup exec pop dup exec pop } }{ { [ currentfile $z {readstring readhexstring}datatype get /pop cvx ]cvx bind } }ifelse }{ (error, can't use level2 data acquisition procs for level1)print flush stop }ifelse store }bd /:j{im_save restore}bd /:g { 1 setgray 0 0 1 1 rF 0 setgray iw ih polarity[iw 0 0 ih 0 0]setupimageproc imagemask }bd /:h { setrgbcolor 0 0 1 1 rF setrgbcolor iw ih polarity[iw 0 0 ih 0 0]setupimageproc imagemask }bd /:i { setrgbcolor iw ih polarity[iw 0 0 ih 0 0]setupimageproc imagemask }bd %%EndFile level2 endnoload level2 not startnoload %%BeginFile: adobe_psp_level2_basicimage %%Copyright: Copyright 1990-1993 Adobe Systems Incorporated. All Rights Reserved. /$j 9 dict dup begin /ImageType 1 def /MultipleDataSource false def end def /im_save Z /setupimageproc Z /polarity Z /smoothflag Z /bpc Z /ih Z /iw Z /datatype Z /:f { /im_save save store /datatype xs datatype 0 lt datatype 4 gt or{ (error, datatype out of range)print flush stop }if /setupimageproc{ { currentfile } { currentfile 0(%ADOeod)/SubFileDecode filter/ASCIIHexDecode filter } { currentfile/RunLengthDecode filter } { currentfile/ASCII85Decode filter/RunLengthDecode filter } { currentfile/ASCII85Decode filter } }datatype get store { [1 0] }{ [0 1] }ifelse /polarity xs /smoothflag xs :T scale pop /bpc xs /ih xs /iw xs $c setcolorspace }bd /:j{im_save restore}bd /:g { 1 G 0 0 1 1 rF 0 G $j dup begin /Width iw def /Height ih def /Decode polarity def /ImageMatrix[iw 0 0 ih 0 0]def /DataSource setupimageproc def /BitsPerComponent 1 def /Interpolate smoothflag def end imagemask }bd /:h { :F 0 0 1 1 rF :F $j dup begin /Width iw def /Height ih def /Decode polarity def /ImageMatrix[iw 0 0 ih 0 0]def /DataSource setupimageproc def /BitsPerComponent 1 def /Interpolate smoothflag def end imagemask }bd /:i { :F $j dup begin /Width iw def /Height ih def /Decode polarity def /ImageMatrix[iw 0 0 ih 0 0]def /DataSource setupimageproc def /BitsPerComponent 1 def /Interpolate smoothflag def end imagemask }bd %%EndFile level2 not endnoload %%BeginFile: adobe_psp_smooth %%Copyright: Copyright 1991-1993 Adobe Systems Incorporated. All Rights Reserved. /junk Z /$z Z userdict/sc_smooth known not save systemdict/eexec known systemdict/cexec known and{ countdictstack mark false <1861AEDAE118A9F95F1629C0137F8FE656811DD93DFBEA65E947502E78BA12284B8A58EF0A3 2E272778DAA2ABEC72A84102D591E11D96BA61F57877B895A752D9BEAAC3DFD7D3220E2BDE7 C036467464E0E836748F1DE7AB6216866F130CE7CFCEC8CE050B870C11881EE3E9D70919> {eexec}stopped{ cleartomark countdictstack exch sub dup 0 gt{{end}repeat}{pop}ifelse false }{ {cleartomark pop true}{cleartomark pop false}ifelse }ifelse }{false}ifelse exch restore and level2 not and vmstatus exch sub exch pop 15000 gt and { currentfile eexec }{ /junk save store /$z 4795 string store currentfile $z readhexstring pop pop { currentfile $z readline not { stop }if (%ADOendeexec)eq { exit }if }bind loop junk restore }ifelse bc89dd93a62e673f17beaf79fc308801f2548cc0804b6e7e7211db7d71dcacee61d4db4b cc4c192da6ec1c558421396b4eb1944f656db0dda1626374294528747cd1ee8e10b15c5c 60b4182960a4687e44c92cff1b5d29a6b48ab8be9f8115c642241a4901d75a2b2ba55d27 0620b884f37689503d9c3a603e89a1f7de7447e2b23145af7219c13aad065fe60313c4f1 7d1959166b8493e26ee828d6e76ac472747b40432571d2d101dd3e8696849eb59b70c328 a0d1978eea220593cb3024a3cdecb89dcfa2d5ab3990b0bbc1a0c3351bfbd614917e7ede ef79cb8843325e4a81a80e809250ce8cf7297b5c684b53a56538b373cb085ec7436f82a2 e48b4789de5ac368defd97ca81e1e7a584b7e40bcf852c3d4f6cc387172784295be04ca2 0793987d64efc3cec658553cbe610fa9ebfe74341192cfcc6ecfd0a4843b740cbfd5ba5f 4c076050268792190676f76cacc26be628f8ae1c48419803c2a5108f6b1bec6664b06248 6a083d8092cb3c82b90bded3eed0387490fe971d6614c5d0259a846d43abb22e0dc06aa5 6911c9f53cf5524e138662db3fa2e6cdfe30873d916ed70e4962ed78b32491bee9a20a36 8be439dc6245d5751e6899e2214c07df7a87b66b1aba9a8196db2add3d3c4e3057dc9a9c dae1cc7884a6f29a5568b1ad64143fd479b8b4a8fbef4db889fe42edaadef0276f79d192 245b64299ad347b03ecf887db96b16fc319a1c7e59718ac7ff7bc7bafd4523bd88fd5ba8 1730817c2f529d3060cb591fe565d778fc989e7e14f7c2a7b85785c53af35fbe738da838 cdf80c9a048f4d7dbd58e2c9f527d2d3b2ad633da1005036298ec8533b94f84e9246289c f03336f4a7f657afbcbdd7b5e16187273c459f5626a5667db4fbf8b85ef2363ee6d89bd0 f402408cae3065fecf609fa290047e9656d853739f33b06d64a4a57f66f37f7da39fa89d 28962fddb76e8d05683c090664175dda6a1be57698894fd9f0f9d8da411b3f33b3b9c8d4 50a27c37e4a0e503418cd6c02cf60fa7fbb6f6f3e7509a45a54343ba3361168d895a27eb 6923ab65b019b188fe21c804629f2be2a20e6417841b4c8d5d68fb38db71ac7174e68d03 0611ea29f9ca740d0aef611a1f0003e1d136a539ed28d956a2a36bc7ae0ee290bd818175 3537e39be7777de1004964c769ec7e933b17c852cbd2da4cc100d9d3e141106eea9cc29a b1c910ead768527a02711ac035262c93a4548f67fb501a971e0a86d819547bac7c09f5fb aec454c9c7276f5e317cc8fd8876e7f90dc128f03052a756cf6db9876fe5a31c9d6a139b d46eb34272ff7992b86c88420ab07e801a39e91afb3c048b40913dc2d984e0c347b3daea 4e1ce5a15c8df7b65a0b89136f6a48a92b8f096d708a2bea4390f0454dcc3d9cd4f6b24d 8f06faa17694172213c481ceaa1f7fe33f1389142f017874560e1b0272385585fc5681de 4a909566cdcf9af80dfde23e9ad55083bb9422ae57b99bf3d5f081a4cbe0172f236abbb5 06fbbee46987543fc545e81ecd61477fadec55640ce9e41f8cbcd409f0e64c1b83193885 dffe0c4c383de781943a2a73ad1e0cbee0dccdbc3bbbc010f3adc8aa597210cae47003d2 952b8e874e1dee33ef1a78180a3ef6b22e1a66385147f550678510b15ed1a02fc85e736e 818f03b188d6a23f070e5720195a8e4c295d27129a5adedc1a95145d5e758649acebaec5 3d14cbc9feaf3abcecc976c03d00ea640c3b852baad7d8ab28c593cb74cbe2e98ea0b35c 8827eb3def1a79af837fb8468b2042acaf226b1f6d11abab2884f3fe49772325d273f893 82badc7b3b26e43c3f6170eec2c607cbe22225b9469de5509d31bafa1729c416089aeb1b 3b5477a985acdce47557bf29130d6232d2003a4314bf46c9c9383c437f1f2597f361405a b92f371458f13d8d400d78140df094a559bec9d240993f2d811f0d4eba7678773bb6c765 caf33bc77c0e2e156538b04423e513cb933d9ac8cec0444e0309bdb5c70f02a71f49cc99 7b8d98ecbaad1d53daa2811b07df94b2ec574326d760892fd1886703eed816bf2db96bbe f2ea914cef918d251a1203d93d549aa438a1309ce179c233111175d9e8bb6064dc2d52db 0976650b1d5d194eab20ed3e500db4410852390e69e56e4ab71e97a87680fa620d8d32d5 b93e40cdec16ed20af734e792ddb938b8a65ccb811f369cc1e9e8819e76d7908e310e5ea 018c05d2db74abc0e8e5da75431324a3ba298820009d6fcc9d5693ec900aab8745112928 ef24a8da713dc8ecebb84394f0058335dafb459971cf20e8c15d40f35643a0c56c95bd86 faefe8e251fb9f79a6db5e481032f812454181a73375ab1efe575d745fe7073adaf60865 e992c7f5e969f4e267b323bb022a7f8b1b480a97ca735212b4d47aff196f37fa177c765a f03487b323f2ce11314906d04dcb0c3c770ea581fcff70cc1553b4615a6d8dfd69001581 77a9fcc035cb44d630b99cdae09de33c09c9ab8bcc021e72fd88cccf3a9cd578a34a3f96 ae636047fc5f468d22cea0cf509e1588563c7e25d4f0d41b30373dfd1cb69a8e37a51a57 5d1cab7a3c9d04f3d388db04ed78d3e81e7b53dffa94507df197e467565d4169fc996e46 671f62236b00f4e9dc36bd3709400771ed4b335bcdb3c2974c0a00c03717ed980e98dc1b 2473f38bd1e1fe4da0fea5169aa1e06054315579a5898bbe3c9fabb829485562e9d25248 142575f3bfd311dde2297c7883b0b9ed0c3ffe3358880c8c77be01cd6408dc743634006f d888ffc1e4562ed1166bbdcbe971a269afae52a8a384eaf8880433a053bd072accc62214 04bb18e98b9cebb3c05e56216b56174bd432e41b8c82c82d7114adb16ad941fe87c0657e 03203fc26ed43096e7e262a8f86fc07506b3ffcb5888bcbd3482977716a337a54c0649c1 2579b4322afcb34486a5593fb9d58cb16a0368f593c3c52608bf31c6a3b48a04be605c60 b15ea2670c3e89d293ba065db7d5471d3f56d7ffe3ba48814d5a1f4a81d9865d1f2340cc 3e5ced23ce6827065312bb9ae13e0d3cc53e79aaa764a229be203d1b45963d17e983f72a f97bac50984a360768f459585745d94f7b77457bb8bc802332aef4e65ae7200d94750aea b4ede71ade6ee000cf122866f514747784f7e497a6e48b82467515f474d38ec690bac331 d8246eacf2b10d7f1b1b74b1020843b3d934115e23fc1845e5161f5d494badc22f5e68fa 4d1cb3933ac6467e3cc58099adcf4832c156ce1714ee44c6368dee76483e47260dda3af1 97f938530475ede86f1b7ccfeeaeab2518f1c05ba983ada09c069d0f5e7e34c7832ec4c1 9e68e78a51e25540cadf7b64d1eca1141816aba211cea9b8aa4ff9542f26cd6adabe28bc 03c20d2fded392cc160e5ca6f8216611e41b504567927a560537a57e09dd8db552fab25d 59318ad3f7e6b6e10ad49fbb4caf8d5205d494666f5c51a599df65d2c89fe65c92ec733d 78205e987659e02d244684cff18d2b6f1d0d33ccae32339b840246a50cccebc952c7e705 d30fcb5dc94da2eab7ba3c7f9fe536eba4971a8b8e0744a0a094d531ae611042c347fac7 3b770c445121464594a2c5eb9d923f0fe2f33500b403e4b5daf64acd4a4a89d8469be57f a393a844e082dec5af117b77e7be0eb6474eb47b00503bc68c809f0de147f7d0f1f68798 89b1781d09c0dc12c882dba17e23de1311321fa851a94c51a8801a4bf7c888e4805b1fc8 2fe638aaabb33b13ab0ae024b0b767108a068d562ebd11a91ad8706df9360a914927b752 ddb4d176f72661d12a6349a58a8d688b311ec8e1797b011dbb47760765b88a651b42cace e60730553040e64711fff10e3285171ed1dae0545b6cfe3503b24f9d135d04d467372b11 ef3c1b9aa7c4272e281df0b6e7cc7e7984b00cbda5bbd81c939213c32176b5e062660e54 8943afe1e39a38cb171d7591c01ac4eea3963572ce008d48727ec8efc0ead1cc4c86d9ce 3d9d5c21f58a41359f2599d4cb15762366c3d3c5b7abe7970a312ea2fb14f5e74f78284a 624fe71f362f4b4d892ac6a87cf8794982964aa0e6153477da1484d35787edb8a2aad90b 3cada91934c118098617e1254d834d86154e6585628663741ae0d7bf339b168d4acec9da 94c12bd5449ecf97a7483e27c47160f838ac076f79b82fc0bd8a3b0011bd0bbb2e6a38ff a7a63daf463cacb10f56c459bec699ecbcc52be2e5c57bd013c4682b01199cdd89ad2bd1 8584b05e6178c2d6fdc6e19a375ae4a91428d4c0aff2d07e5b6d159351475e57419f2ec8 a343d209e36ddb078027e03d4f179fbf675373c485be1a147ffda00821aba79187471ef9 55f197d6bf0f442244d5b4d1e8392ba11965b6bfa8db30c0e48984883a9b6ec840a9b6fc 93df40c82906dac253e0afd633c336cedac8dd7213e4766761ec3cf3a8aacb1fe1bf2d61 d64c5addaf1d836e199df0ef5e61029f1e6a28c17eba0d8bdf81f358058086ee365b4127 a1bb4b273b84a825fdcc4ebd3abdd7ca243788e1eb48aed96626bd2f2ef8a2e1a082acb6 64b5af60797d9ad021ac616e4d65c1ddbc4a74928b7ab089a10db9312a18d682cccce0b5 53e2f454af0ca21f59b96ee7d71a97db2607dba56daad1bef91c66c44f6fc53d2b4bfebb 876cd478243a9454e8864f65067787b96cb4b3f92a7c90f959ce3324c94590348a8d2709 f4feea7adaf4c56199da203d8f4b9866fe7362d86401b0cfe1913476eb9f7f4d4df0f2f3 8e7ee153c99dda1ccc6eec2cd1b76c52c553ceca04ad525fc17a4a7af197d158c02e6469 cd7e3be4b934ed0e1499153bb98b4363159a60c9ce892af085511cfc31cfa7fa1baf0e22 d138b6a54e93532486b633024d18afd6a610ede93b2a554abc44da890144ff060d1db1e3 e57df15229afe56c49e3c7f68e6ef0221942945f3c6675b498e94fd834bfcd869bba0a90 179d3eb859ea6b749871a62c0e8513ab69b63e35b5bf8060f25442a6670293cee9a86928 997a54929695b3eda64483ecdf8cfb2732729a652e08a3aa82ecb5ac45aad7227f7f7ee9 1d8c222933cfac18561f27939ca29fbf5eebd634555856519cd2f1573281514aff3c6091 5142196c57177ef2086958fbb3fae8f448118c435ae82b7b17a8445e0806b8442e1f9347 c7940af7342dc3d5638958f9a3952768f6c244920e281a163cc87fbdbec99080b8d7e24b 9e35e152aa600a6a4faebb140857e536bb819f4cd9992b9dfaa60ac33a8ff2ed14c791e7 0290e5f6d810488d672224bfeeca6907b41f46489091322b6830a8424fa2a0061151ee61 ef1cfb1a83c4538025605554ed3c734fd8e39bd6da4af6e5a57593da83fd9f511af49b84 5ef7cb34495b54070ea204daff2e266f5a1619928e73de256979f4afdeb42b889064461b f7263f82a2c233d113de9ba4bc415ed68241bc3862a34050479aa86eabb80cef561ad640 80be73a5da7fbb4905bee2fbbbc7c85a5512c6e747a5eb18942e47c17e5da1127910d8e6 ed7a37d3b846cfda6b0adc8dd594ffe14995b32babcb4d99869090abd57e8ab397e33406 2c7790b673d184738a9e9d578f54ccfcdcc46200d2bb07c5dea46261680dccb4f011428f 289c2049ff81040685aec9ae8c9016c491d02f14f2c4fd79e053147520d59d034c470569 e602c662af4aafc5d2fb0d3af218b26b769ac25fe9999ba3c2eaa8a9ffa93a6f4b743608 f5797772e53cfd2f3c6a45b1a843fcfc6aedc66bc35db923bea051301fa5a959a11eb0b6 f02f7c4e6b004ce548b77e032e36f93cce55f507d5892b32da81a7ce5016326aacd06dd5 0a1b3c615abf06ab6eb1bd643f3c3d7fbc9e18bc11ee29b2113d5c458f20713d3b811da8 883f8b95557ffb1eaf229b89fc98f7623ff9140bcebc6b8677ad7d99373e5757292a3d6a 83a5c053e61224b4dc14e42626637e714c514092e569101ce75f0533605802455f03bf0e 336c0f9788569f3b2b4b79c01628abc3b243decb3c55e1273ff7b83ae61d936bd413580f 3f279437da1fdad63d785ff7bedd815a6d6e4964231adf28640794c33a30686e5f60fe78 c5e87ffd27a84452dc111bbd7c2d0b4e7781c102547f5533ea676a33b8d58918f197a8cd a1e90be9620e43af9d5b07ee2ae5d702683c9a6973fdaafaec74d62cb29b18272b3f8840 a1a8372ddf4bfee1b7ea037ed41fdc2cb1cb4da3ccb3e121354db0d5bc83c4d4c323083d 75dd32c20607f81fcd221751c5af21775659e804b9941cf6fbe4c8846be20e546f88a588 7bbff8cab4489883fdd2be613313174c015d69eee40eee4242e173aaac87585597feff69 a64f4ef2dbf00dbfe9ad946892816711c7199d4068d8494ba1df614d9bbe1c7b63996e98 12b913966a42a41be0dc85feff232e625f4dd0b01cb7674b232e89d5da143f9d12a9d8a9 aa8b62038721ad9e4a6438cb842d1828458fc25e5b0b6ea795f7a14d2f55f1451c615f4c 211469611d1348952e655e1d93188c0dc6dd719630a42fe5baf8cde0c03b1e0aa76a2cd4 fec86a3042f8a2ea5af50a43af52c1217f6be45b152e47d165b89a54ede432f1eb3ed3ef 428c228dd53c44db15541704b99413b465ff65ca0e9d6be932a18eca713c71ba7dc89238 1e0c2c62cf8567df2f997e58ed2c1ffe17d2fc96db942ce3950e28d1287b85ff7d07adb9 059629dc89b9b0ed2213e45d8a20188cae18f3391887387bf8ba0a12fe21fa0aa521bfa3 718f7abe76388e 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %ADOendeexec %%EndFile %%BeginFile: adobe_psp_uniform_graphics %%Copyright: Copyright 1990-1993 Adobe Systems Incorporated. All Rights Reserved. /@a { np :M 0 rl :L 0 exch rl 0 rl :L fill }bd /@b { np :M 0 rl 0 exch rl :L 0 rl 0 exch rl fill }bd /arct where { pop }{ /arct { arcto pop pop pop pop }bd }ifelse /x1 Z /x2 Z /y1 Z /y2 Z /rad Z /@q { /rad xs /y2 xs /x2 xs /y1 xs /x1 xs np x2 x1 add 2 div y1 :M x2 y1 x2 y2 rad arct x2 y2 x1 y2 rad arct x1 y2 x1 y1 rad arct x1 y1 x2 y1 rad arct fill }bd /@s { /rad xs /y2 xs /x2 xs /y1 xs /x1 xs np x2 x1 add 2 div y1 :M x2 y1 x2 y2 rad arct x2 y2 x1 y2 rad arct x1 y2 x1 y1 rad arct x1 y1 x2 y1 rad arct :K stroke }bd /@i { np 0 360 arc fill }bd /@j { gS np :T scale 0 0 .5 0 360 arc fill gR }bd /@e { np 0 360 arc :K stroke }bd /@f { np $m currentmatrix pop :T scale 0 0 .5 0 360 arc :K $m setmatrix stroke }bd /@k { gS np :T 0 0 :M 0 0 5 2 roll arc fill gR }bd /@l { gS np :T 0 0 :M scale 0 0 .5 5 -2 roll arc fill gR }bd /@m { np arc stroke }bd /@n { np $m currentmatrix pop :T scale 0 0 .5 5 -2 roll arc $m setmatrix stroke }bd %%EndFile %%BeginFile: adobe_psp_customps %%Copyright: Copyright 1990-1993 Adobe Systems Incorporated. All Rights Reserved. /$t Z /$p Z /$s Z /$o 1. def /2state? false def /ps Z level2 startnoload /pushcolor/currentrgbcolor ld /popcolor/setrgbcolor ld /setcmykcolor where { pop/currentcmykcolor where { pop/pushcolor/currentcmykcolor ld /popcolor/setcmykcolor ld }if }if level2 endnoload level2 not startnoload /pushcolor { currentcolorspace $c eq { currentcolor currentcolorspace true }{ currentcmykcolor false }ifelse }bd /popcolor { { setcolorspace setcolor }{ setcmykcolor }ifelse }bd level2 not endnoload /pushstatic { ps 2state? $o $t $p $s }bd /popstatic { /$s xs /$p xs /$t xs /$o xs /2state? xs /ps xs }bd /pushgstate { save errordict/nocurrentpoint{pop 0 0}put currentpoint 3 -1 roll restore pushcolor currentlinewidth currentlinecap currentlinejoin currentdash exch aload length np clippath pathbbox $m currentmatrix aload pop }bd /popgstate { $m astore setmatrix 2 index sub exch 3 index sub exch rC array astore exch setdash setlinejoin setlinecap lw popcolor np :M }bd /bu { pushgstate gR pushgstate 2state? { gR pushgstate }if pushstatic pm restore mT concat }bd /bn { /pm save store popstatic popgstate gS popgstate 2state? { gS popgstate }if }bd /cpat{pop 64 div G 8{pop}repeat}bd %%EndFile %%BeginFile: adobe_psp_basic_text %%Copyright: Copyright 1990-1993 Adobe Systems Incorporated. All Rights Reserved. /S/show ld /A{ 0.0 exch ashow }bd /R{ 0.0 exch 32 exch widthshow }bd /W{ 0.0 3 1 roll widthshow }bd /J{ 0.0 32 4 2 roll 0.0 exch awidthshow }bd /V{ 0.0 4 1 roll 0.0 exch awidthshow }bd /fcflg true def /fc{ fcflg{ vmstatus exch sub 50000 lt{ (%%[ Warning: Running out of memory ]%%\r)print flush/fcflg false store }if pop }if }bd /$f[1 0 0 -1 0 0]def /:ff{$f :mf}bd /MacEncoding StandardEncoding 256 array copy def MacEncoding 39/quotesingle put MacEncoding 96/grave put /Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute /agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute/egrave /ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde/oacute /ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis /dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/notequal/AE/Oslash /infinity/plusminus/lessequal/greaterequal/yen/mu/partialdiff/summation /product/pi/integral/ordfeminine/ordmasculine/Omega/ae/oslash /questiondown/exclamdown/logicalnot/radical/florin/approxequal/Delta/guillemotleft /guillemotright/ellipsis/space/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide/lozenge /ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright/fi/fl /daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex/Idieresis/Igrave /Oacute/Ocircumflex/apple/Ograve/Uacute/Ucircumflex/Ugrave/dotlessi/circumflex/tilde /macron/breve/dotaccent/ring/cedilla/hungarumlaut/ogonek/caron MacEncoding 128 128 getinterval astore pop level2 startnoload /copyfontdict { findfont dup length dict begin { 1 index/FID ne{def}{pop pop}ifelse }forall }bd level2 endnoload level2 not startnoload /copyfontdict { findfont dup length dict copy begin }bd level2 not endnoload md/fontname known not{ /fontname/customfont def }if /Encoding Z /:mre { copyfontdict /Encoding MacEncoding def fontname currentdict end definefont :ff def }bd /:bsr { copyfontdict /Encoding Encoding 256 array copy def Encoding dup }bd /pd{put dup}bd /:esr { pop pop fontname currentdict end definefont :ff def }bd /scf { scalefont def }bd /scf-non { $m scale :mf setfont }bd /ps Z /fz{/ps xs}bd /sf/setfont ld /cF/currentfont ld /mbf { /makeblendedfont where { pop makeblendedfont /ABlend exch definefont }{ pop }ifelse def }def %%EndFile /currentpacking where {pop sc_oldpacking setpacking}if end %%EndProlog %%BeginSetup md begin countdictstack[{ %%BeginFeature: *PageSize Letter statusdict /lettertray get exec %%EndFeature }featurecleanup (Raffaele Esposito)setjob /mT[1 0 0 -1 14 780]def /sD 16 dict def 300 level2{1 dict dup/WaitTimeout 4 -1 roll put setuserparams}{statusdict/waittimeout 3 -1 roll put}ifelse %%IncludeFont: CMBX10 %%IncludeFont: CMR10 %%IncludeFont: CMR7 %%IncludeFont: CMBX8 %%IncludeFont: CMR8 %%IncludeFont: CMMI8 %%IncludeFont: CMSY8 %%IncludeFont: CMMI6 %%IncludeFont: CMR6 %%IncludeFont: CMSY6 %%IncludeFont: CMMI10 %%IncludeFont: CMMI7 %%IncludeFont: CMSY10 %%IncludeFont: CMEX10 %%IncludeFont: CMSY7 %%IncludeFont: CMMI5 %%IncludeFont: CMR5 %%IncludeFont: CMTI10 %%IncludeFont: CMSY5 %%IncludeFont: Helvetica %%IncludeFont: CMSL10 /f0_1/CMBX10 :bsr 32/space pd :esr /f0_12 f0_1 12 scf /f1_1/CMR10 :bsr 32/space pd 160/suppress pd :esr /f1_12 f1_1 12 scf /f2_1/CMR7 :bsr 32/space pd :esr /f2_12 f2_1 12 scf /f3_1/CMBX8 :bsr 32/space pd :esr /f3_12 f3_1 12 scf /f4_1/CMR8 :bsr 32/space pd :esr /f4_12 f4_1 12 scf /f5_1/CMMI8 :bsr 32/space pd :esr /f5_12 f5_1 12 scf /f6_1/CMSY8 :bsr 32/space pd :esr /f6_12 f6_1 12 scf /f7_1/CMMI6 :bsr 32/space pd :esr /f7_12 f7_1 12 scf /f8_1/CMR6 :bsr 32/space pd :esr /f8_12 f8_1 12 scf /f9_1/CMSY6 :bsr 32/space pd :esr /f9_12 f9_1 12 scf /f10_1/CMMI10 :bsr 32/space pd :esr /f10_12 f10_1 12 scf /f11_1/CMMI7 :bsr 32/space pd :esr /f11_12 f11_1 12 scf /f12_1/CMSY10 :bsr 32/space pd :esr /f12_12 f12_1 12 scf /f13_1/CMEX10 :bsr 32/space pd :esr /f13_12 f13_1 12 scf /f14_1/CMSY7 :bsr 32/space pd :esr /f14_12 f14_1 12 scf /f15_1/CMMI5 :bsr 32/space pd :esr /f15_12 f15_1 12 scf /f16_1/CMR5 :bsr 32/space pd :esr /f16_12 f16_1 12 scf /f17_1/CMTI10 :bsr 32/space pd :esr /f17_12 f17_1 12 scf /f18_1/CMSY5 :bsr 32/space pd :esr /f18_12 f18_1 12 scf /f19_1/Helvetica :mre /f19_12 f19_1 12 scf /f20_1 f19_1 1.04 scf /f20_18 f20_1 18 scf /f20_14 f20_1 14 scf /f20_9 f20_1 9 scf /f21_1/CMSL10 :bsr 32/space pd :esr /f21_12 f21_1 12 scf /Courier findfont[10 0 0 -10 0 0]:mf setfont /TeXdict 50 dict def TeXdict begin /invert matrix def 0 1 255 {1 string dup 0 4 -1 roll put cvn} bind for 256 array astore /AbsoluteEncoding exch def /bd {bind def}bind def /y{0 exch moveto}bd /s{exch currentpoint exch pop moveto show}bd /f{fonts exch get setfont}bd /pr{.25 add round .25 sub exch}bd /p{transform pr pr itransform}bd /r{newpath p moveto 1 index 0 rlineto 0 exch neg rlineto neg 0 rlineto closepath fill}bd /mul2{dup 4 -1 roll mul 3 1 roll mul}bd /sps{/state save def translate 72.27 72 div mul2 neg scale newpath userdict begin /showpage{}def}bd /eps{state restore}bd /fdef{exch 0 0 2 index neg 0 0 invert astore makefont fonts 3 1 roll put}bd /fdict{9 dict dup begin /FontType 3 def /FontMatrix [72.27 5 index div 0 0 2 index 0 0] def /FontBBox [-20 -20 100 100] def /CharDefs 256 array def /Encoding AbsoluteEncoding def /CharTx matrix def /BuildChar{exch begin CharDefs exch get dup null eq {pop}{DoCh} ifelse end} def end definefont pop pop}bd /.e {exch dup length dict exch {1 index /FID ne {3 copy put} if pop pop} forall exch 1 index /Encoding get 256 array copy exch 0 exch {dup type /nametype eq{3 copy put pop 1 add}{exch pop}ifelse}forall pop 1 index exch /Encoding exch put /encodefont exch definefont} bd /.c {[exch 0 0 1 0 0] makefont}bd /.s {[1 0 4 -1 roll 1 0 0] makefont}bd /.o {/old exch def old length 2 add dict /FontDef exch def old {exch dup /FID ne {exch FontDef 3 1 roll put} {pop pop}ifelse}forall FontDef dup /PaintType 2 put /StrokeWidth 20 put /testfont FontDef definefont}bd /.t {1 index setfont 1.0 sub ( ) stringwidth pop mul exch dup length 2 add dict dup /Metrics 3 index /CharStrings get length dict dup 4 1 roll put 3 -1 roll { 1 index /FID ne { 3 index 3 1 roll put } { pop pop } ifelse } forall 1 index /Encoding get 0 1 255 { 1 index 1 index get dup /.notdef ne { exch 1 string dup 0 4 -1 roll put stringwidth pop 5 index add 1000 mul 3 index 3 1 roll put } { pop pop } ifelse } for pop pop exch pop /trackfont exch definefont}bd /DoCh{dup 0 get 0 2 index 1 4 getinterval aload pop setcachedevice dup dup 5 get exch 6 get true CharTx dup dup 6 index 7 get 4 exch put 5 index 8 get 5 exch put 4 index 9 get imagemask pop}bd /setcmykcolor where {pop} { /setcmykcolor {exch .11 mul add exch .59 mul add exch .30 mul add 1 exch sub setgray} bind def /currentcmykcolor {0 0 0 1 currentgray sub} def } ifelse /setcustomcolor where {pop} { /findcmykcustomcolor {5 packedarray} def /setoverprint {pop} def /setcustomcolor {exch aload pop pop 4 { 4 index mul 4 1 roll} repeat 5 -1 roll pop setcmykcolor} def } ifelse /do-bop{/bop-hook where{pop gsave initmatrix bop-hook grestore}if}def /do-end{/end-hook where{pop gsave initmatrix end-hook grestore}if}def /resolution 72.27 def /fonts 23 array def 60 1200 1000 div mul 5 mul /msbm5-393216 fdict 60 1200 1000 div mul 10 mul /msbm10-786432 fdict 60 1200 1000 div mul 7 mul /msbm7-550502 fdict 19 5 1200 1000 div mul /msbm5-393216 findfont fdef 20 10 1200 1000 div mul /msbm10-786432 findfont fdef 21 7 1200 1000 div mul /msbm7-550502 findfont fdef end %%EndSetup %%Page: 1 1 %%BeginPageSetup initializepage (Raffaele Esposito; page: 1 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f0_12 sf ( )S -996 -1000 :M f1_12 sf ( )S -993 -1000 :M f2_12 sf ( )S -989 -1000 :M f3_12 sf ( )S -985 -1000 :M f4_12 sf ( )S -981 -1000 :M f5_12 sf ( )S -973 -1000 :M f6_12 sf ( )S -960 -1000 :M f7_12 sf ( )S -950 -1000 :M f8_12 sf ( )S f9_12 sf ( )S f10_12 sf ( )S -924 -1000 :M f11_12 sf ( )S -915 -1000 :M f12_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 1200 1000 div mul /CMBX10 findfont fdef 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 3 8 1200 1000 div mul /CMBX8 findfont fdef 4 8 1200 1000 div mul /CMR8 findfont fdef 5 8 1200 1000 div mul /CMMI8 findfont fdef 6 8 1200 1000 div mul /CMSY8 findfont fdef 7 6 1200 1000 div mul /CMMI6 findfont fdef 8 6 1200 1000 div mul /CMR6 findfont fdef 9 6 1200 1000 div mul /CMSY6 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 58 60 translate 72 72.27 div dup scale 0 f 24.404 y -6.994 (Phase)s 33.183 (segregation)s 105.834 (dynamics)s 166.669 (for)s 188.069 (the)s 212.027 (Blume-Cap)s 280.493 (el)s 295.251 (mo)s 314.035 (del)s 336.459 (with)s 367.893 (Kac)s 396.151 (in)s 407.267 (teraction.)s 1 f 69.657 y 136.183 (R.)s 152.35 (Marra)s 2 f 65.302 y 188.75 (1)s 1 f 69.657 y 204.962 (and)s 235.124 (M.)s 253.457 (Mourragui)s 2 f 65.302 y 312.524 (2)s 3 f 166.977 y 42.11 (Abstract:)s 4 f 104.816 (W)s 114.44 (e)s 121.834 (consider)s 161.027 (the)s 178.054 (Glaub)s 205.606 (er)s 216.976 (and)s 236.27 (Ka)s 249.01 (w)s 256.093 (asaki)s 281.394 (dynamics)s 325.962 (for)s 341.015 (the)s 358.042 (Blume-Cap)s 408.613 (el)s 177.777 y 42.11 (spin)s 62.798 (mo)s 76.682 (del)s 92.213 (with)s 114.545 (w)s 121.629 (eak)s 139.143 (long)s 160.342 (range)s 187.215 (in)s 195.432 (teraction)s 237.605 (on)s 250.87 (the)s 267.535 (in\257nite)s 301.2 (lattice:)s 335.883 (a)s 343.481 (ferromagnetic)s 406.913 (d-)s 188.577 y 42.11 (dimensional)s 97.149 (lattice)s 127.197 (system)s 159.909 (with)s 182.024 (the)s 198.473 (spin)s 218.944 (v)s 223.761 (ariable)s 5 f 256.084 (\276)s 4 f 264.539 (taking)s 294.871 (v)s 299.688 (alues)s 324.126 (in)s 6 f 334.908 (f\241)s 4 f 347.941 (1)s 5 f 353.041 (;)s 4 f 357.575 (0)s 5 f 362.675 (;)s 4 f 367.208 (1)s 6 f 372.308 (g)s 4 f 379.69 (and)s 398.405 (pair)s 199.377 y 42.11 (Kac)s 63.568 (p)s 69.518 (oten)s 88.502 (tial)s 5 f 107.136 (\260)s 7 f 195.989 y 112.957 (d)s 5 f 199.377 y 118.182 (J)s 4 f 124.656 (\050)s 5 f 128.623 (\260)s 4 f 134.443 (\050)s 6 f 138.41 (j)s 5 f 141.243 (i)s 6 f 147.316 (\241)s 5 f 157.851 (j)s 6 f 162.529 (j)s 4 f 165.362 (\051\051)s 5 f 173.296 (;)s 177.829 (\260)s 187.318 (\076)s 4 f 198.919 (0)s 5 f 204.02 (;)s 208.553 (i;)s 216.559 (j)s 6 f 224.906 (2)s 5 f 235.374 (Z)s 237.864 (Z)s 7 f 195.989 y 247.154 (d)s 4 f 199.377 y 252.38 (.)s 261.25 (The)s 282.718 (Ka)s 295.458 (w)s 302.541 (asaki)s 328.883 (dynamics)s 374.491 (conserv)s 407.423 (es)s 210.177 y 42.11 (the)s 60.262 (empirical)s 105.056 (a)s 109.873 (v)s 114.973 (erages)s 146.224 (of)s 5 f 158.426 (\276)s 4 f 168.584 (and)s 5 f 189.003 (\276)s 8 f 206.789 y 195.176 (2)s 4 f 210.177 y 204.161 (corresp)s 236.252 (onding)s 270.271 (to)s 283.323 (lo)s 291.539 (cal)s 307.991 (magnetization)s 374.877 (and)s 395.296 (lo)s 403.513 (cal)s 220.977 y 42.11 (concen)s 71.861 (tration.)s 109.795 (W)s 119.419 (e)s 127.229 (study)s 155.212 (the)s 172.656 (b)s 178.606 (eha)s 193.623 (viour)s 219.858 (of)s 231.352 (the)s 248.796 (system)s 282.503 (under)s 311.288 (the)s 328.732 (Ka)s 341.472 (w)s 348.555 (asaki)s 374.273 (dynamics)s 231.777 y 42.11 (on)s 56.584 (the)s 74.458 (spatial)s 107.69 (scale)s 5 f 132.421 (\260)s 9 f 228.389 y 138.241 (\241)s 8 f 145.174 (1)s 4 f 231.777 y 153.881 (and)s 174.022 (time)s 197.563 (scale)s 5 f 222.294 (\260)s 9 f 228.389 y 228.114 (\241)s 8 f 235.048 (2)s 4 f 231.777 y 240.048 (.)s 248.336 (W)s 257.96 (e)s 266.2 (pro)s 280.659 (v)s 285.759 (e)s 294 (that)s 316.407 (the)s 334.281 (empirical)s 378.798 (a)s 383.614 (v)s 388.714 (erages)s 242.577 y 42.11 (con)s 57.127 (v)s 62.227 (erge)s 84 (in)s 96.131 (the)s 113.928 (limit)s 5 f 138.526 (\260)s 6 f 147.565 (!)s 4 f 160.983 (0)s 169.714 (to)s 182.411 (the)s 200.209 (solutions)s 243.053 (of)s 254.901 (t)s 258.584 (w)s 265.668 (o)s 274.399 (coupled)s 312.03 (equations,)s 360.826 (whic)s 380.943 (h)s 390.24 (are)s 407.48 (in)s 253.377 y 42.11 (the)s 60.16 (form)s 84.735 (of)s 96.834 (the)s 114.884 (\260)s 120.551 (ux)s 135.484 (gradien)s 168.076 (t)s 175.926 (for)s 192 (the)s 210.05 (energy)s 243.125 (functional.)s 296.424 (In)s 309.647 (the)s 327.697 (case)s 349.77 (of)s 361.87 (the)s 379.919 (Glaub)s 407.471 (er)s 264.177 y 42.11 (dynamics)s 88.153 (w)s 95.237 (e)s 104.106 (still)s 124.931 (scale)s 150.291 (the)s 168.793 (space)s 196.986 (as)s 5 f 210.445 (\260)s 9 f 260.789 y 216.265 (\241)s 8 f 223.199 (1)s 4 f 264.177 y 232.534 (but)s 252.17 (lo)s 260.387 (ok)s 275.206 (at)s 288.608 (\257nite)s 315.611 (time)s 339.78 (and)s 360.55 (pro)s 375.008 (v)s 380.108 (e)s 388.977 (in)s 401.813 (the)s 274.977 y 42.11 (limit)s 67.158 (of)s 79.456 (v)s 84.273 (anishing)s 5 f 125.245 (\260)s 4 f 135.146 (the)s 153.394 (la)s 161.044 (w)s 172.492 (of)s 184.79 (large)s 210.413 (n)s 215.797 (um)s 229.68 (b)s 235.63 (er)s 248.22 (for)s 264.493 (the)s 282.741 (empirical)s 327.631 (\257elds.)s 359.765 (The)s 381.413 (limiting)s 285.777 y 42.11 (\257elds)s 69.168 (are)s 87.111 (solutions)s 130.659 (of)s 143.21 (t)s 146.893 (w)s 153.977 (o)s 163.411 (coupled)s 201.745 (nonlo)s 226.396 (cal)s 243.197 (equations.)s 295.64 (Finally)s 326.094 (,)s 333.495 (w)s 340.578 (e)s 349.446 (consider)s 390.112 (a)s 399.546 (non)s 296.577 y 42.11 (gradien)s 74.702 (t)s 82.036 (dynamics)s 127.11 (whic)s 147.227 (h)s 156.261 (conserv)s 189.193 (es)s 201.117 (only)s 223.467 (the)s 241.001 (magnetization)s 307.269 (and)s 327.07 (get)s 344.037 (a)s 352.504 (h)s 357.887 (ydro)s 378.296 (dynamic)s 307.377 y 42.11 (equation)s 84.169 (for)s 100.168 (it)s 110.776 (in)s 123.084 (the)s 141.059 (di\256usiv)s 173.133 (e)s 181.474 (limit)s 206.249 (whic)s 226.366 (h)s 235.841 (is)s 246.506 (again)s 274.114 (in)s 286.422 (the)s 304.397 (form)s 328.897 (of)s 340.921 (the)s 358.896 (\260)s 364.563 (ux)s 379.421 (gradien)s 412.013 (t)s 318.177 y 42.11 (for)s 57.702 (a)s 66.202 (suitable)s 104.226 (energy)s 136.818 (functional.)s 1 f 363.897 y 8.71 (Key)s 33.71 (W)s 45.043 (ords:)s 75.81 (In)s 86.477 (teracting)s 137.177 (particle)s 180.543 (and)s 203.877 (spin)s 229.277 (systems;)s 277.144 (Kac)s 301.81 (p)s 308.81 (oten)s 331.144 (tial;)s 355.81 (h)s 362.144 (ydro)s 386.177 (dynamic)s 380.817 y 8.71 (limits;)s 45.443 (phase)s 78.843 (segregation.)s 0 f 426.189 y -5.69 (1.)s 11.176 (In)s 23.693 (tro)s 42.026 (duction.)s 1 f 450.309 y 8.71 (W)s 20.043 (e)s 30.81 (consider)s 79.01 (particle)s 123.811 (mo)s 140.144 (dels)s 165.644 (whic)s 189.311 (h)s 201.411 (are)s 222.878 (dynamical)s 281.979 (v)s 287.979 (ersions)s 328.912 (of)s 344.013 (lattice)s 382.113 (gases)s 414.347 (with)s 443.113 (Kac)s 467.109 y -5.69 (p)s 1.31 (oten)s 23.643 (tials.)s 58.588 (The)s 84.658 (Kac)s 110.729 (p)s 117.729 (oten)s 140.062 (tials)s 167.533 (are)s 188.97 (functions)s 10 f 242.107 (J)s 11 f 468.909 y 248.761 (\260)s 1 f 467.109 y 254.919 (\050)s 10 f 259.585 (r)s 1 f 265.333 (\051)s 10 f 269.999 (;)s 275.333 (r)s 12 f 286.753 (2)s 1 f 300.426 (I)s 302.599 (R)s 11 f 461.876 y 311.432 (d)s 10 f 467.109 y 317.028 (;)s 322.361 (\260)s 334.913 (\076)s 1 f 349.92 (0,)s 365.008 (suc)s 381.408 (h)s 393.478 (that)s 10 f 420.882 (J)s 11 f 468.909 y 427.536 (\260)s 1 f 467.109 y 433.693 (\050)s 10 f 438.36 (r)s 1 f 444.107 (\051)s 454.447 (=)s 10 f 483.909 y -5.69 (\260)s 11 f 479.555 y 1.189 (d)s 10 f 483.909 y 6.785 (J)s 1 f 14.593 (\050)s 10 f 19.26 (\260)s 26.139 (r)s 1 f 31.886 (\051,)s 43.487 (where)s 10 f 77.689 (J)s 1 f 88.999 (is)s 100.567 (a)s 110.068 (smo)s 131.135 (oth)s 151.97 (function)s 198.471 (of)s 211.639 (compact)s 259.141 (supp)s 284.207 (ort.)s 308.074 (They)s 338.576 (ha)s 350.909 (v)s 356.909 (e)s 365.744 (b)s 372.744 (een)s 393.579 (in)s 403.245 (tro)s 418.946 (duced)s 453.114 (to)s 500.709 y -5.69 (describ)s 31.41 (e)s 40.427 (particle)s 83.477 (\050or)s 102.527 (spin\051)s 132.278 (systems)s 176.495 (with)s 203.512 (w)s 211.845 (eak)s 233.195 (long)s 258.879 (range)s 291.263 (in)s 300.929 (teraction)s 351.313 (b)s 358.313 (et)s 367.98 (w)s 376.313 (een)s 397.33 (t)s 401.663 (w)s 409.997 (o)s 419.68 (particles)s 517.509 y -5.69 (\050[KUE]\051.)s 43.745 (In)s 58.346 (the)s 78.615 (limit)s 10 f 106.883 (\260)s 12 f 117.096 (!)s 1 f 132.429 (0)s 142.031 (the)s 162.299 (v)s 167.966 (an)s 184.234 (der)s 204.535 (W)s 215.869 (aals)s 239.537 (theory)s 276.839 (of)s 290.107 (phase)s 323.109 (transition)s 377.477 (holds)s 408.479 (exactly)s 449.414 (for)s 534.309 y -5.69 (these)s 24.318 (mo)s 40.651 (dels)s 63.992 ([LP].)s 92.934 (Here)s 120.575 (w)s 128.908 (e)s 137.516 (prop)s 161.883 (ose)s 181.224 (to)s 195.166 (consider)s 241.207 (a)s 250.481 (Blume-Cap)s 309.982 (el)s 321.923 (mo)s 338.256 (del)s 356.864 (with)s 383.472 (Kac)s 407.413 (in)s 417.08 (teraction)s 551.109 y -5.69 (that)s 19.853 (w)s 28.187 (e)s 37.064 (call)s 58.607 (Kac-Blume-Cap)s 142.774 (el)s 154.984 (\050KBC\051)s 194.361 (mo)s 210.694 (del.)s 234.542 (The)s 258.752 (Blume-Cap)s 318.252 (el)s 330.462 (mo)s 346.796 (del)s 365.673 (is)s 377.283 (a)s 386.826 (spin)s 411.77 (system)s 451.114 (on)s 567.909 y -5.69 (the)s 13.968 (lattice)s 49.627 (with)s 75.952 (nearest-neigh)s 145.052 (b)s 152.052 (our)s 172.411 (in)s 182.078 (teractions)s 236.503 (suc)s 252.903 (h)s 262.562 (that)s 287.554 (the)s 307.212 (spin)s 331.604 (v)s 337.271 (ariable)s 375.63 (can)s 396.622 (assume)s 437.08 (three)s 584.709 y -5.69 (v)s -.024 (alues:)s 12 f 35.59 (\241)s 1 f 44.924 (1)s 10 f 50.924 (;)s 1 f 56.257 (0)s 10 f 62.257 (;)s 1 f 67.59 (1.)s 83.578 (It)s 97.018 (has)s 118.858 (b)s 125.858 (een)s 147.632 (in)s 157.298 (tro)s 172.998 (duced)s 208.105 (originally)s 261.579 (to)s 276.686 (study)s 310.193 (the)s 331.3 (He)s 2 f 580.355 y 345.633 (3)s 1 f 584.709 y 351.016 (-He)s 2 f 580.355 y 369.35 (4)s 1 f 584.709 y 379.173 (phase)s 413.014 (transition)s 601.509 y -5.69 (\050[B],)s 22.132 ([C]\051.)s 50.121 (The)s 75.444 (structure)s 127.566 (of)s 141.889 (the)s 163.211 (phase)s 197.267 (diagram)s 244.623 (at)s 259.945 (lo)s 268.945 (w)s 282.268 (temp)s 309.268 (erature)s 351.324 (for)s 370.346 (this)s 394.402 (mo)s 410.735 (del)s 430.724 (is)s 443.447 (w)s 451.78 (ell)s 618.309 y -5.69 (understo)s 40.077 (o)s 46.41 (d)s 57.077 (in)s 71.077 (terms)s 104.51 (of)s 118.177 (the)s 138.843 (Pirogo)s 172.71 (v-Sinai)s 213.044 (theory)s 250.744 (\050[BS]\051.)s 144.539 .48 -5.69 632.589 r 2 f 641.555 y -2.674 (1)s 4 f 645.909 y 8.71 (Dipartimen)s 59.289 (to)s 72.379 (di)s 84.903 (Fisica,)s 117.893 (Univ)s 139.133 (ersit\265)s 158.465 (a)s 167.588 (di)s 180.112 (Roma)s 210.339 (T)s 216.856 (or)s 229.955 (V)s 236.745 (ergata,)s 271.533 (Via)s 291.13 (della)s 316.12 (Ricerca)s 353.156 (Scien)s 376.106 (ti\257ca,)s 405.219 (00133)s 434.743 (Roma,)s 662.776 y -5.69 (Italy)s 2 f 672.821 y -2.674 (2)s 4 f 677.176 y 8.71 (UPRESA)s 54.434 (6085,)s 81.068 (Univ)s 102.308 (ersit)s 121.356 (\266)s 121.64 (e)s 129.573 (de)s 143.173 (Rouen,)s 177.877 (76821)s 206.778 (Mon)s 226.601 (t)s 233.968 (Sain)s 252.952 (t)s 260.318 (Aignan,)s 298.559 (F)s 304.362 (rance)s 1 f 705.976 y 226.045 (1)s do-end end endp %%Page: 2 2 %%BeginPageSetup initializepage (Raffaele Esposito; page: 2 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f1_12 sf ( )S -997 -1000 :M f2_12 sf ( )S -993 -1000 :M f10_12 sf ( )S -985 -1000 :M f11_12 sf ( )S -976 -1000 :M f12_12 sf ( )S -964 -1000 :M f13_12 sf ( )S -954 -1000 :M f14_12 sf ( )S -941 -1000 :M f15_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 6.31 y 8.71 (The)s 33.376 (KBC)s 63.877 (mo)s 80.21 (del)s 99.543 (is)s 111.61 (de\257ned)s 152.943 (b)s 159.277 (y)s 169.61 (the)s 190.277 (formal)s 227.977 (Hamiltonian)s 10 f 43.489 y 23.804 (H)s 11 f 45.289 y 33.779 (\260)s 1 f 43.489 y 39.936 (\050)s 10 f 44.603 (\276)s 1 f 51.89 (\051)s 59.89 (=)s 35.37 y 73.997 (1)s 6 .48 73.997 40.729 r 51.72 y 73.997 (2)s 13 f 32.088 y 91.361 (X)s 11 f 58.655 y 83.437 (i;j)s 14 f 94.138 (2)s 11 f 100.605 (Z)s 102.815 (Z)s 15 f 56.255 y 111.581 (d)s 10 f 43.489 y 118.619 (J)s 11 f 45.289 y 125.273 (\260)s 1 f 43.489 y 131.43 (\050)s 10 f 136.097 (i)s 12 f 142.898 (\241)s 10 f 154.898 (j)s 1 f 160.526 (\051)s 13 f 33.768 y 165.193 (\241)s 10 f 43.489 y 170.693 (\276)s 1 f 177.98 (\050)s 10 f 182.647 (i)s 1 f 186.781 (\051)s 12 f 194.115 (\241)s 10 f 206.114 (\276)s 1 f 213.402 (\050)s 10 f 218.069 (j)s 1 f 223.697 (\051)s 13 f 33.768 y 228.364 (\242)s 2 f 36.255 y 233.864 (2)s 12 f 43.489 y 241.914 (\241)s 10 f 253.914 (h)s 2 f 45.289 y 260.828 (1)s 13 f 32.088 y 272.482 (X)s 11 f 58.655 y 268.211 (i)s 14 f 271.606 (2)s 11 f 278.073 (Z)s 280.283 (Z)s 15 f 56.255 y 289.048 (d)s 10 f 43.489 y 296.087 (\276)s 1 f 303.374 (\050)s 10 f 308.041 (i)s 1 f 312.175 (\051)s 12 f 319.508 (\241)s 10 f 331.508 (h)s 2 f 45.289 y 338.422 (2)s 13 f 32.088 y 353.31 (X)s 11 f 58.655 y 345.805 (i)s 14 f 349.201 (22)s 11 f 362.134 (Z)s 364.344 (Z)s 15 f 56.255 y 373.109 (d)s 10 f 43.489 y 380.148 (\276)s 2 f 38.534 y 387.435 (2)s 1 f 43.489 y 392.818 (\050)s 10 f 397.485 (i)s 1 f 401.619 (\051)s 10 f 406.286 (;)s 1 f 439.114 (\0501)s 10 f 449.78 (:)s 1 f 453.114 (1\051)s 88.816 y -5.69 (where)s 10 f 30.371 (h)s 2 f 90.616 y 37.285 (1)s 1 f 88.816 y 48.03 (and)s 10 f 72.725 (h)s 2 f 90.616 y 79.639 (2)s 1 f 88.816 y 90.384 (are)s 111.779 (t)s 116.112 (w)s 124.446 (o)s 135.807 (real)s 160.536 (parameters.)s 231.42 (In)s 247.782 (Section)s 291.144 (2)s 302.505 (w)s 310.839 (e)s 321.534 (pro)s 338.567 (vide)s 365.595 (for)s 385.324 (this)s 410.085 (mo)s 426.419 (del)s 447.114 (the)s 105.616 y -5.69 (analogous)s 50.629 (of)s 65.215 (the)s 86.801 (Leb)s 106.634 (o)s 112.301 (witz-P)s 146.134 (enrose)s 183.82 (theorem,)s 235.003 (sho)s 252.069 (wing)s 281.655 (that)s 308.574 (in)s 323.494 (the)s 345.079 (limit)s 10 f 374.665 (\260)s 12 f 386.41 (!)s 1 f 403.275 (0)s 414.194 (the)s 435.78 (mean)s 122.416 y -5.69 (\257eld)s 19.596 (theory)s 56.582 (of)s 69.534 (the)s 89.487 (Blume-Cap)s 148.987 (el)s 160.939 (mo)s 177.273 (del)s 195.892 (\050[BEG]\051)s 241.26 (b)s 248.26 (ecomes)s 288.28 (exact.)s 324.375 (The)s 348.328 (equilibrium)s 411.313 (prop)s 435.68 (erties)s 139.216 y -5.69 (and)s 18.41 (the)s 39.843 (phase)s 74.01 (diagram)s 121.477 (of)s 135.911 (the)s 157.344 (mo)s 173.677 (del)s 193.777 (in)s 208.544 (the)s 229.978 (limit)s 10 f 259.411 (\260)s 12 f 270.902 (!)s 1 f 287.513 (0)s 298.28 (are)s 319.08 (v)s 325.08 (ery)s 346.213 (in)s 355.88 (teresting.)s 412.28 (There)s 447.747 (are)s 156.016 y -5.69 (t)s -1.357 (w)s 6.976 (o)s 18.068 (order)s 50.56 (parameters)s 113.786 (c)s 118.786 (haracterizing)s 191.945 (the)s 213.703 (equilibrium)s 278.495 (Gibbs)s 314.404 (measure:)s 368.021 (the)s 389.78 (magnetization)s 10 f 172.816 y -5.69 (m)s 1 f 4.846 (,)s 13.641 (the)s 35.477 (mean)s 68.646 (v)s 74.313 (alue)s 100.815 (of)s 115.651 (the)s 137.487 (spin,)s 167.682 (and)s 192.184 (the)s 214.02 (concen)s 249.02 (tration)s 10 f 290.223 (\301)s 1 f 297.373 (,)s 306.167 (the)s 328.003 (mean)s 361.173 (v)s 366.839 (alue)s 393.342 (of)s 408.178 (the)s 430.014 (square)s 189.616 y -5.69 (of)s 9.925 (the)s 32.54 (spin.)s 68.452 (F)s 75.286 (or)s 91.934 (in)s 101.601 (v)s 107.601 (erse)s 133.649 (temp)s 160.65 (erature)s 10 f 203.998 (\257)s 1 f 217.367 (not)s 240.649 (larger)s 276.665 (than)s 306.613 (a)s 318.562 (critical)s 360.543 (v)s 366.21 (alue)s 10 f 393.492 (\257)s 11 f 191.416 y 400.28 (c)s 1 f 189.616 y 411.117 (there)s 443.765 (is)s 457.78 (a)s 206.416 y -5.69 (unique)s 33.449 (Gibbs)s 68.406 (measure)s 115.312 (whic)s 138.979 (h)s 149.785 (is)s 161.991 (indeed)s 200.13 (a)s 210.27 (Bernoulli)s 262.276 (measure)s 309.183 (\050as)s 328.722 (usual)s 360.262 (for)s 378.768 (these)s 409.641 (mean)s 441.78 (\257eld)s 223.216 y -5.69 (theories\051,)s 47.24 (while)s 78.704 (for)s 97.201 (temp)s 124.201 (eratures)s 170.465 (su\261cien)s 212.199 (tly)s 230.663 (small)s 262.193 (\050and)s 290.324 (suitable)s 335.188 (v)s 340.855 (alues)s 371.052 (of)s 384.849 (the)s 405.647 (parameters)s 10 f 240.016 y -5.69 (h)s 2 f 241.816 y 1.224 (1)s 1 f 240.016 y 11.035 (and)s 10 f 34.796 (h)s 2 f 241.816 y 41.709 (2)s 1 f 240.016 y 47.093 (\051)s 56.187 (the)s 77.281 (Gibbs)s 112.526 (measure)s 159.72 (is)s 172.214 (a)s 182.642 (sup)s 201.042 (erp)s 218.075 (osition)s 257.236 (of)s 271.33 (Bernoulli)s 323.625 (measures)s 375.552 (corresp)s 413.352 (onding)s 453.113 (to)s 256.816 y -5.69 (di\256eren)s 33.01 (t)s 42.512 (v)s 48.179 (alues)s 79.081 (of)s 93.584 (the)s 115.086 (couple)s 10 f 153.256 (m;)s 169.125 (\301)s 1 f 176.275 (.)s 187.449 (In)s 203.285 (particular,)s 263.063 (there)s 294.599 (is)s 307.501 (a)s 318.337 (p)s 325.337 (oin)s 341.004 (t)s 350.506 (in)s 365.342 (the)s 386.844 (phase)s 421.08 (diagram)s 273.616 y -5.69 (where)s 29.085 (there)s 59.861 (are)s 79.97 (three)s 110.746 (extremal)s 160.521 (equilibrium)s 224.297 (measures,)s 279.225 (corresp)s 317.025 (onding)s 356.434 (to)s 371.177 (p)s 378.177 (ositiv)s 406.243 (e,)s 419.005 (zero)s 444.447 (and)s 290.416 y -5.69 (negativ)s 32.31 (e)s 41.643 (magnetization.)s 307.336 y 8.71 (W)s 20.043 (e)s 29.497 (study)s 62.685 (t)s 67.018 (w)s 75.351 (o)s 85.472 (Mark)s 113.172 (o)s 118.839 (v)s 129.293 (pro)s 146.993 (cesses)s 181.314 (in)s 195.434 (the)s 216.222 (in\257nite)s 257.009 (v)s 263.009 (olume)s 298.464 (spin)s 323.984 (con\257guration)s 396.805 (space)s 428.993 (\255)s 441.78 (gen-)s 324.136 y -5.69 (erated)s 30.654 (b)s 36.988 (y)s 46.965 (self-adjoin)s 100.032 (t)s 108.343 (op)s 121.343 (erators)s 161.121 (in)s 10 f 174.766 (L)s 2 f 319.781 y 182.932 (2)s 1 f 324.136 y 188.316 (\050\255)s 10 f 201.649 (;)s 206.982 (\271)s 1 f 214.213 (\051,)s 225.929 (where)s 10 f 260.273 (\271)s 1 f 271.148 (is)s 282.859 (a)s 292.504 (Gibbs)s 326.965 (measure)s 373.376 (for)s 391.387 (some)s 10 f 421.098 (\257)s 428.519 (;)s 433.852 (h)s 2 f 325.936 y 440.766 (1)s 10 f 324.136 y 446.15 (;)s 451.483 (h)s 2 f 325.936 y 458.397 (2)s 1 f 340.936 y -5.69 (and)s 18.696 (\257nite)s 10 f 50.415 (\260)s 1 f 57.294 (:)s 68.066 (the)s 89.785 (so-called)s 139.571 (Glaub)s 171.988 (er)s 187.074 (and)s 211.46 (Ka)s 226.46 (w)s 234.793 (asaki)s 266.246 (dynamics.)s 327.137 (They)s 359.189 (can)s 382.242 (b)s 389.242 (e)s 399.628 (describ)s 436.728 (ed)s 453.78 (in)s 357.736 y -5.69 (w)s 2.643 (ords)s 28.559 (as)s 43.109 (follo)s 65.109 (ws:)s 87.084 (in)s 100.9 (the)s 121.383 (Glaub)s 153.8 (er)s 167.65 (dynamics)s 220.533 (eac)s 236.866 (h)s 247.349 (spin)s 272.566 (at)s 287.049 (random)s 330.898 (times)s 362.781 (\260)s 369.448 (ips)s 387.998 (to)s 402.481 (a)s 412.297 (new)s 436.78 (v)s 442.447 (alue)s 374.536 y -5.69 (or)s 10.074 (sta)s 25.141 (ys)s 41.271 (unc)s 59.605 (hanged)s 102.002 (with)s 130.4 (probabilities)s 200.231 (dep)s 219.231 (ending)s 258.962 (on)s 276.693 (the)s 298.423 (di\256erence)s 353.188 (of)s 367.918 (energy)s 407.349 (b)s 414.349 (efore)s 444.447 (and)s 391.336 y -5.69 (after)s 22.382 (the)s 42.754 (\260)s 49.421 (ip.)s 67.99 (In)s 82.695 (the)s 103.068 (Ka)s 118.068 (w)s 126.401 (asaki)s 156.507 (dynamics)s 209.279 (t)s 213.613 (w)s 221.946 (o)s 231.652 (neigh)s 259.318 (b)s 266.318 (oring)s 296.724 (spins)s 326.563 (at)s 340.935 (random)s 384.674 (times)s 416.447 (exc)s 433.113 (hange)s 408.136 y -5.69 (their)s 22.41 (v)s 28.076 (alues,)s 60.996 (or)s 75.096 (sta)s 90.162 (y)s 99.896 (unc)s 118.229 (hanged,)s 162.415 (with)s 189.149 (jump)s 219.548 (rates)s 248.381 (again)s 279.781 (dep)s 298.781 (ending)s 336.848 (on)s 352.914 (the)s 372.98 (energy)s 410.747 (di\256erence.)s 424.936 y -5.69 (The)s 19.088 (latter)s 51.899 (sto)s 67.633 (c)s 72.633 (hastic)s 107.477 (ev)s 118.811 (olution)s 159.589 (conserv)s 198.356 (es)s 212.534 (the)s 233.312 (di\256erence)s 287.123 (and)s 310.568 (the)s 331.346 (sum)s 356.857 (b)s 363.857 (et)s 373.524 (w)s 381.857 (een)s 403.302 (the)s 424.08 (n)s 430.413 (um)s 446.747 (b)s 453.747 (er)s 441.736 y -5.69 (of)s 8.22 (spins)s 38.596 (plus)s 64.24 (and)s 87.816 (min)s 107.483 (us)s 123.126 (\050resp)s 149.56 (ectiv)s 174.226 (ely)s 193.469 (total)s 222.379 (magnetization)s 300.623 (and)s 324.199 (total)s 353.109 (concen)s 388.109 (tration\051,)s 436.447 (while)s 458.536 y -5.69 (the)s 14.588 (former)s 52.599 (do)s 65.6 (es)s 79.278 (not.)s 105.148 (Moreo)s 137.848 (v)s 143.848 (er,)s 160.904 (the)s 181.182 (jump)s 211.794 (rates)s 240.839 (dep)s 259.839 (end)s 282.117 (on)s 298.395 (the)s 318.673 (magnetic)s 369.618 (\257elds)s 10 f 399.963 (h)s 2 f 460.336 y 406.877 (1)s 10 f 458.536 y 412.26 (;)s 417.593 (h)s 2 f 460.336 y 424.507 (2)s 1 f 458.536 y 433.502 (in)s 447.113 (the)s 475.336 y -5.69 (Glaub)s 26.727 (er)s 40.567 (dynamics)s 93.44 (and)s 116.581 (do)s 133.054 (not)s 154.194 (in)s 168.001 (the)s 188.475 (Ka)s 203.475 (w)s 211.808 (asaki)s 242.015 (one.)s 268.617 (As)s 286.157 (a)s 295.964 (consequence,)s 366.876 (all)s 383.35 (the)s 403.823 (Gibbs)s 438.447 (mea-)s 492.136 y -5.69 (sures)s 24.597 (whatev)s 61.93 (er)s 76.084 (are)s 10 f 96.237 (h)s 2 f 493.936 y 103.151 (1)s 10 f 492.136 y 108.534 (;)s 113.868 (h)s 2 f 493.936 y 120.781 (2)s 1 f 492.136 y 130.285 (are)s 150.438 (in)s 160.105 (v)s 165.772 (arian)s 192.139 (t)s 200.925 (for)s 219.412 (the)s 240.199 (Ka)s 255.199 (w)s 263.533 (asaki)s 294.053 (dynamics,)s 350.603 (while)s 382.057 (for)s 400.543 (the)s 421.33 (Glaub)s 453.747 (er)s 508.936 y -5.69 (dynamics)s 48.391 (the)s 70.073 (only)s 97.421 (in)s 107.088 (v)s 112.754 (arian)s 139.121 (t)s 148.803 (measures)s 201.317 (are)s 222.365 (the)s 244.047 (Gibbs)s 279.878 (measures)s 332.393 (with)s 360.741 (the)s 382.423 (v)s 388.09 (alues)s 419.171 (of)s 10 f 433.853 (h)s 2 f 510.736 y 440.766 (1)s 10 f 508.936 y 446.15 (;)s 451.483 (h)s 2 f 510.736 y 458.397 (2)s 1 f 525.736 y -5.69 (equal)s 25.977 (to)s 40.643 (those)s 72.043 (app)s 91.71 (earing)s 127.743 (in)s 141.743 (the)s 162.41 (jump)s 193.41 (rates.)s 542.656 y 8.71 (W)s 20.043 (e)s 29.924 (scale)s 59.204 (the)s 80.418 (lattice)s 117.632 (spacing)s 160.913 (b)s 167.247 (y)s 10 f 178.127 (\260)s 1 f 189.554 (and)s 213.435 (lo)s 223.101 (ok)s 239.982 (\257rst)s 265.296 (at)s 280.51 (the)s 301.724 (b)s 308.724 (eha)s 326.391 (viour)s 357.971 (of)s 372.185 (the)s 393.399 (system)s 433.747 (under)s 559.456 y -5.69 (the)s 15.453 (Glaub)s 47.869 (er)s 62.379 (dynamics)s 115.922 (in)s 130.398 (the)s 151.541 (limit)s 10 f 180.684 (\260)s 12 f 191.691 (!)s 1 f 207.818 (0.)s 223.913 (W)s 235.246 (e)s 245.056 (sho)s 262.123 (w)s 275.266 (that)s 301.742 (the)s 322.885 (empirical)s 375.394 (a)s 381.061 (v)s 387.061 (erages)s 423.637 (of)s 437.78 (mag-)s 576.256 y -5.69 (netization)s 50.528 (and)s 74.08 (concen)s 109.08 (tration)s 149.331 (con)s 166.998 (v)s 172.998 (erges)s 203.316 (w)s 211.65 (eakly)s 243.201 (in)s 257.419 (probabilit)s 308.453 (y)s 319.004 (to)s 333.889 (the)s 354.774 (solution)s 400.392 (of)s 414.277 (the)s 435.162 (set)s 454.114 (of)s 593.056 y -5.69 (t)s -1.357 (w)s 6.976 (o)s 16.976 (coupled)s 60.977 (non)s 84.31 (lo)s 93.977 (cal)s 112.643 (equations)s 166.377 (\0503.7\051)s 195.044 (and)s 218.377 (\0503.8\051)s 247.044 (\050in)s 265.71 (Section)s 307.71 (3\051.)s 609.976 y 8.71 (T)s 16.376 (o)s 26.694 (get)s 47.012 (a)s 57.33 (de\257nite)s 100.315 (limit)s 129.299 (in)s 143.617 (the)s 164.602 (case)s 190.319 (of)s 204.304 (the)s 225.288 (Ka)s 240.288 (w)s 248.622 (asaki)s 279.34 (dynamics)s 332.724 (w)s 341.058 (e)s 350.709 (ha)s 363.042 (v)s 369.042 (e)s 378.693 (to)s 393.678 (scale)s 422.729 (also)s 447.114 (the)s 626.776 y -5.69 (time)s 20.859 (as)s 10 f 34.808 (\260)s 14 f 622.421 y 41.687 (\241)s 2 f 49.187 (2)s 1 f 626.776 y 57.787 ([GLP].)s 96.086 (This)s 122.701 (is)s 133.984 (a)s 143.2 (pro)s 160.9 (cess)s 184.249 (with)s 210.798 (t)s 215.131 (w)s 223.465 (o)s 232.68 (conserv)s 271.114 (ation)s 300.996 (la)s 309.996 (ws.)s 331.801 (W)s 343.135 (e)s 351.684 (pro)s 368.717 (v)s 374.717 (e)s 383.266 (also)s 406.549 (in)s 419.765 (this)s 442.38 (case)s 643.576 y -5.69 (a)s 4.294 (la)s 13.294 (w)s 25.944 (of)s 39.595 (large)s 68.946 (n)s 75.279 (um)s 91.612 (b)s 98.612 (ers)s 117.363 (for)s 135.714 (the)s 156.364 (empirical)s 208.382 (a)s 214.048 (v)s 220.048 (erages)s 256.132 (of)s 10 f 269.783 (\276)s 1 f 281.054 (and)s 10 f 304.372 (\276)s 2 f 639.221 y 311.659 (2)s 1 f 643.576 y 317.042 (,)s 324.363 (resp)s 346.13 (ectiv)s 370.796 (ely)s 389.78 (magnetization)s 660.376 y -5.69 (and)s 16.516 (concen)s 51.516 (tration.)s 95.84 (Their)s 127.413 (limits)s 159.686 (satisfy)s 196.025 (the)s 215.565 (set)s 233.171 (of)s 245.71 (t)s 250.044 (w)s 258.377 (o)s 267.25 (coupled)s 310.123 (non)s 332.329 (lo)s 341.995 (cal)s 359.535 (second)s 397.141 (order)s 427.414 (in)s 437.08 (tegro)s 677.176 y -5.69 (di\256eren)s 33.01 (tial)s 54.351 (equations)s 108.092 (\0503.5\051)s 136.766 (in)s 150.774 (Section)s 192.781 (3.)s 207.471 (These)s 242.212 (equations)s 295.953 (can)s 317.96 (b)s 324.96 (e)s 334.301 (put)s 356.309 (in)s 370.317 (a)s 380.324 (nicely)s 414.665 (form)s 443.039 (as)s 457.78 (a)s 705.976 y 226.045 (2)s do-end end endp %%Page: 3 3 %%BeginPageSetup initializepage (Raffaele Esposito; page: 3 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f1_12 sf ( )S -997 -1000 :M f2_12 sf ( )S -993 -1000 :M f10_12 sf ( )S -985 -1000 :M f11_12 sf ( )S -976 -1000 :M f12_12 sf ( )S -964 -1000 :M f13_12 sf ( )S -954 -1000 :M f14_12 sf ( )S -941 -1000 :M f15_12 sf ( )S -930 -1000 :M f16_12 sf ( )S -925 -1000 :M f17_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 16 5 1200 1000 div mul /CMR5 findfont fdef 17 10 1200 1000 div mul /CMTI10 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 6.31 y -5.69 (gradien)s 32.677 (t)s 41.343 (\260)s 48.01 (o)s 53.677 (w)s 66.343 (of)s 80.01 (the)s 100.677 (free)s 123.71 (energy)s 162.077 (functional)s 12 f 218.41 (F)s 13 f 26.398 y 87.856 (Z)s 10 f 42.731 y 101.856 (dr)s 113.849 (f)s 2 f 37.777 y 121.015 (0)s 13 f 33.011 y 126.399 (\241)s 10 f 42.731 y 131.899 (u)s 6.869 .48 131.899 44.651 r 1 f 42.731 y 138.768 (\050)s 10 f 143.435 (r)s 1 f 149.182 (\051)s 13 f 33.011 y 153.849 (\242)s 1 f 42.731 y 162.016 (+)s 34.613 y 175.456 (1)s 6 .48 175.456 39.971 r 50.963 y 175.456 (2)s 13 f 26.398 y 184.895 (Z)s 10 f 42.731 y 198.895 (dr)s 13 f 26.398 y 212.888 (Z)s 10 f 42.731 y 226.888 (dr)s 14 f 37.777 y 238.882 (0)s 10 f 42.731 y 242.248 (J)s 1 f 250.057 (\050)s 10 f 254.723 (r)s 12 f 263.137 (\241)s 10 f 275.137 (r)s 14 f 37.777 y 280.884 (0)s 1 f 42.731 y 284.251 (\051[)s 10 f 292.251 (m)s 1 f 302.787 (\050)s 10 f 307.454 (r)s 1 f 313.201 (\051)s 12 f 320.534 (\241)s 10 f 332.534 (m)s 1 f 343.07 (\050)s 10 f 347.737 (r)s 14 f 37.777 y 353.484 (0)s 1 f 42.731 y 356.851 (\051])s 2 f 37.777 y 364.851 (2)s 1 f 42.731 y 439.114 (\0501)s 10 f 449.78 (:)s 1 f 453.114 (2\051)s 80.588 y -5.69 (where)s 10 f 29.01 (u)s 6.869 .48 29.01 82.508 r 1 f 80.588 y 39.213 (:=)s 55.213 (\050)s 10 f 59.879 (m;)s 75.749 (\301)s 1 f 82.899 (\051)s 91.565 (and)s 10 f 114.899 (f)s 2 f 76.233 y 122.065 (0)s 1 f 80.588 y 127.449 (\050)s 10 f 132.115 (u)s 6.869 .48 132.115 82.508 r 1 f 80.588 y 138.985 (\051)s 147.652 (is)s 10 f 117.194 y 25.646 (f)s 2 f 112.239 y 32.813 (0)s 13 f 107.474 y 38.196 (\241)s 10 f 117.194 y 43.696 (u)s 6.869 .48 43.696 119.114 r 1 f 117.194 y 50.566 (\051)s 58.566 (:=)s 12 f 73.899 (\241)s 10 f 85.899 (m)s 2 f 112.239 y 96.435 (2)s 1 f 117.194 y 104.485 (+)s 10 f 116.485 (\301)s 1 f 126.302 (+)s 10 f 138.302 (\257)s 14 f 112.239 y 145.723 (\241)s 2 f 153.223 (1)s 13 f 103.874 y 158.606 (h)s 1 f 109.076 y 165.713 (1)s 6 .48 165.713 114.434 r 125.425 y 165.713 (2)s 117.194 y 173.153 (\050)s 10 f 177.819 (m)s 1 f 191.022 (+)s 10 f 203.022 (\301)s 1 f 210.172 (\051)s 216.839 (log)s 232.339 (\050)s 10 f 237.005 (m)s 1 f 250.208 (+)s 10 f 262.208 (\301)s 1 f 269.358 (\051)s 276.691 (+)s 109.076 y 290.131 (1)s 6 .48 290.131 114.434 r 125.425 y 290.131 (2)s 117.194 y 297.571 (\050)s 10 f 302.238 (\301)s 12 f 312.055 (\241)s 10 f 324.055 (m)s 1 f 334.591 (\051)s 341.257 (log)s 356.758 (\050)s 10 f 361.424 (\301)s 12 f 371.241 (\241)s 10 f 383.241 (m)s 1 f 393.777 (\051+)s 147.625 y 143.233 (\0501)s 12 f 156.566 (\241)s 10 f 168.566 (\301)s 1 f 175.716 (\051)s 182.383 (log)s 197.883 (\0501)s 12 f 211.216 (\241)s 10 f 223.216 (\301)s 1 f 230.366 (\051)s 12 f 237.699 (\241)s 10 f 249.699 (\301)s 1 f 258.849 (log)s 276.349 (2)s 13 f 134.305 y 282.349 (i)s 10 f 147.625 y 288.016 (:)s 1 f 131.384 y 439.114 (\0501)s 10 f 449.78 (:)s 1 f 453.114 (3\051)s 182.18 y -5.69 (The)s 18.976 (equations)s 72.71 (\0503.5\051)s 101.377 (b)s 108.377 (ecome)s 10 f 224.968 y 145.426 (@)s 11 f 226.768 y 151.797 (t)s 10 f 224.968 y 156.022 (u)s 11 f 226.768 y 162.891 (\256)s 1 f 224.968 y 173.063 (=)s 11 f 209.968 y 191.898 (d)s 13 f 213.568 y 185.73 (X)s 11 f 239.127 y 186.624 (i)s 2 f 190.019 (=1)s 13 f 213.568 y 209.224 (X)s 11 f 239.402 y 205.063 (\257)s 2 f 210.936 (=1)s 11 f 223.086 (;)s 2 f 225.936 (2)s 10 f 224.968 y 232.719 (@)s 11 f 226.768 y 239.09 (i)s 13 f 215.248 y 243.085 (\243)s 10 f 224.968 y 248.085 (M)s 11 f 226.768 y 259.727 (\256;\257)s 10 f 224.968 y 275.288 (@)s 11 f 226.768 y 281.659 (i)s 10 f 216.85 y 288.857 (\261)s 12 f 294.645 (F)s 19.13 .48 287.094 222.208 r 10 f 233.2 y 287.094 (\261)s 292.882 (u)s 11 f 235 y 299.751 (\257)s 13 f 215.248 y 307.664 (\244)s 1 f 224.968 y 439.114 (\0501)s 10 f 449.78 (:)s 1 f 453.114 (4\051)s 268.323 y -5.69 (and)s 17.643 (in)s 31.643 (v)s 37.643 (ectorial)s 80.343 (form)s 10 f 294.123 y 171.095 (@)s 11 f 295.923 y 177.466 (t)s 10 f 294.123 y 181.691 (u)s 6.869 .48 181.691 296.043 r 1 f 294.123 y 191.894 (=)s 12 f 204.561 (r)s 217.227 (\242)s 13 f 273.603 y 223.227 (\303)s 10 f 294.123 y 232.727 (M)s 12 f 245.677 (r)s 10 f 286.005 y 257.117 (\261)s 12 f 262.905 (F)s 15.604 .48 257.117 291.363 r 10 f 302.355 y 258.591 (\261)s 264.378 (u)s 6.869 .48 264.378 304.275 r 13 f 273.603 y 274.161 (!)s 10 f 294.123 y 283.661 (;)s 1 f 439.114 (\0501)s 10 f 449.78 (:)s 1 f 453.114 (5\051)s 332.239 y -5.69 (where)s 11 f 327.514 y 33.204 (\261)s 14 f 37.871 (F)s 16.42 .48 31.188 329.479 r 11 f 336.377 y 31.188 (\261)s 35.854 (u)s 15 f 337.577 y 41.528 (\256)s 1 f 332.239 y 53.786 (denote)s 93.191 (the)s 114.596 (functional)s 171.668 (deriv)s 197.368 (ativ)s 217.368 (e)s 227.439 (of)s 12 f 241.844 (F)s 1 f 256.399 (with)s 284.471 (resp)s 306.237 (ect)s 326.309 (to)s 10 f 341.714 (u)s 11 f 334.039 y 348.583 (\256)s 1 f 332.239 y 360.16 (and)s 10 f 384.232 (M)s 1 f 401.92 (is)s 414.725 (the)s 436.129 (2)s 12 f 445.288 (\243)s 1 f 457.78 (2)s 349.039 y -5.69 (mobilit)s 31.31 (y)s 41.643 (matrix)s 10 f 388.28 y 138.592 (M)s 1 f 154.876 (=)s 10 f 167.542 (\257)s 1 f 174.963 (\0501)s 12 f 188.296 (\241)s 10 f 200.296 (\301)s 1 f 207.446 (\051)s 13 f 371.36 y 214.113 (\265)s 10 f 382.401 y 224.946 (\301)s 1 f 234.763 (+)s 11 f 377.047 y 248.203 (\301)s 16 f 373.426 y 253.973 (2)s 14 f 377.047 y 258.656 (\241)s 11 f 266.156 (m)s 16 f 373.426 y 274.672 (2)s 31.152 .48 248.203 379.641 r 2 f 386.539 y 254.752 (1)s 14 f 259.536 (\241)s 11 f 267.036 (\301)s 10 f 382.401 y 292.795 (m)s 396.801 y 247.603 (m)s 294.488 (\301)s 13 f 371.36 y 305.331 (\266)s 10 f 388.28 y 316.164 (:)s 1 f 439.114 (\0501)s 10 f 449.78 (:)s 1 f 453.114 (6\051)s 421.358 y -5.69 (It)s 7.31 (is)s 19.376 (easy)s 45.777 (to)s 60.443 (see)s 79.843 (that)s 12 f 105.843 (F)s 1 f 119.66 (is)s 131.727 (a)s 141.727 (Liapuno)s 184.227 (v)s 194.56 (functional)s 250.894 (for)s 269.26 (\0501.5\051.)s 302.594 (In)s 317.594 (fact)s 10 f 456.028 y 122.301 (d)s 10.579 .48 120.135 461.386 r 472.378 y 120.135 (dt)s 12 f 464.146 y 132.154 (F)s 1 f 145.304 (=)s 12 f 157.97 (\241)s 11 f 449.146 y 175.473 (d)s 13 f 452.746 y 169.304 (X)s 11 f 478.305 y 170.198 (i)s 2 f 173.593 (=1)s 449.146 y 199.801 (2)s 13 f 452.746 y 193.526 (X)s 11 f 478.58 y 188.637 (\256;\257)s 2 f 203.598 (=1)s 13 f 447.813 y 217.748 (Z)s 10 f 464.146 y 231.748 (dr)s 243.742 (@)s 11 f 465.946 y 250.112 (i)s 10 f 456.028 y 257.493 (\261)s 12 f 263.281 (F)s 19.496 .48 255.547 461.386 r 10 f 472.378 y 255.547 (\261)s 261.335 (u)s 11 f 474.178 y 268.204 (\256)s 10 f 464.146 y 276.483 (M)s 11 f 465.946 y 288.125 (\256;\257)s 10 f 464.146 y 303.686 (@)s 11 f 465.946 y 310.057 (i)s 10 f 456.028 y 317.255 (\261)s 12 f 323.043 (F)s 19.13 .48 315.492 461.386 r 10 f 472.378 y 315.492 (\261)s 321.28 (u)s 11 f 474.178 y 328.149 (\257)s 10 f 464.146 y 336.062 (:)s 1 f 439.114 (\0501)s 10 f 449.78 (:)s 1 f 453.114 (7\051)s 508.936 y -5.69 (The)s 18 (homogeneous)s 90.424 (minimizers)s 150.214 (of)s 162.905 (the)s 182.595 (functional)s 12 f 237.952 (F)s 1 f 250.793 (coincide)s 295.816 (with)s 322.173 (the)s 341.864 (minimizers)s 401.654 (of)s 10 f 414.344 (f)s 2 f 504.581 y 421.511 (0)s 1 f 508.936 y 426.895 (,)s 433.447 (whic)s 457.114 (h)s 525.736 y -5.69 (has)s 15.236 (a)s 24.763 (unique)s 63.289 (minimizer)s 118.849 (but)s 140.376 (it)s 151.902 (is)s 163.495 (not)s 184.355 (con)s 202.022 (v)s 208.022 (ex)s 223.215 (for)s 10 f 241.108 (\257)s 1 f 252.055 (large)s 280.949 (enough.)s 326.791 (The)s 350.984 (con)s 368.651 (v)s 374.651 (ex)s 389.844 (en)s 401.51 (v)s 407.51 (elop)s 429.177 (e)s 438.037 (of)s 10 f 451.23 (f)s 2 f 521.381 y 458.397 (0)s 1 f 542.536 y -5.69 (is)s 6.571 (the)s 27.433 (free)s 50.661 (energy)s 10 f 89.223 (f)s 1 f 100.584 (of)s 114.446 (the)s 135.307 (KBC)s 166.002 (mo)s 182.336 (del)s 201.864 (at)s 10 f 216.725 (\260)s 1 f 227.263 (=)s 240.254 (0)s 250.449 (and)s 273.977 (has)s 295.572 (some)s 325.834 (\260)s 332.501 (at)s 347.362 (parts)s 378.324 (whic)s 401.99 (h)s 412.852 (single)s 446.447 (out)s 559.336 y -5.69 (a)s 4.203 (region)s 10 f 40.13 (F)s 1 f 53.407 (\050)s 17 f 58.074 (forbidden)s 1 f 110.574 (region\051)s 151.167 (in)s 10 f 165.061 (D)s 1 f 178.663 (=)s 12 f 191.329 (f)s 1 f 197.329 (\050)s 10 f 201.996 (m;)s 217.865 (\301)s 1 f 225.015 (\051)s 233.015 (:)s 10 f 239.682 (\301)s 12 f 250.165 (2)s 1 f 261.498 ([0)s 10 f 270.832 (;)s 1 f 276.165 (1])s 10 f 285.498 (;)s 290.832 (m)s 12 f 304.701 (\267)s 10 f 317.368 (\301)s 12 f 324.518 (g)s 1 f 330.518 (,)s 337.766 (the)s 358.326 (domain)s 400.886 (of)s 414.447 (de\257nition)s 576.136 y -5.69 (of)s 10 f 8.569 (f)s 2 f 571.781 y 15.736 (0)s 1 f 576.136 y 21.119 (,)s 29.193 (suc)s 45.593 (h)s 56.852 (that)s 83.444 (for)s 102.403 (no)s 119.662 (v)s 125.329 (alue)s 151.254 (of)s 165.514 (the)s 186.773 (c)s 191.773 (hemical)s 236.365 (p)s 243.365 (oten)s 265.698 (tials)s 10 f 292.357 (h)s 2 f 577.936 y 299.271 (1)s 10 f 576.136 y 304.655 (;)s 309.988 (h)s 2 f 577.936 y 316.902 (2)s 1 f 576.136 y 326.878 (there)s 358.17 (is)s 370.829 (an)s 388.088 (extremal)s 438.38 (state)s 592.936 y -5.69 (with)s 22.067 (magnetization)s 100.49 (and)s 124.247 (concen)s 159.247 (tration)s 199.704 (in)s 10 f 214.127 (F)s 1 f 223.51 (.)s 233.447 (An)s 248.78 (y)s 259.537 (Gibbs)s 294.777 (measure)s 341.967 (with)s 369.724 (a)s 375.391 (v)s 381.391 (erages)s 10 f 417.914 (m)s 1 f 432.873 (and)s 10 f 456.63 (\301)s 1 f 609.736 y -5.69 (in)s 10 f 8.31 (F)s 1 f 21.693 (has)s 43.093 (to)s 57.76 (b)s 64.76 (e)s 74.093 (a)s 84.093 (linear)s 117.46 (sup)s 135.86 (erp)s 152.893 (osition)s 191.627 (of)s 205.294 (the)s 225.96 (extremal)s 275.66 (states)s 309.794 (with)s 337.127 (\050)s 10 f 341.794 (m;)s 357.663 (\301)s 1 f 364.813 (\051)s 10 f 374.146 (=)s 12 f 372.813 (2)s 10 f 384.146 (F)s 1 f 393.53 (.)s 626.656 y 8.71 (These)s 45.216 (prop)s 69.582 (erties)s 103.455 (of)s 118.894 (the)s 141.333 (energy)s 181.472 (functional)s 239.578 (should)s 279.418 (allo)s 297.751 (w)s 312.19 (to)s 328.629 (relate)s 363.768 (concepts)s 414.274 (of)s 429.714 (stable,)s 643.456 y -5.69 (unstable)s 42.377 (and)s 65.71 (metastable)s 126.443 (phases)s 164.577 (with)s 191.91 (the)s 212.577 (b)s 219.577 (eha)s 237.244 (viour)s 268.277 (of)s 281.944 (the)s 302.61 (solutions)s 352.744 (of)s 366.411 (\0501.5\051)s 660.376 y 8.71 (Glaub)s 41.127 (er)s 55.318 (and)s 78.809 (Ka)s 93.809 (w)s 102.142 (asaki)s 132.7 (dynamics)s 185.925 (for)s 204.45 (the)s 225.274 (Ising)s 254.499 (mo)s 270.832 (del)s 290.324 (with)s 317.815 (Kac)s 342.64 (p)s 349.64 (oten)s 371.973 (tial)s 393.464 (ha)s 405.798 (v)s 411.798 (e)s 421.289 (b)s 428.289 (een)s 449.78 (in-)s 677.176 y -5.69 (v)s .31 (estigated)s 50.169 (thoroughly)s 110.327 (\050)s 118.119 ([GLP])s 152.994 (and)s 175.453 (references)s 229.711 (therein)s 269.537 (\051,)s 280.837 (pro)s 297.87 (viding)s 333.329 (a)s 342.455 (microscopic)s 406.347 (description)s 705.976 y 226.045 (3)s do-end end endp %%Page: 4 4 %%BeginPageSetup initializepage (Raffaele Esposito; page: 4 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f1_12 sf ( )S -997 -1000 :M f2_12 sf ( )S -993 -1000 :M f10_12 sf ( )S -985 -1000 :M f11_12 sf ( )S -976 -1000 :M f12_12 sf ( )S -964 -1000 :M f14_12 sf ( )S -950 -1000 :M f16_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 16 5 1200 1000 div mul /CMR5 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 6.31 y -5.69 (of)s 8.436 (segregation)s 71.662 (phenomena.)s 141.039 (W)s 152.372 (e)s 162.165 (refer)s 190.357 (for)s 209.183 (Glaub)s 241.6 (er)s 256.092 (to)s 271.218 (the)s 292.344 (series)s 324.97 ([DOPT])s 371.428 (and)s 395.221 (for)s 414.047 (Ka)s 429.047 (w)s 437.38 (asaki)s 23.11 y -5.69 (to)s 9.967 (the)s 31.625 (pap)s 51.292 (ers)s 71.049 (b)s 77.382 (y)s 88.707 ([GL],)s 120.614 (where)s 156.305 (the)s 177.963 (authors)s 222.387 (study)s 256.445 (the)s 278.102 (Ka)s 293.102 (w)s 301.436 (asaki)s 332.826 (dynamics,)s 390.465 (with)s 418.789 (one)s 441.78 (con-)s 39.91 y -5.69 (serv)s 14.743 (ation)s 46.44 (la)s 55.44 (w,)s 72.727 (for)s 92.124 (the)s 113.821 (Ising)s 143.917 (mo)s 160.251 (del)s 180.614 (with)s 208.977 (Kac)s 234.674 (p)s 241.674 (oten)s 264.007 (tial)s 286.371 (on)s 304.067 (a)s 315.097 (torus.)s 353.62 (Moreo)s 386.32 (v)s 392.32 (er)s 407.384 (they)s 435.414 (pro)s 452.447 (v)s 458.447 (e)s 56.71 y -5.69 (the)s 16.1 (h)s 22.433 (ydro)s 46.467 (dynamical)s 105.257 (limit)s 135.048 (b)s 141.381 (y)s 152.838 (using)s 185.362 (Radon-Nico)s 247.528 (dym)s 275.652 (deriv)s 301.352 (ativ)s 321.352 (e)s 331.809 (metho)s 364.809 (ds)s 381.333 (and)s 405.79 (discuss)s 447.113 (the)s 73.51 y -5.69 (in)s 3.976 (terface)s 43.01 (motion)s 83.677 (and)s 107.01 (the)s 127.677 (segregation)s 190.444 (b)s 197.444 (eha)s 215.11 (viour)s 246.144 (\050see)s 270.21 (for)s 288.577 (recen)s 315.61 (t)s 324.277 (dev)s 342.277 (elopmen)s 385.277 (ts)s 398.677 ([CCO]\051.)s 94.226 y 8.71 (W)s 20.043 (e)s 29.761 (w)s 38.094 (ould)s 65.146 (notice)s 100.864 (that)s 127.249 (the)s 148.3 (mean)s 180.685 (\257eld)s 207.069 (free)s 230.487 (energy)s 269.239 (functional)s 325.957 (for)s 344.708 (the)s 365.76 (Ising)s 395.211 (mo)s 411.544 (del)s 431.262 (is)s 443.714 (also)s 111.026 y -5.69 (not)s 15.395 (con)s 33.062 (v)s 39.062 (ex)s 54.481 (for)s 10 f 72.599 (\257)s 1 f 83.772 (large)s 112.891 (and,)s 139.359 (since)s 168.511 (the)s 188.93 (\257rst)s 213.449 (order)s 244.601 (phase)s 277.753 (transition)s 332.272 (in)s 346.024 (the)s 366.443 (Ising)s 395.261 (mo)s 411.595 (del)s 430.68 (o)s 437.014 (ccurs)s 127.826 y -5.69 (at)s 8.766 (zero)s 33.922 (magnetic)s 85.045 (\257eld,)s 114.21 (has)s 135.4 (a)s 145.19 (symmetric)s 203.413 (double)s 241.869 (w)s 250.202 (ell)s 265.992 (structure.)s 322.055 (In)s 336.845 (the)s 357.301 (KBC)s 387.59 (mo)s 403.924 (del)s 423.047 (instead,)s 144.626 y -5.69 (the)s 16.348 (phase)s 51.12 (transition)s 107.258 (\050in)s 127.296 (the)s 149.334 (sense)s 181.506 (of)s 196.544 (co)s 208.211 (existence)s 260.649 (of)s 275.687 (phases\051)s 319.859 (tak)s 336.525 (es)s 351.963 (place)s 384.002 (at)s 400.04 (non)s 424.745 (zero)s 10 f 451.483 (h)s 2 f 146.426 y 458.397 (1)s 1 f 161.426 y -5.69 (and/or)s 10 f 34.343 (h)s 2 f 163.226 y 41.257 (2)s 1 f 161.426 y 46.64 (.)s 182.143 y 8.71 (Finally)s 44.543 (,)s 51.086 (w)s 59.419 (e)s 67.764 (ha)s 80.098 (v)s 86.098 (e)s 94.442 (also)s 117.521 (studied)s 158.599 (a)s 167.611 (di\256eren)s 206.311 (t)s 213.989 (kind)s 240.001 (of)s 252.679 (dynamics,)s 308.289 (whic)s 331.955 (h)s 341.634 (is)s 352.712 (in)s 365.723 (a)s 374.735 (w)s 383.068 (a)s 388.735 (y)s 398.08 (in)s 407.747 (termediate)s 198.943 y -5.69 (b)s 1.31 (et)s 10.977 (w)s 19.31 (een)s 41.002 (Glaub)s 73.419 (er)s 87.812 (and)s 111.504 (Ka)s 126.504 (w)s 134.838 (asaki)s 165.597 (in)s 179.956 (the)s 200.982 (fact)s 225.008 (that)s 251.368 (it)s 263.727 (conserv)s 302.494 (es)s 316.92 (only)s 343.612 (one)s 365.972 (quan)s 391.305 (tit)s 403.638 (y)s 408.972 (,)s 416.754 (the)s 437.78 (mag-)s 215.743 y -5.69 (netization.)s 55.021 (Under)s 91.403 (this)s 114.818 (dynamics)s 167.9 (a)s 177.915 (b)s 184.915 (ond)s 208.263 (\050)s 10 f 212.93 (i;)s 222.397 (j)s 1 f 228.026 (\051)s 236.708 (\050namely)s 283.056 (a)s 293.071 (couple)s 330.419 (of)s 344.101 (neigh)s 371.768 (b)s 378.768 (oring)s 409.483 (sites)s 10 f 436.298 (i)s 1 f 444.447 (and)s 10 f 232.543 y -5.69 (j)s 1 f -.062 (\051)s 9.529 (c)s 14.529 (hanges)s 54.853 (its)s 72.51 (con\257guration)s 146.134 (\050)s 10 f 150.801 (\276)s 1 f 158.088 (\050)s 10 f 162.755 (i)s 1 f 166.889 (\051)s 10 f 171.556 (;)s 176.889 (\276)s 1 f 184.177 (\050)s 10 f 188.843 (j)s 1 f 194.472 (\051\051)s 208.729 (or)s 224.353 (sta)s 239.42 (ys)s 255.41 (unc)s 273.744 (hanged,)s 319.565 (with)s 347.823 (probabilit)s 398.856 (y)s 410.113 (dep)s 429.113 (ending)s 249.343 y -5.69 (on)s 11.494 (the)s 32.679 (energy)s 71.564 (di\256erence,)s 129.245 (to)s 144.429 (a)s 154.947 (new)s 180.132 (con\257guration)s 253.35 (\050)s 10 f 258.017 (\276)s 14 f 244.988 y 265.304 (0)s 1 f 249.343 y 268.671 (\050)s 10 f 273.338 (i)s 1 f 277.472 (\051)s 10 f 282.138 (;)s 287.472 (\276)s 14 f 244.988 y 294.759 (0)s 1 f 249.343 y 298.126 (\050)s 10 f 302.792 (j)s 1 f 308.421 (\051\051)s 322.272 (in)s 336.79 (suc)s 353.19 (h)s 364.375 (a)s 374.893 (w)s 383.226 (a)s 388.893 (y)s 399.744 (that)s 426.262 (in)s 440.78 (eac)s 457.114 (h)s 266.143 y -5.69 (site)s 16.286 (of)s 29.862 (the)s 50.439 (b)s 57.439 (ond)s 80.682 (the)s 101.258 (spin)s 126.568 (v)s 132.234 (ariable)s 171.511 (c)s 176.511 (hanges)s 215.82 (b)s 222.154 (y)s 232.396 (1)s 242.306 (and)s 10 f 265.549 (\276)s 1 f 272.837 (\050)s 10 f 277.503 (i)s 1 f 281.637 (\051)s 288.79 (+)s 10 f 300.609 (\276)s 1 f 307.896 (\050)s 10 f 312.563 (j)s 1 f 318.192 (\051)s 326.192 (=)s 10 f 338.858 (\276)s 14 f 261.788 y 346.146 (0)s 1 f 266.143 y 349.512 (\050)s 10 f 354.179 (i)s 1 f 358.313 (\051)s 365.466 (+)s 10 f 377.285 (\276)s 14 f 261.788 y 384.572 (0)s 1 f 266.143 y 387.939 (\050)s 10 f 392.606 (j)s 1 f 398.234 (\051.)s 411.537 (Hence)s 447.114 (the)s 282.943 y -5.69 (magnetization)s 73.165 (sta)s 88.231 (ys)s 104.153 (constan)s 143.886 (t)s 153.407 (during)s 192.296 (the)s 213.817 (ev)s 225.15 (olution,)s 270.219 (while)s 302.407 (the)s 323.928 (n)s 330.261 (um)s 346.595 (b)s 353.595 (er)s 368.483 (of)s 383.004 (0\047s)s 401.926 (can)s 424.78 (c)s 429.78 (hange.)s 299.743 y -5.69 (F)s 1.143 (or)s 16.198 (example,)s 66.975 (c)s 71.975 (hanges)s 111.73 (from)s 140.452 (a)s 150.807 (b)s 157.807 (ond)s 181.495 (con\257guration)s 254.55 (\050)s 12 f 259.217 (\241)s 1 f 268.55 (1)s 10 f 274.55 (;)s 1 f 279.884 (1\051)s 294.905 (to)s 309.927 (a)s 320.282 (con\257guration)s 393.337 (\0500)s 10 f 404.004 (;)s 1 f 409.337 (0\051)s 424.359 (or)s 439.413 (from)s 316.543 y -5.69 (\0500)s 10 f 4.977 (;)s 1 f 10.31 (0\051)s 25.147 (to)s 39.985 (\050)s 12 f 44.651 (\241)s 1 f 53.985 (1)s 10 f 59.985 (;)s 1 f 65.318 (1\051)s 80.156 (are)s 100.36 (p)s 107.36 (ossible:)s 150.501 (a)s 160.672 (sort)s 184.943 (of)s 198.78 (annihilation)s 265.618 (and)s 289.122 (creation)s 335.326 (pro)s 353.026 (cess.)s 382.339 (The)s 407.176 (jump)s 438.347 (rates)s 333.343 y -5.69 (are)s 14.596 (c)s 19.596 (hosen)s 53.248 (to)s 68.167 (satisfy)s 105.886 (the)s 126.805 (detailed)s 172.391 (balance)s 215.977 (with)s 243.563 (resp)s 265.33 (ect)s 284.915 (to)s 299.835 (the)s 320.754 (the)s 341.673 (Gibbs)s 376.742 (measures)s 428.494 (for)s 447.114 (the)s 350.143 y -5.69 (Hamiltonian)s 63.659 (\0501.1\051)s 92.675 (with)s 10 f 120.358 (h)s 2 f 351.943 y 127.272 (2)s 1 f 350.143 y 136.57 (=)s 149.819 (1.)s 165.534 (W)s 176.867 (e)s 186.55 (deriv)s 212.583 (e)s 222.266 (under)s 256.648 (the)s 277.664 (di\256usiv)s 315.398 (e)s 325.08 (scaling)s 364.829 (an)s 381.845 (equation)s 431.195 (for)s 10 f 449.911 (m)s 1 f 460.447 (,)s 366.943 y -5.69 (while)s 10 f 25.464 (\301)s 1 f 36.435 (on)s 52.922 (suc)s 69.322 (h)s 79.81 (a)s 89.63 (long)s 115.451 (time)s 142.605 (scale)s 171.159 (has)s 192.38 (already)s 234.568 (relaxed)s 276.089 (to)s 290.576 (the)s 311.063 (equilibrium)s 374.584 (and)s 397.739 (its)s 414.293 (e\256ect)s 445.78 (can)s 383.743 y -5.69 (b)s 1.31 (e)s 10.431 (seen)s 36.285 (in)s 50.073 (the)s 70.528 (mobilit)s 107.528 (y)s 117.649 (app)s 137.316 (earing)s 173.137 (in)s 186.925 (the)s 207.379 (equation)s 256.167 (for)s 10 f 274.321 (m)s 1 f 284.857 (.)s 293.453 (This)s 320.641 (dynamics)s 373.496 (is)s 385.35 (of)s 398.805 (the)s 419.259 (so)s 433.78 (called)s 400.543 y -5.69 (non)s 17.414 (gradien)s 55.781 (t)s 64.219 (t)s 68.553 (yp)s 81.886 (e)s 90.991 ([Sp])s 114.762 (and)s 137.867 (the)s 158.305 (pro)s 176.005 (of)s 189.443 (of)s 202.881 (the)s 223.319 (h)s 229.652 (ydro)s 253.685 (dynamic)s 301.79 (limit)s 330.228 (relies)s 360.766 (on)s 377.204 (the)s 397.642 (non)s 420.747 (gradien)s 459.114 (t)s 417.343 y -5.69 (metho)s 27.31 (d)s 37.977 ([V].)s 438.059 y 8.71 (In)s 24.443 (Section)s 67.177 (2)s 77.911 (w)s 86.244 (e)s 96.311 (describ)s 133.411 (e)s 143.478 (the)s 164.878 (equilibrium)s 229.312 (prop)s 253.679 (erties)s 286.512 (of)s 300.913 (the)s 322.313 (KBC)s 353.546 (mo)s 369.879 (del)s 389.946 (and)s 414.013 (pro)s 431.047 (v)s 437.047 (e)s 447.114 (the)s 454.859 y -5.69 (limit)s 10 f 22.506 (\260)s 12 f 32.719 (!)s 1 f 48.052 (0)s 57.582 (for)s 75.478 (the)s 95.674 (in\257nite)s 135.87 (v)s 141.87 (olume)s 176.733 (free)s 199.296 (energy)s 237.193 (and)s 260.056 (pressure.)s 311.432 (In)s 325.962 (Section)s 367.491 (3)s 377.021 (w)s 385.354 (e)s 394.217 (in)s 403.884 (tro)s 419.584 (duce)s 447.114 (the)s 471.659 y -5.69 (Glaub)s 26.727 (er)s 40.154 (and)s 62.882 (Ka)s 77.882 (w)s 86.215 (asaki)s 116.01 (dynamics)s 168.471 (and)s 191.198 (state)s 219.993 (the)s 240.054 (main)s 269.448 (theorems,)s 323.73 (whose)s 358.525 (pro)s 376.225 (ofs)s 394.019 (are)s 413.447 (con)s 431.114 (tained)s 488.459 y -5.69 (in)s 8.88 (Sections)s 56.184 (4)s 66.755 (and)s 90.659 (5.)s 107.037 (In)s 122.608 (Section)s 165.178 (6)s 175.749 (w)s 184.082 (e)s 193.986 (pro)s 211.019 (v)s 217.019 (e)s 226.923 (the)s 248.16 (h)s 254.494 (ydro)s 278.527 (dynamic)s 327.431 (limit)s 356.668 (for)s 375.606 (the)s 396.843 (non)s 420.747 (gradien)s 459.114 (t)s 505.259 y -5.69 (dynamics.)s 525.976 y 8.71 (The)s 35.174 (pro)s 52.874 (of)s 68.339 (of)s 83.803 (the)s 106.267 (h)s 112.601 (ydro)s 136.634 (dynamical)s 196.098 (limit)s 226.563 (for)s 246.727 (the)s 269.192 (Ka)s 284.192 (w)s 292.525 (asaki)s 324.723 (dynamics)s 379.587 (is)s 393.451 (based)s 428.649 (on)s 447.114 (the)s 542.776 y -5.69 (metho)s 27.31 (d)s 37.42 (of)s 50.53 ([GPV].)s 90.557 (This)s 117.401 (metho)s 150.401 (d)s 160.511 (has)s 181.355 (b)s 188.355 (een)s 209.132 (extended)s 259.575 (to)s 273.685 (in\257nite)s 313.796 (v)s 319.796 (olume)s 354.573 (b)s 360.906 (y)s 370.683 (F)s 377.516 (ritz)s 398.993 ([F],)s 420.27 (b)s 426.603 (y)s 436.38 (using)s 559.576 y -5.69 (a)s 5.234 (b)s 12.234 (ound)s 43.158 (uniform)s 89.116 (in)s 104.041 (the)s 125.631 (v)s 131.632 (olume)s 167.889 (for)s 187.18 (the)s 208.771 (en)s 220.438 (trop)s 242.138 (y)s 253.396 (pro)s 271.096 (duction.)s 321.869 (In)s 337.793 (the)s 359.384 (pap)s 379.051 (er)s 394.008 (b)s 400.341 (y)s 411.599 (Y)s 419.599 (au)s 437.19 ([Y])s 457.78 (a)s 576.376 y -5.69 (di\256eren)s 33.01 (t)s 43.128 (pro)s 60.828 (of)s 75.947 (of)s 91.065 (the)s 113.183 (uniform)s 159.668 (en)s 171.335 (trop)s 193.035 (y)s 204.82 (pro)s 222.52 (duction)s 267.305 (b)s 274.305 (ound)s 305.757 (has)s 328.608 (b)s 335.608 (een)s 358.393 (giv)s 373.727 (en)s 391.178 (for)s 410.997 (Ginzburg-)s 593.176 y -5.69 (Landau)s 37.672 (mo)s 54.005 (dels)s 77.934 (and)s 101.13 (in)s 114.992 ([LM])s 144.021 (this)s 167.283 (approac)s 208.316 (h)s 218.845 (has)s 240.107 (b)s 247.107 (een)s 268.303 (used)s 295.565 (to)s 310.094 (pro)s 327.127 (v)s 333.127 (e)s 342.322 (h)s 348.656 (ydro)s 372.689 (dynamic)s 420.885 (limit)s 449.414 (for)s 609.976 y -5.69 (a)s 4.922 (class)s 33.667 (of)s 47.946 (zero)s 73.924 (range)s 107.236 (mo)s 123.57 (dels.)s 154.139 (W)s 165.472 (e)s 175.417 (follo)s 197.418 (w)s 210.696 (the)s 231.975 (latter)s 265.287 (approac)s 306.32 (h)s 317.599 (and)s 341.544 (pro)s 358.578 (v)s 364.578 (e)s 374.523 (a)s 385.135 (uniform)s 430.78 (b)s 437.78 (ound)s 626.776 y -5.69 (for)s 12.826 (the)s 33.643 (en)s 45.31 (trop)s 67.01 (y)s 77.493 (pro)s 95.193 (duction,)s 142.047 (whic)s 165.714 (h)s 176.531 (is)s 188.747 (the)s 209.564 (time)s 237.047 (deriv)s 262.747 (ativ)s 282.747 (e)s 292.23 (of)s 306.047 (the)s 326.864 (en)s 338.53 (trop)s 360.23 (y)s 365.564 (.)s 374.68 (Here)s 403.197 (w)s 411.53 (e)s 421.013 (consider)s 643.576 y -5.69 (not)s 15.833 (the)s 36.689 (en)s 48.356 (trop)s 70.056 (y)s 80.579 (but)s 102.769 (the)s 123.626 (relativ)s 156.992 (e)s 166.515 (en)s 178.182 (trop)s 199.882 (y)s 210.405 (of)s 224.262 (the)s 245.118 (densit)s 276.185 (y)s 286.708 (of)s 300.564 (the)s 321.421 (pro)s 339.121 (cess)s 363.444 (with)s 390.967 (resp)s 412.734 (ect)s 432.257 (to)s 447.114 (the)s 660.376 y -5.69 (Bernoulli)s 46.617 (measure)s 10 f 93.824 (\272)s 11 f 662.176 y 99.752 (h)s 16 f 663.376 y 105.37 (1)s 11 f 662.176 y 110.054 (;h)s 16 f 663.376 y 118.522 (2)s 1 f 660.376 y 128.246 (parametrized)s 201.42 (b)s 207.753 (y)s 218.527 (the)s 239.634 (c)s 244.634 (hemical)s 289.074 (p)s 296.075 (oten)s 318.408 (tials,)s 348.359 (whic)s 372.025 (h)s 383.132 (is)s 395.64 (not)s 417.413 (in)s 427.08 (v)s 432.747 (arian)s 459.114 (t)s 677.176 y -5.69 (for)s 14.117 (the)s 36.224 (pro)s 53.925 (cess.)s 87.046 (Nev)s 107.38 (ertheless,)s 161.347 (the)s 183.455 (b)s 190.455 (ound)s 221.895 (of)s 237.003 (this)s 261.843 (pro)s 279.543 (duction)s 324.317 (of)s 339.425 (en)s 351.091 (trop)s 372.792 (y)s 384.566 (will)s 408.673 (b)s 415.673 (e)s 426.447 (enough)s 705.976 y 226.045 (4)s do-end end endp %%Page: 5 5 %%BeginPageSetup initializepage (Raffaele Esposito; page: 5 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f1_12 sf ( )S -997 -1000 :M f2_12 sf ( )S -993 -1000 :M f10_12 sf ( )S -985 -1000 :M f11_12 sf ( )S -976 -1000 :M f12_12 sf ( )S -964 -1000 :M f13_12 sf ( )S -954 -1000 :M f14_12 sf ( )S -941 -1000 :M f15_12 sf ( )S -930 -1000 :M f16_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 16 5 1200 1000 div mul /CMR5 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 6.31 y -5.69 (for)s 13.836 (the)s 35.661 (GPV)s 67.403 (metho)s 100.403 (d)s 112.229 (to)s 128.055 (w)s 136.388 (ork.)s 165.565 (In)s 181.724 (fact,)s 210.173 (it)s 223.333 (is)s 236.558 (easy)s 264.118 (to)s 279.943 (sho)s 297.01 (w)s 310.836 (that)s 337.995 (the)s 359.821 (Ka)s 374.821 (w)s 383.154 (asaki)s 414.713 (dynamics)s 23.11 y -5.69 (\050tough)s 28.643 (t)s 37.445 (of)s 51.247 (as)s 66.116 (a)s 76.251 (lattice)s 113.053 (gas)s 133.922 (dynamics\051)s 191.791 (is)s 203.993 (a)s 214.128 (w)s 222.461 (eak)s 244.263 (p)s 251.263 (erturbation)s 314.799 (\050and)s 342.934 (reduces)s 385.836 (at)s 10 f 400.638 (\257)s 1 f 411.618 (=)s 424.51 (0)s 434.645 (to\051)s 454.114 (of)s 39.91 y -5.69 (the)s 14.49 (follo)s 36.49 (wing)s 64.671 (generalized)s 126.218 (symmetric)s 184.166 (exclusion)s 235.413 (pro)s 253.113 (cess)s 276.76 (\050GSEP\051:)s 325.358 (eac)s 341.691 (h)s 351.872 (particle)s 394.752 (on)s 410.933 (the)s 431.114 (lattice)s 56.71 y -5.69 (jumps)s 30.677 (at)s 45.978 (random)s 90.645 (times)s 123.346 (to)s 138.647 (a)s 149.281 (nearest)s 191.348 (neigh)s 219.015 (b)s 226.015 (our)s 248.015 (site)s 10 f 270.716 (x)s 1 f 282.208 (if)s 293.842 (and)s 317.81 (only)s 344.777 (if)s 356.411 (there)s 387.745 (is)s 400.446 (at)s 415.746 (most)s 445.78 (one)s 73.51 y -5.69 (particle)s 37.008 (in)s 10 f 50.34 (x)s 1 f 57.198 (.)s 65.642 (Hence)s 100.64 (the)s 120.639 (state)s 149.37 (of)s 162.369 (the)s 182.367 (system)s 221.499 (on)s 237.497 (times)s 10 f 268.896 (\260)s 14 f 69.155 y 275.775 (\241)s 2 f 283.275 (2)s 1 f 73.51 y 291.99 (will)s 313.988 (b)s 320.988 (e)s 329.653 (v)s 335.653 (ery)s 355.352 (close)s 383.417 (to)s 397.415 (the)s 417.413 (in)s 427.08 (v)s 432.747 (arian)s 459.113 (t)s 90.31 y -5.69 (measures)s 46.79 (for)s 66.138 (the)s 87.785 (GSEP)s 125.181 (pro)s 142.881 (cess,)s 171.574 (whic)s 195.24 (h)s 206.888 (are)s 227.902 (the)s 249.549 (Bernoulli)s 302.396 (measure)s 10 f 350.144 (\272)s 11 f 92.11 y 356.071 (h)s 16 f 93.31 y 361.69 (1)s 11 f 92.11 y 366.373 (;h)s 16 f 93.31 y 374.841 (2)s 1 f 90.31 y 380.124 (.)s 391.733 (Therefore)s 447.114 (the)s 107.11 y -5.69 (uniform)s 40.105 (b)s 47.105 (ound)s 77.866 (for)s 96.994 (this)s 121.156 (en)s 132.822 (trop)s 154.522 (y)s 165.617 (pro)s 183.317 (duction)s 227.412 (will)s 250.84 (b)s 257.84 (e)s 267.935 (su\261cien)s 309.668 (t)s 319.096 (to)s 334.524 (pro)s 351.557 (v)s 357.557 (e)s 367.652 (the)s 389.08 (h)s 395.413 (ydro)s 419.447 (dynamic)s 123.91 y -5.69 (limit.)s 27.595 (The)s 52.118 (pro)s 69.818 (of)s 83.341 (in)s 97.197 (the)s 117.72 (case)s 142.976 (of)s 156.499 (the)s 177.021 (Glaub)s 209.438 (er)s 223.328 (dynamics)s 276.25 (is)s 288.173 (simpler:)s 334.868 (martingales)s 399.491 (metho)s 432.491 (ds)s 447.747 (are)s 140.71 y -5.69 (enough.)s 42.398 (In)s 58.094 (b)s 65.094 (oth)s 87.123 (cases)s 117.953 (it)s 130.649 (has)s 152.745 (b)s 159.745 (een)s 181.774 (necessary)s 235.637 (to)s 251 (pro)s 268.033 (v)s 274.033 (e)s 284.062 (uniqueness)s 345.225 (theorems)s 397.355 (for)s 416.417 (the)s 437.78 (w)s 446.113 (eak)s 157.51 y -5.69 (solutions)s 44.443 (of)s 58.11 (the)s 78.777 (limiting)s 123.443 (equations.)s 174.43 y 8.71 (The)s 34.341 (non)s 58.639 (gradien)s 97.005 (t)s 106.636 (dynamics)s 160.667 (studied)s 203.698 (in)s 218.663 (Section)s 261.627 (6)s 272.592 (when)s 304.889 (form)s 328.923 (ulated)s 366.554 (in)s 381.518 (the)s 403.149 (language)s 454.113 (of)s 191.23 y -5.69 (lattice)s 30.708 (gases)s 61.239 (is)s 73.036 (a)s 82.767 (w)s 91.101 (eak)s 112.498 (p)s 119.498 (erturbation)s 182.629 (of)s 196.027 (a)s 205.758 (non)s 228.823 (gradien)s 267.189 (t)s 275.587 (generalized)s 337.351 (simple)s 374.482 (exclusion)s 425.947 (pro)s 443.647 (cess)s 208.03 y -5.69 (in)s 3.976 (tro)s 19.677 (duced)s 55.429 (in)s 70.514 ([KLO].)s 111.767 (The)s 137.519 (di\256usion)s 187.005 (co)s 198.672 (e\261cien)s 234.338 (t)s 244.091 (for)s 263.543 (this)s 288.028 (pro)s 305.728 (cess)s 330.947 (is)s 344.1 (not)s 366.519 (a)s 377.604 (constan)s 417.338 (t,)s 430.695 (lik)s 443.361 (e)s 453.78 (in)s 224.83 y -5.69 (the)s 16.728 (symmetric)s 76.912 (exclusion)s 130.397 (pro)s 148.097 (cess)s 173.981 (considered)s 234.499 (b)s 241.499 (efore,)s 276.055 (but)s 299.806 (a)s 311.557 (function)s 360.309 (of)s 375.727 (the)s 398.144 (densit)s 429.211 (y)s 441.296 (as)s 457.78 (a)s 241.63 y -5.69 (consequence)s 63.204 (of)s 78.032 (the)s 99.859 (non)s 124.354 (gradien)s 162.721 (t)s 172.548 (c)s 177.548 (haracter)s 226.109 (of)s 240.937 (the)s 262.765 (dynamics.)s 323.981 (W)s 335.314 (e)s 345.809 (w)s 354.142 (ork)s 376.336 (in)s 391.497 (this)s 416.058 (case)s 442.619 (in)s 457.78 (a)s 258.43 y -5.69 (torus,)s 29.401 (the)s 50.86 (extension)s 104.72 (to)s 120.179 (in\257nite)s 161.638 (v)s 167.638 (olume)s 203.764 (b)s 210.764 (eing)s 236.891 (more)s 267.717 (in)s 277.383 (v)s 283.383 (olv)s 298.717 (ed)s 315.509 (b)s 322.509 (ecause)s 360.702 (of)s 375.161 (the)s 396.621 (non)s 420.747 (gradien)s 459.114 (t)s 275.23 y -5.69 (nature)s 32.36 (of)s 46.044 (the)s 66.727 (problem.)s 118.144 (The)s 142.828 (pro)s 160.528 (of)s 174.211 (is)s 186.295 (based)s 219.712 (again)s 251.729 (on)s 268.412 (the)s 289.096 (metho)s 322.096 (d)s 332.779 (of)s 346.463 ([GPV])s 383.73 (and)s 407.08 (on)s 423.763 (the)s 444.447 (non)s 292.03 y -5.69 (gradien)s 32.677 (t)s 41.081 (tec)s 56.081 (hniques)s 99.551 (of)s 112.956 ([V],)s 135.693 (that)s 161.43 (ha)s 173.764 (v)s 179.764 (e)s 188.835 (to)s 203.239 (b)s 210.239 (e)s 219.309 (adapted)s 265.047 (to)s 279.451 (deal)s 304.522 (with)s 331.593 (the)s 351.997 (p)s 358.997 (erturbation.)s 426.976 (Also)s 453.78 (in)s 308.83 y -5.69 (this)s 17.878 (case,)s 46.821 (w)s 55.155 (e)s 64.656 (will)s 87.491 (use)s 108.393 (as)s 123.294 (reference)s 173.862 (measure)s 220.797 (the)s 241.632 (Bernoulli)s 293.667 (measure,)s 343.977 (parametrized)s 416.879 (this)s 440.447 (time)s 325.63 y -5.69 (only)s 21.595 (b)s 27.929 (y)s 39.214 (the)s 60.833 (magnetic)s 113.118 (\257eld,)s 143.641 (whic)s 167.308 (h)s 178.927 (is)s 191.945 (not)s 214.231 (in)s 223.897 (v)s 229.564 (arian)s 255.931 (t)s 265.549 (for)s 284.868 (the)s 306.487 (dynamics.)s 367.076 (As)s 385.762 (a)s 396.714 (consequence,)s 342.43 y -5.69 (since)s 24.37 (the)s 45.697 (dynamics)s 99.424 (is)s 112.151 (non)s 136.145 (gradien)s 174.512 (t,)s 187.337 (in)s 201.997 (the)s 223.324 (limiting)s 268.652 (equation)s 318.312 (there)s 349.672 (is)s 362.399 (a)s 373.06 (new)s 398.387 (term)s 427.747 (related)s 359.23 y -5.69 (to)s 8.974 (the)s 29.639 (solution)s 75.036 (of)s 88.701 (the)s 109.365 (non)s 132.696 (gradien)s 171.063 (t)s 179.728 (problem)s 226.425 (for)s 244.79 (the)s 265.454 (unp)s 285.788 (erturb)s 318.854 (ed)s 334.852 (pro)s 352.552 (cess.)s 381.351 (The)s 406.016 (presence)s 454.114 (of)s 376.03 y -5.69 (this)s 18.154 (term)s 47.298 (is)s 59.808 (crucial)s 98.952 (to)s 114.063 (recognize)s 166.54 (that)s 192.984 (the)s 214.095 (limiting)s 259.206 (equation)s 308.65 (is)s 321.16 (in)s 335.604 (the)s 356.715 (form)s 385.526 (of)s 399.636 (the)s 420.747 (gradien)s 459.114 (t)s 392.83 y -5.69 (\260)s .976 (ux)s 18.004 (for)s 36.398 (a)s 46.426 (free)s 69.487 (energy)s 107.881 (functional.)s 168.964 (That)s 198.992 (is)s 211.086 (a)s 221.114 (general)s 262.508 (fact)s 286.203 (for)s 304.597 (non)s 327.958 (gradien)s 366.325 (t)s 375.019 (dynamics)s 428.113 (w)s 436.447 (eakly)s 409.63 y -5.69 (p)s 1.31 (erturb)s 34.377 (ed)s 50.377 (b)s 56.71 (y)s 67.043 (a)s 77.043 (Kac)s 101.71 (p)s 108.71 (oten)s 131.043 (tial,)s 155.71 (\050see)s 179.777 ([GLM]\051.)s 226.36 (The)s 251.027 (limiting)s 295.694 (equation)s 344.694 (is)s 10 f 450.446 y 172.711 (@)s 11 f 452.246 y 179.081 (t)s 10 f 450.446 y 183.306 (m)s 1 f 197.176 (=)s 12 f 209.843 (r)s 222.509 (\242)s 13 f 429.926 y 228.509 (\303)s 1 f 450.446 y 238.009 (\247)s 12 f 246.676 (r)s 10 f 442.328 y 259.459 (\261)s 12 f 265.246 (G)s 16.324 .48 258.116 447.686 r 10 f 458.677 y 258.116 (\261)s 263.903 (m)s 13 f 429.926 y 275.879 (!)s 1 f 491.262 y -5.69 (with)s 21.643 (the)s 42.31 (energy)s 80.677 (functional)s 12 f 137.01 (G)s 1 f 144.86 (\050)s 10 f 149.527 (m)s 1 f 160.063 (\050)s 10 f 164.73 (r)s 1 f 170.477 (\051\051)s 183.81 (of)s 197.477 (the)s 218.144 (form)s 13 f 511.077 y 86.529 (Z)s 10 f 527.411 y 100.529 (dr)s 112.522 (g)s 2 f 522.456 y 118.676 (0)s 13 f 517.691 y 124.059 (\241)s 10 f 527.411 y 129.559 (m)s 1 f 140.095 (\050)s 10 f 144.762 (r)s 1 f 150.509 (\051)s 13 f 517.691 y 155.176 (\242)s 1 f 527.411 y 163.343 (+)s 519.293 y 176.783 (1)s 6 .48 176.783 524.651 r 535.642 y 176.783 (2)s 13 f 511.077 y 186.223 (Z)s 10 f 527.411 y 200.223 (dr)s 13 f 511.077 y 214.216 (Z)s 10 f 527.411 y 228.216 (dr)s 14 f 522.456 y 240.209 (0)s 10 f 527.411 y 243.575 (J)s 1 f 251.384 (\050)s 10 f 256.05 (r)s 12 f 264.464 (\241)s 10 f 276.464 (r)s 14 f 522.456 y 282.211 (0)s 1 f 527.411 y 285.578 (\051[)s 10 f 293.578 (m)s 1 f 304.114 (\050)s 10 f 308.781 (r)s 1 f 314.528 (\051)s 12 f 321.861 (\241)s 10 f 333.861 (m)s 1 f 344.397 (\050)s 10 f 349.064 (r)s 14 f 522.456 y 354.811 (0)s 1 f 527.411 y 358.178 (\051])s 2 f 522.456 y 366.178 (2)s 1 f 527.411 y 439.114 (\0501)s 10 f 449.78 (:)s 1 f 453.114 (8\051)s 562.893 y -5.69 (where)s 10 f 595.561 y 2.822 (g)s 2 f 590.606 y 8.976 (0)s 13 f 585.84 y 14.359 (\241)s 10 f 595.561 y 19.859 (m)s 1 f 30.396 (\051)s 38.395 (:=)s 12 f 53.729 (\241)s 10 f 65.729 (m)s 2 f 590.606 y 76.265 (2)s 10 f 595.561 y 81.648 (\257)s 14 f 590.606 y 89.069 (\241)s 2 f 96.569 (1)s 13 f 582.24 y 101.952 (h)s 1 f 587.442 y 109.059 (1)s 6 .48 109.059 592.8 r 603.792 y 109.059 (2)s 595.561 y 116.499 (\050)s 10 f 121.166 (m)s 1 f 134.369 (+)s 10 f 146.369 (\301)s 1 f 153.519 (\050)s 10 f 158.185 (m)s 1 f 168.721 (\051\051)s 180.055 (log)s 195.555 (\050)s 10 f 200.221 (m)s 1 f 213.424 (+)s 10 f 225.424 (\301)s 1 f 232.574 (\050)s 10 f 237.241 (m)s 1 f 247.777 (\051\051)s 259.777 (+)s 587.442 y 273.217 (1)s 6 .48 273.217 592.8 r 603.792 y 273.217 (2)s 595.561 y 280.657 (\050)s 10 f 285.324 (\301)s 1 f 292.474 (\050)s 10 f 297.14 (m)s 1 f 307.676 (\051)s 12 f 315.01 (\241)s 10 f 327.01 (m)s 1 f 337.546 (\051)s 344.212 (log)s 359.713 (\050)s 10 f 364.379 (\301)s 1 f 371.529 (\050)s 10 f 376.196 (m)s 1 f 386.732 (\051)s 12 f 394.065 (\241)s 10 f 406.065 (m)s 1 f 416.601 (\051+)s 625.992 y 51.062 (\0501)s 12 f 64.395 (\241)s 10 f 76.395 (\301)s 1 f 83.545 (\050)s 10 f 88.212 (m)s 1 f 98.748 (\051\051)s 110.082 (log)s 125.582 (\0501)s 12 f 138.915 (\241)s 10 f 150.915 (\301)s 1 f 158.065 (\050)s 10 f 162.732 (m)s 1 f 173.268 (\051\051)s 12 f 185.268 (\241)s 10 f 197.268 (\301)s 1 f 204.418 (\050)s 10 f 209.084 (m)s 1 f 219.621 (\051)s 226.287 (log)s 243.787 (2)s 13 f 612.672 y 249.787 (i)s 1 f 609.751 y 439.114 (\0501)s 10 f 449.78 (:)s 1 f 453.114 (9\051)s 660.376 y -5.69 (and)s 10 f 18.25 (\301)s 1 f 25.4 (\050)s 10 f 30.067 (m)s 1 f 40.603 (\051)s 49.614 (=)s 10 f 58.947 (\074)s 72.625 (\276)s 2 f 656.021 y 79.912 (2)s 10 f 660.376 y 89.64 (\076)s 11 f 662.176 y 98.973 (\272)s 15 f 663.449 y 103.784 (h)s 16 f 665.249 y 108.75 (1)s 15 f 663.449 y 113.433 (;)s 16 f 116.183 (0)s 1 f 660.376 y 126.073 (with)s 10 f 154.013 (h)s 2 f 662.176 y 160.927 (1)s 1 f 660.376 y 170.917 (determined)s 234.224 (as)s 249.564 (a)s 260.17 (function)s 307.777 (of)s 10 f 322.05 (m)s 1 f 337.193 (via)s 10 f 357.466 (m)s 1 f 368.003 (\050)s 10 f 372.669 (h)s 2 f 662.176 y 379.583 (1)s 1 f 660.376 y 384.967 (\051)s 393.977 (=)s 10 f 403.311 (\074)s 416.988 (\276)s 428.62 (\076)s 11 f 662.176 y 437.954 (\272)s 15 f 663.449 y 442.765 (h)s 16 f 665.249 y 447.73 (1)s 15 f 663.449 y 452.413 (;)s 16 f 455.164 (0)s 1 f 660.376 y 460.447 (.)s 677.176 y -5.69 (The)s 19.938 (mobilit)s 56.938 (y)s 68.232 (is)s 81.26 (giv)s 96.594 (en)s 113.555 (b)s 119.888 (y)s 131.183 (the)s 152.811 (Einstein)s 200.672 (relation)s 245.667 (\247)s 259.269 (=)s 10 f 273.538 (D)s 1 f 283.806 (\050)s 10 f 288.473 (m)s 1 f 299.009 (\051)s 10 f 303.675 (\302)s 1 f 311.184 (\050)s 10 f 315.85 (m)s 1 f 326.387 (\051,)s 339.588 (with)s 10 f 367.883 (\302)s 1 f 380.352 (the)s 401.98 (susceptivit)s 457.447 (y)s 705.976 y 226.045 (5)s do-end end endp %%Page: 6 6 %%BeginPageSetup initializepage (Raffaele Esposito; page: 6 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f0_12 sf ( )S -996 -1000 :M f1_12 sf ( )S -993 -1000 :M f2_12 sf ( )S -989 -1000 :M f10_12 sf ( )S -981 -1000 :M f11_12 sf ( )S -972 -1000 :M f12_12 sf ( )S -960 -1000 :M f13_12 sf ( )S -951 -1000 :M f14_12 sf ( )S -937 -1000 :M f15_12 sf ( )S -926 -1000 :M f16_12 sf ( )S -921 -1000 :M f18_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 1200 1000 div mul /CMBX10 findfont fdef 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 16 5 1200 1000 div mul /CMR5 findfont fdef 18 5 1200 1000 div mul /CMSY5 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 6.31 y -5.69 (and)s 10 f 18.455 (D)s 1 f 33.534 (the)s 55.012 (di\256usion)s 104.224 (co)s 115.891 (e\261cien)s 151.557 (t,)s 164.572 (whic)s 188.238 (h)s 199.716 (is)s 212.595 (giv)s 227.928 (en)s 244.739 (b)s 251.073 (y)s 262.217 (the)s 283.696 (Green-Kub)s 342.146 (o)s 352.957 (form)s 376.991 (ula)s 397.802 ([KLO].)s 438.78 (Note)s 23.11 y -5.69 (that)s 10 f 19.634 (g)s 2 f 18.755 y 25.789 (0)s 1 f 23.11 y 31.172 (\050)s 10 f 35.839 (m)s 1 f 46.375 (\051)s 54.366 (coincide)s 99.691 (with)s 126.349 (the)s 146.34 (functional)s 10 f 201.998 (f)s 2 f 18.755 y 209.165 (0)s 1 f 23.11 y 217.873 (in)s 231.197 (\0501.3\051,)s 262.657 (asso)s 284.457 (ciated)s 319.115 (to)s 333.106 (the)s 353.098 (Hamiltonian)s 421.422 (\0501.1\051)s 449.414 (for)s 10 f 39.91 y -5.69 (h)s 2 f 41.71 y 1.224 (2)s 1 f 39.91 y 9.94 (=)s 22.607 (1,)s 35.335 (when)s 65.913 (ev)s 76.913 (aluated)s 118.823 (in)s 13 f 30.19 y 132.067 (\241)s 10 f 39.91 y 137.567 (m;)s 153.436 (\301)s 1 f 160.586 (\050)s 10 f 165.253 (m)s 1 f 175.789 (\051)s 13 f 30.19 y 180.456 (\242)s 1 f 39.91 y 185.956 (.)s 194.371 (This)s 221.014 (is)s 232.325 (due)s 254.235 (to)s 268.146 (the)s 288.056 (fact)s 310.967 (that)s 10 f 336.211 (\301)s 1 f 346.605 (is)s 357.915 (a)s 367.159 (fast)s 389.47 (v)s 395.136 (ariable)s 433.747 (under)s 56.71 y -5.69 (this)s 17.71 (dynamics)s 70.777 (and)s 94.11 (in)s 108.11 (the)s 128.777 (di\256usiv)s 166.51 (e)s 175.843 (limit)s 204.51 (it)s 216.51 (relaxes)s 256.277 (to)s 270.944 (its)s 287.677 (equilibrium)s 351.377 (v)s 357.044 (alue)s 10 f 382.377 (\074)s 395.044 (\276)s 2 f 52.355 y 402.331 (2)s 10 f 56.71 y 411.048 (\076)s 11 f 58.51 y 420.381 (\272)s 15 f 59.783 y 425.192 (h)s 16 f 61.583 y 430.158 (1)s 15 f 59.783 y 434.841 (;)s 16 f 437.591 (0)s 1 f 56.71 y 442.875 (.)s 73.63 y 8.71 (The)s 33.349 (con)s 51.015 (v)s 57.015 (ergence)s 99.687 (result)s 133.093 (that)s 159.065 (w)s 167.398 (e)s 176.704 (get)s 196.676 (in)s 210.648 (this)s 234.02 (case)s 259.392 (is)s 271.431 (w)s 279.764 (eak)s 297.098 (er)s 311.103 (that)s 337.075 (the)s 357.714 (one)s 379.686 (for)s 398.025 (Glaub)s 430.442 (er)s 444.447 (and)s 90.43 y -5.69 (Ka)s 9.31 (w)s 17.643 (asaki,)s 51.008 (b)s 58.008 (ecause)s 94.947 (w)s 103.281 (e)s 112.153 (are)s 131.726 (not)s 152.599 (able)s 177.471 (to)s 191.677 (pro)s 208.711 (v)s 214.711 (e)s 223.583 (the)s 243.789 (uniqueness)s 303.795 (of)s 317.001 (the)s 337.207 (h)s 343.541 (ydro)s 367.574 (dynamic)s 415.447 (equation,)s 107.23 y -5.69 (due)s 18.512 (to)s 34.715 (the)s 56.918 (fact)s 82.12 (that)s 109.656 (the)s 131.859 (only)s 159.728 (regularit)s 204.128 (y)s 215.998 (prop)s 240.364 (ert)s 254.731 (y)s 266.6 (kno)s 285.267 (wn)s 306.136 (for)s 326.039 (the)s 348.242 (di\256usion)s 398.178 (co)s 409.844 (e\261cien)s 445.511 (t)s 455.714 (is)s 124.03 y -5.69 (con)s 11.976 (tin)s 26.31 (uit)s 40.643 (y)s 45.977 (.)s 58.864 (Could)s 95.604 (the)s 117.677 (Lipsc)s 144.911 (hitz)s 170.317 (con)s 187.984 (tin)s 202.317 (uit)s 216.651 (y)s 228.391 (for)s 10 f 248.164 (D)s 1 f 263.839 (b)s 270.839 (e)s 281.58 (pro)s 298.613 (v)s 304.613 (en)s 322.02 (w)s 330.353 (e)s 341.093 (w)s 349.426 (ould)s 377.5 (get)s 398.907 (the)s 420.98 (stronger)s 140.83 y -5.69 (con)s 11.976 (v)s 17.977 (ergence)s 60.677 (result.)s 0 f 186.202 y -5.69 (2.)s 11.176 (The)s 39.368 (Kac-Blume-Cap)s 136.092 (el)s 150.851 (mo)s 169.634 (del.)s 1 f 209.909 y 8.71 (The)s 33.513 (Blume-Cap)s 93.013 (el)s 105.816 (mo)s 122.149 (del)s 141.618 (is)s 153.821 (a)s 163.957 (mo)s 180.291 (del)s 199.76 (of)s 213.563 (spins)s 243.833 (with)s 271.302 (v)s 276.969 (alues)s 307.172 (0)s 10 f 313.172 (;)s 12 f 318.505 (\247)s 1 f 327.838 (1)s 337.975 (with)s 365.444 (nearest)s 407.014 (neigh)s 434.68 (b)s 441.68 (ours)s 226.709 y -5.69 (in)s 3.976 (teraction,)s 57.568 (originally)s 110.049 (in)s 119.716 (tro)s 135.416 (duced)s 169.53 (to)s 183.645 (study)s 216.159 (the)s 236.273 (Helium)s 277.388 (phase)s 310.236 (transition.)s 369.485 (Here)s 397.299 (w)s 405.633 (e)s 414.414 (in)s 424.08 (tro)s 439.78 (duce)s 243.509 y -5.69 (a)s 5.52 (mo)s 21.853 (del)s 42.396 (that)s 69.606 (w)s 77.939 (e)s 88.483 (call)s 111.692 (Kac-Blume-Cap)s 195.859 (el)s 209.736 (\050KBC\051)s 250.778 (mo)s 267.111 (del)s 287.654 (whic)s 311.321 (h)s 323.197 (is)s 336.474 (a)s 347.684 (mo)s 364.017 (del)s 384.56 (of)s 399.437 (spins)s 430.78 (taking)s 260.309 y -5.69 (v)s -.024 (alues)s 31.54 (in)s 12 f 47.038 (f\241)s 1 f 62.371 (1)s 10 f 68.371 (;)s 1 f 73.704 (0)s 10 f 79.704 (;)s 1 f 85.038 (1)s 12 f 91.038 (g)s 1 f 102.535 (on)s 120.699 (a)s 10 f 132.196 (d)s 1 f 138.442 (-dimensional)s 210.006 (lattice)s 10 f 248.17 (Z)s 251.22 (Z)s 11 f 255.076 y 262.27 (d)s 1 f 260.309 y 273.363 (and)s 298.194 (in)s 307.86 (teracting)s 360.058 (b)s 366.391 (y)s 378.222 (means)s 416.452 (of)s 431.616 (a)s 443.114 (Kac)s 277.109 y -5.69 (p)s 1.31 (oten)s 23.643 (tial.)s 294.029 y 8.71 (A)s 21.71 (Kac)s 46.377 (p)s 53.377 (oten)s 75.71 (tial)s 97.043 (is)s 109.11 (a)s 119.11 (function)s 10 f 166.11 (J)s 11 f 295.829 y 172.764 (\260)s 1 f 294.029 y 178.922 (\050)s 10 f 183.588 (r)s 1 f 189.335 (\051,)s 10 f 201.335 (\260)s 211.548 (\076)s 1 f 224.215 (0,)s 237.548 (suc)s 253.948 (h)s 264.615 (that)s 10 f 323.369 y 138.786 (J)s 11 f 325.169 y 145.44 (\260)s 1 f 323.369 y 151.598 (\050)s 10 f 156.264 (r)s 1 f 162.012 (\051)s 170.011 (=)s 10 f 182.678 (\260)s 11 f 318.415 y 189.557 (d)s 10 f 323.369 y 195.153 (J)s 13 f 313.649 y 202.961 (\241)s 10 f 323.369 y 208.461 (\260)s 215.341 (r)s 13 f 313.649 y 221.088 (\242)s 10 f 323.369 y 226.588 (;)s 1 f 243.921 (for)s 262.288 (all)s 10 f 278.955 (r)s 12 f 288.035 (2)s 1 f 299.368 (I)s 301.542 (R)s 11 f 318.136 y 310.375 (d)s 10 f 323.369 y 315.971 (:)s 1 f 352.71 y -5.69 (where)s 10 f 28.488 (J)s 12 f 39.63 (2)s 50.963 (C)s 2 f 348.355 y 57.982 (2)s 1 f 352.71 y 63.365 (\050I)s 70.205 (R)s 11 f 347.476 y 79.038 (d)s 1 f 352.71 y 84.634 (\051)s 92.779 (is)s 104.324 (a)s 113.802 (non)s 136.614 (negativ)s 174.614 (e)s 183.426 (function)s 229.905 (supp)s 254.971 (orted)s 285.816 (in)s 299.295 (the)s 319.44 (unit)s 344.252 (ball,)s 370.501 (with)s 13 f 343.043 y 397.313 (R)s 2 f 356.976 y 402.98 (I)s 404.287 (R)s 15 f 354.203 y 411.253 (d)s 10 f 352.71 y 418.891 (J)s 1 f 426.7 (\050)s 10 f 431.366 (r)s 1 f 437.114 (\051)s 445.114 (=)s 457.78 (1)s 369.51 y -5.69 (and)s 10 f 17.643 (J)s 1 f 25.452 (\050)s 10 f 30.118 (r)s 1 f 35.865 (\051)s 43.865 (=)s 10 f 56.532 (J)s 1 f 64.34 (\050)s 12 f 69.007 (\241)s 10 f 78.34 (r)s 1 f 84.088 (\051)s 92.754 (for)s 111.121 (all)s 10 f 127.788 (r)s 12 f 136.868 (2)s 1 f 148.201 (I)s 150.375 (R)s 159.208 (.)s 386.43 y 8.71 (The)s 33.732 (spin)s 59.488 (v)s 65.154 (ariable)s 104.877 (in)s 119.232 (the)s 140.254 (site)s 10 f 162.677 (i)s 12 f 170.737 (2)s 10 f 182.663 (Z)s 185.713 (Z)s 11 f 381.196 y 196.763 (d)s 1 f 386.43 y 206.714 (is)s 219.136 (denoted)s 264.825 (b)s 271.158 (y)s 10 f 281.847 (\276)s 1 f 289.135 (\050)s 10 f 293.801 (i)s 1 f 297.935 (\051)s 306.958 (and)s 330.647 (the)s 351.669 (in\257nite)s 392.691 (v)s 398.691 (olume)s 434.38 (phase)s 403.23 y -5.69 (space)s 27.125 (is)s 12 f 39.94 (f\241)s 1 f 55.274 (1)s 10 f 61.274 (;)s 1 f 66.607 (0)s 10 f 72.607 (;)s 1 f 77.94 (1)s 12 f 83.94 (g)s 11 f 398.875 y 89.94 (Z)s 92.15 (Z)s 15 f 395.253 y 100.916 (d)s 1 f 403.23 y 106.554 (.)s 117.466 (A)s 131.214 (con\257guration)s 204.663 (is)s 217.478 (a)s 228.226 (function)s 10 f 275.975 (\276)s 1 f 287.843 (:)s 10 f 295.757 (Z)s 298.807 (Z)s 11 f 397.996 y 309.857 (d)s 12 f 403.23 y 320.033 (\241)s 327.367 (!)s 343.948 (f\241)s 1 f 359.281 (1)s 10 f 365.281 (;)s 1 f 370.614 (0)s 10 f 376.614 (;)s 1 f 381.948 (+1)s 12 f 397.281 (g)s 1 f 403.281 (,)s 411.55 (that)s 438.298 (is)s 451.114 (an)s 420.03 y -5.69 (elemen)s 29.977 (t)s 38.216 (of)s 51.455 (\255)s 63.455 (=)s 12 f 76.121 (f\241)s 1 f 91.455 (1)s 10 f 97.455 (;)s 1 f 102.788 (0)s 10 f 108.788 (;)s 1 f 114.121 (+1)s 12 f 129.455 (g)s 11 f 415.675 y 135.455 (Z)s 137.665 (Z)s 15 f 412.053 y 146.43 (d)s 1 f 420.03 y 152.069 (.)s 160.593 (F)s 167.426 (or)s 181.699 (an)s 194.032 (y)s 203.938 (\244)s 12 f 215.604 (\275)s 10 f 228.271 (Z)s 231.321 (Z)s 11 f 414.796 y 242.371 (d)s 1 f 420.03 y 247.966 (,)s 254.958 (denote)s 293.197 (b)s 299.53 (y)s 10 f 309.436 (\276)s 2 f 421.83 y 316.293 (\244)s 1 f 420.03 y 323.46 (,)s 330.451 (the)s 350.69 (restriction)s 407.73 (to)s 421.969 (\244)s 433.874 (of)s 447.114 (the)s 436.83 y -5.69 (con\257guration)s 10 f 67.01 (\276)s 1 f 74.297 (,)s 10 f 81.631 (\276)s 2 f 438.63 y 88.488 (\244)s 1 f 436.83 y 98.988 (=)s 12 f 111.654 (f)s 10 f 117.654 (\276)s 1 f 124.942 (\050)s 10 f 129.609 (i)s 1 f 133.743 (\051)s 10 f 138.409 (;)s 151.743 (i)s 12 f 159.21 (2)s 1 f 170.543 (\244)s 12 f 178.877 (g)s 1 f 184.877 (.)s 453.75 y 8.71 (The)s 32.995 (Gibbs)s 67.43 (measure,)s 117.225 (with)s 144.178 (p)s 151.178 (oten)s 173.511 (tial)s 10 f 194.463 (J)s 11 f 455.55 y 201.117 (\260)s 1 f 453.75 y 207.274 (\050)s 10 f 211.941 (r)s 1 f 217.688 (\051)s 225.974 (and)s 248.926 (c)s 253.926 (hemical)s 297.544 (p)s 304.544 (oten)s 326.878 (tials)s 10 f 352.563 (h)s 2 f 455.55 y 359.477 (1)s 10 f 453.75 y 364.86 (;)s 370.194 (h)s 2 f 455.55 y 377.108 (2)s 1 f 453.75 y 386.11 (at)s 400.395 (in)s 410.062 (v)s 416.062 (erse)s 439.78 (tem-)s 470.55 y -5.69 (p)s 1.31 (erature)s 10 f 42.658 (\257)s 53.412 (\076)s 1 f 66.078 (0,)s 79.37 (in)s 93.318 (a)s 103.266 (\257nite)s 133.88 (v)s 139.88 (olume)s 175.162 (\244)s 187.443 (and)s 210.724 (b)s 217.724 (oundary)s 264.705 (condition)s 10 f 317.32 (\273)s 1 f 327.07 (is)s 339.084 (the)s 359.699 (probabilit)s 410.732 (y)s 421.013 (measure)s 10 f 487.35 y -5.69 (\271)s 11 f 481.583 y 1.54 (\257)s 7.413 (;\273)s 490.876 y 1.54 (\260)s 7.098 (;)s 2 f 9.948 (\244)s 1 f 487.35 y 21.114 (on)s 37.781 (\255)s 10 f 521.07 y 132.653 (\271)s 11 f 515.303 y 139.884 (\257)s 145.757 (;\273)s 524.596 y 139.884 (\260)s 145.441 (;)s 2 f 148.291 (\244)s 1 f 521.07 y 155.458 (\050)s 10 f 160.125 (\276)s 1 f 167.412 (\051)s 175.412 (=)s 512.951 y 198.402 (1)s 23.766 .48 189.519 518.31 r 10 f 531.349 y 189.519 (Z)s 11 f 525.583 y 198.569 (\257)s 204.442 (;\273)s 534.876 y 197.71 (\260)s 203.268 (;)s 2 f 206.118 (\244)s 1 f 521.07 y 216.724 (exp)s 13 f 507.749 y 237.058 (\263)s 12 f 521.07 y 246.891 (\241)s 10 f 258.891 (\257)s 266.312 (H)s 11 f 522.87 y 276.287 (\260)s 1 f 521.07 y 282.444 (\050)s 10 f 287.111 (\276)s 2 f 522.87 y 293.968 (\244)s 12 f 521.07 y 301.134 (j)s 10 f 304.468 (\273)s 1 f 310.27 (\051)s 13 f 507.749 y 314.937 (\264)s 10 f 521.07 y 322.103 (:)s 1 f 560.483 y -5.69 (where)s 10 f 28.504 (Z)s 11 f 554.716 y 37.554 (\257)s 43.427 (;\273)s 564.009 y 36.695 (\260)s 42.253 (;)s 2 f 45.103 (\244)s 1 f 560.483 y 55.763 (is)s 67.324 (the)s 87.485 (normalization)s 163.012 (constan)s 202.745 (t)s 210.906 (and)s 10 f 233.733 (H)s 11 f 562.283 y 243.708 (\260)s 1 f 560.483 y 249.866 (\050)s 10 f 254.532 (\276)s 2 f 562.283 y 261.389 (\244)s 1 f 560.483 y 268.556 (\051)s 276.716 (is)s 288.277 (the)s 308.438 (formal)s 345.632 (Hamiltonian)s 414.126 (in)s 427.62 (a)s 437.114 (\257nite)s 577.283 y -5.69 (subset)s 31.11 (\244)s 43.443 (of)s 10 f 57.11 (Z)s 60.16 (Z)s 11 f 572.049 y 71.21 (d)s 1 f 577.283 y 76.805 (,)s 84.139 (for)s 102.505 (the)s 123.172 (con\257guration)s 10 f 195.872 (\276)s 2 f 579.083 y 202.729 (\244)s 10 f 612.808 y 49.212 (H)s 11 f 614.608 y 59.187 (\260)s 1 f 612.808 y 65.344 (\050)s 10 f 70.011 (\276)s 2 f 614.608 y 76.868 (\244)s 1 f 612.808 y 84.034 (\051)s 92.034 (=)s 604.69 y 106.141 (1)s 6 .48 106.141 610.048 r 621.039 y 106.141 (2)s 13 f 601.408 y 118.838 (X)s 15 f 625.486 y 117.021 (i;j)s 18 f 126.855 (2)s 16 f 132.522 (\244)s 15 f 632.336 y 120.879 (i)s 18 f 124.081 (6)s 16 f 124.081 (=)s 15 f 130.248 (j)s 10 f 612.808 y 141.429 (J)s 11 f 614.608 y 148.083 (\260)s 1 f 612.808 y 154.24 (\050)s 10 f 158.907 (i)s 12 f 165.708 (\241)s 10 f 177.708 (j)s 1 f 183.336 (\051)s 13 f 603.088 y 188.003 (\241)s 10 f 612.808 y 193.503 (\276)s 1 f 200.791 (\050)s 10 f 205.457 (i)s 1 f 209.591 (\051)s 12 f 216.925 (\241)s 10 f 228.925 (\276)s 1 f 236.212 (\050)s 10 f 240.879 (j)s 1 f 246.507 (\051)s 13 f 603.088 y 251.174 (\242)s 2 f 605.574 y 256.674 (2)s 12 f 612.808 y 264.724 (\241)s 10 f 276.724 (h)s 2 f 614.608 y 283.638 (1)s 13 f 601.408 y 291.021 (X)s 11 f 627.148 y 291.474 (i)s 14 f 294.869 (2)s 2 f 301.335 (\244)s 10 f 612.808 y 310.354 (\276)s 1 f 317.642 (\050)s 10 f 322.309 (i)s 1 f 326.443 (\051)s 12 f 333.776 (\241)s 10 f 345.776 (h)s 2 f 614.608 y 352.69 (2)s 13 f 601.408 y 360.073 (X)s 11 f 627.148 y 360.526 (i)s 14 f 363.921 (2)s 2 f 370.388 (\244)s 10 f 612.808 y 379.407 (\276)s 2 f 607.853 y 386.694 (2)s 1 f 612.808 y 392.077 (\050)s 10 f 396.744 (i)s 1 f 400.878 (\051)s 10 f 405.545 (;)s 1 f 439.114 (\0502)s 10 f 449.78 (:)s 1 f 453.114 (1\051)s 660.376 y -5.69 (The)s 19.593 (in\257nite)s 60.876 (v)s 66.876 (olume)s 102.825 (Gibbs)s 138.258 (measure)s 10 f 185.641 (\271)s 11 f 662.176 y 192.871 (\260)s 198.429 (;\257)s 1 f 660.376 y 212.368 (is)s 225.051 (a)s 235.667 (probabilit)s 286.7 (y)s 297.65 (measure)s 345.033 (on)s 362.316 (\255)s 375.598 (that)s 402.215 (can)s 424.831 (b)s 431.831 (e)s 441.78 (con-)s 677.176 y -5.69 (structed)s 41.077 (b)s 47.41 (y)s 57.743 (some)s 87.81 (suitable)s 132.543 (limiting)s 177.21 (pro)s 194.91 (cedure.)s 705.976 y 226.045 (6)s do-end end endp %%Page: 7 7 %%BeginPageSetup initializepage (Raffaele Esposito; page: 7 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f0_12 sf ( )S -996 -1000 :M f1_12 sf ( )S -993 -1000 :M f2_12 sf ( )S -989 -1000 :M f10_12 sf ( )S -981 -1000 :M f11_12 sf ( )S -972 -1000 :M f12_12 sf ( )S -960 -1000 :M f13_12 sf ( )S -951 -1000 :M f14_12 sf ( )S -937 -1000 :M f16_12 sf ( )S -932 -1000 :M f17_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 1200 1000 div mul /CMBX10 findfont fdef 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 16 5 1200 1000 div mul /CMR5 findfont fdef 17 10 1200 1000 div mul /CMTI10 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 6.31 y 8.71 (The)s 33.105 (c)s 38.105 (haracteristics)s 111.367 (of)s 124.763 (mo)s 141.096 (dels)s 164.892 (with)s 191.954 (Kac)s 216.349 (p)s 223.35 (oten)s 245.683 (tials)s 271.478 (is)s 283.274 (that)s 309.003 (the)s 329.398 (range)s 361.827 (of)s 375.222 (the)s 395.618 (in)s 405.285 (teraction)s 455.714 (is)s 10 f 23.11 y -5.69 (\260)s 14 f 18.755 y 1.189 (\241)s 2 f 8.689 (1)s 1 f 23.11 y 17.971 (and)s 41.203 (the)s 61.769 (strength)s 109.101 (is)s 10 f 121.066 (\260)s 11 f 18.755 y 127.945 (d)s 1 f 23.11 y 133.541 (,)s 140.793 (while)s 172.025 (the)s 192.591 (total)s 221.156 (in)s 230.823 (teraction)s 281.421 (with)s 308.653 (all)s 325.219 (the)s 345.784 (other)s 377.049 (spins)s 407.081 (sta)s 422.148 (ys)s 437.113 (\257nite)s 39.91 y -5.69 (indep)s 23.31 (enden)s 53.643 (tly)s 73.328 (of)s 10 f 88.347 (\260)s 1 f 95.226 (.)s 107.948 (Hence)s 144.966 (Kac)s 170.985 (p)s 177.985 (oten)s 200.318 (tial)s 223.003 (in)s 232.67 (teractions)s 289.455 (are)s 310.84 (useful)s 346.592 (to)s 362.61 (study)s 397.028 (the)s 419.047 (so-called)s 56.71 y -5.69 (mean)s 26.328 (\257eld)s 52.347 (limit)s 10 f 81.032 (\260)s 12 f 91.276 (!)s 1 f 106.64 (0.)s 121.362 (The)s 146.047 (in\257nite)s 186.732 (v)s 192.732 (olume)s 228.084 (free-energy)s 289.503 (for)s 307.888 (the)s 328.573 (Kac)s 353.258 (Ising)s 382.343 (mo)s 398.677 (del)s 418.028 (has)s 439.447 (b)s 446.447 (een)s 73.51 y -5.69 (computed)s 49.795 (in)s 63.946 (the)s 84.764 (limit)s 10 f 113.582 (\260)s 12 f 124.047 (!)s 1 f 139.633 (0)s 149.784 (b)s 156.117 (y)s 166.602 (Leb)s 186.436 (o)s 192.102 (witz)s 218.254 (and)s 241.738 (P)s 249.572 (enrose)s 286.49 (\050[LP]\051,)s 325.641 (and)s 349.126 (the)s 369.944 (result)s 403.529 (agrees)s 439.78 (\050and)s 90.31 y -5.69 (giv)s 9.643 (e)s 19.991 (rigorous)s 67.139 (supp)s 92.206 (ort)s 112.588 (to\051)s 132.936 (with)s 161.284 (the)s 182.965 (V)s 190.965 (an)s 208.647 (der)s 230.362 (W)s 241.695 (aals)s 266.777 (theory)s 299.477 (.)s 311.188 (The)s 336.869 (analogous)s 393.284 (result)s 427.732 (for)s 447.114 (the)s 107.11 y -5.69 (KBC)s 24.81 (mo)s 41.143 (del)s 60.477 (is)s 0 f 141.101 y -5.69 (Theorem)s 53.021 (2.1)s 17 f 79.463 (\050L)s 91.283 (eb)s 101.71 (owitz-Penr)s 157.536 (ose)s 178.478 (limit\051.)s 217.08 (L)s 223.993 (et)s 10 f 237.882 (p)s 11 f 142.901 y 243.92 (\260)s 1 f 141.101 y 250.077 (\050)s 10 f 254.743 (\257)s 262.164 (;)s 267.498 (h)s 2 f 142.901 y 274.412 (1)s 10 f 141.101 y 279.795 (;)s 285.128 (h)s 2 f 142.901 y 292.042 (2)s 1 f 141.101 y 297.425 (\051)s 17 f 306.475 (b)s 311.381 (e)s 321.284 (the)s 341.306 (pr)s 351.886 (essur)s 378.106 (e)s 388.009 (in)s 402.818 (the)s 422.84 (thermo-)s 157.901 y -5.69 (dynamic)s 42.456 (limit)s 70.976 (at)s 10 f 85.389 (\260)s 95.602 (\076)s 1 f 108.268 (0)s 17 f 114.268 (.)s 123.468 (Then)s 1 f 199.891 y 31.587 (lim)s 11 f 207.304 y 29.967 (\260)s 14 f 35.524 (!)s 2 f 45.091 (0)s 10 f 199.891 y 51.874 (p)s 11 f 201.691 y 57.912 (\260)s 1 f 199.891 y 64.069 (\050)s 10 f 68.736 (\257)s 76.156 (;)s 81.49 (h)s 2 f 201.691 y 88.404 (1)s 10 f 199.891 y 93.787 (;)s 99.12 (h)s 2 f 201.691 y 106.034 (2)s 1 f 199.891 y 111.417 (\051)s 119.417 (=)s 160.921 (sup)s 2 f 210.524 y 132.084 (\050)s 11 f 135.834 (m;\301)s 2 f 152.969 (:)s 14 f 155.686 (j)s 11 f 158.536 (m)s 14 f 167.051 (j\267)s 11 f 177.401 (\301;\301)s 14 f 191.791 (\267)s 2 f 199.291 (1\051)s 13 f 186.571 y 209.825 (h)s 10 f 199.891 y 215.491 (m)s 2 f 194.936 y 226.028 (2)s 12 f 199.891 y 234.078 (\241)s 10 f 246.077 (\301)s 1 f 255.894 (+)s 10 f 267.894 (\257)s 14 f 194.936 y 275.315 (\241)s 2 f 282.815 (1)s 10 f 199.891 y 288.198 (s)s 1 f 293.823 (\050)s 10 f 298.49 (m;)s 314.359 (\301)s 1 f 321.509 (\051)s 328.843 (+)s 10 f 340.843 (h)s 2 f 201.691 y 347.757 (1)s 10 f 199.891 y 353.14 (m)s 1 f 366.343 (+)s 10 f 378.343 (h)s 2 f 201.691 y 385.257 (2)s 10 f 199.891 y 390.64 (\301)s 13 f 186.571 y 397.79 (i)s 1 f 199.891 y 439.114 (\0502)s 10 f 449.78 (:)s 1 f 453.114 (2\051)s 17 f 235.894 y -5.69 (wher)s 18.383 (e)s 10 f 28.077 (s)s 1 f 33.702 (\050)s 10 f 38.369 (m;)s 54.238 (\301)s 1 f 61.388 (\051)s 17 f 70.229 (is)s 82.99 (the)s 102.803 (entr)s 123.503 (opy)s 145.771 (of)s 159.758 (a)s 170.065 (Bernoul)s 212.092 (li)s 223.012 (pr)s 233.592 (o)s 239.112 (c)s 244.019 (ess)s 263.526 (in)s 1 f 278.127 (\255)s 17 f 290.967 (with)s 316.915 (aver)s 338.535 (age)s 359.882 (spin)s 385.522 (e)s 390.429 (qual)s 415.763 (to)s 10 f 430.057 (m)s 17 f 444.767 (and)s 252.694 y -5.69 (aver)s 15.93 (age)s 37.396 (squar)s 64.843 (e)s 74.656 (spin)s 100.416 (e)s 105.322 (qual)s 130.775 (to)s 10 f 145.189 (\301)s 17 f 156.632 (\050)s 10 f 165.832 (m)s 17 f 180.661 (is)s 193.541 (the)s 213.474 (magnetization)s 290.754 (and)s 10 f 314.06 (\301)s 17 f 325.504 (is)s 338.384 (c)s 343.29 (al)s 353.104 (le)s 361.077 (d)s 371.503 (c)s 376.41 (onc)s 394.197 (entr)s 414.896 (ation\051.)s 10 f 294.683 y .31 (s)s 1 f 5.935 (\050)s 10 f 10.602 (m;)s 26.471 (\301)s 1 f 33.621 (\051)s 41.621 (=)s 12 f 54.288 (\241)s 1 f 286.565 y 65.061 (1)s 6 .48 65.061 291.923 r 302.915 y 65.061 (2)s 294.683 y 72.501 (\050)s 10 f 77.168 (m)s 1 f 89.345 (+)s 10 f 100.319 (\301)s 1 f 107.469 (\051)s 114.136 (log)s 129.636 (\050)s 10 f 134.302 (m)s 1 f 146.48 (+)s 10 f 157.454 (\301)s 1 f 164.604 (\051)s 12 f 170.912 (\241)s 1 f 286.565 y 183.326 (1)s 6 .48 183.326 291.923 r 302.915 y 183.326 (2)s 294.683 y 190.766 (\050)s 10 f 195.433 (\301)s 12 f 204.224 (\241)s 10 f 215.198 (m)s 1 f 225.734 (\051)s 232.401 (log)s 247.901 (\050)s 10 f 252.567 (\301)s 12 f 261.358 (\241)s 10 f 272.333 (m)s 1 f 282.869 (\051)s 12 f 289.177 (\241)s 1 f 300.151 (\0501)s 12 f 312.459 (\241)s 10 f 323.433 (\301)s 1 f 330.583 (\051)s 337.25 (log)s 352.75 (\0501)s 12 f 365.057 (\241)s 10 f 376.032 (\301)s 1 f 383.182 (\051)s 389.489 (+)s 10 f 400.464 (\301)s 1 f 409.613 (log)s 427.113 (2)s 439.114 (\0502)s 10 f 449.78 (:)s 1 f 453.114 (3\051)s 353.744 y 8.71 (The)s 33.376 (free)s 56.41 (energy)s 10 f 94.777 (f)s 1 f 101.943 (\050)s 10 f 106.61 (\257)s 114.031 (;)s 119.364 (m;)s 135.234 (\301)s 1 f 142.384 (\051)s 151.05 (is)s 163.117 (de\257ned)s 204.45 (as)s 219.184 (the)s 239.85 (Legendre)s 291.384 (transform)s 346.517 (of)s 360.184 (the)s 380.851 (pressure)s 427.717 (as)s 10 f 383.614 y 5.455 (f)s 1 f 12.622 (\050)s 10 f 17.289 (\257)s 24.71 (;)s 30.043 (m;)s 45.912 (\301)s 1 f 53.062 (\051)s 61.062 (=)s 80.172 (sup)s 2 f 394.247 y 73.729 (\050)s 11 f 77.479 (h)s 16 f 395.447 y 83.097 (1)s 11 f 394.247 y 87.78 (;h)s 16 f 395.447 y 96.249 (2)s 2 f 394.247 y 100.932 (\051)s 1 f 383.614 y 104.682 ([)s 10 f 108.015 (h)s 2 f 385.414 y 114.929 (1)s 10 f 383.614 y 120.313 (m)s 1 f 133.515 (+)s 10 f 145.515 (h)s 2 f 385.414 y 152.429 (2)s 10 f 383.614 y 157.813 (\301)s 12 f 167.629 (\241)s 10 f 179.629 (p)s 1 f 185.667 (\050)s 10 f 190.333 (\257)s 197.754 (;)s 203.087 (h)s 2 f 385.414 y 210.001 (1)s 10 f 383.614 y 215.385 (;)s 220.718 (h)s 12 f 230.298 (\241)s 1 f 242.298 (2\051])s 259.632 (=)s 10 f 272.298 (C)s 281.733 (E)s 13 f 370.294 y 291.283 (h)s 12 f 383.614 y 299.617 (\241)s 10 f 311.617 (m)s 2 f 378.659 y 322.153 (2)s 1 f 383.614 y 330.203 (+)s 10 f 342.203 (\301)s 12 f 352.019 (\241)s 10 f 364.019 (\257)s 14 f 378.659 y 371.44 (\241)s 2 f 378.94 (1)s 10 f 383.614 y 384.323 (s)s 1 f 389.948 (\050)s 10 f 394.615 (m;)s 410.485 (\301)s 1 f 417.635 (\051)s 13 f 370.294 y 422.301 (i)s 1 f 383.614 y 439.114 (\0502)s 10 f 449.78 (:)s 1 f 453.114 (4\051)s 418.95 y -5.69 (where)s 29.113 (CE)s 50.049 (denotes)s 93.552 (con)s 111.218 (v)s 117.218 (ex)s 132.988 (en)s 144.654 (v)s 150.654 (elop)s 172.321 (e.)s 186.63 (The)s 211.399 (complemen)s 269.733 (tary)s 295.535 (result)s 329.072 (in)s 343.174 (the)s 363.944 (canonical)s 416.714 (ensem)s 448.447 (ble)s 435.75 y -5.69 (is)s 0 f 469.742 y -5.69 (Theorem)s 52.91 (2.2)s 17 f 79.143 (De\257ne)s 117.029 (the)s 136.962 (fr)s 145.089 (e)s 149.995 (e)s 159.809 (ener)s 182.042 (gy)s 10 f 197.682 (f)s 11 f 471.542 y 203.557 (\260)s 1 f 469.742 y 209.714 (\050)s 10 f 214.381 (\257)s 221.802 (;)s 227.135 (m;)s 243.004 (\301)s 1 f 250.154 (\051)s 17 f 259.114 (at)s 10 f 273.528 (\260)s 283.74 (\076)s 1 f 296.407 (0)s 17 f 306.7 (as)s 322.033 (fol)s 335.527 (lows:)s 486.662 y 8.71 (Consider)s 59.769 (the)s 79.703 (p)s 85.223 (artition)s 128.922 (function)s 176.149 (in)s 190.869 (the)s 210.802 (c)s 215.708 (anonic)s 250.055 (al)s 263.548 (ensemble)s 10 f 511.731 y 133.456 (Z)s 2 f 513.531 y 141.648 (\244)s 1 f 511.731 y 148.815 (\050)s 10 f 153.481 (N)s 14 f 506.776 y 164.431 (\241)s 10 f 511.731 y 172.531 (;)s 177.865 (N)s 2 f 506.776 y 188.815 (0)s 1 f 511.731 y 194.198 (\051)s 202.198 (=)s 13 f 500.331 y 215.329 (X)s 11 f 526.071 y 214.864 (\276)s 14 f 220.727 (2)s 2 f 227.193 (\241)s 1 f 511.731 y 235.127 (exp)s 13 f 498.411 y 255.46 (\263)s 12 f 511.731 y 265.293 (\241)s 10 f 277.293 (\257)s 284.714 (H)s 11 f 513.531 y 294.689 (\260)s 1 f 511.731 y 300.846 (\050)s 10 f 305.513 (\276)s 1 f 312.8 (\051)s 13 f 498.411 y 317.467 (\264)s 1 f 511.731 y 439.114 (\0502)s 10 f 449.78 (:)s 1 f 453.114 (5\051)s 17 f 549.976 y -5.69 (wher)s 18.383 (e)s 1 f 28.08 (\241)s 17 f 39.757 (is)s 52.52 (the)s 72.337 (set)s 90.927 (of)s 104.918 (c)s 109.824 (on\257gur)s 145.857 (ations)s 12 f 181.621 (f)s 10 f 187.621 (\276)s 12 f 194.908 (g)s 204.242 (2)s 1 f 215.575 (\255)s 2 f 551.776 y 224.241 (\244)s 17 f 549.976 y 235.585 (such)s 262.762 (that)s 287.179 (the)s 306.996 (numb)s 334.902 (er)s 349.659 (of)s 363.649 (spins)s 10 f 394.199 (\276)s 1 f 404.82 (=)s 417.487 (1)s 17 f 427.664 (is)s 440.427 (\257xe)s 457.647 (d)s 566.776 y -5.69 (to)s 9.019 (b)s 13.926 (e)s 10 f 24.036 (N)s 14 f 562.422 y 34.985 (\241)s 17 f 566.776 y 47.675 (and)s 71.278 (the)s 91.507 (numb)s 119.414 (er)s 134.583 (of)s 148.986 (spins)s 10 f 179.949 (\276)s 1 f 191.107 (=)s 204.31 (0)s 17 f 214.9 (is)s 10 f 228.076 (N)s 2 f 562.422 y 239.026 (0)s 17 f 566.776 y 244.409 (.)s 254.498 (L)s 261.411 (et)s 10 f 275.508 (N)s 17 f 291.047 (b)s 295.954 (e)s 306.063 (the)s 326.293 (total)s 354.189 (numb)s 382.095 (er)s 397.265 (of)s 411.668 (spins)s 442.631 (in)s 457.647 (a)s 583.576 y -5.69 (\257nite)s 25.283 (volume)s 1 f 66.069 (\244)s 17 f 78.696 (and)s 102.002 (put)s 10 f 620.919 y 134.403 (m)s 1 f 148.272 (=)s 612.801 y 164.854 (1)s 10.95 .48 162.379 618.159 r 10 f 629.151 y 162.379 (N)s 11 f 605.919 y 181.185 (N)s 13 f 609.519 y 176.769 (X)s 11 f 635.078 y 177.663 (i)s 2 f 181.058 (=1)s 10 f 620.919 y 196.102 (\276)s 1 f 203.39 (\050)s 10 f 208.056 (i)s 1 f 212.191 (\051)s 220.191 (=)s 612.801 y 236.772 (1)s 10.95 .48 234.297 618.159 r 10 f 629.151 y 234.297 (N)s 1 f 620.919 y 246.687 ([)s 10 f 250.02 (N)s 12 f 263.637 (\241)s 1 f 275.637 (2)s 10 f 281.637 (N)s 14 f 615.964 y 292.587 (\241)s 10 f 620.919 y 300.687 (N)s 2 f 615.964 y 311.637 (0)s 1 f 620.919 y 317.02 (])s 10 f 320.354 (;)s 666.618 y 134.403 (\301)s 1 f 144.886 (=)s 658.499 y 161.468 (1)s 10.95 .48 158.993 663.858 r 10 f 674.849 y 158.993 (N)s 11 f 651.618 y 177.799 (N)s 13 f 655.217 y 173.383 (X)s 11 f 680.776 y 174.277 (i)s 2 f 177.672 (=1)s 1 f 666.618 y 190.716 (\050)s 10 f 195.383 (\276)s 1 f 202.67 (\050)s 10 f 207.337 (i)s 1 f 211.471 (\051\051)s 2 f 661.663 y 220.805 (2)s 1 f 666.618 y 229.521 (=)s 658.499 y 246.103 (1)s 10.95 .48 243.628 663.858 r 10 f 674.849 y 243.628 (N)s 1 f 666.618 y 256.018 ([)s 10 f 259.351 (N)s 12 f 272.968 (\241)s 10 f 284.968 (N)s 2 f 661.663 y 295.918 (0)s 1 f 666.618 y 301.301 (])s 10 f 304.634 (:)s 1 f 643.477 y 439.114 (\0502)s 10 f 449.78 (:)s 1 f 453.114 (6\051)s 705.976 y 226.045 (7)s do-end end endp %%Page: 8 8 %%BeginPageSetup initializepage (Raffaele Esposito; page: 8 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f1_12 sf ( )S -997 -1000 :M f2_12 sf ( )S -993 -1000 :M f10_12 sf ( )S -985 -1000 :M f11_12 sf ( )S -976 -1000 :M f12_12 sf ( )S -964 -1000 :M f13_12 sf ( )S -954 -1000 :M f14_12 sf ( )S -941 -1000 :M f16_12 sf ( )S -936 -1000 :M f17_12 sf ( )S -933 -1000 :M f18_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 16 5 1200 1000 div mul /CMR5 findfont fdef 17 10 1200 1000 div mul /CMTI10 findfont fdef 18 5 1200 1000 div mul /CMSY5 findfont fdef 58 60 translate 72 72.27 div dup scale 17 f 6.31 y 8.71 (The)s 33.243 (fr)s 41.37 (e)s 46.276 (e)s 56.089 (ener)s 78.323 (gy)s 93.962 (at)s 10 f 108.376 (\260)s 118.588 (\076)s 1 f 131.255 (0)s 17 f 141.548 (in)s 156.268 (the)s 176.201 (thermo)s 212.234 (dynamic)s 260.381 (limit)s 288.901 (is)s 301.78 (de\257ne)s 331.834 (d)s 342.26 (as)s 10 f 64.168 y 105.345 (f)s 11 f 65.968 y 111.22 (\260)s 1 f 64.168 y 117.377 (\050)s 10 f 122.044 (\257)s 129.464 (;)s 134.798 (m;)s 150.667 (\301)s 1 f 157.817 (\051)s 165.817 (:=)s 203.577 (lim)s 2 f 72.568 y 181.817 (\244)s 11 f 188.384 (;N)s 18 f 70.168 y 199.735 (\241)s 11 f 72.568 y 206.835 (;N)s 16 f 70.168 y 218.187 (0)s 14 f 72.568 y 222.871 (!1)s 10 f 64.168 y 244.004 (N)s 14 f 59.214 y 254.954 (\241)s 2 f 262.454 (1)s 1 f 64.168 y 269.837 (log)s 10 f 287.337 (Z)s 2 f 65.968 y 295.529 (\244)s 1 f 64.168 y 302.696 (\050)s 10 f 307.362 (N)s 14 f 59.214 y 318.312 (\241)s 10 f 64.168 y 326.412 (;)s 331.746 (N)s 2 f 59.214 y 342.695 (0)s 1 f 64.168 y 348.079 (\051)s 17 f 115.706 y -5.69 (wher)s 18.383 (e)s 28.196 (the)s 48.129 (limit)s 76.649 (is)s 89.529 (taken)s 121.729 (in)s 136.449 (such)s 163.742 (a)s 174.168 (way)s 198.395 (that)s 222.928 (\0502.6\051)s 252.981 (hold.)s 138.66 y 8.71 (Then)s 1 f 173.564 y 109.882 (lim)s 11 f 180.978 y 108.262 (\260)s 14 f 113.819 (!)s 2 f 123.386 (0)s 10 f 173.564 y 130.169 (f)s 11 f 175.364 y 136.044 (\260)s 1 f 173.564 y 142.202 (\050)s 10 f 146.868 (\257)s 154.289 (;)s 159.622 (m)s 1 f 170.159 (\051)s 178.159 (=)s 10 f 190.825 (C)s 200.26 (E)s 13 f 160.244 y 209.81 (h)s 12 f 173.564 y 218.143 (\241)s 10 f 230.143 (m)s 2 f 168.61 y 240.68 (2)s 1 f 173.564 y 248.729 (+)s 10 f 260.729 (\301)s 12 f 270.546 (\241)s 10 f 282.546 (\257)s 14 f 168.61 y 289.967 (\241)s 2 f 297.467 (1)s 10 f 173.564 y 302.85 (s)s 1 f 308.475 (\050)s 10 f 313.142 (m;)s 329.011 (\301)s 1 f 336.161 (\051)s 13 f 160.244 y 340.828 (i)s 10 f 173.564 y 346.495 (:)s 1 f 439.114 (\0502)s 10 f 449.78 (:)s 1 f 453.114 (7\051)s 256.894 y 8.71 (The)s 33.636 (pro)s 51.336 (of)s 65.263 (of)s 79.189 (this)s 102.849 (theorem)s 149.809 (is)s 162.135 (similar)s 201.828 (to)s 216.755 (the)s 237.681 (one)s 259.941 (of)s 273.867 (the)s 294.794 (Leb)s 314.627 (o)s 320.294 (witz-P)s 354.127 (enrose)s 391.154 (theorem)s 438.113 ([LP],)s 273.694 y -5.69 (\050see)s 19.221 (also)s 44.132 ([DP]\051)s 77.643 (and)s 101.821 (will)s 125.332 (not)s 147.51 (b)s 154.51 (e)s 164.688 (giv)s 180.022 (en)s 196.866 (explicitly)s 249.711 (here.)s 282.945 (W)s 294.279 (e)s 304.457 (only)s 331.635 (remark)s 373.546 (that)s 400.391 (the)s 421.902 (pro)s 439.602 (of)s 454.113 (of)s 290.494 y -5.69 ([LP])s 20.961 (is)s 33.346 (based)s 67.064 (on)s 84.048 (a)s 94.366 (blo)s 110.7 (c)s 115.7 (k)s 126.351 (spin)s 152.069 (renormalization)s 238.454 (pro)s 256.154 (cedure)s 294.505 (and)s 318.157 (the)s 339.141 (main)s 369.459 (p)s 376.46 (oin)s 392.126 (t)s 401.111 (in)s 415.429 (the)s 436.414 (pro)s 454.114 (of)s 307.294 y -5.69 (is)s 6.035 (writing)s 47.06 (the)s 67.386 (renormalized)s 138.444 (Hamiltonian)s 207.103 (for)s 225.128 (the)s 245.454 (blo)s 261.787 (c)s 266.787 (k)s 276.779 (spins)s 306.571 (\050whose)s 346.296 (expression)s 403.788 (will)s 426.114 (dep)s 445.114 (end)s 324.094 y -5.69 (on)s 11.927 (the)s 33.544 (form)s 62.861 (of)s 77.478 (the)s 99.094 (in)s 108.761 (teraction\051.)s 171.645 (Since)s 203.929 (the)s 225.546 (in)s 235.212 (teraction)s 286.863 (term)s 316.513 (in)s 331.463 (the)s 353.08 (KBC)s 384.53 (mo)s 400.863 (del)s 421.147 (is)s 434.163 (a)s 445.114 (t)s 449.447 (w)s 457.78 (o)s 340.894 y -5.69 (b)s 1.31 (o)s 7.643 (dy)s 25.127 (in)s 34.793 (teraction)s 85.977 (lik)s 98.644 (e)s 108.461 (in)s 122.944 (the)s 144.094 (Ising)s 173.645 (mo)s 189.978 (del)s 209.795 (this)s 233.678 (part)s 260.195 (of)s 274.345 (the)s 295.496 (pro)s 313.196 (of)s 327.346 (go)s 339.679 (es)s 354.229 (trough)s 393.413 (in)s 407.897 (almost)s 447.113 (the)s 357.694 y -5.69 (same)s 24.673 (w)s 33.006 (a)s 38.673 (y)s 44.006 (.)s 53.561 (Ob)s 69.227 (viously)s 104.961 (,)s 112.664 (the)s 133.627 (en)s 145.294 (trop)s 166.994 (y)s 177.623 (will)s 200.586 (dep)s 219.586 (end)s 242.549 (on)s 259.512 (whic)s 283.178 (h)s 294.141 (are)s 314.47 (the)s 335.433 (v)s 341.1 (alues)s 371.463 (of)s 385.425 (the)s 406.388 (spin)s 432.084 (and)s 455.714 (is)s 374.494 y -5.69 (in)s 8.31 (fact)s 31.977 (di\256eren)s 70.677 (t)s 79.343 (from)s 107.71 (the)s 128.377 (one)s 150.377 (computed)s 205.71 (in)s 219.71 ([LP].)s 414.521 y 8.71 (The)s 33.271 (phase)s 66.566 (structure)s 117.927 (of)s 131.489 (the)s 152.05 (mo)s 168.384 (del)s 187.612 (at)s 10 f 202.173 (\260)s 1 f 212.386 (=)s 225.052 (0)s 234.947 (is)s 246.908 (v)s 252.908 (ery)s 273.17 (ric)s 286.203 (h.)s 301.501 (T)s 309.168 (o)s 319.063 (discuss)s 359.157 (the)s 379.719 (phase)s 413.014 (transition)s 431.321 y -5.69 (w)s 2.643 (e)s 10.727 (can)s 31.478 (for)s 48.595 (example)s 94.346 (examine)s 140.097 (the)s 159.514 (function)s 10 f 205.265 (p)s 2 f 426.966 y 211.303 (0)s 1 f 431.321 y 220.019 (:=)s 10 f 236.019 (m)s 2 f 426.966 y 246.555 (2)s 12 f 431.321 y 252.107 (\241)s 10 f 261.608 (\301)s 1 f 268.926 (+)s 10 f 278.428 (\257)s 14 f 426.966 y 285.849 (\241)s 2 f 293.349 (1)s 10 f 431.321 y 298.732 (s)s 1 f 304.357 (\050)s 10 f 309.024 (m;)s 324.893 (\301)s 1 f 332.043 (\051)s 336.878 (+)s 10 f 346.379 (h)s 2 f 433.121 y 353.293 (1)s 10 f 431.321 y 358.677 (m)s 1 f 369.381 (+)s 10 f 378.882 (h)s 2 f 433.121 y 385.796 (2)s 10 f 431.321 y 391.179 (\301)s 1 f 401.08 (determining)s 448.121 y -5.69 (the)s 14.976 (pressure)s 61.843 (in)s 75.843 (\0502.2\051.)s 109.177 (The)s 133.843 (extremals)s 188.277 (of)s 201.943 (the)s 222.61 (function)s 10 f 269.61 (p)s 2 f 443.766 y 275.648 (0)s 1 f 448.121 y 285.031 (are)s 305.064 (determined)s 367.765 (b)s 374.098 (y)s 384.431 (the)s 405.098 (equations)s 10 f 504.179 y 106.332 (m)s 1 f 120.201 (=)s 10 f 132.868 (\301)s 1 f 142.018 (tanh)s 166.018 (\0502)s 10 f 176.685 (\257)s 184.105 (m)s 1 f 197.308 (+)s 10 f 209.308 (\257)s 216.729 (h)s 2 f 505.979 y 223.643 (1)s 1 f 504.179 y 229.026 (\051)s 10 f 233.693 (;)s 524.579 y 106.332 (\301)s 1 f 116.815 (=)s 129.482 (exp)s 12 f 147.815 (f\241)s 10 f 163.149 (\257)s 1 f 170.569 (\050)s 10 f 175.236 (h)s 2 f 526.379 y 182.15 (2)s 12 f 524.579 y 190.2 (\241)s 1 f 202.2 (1\051)s 12 f 212.867 (g)s 1 f 218.867 (\0501)s 12 f 232.2 (\241)s 10 f 244.2 (\301)s 1 f 251.35 (\051)s 258.016 (cosh)s 280.75 (\0502)s 10 f 291.417 (\257)s 298.837 (m)s 1 f 312.04 (+)s 10 f 324.04 (\257)s 331.461 (h)s 2 f 526.379 y 338.375 (1)s 1 f 524.579 y 343.758 (\051)s 10 f 348.425 (:)s 1 f 514.379 y 439.114 (\0502)s 10 f 449.78 (:)s 1 f 453.114 (8\051)s 576.376 y 8.71 (These)s 43.623 (equations)s 97.536 (can)s 119.715 (b)s 126.715 (e)s 136.228 (solv)s 156.295 (ed)s 172.474 (n)s 178.808 (umerically)s 232.174 (.)s 241.38 (F)s 248.213 (or)s 10 f 263.093 (\257)s 12 f 274.146 (\267)s 1 f 573.209 y 288.822 (\271)s 10 f 576.376 y 287.112 (\257)s 11 f 578.176 y 293.899 (c)s 1 f 576.376 y 302.42 (=)s 2 f 571.651 y 316.826 (1)s 4.783 .48 316.826 573.616 r 580.514 y 316.826 (2)s 1 f 576.376 y 327.229 (there)s 358.108 (is)s 370.354 (only)s 396.867 (one)s 419.047 (solution,)s 593.176 y -5.69 (while)s 26.192 (for)s 10 f 45.107 (\257)s 56.775 (\076)s 1 f 590.009 y 72.066 (\271)s 10 f 593.176 y 70.356 (\257)s 11 f 594.976 y 77.143 (c)s 1 f 593.176 y 86.58 (the)s 107.795 (equations)s 162.077 (admit)s 197.292 (more)s 227.874 (than)s 256.423 (one)s 278.971 (solution)s 324.92 (and)s 348.801 (the)s 370.016 (function)s 417.565 (can)s 440.113 (ha)s 452.447 (v)s 458.447 (e)s 609.976 y -5.69 (more)s 23.147 (than)s 49.95 (one)s 70.754 (maxim)s 106.087 (um)s 125.557 (for)s 142.728 (suitable)s 186.265 (v)s 191.931 (alues)s 220.802 (of)s 10 f 233.272 (h)s 2 f 611.776 y 240.186 (1)s 1 f 609.976 y 248.373 (and)s 10 f 270.509 (h)s 2 f 611.776 y 277.423 (2)s 1 f 609.976 y 282.807 (.)s 291.075 (F)s 297.908 (or)s 10 f 311.411 (\257)s 1 f 321.636 (in)s 334.439 (the)s 353.91 (in)s 363.576 (terv)s 383.943 (al)s 396.08 ([)s 2 f 605.251 y 400.853 (1)s 4.783 .48 400.853 607.216 r 614.114 y 400.853 (2)s 10 f 609.976 y 407.076 (;)s 2 f 605.251 y 413.85 (3)s 4.783 .48 413.85 607.216 r 614.114 y 413.85 (2)s 1 f 609.976 y 420.073 (])s 426.21 (there)s 455.714 (is)s 626.776 y -5.69 (in)s 7.269 (the)s 26.894 (plane)s 10 f 57.853 (\257)s 65.274 (;)s 70.608 (h)s 2 f 628.576 y 77.522 (2)s 1 f 626.776 y 85.864 (a)s 94.823 (line)s 116.448 (of)s 129.074 (second)s 166.767 (order)s 197.126 (phase)s 229.485 (transition,)s 286.752 (whic)s 310.419 (h)s 320.044 (c)s 325.044 (hanges)s 363.403 (to)s 377.029 (\257rst)s 400.755 (order)s 431.114 (\050made)s 643.576 y -5.69 (of)s 8.371 (triple)s 40.799 (p)s 47.799 (oin)s 63.466 (ts\051)s 81.927 (at)s 10 f 96.989 (\257)s 1 f 108.401 (=)s 640.409 y 123.435 (\271)s 10 f 643.576 y 121.725 (\257)s 11 f 645.376 y 128.512 (c)s 1 f 643.576 y 137.796 (and)s 10 f 161.524 (h)s 2 f 645.376 y 168.438 (2)s 1 f 643.576 y 177.812 (=)s 191.136 (1)s 200.066 (+)s 2 f 638.851 y 213.769 (4)s 4.783 .48 213.769 640.816 r 647.714 y 213.769 (3)s 1 f 643.576 y 221.992 (ln)s 233.992 (2.)s 249.843 (The)s 274.904 (p)s 281.904 (oin)s 297.571 (t)s 10 f 306.632 (\257)s 1 f 318.044 (=)s 2 f 638.851 y 332.809 (3)s 4.783 .48 332.809 640.816 r 647.714 y 332.809 (2)s 10 f 643.576 y 339.032 (;)s 344.365 (h)s 2 f 645.376 y 351.279 (1)s 1 f 643.576 y 360.654 (=)s 373.978 (0)s 10 f 379.978 (;)s 385.311 (h)s 2 f 645.376 y 392.225 (2)s 1 f 643.576 y 401.6 (=)s 414.924 (1)s 423.854 (+)s 2 f 638.851 y 437.557 (4)s 4.783 .48 437.557 640.816 r 647.714 y 437.557 (3)s 1 f 643.576 y 445.78 (ln)s 457.78 (2)s 660.376 y -5.69 (is)s 6.874 (called)s 41.372 (tricritical)s 94.603 (p)s 101.603 (oin)s 117.27 (t.)s 132.097 (W)s 143.43 (e)s 153.261 (refer)s 181.492 (for)s 200.357 (details)s 238.921 (to)s 254.086 (the)s 275.25 (pap)s 294.917 (er)s 309.448 ([BEG].)s 350.029 (In)s 365.527 (Fig.)s 392.854 (1)s 403.351 (there)s 434.549 (is)s 447.114 (the)s 677.176 y -5.69 (graph)s 28.343 (of)s 12 f 42.01 (\241)s 10 f 51.343 (p)s 2 f 672.821 y 57.381 (0)s 1 f 677.176 y 66.764 (as)s 81.497 (a)s 91.497 (function)s 138.498 (of)s 10 f 152.164 (m)s 1 f 166.7 (\050b)s 177.7 (y)s 188.034 (means)s 224.767 (of)s 238.434 (\0502.8\051)s 267.101 (\051)s 275.767 (at)s 290.434 (a)s 300.434 (three-phases)s 369.267 (co)s 380.934 (existence)s 432.001 (p)s 439.001 (oin)s 454.668 (t.)s 705.976 y 226.045 (8)s do-end end endp %%Page: 9 9 %%BeginPageSetup initializepage (Raffaele Esposito; page: 9 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC 169 145 242 148 rC 288 177 1 36 242 148 169 145 T T 1 :f :g 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000600C0000000000000000000000000000000000000000000000000000000000000000000090040000000000000000000000000000000000000000000000000000000000000000000090040000000000000000000000000000000000000000000000000002000000000000000090040600000000000000000000100000000000000000000000000002000000000000000091840400000 0000000000000001000000000000000000000000000020000000000000000618E0400000000000000000000100000000000000000000000000002000000000000000000000400000000000000000000100000000000000000000000000002000000000000000000000600000000000000000000200000000000000000000000000002000000000000000000000400000000000000000000200000000000000000000000000002000000000000000000000400000000000000000000200000000000000000000000000 001000000000000000000000400000000000000000000200000000000000000000000000001000000000000000000000600000000000000000000200000000000000000000000000001000000000000000000000400000000000000000000200000000000000000000000000001000000000000000000000400000000000000000000200000000000000000000000000001000000000000000000000400000000000000000000400000000000000000000000000001000000000000000000000400000000000000000 000400000000000000000000000000000800000000000000000000600000000000000000000400000000000000000000000000000800000000000000000000400000000000000000000400000000000000000000000000000800000000000000000000400000000000000000000400000000000000000000000000000800000000000000000000400000000000000000000400000000000000000000000000000800000000000000000000600000000000000000000400000000000000000000000000000800000000 000060063CF04000000000000000000008000000000000000000000000000004000000000000900904804000000000000000000008000000000000000000000000000004000000000000900908E04000000000000000000008000000000000000000000000000004000000000000900908106000000000000000000008000000000000000000000000000004000000000000918910104000000000000000000008000000000000000000000000000004000000000000618610E0400000000000000000000800000000 000000000000000000000400000000000000000000400000000000000000001000000000000000000000000000000200000000000000000000600000000000000000001000000000000000000000000000000200000000000000000000400000000000000000001000000000000000000000000000000200000000000000000000400000000000000000001000000000000000000000000000000200000000000000000000400000000000000000001000000000000000000000000000000200000000000000000000 600000000000000000002000000000000000000000000000000200000000000000000000400000000000000000002000000000000000000000000000000100000000000000000000400000000000000000002000000000000000000000000000000100000000000000000000400000000000000000002000000000000000000000000000000100000000000000000000400000000000000000002000000000000000000000000000000100000000000000000000600000000000000000002000000000000000000000 0000000001000000000000000000004000000000000000000040000000000000000000000000000000800000000000000000004000000000000000000040000000000000000000000000000000800000000000000000004000000000000000000040000000000000000000000000000000800000000000000000006000000000000000000040000000000000000000000000000000800000000000018018F0400000000000000000004000000000000000000000000000000040000000000002402480400000000000 0000000080000000000000000000000000000000400000000000024024E04000000000000000000080000000000000000000000000000000400000000000024024106000000000000000000080000000000000000000000000000000400000000000024624104000000000000000000080000000000000000000000000000000200000000000018618E0400000000000000000008000000000000000000000000000000020000000000000000000400000000000000000010000000000000000000000000000000020 0000000000000000006000000000000000000100000000000000000000000000000000200000000000000000004000080000000000000100000000000000000000000000000000200000000000000C000040000C0000000000000100000000000000000000000000000000100000000000000C000040000C0000000000000100000000000000000000000000000000100000000000000C000060000C0000000000000200000000000000000000000000000000100000000000000C000040000C000000000000020000 00000000000000000000000000001000000000000014000040000A000000000000020000000000000000000000000000000008000000000000140000400012000000000000020000000000000000000000000000000008000000000000120000400012000000000000040000000000000000000000000000000008000000000000220000600011000000000000040000000000000000000000000000000008000000000000220000400011000000000000040000000000000000000000000000000004000000000000 2200004000110000000000000800000000000000000000000000000000040000000000004100004000108000000000000800000000000000000000000000000000040000000000004100006000208000000000000800000000000000000000000000000000040000000000608718F04000204000000000000800000000000000000000000000000000020000000000908924804000204000000000001000000000000000000000000000000000020000000000908904E0400020400000000000100000000000000000 00000000000000000200000000009109081060004020000000000010000000000000000000000000000000000100000000009189101040004020000000000010000000000000000000000000000000000100000000006186BCE0400040100000000000200000000000000000000000000000000001000000000002008000400040100000000000200000000000000000000000000000000000800000000002008000600040100000000000200000000000000000000000000000000000800000000004008000400080 080000000000400000000000000000000000000000000000800000000004008000400080080000000000400000000000000000000000000000000000800000000004008000400080040000000000400000000000000000000000000000000000400000000008008000600080040000000000400000000000000000000000000000000000400000000008004000400100040000000000800000000000000000000000000000000000400000000010004000400100020000000000800000000000000000000000000000 000000200000000010004000400100020000000000800000000000000000000000000000000000200000000020004000400100010000000001000000000000000000000000000000000000200000000020004000600200010000000001000000000000000000000000000000000000100000000020002000400200008000000001000000000000000000000000000000000000100000000040002000400200008000000002000000000000000000000000000000000000080000000040002000400200008000000002 000000000000000000000000000000000000080000000080001000600200004000000002000000000000000000000000000000000000080000000080001000400400004000000004000000000000000000000100000000000000048000000100001000400400002000000044000000000000002000000100010001000080048000800180008800400440006000400044004000200020002000007FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF80000000000000000000020000 0004000008004008000010000000080000000000000000000000000000000000000200000004000008004008000008000000100000000000000000000000000000000000000100000008000004004008000008000000100000000000000000000000000000000000000100000008000004006008000004000000200000000000000000000018018000000000000D00C0001000000400401000000400003023000000000000180180002402800000000000128120001000000200401000000200004844800000000000 2402800024028000000000001280200020000001004010000001000048408000000000002402800FA403C00000000007D240400020000001006020000001000048810000000000002403C00024608000000000001270800040000000804020000000800049C2000000000000246080001861C000000000000C31E00040000000804040000000800032C78000000000001861C0000000000000000000001000008000000040408000000040000200000000000000000000000000000000000000001000010000000020 4080000000200004000000000000000000000000000000000000000008000200000000206100000000100008000000000000000000000000000000000000000004000400000000104200000000080010000000000000000000000000000000000000000002000800000000104400000000040020000000000000000000000000000000000000000001003000000000084400000000020020000000000000000000000000000000000000000000C0400000000006680000000001C1C000000000000000000000000000 00000000000000003F8000600618F1F000000000007F00000000000000000000000000000000000000000000000000900924804000000000000000000000000000000000000000000000000000000000000000900904E0400000000000000000000000000000000000000000000000000000000000003E90090810600000000000000000000000000000000000000000000000000000000000000091891010400000000000000000000000000000000000000000000000000000000000000061863CE0400000000000 000000000000000000000000000000000000000000000000000000000000400000000000000000000000000000000000000000000000000000000000000000000000600000000000000000000000000000000000000000000000000000000000000000000000400000000000000000000000000000000000000000000000000000000000000000000000400000000000000000000000000000000000000000000000000000000000000000000000400000000000000000000000000000000000000000000000000000000000000000000000600000000000000000000000000000000000000000000000000000000000000000000000400000 000000000000000000000000000000000000000000000000000000000000000000400000000000000000000000000000000000000000000000000000000000000000000000400000000000000000000000000000000000000000000000000000000000000000000000400000000000000000000000000000000000000000000000000000000000000000000000600000000000000000000000000000000000000000000000000000000000000000000000400000000000000000000000000000000000000000000000 0000000000000000000000004000000000000000000000000000000000000000000000000000000000000000000000004000000000000000000000000000000000000000000000000000000000000000000000006000000000000000000000000000000000000000000000000000000000000000018018F04000000000000000000000000000000000000000000000000000000000000000024024804000000000000000000000000000000000000000000000000000000000000000024024E0400000000000000000 0000000000000000000000000000000000000000000000FA4024106000000000000000000000000000000000000000000000000000000000000000024624104000000000000000000000000000000000000000000000000000000000000000018618E0400000000000000000000000000000000000000000000000000000000000000000000000400000000000000000000000000000000000000000000000000000000000000000000000600000000000000000000000000000000000000000000000000000000000 000000000000400000000000000000000000000000000000000000000000000000000000000000000000400000000000000000000000000000000000000000000000000000000000000000000000400000000000000000000000000000000000000000000000000000000000000000000000600000000000000000000000000000000000000000000000000000000000000000000000400000000000000000000000000000000000000000000000000000000000000000000000400000000000000000000000000000 000000000000000000000000000000000000000000400000000000000000000000000000000000000000000000000000000000000000000000400000000000000000000000000000000000000000000000000000000000000000000000600000000000000000000000000000000000000000000000000000000000000000000000400000000000000000000000000000000000000000000000000000000000000000000000400000000000000000000000000000000000000000000000000000000000000000000000 400000000000000000000000000000000000000000000000000000000000000000000000600000000000000000000000000000000000000000000000000000000000000060063CF04000000000000000000000000000000000000000000000000000000000000000900904804000000000000000000000000000000000000000000000000000000000000000900908E0400000000000000000000000000000000000000000000000000000000000003E90090810600000000000000000000000000000000000000000 0000000000000000000000918910104000000000000000000000000000000000000000000000000000000000000000618610E0400000000000000000000000000000000000000000000000000000000000000000000000400000000000000000000000000000000000000000000000000000000000000000000000600000000000000000000000000000000000000000000000000000000000000000000000400000000000000000000000000000000000000000000000000000000000000000000000400000000000 000000000000000000000000000000000000000000000000000000000000400000000000000000000000000000000000000000000000000000000000000000000000600000000000000000000000000000000000000000000000000000000000000000000000400000000000000000000000000000000000000000000000000000000000000000000000400000000000000000000000000000000000000000000000000000000000000000000000400000000000000000000000000000000000000000000000000000 000000000000000000400000000000000000000000000000000000000000000000000000000000000000000000600000000000000000000000000000000000000000000000000000000000000000000000400000000000000000000000000000000000000000000000000000000000000000000000400000000000000000000000000000000000000000000000000000000000000000000000400000000000000000000000000000000000000000000000000000000000000000000000600000000000000000000000 0000000000000000000000000000000000000000000600C0400000000000000000000000000000000000000000000000000000000000000000090040400000000000000000000000000000000000000000000000000000000000000000090040400000000000000000000000000000000000000000000000000000000000000003E90040600000000000000000000000000000000000000000000000000000000000000000091840000000000000000000000000000000000000000000000000000000000000000000 0618E0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000%ADOeod :j gR gS 169 428 232 185 rC np 267 447 :M 270 458 :L 267 458 :L 264 458 :L 267 447 :L eofill -1 -1 268 599 1 1 267 458 @b np 365 537 :M 353 541 :L 353 537 :L 353 534 :L 365 537 :L eofill 177 538 -1 1 354 537 1 177 537 @a 386 542 15 17 rC gS .838 .841 scale 463.253 660.01 :M f20_14 sf (h)S gR gS .838 .841 scale 471.611 660.01 :M f20_9 sf (1)S gR gR gS 235 428 17 18 rC gS .838 .841 scale 284.16 524.44 :M f20_14 sf (h)S gR gS .838 .841 scale 291.324 524.44 :M f20_9 sf (2)S gR gR gS 0 0 583 768 rC 267 506 :M 282.329 521.325 292.662 531.992 298 538 :C 303.329 543.992 320.995 560.658 351 588 :C stroke 268 506 :M 251.996 521.325 241.33 531.992 236 538 :C 230.663 543.992 213.33 560.658 184 588 :C stroke 348 458 17 22 rC gS .838 .841 scale 419.077 564.873 :M f20_18 sf (+)S gR gR gS 169 458 13 22 rC gS .838 .841 scale 202.972 564.873 :M f20_18 sf (-)S gR gR gS 280 595 15 18 rC gS .838 .841 scale 337.888 723.038 :M f20_14 sf (0)S gR gR gS 254 490 10 14 rC gS .838 .841 scale 305.652 593.414 :M f19_12 sf (k)S gR gR gS 159 418 252 205 rC -1000 -1000 :M f1_12 sf ( )S -997 -1000 :M f2_12 sf ( )S -993 -1000 :M f10_12 sf ( )S -985 -1000 :M f11_12 sf ( )S -976 -1000 :M f12_12 sf ( )S -964 -1000 :M f14_12 sf ( )S gR gS 0 0 583 768 rC 0 0 :M initclip TeXdict begin do-bop 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 251.23 y 8.71 (Fig.1)s 12 f 43.21 (\241)s 10 f 52.543 (p)s 2 f 246.875 y 58.581 (0)s 1 f 251.23 y 63.964 (\050)s 10 f 68.631 (m;)s 84.5 (\301)s 1 f 91.65 (\050)s 10 f 96.317 (m)s 1 f 106.853 (\051\051)s 120.186 (at)s 10 f 134.853 (\257)s 1 f 145.607 (=)s 158.274 (3)s 10 f 164.274 (:)s 1 f 167.607 (76)s 10 f 179.607 (;)s 184.941 (h)s 2 f 253.03 y 191.854 (1)s 1 f 251.23 y 200.571 (=)s 213.238 (0)s 10 f 219.238 (;)s 224.571 (h)s 2 f 253.03 y 231.485 (2)s 1 f 251.23 y 240.201 (=)s 252.868 (0)s 10 f 258.868 (:)s 1 f 262.201 (06.)s 274.978 y 8.71 (In)s 25.346 (Fig.2)s 57.482 (it)s 71.118 (is)s 84.82 (sho)s 101.887 (wn)s 122.856 (the)s 145.159 (phase)s 180.194 (diagram)s 228.53 (in)s 244.166 (the)s 266.469 (plane)s 10 f 300.105 (h)s 2 f 276.778 y 307.019 (1)s 10 f 274.978 y 312.402 (;)s 317.735 (h)s 2 f 276.778 y 324.649 (2)s 1 f 274.978 y 330.033 (,)s 339.411 (for)s 10 f 359.413 (\257)s 1 f 372.47 (large.)s 411.411 (There)s 447.747 (are)s 291.778 y -5.69 (three)s 24.386 (lines)s 51.163 (of)s 64.206 (phase)s 96.982 (co)s 108.649 (existence)s 159.092 (stemming)s 213.202 (from)s 240.945 (a)s 250.322 (triple)s 281.731 (p)s 288.731 (oin)s 304.398 (t)s 312.441 (whic)s 336.108 (h)s 346.151 (separate)s 392.961 (the)s 413.004 (one)s 434.38 (phase)s 308.578 y -5.69 (regions.)s 42.4 (In)s 58.286 (the)s 79.838 (semiplane)s 10 f 136.124 (h)s 2 f 310.378 y 143.038 (1)s 10 f 308.578 y 153.231 (\076)s 1 f 167.374 (0)s 178.259 (\050)s 10 f 182.926 (h)s 2 f 310.378 y 189.84 (1)s 10 f 308.578 y 200.033 (\074)s 1 f 214.175 (0\051)s 229.728 (there)s 261.313 (is)s 274.266 (a)s 285.152 (line)s 308.704 (of)s 323.256 (co)s 334.923 (existence)s 386.875 (of)s 401.428 (phases)s 440.447 (with)s 325.378 y -5.69 (p)s 1.31 (ositiv)s 29.377 (e)s 40.166 (\050negativ)s 82.832 (e\051)s 98.288 (and)s 123.077 (zero)s 149.9 (magnetization)s 229.355 (and)s 254.145 (along)s 287.6 (the)s 309.723 (line)s 10 f 333.845 (h)s 2 f 327.178 y 340.759 (1)s 1 f 325.378 y 351.902 (=)s 366.995 (0)s 10 f 372.995 (;)s 378.328 (h)s 2 f 327.178 y 385.242 (2)s 10 f 325.378 y 396.384 (\076)s 411.477 (k)s 1 f 423.558 (there)s 455.714 (is)s 342.178 y -5.69 (co)s 5.976 (existence)s 57.043 (of)s 70.71 (phases)s 108.843 (with)s 136.177 (p)s 143.177 (ositiv)s 171.243 (e)s 180.577 (and)s 203.91 (negativ)s 241.91 (e)s 251.244 (magnetization.)s 1 f 572.208 y 8.71 (Fig.2)s 39.21 (Phase)s 74.11 (diagram)s 120.81 (at)s 10 f 135.477 (\257)s 146.231 (\076\076)s 168.231 (\257)s 11 f 574.008 y 175.018 (c)s 1 f 572.208 y 179.907 (.)s 595.957 y 8.71 (Finally)s 49.543 (w)s 57.877 (e)s 67.21 (note)s 93.877 (that)s 119.877 (the)s 140.543 (function)s 10 f 617.545 y 153.094 (f)s 2 f 612.59 y 160.261 (0)s 1 f 617.545 y 168.978 (:=)s 12 f 184.978 (\241)s 10 f 194.311 (m)s 2 f 612.59 y 204.847 (2)s 1 f 617.545 y 212.897 (+)s 10 f 224.897 (\301)s 12 f 234.714 (\241)s 10 f 246.714 (\257)s 14 f 612.59 y 254.134 (\241)s 2 f 261.635 (1)s 10 f 617.545 y 267.018 (s)s 1 f 272.643 (\050)s 10 f 277.31 (m;)s 293.179 (\301)s 1 f 300.329 (\051)s 639.133 y -5.69 (is)s 6.376 (not)s 27.71 (con)s 45.377 (v)s 51.377 (ex)s 67.043 (for)s 10 f 85.41 (\257)s 96.164 (\076)s 2 f 634.408 y 110.271 (1)s 4.783 .48 110.271 636.373 r 643.271 y 110.271 (2)s 1 f 639.133 y 116.494 (.)s 125.161 (In)s 140.161 (fact)s 10 f 670.745 y 139.566 (H)s 150.516 (ess)s 1 f 167.354 (\050)s 10 f 172.02 (f)s 2 f 665.79 y 179.187 (0)s 1 f 670.745 y 184.57 (\051)s 192.57 (=)s 662.626 y 219.635 (2)s 10 f 225.635 (\257)s 1 f 233.056 (\050)s 10 f 237.723 (m)s 2 f 658.272 y 248.259 (2)s 12 f 662.626 y 256.309 (\241)s 10 f 268.309 (\301)s 1 f 275.459 (\051)s 282.792 (+)s 294.792 (1)s 107.074 .48 206.677 667.984 r 678.976 y 206.677 (\050)s 10 f 211.344 (\257)s 2 f 675.509 y 218.764 (2)s 1 f 678.976 y 224.148 (\0501)s 12 f 237.481 (\241)s 10 f 249.481 (\301)s 1 f 256.631 (\051\050)s 10 f 265.964 (\301)s 2 f 675.509 y 273.114 (2)s 12 f 678.976 y 281.164 (\241)s 10 f 293.164 (m)s 2 f 675.509 y 303.701 (2)s 1 f 678.976 y 309.084 (\051)s 10 f 670.745 y 315.191 (:)s 1 f 439.114 (\0502)s 10 f 449.78 (:)s 1 f 453.114 (9\051)s 705.976 y 226.045 (9)s do-end end endp %%Page: 10 10 %%BeginPageSetup initializepage (Raffaele Esposito; page: 10 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC 135 214 330 183 rC 687 381 1 86 330 183 135 214 T T 1 :f :g 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000040000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000001000000000004000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000 000000040000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000002000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000200000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000020000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000002000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000100000000000200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000020000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000 000002000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000020000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000002000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000010000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000 000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000001000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000001000000000001000000000000000000000000000000000000000000000000003FF80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000800000000000000000000000000000000000000000000000FFFFFFFFFFF800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000007007 0080000000000000000000000000000000000000000000007F00FC1FC3F83FFC0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000088083FF80000000000000000000000000000000000000000001FFFFF00003FFFFFFFE0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000880F008000000000000000000000000000000000000000000FF801E0FE03E1 C03C077F800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000880880800000000000000000000000000000000000000001FF801E0001FC003803E0E0FE000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000088088080000000000000000000000000000000000000000EFFFFF000038E0007007FDC1FF00000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000100000088088080000000000000000000000000000000000000007F80030FE03C01E000FF833FFFFF800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000007087008000000000000000000000000000000000000003E20004001FC0001C0F9800C0703FFC000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000 800000000000000000000000000000000000001C0C00180002700003F00700380E067FE0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000080000000000000000000000000000000000000E0300060000C0E00076000C00601C18EFF80000000000000000000000000000380000000000000000000000000000000000000000000000000000000010000000000004000000000000000000000000000000000000780400080001001C01818 00300180FF71C3FC000000000000000000000000007DC0000000000000000000000000000000000000000000000000000000010000000000004000000000000000000000000000000000003A0180030000600038E006000E03FF0CFFF867FFFFFFFFFC000000000000000FBF6000000000000000000000000000000000000000000000000000000001000000000000400000000000000000000000000000000001CC0FFFFF000180000700018001FC1802033FFC7F87000303FFFFFFFFFFFFFFF7F7BC020000000000 0000000000000000000000000000000000000000000100000000000040000000000000000000000000000000000631F0FFD8FF020000058000600E40040180C19FFFFFFFFFFF8100008000803FFFBDFBFC000000000000000000000000000000000000000000000000000001000000000000400000000000000000000000000000000018FE07E0601CFC00001860001870300300602060EFFFFFF8307FFFFFFFFFFFCFFBCFEFFC000000000000000000000000000000000000000000000000000001000000000000400000000000000000000000000000000063C43C0080FF 03800020180007800C00C010181C187FFF87FFF820002007FFF7FE7FBFF80000000000000000000000000000000000000000000000000000010000000000004000000000000000000000000000000001DC1BD8031F800C7800C006001D800200200C0603070DFFFFFFFFFFFFFFF9FFFFCFFFFFF80000000000000000000000000000000000000000000000000000010000000000004000000000000000000000000000000007603C200FE3007FCE0300018060400180180FFFFFFFFF9FFFF820FFFFFFFE7FE7F7DEFF B0000000000000000000000000000000000000000000000000000001000000000000400000000000000000000000000000001FC0E0C07C0C07E039D40000638030006007F080402023FFF7FFFFFFFFFFFF9FFBFFFBBF70000000000000000000000000000000000000000000000000000001000000000000400000000000000000000000000000007D87030FC010FE01FEF800001C000C0010F900603018181BFFFFFFFFFFFFFFE7FDFFDFFFE000000000000000000000000000000000000000000000000000000100 000000000020000000000000000000000000000001F23E05F1807F181F8FEC0000140003000F00C010080606041FFFFFFFFFFFFFF9FFDEFFBEA0000000000000000000000000000000000000000000000000000001000000000000200000000000000000000000000000038DD83E0203E063F8FE038000230000803A00200C060101030CFFFFFFFFFFFFFFFFE7FEFD400000000000000000000000000000000000000000000000000000010000000000002000000000000000000000000000000E1E21E00C3E01FCFF E000600040C00061C10010020180C0C0C31FFFFFFFFFFFFFF3FF7FFBC00000000000000000000000000000000000000000000000000000010000000000002000000000000000000000000000001870CE4033CC0F83FE000018018020001E00C00C018040FFFFFE839DFFFFFFFFFFFFFBFFFE80000000000000000000000000000000000000000000000000000001000000000000200000000000000000000000000000718371807C10781EE000000702001800140020020040FF08080DFFFF8FFFFFFFFFFF3F7EAD00 000000000000000000000000000000000000000000000000000001000000000000200000000000000000000000000001C7078203C023B0F700000000C400040022001801803F08060602181BFF7FFFFFFFCFFBFBDA000000000000000000000000000000000000000000000000000000010000000000002000000000000000000000000000039E1C041E00DCC7F80000000038000300C180040043C80601018187061BFFFFFFFFFE3FFFFC000000000000000000000000000000000000000000000000000000010000 0000000020000000000000000000000000000FE86018E401E17F8000000000080000C1004002003C040100C04060C1871C6FFFFFFFFBFDB8000000000000000000000000000000000000000000000000000000010000000E002020000000000000000000000000001F11C027180F079C00000000000600002200200180E80300C030303FFFFFFFF870C0FC3FFFF000000000000000000000000000000000000000000000000000000001000000110067FF000000000000000000000000006C26807820783CE0000000 00000100001C0018004704008020081FC40818307FFFFF0FCFC920000000000000000000000000000000000000000000000000000000010000001100A01000000000000000000000000000B0F901C0C3E1E700000000000000C00014000400380300401807E20306060818E0FFF0FE12C000000000000000000000000000000000000000000000000000000001000000110120100000000000000000000000000141C60E013C8FB80000000000000020002200030068008030043901808181860FFF1C3F19FF800000 00000000000000000000000000000000000000000000000000010000001101F0100000000000000000000000000383087403C3F7C0000000000000001000418000818400400803C080406040FFF18383E1E1890000000000000000000000000000000000000000000000000000000001000000110020100000000000000000000000000F0C11880E0F1E00000000000000000C0080400046020020043C804020107F106060FC3F1FFE0000000000000000000000000000000000000000000000000000000001000000 0E1020100000000000000000000000001E302E10703870000000000000000002010020003801801803C04030180F880C1C1F0E37184400000000000000000000000000000000000000000000000000000000010000000000001000000000000000000000000034E07063A1C380000000000000000001820018002800400406802008043A060303E601C0F088000000000000000000000000000000000000000000000000000000000100000000000010000000000000000000000000FB41808CC78C00000000000000 00000044000400440020023840100403C101008EC1C7718FF8000000000000000000000000000000000000000000000000000000000100000000000010000000000000000000000001A48601711A30000000000000000000003800030182001801C0200C021C8080C07020380E0210000000000000000000000000000000000000000000000000000000000100000000000010000000000000000000000003591C0386E5C000000000000000000000080000820100040340100201E0406021D818EC09C42000000000 0000000000000000000000000000000000000000000000000100000000000008000000000000000000000004E6680C0B1E00000000000000000000000400004400800204200C01034020101E040703103C400000000000000000000000000000000000000000000000000000000001000000000000080000000000000000000000198990301C38000000000000000000000002000038004001181002008C20180874031D80E023C0000000000000000000000000000000000000000000000000000000000100000000 0000080000000000000000000000261620E060C0000000000000000000000001000028002000E0080100701004078300E0409C40800000000000000000000000000000000000000000000000000000000001000000000000080000000000000000000000483843418300000000000000000000000000800044001000A0040080D008020500C0A03103C100000000000000000000000000000000000000000000000000000000000100000000000008000000000000000000000090609C870C00000000000000000000 0000004000820008011002004708060118C023180E013A0000000000000000000000000000000000000000000000000000000000010000000000000800000000000000000000012181611A300000000000000000000000000030010100040608010038040100E0201C060B0206000000000000000000000000000000000000000000000000000000000001000000000000080000000000000000000002C203826DC00000000000000000000000000008020080020804008028020081A010140110E404000000000000 0000000000000000000000000000000000000000000000010000000000000800000000000000000000058C060596000000000000000000000000000004040040011002004044010046100C2300E0180400000000000000000000000000000000000000000000000000000000000100000000000008000000000000000000000B18180E3800000000000000000000000000000208002000E00100208200803808024080A017040000000000000000000000000000000000000000000000000000000000010000000000 000800000000000000000000167020186000000000000000000000000000000110001000A000801101004028060180611810E800000000000000000000000000000000000000000000000000000000000100000000000004000000000000000000003CA0C06180000000000000000000000000000000A00008011000400E008020C40101401206201800000000000000000000000000000000000000000000000000000000000100000000000004000000000000000000006B43818600000000000000000000000000 000000600004020800200A004011020082200C0140100000000000000000000000000000000000000000000000000000000000010000000000000400000000000000000000D485030800000000000000000000000000000000100002040400101100200E010044100A00C0100000000000000000000000000000000000000000000000000000000000010000000000000400000000000000000001B91A0E3000000000000000000000000000000000080001080200082080100A0080380C1100B02000000000000000 00000000000000000000000000000000000000000000010000000000000400000000000000000003622434C00000000000000000000000000000000004000090010004404008110040280220C10C200000000000000000000000000000000000000000000000000000000000010000000000000400000000000000000004C4C84900000000000000000000000000000000000200006000800280200420802044014022034000000000000000000000000000000000000000000000000000000000000100000001C01C 04000000000000000000090B11960000000000000000000000000000000000010000200040030010024040108200C01400C0000000000000000000000000000000000000000000000000000000000001000000022022FFE00000000000000000121426380000000000000000000000000000000000008000500020050008018020090100A00C00800000000000000000000000000000000000000000000000000000000000010000000220020400000000000000000024184860000000000000000000000000000000 0000004000880010088004028010060081100A0080000000000000000000000000000000000000000000000000000000000001000000022004020000000000000000005820B0C000000000000000000000000000000000000020010400081040020440080500420809808000000000000000000000000000000000000000000000000000000000000100000002200802000000000000000000B040C3000000000000000000000000000000000000001002020004202001082004088024061041000000000000000000 00000000000000000000000000000000000000000001000000022010020000000000000000016181040000000000000000000000000000000000000008020100024010009010021040180110310000000000000000000000000000000000000000000000000000000000000100000001C23E02000000000000000002A3061800000000000000000000000000000000000000040400800180080060080120200800A00A0000000000000000000000000000000000000000000000000000000000000100000000000002000000000000000005460C6000000000000000000000 0000000000000000000208004001000400200400C01014006006000000000000000000000000000000000000000000000000000000000000010000000000000200000000000000000E9C3880000000000000000000000000000000000000000110002002800200500200A0082200500400000000000000000000000000000000000000000000000000000000000001000000000000020000000000000000192853000000000000000000000000000000000000000000A0001004400100880101100421004804000000 000000000000000000000000000000000000000000000000000000010000000000000200000000000000003251AC00000000000000000000000000000000000000000060000804200081040082080240C084040000000000000000000000000000000000000000000000000000000000000100000000000002000000000000000065A650000000000000000000000000000000000000000000100004081000420200440401802103080000000000000000000000000000000000000000000000000000000000000100 0000000000020000000000000000CA48E0000000000000000000000000000000000000000000080002100800240200280200801100880000000000000000000000000000000000000000000000000000000000000100000000000001000000000000000114B180000000000000000000000000000000000000000000040001100400180100100101400A005000000000000000000000000000000000000000000000000000000000000001000000000000010000000000000002194200000000000000000000000000 000000000000000000020000A002000800801000812006003000000000000000000000000000000000000000000000000000000000000001000000000000010000000000000002218C0000000000000000000000000000000000000000000001000040010014004028004210050010000000000000000000000000000000000000000000000000000000000000010000000000000100000000000000044210000000000000000000000000000000000000000000000080004000802200204400240804802000000000 000000000000000000000000000000000000000000000000000001000000000000010000000000000008842000000000000000000000000000000000000000000000004000A00040210020420014040440200000000000000000000000000000000000000000000000000000000000000100000000000001000000000000001108400000000000000000000000000000000000000000000000200090002041001081000802082020000000000000000000000000000000000000000000000000000000000000010000 000000000100000000000000131080000000000000000000000000000000000000000000000020010800108080088080080108104000000000000000000000000000000000000000000000000000000000000001000000000000010000000000000026310000000000000000000000000000000000000000000000001002040008804005004014008808400000000000000000000000000000000000000000000000000000000000000100000000000001000000000000004C62000000000000000000000000000000 00000000000000000008020200050020020020220050044000000000000000000000000000000000000000000000000000000000000001000000000000010000000000000059CC000000000000000000000000000000000000000000000000040402000200200200102100300280000000000000000000000000000000000000000000000000000000000000010000000000000080000000000000B2900000000000000000000000000000000000000000000000000204010002001005000840802801800000000000 0000000000000000000000000000000000000000000000000001000000000000008000000000000154A0000000000000000000000000000000000000000000000000010800800500080480044040240080000000000000000000000000000000000000000000000000000000000000010000000000000080000000000002A94000000000000000000000000000000000000000000000000000900040048004084002802042010000000000000000000000000000000000000000000000000000000000000001000000 00000000800000000000035280000000000000000000000000000000000000000000000000005000200840020820010010410100000000000000000000000000000000000000000000000000000000000000010000000000038080000000000006A500000000000000000000000000000000000000000000000000002000100840021010010008408100000000000000000000000000000000000000000000000000000000000000010000000000045FFC00000000000D4A0000000000000000000000000000000000 00000000000000000020001010200120080280048042000000000000000000000000000000000000000000000000000000000000000100000000000440800000000000098C0000000000000000000000000000000000000000000000000000100008201000A0080240028022000000000000000000000000000000000000000000000000000000000000000100000000000440800000000000121000000000000000000000000000000000000000000000000000000800042008004004022001001200000000000000 0000000000000000000000000000000000000000000000000100000000000440800000000000242000000000000000000000000000000000000000000000000000000400024004004002041001000C00000000000000000000000000000000000000000000000000000000000000010000000000044080000000000048400000000000000000000000000000000000000000000000000000020001400400A0010408028004000000000000000000000000000000000000000000000000000000000000000100000000 0003804000000000005080000000000000000000000000000000000000000000000000000002000080020090008804024004000000000000000000000000000000000000000000000000000000000000000100000000000000400000000000B1000000000000000000000000000000000000000000000000000000010000800101080048040220080000000000000000000000000000000000000000000000000000000000000001000000000000004000000000016200000000000000000000000000000000000000 000000000000000000800140008108002802041008000000000000000000000000000000000000000000000000000000000000000100000000000000400000000002C40000000000000000000000000000000000000000000000000000000040012000820400100104080800000000000000000000000000000000000000000000000000000000000000010000000000000040000000000398000000000000000000000000000000000000000000000000000000002001100042020010008804080000000000000000 00000000000000000000000000000000000000000000000100000000000000400000000007200000000000000000000000000000000000000000000000000000000020021000240100280048021000000000000000000000000000000000000000000000000000000000000000010000000000000040000000000D400000000000000000000000000000000000000000000000000000000010020800140100240028011000000000000000000000000000000000000000000000000000000000000000010000000000 000040000000001A8000000000000000000000000000000000000000000000000000000000080404000800804200100090000000000000000000000000000000000000000000000000000000000000000100000000000000400000000035000000000000000000000000000000000000000000000000000000000004040200080040420010006000000000000000000000000000000000000000000000000000000000000000010000000000000020000000002A000000000000000000000000000000000000000000 000000000000000002080200140020410018002000000000000000000000000000000000000000000000000000000000000000010000000000000020000000005400000000000000000000000000000000000000000000000000000000000208010012001080802400200000000000000000000000000000000000000000000000000000000000000001000000000000002000000000980000000000000000000000000000000000000000000000000000000000010800801200108040220020000000000000000000 000000000000000000000000000000000000000000000100000000000000200000000120000000000000000000000000000000000000000000000000000000000000900040210009004021004000000000000000000000000000000000000000000000000000000000000000010000000000000020000000014000000000000000000000000000000000000000000000000000000000000050004020800500204080400000000000000000000000000000000000000000000000000000000000000001000000000000 002000000002800000000000000000000000000000000000000000000000000000000000002000202040020010404040000000000000000000000000000000000000000000000000000000000000000100000000000000200000000500000000000000000000000000000000000000000000000000000000000000200010404002000840404000000000000000000000000000000000000000000000000000000000000000010000000000000020000000060000000000000000000000000000000000000000000000 00000000000000001000084020030008802080000000000000000000000000000000000000000000000000000000000000000100000000000000200000000A000000000000000000000000000000000000000000000000000000000000000800088010048004801080000000000000000000000000000000000000000000000000000000000000000100000000000000200000001400000000000000000000000000000000000000000000000000000000000000080004801004400280088000000000000000000000 00000000000000000000000000000000000000000001000000000000001000000028000000000000000000000000000000000000000000000000000000000000000400028008044001000480000000000000000000000000000000000000000000000000000000000000000100000000000000100000003000000000000000000000000000000000000000000000000000000000000000020001000408200100030000000000000000000000000000000000000000000000000000000000000000010000000007007010000000600000000000000000000000000000000000 0000000000000000000000000000020001000408100180010000000000000000000000000000000000000000000000000000000000000000010000000008808BFF800000C0000000000000000000000000000000000000000000000000000000000000000100028002080802400100000000000000000000000000000000000000000000000000000000000000000100000000088008100000008000000000000000000000000000000000000000000000000000000000000000008002400110040220010000000000 0000000000000000000000000000000000000000000000000000000100000003E8801010000001800000000000000000000000000000000000000000000000000000000000000000800240009004021002000000000000000000000000000000000000000000000000000000000000000001000000000880201000000300000000000000000000000000000000000000000000000000000000000000000040042000900202100200000000000000000000000000000000000000000000000000000000000000000100 00000008804010000006000000000000000000000000000000000000000000000000000000000000000000200420006001020802000000000000000000000000000000000000000000000000000000000000000001000000000708F810000004000000000000000000000000000000000000000000000000000000000000000000100410002000840402000000000000000000000000000000000000000000000000000000000000000001000000000000001000000800000000000000000000000000000000000000 000000000000000000000000000010080800200084020200000000000000000000000000000000000000000000000000000000000000000100000000000000080000100000000000000000000000000000000000000000000000000000000000000000000808080030004401040000000000000000000000000000000000000000000000000000000000000000010000000000000008000010000000000000000000000000000000000000000000000000000000000000000000041004004800240084000000000000 000000000000000000000000000000000000000000000000000001000000000000000800000000000000000000000000000000000000000000000000000000000000000000000004100200480018008400000000000000000000000000000000000000000000000000000000000000000100000000000000080000000000000000000000000000000000000000000000000000000000000000000000000210020044000800440000000000000000000000000000000000000000000000000000000000000000010000 00000000000800000000000000000000000000000000000000000000000000000000000000000000000001200100820008002400000000000000000000000000000000000000000000000000000000000000000100000000000000080000000000000000000000000000000000000000000000000000000000000000000000000120008081000C001800000000000000000000000000000000000000000000000000000000000000000100000000000000080000000000000000000000000000000000000000000000 0000000000000000000000000000A0008081001200080000000000000000000000000000000000000000000000000000000000000000010000000000000008000000000000000000000000000000000000000000000000000000000000000000000000004000410080110008000000000000000000000000000000000000000000000000000000000000000001000000000000000800000000000000000000000000000000000000000000000000000000000000000000000000400041004011000800000000000000 000000000000000000000000000000000000000000000000000100000000000000040000000000000000000000000000000000000000000000000000000000000000000000000020002100401080080000000000000000000000000000000000000000000000000000000000000000010000000000000004000000000000000000000000000000000000000000000000000000000000000000000000001000120020204010000000000000000000000000000000000000000000000000000000000000000001000000 000000000400000000000000000000000000000000000000000000000000000000000000000000000000100012001020401000000000000000000000000000000000000000000000000000000000100000000100000000000000040000000000000000000000000000000000000000000000000000000000000000000000000008000A00102020100000000000000000000000000000000000000000000000000000000060000000010000000000000004000000000000000000000000000000000000000000000000 000000000000000000000000000400040008401010000000000000000000000000000000000000000000000000000000008000000001000000000000000400000000000000000000000000000000000000000000000000000000000000000000000000040004000440081000000000000000000000000000000000000000000000000000000003000000000100000000000000040000000000000000000000000000000000000000000000000000000000000000000000000002000600024008200000000000000000 000000000000000000000000000000000000000C00000000010000000000000004000000000000000000000000000000000000000000000000000000000000000000000000000100090002400420000000000000000000000000000000000000000000000000000000100000000001000000000000000400000000000000000000000000000000000000000000000000000000000000000000000000010009000180022000000000000000000000000000000000000000000000000000000060000000000100000000 000000040000000000000000000000000000000000000000000000000000000000000000000000000000800880008002200000000000000000000000000000000000000000000000000000018000000000010000000001C004020000000000000000000000000000000000000000000000000000000000000000000000000000400840008001200000000000000000000000000000000000000000000000000000060000000000010000000002200CFFE0000000000000000000000000000000000000000000000000 0000000000000000000000000040084000C000C0000000000000000000000000000000000000000000000000000008000000000001000000000220140200000000000000000000000000000000000000000000000000000000000000000000000000002010200120004000000000000000000000000000000000000000000000000000003000000000000100000000FA202402000000000000000000000000000000000000000000000000000000000000000000000000000010101001200040000000000000000000 0000000000000000000000000000000000C00000000000010000000002203E0200000000000000000000000000000000000000000000000000000000000000000000000000001010100110004000000000000000000000000000000000000000000000000000030000000000000100000000022004020000000000000000000000000000000000000000000000000000000000000000000000000000081008010800400000000000000000000000000000000000000000000000000004000000000000010000000001 C20402000000000000000000000000000000000000000000000000000000000000000000000000000004200402040080000000000000000000000000000000000000000000000000001800000000000001000000000000000200000000000000000000000000000000000000000000000000000000000000000000000000000420020204008000000000000000000000000000000000000000000000000000600000000000000100000000000000020000000000000000000000000000000000000000000000000000 000000000000000000000000022002020200800000000000000000000000000000000000000000000000000080000000000000010000000000000002000000000000000000000000000000000000000000000000000000000000000000000000000001200102010080000000000000000000000000000000000000000000000000030000000000000001000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000120008201008000000000000000000000 00000000000000000000000000000C00000000000000010000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000C000840080800000000000000000000000000000000000000000000000003000000000000000010000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000400044004100000000000000000000000000000000000000000000000000400000000000000001000000000000 000100000000000000000000000000000000000000000000000000000000000000000000000000000040002400410000000000000000000000000000000000000000000000000180000000000000000100000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000002000240021000000000000000000000000000000000000000000000001060000000000000000010000000000000001000000000000000000000000000000000000000000000000000000 0000000000000000000000002000180011000000000000000000000000000000000000000000000000C800000000000000000100000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000001000080009000000000000000000000000000000000000000000000000300000000000000000010000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000080008000A000000000000000000000000 000000000000000000000000D8000000000000000001000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000008000C000600000000000000000000000000000000000000000000000306000000000000000001000000000000000080000000000000000000000000000000000000000000000000000000000000000000000000000004000A0002000000000000000000000000000000000000000000000004000000000000000000010000000000000000800000000000000000000000000000000000000000 000000000000000000000000000000000000040012000200000000000000000000000000000000000000000000001800000000000000000001000000000000000080000000000000000000000000000000000000000000000000000000000000000000000000000002001100020000000000000000000000000000000000000000000000600000000000000000000100000000000000008000000000000000000000000000000000000000000000000000000000000000000000000000000100110002000000000000 00000000000000000000000000000000018001C01C00000000000001000000000000000080000000000000000000000000000000000000000000000000000000000000000000000000000001001080040000000000000000000000000000000000000000000002000220220000000000000100000000000000008000000000000000000000000000000000000000000000000000000000000000000000000000000080104004000000000000000000000000000000000000000000000C000220020000000000000100 000000000000008000000000000000000000000000000000000000000000000000000000000000000000000000000080204004000000000000000000000000000000000000000000003000022004000000000000010000000000000000800000000000000000000000000000000000000000000000000000000000000000000000000000004020200400000000000000000000000000000000000000000000400002200800000000000001000000000038038080000000000000000000000000000000000000000000 0000000000000000000000000000000000002020200400000000000000000000000000000000000000000001800002201000000000000001000000000044041FFC0000000000000000000000000000000000000000000000000000000000000000000000000000002020100800000000000000000000000000000000000000000006000001C23E000000000000010000000000440780400000000000000000000000000000000000000000000000000000000000000000000000000000001020080800000000000000 000000000000000000000000000018000000000000000000000001000000001F44044040000000000000000000000000000000000000000000000000000000000000000000000000000000104008080000000000000000000000000000000000000000002000000000000000000000000100000000004404404000000000000000000000000000000000000000000000000000000000000000000000000000000008400408000000000000000000000000000000000000000000C00000000000000000000000010000 000000440440400000000000000000000000000000000000000000000000000000000000000000000000000000000440040800000000000000000000000000000000000000000300000000000000000000000001000000000038438040000000000000000000000000000000000000000000000000000000000000000000000000000000044002100000000000000000000000000000000000000000040000000000000000000000000100000000000000006000000000000000000000000000000000000000000000 0000000000000000000000000000000000024001100000000000000000000000000000000000000000180000000000000000000000000100000000000000001E0000000000000000000000000000000000000000000000000000000000000000000000000000000280011000000000000000000000000000000000000000006000000000000000000000000001000000000000000001E00080000000000000000000000000000000000000000000000000000000000000000000000000018000900000000000000000 00000000000000000000000180000000000000000000000000010000000000000000001E0100000000000000000000000000000000000000000000000000000000000000000000000000008000900000000000000000000000000000000000000002000000000000000000000000000100000000000000000001E20000000000000000000000000000000000000000000000000000000000000000000000000000800060000000000000000000000000000000000000000C0000000000000000000000000001000000 000000000000001E0000000000000000000000000000000000000000000000000000000000000000000000000000400020000000000000000000000000000000000000003000000000000000000000000000010000000000000000000005C00000000000000000000000000000000000000000000000000000000000000000000000000040002000000000000000000000000000000000000040C0000000000000000000000000000100000000000000000000083C0000000000000000000000000000000000000000 000000000000000000000000000000000020002000000000000000000000000000000000000021000000000000000000000000000001000000000000000000000803C0000000000000000000000000000000000000000000000000000000000000000000000000100020000000000000000000000000000000000000160000000000000000000000000000010000000000000000000000003C000000000000000000000000000000000000000000000000000000000000000000000000100020000000000000000000 0000000000000000001C00000000000000000000000000000100000000000000000000000003C0000000000000000000000000000000000000000000000000000000000000000000000008004000000000000000000000000000000000000022000000000000000000000000000001000000000000000000000000003C0000000000000000000000000000000000000000000000000000000000000000000000080040000000000000000000000000000000000000C180000000000000000000000000000100000000 000000001C01C0000003C0080000000000000000000000000000000000000000000000000000000000000000000400400000000000000000000000000000000000030000000000000000000000000000000100000000000000002202200000003C1000000000000000000000000000000000000000000000000000000000000000000002004000000000000000000000000000000000000C00000000000000000000000000000001000000000000000022022000000003E00000000000000000000000000000000000 0000000000000000000000000000000002004000000000000000000000000000000000001000000000000000000000000000000001000000000000000FA201C0000000007C0000000000000000000000000000000000000000000000000000000000000000000100400000000000000000000000000000000000600070010000000000000000000000000100000000000000002202200000000083C0000000000000000000000000000000000000000000000000000000000000000001004000000000000000000000 000000000000018000880300000000000000000000000001000000000000000022022000000000803C00000000000000000000000000000000000000000000000000000000000000000080400000000000000000000000000000000002000088050000000000000000000000000100000000000000001C21C0000000000003C000000000000000000000000000000000000000000000000000000000000000004080000000000000000000000000000000000C00008809000000000000000000000000010000000000 000000000000000000000000380000000000000000000000000000000000000000000000000000000000000000408000000000000000000000000000000000300000880F800000000000000000000000010000000000000000000000000000000000078000000000000000000000000000000000000000000000000000000000000000208000000000000000000000000000000000C0000088010000000000000000000000000100000000000000000000000001C01C00000078004000000000000000000000000000 00000000000000000000000000000000208000000000000000000000000000000001000000708100000000000000000000000001000000000000000000000000022020000000078080000000000000000000000000000000000000000000000000000000000010800000000000000000000000000000000600000000000000000000000000000000000100000000000000000000000002203C000000007900000000000000000000000000000000000000000000000000000000000008800000000000000000000000 0000000018000000000000000000000000000000000001000000000000000000000000FA2022000000000780000000000000000000000000000000000000000000000000000000000008800000000000000000000000000000002000000000000000000000000000000000000100000000000000000000000002202200000000027800000000000000000000000000000000000000000000000000000000000500000000000000000000000000000000C0000000000000000000000000000000000001000000000000 000000000000022022000000000407800000000000000000000000000000000000000000000000000000000005000000000000000000000000000000030000000000000000000000000000000000000100000000000000000000000001C21C0000000004007800000000000000000000000000000000000000000000000000000000030000000000000000000000000000000C000000000000000000000000000000000000010000000000000000000000000000000000000000000780000000000000000000000000 000000000000000000000000000000010000000000000000000000000000001000000000000000000000000000000000000001000000000000000000000000000000000000000000007800000000000000000000000000000000000000000000000000000001000000000000000000000000000000600000000000000000000000000000000000000100000000000000000000000000000000000000000000078002000000000000000000000000000000000000000000000000000000000000000000000000000000 0001800000000000000000000000000000000000000100000000000000000000000000000000000E0020000000780400000000000000000000000000000000000000000000000000000000000000000000000000000000060000000000000000000000000000000000000001000000000000000000000000000000000011006000000007080000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000000000000000000000000100000000000000000000000000000000001100A000000000F000000000 0000000000000000000000000000000000000000000000000000000000000000000000103000000000000000000000000000000000000000010000000000000000000000000000000007D10120000000002F0000000000000000000000000000000000000000000000000000000000000000000000000000000CC0000000000000000000000000000000000000000100000000000000000000000000000000001101F00000000040F00000000000000000000000000000000000000000000000000000000000000000 00000000000003000000000000000000000000000000000000000001000000000000000000000000000000000011002000000000400F00000000000000000000000000000000000000000000000000000000000000000000000000000780000000000000000000000000000000000000000100000000000000000000000000000000000E1020000000000000F0000000000000000000000000000000000000000000000000000000000000000000000000001860000000000000000000000000000000000000000100 000000000000000000000000000000000000000000000000000F0000000000000000000000000000000000000000000000000000000000000000000000000060000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000F00000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000000000000000000000000000100000000000000000000000000000000000000000000E00E0000000F0020 000000000000000000000000000000000000000000000000000000000000000000030000000000000000000000000000000000000000000100000000000000000000000000000000000000000001101100000000F0400000000000000000000000000000000000000000000000000000000000000000000C001C01C0000000000000000000000000000000000001000000000000000000000000000000000000000000011001000000000F800000000000000000000000000000000000000000000000000000000000 0000000010002202000000000000000000000000000000000000010000000000000000000000000000000000000000007D10020000000000F000000000000000000000000000000000000000000000000000000000000000000060002203C00000E000000000000000000000000000000100000000000000000000000000000000000000000001100400000000010F00000000000000000000000000000000000000000000000000000000000000000180002202200001100000000000000000000000000000010000 00000000000000000000000000000000000000011008000000000200E00000000000000000000000000000000000000000000000000000000000000006000022022000010000000000000000000000000000000100000000000000000000000000000000000000000000E11F0000000002001E0000000000000000000000000000000000000000000000000000000000000008000022022000010000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000001 E00000000000000000000000000000000000000000000000000000000000003000001C21C00000F0000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000001E000000000000000000000000000000000000000000000000000000000000C000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000001E0010000000000000000000000000000000000000000000000000000 000300000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000700000001E0200000000000000000000000000000000000000000000000000000004000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000008800000001E400000000000000000000000000000000000000000000000000000018000000000000000000000000000000000000000000000001000000 0000000000000000000000000000000000000000000000000088000000001E0000000000000000000000000000000000000000000000000000006000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000880000000009E00000000000000000000000000000000000000000000000000000800000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000088000000 00101E0000000000000000000000000000000000000000000000000003000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000088000000001001E00000000000000000000000000000000000000000000000000C0000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000700000000000001E00000000000000000000000000000000000000000000000030 00000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000001E0000000000000000000000000000000000000000000000040000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000001C0010000000000000000000000000000000000000000001800000000000000000000000000000000000000000000000000100000000 000000000000000000000000000000000000000000000000000000380380000003C0200000000000000000000000000000000000000000060000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000004404400000003C400000000000000000000000000000000000000004080000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000004400 4000000003C000000000000000000000000000000000000000033000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000044008000000000BC0000000000000000000000000000000000000000C00000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000004401000000000103C000000000000000000000000000000000000003600000 0000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000044020000000001003C00000000000000000000000000000000000004180000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000003847C0000000000003C00000000000000000000000000000000000180000000000000000000000000000000000000000000000000000010000000000 00000000000000000000000000000000000000000000000000000000000000000000003C0000000000000000000000000000000000600000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000003C0000000000000000000000000000000018000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000F00000000000 000380080000003C008000000000000000000000000000020007007000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000A800000000000004401800000003C100000000000000000000000000000C0008808800000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000A8000000000000044028000000003E0000000000000000000000000000300008808800 000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000A800000000000004404800000000038000000000000000000000000000400008807000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000A800000000000004407C000000000478000000000000000000000000018000088088000000000000000000000000000000000000000000000001000000000000 000000000000000000000000000000000000000000000000000000000004400800000000080780000000000000000000000006000008808800000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000384080000000008007800000000000000000000001800000708700000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000 0000000000000000000780000000000000000000002000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007800000000000000000000C0000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007800800000000000000030000000000000000 00000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000001C01C0000000781000000000000000040000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000022020000000007A000000000000000180000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000 00000000000000000000002203C000000000780000000000000060000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000002202200000000047800000000000018000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000220220000000008078000000000002000000 000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000022022000000000800780000000000C00000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000001C21C00000000000007000000000300000000000000000000000000000000000000000000000000000000000000100 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000F00000000C0000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000F00001010000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000001C01C0000000F0040860000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002202200000000F0805800000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000022022000000000F00300000000000 000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002201C0000000002F0C80000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002202200000000040F0600000000000000000000000000000000000000000000000000000000000000010000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000022022000000000400000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001C21C00000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000004000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000200000C00000000000 000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000060000040000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002000004000000000000000000000000000000000000000000000000000000000000001000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000200000400000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000020000040000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000002000004000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000200000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000001%ADOeod :j gR gS 125 204 350 203 rC -1000 -1000 :M f0_12 sf ( )S -996 -1000 :M f1_12 sf ( )S -993 -1000 :M f2_12 sf ( )S -989 -1000 :M f10_12 sf ( )S -981 -1000 :M f11_12 sf ( )S -972 -1000 :M f12_12 sf ( )S -960 -1000 :M f14_12 sf ( )S gR gS 0 0 583 768 rC 0 0 :M initclip TeXdict begin do-bop 0 10 1200 1000 div mul /CMBX10 findfont fdef 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 6.31 y 8.71 (The)s 32.366 (Hessian)s 75.155 (is)s 86.211 (negativ)s 124.211 (e)s 132.534 (in)s 145.523 (the)s 165.179 (region)s 10 f 200.202 (\301)s 12 f 207.997 (\241)s 10 f 217.976 (m)s 2 f 1.955 y 228.512 (2)s 10 f 6.31 y 237.229 (\076)s 1 f 249.895 (\0502)s 10 f 260.562 (\257)s 1 f 267.983 (\051)s 14 f 1.955 y 272.65 (\241)s 2 f 280.15 (1)s 1 f 6.31 y 285.533 (.)s 293.863 (Hence)s 10 f 328.519 (f)s 1 f 335.685 (,)s 342.21 (the)s 361.866 (free)s 383.889 (energy)s 421.245 (at)s 10 f 434.901 (\260)s 1 f 445.114 (=)s 457.78 (0)s 23.11 y -5.69 (de\257ned)s 35.303 (in)s 48.963 (\0502.4\051)s 77.29 (as)s 91.683 (the)s 112.01 (con)s 129.677 (v)s 135.677 (ex)s 151.003 (en)s 162.67 (v)s 168.67 (elop)s 190.337 (e)s 199.33 (of)s 10 f 212.657 (f)s 2 f 18.755 y 219.823 (0)s 1 f 23.11 y 225.207 (,)s 232.268 (has)s 253.328 (some)s 283.055 (\260)s 289.721 (at)s 304.048 (parts)s 334.475 (for)s 10 f 352.501 (\257)s 363.255 (\076)s 2 f 18.385 y 377.362 (1)s 4.783 .48 377.362 20.35 r 27.248 y 377.362 (2)s 1 f 23.11 y 383.585 (,)s 390.647 (corresp)s 428.447 (onding)s 39.91 y -5.69 (to)s 10.225 (regions)s 52.24 (in)s 10 f 67.488 (D)s 1 f 83.17 (=)s 12 f 97.918 (f)s 10 f 103.918 (m;)s 119.787 (\301)s 1 f 132.351 (:)s 10 f 141.098 (\301)s 12 f 153.662 (2)s 1 f 167.076 ([0)s 10 f 176.409 (;)s 1 f 181.742 (1])s 10 f 191.076 (;)s 196.409 (m)s 12 f 212.359 (\267)s 10 f 227.106 (\301)s 12 f 234.256 (g)s 1 f 245.505 (suc)s 261.905 (h)s 273.82 (that)s 301.068 (the)s 322.983 (v)s 328.983 (ectorial)s 372.932 (function)s 10 f 421.18 (h)s 6.914 .48 421.18 41.83 r 1 f 39.91 y 428.094 (\050)s 10 f 432.761 (m;)s 448.63 (\301)s 1 f 455.78 (\051,)s 10 f 56.71 y -5.69 (h)s 6.914 .48 -5.69 58.63 r 1 f 56.71 y 4.829 (:=)s 21.102 (\050)s 10 f 25.768 (h)s 2 f 58.51 y 32.682 (1)s 10 f 56.71 y 38.066 (;)s 43.399 (h)s 2 f 58.51 y 50.313 (2)s 1 f 56.71 y 55.696 (\051)s 64.526 (cannot)s 104.023 (b)s 111.023 (e)s 120.52 (in)s 130.187 (v)s 136.187 (erted.)s 172.044 (W)s 183.377 (e)s 192.874 (call)s 215.037 (this)s 238.601 (region)s 274.798 (in)s 10 f 288.961 (D)s 1 f 303.393 (forbidden)s 357.256 (region)s 393.453 (and)s 416.95 (denote)s 455.78 (it)s 73.51 y -5.69 (b)s .643 (y)s 10 f 9.743 (F)s 1 f 19.127 (.)s 27.382 (A)s 39.148 (p)s 46.148 (oin)s 61.815 (t)s 69.248 (\050)s 76.183 (\271)s 10 f 73.915 (m)s 84.451 (;)s 1 f 70.343 y 91.359 (\271)s 10 f 73.51 y 89.784 (\301)s 1 f 96.934 (\051)s 12 f 104.934 (2)s 10 f 116.268 (F)s 1 f 128.418 (has)s 148.585 (the)s 168.018 (prop)s 192.385 (ert)s 206.752 (y)s 215.852 (that)s 240.619 (the)s 260.052 (equations)s 10 f 312.552 (m)s 1 f 323.089 (\050)s 10 f 327.755 (h)s 2 f 75.31 y 334.669 (1)s 10 f 73.51 y 340.053 (;)s 345.386 (h)s 2 f 75.31 y 352.3 (2)s 1 f 73.51 y 357.683 (\051)s 365.683 (=)s 380.618 (\271)s 10 f 378.35 (m)s 388.886 (;)s 394.219 (\301)s 1 f 401.369 (\050)s 10 f 406.036 (h)s 2 f 75.31 y 412.95 (1)s 10 f 73.51 y 418.333 (;)s 423.666 (h)s 2 f 75.31 y 430.58 (2)s 1 f 73.51 y 435.964 (\051)s 443.964 (=)s 70.343 y 458.205 (\271)s 10 f 73.51 y 456.63 (\301)s 1 f 90.31 y -5.69 (cannot)s 33.643 (b)s 40.643 (e)s 49.977 (solv)s 70.043 (ed)s 86.043 (for)s 104.41 (\050)s 10 f 109.077 (h)s 2 f 92.11 y 115.991 (1)s 10 f 90.31 y 121.374 (;)s 126.707 (h)s 2 f 92.11 y 133.621 (2)s 1 f 90.31 y 139.004 (\051.)s 1 f 355.15 y 8.71 (Fig.3)s 10 f 43.21 (f)s 2 f 350.795 y 50.377 (0)s 1 f 355.15 y 55.76 (\050)s 10 f 60.427 (m;)s 76.296 (\301)s 1 f 83.446 (\051)s 92.113 (at)s 10 f 106.779 (\257)s 1 f 117.534 (=)s 130.2 (2)s 389.141 y 8.71 (Remark.)s 406.061 y 8.71 (This)s 36.59 (mo)s 52.924 (del)s 72.738 (can)s 95.218 (also)s 119.766 (b)s 126.766 (e)s 136.58 (lo)s 146.246 (ok)s 158.246 (ed)s 174.727 (at)s 189.874 (as)s 205.088 (a)s 215.569 (lattice)s 252.716 (gas)s 273.93 (of)s 288.077 (t)s 292.411 (w)s 300.744 (o)s 311.224 (sp)s 322.958 (ecies)s 351.505 (of)s 365.652 (particles)s 414.233 (suc)s 430.633 (h)s 441.78 (that)s 422.861 y -5.69 (in)s 8.214 (eac)s 24.547 (h)s 35.118 (site)s 57.089 (of)s 70.659 (the)s 91.23 (lattice)s 127.801 (there)s 158.405 (is)s 170.376 (at)s 184.946 (most)s 214.25 (one)s 236.154 (particle)s 279.425 (for)s 297.696 (eac)s 314.029 (h)s 324.6 (sp)s 336.333 (ecies.)s 369.035 (A)s 381.939 (w)s 390.272 (a)s 395.939 (y)s 406.176 (of)s 419.747 (realizing)s 439.661 y -5.69 (the)s 16.821 (corresp)s 54.621 (ondence)s 102.465 (is)s 116.377 (for)s 136.588 (example)s 185.432 (the)s 207.943 (follo)s 229.943 (wing.)s 268.81 (Call)s 10 f 295.988 (\264)s 11 f 441.461 y 301.946 (b)s 1 f 439.661 y 306.766 (\050)s 10 f 311.433 (i)s 1 f 315.567 (\051)s 326.641 (=)s 342.382 (1)s 10 f 348.382 (;)s 1 f 353.715 (0)s 10 f 359.715 (;)s 377.048 (\264)s 11 f 441.461 y 383.007 (r)s 1 f 439.661 y 388.32 (\050)s 10 f 392.987 (i)s 1 f 397.121 (\051)s 408.195 (=)s 423.936 (1)s 10 f 429.936 (;)s 1 f 435.269 (0)s 447.114 (the)s 456.461 y -5.69 (o)s .643 (ccupation)s 54.482 (n)s 60.815 (um)s 77.149 (b)s 84.149 (er)s 97.354 (in)s 110.526 (the)s 130.364 (site)s 10 f 151.603 (i)s 1 f 158.909 (of)s 171.747 (the)s 191.586 (particles)s 238.858 (of)s 251.697 (color)s 280.235 (blue)s 305.407 (and)s 327.912 (red)s 347.784 (resp)s 369.551 (ectiv)s 394.218 (ely)s 408.218 (.)s 416.608 (Then)s 447.114 (the)s 473.261 y -5.69 (relation)s 10 f 37.866 (\276)s 1 f 45.153 (\050)s 10 f 49.82 (i)s 1 f 53.954 (\051)s 61.954 (=)s 10 f 74.621 (\264)s 11 f 475.061 y 80.579 (b)s 1 f 473.261 y 85.399 (\050)s 10 f 90.066 (i)s 1 f 94.2 (\051)s 12 f 100.579 (\241)s 10 f 111.624 (\264)s 11 f 475.061 y 117.582 (r)s 1 f 473.261 y 122.896 (\050)s 10 f 127.563 (i)s 1 f 131.697 (\051)s 139.886 (determine)s 195.442 (a)s 204.965 (lattice)s 241.154 (gas)s 261.411 (of)s 274.6 (particles)s 322.223 (blue)s 347.745 (and)s 370.601 (red)s 390.824 (with)s 417.68 (repulsiv)s 458.447 (e)s 490.061 y -5.69 (in)s 3.976 (teraction)s 53.796 (b)s 60.796 (et)s 70.463 (w)s 78.796 (een)s 99.249 (particles)s 146.469 (of)s 159.256 (the)s 179.042 (same)s 208.228 (color)s 236.715 (and)s 259.168 (attractiv)s 304.535 (e)s 312.988 (in)s 322.654 (teraction)s 372.474 (b)s 379.474 (et)s 389.141 (w)s 397.474 (een)s 417.927 (the)s 437.714 (same)s 506.861 y -5.69 (colors.)s 32.879 (Under)s 68.655 (this)s 91.463 (corresp)s 129.263 (ondence)s 174.672 (a)s 184.081 (con\257guration)s 256.189 (of)s 269.265 (particles)s 10 f 316.773 (\264)s 1 f 326.571 (with)s 353.313 (t)s 357.646 (w)s 365.979 (o)s 375.388 (particles)s 422.896 (in)s 436.305 (a)s 445.714 (site)s 10 f 523.661 y -5.69 (i)s 1 f 2.444 (is)s 14.511 (iden)s 36.177 (tical)s 62.844 (to)s 77.511 (a)s 87.511 (con\257guration)s 10 f 160.211 (\263)s 1 f 170.346 (with)s 197.68 (no)s 214.346 (particles)s 262.446 (in)s 10 f 276.447 (i)s 1 f 280.581 (.)s 540.581 y 8.71 (Finally)s 49.961 (w)s 58.294 (e)s 68.045 (note)s 95.129 (that)s 121.546 (the)s 142.63 (relation)s 10 f 187.081 (\276)s 1 f 194.369 (\050)s 10 f 199.036 (i)s 1 f 203.17 (\051)s 211.865 (=)s 10 f 225.228 (\264)s 1 f 231.617 (\050)s 10 f 236.283 (i)s 1 f 240.417 (\051)s 12 f 248.029 (\241)s 1 f 260.307 (1)s 270.725 (links)s 299.542 (the)s 320.626 (mo)s 336.96 (del)s 356.71 (to)s 371.794 (a)s 382.212 (lattice)s 419.296 (gas)s 440.447 (with)s 557.381 y -5.69 (one)s 16.31 (sp)s 28.043 (ecies)s 56.11 (of)s 69.777 (particles)s 117.877 (with)s 145.21 (at)s 159.877 (most)s 189.277 (t)s 193.61 (w)s 201.943 (o)s 211.943 (particles)s 260.043 (p)s 267.044 (er)s 281.077 (site.)s 0 f 602.754 y -5.69 (3.)s 11.176 (Glaub)s 48.284 (er)s 64.893 (and)s 91.534 (Ka)s 108.676 (w)s 118.259 (asaki)s 152.835 (dynamics.)s 1 f 626.656 y 8.71 (W)s 20.043 (e)s 31.207 (consider)s 79.805 (t)s 84.139 (w)s 92.472 (o)s 104.303 (kinds)s 137.867 (of)s 153.365 (dynamics)s 208.263 (for)s 228.46 (the)s 250.958 (spin)s 278.189 (system)s 319.82 (in)s 329.487 (tro)s 345.187 (duced)s 381.685 (in)s 397.516 (the)s 420.013 (previous)s 643.456 y -5.69 (Section:)s 42.296 (the)s 63.622 (Glaub)s 96.039 (er)s 110.731 (and)s 134.724 (Ka)s 149.724 (w)s 158.058 (asaki)s 189.117 (dynamics,)s 246.342 (the)s 267.668 (latter)s 301.027 (conserving)s 360.787 (b)s 367.787 (oth)s 389.78 (magnetization)s 660.256 y -5.69 (and)s 17.643 (concen)s 52.643 (tration.)s 677.176 y 8.71 (F)s 15.543 (or)s 30.544 (\050)s 10 f 35.211 (i;)s 44.678 (j)s 1 f 50.307 (\051)s 12 f 58.808 (2)s 10 f 70.643 (Z)s 73.694 (Z)s 11 f 671.943 y 84.743 (d)s 12 f 677.176 y 93.206 (\243)s 10 f 105.407 (Z)s 108.457 (Z)s 11 f 671.943 y 119.507 (d)s 1 f 677.176 y 125.102 (,)s 10 f 132.812 (k)s 12 f 143.272 (2)s 10 f 155.107 (Z)s 158.157 (Z)s 11 f 671.943 y 169.207 (d)s 1 f 677.176 y 174.802 (,)s 10 f 182.512 (\276)s 12 f 193.634 (2)s 1 f 205.469 (\255)s 218.437 (and)s 242.071 (an)s 254.405 (y)s 265.039 (cylinder)s 311.04 (function)s 10 f 358.341 (F)s 1 f 371.559 (:)s 378.727 (\255)s 12 f 391.229 (\241)s 398.562 (!)s 1 f 414.397 (I)s 416.571 (R)s 425.404 (,)s 433.114 (de\257ne)s 705.976 y 223.045 (10)s do-end end endp %%Page: 11 11 %%BeginPageSetup initializepage (Raffaele Esposito; page: 11 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f1_12 sf ( )S -997 -1000 :M f2_12 sf ( )S -993 -1000 :M f10_12 sf ( )S -985 -1000 :M f11_12 sf ( )S -976 -1000 :M f12_12 sf ( )S -964 -1000 :M f13_12 sf ( )S -954 -1000 :M f14_12 sf ( )S -941 -1000 :M f15_12 sf ( )S -930 -1000 :M f16_12 sf ( )S -925 -1000 :M f18_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 16 5 1200 1000 div mul /CMR5 findfont fdef 18 5 1200 1000 div mul /CMSY5 findfont fdef fonts 19 get /CharDefs get dup 90[3.321 0 -1 3 4 3 5 0 1 {<20E0A0E080>}]put pop fonts 20 get /CharDefs get dup 90[6.642 1 0 7 7 6 7 -1 0 {}]put pop fonts 21 get /CharDefs get dup 90[4.649 0 -1 5 6 5 7 0 1 {<08F86050307880>}]put pop 58 60 translate 72 72.27 div dup scale 13 f -3.41 y -5.69 (\241)s 12 f 6.31 y -.19 (r)s 11 f 8.11 y 9.81 (i;j)s 10 f 6.31 y 21.111 (F)s 13 f -3.41 y 30.495 (\242)s 1 f 6.31 y 35.995 (\050)s 10 f 40.661 (\276)s 1 f 47.949 (\051,)s 13 f -3.41 y 59.949 (\241)s 12 f 6.31 y 65.449 (r)s 2 f 1.176 y 75.449 (+)s 11 f 9.93 y 75.449 (k)s 10 f 6.31 y 83.416 (F)s 13 f -3.41 y 92.799 (\242)s 1 f 6.31 y 98.299 (\050)s 10 f 102.966 (\276)s 1 f 110.253 (\051)s 118.92 (and)s 13 f -3.41 y 142.253 (\241)s 12 f 6.31 y 147.753 (r)s 14 f 1.176 y 157.753 (\241)s 11 f 9.93 y 157.753 (k)s 10 f 6.31 y 165.853 (F)s 13 f -3.41 y 175.237 (\242)s 1 f 6.31 y 180.737 (\050)s 10 f 185.403 (\276)s 1 f 192.691 (\051)s 201.358 (b)s 207.691 (y)s 13 f 29.044 y 147.094 (\241)s 12 f 38.764 y 152.594 (r)s 11 f 40.564 y 162.594 (i;j)s 10 f 38.764 y 173.896 (F)s 13 f 29.044 y 183.279 (\242)s 1 f 38.764 y 188.779 (\050)s 10 f 193.446 (\276)s 1 f 200.733 (\051)s 208.733 (=)s 10 f 221.4 (F)s 1 f 230.783 (\050)s 10 f 235.45 (\276)s 11 f 33.81 y 242.737 (i;j)s 1 f 38.764 y 254.039 (\051)s 12 f 261.372 (\241)s 10 f 273.372 (F)s 1 f 282.755 (\050)s 10 f 287.422 (\276)s 1 f 294.71 (\051)s 10 f 302.71 (;)s 13 f 49.444 y 150.296 (\241)s 12 f 59.164 y 155.796 (r)s 14 f 54.031 y 165.796 (\247)s 11 f 62.784 y 165.796 (k)s 10 f 59.164 y 173.896 (F)s 13 f 49.444 y 183.279 (\242)s 1 f 59.164 y 188.779 (\050)s 10 f 193.446 (\276)s 1 f 200.733 (\051)s 208.733 (=)s 10 f 221.4 (F)s 1 f 230.783 (\050)s 10 f 235.45 (\276)s 14 f 54.21 y 242.737 (\247)s 11 f 250.237 (;k)s 1 f 59.164 y 258.992 (\051)s 12 f 266.325 (\241)s 10 f 278.325 (F)s 1 f 287.708 (\050)s 10 f 292.375 (\276)s 1 f 299.662 (\051)s 10 f 307.662 (;)s 1 f 91.019 y -5.69 (where)s 10 f 29.01 (\276)s 11 f 86.664 y 36.297 (i;j)s 1 f 91.019 y 51.599 (is)s 63.665 (a)s 73.665 (con\257guration)s 146.366 (obtained)s 195.699 (from)s 10 f 224.066 (\276)s 1 f 235.353 (b)s 241.687 (y)s 252.02 (in)s 261.687 (terc)s 281.387 (hanging)s 326.72 (the)s 347.387 (v)s 353.053 (alue)s 378.387 (at)s 10 f 393.054 (i)s 1 f 401.188 (and)s 10 f 424.521 (j)s 1 f 434.15 (:)s 13 f 125.974 y 149.541 (\241)s 10 f 135.694 y 155.041 (\276)s 11 f 130.739 y 162.329 (i;j)s 13 f 125.974 y 173.63 (\242)s 1 f 135.694 y 181.13 (\050)s 10 f 185.797 (l)s 1 f 189.614 (\051)s 197.613 (=)s 13 f 111.094 y 210.28 (8)s 121.894 y 210.28 (\074)s 143.494 y 210.28 (:)s 10 f 121.294 y 222.947 (\276)s 1 f 230.234 (\050)s 10 f 234.901 (l)s 1 f 238.718 (\051)s 257.196 (if)s 10 f 268.196 (l)s 12 f 275.346 (6)s 1 f 275.346 (=)s 10 f 288.013 (i;)s 297.48 (j)s 135.694 y 222.947 (\276)s 1 f 230.234 (\050)s 10 f 234.901 (j)s 1 f 240.529 (\051)s 257.196 (if)s 10 f 268.196 (l)s 1 f 275.346 (=)s 10 f 288.013 (i)s 150.094 y 222.947 (\276)s 1 f 230.234 (\050)s 10 f 234.901 (i)s 1 f 239.035 (\051)s 257.196 (if)s 10 f 268.196 (l)s 1 f 275.346 (=)s 10 f 288.013 (j)s 1 f 297.641 (,)s 182.223 y -5.69 (and)s 10 f 17.643 (\276)s 14 f 177.869 y 24.931 (\247)s 11 f 32.431 (;k)s 1 f 182.223 y 45.185 (is)s 57.252 (de\257ned)s 98.585 (as)s 13 f 207.645 y 119.136 (\241)s 10 f 217.365 y 124.636 (\276)s 14 f 212.41 y 131.923 (\247)s 11 f 139.423 (;k)s 13 f 207.645 y 148.177 (\242)s 1 f 217.365 y 155.677 (\050)s 10 f 160.344 (l)s 1 f 164.161 (\051)s 172.161 (=)s 13 f 200.445 y 184.827 (\275)s 10 f 210.165 y 195.827 (\276)s 1 f 203.115 (\050)s 10 f 207.781 (l)s 1 f 211.598 (\051)s 287.406 (if)s 10 f 298.406 (l)s 12 f 305.556 (6)s 1 f 305.556 (=)s 10 f 318.223 (k)s 224.565 y 195.827 (\276)s 1 f 203.115 (\050)s 10 f 207.781 (k)s 1 f 214.406 (\051)s 12 f 221.74 (\247)s 1 f 233.74 (1)s 243.073 (mo)s 259.406 (d)s 269.406 (3)s 287.406 (if)s 10 f 298.406 (l)s 1 f 305.556 (=)s 10 f 318.223 (k)s 1 f 328.848 (.)s 254.96 y 8.71 (The)s 34.649 (Ka)s 49.649 (w)s 57.983 (asaki)s 89.655 (dynamics)s 143.995 (with)s 172.601 (parameter)s 10 f 231.274 (\257)s 12 f 244.149 (\270)s 1 f 258.937 (0)s 270.21 (is)s 283.549 (the)s 305.489 (unique)s 345.762 (Mark)s 373.462 (o)s 379.128 (v)s 390.735 (pro)s 408.435 (cess)s 433.841 (on)s 451.78 (\255,)s 271.76 y -5.69 (whose)s 29.71 (pregenerator)s 99.81 (I)s 101.983 (L)s 11 f 266.527 y 109.483 (K)s 117.618 (;\257)s 274.727 y 109.483 (\260)s 1 f 271.76 y 130.941 (acts)s 155.675 (on)s 172.341 (the)s 193.008 (cylinder)s 238.708 (functions)s 290.442 (as)s 13 f 298.181 y 105.629 (\241)s 1 f 307.901 y 111.129 (I)s 113.302 (L)s 11 f 302.668 y 120.802 (K)s 128.937 (;\257)s 310.868 y 120.802 (\260)s 10 f 307.901 y 138.26 (f)s 13 f 298.181 y 145.427 (\242)s 1 f 307.901 y 150.927 (\050)s 10 f 155.594 (\276)s 1 f 162.881 (\051)s 170.881 (=)s 13 f 296.501 y 190.988 (X)s 15 f 322.435 y 187.385 (i;j)s 18 f 197.22 (2)s 19 f 202.887 (Z)s 15 f 320.668 y 206.886 (d)s 18 f 329.541 y 184.988 (j)s 15 f 187.738 (i)s 18 f 190.939 (\241)s 15 f 197.439 (j)s 18 f 201.322 (j)s 16 f 204.072 (=1)s 10 f 307.901 y 217.762 (C)s 11 f 302.947 y 227.197 (K)s 235.332 (;\257)s 310.868 y 226.339 (\260)s 1 f 307.901 y 244.655 (\050)s 10 f 249.322 (i;)s 258.789 (j)s 1 f 264.418 (;)s 10 f 269.751 (\276)s 1 f 277.039 (\051)s 13 f 294.581 y 281.706 (h)s 298.181 y 287.372 (\241)s 12 f 307.901 y 292.872 (r)s 11 f 309.701 y 302.872 (i;j)s 10 f 307.901 y 314.174 (f)s 13 f 298.181 y 321.34 (\242)s 1 f 307.901 y 326.84 (\050)s 10 f 331.507 (\276)s 1 f 338.795 (\051)s 13 f 294.581 y 343.461 (i)s 10 f 307.901 y 349.128 (:)s 1 f 361.049 y -5.69 (Here)s 23.576 (and)s 47.808 (in)s 62.707 (the)s 84.273 (follo)s 106.273 (wing)s 12 f 135.839 (j)s 10 f 139.172 (:)s 12 f 142.506 (j)s 1 f 150.738 (stands)s 189.104 (for)s 208.37 (the)s 229.936 (max)s 257.168 (norm)s 289.434 (of)s 304 (I)s 306.173 (R)s 11 f 355.816 y 315.006 (d)s 1 f 361.049 y 320.602 (.)s 331.966 (F)s 338.799 (or)s 354.398 (\050)s 10 f 359.065 (i;)s 368.533 (j)s 1 f 374.161 (\051)s 12 f 383.66 (2)s 20 f 396.491 (Z)s 11 f 356.695 y 404.491 (d)s 12 f 361.049 y 413.353 (\243)s 20 f 425.952 (Z)s 11 f 356.695 y 433.952 (d)s 1 f 361.049 y 444.447 (and)s 10 f 377.849 y -5.69 (\276)s 12 f 4.931 (2)s 1 f 16.264 (\255,)s 32.264 (the)s 52.931 (rate)s 10 f 77.631 (C)s 11 f 373.495 y 87.066 (K)s 95.201 (;\257)s 380.816 y 86.207 (\260)s 1 f 377.849 y 104.524 (\050)s 10 f 109.19 (i;)s 118.658 (j)s 1 f 124.286 (;)s 10 f 129.62 (\276)s 1 f 136.907 (\051)s 145.574 (is)s 157.64 (giv)s 172.974 (en)s 188.974 (b)s 195.307 (y)s 10 f 407.591 y 139.836 (C)s 11 f 402.636 y 149.271 (K)s 157.406 (;\257)s 410.557 y 148.412 (\260)s 1 f 407.591 y 166.729 (\050)s 10 f 171.395 (i;)s 180.863 (j)s 1 f 186.491 (;)s 10 f 191.825 (\276)s 1 f 199.112 (\051)s 207.112 (=)s 219.779 (\251)s 13 f 397.871 y 228.445 (\251)s 10 f 407.591 y 235.445 (\257)s 13 f 397.871 y 242.866 (\241)s 12 f 407.591 y 248.366 (r)s 11 f 409.391 y 258.366 (i;j)s 10 f 407.591 y 269.668 (H)s 11 f 409.391 y 279.643 (\260)s 1 f 407.591 y 285.8 (\050)s 10 f 290.467 (\276)s 1 f 297.754 (\051)s 13 f 397.871 y 302.421 (\242)s 307.921 (\252)s 10 f 407.591 y 314.921 (:)s 1 f 437.332 y -5.69 (Here)s 22.792 (\251)s 34.985 (:)s 41.845 (I)s 44.018 (R)s 12 f 56.378 (\241)s 63.711 (!)s 1 f 79.237 (I)s 81.41 (R)s 2 f 439.132 y 90.244 (+)s 1 f 437.332 y 102.326 (is)s 114.509 (a)s 124.624 (con)s 142.291 (tin)s 156.625 (uously)s 194.474 (di\256eren)s 233.174 (tiable)s 266.623 (function)s 313.739 (in)s 327.855 (a)s 337.97 (neigh)s 365.637 (b)s 372.637 (orho)s 396.337 (o)s 402.671 (d)s 413.453 (of)s 427.235 (0,)s 440.714 (suc)s 457.113 (h)s 454.132 y -5.69 (that)s 20.31 (\251\0500\051)s 47.643 (=)s 60.31 (1)s 70.31 (and)s 93.643 (satis\257es)s 137.843 (detailed)s 183.177 (balance)s 226.51 (condition)s 279.177 (\050cf.)s 301.51 ([GL])s 329.094 (and)s 352.427 ([GLP]\051)s 483.874 y 155.887 (\251\050)s 10 f 169.22 (E)s 1 f 178.77 (\051)s 186.77 (=)s 199.437 (exp)s 13 f 474.154 y 219.77 (\241)s 12 f 483.874 y 227.937 (\241)s 10 f 239.937 (E)s 13 f 474.154 y 249.487 (\242)s 1 f 483.874 y 254.987 (\251)s 13 f 474.154 y 263.653 (\241)s 12 f 483.874 y 271.82 (\241)s 10 f 283.82 (E)s 13 f 474.154 y 293.37 (\242)s 10 f 483.874 y 298.87 (:)s 1 f 439.114 (\0503)s 10 f 449.78 (:)s 1 f 453.114 (1\051)s 513.735 y 8.71 (The)s 33.376 (generator)s 86.777 (of)s 100.443 (the)s 121.11 (Glaub)s 153.527 (er)s 167.56 (ev)s 178.893 (olution)s 219.56 (is)s 231.627 (giv)s 246.96 (en)s 262.96 (b)s 269.294 (y)s 13 f 533.756 y 118.418 (\241)s 1 f 543.477 y 123.918 (I)s 126.092 (L)s 11 f 538.243 y 133.592 (G;\257)s 546.443 y 133.592 (\260)s 10 f 543.477 y 150.386 (f)s 13 f 533.756 y 157.552 (\242)s 1 f 543.477 y 163.052 (\050)s 10 f 167.719 (\276)s 1 f 175.007 (\051)s 183.007 (=)s 13 f 532.076 y 197.256 (X)s 11 f 558.643 y 195.673 (i)s 14 f 199.068 (2)s 21 f 205.535 (Z)s 15 f 556.243 y 211.135 (d)s 10 f 543.477 y 218.173 (C)s 11 f 538.522 y 227.608 (G;)s 14 f 237.929 (\247)s 11 f 546.443 y 226.75 (\260)s 1 f 543.477 y 246.029 (\050)s 10 f 250.696 (i)s 1 f 254.83 (;)s 10 f 260.163 (\276)s 1 f 267.451 (\051)s 13 f 530.156 y 272.118 (h)s 533.756 y 277.784 (\241)s 12 f 543.477 y 283.284 (r)s 14 f 538.343 y 293.284 (\247)s 11 f 546.821 y 293.284 (i)s 10 f 543.477 y 301.384 (f)s 13 f 533.756 y 308.551 (\242)s 1 f 543.477 y 314.051 (\050)s 10 f 318.718 (\276)s 1 f 326.005 (\051)s 13 f 530.156 y 330.672 (i)s 10 f 543.477 y 336.339 (:)s 1 f 588.315 y -5.69 (where)s 29.01 (the)s 49.677 (rates)s 10 f 79.11 (C)s 11 f 583.96 y 88.545 (G;)s 14 f 98.866 (\247)s 11 f 591.282 y 87.687 (\260)s 1 f 588.315 y 106.966 (\050)s 10 f 111.633 (i)s 1 f 115.767 (;)s 10 f 121.1 (\276)s 1 f 128.388 (\051)s 137.054 (are)s 157.088 (de\257ned)s 198.421 (as)s 10 f 626.508 y 132.533 (C)s 11 f 621.553 y 141.968 (G;)s 14 f 152.289 (\247)s 11 f 629.474 y 141.11 (\260)s 1 f 626.508 y 160.389 (\050)s 10 f 165.056 (i)s 1 f 169.19 (;)s 10 f 174.523 (\276)s 1 f 181.811 (\051)s 189.811 (=)s 618.39 y 203.917 (1)s 6 .48 203.917 623.748 r 634.739 y 203.917 (2)s 618.39 y 263.791 (1)s 107.986 .48 212.797 623.748 r 638.988 y 212.797 (1)s 221.464 (+)s 233.464 (exp)s 13 f 625.668 y 253.797 (\263)s 10 f 638.988 y 260.964 (\257)s 13 f 629.268 y 268.385 (\241)s 12 f 638.988 y 273.885 (r)s 14 f 633.854 y 283.885 (\247)s 11 f 642.333 y 283.885 (i)s 10 f 638.988 y 291.985 (H)s 11 f 640.788 y 301.96 (\260)s 13 f 629.268 y 308.117 (\242)s 625.668 y 313.617 (\264)s 10 f 626.508 y 322.224 (:)s 1 f 677.176 y -5.69 (corresp)s 32.11 (onding)s 71.443 (to)s 86.11 (the)s 106.777 (c)s 111.777 (hoice)s 142.443 (\251\050)s 10 f 155.777 (E)s 1 f 165.327 (\051)s 173.327 (=)s 2 f 672.451 y 187.433 (1)s 4.783 .48 187.433 674.416 r 681.314 y 187.433 (2)s 13 f 667.456 y 193.657 (\243)s 1 f 677.176 y 198.657 (1)s 207.323 (+)s 219.323 (exp)s 10 f 239.657 (E)s 13 f 667.456 y 249.207 (\244)s 14 f 669.943 y 254.207 (\241)s 2 f 261.707 (1)s 1 f 677.176 y 267.09 (.)s 705.976 y 223.045 (11)s do-end end endp %%Page: 12 12 %%BeginPageSetup initializepage (Raffaele Esposito; page: 12 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f0_12 sf ( )S -996 -1000 :M f1_12 sf ( )S -993 -1000 :M f2_12 sf ( )S -989 -1000 :M f10_12 sf ( )S -981 -1000 :M f11_12 sf ( )S -972 -1000 :M f12_12 sf ( )S -960 -1000 :M f13_12 sf ( )S -951 -1000 :M f14_12 sf ( )S -937 -1000 :M f15_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 1200 1000 div mul /CMBX10 findfont fdef 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 6.31 y 8.71 (Notice)s 47.368 (that)s 74.361 (the)s 96.019 (quan)s 121.353 (tities)s 13 f -3.41 y 152.411 (\241)s 12 f 6.31 y 157.911 (r)s 11 f 8.11 y 167.911 (i;j)s 10 f 6.31 y 179.213 (H)s 11 f 8.11 y 189.188 (\260)s 13 f -3.41 y 195.345 (\242)s 1 f 6.31 y 205.837 (and)s 13 f -3.41 y 230.162 (\241)s 12 f 6.31 y 235.662 (r)s 14 f 1.176 y 245.662 (\247)s 11 f 9.655 y 245.662 (i)s 10 f 6.31 y 253.762 (H)s 11 f 8.11 y 263.737 (\260)s 13 f -3.41 y 269.895 (\242)s 1 f 6.31 y 280.387 (are)s 301.412 (w)s 309.745 (ell)s 326.737 (de\257ned)s 369.063 (since)s 399.455 (they)s 427.447 (in)s 437.113 (v)s 443.113 (olv)s 458.447 (e)s 23.11 y -5.69 (only)s 20.262 (a)s 29.881 (\257nite)s 60.166 (n)s 66.5 (um)s 82.833 (b)s 89.833 (er)s 103.485 (of)s 116.771 (non)s 139.723 (zero)s 164.708 (di\256erences.)s 227.681 (F)s 234.515 (or)s 248.834 (the)s 269.119 (pro)s 286.819 (of)s 300.105 (of)s 313.39 (the)s 333.676 (existence)s 384.361 (and)s 407.313 (uniqueness)s 39.91 y -5.69 (of)s 7.977 (these)s 38.71 (Mark)s 66.41 (o)s 72.077 (v)s 82.41 (pro)s 100.11 (cesses,)s 137.643 (w)s 145.977 (e)s 155.31 (refer)s 183.043 (to)s 197.71 (Liggett)s 239.21 ([Li].)s 56.83 y 8.71 (In)s 24.324 (the)s 45.604 (case)s 71.618 (of)s 85.899 (Ka)s 100.899 (w)s 109.232 (asaki)s 140.247 (dynamics,)s 197.414 (if)s 10 f 209.028 (\257)s 1 f 220.805 (=)s 234.495 (0,)s 248.596 (the)s 269.877 (ev)s 281.21 (olution)s 322.491 (reduces)s 365.872 (to)s 381.152 (a)s 391.766 (simple)s 429.78 (kno)s 448.447 (wn)s 73.63 y -5.69 (pro)s 12.01 (cess.)s 44.469 (In)s 60.689 (the)s 82.576 (setting)s 123.195 (of)s 138.082 (the)s 159.968 (lattice)s 197.855 (gas)s 219.808 (with)s 248.361 (one)s 271.581 (sp)s 283.314 (ecies)s 312.601 (of)s 327.487 (particles)s 376.807 (this)s 401.427 (dynamics)s 455.714 (is)s 90.43 y -5.69 (a)s 4.641 (generalized)s 67.006 (simple)s 104.737 (exclusion)s 156.802 (pro)s 174.502 (cess)s 198.966 (GSEP)s 235.714 ([KL])s 263.545 (with)s 291.21 (rate)s 316.241 (one,)s 341.988 (and)s 365.653 (w)s 373.986 (e)s 383.651 (shall)s 412.049 (denote)s 451.047 (its)s 107.23 y -5.69 (pregenerator)s 63.536 (simply)s 101.063 (b)s 107.396 (y)s 116.856 (I)s 119.029 (L)s 2 f 101.996 y 126.529 (0)s 1 f 107.23 y 131.912 (.)s 140.288 (It)s 152.414 (di\256ers)s 187.307 (from)s 214.8 (the)s 234.593 (usual)s 265.119 (SEP)s 291.245 (for)s 308.738 (the)s 328.531 (exclusion)s 379.391 (rule)s 402.55 (in)s 412.217 (v)s 418.217 (olv)s 433.55 (ed:)s 453.78 (in)s 124.03 y -5.69 (eac)s 10.643 (h)s 21.249 (p)s 28.249 (oin)s 43.916 (t)s 52.522 (are)s 72.495 (allo)s 90.828 (w)s 99.161 (ed)s 115.101 (at)s 129.707 (most)s 159.046 (t)s 163.379 (w)s 171.713 (o)s 181.652 (particles.)s 234.399 (W)s 245.732 (e)s 255.005 (shall)s 283.011 (see)s 302.35 (in)s 316.289 (Section)s 358.229 (3)s 368.168 (that)s 394.108 (the)s 414.714 (dynamics)s 140.83 y -5.69 (with)s 10 f 22.277 (\257)s 34.087 (\076)s 1 f 47.809 (0)s 58.443 (is)s 71.143 (a)s 81.777 (w)s 90.11 (eak)s 112.41 (p)s 119.41 (erturbation)s 183.444 (of)s 197.744 (this)s 221.778 (simple)s 259.811 (exclusion.)s 318.112 (As)s 336.479 (explained)s 390.78 (in)s 405.413 (the)s 426.713 (remark)s 157.63 y -5.69 (in)s 8.459 (section)s 48.674 (3,)s 62.194 (the)s 83.009 (Ka)s 98.009 (w)s 106.342 (asaki)s 136.891 (dynamics)s 190.107 (can)s 212.256 (also)s 236.471 (b)s 243.471 (e)s 252.954 (in)s 262.62 (terpreted)s 314.836 (as)s 329.718 (the)s 350.534 (motion)s 391.349 (of)s 405.165 (t)s 409.498 (w)s 417.831 (o)s 427.98 (sp)s 439.714 (ecies)s 174.43 y -5.69 (of)s 9.967 (particles,)s 63.888 (mo)s 79.555 (ving)s 107.879 (as)s 124.602 (a)s 136.593 (symmetric)s 197.017 (simple)s 236.407 (exclusion)s 290.131 (pro)s 307.831 (cess)s 333.954 (with)s 363.278 (rate)s 389.969 (one,)s 417.79 (with)s 447.114 (the)s 191.23 y -5.69 (exclusion)s 45.605 (rule)s 10 f 69.201 (\264)s 11 f 193.03 y 75.159 (b)s 1 f 191.23 y 81.77 (+)s 10 f 92.894 (\264)s 11 f 193.03 y 98.853 (r)s 12 f 191.23 y 107.5 (\267)s 1 f 120.166 (1,)s 133.149 (suc)s 149.549 (h)s 159.778 (that)s 185.34 (also)s 208.969 (jumps)s 244.265 (exc)s 260.932 (hanging)s 305.827 (colors)s 339.489 (b)s 346.489 (et)s 356.156 (w)s 364.489 (een)s 385.385 (neigh)s 413.051 (b)s 420.051 (our)s 440.98 (sites)s 208.03 y -5.69 (are)s 14.71 (allo)s 33.043 (w)s 41.377 (ed.)s 63.144 (If)s 75.511 (suc)s 91.911 (h)s 102.944 (jumps)s 139.045 (are)s 159.445 (forbidden)s 213.512 (the)s 234.545 (system)s 274.712 (b)s 281.712 (ecomes)s 322.813 (a)s 333.179 (non)s 356.88 (gradien)s 395.246 (t)s 404.28 (system)s 444.447 (and)s 224.83 y -5.69 (the)s 14.976 (di\256usion)s 63.377 (co)s 75.043 (e\261cien)s 110.71 (t)s 119.377 (in)s 133.377 (this)s 156.777 (case)s 182.177 (is)s 194.243 (di\256eren)s 232.944 (t)s 241.61 (from)s 269.977 (one.\050)s 299.977 ([Q]\051.)s 241.75 y 8.71 (Since)s 40.047 (the)s 60.718 (Ka)s 75.718 (w)s 84.051 (asaki)s 114.455 (dynamics)s 167.526 (conserv)s 206.293 (es)s 220.364 (magnetization)s 298.368 (and)s 321.705 (concen)s 356.705 (tration)s 396.743 (the)s 417.413 (in)s 427.08 (v)s 432.747 (arian)s 459.114 (t)s 258.55 y -5.69 (measures)s 46.957 (will)s 70.77 (b)s 77.77 (e)s 88.25 (Gibbs)s 124.213 (measures)s 176.86 (parametrized)s 250.74 (b)s 257.073 (y)s 268.553 (t)s 272.887 (w)s 281.22 (o)s 292.367 (c)s 297.367 (hemical)s 342.513 (p)s 349.513 (oten)s 371.847 (tials.)s 406.02 (It)s 420.167 (is)s 433.38 (useful)s 275.35 y -5.69 (to)s 9.42 (in)s 19.086 (tro)s 34.787 (duce)s 63.23 (the)s 84.34 (in)s 94.007 (v)s 99.673 (arian)s 126.04 (t)s 135.15 (measures)s 187.093 (for)s 205.903 (the)s 227.013 (exclusion)s 279.19 (pro)s 296.89 (cess)s 321.467 (GSEP)s 352.884 (,)s 360.66 (whic)s 384.327 (h)s 395.437 (are)s 415.914 (Bernoulli)s 292.15 y -5.69 (measures)s 45.873 (dep)s 64.873 (ending)s 103.602 (on)s 120.332 (t)s 124.665 (w)s 132.999 (o)s 143.062 (parameters.)s 210.051 (F)s 216.884 (or)s 231.647 (eac)s 247.98 (h)s 258.71 (p)s 265.71 (ositiv)s 293.777 (e)s 303.173 (in)s 312.839 (teger)s 10 f 342.936 (n)s 1 f 350.139 (,)s 357.551 (denote)s 396.28 (b)s 402.614 (y)s 413.01 (\244)s 11 f 293.95 y 421.343 (n)s 12 f 292.15 y 431.313 (\275)s 10 f 444.085 (Z)s 447.135 (Z)s 11 f 286.916 y 458.185 (d)s 1 f 308.95 y -5.69 (the)s 15.566 (sublattice)s 70.888 (of)s 85.144 (size)s 108.466 (\0502)s 10 f 119.133 (n)s 1 f 129.395 (+)s 141.788 (1\051)s 11 f 304.595 y 152.454 (d)s 1 f 308.95 y 158.05 (,)s 166.12 (\244)s 11 f 310.75 y 174.453 (n)s 1 f 308.95 y 185.3 (=)s 12 f 198.948 (f\241)s 10 f 214.282 (n;)s 12 f 226.818 (\242)s 232.151 (\242)s 237.484 (\242)s 10 f 242.818 (;)s 248.151 (n)s 12 f 255.354 (g)s 11 f 304.595 y 261.354 (d)s 1 f 308.95 y 266.949 (.)s 277.383 (F)s 284.216 (or)s 10 f 299.505 (A)s 1 f 312.821 (=)s 326.469 (\050)s 10 f 331.136 (a;)s 342.812 (b)s 1 f 347.962 (\051)s 12 f 356.944 (2)s 1 f 369.259 ([)s 12 f 372.592 (\241)s 1 f 381.925 (1)s 10 f 387.925 (;)s 1 f 393.259 (1])s 12 f 405.651 (\243)s 1 f 418.044 ([0)s 10 f 427.377 (;)s 1 f 432.711 (1],)s 450.114 (w)s 458.447 (e)s 325.75 y -5.69 (de\257ne)s 28.94 (\271)s 10 f 28.261 (\272)s 11 f 327.55 y 34.189 (A)s 1 f 325.75 y 45.29 (as)s 59.307 (the)s 79.258 (pro)s 96.958 (duct)s 123.576 (measure)s 169.627 (on)s 185.578 (\255)s 197.529 (with)s 224.147 (c)s 229.147 (hemical)s 272.431 (p)s 279.431 (oten)s 301.764 (tial)s 10 f 322.382 (A)s 1 f 334.666 (suc)s 351.066 (h)s 361.017 (that,)s 389.778 (for)s 407.429 (all)s 423.38 (p)s 430.38 (ositiv)s 458.447 (e)s 342.55 y -5.69 (in)s 3.976 (teger)s 10 f 34.01 (n)s 1 f 41.213 (,)s 48.546 (the)s 69.213 (restriction)s 127.359 (\271)s 10 f 126.679 (\272)s 11 f 344.35 y 132.607 (A;n)s 1 f 342.55 y 153.206 (of)s 167.552 (\271)s 10 f 166.873 (\272)s 11 f 344.35 y 172.8 (A)s 1 f 342.55 y 184.617 (to)s 199.284 (\255)s 11 f 344.35 y 207.95 (n)s 1 f 342.55 y 218.482 (is)s 230.549 (giv)s 245.883 (en)s 261.883 (b)s 268.216 (y)s 10 f 377.299 y 110.591 (d)s 1 f 117.516 (\271)s 10 f 116.837 (\272)s 11 f 379.099 y 122.764 (A;n)s 1 f 377.299 y 142.696 (=)s 10 f 155.363 (Z)s 14 f 372.166 y 164.413 (\241)s 2 f 171.913 (1)s 11 f 380.826 y 163.555 (A;n)s 1 f 377.299 y 182.153 (exp)s 13 f 363.979 y 202.487 (n)s 10 f 377.299 y 210.487 (a)s 13 f 365.899 y 221.32 (X)s 11 f 391.639 y 218.83 (i)s 14 f 222.225 (2)s 2 f 228.691 (\244)s 15 f 392.839 y 235.258 (n)s 10 f 377.299 y 243.143 (\276)s 1 f 250.43 (\050)s 10 f 255.097 (i)s 1 f 259.231 (\051)s 266.564 (+)s 10 f 278.564 (b)s 13 f 365.899 y 288.204 (X)s 11 f 391.639 y 285.714 (i)s 14 f 289.11 (2)s 2 f 295.576 (\244)s 15 f 392.839 y 302.143 (n)s 10 f 377.299 y 310.028 (\276)s 2 f 372.345 y 317.315 (2)s 1 f 377.299 y 322.698 (\050)s 10 f 327.365 (i)s 1 f 331.499 (\051)s 13 f 363.979 y 336.166 (o)s 10 f 377.299 y 344.166 (;)s 1 f 420.556 y -5.69 (where)s 10 f 28.394 (Z)s 11 f 422.356 y 36.586 (A;n)s 1 f 420.556 y 56.568 (is)s 68.019 (the)s 88.07 (normalization)s 163.488 (constan)s 203.221 (t.)s 216.349 (F)s 223.182 (or)s 237.267 (\050)s 10 f 241.933 (a;)s 253.61 (b)s 1 f 258.76 (\051)s 12 f 266.76 (2)s 1 f 278.093 ([)s 12 f 281.426 (\241)s 1 f 290.759 (1)s 10 f 296.76 (;)s 1 f 302.093 (1])s 12 f 312.861 (\243)s 1 f 323.629 ([0)s 10 f 332.963 (;)s 1 f 338.296 (1])s 351.013 (let)s 10 f 367.731 (m)s 1 f 381.6 (=)s 10 f 394.267 (m)s 1 f 404.803 (\050)s 10 f 409.47 (a;)s 421.146 (b)s 1 f 426.296 (\051)s 434.347 (\050resp.)s 10 f 437.356 y -5.69 (\301)s 1 f 4.793 (=)s 10 f 17.46 (\301)s 1 f 24.61 (\050)s 10 f 29.276 (a;)s 40.953 (b)s 1 f 46.103 (\051\051)s 59.436 (b)s 66.436 (e)s 75.769 (the)s 96.436 (exp)s 115.103 (ectation)s 161.103 (of)s 10 f 174.77 (\276)s 1 f 182.057 (\0500\051)s 201.39 (\050resp.)s 10 f 236.157 (\276)s 2 f 433.001 y 243.445 (2)s 1 f 437.356 y 248.828 (\0500\051\051)s 272.828 (under)s 307.541 (\271)s 10 f 306.861 (\272)s 11 f 439.156 y 312.789 (A;n)s 1 f 437.356 y 329.388 (:)s 13 f 458.785 y 157.67 (\050)s 10 f 469.105 y 169.337 (m)s 1 f 179.873 (\050)s 10 f 184.54 (a;)s 196.216 (b)s 1 f 201.366 (\051)s 212.699 (=)s 0 f 228.699 (E)s 2 f 464.151 y 238.318 (\271)s 11 f 237.766 (\272)s 15 f 465.357 y 242.577 (A;n)s 13 f 459.385 y 258.028 (\241)s 10 f 469.105 y 263.528 (\276)s 1 f 270.816 (\0500\051)s 13 f 459.385 y 286.149 (\242)s 10 f 489.505 y 169.337 (\301)s 1 f 176.487 (\050)s 10 f 181.154 (a;)s 192.83 (b)s 1 f 197.98 (\051)s 209.313 (=)s 0 f 225.313 (E)s 2 f 484.551 y 234.932 (\271)s 11 f 234.38 (\272)s 15 f 485.757 y 239.191 (A;n)s 13 f 479.785 y 254.642 (\241)s 10 f 489.505 y 260.142 (\276)s 2 f 484.551 y 267.43 (2)s 1 f 489.505 y 272.813 (\0500\051)s 13 f 479.785 y 288.147 (\242)s 10 f 489.505 y 293.647 (:)s 1 f 520.822 y -5.69 (Observ)s 31.077 (e)s 41.057 (that)s 67.705 (the)s 89.019 (function)s 136.667 (\252)s 150.647 (de\257ned)s 192.628 (on)s 209.942 (])s 12 f 216.374 (\241)s 1 f 228.806 (1)s 10 f 234.806 (;)s 1 f 240.139 (1[)s 12 f 249.472 (\243)s 1 f 258.806 (]0)s 10 f 268.139 (;)s 1 f 273.472 (1[)s 287.453 (b)s 293.786 (y)s 304.767 (\252\050)s 10 f 318.767 (a;)s 330.444 (b)s 1 f 335.594 (\051)s 344.673 (=)s 358.418 (\050)s 10 f 363.085 (m;)s 378.955 (\301)s 1 f 386.105 (\051)s 395.419 (is)s 408.133 (a)s 418.78 (bijection)s 542.422 y -5.69 (from)s 22.37 (])s 12 f 27.757 (\241)s 1 f 39.144 (1)s 10 f 45.144 (;)s 1 f 50.477 (1[)s 12 f 59.81 (\243)s 1 f 69.144 (]0)s 10 f 78.477 (;)s 1 f 83.81 (1[)s 96.837 (to)s 10 f 111.197 (I)s 1 f 120.747 (=)s 13 f 529.102 y 133.414 (n)s 1 f 542.422 y 141.414 (\050)s 10 f 146.08 (m;)s 161.95 (\301)s 1 f 169.1 (\051)s 180.793 (:)s 191.153 (0)s 10 f 200.486 (\074)s 213.153 (\301)s 223.636 (\074)s 1 f 236.303 (1)s 10 f 242.303 (;)s 12 f 247.636 (\241)s 1 f 256.97 (1)s 10 f 266.303 (\074)s 278.969 (m)s 292.839 (\074)s 305.505 (\301)s 13 f 529.102 y 312.655 (o)s 1 f 542.422 y 320.655 (.)s 329.22 (F)s 336.053 (or)s 350.447 (ev)s 361.78 (ery)s 10 f 381.84 (P)s 1 f 394.544 (=)s 407.211 (\050)s 10 f 411.878 (m;)s 427.747 (\301)s 1 f 434.897 (\051)s 12 f 442.897 (2)s 10 f 454.23 (I)s 1 f 460.447 (,)s 559.222 y -5.69 (w)s 2.643 (e)s 11.976 (denote)s 50.643 (b)s 56.977 (y)s 10 f 67.31 (\272)s 11 f 561.022 y 73.238 (P)s 79.606 (;n)s 1 f 559.222 y 92.988 (the)s 113.654 (pro)s 131.354 (duct)s 158.688 (measure)s 205.454 (suc)s 221.854 (h)s 232.521 (that)s 13 f 580.651 y 171.628 (\050)s 10 f 590.971 y 183.295 (m)s 1 f 200.498 (=)s 0 f 216.497 (E)s 11 f 586.017 y 225.564 (\272)s 15 f 587.223 y 230.375 (P)s 235.836 (;n)s 13 f 581.251 y 245.07 (\243)s 10 f 590.971 y 250.07 (\276)s 1 f 257.358 (\0500\051)s 13 f 581.251 y 272.691 (\244)s 10 f 611.371 y 183.295 (\301)s 1 f 197.111 (=)s 0 f 213.111 (E)s 11 f 606.417 y 222.178 (\272)s 15 f 607.623 y 226.989 (P)s 232.449 (;n)s 13 f 601.651 y 241.684 (\243)s 10 f 611.371 y 246.684 (\276)s 2 f 606.417 y 253.972 (2)s 1 f 611.371 y 259.355 (\0500\051)s 13 f 601.651 y 274.689 (\244)s 10 f 611.371 y 279.689 (:)s 1 f 601.171 y 439.114 (\0503)s 10 f 449.78 (:)s 1 f 453.114 (2\051)s 643.576 y 8.71 (W)s 20.043 (e)s 29.623 (tak)s 46.29 (e)s 10 f 55.869 (\260)s 14 f 639.221 y 62.749 (\241)s 2 f 70.249 (1)s 1 f 643.576 y 75.632 (,)s 83.274 (the)s 104.187 (range)s 137.133 (of)s 151.046 (the)s 171.96 (in)s 181.626 (teraction,)s 235.968 (as)s 250.948 (macroscopic)s 318.628 (space)s 350.941 (unit)s 376.521 (and)s 400.1 (consider)s 447.114 (the)s 660.376 y -5.69 (limit)s 10 f 23.922 (\260)s 12 f 35.709 (!)s 1 f 52.618 (0.)s 70.119 (W)s 81.453 (e)s 91.731 (w)s 100.064 (an)s 112.398 (t)s 122.01 (to)s 137.621 (establish)s 188.033 (for)s 207.345 (b)s 214.345 (oth)s 236.623 (Ka)s 251.623 (w)s 259.957 (asaki)s 291.302 (and)s 315.58 (Glaub)s 347.997 (er)s 362.975 (dynamics,)s 420.557 (a)s 431.502 (la)s 440.502 (w)s 454.114 (of)s 677.176 y -5.69 (large)s 23.913 (n)s 30.247 (um)s 46.58 (b)s 53.58 (ers)s 72.584 (for)s 91.188 (the)s 112.091 (empirical)s 164.362 (\257elds)s 195.332 (corresp)s 233.132 (onding)s 272.702 (to)s 287.606 (magnetization)s 365.843 (and)s 389.413 (concen)s 424.413 (tration.)s 705.976 y 223.045 (12)s do-end end endp %%Page: 13 13 %%BeginPageSetup initializepage (Raffaele Esposito; page: 13 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f0_12 sf ( )S -996 -1000 :M f1_12 sf ( )S -993 -1000 :M f2_12 sf ( )S -989 -1000 :M f10_12 sf ( )S -981 -1000 :M f11_12 sf ( )S -972 -1000 :M f12_12 sf ( )S -960 -1000 :M f13_12 sf ( )S -951 -1000 :M f14_12 sf ( )S -937 -1000 :M f15_12 sf ( )S -926 -1000 :M f17_12 sf ( )S -923 -1000 :M f21_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 1200 1000 div mul /CMBX10 findfont fdef 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 17 10 1200 1000 div mul /CMTI10 findfont fdef 22 10 1200 1000 div mul /CMSL10 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 6.31 y -5.69 (In)s 10.497 (the)s 32.352 (Glaub)s 64.769 (er)s 79.989 (case)s 106.577 (w)s 114.91 (e)s 125.431 (lo)s 135.098 (ok)s 152.619 (at)s 168.473 (the)s 190.328 (b)s 197.328 (eha)s 214.994 (viour)s 247.215 (of)s 262.07 (the)s 283.924 (\257elds)s 315.845 (for)s 335.399 (\257nite)s 367.254 (time,)s 399.405 (while)s 431.926 (in)s 447.114 (the)s 23.11 y -5.69 (Ka)s 9.31 (w)s 17.643 (asaki)s 49.641 (case)s 76.64 (the)s 98.905 (relev)s 123.271 (an)s 135.605 (t)s 145.87 (time)s 174.801 (scale)s 205.133 (is)s 10 f 218.798 (\260)s 14 f 18.755 y 225.677 (\241)s 2 f 233.177 (2)s 1 f 23.11 y 238.561 (.)s 252.022 (Fix)s 275.12 (a)s 286.719 (sequence)s 338.05 (of)s 353.315 (probabilit)s 404.349 (y)s 416.28 (measures)s 13 f 30.19 y -5.69 (\241)s 10 f 39.91 y -.19 (\271)s 11 f 35.555 y 7.04 (\260)s 13 f 30.19 y 13.198 (\242)s 11 f 44.71 y 18.698 (\260)s 1 f 39.91 y 24.855 (,)s 33.386 (asso)s 55.186 (ciated)s 91.477 (to)s 107.102 (the)s 128.727 (same)s 159.752 (initial)s 195.377 (pro\257le)s 13 f 30.19 y 233.035 (\241)s 10 f 39.91 y 238.535 (m)s 2 f 41.71 y 249.071 (0)s 10 f 39.91 y 254.454 (;)s 259.787 (\301)s 2 f 41.71 y 266.938 (0)s 13 f 30.19 y 272.321 (\242)s 1 f 39.91 y 282.751 (:)s 291.014 (I)s 293.188 (R)s 11 f 34.676 y 302.021 (d)s 12 f 39.91 y 310.922 (\243)s 1 f 323.56 (I)s 325.734 (R)s 11 f 34.676 y 334.567 (d)s 12 f 39.91 y 345.092 (\241)s 352.426 (!)s 10 f 369.356 (I)s 1 f 380.531 (in)s 395.489 (the)s 417.113 (follo)s 439.114 (wing)s 56.71 y -5.69 (sense)s 93.106 y 51.721 (lim)s 11 f 100.519 y 50.101 (\260)s 14 f 55.658 (!)s 2 f 65.225 (0)s 10 f 93.106 y 72.008 (\271)s 11 f 88.151 y 79.239 (\260)s 13 f 72.586 y 85.396 (\050)s 97.062 (\042)s 79.306 y 104.062 (\257)s 86.506 y 104.062 (\257)s 93.706 y 104.062 (\257)s 10 f 93.106 y 108.062 (\260)s 11 f 88.151 y 114.942 (d)s 13 f 81.706 y 126.808 (X)s 11 f 108.646 y 122.537 (i)s 14 f 125.932 (2)s 11 f 132.399 (Z)s 134.609 (Z)s 15 f 105.872 y 143.375 (d)s 10 f 93.106 y 150.413 (U)s 1 f 159.914 (\050)s 10 f 164.581 (i\260)s 1 f 175.595 (\051)s 10 f 180.261 (\276)s 1 f 187.549 (\050)s 10 f 192.216 (i)s 1 f 196.35 (\051)s 12 f 203.683 (\241)s 13 f 76.772 y 215.683 (Z)s 2 f 104.039 y 222.35 (I)s 223.656 (R)s 15 f 101.266 y 230.623 (d)s 10 f 93.106 y 238.261 (U)s 1 f 247.763 (\050)s 10 f 252.43 (x)s 1 f 259.288 (\051)s 10 f 263.955 (m)s 2 f 94.906 y 274.491 (0)s 1 f 93.106 y 279.874 (\050)s 10 f 284.541 (x)s 1 f 291.399 (\051)s 10 f 296.066 (dx)s 13 f 79.306 y 309.17 (\257)s 86.506 y 309.17 (\257)s 93.706 y 309.17 (\257)s 1 f 139.882 y 122.767 (+)s 13 f 126.081 y 134.767 (\257)s 133.282 y 134.767 (\257)s 140.482 y 134.767 (\257)s 10 f 139.882 y 138.767 (\260)s 11 f 134.927 y 145.647 (d)s 13 f 128.482 y 157.513 (X)s 11 f 155.422 y 153.242 (i)s 14 f 156.637 (2)s 11 f 163.104 (Z)s 165.314 (Z)s 15 f 152.648 y 174.08 (d)s 10 f 139.882 y 181.118 (V)s 1 f 190.784 (\050)s 10 f 195.451 (i\260)s 1 f 206.465 (\051)s 10 f 211.131 (\276)s 1 f 218.419 (\050)s 10 f 223.086 (i)s 1 f 227.22 (\051)s 2 f 134.927 y 231.886 (2)s 12 f 139.882 y 239.936 (\241)s 13 f 123.548 y 251.936 (Z)s 2 f 150.815 y 258.603 (I)s 259.91 (R)s 15 f 148.042 y 266.876 (d)s 10 f 139.882 y 274.514 (V)s 1 f 284.181 (\050)s 10 f 288.848 (x)s 1 f 295.706 (\051)s 10 f 300.373 (\301)s 2 f 141.682 y 307.523 (0)s 1 f 139.882 y 312.906 (\050)s 10 f 317.573 (x)s 1 f 324.431 (\051)s 10 f 329.098 (dx)s 13 f 126.081 y 342.202 (\257)s 133.282 y 342.202 (\257)s 140.482 y 342.202 (\257)s 119.361 y 346.202 (#)s 10 f 139.882 y 356.535 (\076)s 369.202 (\261)s 13 f 119.361 y 374.989 (\051)s 1 f 139.882 y 387.989 (=)s 400.656 (0)s 10 f 406.656 (;)s 1 f 117.681 y 439.114 (\0503)s 10 f 449.78 (:)s 1 f 453.114 (3\051)s 192.12 y -5.69 (for)s 12.677 (ev)s 24.01 (ery)s 44.377 (con)s 62.043 (tin)s 76.377 (uous)s 104.443 (functions)s 10 f 156.177 (U)s 164.345 (;)s 169.678 (V)s 1 f 182.678 (:)s 189.345 (I)s 191.518 (R)s 11 f 186.886 y 200.352 (d)s 12 f 192.12 y 209.28 (\241)s 216.614 (!)s 1 f 231.947 (I)s 234.12 (R)s 246.954 (with)s 274.287 (compact)s 322.287 (supp)s 347.354 (ort,)s 370.054 (and)s 393.387 (ev)s 404.721 (ery)s 10 f 425.087 (\261)s 434.208 (\076)s 1 f 446.875 (0.)s 212.572 y 8.71 (Denote)s 49.928 (b)s 56.262 (y)s 0 f 66.647 (P)s 2 f 206.338 y 76.08 (\050)s 11 f 79.83 (K)s 2 f 88.482 (\051)s 11 f 92.232 (;\257)s 215.342 y 76.08 (\271)s 15 f 212.942 y 81.915 (\260)s 13 f 202.852 y 105.607 (\241)s 1 f 212.572 y 111.107 (resp.)s 0 f 141.362 (P)s 2 f 206.338 y 150.796 (\050)s 11 f 154.546 (G)s 2 f 162.017 (\051)s 11 f 165.767 (;\257)s 215.342 y 150.796 (\271)s 15 f 212.942 y 156.63 (\260)s 13 f 202.852 y 175.09 (\242)s 1 f 212.572 y 184.642 (the)s 205.36 (probabilit)s 256.394 (y)s 266.779 (measure)s 313.598 (on)s 330.316 (the)s 351.035 (path)s 379.087 (space)s 10 f 411.205 (D)s 1 f 421.473 (\050I)s 428.314 (R)s 2 f 214.372 y 437.147 (+)s 10 f 212.572 y 445.114 (;)s 1 f 450.447 (\255\051)s 229.372 y -5.69 (corresp)s 32.11 (onding)s 70.199 (to)s 83.622 (the)s 103.045 (Mark)s 130.745 (o)s 136.411 (v)s 145.501 (pro)s 163.201 (cess)s 13 f 219.652 y 186.09 (\241)s 10 f 229.372 y 191.59 (\276)s 1 f 198.878 (\050)s 10 f 203.544 (t;)s 213.211 (:)s 1 f 216.544 (\051)s 13 f 219.652 y 221.211 (\242)s 11 f 234.172 y 226.711 (t)s 14 f 230.336 (\270)s 2 f 237.836 (0)s 1 f 229.372 y 245.976 (with)s 272.065 (the)s 291.488 (generator)s 10 f 343.644 (\260)s 14 f 225.017 y 350.523 (\241)s 2 f 358.023 (2)s 1 f 229.372 y 363.407 (I)s 365.58 (L)s 11 f 224.138 y 373.08 (K)s 381.215 (;\257)s 232.338 y 373.08 (\260)s 13 f 219.652 y 393.294 (\241)s 1 f 229.372 y 398.794 (resp.)s 428.479 (I)s 430.653 (L)s 11 f 224.138 y 438.153 (G;\257)s 232.338 y 438.153 (\260)s 13 f 219.652 y 454.947 (\242)s 1 f 229.372 y 460.447 (,)s 253.063 y -5.69 (and)s 17.029 (starting)s 61.182 (from)s 10 f 88.935 (\271)s 11 f 248.708 y 96.166 (\260)s 1 f 253.063 y 102.323 (,)s 109.165 (and)s 131.885 (b)s 138.218 (y)s 0 f 147.938 (E)s 2 f 246.83 y 157.004 (\050)s 11 f 160.754 (K)s 2 f 169.406 (\051)s 11 f 173.156 (;\257)s 255.833 y 157.004 (\271)s 15 f 253.433 y 162.839 (\260)s 13 f 243.343 y 185.865 (\241)s 1 f 253.063 y 191.365 (resp.)s 0 f 221.261 (E)s 2 f 246.83 y 230.327 (\050)s 11 f 234.077 (G)s 2 f 241.549 (\051)s 11 f 245.299 (;\257)s 255.833 y 230.327 (\271)s 15 f 253.433 y 236.162 (\260)s 13 f 243.343 y 254.622 (\242)s 1 f 253.063 y 263.508 (the)s 283.561 (exp)s 302.227 (ectation)s 347.614 (with)s 374.333 (resp)s 396.1 (ect)s 414.819 (to)s 0 f 428.872 (P)s 2 f 246.83 y 438.306 (\050)s 11 f 442.056 (K)s 2 f 450.707 (\051)s 11 f 454.457 (;\257)s 255.833 y 438.306 (\271)s 15 f 253.433 y 444.14 (\260)s 13 f 265.079 y -5.69 (\241)s 1 f 274.799 y -.19 (resp.)s 0 f 34.731 (P)s 2 f 268.566 y 44.164 (\050)s 11 f 47.914 (G)s 2 f 55.385 (\051)s 11 f 59.135 (;\257)s 277.569 y 44.164 (\271)s 15 f 275.169 y 49.999 (\260)s 13 f 265.079 y 68.458 (\242)s 1 f 274.799 y 73.958 (.)s 87.445 (Denote)s 130.219 (b)s 136.552 (y)s 12 f 148.493 (C)s 2 f 270.445 y 155.511 (2)s 11 f 278.105 y 154.811 (K)s 1 f 274.799 y 164.063 (\050I)s 170.903 (R)s 11 f 269.566 y 179.736 (d)s 1 f 274.799 y 185.332 (\051)s 195.605 (the)s 217.879 (space)s 251.552 (of)s 266.826 (real)s 291.799 (t)s 296.133 (wice)s 324.406 (con)s 342.073 (tin)s 356.406 (uously)s 395.747 (di\256eren)s 434.447 (tiable)s 291.599 y -5.69 (functions)s 46.043 (with)s 73.377 (compact)s 121.377 (supp)s 146.443 (ort.)s 312.051 y 8.71 (The)s 33.376 (main)s 63.377 (result)s 96.81 (of)s 110.477 (this)s 133.877 (Section)s 175.877 (is)s 187.943 (the)s 208.61 (follo)s 230.61 (wing)s 259.277 (theorem.)s 0 f 349.575 y -5.69 (Theorem)s 52.91 (3.1)s 17 f 79.143 (Under)s 115.816 (\0503.3\051,)s 149.549 (for)s 168.715 (any)s 10 f 191.715 (\261)s 200.836 (\076)s 1 f 213.503 (0)s 17 f 219.503 (,)s 10 f 227.476 (t)s 12 f 235.143 (\270)s 1 f 247.809 (0)s 17 f 258.102 (and)s 10 f 281.409 (U)s 289.577 (;)s 294.911 (V)s 12 f 307.91 (2)s 319.244 (C)s 2 f 345.22 y 326.262 (2)s 11 f 352.88 y 325.562 (K)s 1 f 349.575 y 334.814 (\050I)s 341.654 (R)s 11 f 344.342 y 350.487 (d)s 1 f 349.575 y 356.083 (\051)s 17 f 365.043 (the)s 384.976 (fol)s 398.469 (lowing)s 435.882 (holds)s 1 f 376.855 y 4.443 (\050i\051)s 22 f 23.11 (Ka)s 38.11 (w)s 46.443 (asaki)s 76.843 (dynamics.)s 1 f 430.651 y 46.813 (lim)s 11 f 438.065 y 45.192 (\260)s 14 f 50.75 (!)s 2 f 60.316 (0)s 0 f 430.651 y 67.1 (P)s 2 f 424.418 y 76.533 (\050)s 11 f 80.283 (K)s 2 f 88.935 (\051)s 11 f 92.685 (;\257)s 433.421 y 76.533 (\271)s 15 f 431.021 y 82.368 (\260)s 13 f 410.131 y 102.008 (\050)s 113.674 (\042)s 416.851 y 120.674 (\257)s 424.051 y 120.674 (\257)s 431.251 y 120.674 (\257)s 10 f 430.651 y 124.674 (\260)s 11 f 425.697 y 131.554 (d)s 13 f 419.251 y 143.42 (X)s 11 f 446.191 y 139.149 (i)s 14 f 142.544 (2)s 11 f 149.011 (Z)s 151.221 (Z)s 15 f 443.418 y 159.986 (d)s 10 f 430.651 y 167.025 (U)s 1 f 176.526 (\050)s 10 f 181.193 (i\260)s 1 f 192.207 (\051)s 10 f 196.873 (\276)s 1 f 204.161 (\050)s 10 f 208.827 (t;)s 218.494 (i)s 1 f 222.628 (\051)s 12 f 229.961 (\241)s 13 f 414.318 y 241.961 (Z)s 2 f 441.585 y 248.628 (I)s 249.935 (R)s 15 f 438.811 y 256.901 (d)s 10 f 430.651 y 264.54 (U)s 1 f 274.041 (\050)s 10 f 278.708 (x)s 1 f 285.566 (\051)s 10 f 290.233 (m)s 1 f 300.769 (\050)s 10 f 305.436 (t;)s 315.102 (x)s 1 f 321.961 (\051)s 10 f 326.627 (dx)s 13 f 416.851 y 339.732 (\257)s 424.051 y 339.732 (\257)s 431.251 y 339.732 (\257)s 1 f 477.427 y 117.859 (+)s 13 f 463.627 y 129.859 (\257)s 470.827 y 129.859 (\257)s 478.027 y 129.859 (\257)s 10 f 477.427 y 133.859 (\260)s 11 f 472.473 y 140.738 (d)s 13 f 466.027 y 152.605 (X)s 11 f 492.967 y 148.334 (i)s 14 f 151.729 (2)s 11 f 158.196 (Z)s 160.406 (Z)s 15 f 490.194 y 169.171 (d)s 10 f 477.427 y 176.209 (V)s 1 f 185.876 (\050)s 10 f 190.543 (i\260)s 1 f 201.556 (\051)s 10 f 206.223 (\276)s 1 f 213.511 (\050)s 10 f 218.177 (t;)s 227.844 (i)s 1 f 231.978 (\051)s 2 f 472.473 y 236.645 (2)s 12 f 477.427 y 244.695 (\241)s 13 f 461.094 y 256.695 (Z)s 2 f 488.361 y 263.361 (I)s 264.668 (R)s 15 f 485.587 y 271.635 (d)s 10 f 477.427 y 279.273 (V)s 1 f 288.939 (\050)s 10 f 293.606 (x)s 1 f 300.464 (\051)s 10 f 305.131 (\301)s 1 f 312.281 (\050)s 10 f 316.948 (t;)s 326.614 (x)s 1 f 333.473 (\051)s 10 f 338.139 (dx)s 13 f 463.627 y 351.244 (\257)s 470.827 y 351.244 (\257)s 478.027 y 351.244 (\257)s 456.907 y 355.244 (#)s 10 f 477.427 y 365.577 (\076)s 378.244 (\261)s 13 f 456.907 y 384.031 (\051)s 1 f 477.427 y 397.031 (=)s 409.698 (0)s 10 f 415.698 (;)s 1 f 455.227 y 439.114 (\0503)s 10 f 449.78 (:)s 1 f 453.114 (4\051)s 22 f 534.799 y 23.11 (where)s 13 f 525.079 y 57.81 (\241)s 10 f 534.799 y 63.31 (m;)s 79.179 (\301)s 13 f 525.079 y 86.329 (\242)s 22 f 534.799 y 95.829 (is)s 107.896 (the)s 128.563 (unique)s 167.563 (w)s 175.896 (eak)s 197.563 (solution)s 242.963 (of)s 10 f 584.447 y 115.127 (@)s 11 f 586.247 y 121.498 (t)s 10 f 584.447 y 125.723 (m)s 1 f 139.592 (=)s 12 f 152.259 (r)s 164.926 (\242)s 13 f 571.126 y 170.925 (h)s 12 f 584.447 y 176.592 (r)s 10 f 186.592 (m)s 12 f 199.795 (\241)s 1 f 211.795 (2)s 10 f 217.795 (\257)s 13 f 574.726 y 225.216 (\241)s 10 f 584.447 y 230.716 (\301)s 12 f 240.532 (\241)s 1 f 252.532 (\050)s 10 f 257.199 (m)s 1 f 267.735 (\051)s 2 f 579.492 y 272.402 (2)s 13 f 574.726 y 277.785 (\242)s 283.285 (\241)s 12 f 584.447 y 288.785 (r)s 10 f 298.785 (J)s 12 f 309.26 (\244)s 10 f 317.927 (m)s 13 f 574.726 y 328.463 (\242)s 571.126 y 333.963 (i)s 10 f 584.447 y 339.63 (;)s 614.447 y 118.513 (@)s 11 f 616.247 y 124.884 (t)s 10 f 614.447 y 129.109 (\301)s 1 f 139.592 (=)s 12 f 152.259 (r)s 164.926 (\242)s 13 f 601.127 y 170.925 (h)s 12 f 614.447 y 176.592 (r)s 10 f 186.592 (\301)s 12 f 196.409 (\241)s 1 f 208.409 (2)s 10 f 214.409 (\257)s 221.83 (m)s 13 f 604.727 y 232.366 (\241)s 1 f 614.447 y 237.866 (1)s 12 f 246.532 (\241)s 10 f 258.532 (\301)s 13 f 604.727 y 265.682 (\242)s 271.182 (\241)s 12 f 614.447 y 276.682 (r)s 10 f 286.682 (J)s 12 f 297.157 (\244)s 10 f 305.824 (m)s 13 f 604.727 y 316.36 (\242)s 601.127 y 321.86 (i)s 10 f 614.447 y 327.527 (;)s 640.847 y 125.723 (m)s 1 f 136.259 (\0500)s 10 f 146.926 (;)s 12 f 152.259 (\242)s 1 f 155.592 (\051)s 163.592 (=)s 10 f 176.259 (m)s 2 f 642.647 y 186.795 (0)s 10 f 640.847 y 192.178 (;)s 209.512 (\301)s 1 f 216.662 (\0500)s 10 f 227.328 (;)s 12 f 232.662 (\242)s 1 f 235.995 (\051)s 243.995 (=)s 10 f 256.662 (\301)s 2 f 642.647 y 263.812 (0)s 1 f 610.847 y 439.114 (\0503)s 10 f 449.78 (:)s 1 f 453.114 (5\051)s 22 f 677.176 y -5.69 (where)s 12 f 29.01 (\244)s 22 f 39.01 (denotes)s 82.41 (the)s 103.077 (con)s 120.743 (v)s 126.743 (olution)s 167.41 (on)s 184.077 (the)s 204.743 (spatial)s 243.477 (v)s 249.144 (ariable.)s 1 f 705.976 y 223.045 (13)s do-end end endp %%Page: 14 14 %%BeginPageSetup initializepage (Raffaele Esposito; page: 14 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f0_12 sf ( )S -996 -1000 :M f1_12 sf ( )S -993 -1000 :M f2_12 sf ( )S -989 -1000 :M f10_12 sf ( )S -981 -1000 :M f11_12 sf ( )S -972 -1000 :M f12_12 sf ( )S -960 -1000 :M f13_12 sf ( )S -951 -1000 :M f14_12 sf ( )S -937 -1000 :M f15_12 sf ( )S -926 -1000 :M f16_12 sf ( )S -921 -1000 :M f21_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 1200 1000 div mul /CMBX10 findfont fdef 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 16 5 1200 1000 div mul /CMR5 findfont fdef 22 10 1200 1000 div mul /CMSL10 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 6.31 y 1.11 (\050ii\051)s 22 f 23.11 (Glaub)s 55.527 (er)s 69.56 (dynamics.)s 1 f 41.748 y 39.027 (lim)s 11 f 49.161 y 37.407 (\260)s 14 f 42.964 (!)s 2 f 52.531 (0)s 0 f 41.748 y 59.314 (P)s 2 f 35.515 y 68.747 (\050)s 11 f 72.497 (G)s 2 f 79.968 (\051)s 11 f 83.718 (;\257)s 44.518 y 68.747 (\271)s 15 f 42.118 y 74.582 (\260)s 13 f 21.228 y 93.041 (\050)s 104.708 (\042)s 27.948 y 111.708 (\257)s 35.148 y 111.708 (\257)s 42.348 y 111.708 (\257)s 10 f 41.748 y 115.708 (\260)s 11 f 36.793 y 122.588 (d)s 13 f 30.348 y 134.454 (X)s 11 f 57.288 y 130.183 (i)s 14 f 133.578 (2)s 11 f 140.045 (Z)s 142.255 (Z)s 15 f 54.515 y 151.02 (d)s 10 f 41.748 y 158.059 (U)s 1 f 167.56 (\050)s 10 f 172.227 (i\260)s 1 f 183.24 (\051)s 10 f 187.907 (\276)s 1 f 195.195 (\050)s 10 f 199.861 (t;)s 209.528 (i)s 1 f 213.662 (\051)s 12 f 220.995 (\241)s 13 f 25.415 y 232.995 (Z)s 2 f 52.682 y 239.662 (I)s 240.969 (R)s 15 f 49.908 y 247.935 (d)s 10 f 41.748 y 255.574 (U)s 1 f 265.075 (\050)s 10 f 269.742 (x)s 1 f 276.6 (\051)s 10 f 281.267 (m)s 2 f 36.793 y 291.803 (\050)s 11 f 295.553 (G)s 2 f 303.024 (\051)s 1 f 41.748 y 307.374 (\050)s 10 f 312.041 (t;)s 321.708 (x)s 1 f 328.566 (\051)s 10 f 333.233 (dx)s 13 f 27.948 y 346.337 (\257)s 35.148 y 346.337 (\257)s 42.348 y 346.337 (\257)s 1 f 88.524 y 110.073 (+)s 13 f 74.724 y 122.073 (\257)s 81.924 y 122.073 (\257)s 89.124 y 122.073 (\257)s 10 f 88.524 y 126.073 (\260)s 11 f 83.569 y 132.953 (d)s 13 f 77.124 y 144.819 (X)s 11 f 104.064 y 140.548 (i)s 14 f 143.943 (2)s 11 f 150.41 (Z)s 152.62 (Z)s 15 f 101.291 y 161.386 (d)s 10 f 88.524 y 168.424 (V)s 1 f 178.09 (\050)s 10 f 182.757 (i\260)s 1 f 193.771 (\051)s 10 f 198.437 (\276)s 1 f 205.725 (\050)s 10 f 210.392 (t;)s 220.058 (i)s 1 f 224.192 (\051)s 2 f 83.569 y 228.859 (2)s 12 f 88.524 y 236.909 (\241)s 13 f 72.191 y 248.909 (Z)s 2 f 99.457 y 255.576 (I)s 256.882 (R)s 15 f 96.684 y 263.849 (d)s 10 f 88.524 y 271.487 (V)s 1 f 281.154 (\050)s 10 f 285.821 (x)s 1 f 292.679 (\051)s 10 f 297.346 (\301)s 2 f 83.569 y 304.496 (\050)s 11 f 308.246 (G)s 2 f 315.717 (\051)s 1 f 88.524 y 320.067 (\050)s 10 f 324.733 (t;)s 334.4 (x)s 1 f 341.258 (\051)s 10 f 345.925 (dx)s 13 f 74.724 y 359.029 (\257)s 81.924 y 359.029 (\257)s 89.124 y 359.029 (\257)s 68.004 y 363.029 (#)s 10 f 88.524 y 373.363 (\076)s 386.029 (\261)s 13 f 68.004 y 391.817 (\051)s 1 f 88.524 y 404.817 (=)s 417.483 (0)s 10 f 423.483 (;)s 1 f 66.324 y 439.114 (\0503)s 10 f 449.78 (:)s 1 f 453.114 (6\051)s 22 f 127.993 y 23.11 (where)s 13 f 118.272 y 57.81 (\241)s 10 f 127.993 y 63.31 (m)s 2 f 123.638 y 73.846 (\050)s 11 f 77.596 (G)s 2 f 85.067 (\051)s 10 f 127.993 y 89.417 (;)s 94.751 (\301)s 2 f 123.638 y 101.901 (\050)s 11 f 105.651 (G)s 2 f 113.122 (\051)s 13 f 118.272 y 117.472 (\242)s 22 f 127.993 y 126.972 (is)s 139.038 (the)s 159.705 (unique)s 198.705 (w)s 207.039 (eak)s 228.705 (solution)s 274.105 (of)s 13 f 145.031 y 109.09 (8)s 155.831 y 109.09 (\076)s 159.431 y 109.09 (\076)s 163.031 y 109.09 (\076)s 166.631 y 109.09 (\074)s 188.231 y 109.09 (\076)s 191.831 y 109.09 (\076)s 195.431 y 109.09 (\076)s 199.031 y 109.09 (:)s 10 f 161.831 y 121.756 (@)s 11 f 163.631 y 128.127 (t)s 13 f 144.911 y 134.352 (\265)s 10 f 154.631 y 145.186 (m)s 16 f 150.276 y 155.722 (\050)s 15 f 158.972 (G)s 16 f 165.356 (\051)s 10 f 169.031 y 146.879 (\301)s 16 f 164.676 y 154.029 (\050)s 15 f 157.279 (G)s 16 f 163.663 (\051)s 13 f 144.911 y 171.206 (\266)s 1 f 161.831 y 183.373 (=)s 12 f 196.039 (G)s 11 f 156.876 y 203.889 (\257)s 13 f 144.911 y 212.362 (\265)s 10 f 154.631 y 223.196 (m)s 16 f 150.276 y 233.732 (\050)s 15 f 236.982 (G)s 16 f 243.366 (\051)s 10 f 169.031 y 224.889 (\301)s 16 f 164.676 y 232.039 (\050)s 15 f 235.289 (G)s 16 f 241.673 (\051)s 13 f 144.911 y 249.216 (\266)s 1 f 161.831 y 261.383 (:=)s 13 f 144.911 y 277.383 (\265)s 12 f 154.031 y 288.216 (G)s 11 f 148.264 y 296.066 (\257)s 2 f 157.231 y 295.354 (1)s 13 f 144.311 y 302.539 (\241)s 10 f 154.031 y 308.039 (m)s 16 f 149.676 y 318.575 (\050)s 15 f 321.825 (G)s 16 f 328.209 (\051)s 10 f 154.031 y 332.059 (;)s 337.393 (\301)s 16 f 149.676 y 344.543 (\050)s 15 f 347.793 (G)s 16 f 354.177 (\051)s 13 f 144.311 y 358.027 (\242)s 12 f 171.031 y 288.216 (G)s 11 f 165.264 y 296.066 (\257)s 2 f 174.231 y 295.354 (2)s 13 f 161.311 y 302.539 (\241)s 10 f 171.031 y 308.039 (m)s 16 f 166.676 y 318.575 (\050)s 15 f 321.825 (G)s 16 f 328.209 (\051)s 10 f 171.031 y 332.059 (;)s 337.393 (\301)s 16 f 166.676 y 344.543 (\050)s 15 f 347.793 (G)s 16 f 354.177 (\051)s 13 f 161.311 y 358.027 (\242)s 144.911 y 365.527 (\266)s 182.911 y 123.756 (\265)s 10 f 192.631 y 134.59 (m)s 16 f 188.276 y 145.126 (\050)s 15 f 148.376 (G)s 16 f 154.76 (\051)s 1 f 192.631 y 158.61 (\0500)s 10 f 169.277 (;)s 174.61 (:)s 1 f 177.944 (\051)s 10 f 207.031 y 136.283 (\301)s 16 f 202.676 y 143.433 (\050)s 15 f 146.683 (G)s 16 f 153.067 (\051)s 1 f 207.031 y 156.917 (\0500)s 10 f 167.584 (;)s 172.917 (:)s 1 f 176.25 (\051)s 13 f 182.911 y 184.61 (\266)s 1 f 199.831 y 196.777 (=)s 13 f 182.911 y 209.443 (\265)s 10 f 192.631 y 220.277 (m)s 2 f 194.431 y 230.813 (0)s 10 f 207.031 y 221.97 (\301)s 2 f 208.831 y 229.12 (0)s 13 f 182.911 y 238.196 (\266)s 10 f 199.831 y 249.03 (:)s 1 f 180.431 y 439.114 (\0503)s 10 f 449.78 (:)s 1 f 453.114 (7\051)s 22 f 234.269 y 23.11 (and)s 12 f 46.443 (G)s 11 f 228.502 y 54.293 (\257)s 2 f 237.469 y 53.582 (1)s 22 f 234.269 y 60.766 (,)s 12 f 68.1 (G)s 11 f 228.502 y 75.95 (\257)s 2 f 237.469 y 75.238 (2)s 22 f 234.269 y 86.422 (are)s 106.456 (de\257ned)s 147.789 (as)s 12 f 269.907 y 62.839 (G)s 11 f 264.141 y 70.689 (\257)s 2 f 273.107 y 69.978 (1)s 13 f 260.187 y 77.162 (\241)s 10 f 269.907 y 82.662 (m;)s 98.532 (\301)s 13 f 260.187 y 105.682 (\242)s 1 f 269.907 y 114.515 (=)s 261.789 y 128.622 (1)s 6 .48 128.622 267.147 r 278.139 y 128.622 (4)s 13 f 249.387 y 136.062 (\050)s 1 f 269.907 y 147.728 (tanh)s 10 f 261.789 y 175.168 (\257)s 7.421 .48 175.168 267.147 r 1 f 278.139 y 175.879 (2)s 269.907 y 184.029 (\050)s 10 f 188.696 (\256)s 1 f 199.083 (+)s 10 f 211.083 (h)s 14 f 264.953 y 217.997 (0)s 1 f 269.907 y 221.364 (\051)s 228.697 (+)s 240.697 (tanh)s 10 f 261.789 y 268.137 (\257)s 7.421 .48 268.137 267.147 r 1 f 278.139 y 268.847 (2)s 269.907 y 276.998 (\050)s 10 f 281.665 (\256)s 12 f 292.052 (\241)s 10 f 304.052 (h)s 14 f 264.953 y 310.966 (0)s 1 f 269.907 y 314.333 (\051)s 13 f 249.387 y 318.999 (\051)s 1 f 314.308 y 125.848 (+)s 306.19 y 139.288 (1)s 6 .48 139.288 311.548 r 322.539 y 139.288 (4)s 10 f 306.19 y 148.168 (m)s 10.536 .48 148.168 311.548 r 1 f 322.539 y 150.436 (2)s 13 f 293.787 y 160.145 (\050)s 1 f 314.308 y 171.811 (tanh)s 10 f 306.19 y 199.251 (\257)s 7.421 .48 199.251 311.548 r 1 f 322.539 y 199.962 (2)s 314.308 y 208.112 (\050)s 10 f 212.779 (\256)s 1 f 223.166 (+)s 10 f 235.166 (h)s 14 f 309.353 y 242.08 (0)s 1 f 314.308 y 245.447 (\051)s 12 f 252.78 (\241)s 1 f 264.78 (tanh)s 10 f 306.19 y 292.22 (\257)s 7.421 .48 292.22 311.548 r 1 f 322.539 y 292.93 (2)s 314.308 y 301.081 (\050)s 10 f 305.747 (\256)s 12 f 316.135 (\241)s 10 f 328.135 (h)s 14 f 309.353 y 335.049 (0)s 1 f 314.308 y 338.415 (\051)s 13 f 293.787 y 343.082 (\051)s 12 f 314.308 y 355.415 (\241)s 1 f 306.19 y 368.855 (3)s 6 .48 368.855 311.548 r 322.539 y 368.855 (4)s 10 f 314.308 y 376.295 (m)s 1 f 358.708 y 125.848 (+)s 10 f 350.59 y 139.288 (\301)s 7.15 .48 139.288 355.948 r 1 f 366.939 y 139.863 (4)s 13 f 338.188 y 147.878 (\050)s 1 f 358.708 y 157.545 (2)s 165.545 (tanh)s 10 f 191.545 (\257)s 198.966 (\256)s 12 f 209.353 (\241)s 1 f 350.59 y 222.793 (1)s 6 .48 222.793 355.948 r 366.939 y 222.793 (2)s 358.708 y 232.233 (tanh)s 10 f 350.59 y 259.673 (\257)s 7.421 .48 259.673 355.948 r 1 f 366.939 y 260.384 (2)s 358.708 y 268.534 (\050)s 10 f 273.201 (\256)s 1 f 283.588 (+)s 10 f 295.588 (h)s 14 f 353.753 y 302.502 (0)s 1 f 358.708 y 305.869 (\051)s 12 f 313.202 (\241)s 1 f 350.59 y 326.642 (1)s 6 .48 326.642 355.948 r 366.939 y 326.642 (2)s 358.708 y 336.082 (tanh)s 10 f 350.59 y 363.522 (\257)s 7.421 .48 363.522 355.948 r 1 f 366.939 y 364.232 (2)s 358.708 y 372.383 (\050)s 10 f 377.049 (\256)s 12 f 387.437 (\241)s 10 f 399.437 (h)s 14 f 353.753 y 406.351 (0)s 1 f 358.708 y 409.717 (\051)s 13 f 338.188 y 414.384 (\051)s 12 f 406.146 y 52.002 (G)s 11 f 400.38 y 59.852 (\257)s 2 f 409.346 y 59.14 (2)s 13 f 396.426 y 66.325 (\241)s 10 f 406.146 y 71.825 (m;)s 87.694 (\301)s 13 f 396.426 y 94.844 (\242)s 1 f 406.146 y 103.677 (=)s 398.028 y 117.784 (1)s 6 .48 117.784 403.386 r 414.378 y 117.784 (4)s 13 f 385.626 y 125.224 (\050)s 1 f 406.146 y 136.891 (tanh)s 10 f 398.028 y 164.331 (\257)s 7.421 .48 164.331 403.386 r 1 f 414.378 y 165.041 (2)s 406.146 y 173.192 (\050)s 10 f 177.858 (\256)s 1 f 188.246 (+)s 10 f 200.246 (h)s 14 f 401.192 y 207.16 (0)s 1 f 406.146 y 210.526 (\051)s 12 f 217.86 (\241)s 1 f 229.859 (tanh)s 10 f 398.028 y 257.299 (\257)s 7.421 .48 257.299 403.386 r 1 f 414.378 y 258.01 (2)s 406.146 y 266.16 (\050)s 10 f 270.827 (\256)s 12 f 281.214 (\241)s 10 f 293.214 (h)s 14 f 401.192 y 300.128 (0)s 1 f 406.146 y 303.495 (\051)s 13 f 385.626 y 308.162 (\051)s 1 f 450.547 y 115.011 (+)s 442.429 y 128.451 (1)s 6 .48 128.451 447.787 r 458.778 y 128.451 (4)s 10 f 442.429 y 137.331 (m)s 10.536 .48 137.331 447.787 r 1 f 458.778 y 139.599 (2)s 13 f 430.027 y 149.307 (\050)s 1 f 450.547 y 160.974 (tanh)s 10 f 442.429 y 188.414 (\257)s 7.421 .48 188.414 447.787 r 1 f 458.778 y 189.124 (2)s 450.547 y 197.274 (\050)s 10 f 201.941 (\256)s 12 f 212.329 (\241)s 10 f 224.329 (h)s 14 f 445.592 y 231.242 (0)s 1 f 450.547 y 234.609 (\051)s 241.942 (+)s 253.942 (tanh)s 10 f 442.429 y 281.382 (\257)s 7.421 .48 281.382 447.787 r 1 f 458.778 y 282.093 (2)s 450.547 y 290.243 (\050)s 10 f 294.91 (\256)s 1 f 305.297 (+)s 10 f 317.297 (h)s 14 f 445.592 y 324.211 (0)s 1 f 450.547 y 327.578 (\051)s 13 f 430.027 y 332.245 (\051)s 12 f 494.947 y 115.011 (\241)s 1 f 486.829 y 128.451 (1)s 6 .48 128.451 492.187 r 503.179 y 128.451 (4)s 10 f 486.829 y 137.331 (\301)s 7.15 .48 137.331 492.187 r 1 f 503.179 y 137.906 (2)s 13 f 474.427 y 145.921 (\050)s 1 f 494.947 y 157.587 (tanh)s 10 f 486.829 y 185.027 (\257)s 7.421 .48 185.027 492.187 r 1 f 503.179 y 185.738 (2)s 494.947 y 193.888 (\050)s 10 f 198.555 (\256)s 1 f 208.942 (+)s 10 f 220.942 (h)s 14 f 489.992 y 227.856 (0)s 1 f 494.947 y 231.223 (\051)s 12 f 238.556 (\241)s 1 f 250.556 (tanh)s 10 f 486.829 y 277.996 (\257)s 7.421 .48 277.996 492.187 r 1 f 503.179 y 278.707 (2)s 494.947 y 286.857 (\050)s 10 f 291.524 (\256)s 12 f 301.911 (\241)s 10 f 313.911 (h)s 14 f 489.992 y 320.825 (0)s 1 f 494.947 y 324.192 (\051)s 13 f 474.427 y 328.858 (\051)s 1 f 494.947 y 341.192 (+)s 486.829 y 354.632 (1)s 6 .48 354.632 492.187 r 503.179 y 354.632 (4)s 13 f 485.227 y 362.072 (\241)s 1 f 494.947 y 367.572 (2)s 12 f 376.238 (\241)s 1 f 388.238 (3)s 10 f 394.238 (\301)s 13 f 485.227 y 401.388 (\242)s 10 f 494.947 y 406.888 (:)s 1 f 450.547 y 439.114 (\0503)s 10 f 449.78 (:)s 1 f 453.114 (8\051)s 22 f 527.898 y 23.11 (Here)s 10 f 544.698 y 105.652 (\256)s 1 f 116.706 (=)s 129.373 (2)s 10 f 135.373 (m)s 12 f 148.576 (\244)s 10 f 157.242 (J)s 1 f 167.717 (+)s 10 f 179.717 (h)s 2 f 546.498 y 186.631 (1)s 10 f 544.698 y 195.348 (;)s 212.681 (h)s 14 f 539.743 y 219.595 (0)s 1 f 544.698 y 226.295 (=)s 10 f 238.961 (h)s 2 f 546.498 y 245.875 (2)s 12 f 544.698 y 253.925 (\241)s 13 f 528.364 y 265.925 (Z)s 2 f 555.631 y 272.592 (I)s 273.899 (R)s 15 f 552.858 y 280.865 (d)s 10 f 544.698 y 288.503 (J)s 1 f 296.312 (\050)s 10 f 300.978 (x)s 1 f 307.837 (\051)s 10 f 312.503 (dx)s 1 f 328.941 (=)s 10 f 341.608 (h)s 2 f 546.498 y 348.521 (2)s 12 f 544.698 y 356.571 (\241)s 1 f 368.571 (1)s 10 f 377.905 (:)s 22 f 573.715 y 23.11 (and)s 12 f 46.443 (\244)s 22 f 56.443 (denotes)s 99.843 (the)s 120.51 (con)s 138.177 (v)s 144.177 (olution)s 1 f 180.843 (.)s 607.706 y 8.71 (The)s 33.243 (limiting)s 77.777 (equations)s 131.377 (for)s 149.611 (the)s 170.144 (Ka)s 185.144 (w)s 193.478 (asaki)s 223.745 (dynamics)s 276.678 (can)s 298.545 (b)s 305.545 (e)s 314.745 (rewritten)s 366.679 (in)s 380.546 (a)s 390.413 (nice)s 414.946 (form)s 443.18 (as)s 457.78 (a)s 624.506 y -5.69 (gradien)s 32.677 (t)s 41.3 (\260)s 47.967 (ux)s 64.924 (asso)s 86.724 (ciated)s 122.015 (with)s 149.305 (the)s 169.929 (lo)s 179.596 (cal)s 198.22 (mean)s 230.177 (\257eld)s 256.134 (free)s 279.125 (energy)s 317.448 (functional.)s 378.434 (Put)s 10 f 401.891 (u)s 6.869 .48 401.891 626.426 r 1 f 624.506 y 412.094 (:=)s 428.094 (\050)s 10 f 432.761 (m;)s 448.63 (\301)s 1 f 455.78 (\051.)s 641.306 y -5.69 (De\257ne)s 31.477 (the)s 52.143 (free)s 75.177 (energy)s 113.543 (functional)s 169.877 (as)s 12 f 671.411 y 74.623 (F)s 1 f 84.44 (\050)s 10 f 89.106 (u)s 6.869 .48 89.106 673.331 r 1 f 671.411 y 95.976 (\051)s 103.976 (:=)s 12 f 119.976 (\241)s 1 f 663.293 y 131.46 (1)s 7.421 .48 130.749 668.651 r 10 f 679.643 y 130.749 (\257)s 13 f 655.078 y 141.61 (Z)s 10 f 671.411 y 155.61 (dr)s 171.603 (s)s 13 f 661.691 y 177.228 (\241)s 10 f 671.411 y 182.728 (u)s 6.869 .48 182.728 673.331 r 1 f 671.411 y 189.597 (\050)s 10 f 194.264 (r)s 1 f 200.011 (\051)s 13 f 661.691 y 204.678 (\242)s 12 f 671.411 y 212.845 (\241)s 13 f 655.078 y 224.845 (Z)s 10 f 671.411 y 238.845 (dr)s 13 f 655.078 y 252.838 (Z)s 10 f 671.411 y 266.838 (dr)s 14 f 666.456 y 278.831 (0)s 10 f 671.411 y 282.197 (J)s 1 f 290.006 (\050)s 10 f 294.672 (r)s 12 f 303.086 (\241)s 10 f 315.086 (r)s 14 f 666.456 y 320.833 (0)s 1 f 671.411 y 324.2 (\051)s 10 f 328.867 (m)s 1 f 339.403 (\050)s 10 f 344.07 (r)s 1 f 349.817 (\051)s 10 f 354.484 (m)s 1 f 365.02 (\050)s 10 f 369.686 (r)s 14 f 666.456 y 375.434 (0)s 1 f 671.411 y 378.8 (\051)s 705.976 y 223.045 (14)s do-end end endp %%Page: 15 15 %%BeginPageSetup initializepage (Raffaele Esposito; page: 15 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f0_12 sf ( )S -996 -1000 :M f1_12 sf ( )S -993 -1000 :M f2_12 sf ( )S -989 -1000 :M f10_12 sf ( )S -981 -1000 :M f11_12 sf ( )S -972 -1000 :M f12_12 sf ( )S -960 -1000 :M f13_12 sf ( )S -951 -1000 :M f14_12 sf ( )S -937 -1000 :M f15_12 sf ( )S -926 -1000 :M f16_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 1200 1000 div mul /CMBX10 findfont fdef 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 16 5 1200 1000 div mul /CMR5 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 6.31 y -5.69 (and)s 17.643 (the)s 38.31 (mobilit)s 75.31 (y)s 85.643 (matrix)s 124.677 (as)s 10 f 46.886 y 91.067 (M)s 1 f 107.351 (=)s 12 f 120.017 (\241)s 10 f 129.351 (\257)s 1 f 136.771 ([)s 10 f 140.105 (H)s 151.055 (ess)s 1 f 167.892 (\050)s 10 f 172.559 (s)s 1 f 178.184 (\051])s 14 f 41.931 y 186.184 (\241)s 2 f 193.684 (1)s 1 f 46.886 y 202.401 (=)s 10 f 215.067 (\257)s 1 f 222.488 (\0501)s 12 f 235.821 (\241)s 10 f 247.821 (\301)s 1 f 254.971 (\051)s 13 f 29.966 y 261.638 (\265)s 10 f 41.007 y 272.471 (\301)s 1 f 282.288 (+)s 11 f 35.653 y 295.728 (\301)s 16 f 32.032 y 301.498 (2)s 14 f 35.653 y 306.181 (\241)s 11 f 313.681 (m)s 16 f 32.032 y 322.197 (2)s 31.152 .48 295.728 38.247 r 2 f 45.145 y 302.277 (1)s 14 f 307.061 (\241)s 11 f 314.561 (\301)s 10 f 41.007 y 340.32 (m)s 55.407 y 295.127 (m)s 342.013 (\301)s 13 f 29.966 y 352.856 (\266)s 10 f 46.886 y 363.689 (:)s 1 f 88.129 y -5.69 (Then)s 25.643 (equations)s 79.377 (\0503.5\051)s 108.043 (b)s 115.043 (ecome)s 10 f 118.452 y 177.095 (@)s 11 f 120.252 y 183.466 (t)s 10 f 118.452 y 187.691 (u)s 6.869 .48 187.691 120.372 r 1 f 118.452 y 197.894 (=)s 12 f 210.561 (r)s 13 f 97.931 y 220.561 (\303)s 10 f 118.452 y 230.061 (M)s 12 f 243.011 (r)s 10 f 110.334 y 254.451 (\261)s 12 f 260.238 (F)s 15.604 .48 254.451 115.692 r 10 f 126.683 y 255.924 (\261)s 261.712 (u)s 6.869 .48 261.712 128.603 r 13 f 97.931 y 271.495 (!)s 1 f 157.135 y 8.71 (W)s 20.043 (riting)s 52.743 (the)s 73.41 (free)s 96.443 (energy)s 134.81 (functional)s 12 f 191.143 (F)s 1 f 204.96 (in)s 218.96 (the)s 239.627 (equiv)s 266.96 (alen)s 287.96 (t)s 296.627 (form)s 13 f 176.551 y 87.856 (Z)s 10 f 192.885 y 101.856 (dr)s 113.849 (f)s 2 f 187.93 y 121.015 (0)s 13 f 183.165 y 126.399 (\241)s 10 f 192.885 y 131.899 (u)s 6.869 .48 131.899 194.805 r 1 f 192.885 y 138.768 (\050)s 10 f 143.435 (r)s 1 f 149.182 (\051)s 13 f 183.165 y 153.849 (\242)s 1 f 192.885 y 162.016 (+)s 184.767 y 175.456 (1)s 6 .48 175.456 190.125 r 201.116 y 175.456 (2)s 13 f 176.551 y 184.895 (Z)s 10 f 192.885 y 198.895 (dr)s 13 f 176.551 y 212.888 (Z)s 10 f 192.885 y 226.888 (dr)s 14 f 187.93 y 238.882 (0)s 10 f 192.885 y 242.248 (J)s 1 f 250.057 (\050)s 10 f 254.723 (r)s 12 f 263.137 (\241)s 10 f 275.137 (r)s 14 f 187.93 y 280.884 (0)s 1 f 192.885 y 284.251 (\051[)s 10 f 292.251 (m)s 1 f 302.787 (\050)s 10 f 307.454 (r)s 1 f 313.201 (\051)s 12 f 320.534 (\241)s 10 f 332.534 (m)s 1 f 343.07 (\050)s 10 f 347.737 (r)s 14 f 187.93 y 353.484 (0)s 1 f 192.885 y 356.851 (\051])s 2 f 187.93 y 364.851 (2)s 1 f 226.274 y -5.69 (with)s 10 f 244.596 y 152.651 (f)s 2 f 239.642 y 159.818 (0)s 13 f 234.876 y 165.201 (\241)s 10 f 244.596 y 170.701 (u)s 6.869 .48 170.701 246.516 r 1 f 244.596 y 177.571 (\051)s 185.571 (:=)s 12 f 201.571 (\241)s 10 f 210.904 (m)s 2 f 239.642 y 221.44 (2)s 1 f 244.596 y 229.49 (+)s 10 f 241.49 (\301)s 12 f 251.307 (\241)s 10 f 263.307 (\257)s 14 f 239.642 y 270.728 (\241)s 2 f 278.228 (1)s 10 f 244.596 y 283.611 (s)s 1 f 289.236 (\050)s 10 f 293.903 (u)s 6.869 .48 293.903 246.516 r 1 f 244.596 y 300.772 (\051)s 271.319 y -5.69 (w)s 2.643 (e)s 13.303 (see)s 34.03 (that)s 12 f 61.356 (F)s 1 f 76.5 (reduces)s 120.593 (for)s 140.286 (homogeneous)s 215.013 (pro\257les)s 257.773 (of)s 272.767 (magnetization)s 352.094 (and)s 376.754 (concen)s 411.754 (tration)s 453.114 (to)s 288.119 y -5.69 (the)s 16.131 (non)s 40.619 (con)s 58.286 (v)s 64.286 (ex)s 81.107 (free)s 105.295 (energy)s 10 f 144.817 (f)s 2 f 283.764 y 151.983 (0)s 1 f 288.119 y 162.521 (of)s 177.343 (the)s 199.164 (KBC)s 230.818 (mo)s 247.151 (del,)s 271.261 (so)s 287.149 (that)s 314.304 (the)s 336.125 (stationary)s 394.38 (homogeneous)s 304.919 y -5.69 (solutions)s 45.891 (of)s 61.005 (the)s 83.119 (equations)s 138.3 (\0503.5\051)s 168.414 (coincide)s 215.861 (with)s 244.642 (the)s 266.756 (solutions)s 318.337 (of)s 333.451 (\0502.8\051.)s 371.126 (Moreo)s 403.826 (v)s 409.826 (er,)s 12 f 429.002 (F)s 1 f 444.266 (is)s 457.78 (a)s 321.719 y -5.69 (Liapuno)s 36.81 (v)s 47.166 (functional)s 103.522 (for)s 121.912 (the)s 142.602 (ev)s 153.935 (olution,)s 197.964 (namely)s 239.653 (is)s 251.743 (decreasing)s 309.866 (in)s 323.889 (time)s 351.245 (along)s 383.268 (the)s 403.957 (solutions)s 454.114 (of)s 338.519 y -5.69 (the)s 14.976 (equations)s 68.71 (\0503.5\051.)s 102.043 (This)s 129.443 (follo)s 151.443 (ws)s 168.843 (from)s 197.21 (\0501.7\051)s 225.877 (and)s 249.21 (the)s 269.877 (p)s 276.877 (ositivit)s 312.944 (y)s 323.277 (of)s 336.944 (the)s 357.611 (matrix)s 10 f 396.644 (M)s 1 f 409.594 (.)s 355.946 y 8.71 (On)s 28.047 (the)s 48.051 (con)s 65.718 (trary)s 91.118 (,)s 97.922 (in)s 111.259 (the)s 131.263 (Glaub)s 163.68 (er)s 177.051 (case)s 201.788 (the)s 221.792 (limiting)s 265.797 (equations)s 318.868 (\0503.7\051-\0503.8\051)s 375.539 (are)s 394.909 (rather)s 430.314 (messy)s 460.447 (.)s 372.746 y -5.69 (It)s 9.048 (is)s 22.852 (not)s 45.923 (ev)s 57.256 (en)s 74.994 (kno)s 93.661 (wn)s 114.732 (if)s 127.469 (the)s 149.874 (energy)s 189.978 (functional)s 248.049 (is)s 261.854 (a)s 273.591 (Liapuno)s 316.092 (v)s 328.163 (functional:)s 392.638 (w)s 400.972 (e)s 412.043 (ha)s 424.376 (v)s 430.376 (e)s 441.447 (only)s 389.546 y -5.69 (n)s .643 (umerical)s 49.343 (evidence.)s 406.974 y 8.71 (The)s 33.735 (region)s 70.126 (D)s 83.65 (in)s 98.008 (the)s 119.033 (plane)s 151.391 (\050)s 10 f 156.058 (m;)s 171.927 (\301)s 1 f 179.077 (\051,)s 191.525 (suc)s 207.925 (h)s 218.949 (that)s 10 f 245.307 (D)s 1 f 259.506 (=)s 12 f 272.769 (f)s 10 f 278.769 (m;)s 294.638 (\301)s 1 f 305.718 (:)s 312.982 (0)s 12 f 322.912 (\267)s 10 f 336.175 (\301)s 12 f 347.255 (\267)s 1 f 360.518 (1)s 10 f 366.518 (;)s 12 f 371.851 (j)s 10 f 375.185 (m)s 12 f 385.721 (j)s 392.984 (\267)s 10 f 406.247 (\301;)s 12 f 418.731 (g)s 1 f 429.089 (can)s 451.447 (b)s 458.447 (e)s 423.774 y -5.69 (partitioned)s 56.343 (for)s 74.71 (an)s 87.043 (y)s 97.377 (\257xed)s 10 f 126.377 (\257)s 12 f 137.131 (\270)s 1 f 420.607 y 151.508 (\271)s 10 f 423.774 y 149.797 (\257)s 11 f 425.574 y 156.585 (c)s 1 f 423.774 y 165.473 (in)s 179.473 (three)s 210.173 (parts:)s 441.201 y 8.71 (a\051)s 22.544 (the)s 42.378 (unstable)s 89.612 (region)s 10 f 136.813 (U)s 1 f 149.647 (=)s 12 f 162.314 (f)s 1 f 168.314 (\050)s 10 f 172.981 (m;)s 188.85 (\301)s 1 f 196 (\051)s 12 f 204 (2)s 10 f 215.333 (F)s 1 f 228.05 (:)s 10 f 237.884 (\301)s 12 f 246.035 (\241)s 10 f 256.37 (m)s 2 f 436.846 y 266.906 (2)s 12 f 441.201 y 275.623 (\270)s 1 f 288.289 (\0502)s 10 f 298.956 (\257)s 1 f 306.377 (\051)s 14 f 436.846 y 311.043 (\241)s 2 f 318.544 (1)s 12 f 441.201 y 323.927 (g)s 1 f 329.927 (,)s 336.594 (where)s 10 f 370.461 (F)s 1 f 383.012 (is)s 394.246 (the)s 414.08 (forbidden)s 458.001 y -5.69 (region)s 30.343 (de\257ned)s 71.677 (after)s 100.043 (\0502.9\051.)s 475.429 y 8.71 (b\051)s 24.043 (the)s 44.71 (metastable)s 105.443 (region)s 10 f 153.477 (M)s 1 f 169.76 (=)s 12 f 182.427 (f)s 1 f 188.427 (\050)s 10 f 193.093 (m;)s 208.963 (\301)s 1 f 216.113 (\051)s 12 f 224.113 (2)s 10 f 235.446 (F)s 1 f 248.163 (:)s 10 f 258.829 (\301)s 12 f 268.646 (\241)s 10 f 280.646 (m)s 2 f 471.074 y 291.182 (2)s 10 f 475.429 y 299.898 (\074)s 1 f 312.565 (\0502)s 10 f 323.232 (\257)s 1 f 330.653 (\051)s 14 f 471.074 y 335.319 (\241)s 2 f 342.819 (1)s 12 f 475.429 y 348.203 (g)s 1 f 492.856 y 8.71 (c\051)s 22.71 (the)s 43.376 (stable)s 78.11 (region)s 10 f 126.143 (D)s 12 f 139.078 (\241)s 1 f 151.078 (\050)s 10 f 155.745 (U)s 12 f 167.913 ([)s 10 f 178.58 (M)s 1 f 191.53 (\051.)s 517.112 y 8.71 (The)s 34.45 (segregation)s 98.291 (phenomena)s 162.698 (ma)s 178.364 (y)s 189.771 (app)s 209.438 (ear)s 230.545 (b)s 236.878 (y)s 248.285 (c)s 253.285 (ho)s 266.285 (osing)s 298.092 (an)s 315.833 (initial)s 351.573 (datum)s 390.647 (corresp)s 428.447 (onding)s 533.912 y -5.69 (to)s 10.853 (total)s 41.396 (magnetization)s 121.273 (and)s 146.482 (concen)s 181.482 (tration)s 223.392 (in)s 239.269 (the)s 261.812 (unstable)s 311.755 (region.)s 358.084 (One)s 385.294 (exp)s 403.961 (ects)s 429.904 (that)s 457.78 (a)s 550.712 y -5.69 (stationary)s 51.41 (solution)s 96.81 (of)s 110.477 (the)s 131.143 (equations)s 184.877 (\0503.5\051)s 213.544 (with)s 240.877 (this)s 264.277 (initial)s 298.944 (condition)s 351.611 (b)s 358.611 (e)s 367.944 (unstable.)s 0 f 585.211 y 8.71 (4.)s 25.576 (Diric)s 55.26 (hlet)s 83.051 (form)s 115.951 (estimates)s 176.862 (for)s 198.262 (Ka)s 215.404 (w)s 224.987 (asaki)s 259.563 (dynamics.)s 1 f 610.854 y -5.69 (The)s 19.977 (pro)s 37.677 (of)s 52.344 (of)s 67.011 (Theorem)s 118.711 (3.1)s 139.044 (is)s 152.111 (based)s 186.511 (on)s 204.178 (a)s 215.179 (priori)s 248.912 (estimates)s 302.712 (uniform)s 348.746 (in)s 363.746 (the)s 385.413 (v)s 391.413 (olume)s 427.747 (for)s 447.114 (the)s 627.654 y -5.69 (en)s 5.976 (trop)s 27.677 (y)s 38.26 (and)s 61.844 (the)s 82.761 (Diric)s 108.295 (hlet)s 132.545 (form,)s 164.558 (whic)s 188.225 (h)s 199.142 (are)s 219.426 (giv)s 234.759 (en)s 251.01 (in)s 265.26 (this)s 288.911 (section.)s 334.395 (F)s 341.229 (or)s 356.179 (eac)s 372.513 (h)s 383.43 (p)s 390.43 (ositiv)s 418.497 (e)s 428.08 (in)s 437.747 (teger)s 10 f 644.454 y -5.69 (n)s 1 f 5.513 (and)s 28.846 (a)s 38.846 (measure)s 10 f 85.613 (\271)s 1 f 96.843 (on)s 113.51 (\255)s 11 f 646.254 y 122.177 (n)s 1 f 644.454 y 132.042 (=)s 12 f 144.709 (f\241)s 1 f 160.042 (1)s 10 f 166.042 (;)s 1 f 171.375 (0)s 10 f 177.375 (;)s 1 f 182.709 (1)s 12 f 188.709 (g)s 2 f 640.099 y 194.709 (\244)s 15 f 641.299 y 201.275 (n)s 1 f 644.454 y 207.76 (,)s 215.093 (w)s 223.427 (e)s 232.76 (denote)s 271.427 (b)s 277.76 (y)s 10 f 288.094 (\271)s 11 f 646.254 y 295.324 (n)s 1 f 644.454 y 305.856 (the)s 326.523 (marginal)s 376.556 (of)s 10 f 390.223 (\271)s 1 f 401.454 (on)s 418.12 (\255)s 11 f 646.254 y 426.787 (n)s 1 f 644.454 y 433.319 (,)s 10 f 677.176 y 80.29 (\271)s 11 f 678.976 y 87.52 (n)s 1 f 677.176 y 94.052 (\050)s 10 f 98.719 (\273)s 1 f 104.521 (\051)s 112.521 (=)s 10 f 125.187 (\271)s 13 f 667.456 y 132.418 (\251)s 10 f 677.176 y 139.418 (\276)s 1 f 153.372 (:)s 10 f 163.372 (\276)s 1 f 170.659 (\050)s 10 f 175.326 (i)s 1 f 179.46 (\051)s 187.46 (=)s 10 f 200.127 (\273)s 1 f 205.929 (\050)s 10 f 210.596 (i)s 1 f 214.73 (\051)s 226.063 (for)s 12 f 244.43 (j)s 10 f 247.763 (i)s 12 f 251.897 (j)s 258.564 (\267)s 10 f 271.23 (n)s 13 f 667.456 y 278.433 (\252)s 1 f 677.176 y 293.433 (for)s 311.8 (eac)s 328.133 (h)s 10 f 338.8 (\273)s 12 f 347.935 (2)s 1 f 359.268 (\255)s 11 f 678.976 y 367.935 (n)s 10 f 677.176 y 374.467 (:)s 1 f 705.976 y 223.045 (15)s do-end end endp %%Page: 16 16 %%BeginPageSetup initializepage (Raffaele Esposito; page: 16 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f1_12 sf ( )S -997 -1000 :M f2_12 sf ( )S -993 -1000 :M f10_12 sf ( )S -985 -1000 :M f11_12 sf ( )S -976 -1000 :M f12_12 sf ( )S -964 -1000 :M f13_12 sf ( )S -954 -1000 :M f14_12 sf ( )S -941 -1000 :M f15_12 sf ( )S -930 -1000 :M f16_12 sf ( )S -925 -1000 :M f18_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 16 5 1200 1000 div mul /CMR5 findfont fdef 18 5 1200 1000 div mul /CMSY5 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 6.31 y -5.69 (F)s 1.143 (or)s 15.361 (a)s 24.88 (c)s 29.88 (hemical)s 73.398 (p)s 80.398 (oten)s 102.731 (tial)s 10 f 123.583 (P)s 1 f 132.954 (,)s 139.902 (and)s 162.753 (a)s 172.271 (p)s 179.271 (ositiv)s 207.338 (e)s 216.19 (in)s 225.856 (teger)s 10 f 255.408 (n)s 1 f 262.611 (,)s 269.559 (w)s 277.892 (e)s 286.743 (denote)s 324.928 (b)s 331.262 (y)s 10 f 341.113 (s)s 11 f 8.11 y 346.738 (n)s 1 f 6.31 y 353.27 (\050)s 10 f 357.937 (\271)s 11 f 8.11 y 365.167 (n)s 12 f 6.31 y 371.699 (j)s 10 f 375.033 (\272)s 11 f 8.11 y 380.961 (P)s 387.329 (;n)s 1 f 6.31 y 396.711 (\051)s 404.895 (the)s 425.08 (relativ)s 458.447 (e)s 23.11 y -5.69 (en)s 5.976 (trop)s 27.677 (y)s 38.01 (of)s 10 f 51.677 (\271)s 11 f 24.91 y 58.907 (n)s 1 f 23.11 y 69.439 (with)s 96.773 (resp)s 118.539 (ect)s 137.873 (to)s 10 f 152.539 (\272)s 11 f 24.91 y 158.467 (P)s 164.835 (;n)s 10 f 57.566 y 59.31 (s)s 11 f 59.366 y 64.935 (n)s 1 f 57.566 y 71.467 (\050)s 10 f 76.134 (\271)s 11 f 59.366 y 83.365 (n)s 12 f 57.566 y 89.897 (j)s 10 f 93.23 (\272)s 11 f 59.366 y 99.158 (P)s 105.526 (;n)s 1 f 57.566 y 114.908 (\051)s 122.908 (=)s 149.252 (sup)s 11 f 68.2 y 135.574 (U)s 14 f 143.012 (2)s 11 f 149.479 (C)s 15 f 69.473 y 156.362 (b)s 2 f 68.2 y 160.762 (\050\255)s 15 f 69.4 y 171.362 (n)s 2 f 68.2 y 177.246 (\051)s 13 f 44.246 y 182.996 (n)s 41.233 y 192.996 (Z)s 10 f 57.566 y 206.996 (U)s 1 f 216.498 (\050)s 10 f 221.165 (\276)s 1 f 228.452 (\051)s 10 f 233.119 (d\271)s 11 f 59.366 y 246.595 (n)s 1 f 57.566 y 253.127 (\050)s 10 f 257.794 (\276)s 1 f 265.081 (\051)s 12 f 272.415 (\241)s 1 f 284.415 (log)s 13 f 41.233 y 301.915 (Z)s 10 f 57.566 y 315.915 (e)s 11 f 52.612 y 321.502 (U)s 2 f 328.94 (\050)s 11 f 332.69 (\276)s 2 f 338.552 (\051)s 10 f 57.566 y 342.902 (d\272)s 11 f 59.366 y 355.076 (P)s 361.444 (;n)s 1 f 57.566 y 370.826 (\050)s 10 f 375.492 (\276)s 1 f 382.78 (\051)s 13 f 44.246 y 387.446 (o)s 10 f 57.566 y 395.446 (:)s 1 f 95.189 y -5.69 (In)s 8.886 (this)s 31.862 (form)s 55.895 (ula)s 10 f 75.471 (C)s 11 f 96.989 y 84.048 (b)s 1 f 95.189 y 88.868 (\050\255)s 11 f 96.989 y 102.201 (n)s 1 f 95.189 y 108.733 (\051)s 116.976 (stands)s 154.019 (for)s 171.961 (the)s 192.204 (space)s 223.847 (of)s 237.089 (all)s 253.332 (functions)s 304.641 (on)s 320.884 (\255)s 11 f 96.989 y 329.551 (n)s 1 f 95.189 y 336.083 (.)s 344.608 (Since)s 375.517 (the)s 395.76 (measure)s 10 f 442.103 (\272)s 11 f 96.989 y 448.03 (P)s 454.398 (;n)s 1 f 111.989 y -5.69 (giv)s 9.643 (es)s 24.374 (a)s 35.039 (p)s 42.039 (ositiv)s 70.106 (e)s 80.103 (probabilit)s 131.137 (y)s 142.135 (to)s 157.466 (eac)s 173.799 (h)s 185.13 (con\257guration,)s 261.994 (all)s 279.326 (the)s 300.657 (measures)s 352.821 (on)s 370.152 (\255)s 11 f 113.789 y 378.819 (n)s 1 f 111.989 y 390.016 (are)s 410.713 (absolutely)s 128.789 y -5.69 (con)s 11.976 (tin)s 26.31 (uous)s 54.377 (with)s 81.71 (resp)s 103.477 (ect)s 122.81 (to)s 10 f 137.477 (\272)s 11 f 130.589 y 143.404 (P)s 149.772 (;n)s 1 f 128.789 y 163.154 (and)s 186.488 (w)s 194.821 (e)s 204.154 (ha)s 216.488 (v)s 222.488 (e)s 231.821 (an)s 248.488 (explicit)s 290.821 (form)s 314.855 (ula)s 334.855 (for)s 353.221 (the)s 373.888 (en)s 385.555 (trop)s 407.255 (y)s 417.588 (:)s 10 f 163.246 y 135.001 (s)s 11 f 165.046 y 140.626 (n)s 1 f 163.246 y 147.158 (\050)s 10 f 151.825 (\271)s 11 f 165.046 y 159.055 (n)s 12 f 163.246 y 165.587 (j)s 10 f 168.921 (\272)s 11 f 165.046 y 174.849 (P)s 181.217 (;n)s 1 f 163.246 y 190.599 (\051)s 198.598 (=)s 13 f 146.912 y 211.265 (Z)s 1 f 163.246 y 225.265 (log)s 242.765 (\050)s 10 f 247.432 (f)s 11 f 165.046 y 253.307 (n)s 1 f 163.246 y 259.839 (\050)s 10 f 264.505 (\276)s 1 f 271.793 (\051\051)s 10 f 283.126 (d\271)s 11 f 165.046 y 296.603 (n)s 1 f 163.246 y 303.135 (\050)s 10 f 307.801 (\276)s 1 f 315.089 (\051)s 10 f 319.755 (;)s 1 f 196.602 y -5.69 (where)s 10 f 28.833 (f)s 11 f 198.402 y 34.708 (n)s 1 f 196.602 y 45.063 (is)s 56.953 (the)s 77.443 (probabilit)s 128.477 (y)s 138.633 (densit)s 169.7 (y)s 179.856 (of)s 10 f 193.346 (\271)s 11 f 198.402 y 200.577 (n)s 1 f 196.602 y 210.932 (with)s 238.089 (resp)s 259.855 (ect)s 279.012 (to)s 10 f 293.502 (\272)s 11 f 198.402 y 299.43 (P)s 305.798 (;n)s 1 f 196.602 y 315.18 (.)s 323.787 (Notice)s 361.277 (that)s 387.1 (b)s 393.434 (y)s 403.59 (the)s 424.08 (en)s 435.747 (trop)s 457.447 (y)s 213.402 y -5.69 (con)s 11.976 (v)s 17.977 (exit)s 37.31 (y)s 47.643 (and)s 70.977 (since)s 100.377 (sup)s 11 f 216.335 y 118.443 (\276)s 1 f 213.402 y 126.905 (sup)s 11 f 216.335 y 144.972 (i)s 12 f 213.402 y 150.967 (j)s 10 f 154.301 (\276)s 1 f 161.588 (\050)s 10 f 166.255 (i)s 1 f 170.389 (\051)s 12 f 175.056 (j)s 1 f 182.389 (is)s 194.456 (\257nite,)s 228.456 (w)s 236.789 (e)s 246.122 (ha)s 258.456 (v)s 264.456 (e)s 10 f 240.092 y 177.534 (s)s 11 f 241.892 y 183.159 (n)s 1 f 240.092 y 189.691 (\050)s 10 f 194.358 (\271)s 11 f 241.892 y 201.588 (n)s 12 f 240.092 y 208.12 (j)s 10 f 211.454 (\272)s 11 f 241.892 y 217.381 (P)s 223.749 (;n)s 1 f 240.092 y 233.131 (\051)s 12 f 241.131 (\267)s 10 f 253.798 (C)s 2 f 241.892 y 262.374 (0)s 10 f 240.092 y 267.758 (n)s 11 f 235.137 y 274.961 (d)s 1 f 240.092 y 439.114 (\0504)s 10 f 449.78 (:)s 1 f 453.114 (1\051)s 266.781 y -5.69 (for)s 12.677 (some)s 42.743 (constan)s 82.477 (t)s 10 f 91.143 (C)s 2 f 268.581 y 99.72 (0)s 1 f 266.781 y 109.103 (that)s 135.103 (dep)s 154.103 (ends)s 181.503 (on)s 10 f 198.17 (P)s 1 f 211.541 (\050cf.)s 233.874 ([KL]\051.)s 283.702 y 8.71 (De\257ne)s 45.106 (the)s 65.003 (Diric)s 90.536 (hlet)s 113.766 (form)s 10 f 141.363 (D)s 11 f 285.501 y 151.298 (n)s 1 f 283.702 y 157.83 (\050)s 10 f 162.497 (\271)s 11 f 285.501 y 169.727 (n)s 12 f 283.702 y 176.259 (j)s 10 f 179.593 (\272)s 11 f 285.501 y 185.52 (P)s 191.888 (;n)s 1 f 283.702 y 201.27 (\051)s 209.167 (of)s 222.064 (the)s 241.96 (measure)s 10 f 287.957 (\271)s 11 f 285.501 y 295.187 (n)s 1 f 283.702 y 304.949 (with)s 331.513 (resp)s 353.279 (ect)s 371.843 (to)s 10 f 385.739 (\272)s 11 f 285.501 y 391.667 (P)s 398.035 (;n)s 1 f 283.702 y 410.647 (asso)s 432.447 (ciated)s 300.502 y -5.69 (to)s 8.976 (the)s 29.643 (exclusion)s 81.377 (pro)s 99.077 (cess)s 123.21 (b)s 129.543 (y)s 10 f 333.858 y 99.887 (D)s 11 f 335.658 y 109.822 (n)s 1 f 333.858 y 116.354 (\050)s 10 f 121.021 (\271)s 11 f 335.658 y 128.251 (n)s 12 f 333.858 y 134.783 (j)s 10 f 138.117 (\272)s 11 f 335.658 y 144.044 (P)s 150.412 (;n)s 1 f 333.858 y 159.794 (\051)s 167.794 (=)s 12 f 180.461 (\241)s 13 f 317.525 y 191.794 (Z)s 323.012 y 205.794 (p)s 12.407 .48 217.794 323.012 r 10 f 333.858 y 217.794 (f)s 11 f 335.658 y 223.669 (n)s 1 f 333.858 y 230.201 (\050)s 10 f 234.868 (\276)s 1 f 242.155 (\051)s 13 f 324.138 y 246.822 (\241)s 12 f 333.858 y 252.322 (L)s 2 f 328.903 y 260.599 (0)s 11 f 336.825 y 260.599 (n)s 13 f 323.012 y 267.131 (p)s 12.407 .48 279.131 323.012 r 10 f 333.858 y 279.131 (f)s 11 f 335.658 y 285.006 (n)s 13 f 324.138 y 291.538 (\242)s 1 f 333.858 y 297.038 (\050)s 10 f 301.705 (\276)s 1 f 308.992 (\051)s 10 f 313.659 (d\272)s 11 f 335.658 y 325.832 (P)s 332.2 (;n)s 1 f 333.858 y 341.582 (\050)s 10 f 346.249 (\276)s 1 f 353.536 (\051)s 365.192 y 171.794 (=)s 13 f 353.791 y 191.902 (X)s 15 f 377.87 y 187.142 (i;j)s 18 f 196.976 (2)s 16 f 202.643 (\244)s 15 f 379.07 y 208.11 (n)s 18 f 385.01 y 185.901 (j)s 15 f 188.651 (i)s 18 f 191.852 (\241)s 15 f 198.352 (j)s 18 f 202.235 (j)s 16 f 204.985 (=1)s 10 f 365.192 y 218.676 (I)s 11 f 366.992 y 223.951 (i;j)s 1 f 365.192 y 235.252 (\050)s 10 f 239.919 (f)s 11 f 366.992 y 245.794 (n)s 1 f 365.192 y 252.326 (\051)s 10 f 256.992 (;)s 1 f 411.4 y -5.69 (where)s 10 f 29.01 (I)s 11 f 413.2 y 34.285 (i;j)s 1 f 411.4 y 45.586 (\050)s 10 f 50.253 (:)s 1 f 53.586 (\051)s 62.253 (is)s 74.32 (giv)s 89.653 (en)s 105.653 (b)s 111.986 (y)s 10 f 445.856 y 110.631 (I)s 11 f 447.656 y 115.906 (i;j)s 1 f 445.856 y 127.207 (\050)s 10 f 131.874 (f)s 11 f 447.656 y 137.749 (n)s 1 f 445.856 y 144.281 (\051)s 152.281 (=)s 12 f 164.948 (\241)s 13 f 429.523 y 176.281 (Z)s 435.01 y 190.281 (p)s 12.407 .48 202.281 435.01 r 10 f 445.856 y 202.281 (f)s 11 f 447.656 y 208.156 (n)s 1 f 445.856 y 214.688 (\050)s 10 f 219.355 (\276)s 1 f 226.642 (\051)s 13 f 436.136 y 231.309 (\241)s 12 f 445.856 y 236.809 (L)s 2 f 440.901 y 245.085 (0)s 11 f 448.823 y 245.085 (i;j)s 13 f 435.01 y 256.387 (p)s 12.407 .48 268.387 435.01 r 10 f 445.856 y 268.387 (f)s 11 f 447.656 y 274.262 (n)s 13 f 436.136 y 280.794 (\242)s 1 f 445.856 y 286.294 (\050)s 10 f 290.961 (\276)s 1 f 298.248 (\051)s 10 f 302.915 (d\272)s 11 f 447.656 y 315.088 (P)s 321.456 (;n)s 1 f 445.856 y 330.838 (\050)s 10 f 335.505 (\276)s 1 f 342.792 (\051)s 481.526 y -5.69 (and)s 17.643 (I)s 19.817 (L)s 2 f 476.293 y 27.317 (0)s 11 f 484.493 y 27.317 (n)s 1 f 481.526 y 37.849 (is)s 49.915 (the)s 70.582 (restriction)s 128.049 (of)s 141.715 (the)s 162.382 (pro)s 180.082 (cess)s 204.215 (to)s 218.882 (the)s 239.549 (b)s 246.549 (o)s 252.216 (x)s 262.549 (\244)s 11 f 483.326 y 270.882 (n)s 1 f 508.216 y 183.681 (I)s 185.854 (L)s 2 f 502.982 y 193.354 (0)s 11 f 511.182 y 193.354 (n)s 1 f 508.216 y 203.22 (=)s 13 f 496.816 y 223.327 (X)s 15 f 520.894 y 218.567 (i;j)s 18 f 228.402 (2)s 16 f 234.068 (\244)s 15 f 522.094 y 239.535 (n)s 18 f 528.034 y 217.326 (j)s 15 f 220.076 (i)s 18 f 223.278 (\241)s 15 f 229.778 (j)s 18 f 233.661 (j)s 16 f 236.411 (=1)s 1 f 508.216 y 250.101 (I)s 252.274 (L)s 2 f 502.982 y 259.774 (0)s 11 f 511.182 y 259.774 (i;j)s 10 f 508.216 y 271.076 (:)s 1 f 556.491 y -5.69 (Here)s 22.39 (for)s 40.471 (a)s 50.185 (b)s 57.185 (ond)s 80.232 (\050)s 10 f 84.899 (i;)s 94.366 (j)s 1 f 99.995 (\051)s 12 f 107.995 (2)s 10 f 119.328 (Z)s 122.378 (Z)s 11 f 551.257 y 133.428 (d)s 12 f 556.491 y 141.118 (\243)s 10 f 152.546 (Z)s 155.596 (Z)s 11 f 551.257 y 166.646 (d)s 1 f 556.491 y 172.242 (,)s 179.346 (I)s 181.52 (L)s 2 f 551.257 y 189.02 (0)s 11 f 559.457 y 189.02 (i;j)s 1 f 556.491 y 204.035 (stands)s 241.216 (for)s 259.296 (the)s 279.677 (piece)s 309.391 (of)s 322.771 (generator)s 375.886 (asso)s 397.686 (ciated)s 432.733 (to)s 447.113 (the)s 573.291 y -5.69 (exc)s 10.976 (hange)s 45.643 (of)s 59.31 (spins)s 89.443 (b)s 96.443 (et)s 106.11 (w)s 114.443 (een)s 135.777 (sites)s 10 f 162.577 (i)s 1 f 170.711 (and)s 10 f 194.044 (j)s 1 f 203.673 (for)s 222.039 (the)s 242.706 (exclusion)s 294.44 (pro)s 312.14 (cess.)s 590.211 y 8.71 (De\257ne)s 46.136 (the)s 67.063 (en)s 78.729 (trop)s 100.429 (y)s 12 f 111.023 (S)s 1 f 119.189 (\050)s 10 f 123.856 (\271)s 12 f 131.086 (j)s 10 f 134.42 (\272)s 11 f 592.011 y 140.348 (P)s 1 f 590.211 y 148.349 (\051)s 157.275 (and)s 180.868 (the)s 201.795 (Diric)s 227.328 (hlet)s 251.588 (form)s 12 f 280.215 (D)s 1 f 289.805 (\050)s 10 f 294.471 (\271)s 12 f 301.702 (j)s 10 f 305.035 (\272)s 11 f 592.011 y 310.963 (P)s 1 f 590.211 y 318.964 (\051)s 327.891 (of)s 341.817 (a)s 352.077 (measure)s 10 f 399.103 (\271)s 1 f 410.594 (on)s 427.52 (\255)s 440.447 (with)s 607.011 y -5.69 (resp)s 16.076 (ect)s 35.41 (to)s 10 f 50.077 (\272)s 11 f 608.811 y 56.004 (P)s 1 f 607.011 y 68.006 (as)s 12 f 626.744 y 139.671 (S)s 1 f 147.838 (\050)s 10 f 152.504 (\271)s 12 f 159.735 (j)s 10 f 163.068 (\272)s 11 f 628.544 y 168.996 (P)s 1 f 626.744 y 176.997 (\051)s 184.997 (=)s 10 f 197.664 (\260)s 13 f 615.344 y 206.984 (X)s 11 f 641.102 y 206.543 (n)s 14 f 212.475 (\270)s 2 f 219.975 (1)s 10 f 626.744 y 226.758 (s)s 11 f 628.544 y 232.383 (n)s 1 f 626.744 y 238.915 (\050)s 10 f 243.582 (\271)s 11 f 628.544 y 250.813 (n)s 12 f 626.744 y 257.345 (j)s 10 f 260.678 (\272)s 11 f 628.544 y 266.606 (P)s 272.974 (;n)s 1 f 626.744 y 282.356 (\051)s 10 f 287.022 (e)s 14 f 621.789 y 292.61 (\241)s 11 f 300.11 (\260)s 305.667 (n)s 10 f 626.744 y 312.199 (;)s 12 f 664.86 y 138.248 (D)s 1 f 147.838 (\050)s 10 f 152.504 (\271)s 12 f 159.735 (j)s 10 f 163.068 (\272)s 11 f 666.66 y 168.996 (P)s 1 f 664.86 y 176.997 (\051)s 184.997 (=)s 10 f 197.664 (\260)s 13 f 653.46 y 206.984 (X)s 11 f 679.218 y 206.543 (n)s 14 f 212.475 (\270)s 2 f 219.975 (1)s 10 f 664.86 y 226.758 (D)s 11 f 666.66 y 236.693 (n)s 1 f 664.86 y 243.225 (\050)s 10 f 247.892 (\271)s 11 f 666.66 y 255.123 (n)s 12 f 664.86 y 261.655 (j)s 10 f 264.988 (\272)s 11 f 666.66 y 270.916 (P)s 277.284 (;n)s 1 f 664.86 y 286.666 (\051)s 10 f 291.332 (e)s 14 f 659.905 y 296.92 (\241)s 11 f 304.42 (\260)s 309.977 (n)s 10 f 664.86 y 316.509 (:)s 1 f 705.976 y 223.045 (16)s do-end end endp %%Page: 17 17 %%BeginPageSetup initializepage (Raffaele Esposito; page: 17 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f0_12 sf ( )S -996 -1000 :M f1_12 sf ( )S -993 -1000 :M f2_12 sf ( )S -989 -1000 :M f10_12 sf ( )S -981 -1000 :M f11_12 sf ( )S -972 -1000 :M f12_12 sf ( )S -960 -1000 :M f13_12 sf ( )S -951 -1000 :M f14_12 sf ( )S -937 -1000 :M f15_12 sf ( )S -926 -1000 :M f17_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 1200 1000 div mul /CMBX10 findfont fdef 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 17 10 1200 1000 div mul /CMTI10 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 6.31 y -5.69 (Notice)s 31.93 (that)s 57.883 (b)s 64.217 (y)s 74.503 (\0504.1\051,)s 106.466 (there)s 137.12 (exists)s 170.206 (a)s 180.16 (p)s 187.16 (ositiv)s 215.227 (e)s 224.513 (constan)s 264.247 (t)s 10 f 272.867 (C)s 1 f 286.255 (dep)s 305.255 (ending)s 343.875 (on)s 10 f 360.496 (P)s 1 f 373.82 (suc)s 390.22 (h)s 400.84 (that)s 426.793 (for)s 445.113 (an)s 457.447 (y)s 23.11 y -5.69 (probabilit)s 45.343 (y)s 55.677 (measure)s 10 f 102.443 (\271)s 1 f 113.674 (on)s 130.341 (\255)s 12 f 43.73 y 183.677 (S)s 1 f 191.844 (\050)s 10 f 196.51 (\271)s 12 f 203.741 (j)s 10 f 207.074 (\272)s 11 f 45.53 y 213.002 (P)s 1 f 43.73 y 221.003 (\051)s 12 f 229.003 (\267)s 10 f 241.67 (C)s 251.105 (\260)s 14 f 38.775 y 257.984 (\241)s 11 f 265.484 (d)s 10 f 43.73 y 271.08 (:)s 1 f 439.114 (\0504)s 10 f 449.78 (:)s 1 f 453.114 (2\051)s 74.144 y 8.71 (Through)s 58.392 (this)s 82.107 (section)s 122.488 (w)s 130.822 (e)s 140.47 (consider)s 187.552 (Ka)s 202.552 (w)s 210.885 (asaki)s 241.6 (dynamics)s 294.982 (with)s 322.631 (\257xed)s 351.946 (parameter)s 10 f 409.661 (\257)s 420.94 (\076)s 1 f 434.132 (0)s 444.447 (and)s 90.944 y -5.69 (with)s 23.095 (\257xed)s 53.547 (scaling)s 94.398 (parameter)s 10 f 153.25 (\260)s 14 f 86.589 y 160.13 (\241)s 2 f 167.63 (1)s 1 f 90.944 y 173.013 (.)s 186.035 (W)s 197.368 (e)s 208.153 (shall)s 237.672 (denote)s 277.79 (b)s 284.123 (y)s 13 f 81.223 y 295.909 (\241)s 10 f 90.944 y 301.409 (S)s 11 f 86.589 y 309.459 (K)s 317.594 (;\257)s 93.91 y 308.767 (\260)s 1 f 90.944 y 326.917 (\050)s 10 f 331.583 (t)s 1 f 335.917 (\051)s 13 f 81.223 y 340.583 (\242)s 11 f 95.744 y 346.083 (t)s 14 f 349.708 (\270)s 2 f 357.208 (0)s 1 f 90.944 y 368.043 (the)s 390.162 (semigroup)s 449.047 (as-)s 113.168 y -5.69 (so)s 5.376 (ciated)s 42.277 (to)s 58.511 (the)s 80.745 (generator)s 10 f 135.713 (\260)s 14 f 108.814 y 142.592 (\241)s 2 f 150.092 (2)s 1 f 113.168 y 155.476 (I)s 157.649 (L)s 11 f 107.935 y 165.149 (K)s 173.284 (;\257)s 116.135 y 165.149 (\260)s 1 f 113.168 y 188.175 (\050that)s 220.409 (is)s 234.043 (the)s 256.277 (semigroup)s 315.278 (of)s 330.512 (Ka)s 345.512 (w)s 353.845 (asaki)s 385.813 (dynamics)s 440.447 (with)s 129.968 y -5.69 (parameter)s 10 f 51.98 (\257)s 1 f 59.401 (,)s 67.072 (accelerated)s 129.375 (b)s 135.708 (y)s 10 f 146.312 (\260)s 14 f 125.613 y 153.191 (\241)s 2 f 160.691 (2)s 1 f 129.968 y 166.075 (\051.)s 180.218 (F)s 187.051 (or)s 202.022 (a)s 212.292 (measure)s 10 f 259.328 (\271)s 1 f 270.829 (on)s 287.766 (\255)s 300.702 (w)s 309.036 (e)s 318.639 (shall)s 346.976 (denote)s 385.913 (b)s 392.246 (y)s 10 f 402.849 (\271)s 11 f 125.613 y 410.08 (K)s 418.215 (;)s 422.704 (\257)s 1 f 129.968 y 429.177 (\050)s 10 f 433.844 (t)s 1 f 438.177 (\051)s 447.114 (the)s 146.768 y -5.69 (time)s 21.643 (ev)s 32.977 (olution)s 73.643 (of)s 87.31 (the)s 107.977 (measure)s 10 f 154.743 (\271)s 1 f 165.974 (under)s 200.007 (the)s 220.674 (semigroup)s 10 f 278.108 (S)s 11 f 142.414 y 286.158 (K)s 294.293 (;\257)s 149.735 y 285.466 (\260)s 1 f 146.768 y 307.616 (:)s 10 f 316.282 (\271)s 11 f 142.414 y 323.513 (K)s 331.648 (;\257)s 1 f 146.768 y 340.971 (\050)s 10 f 345.637 (t)s 1 f 349.971 (\051)s 357.971 (=)s 10 f 370.637 (\271S)s 11 f 142.414 y 385.918 (K)s 394.053 (;\257)s 149.735 y 385.226 (\260)s 1 f 146.768 y 403.376 (\050)s 10 f 408.043 (t)s 1 f 412.376 (\051.)s 164.962 y 8.71 (When)s 10 f 44.136 (\257)s 1 f 55.601 (=)s 68.978 (0,)s 82.844 (the)s 103.937 (pro)s 121.637 (cess)s 146.196 (reduces)s 189.389 (to)s 204.482 (the)s 225.575 (generalized)s 288.035 (simple)s 325.861 (exclusion)s 378.021 (pro)s 395.721 (cess)s 420.28 (\050Lemma)s 181.762 y -5.69 (4.1\051,)s 23.697 (and)s 48.674 (in)s 64.317 (particular)s 121.36 (the)s 143.67 (pro)s 161.37 (duct)s 190.347 (measures)s 243.49 (are)s 265.166 (in)s 274.833 (v)s 280.5 (arian)s 306.866 (t)s 317.176 (for)s 337.186 (the)s 359.496 (generator)s 12 f 414.539 (L)s 11 f 177.407 y 422.816 (K)s 430.951 (;)s 2 f 433.801 (0)s 11 f 184.728 y 422.816 (\260)s 1 f 181.762 y 439.184 (.)s 452.78 (In)s 198.562 y -5.69 (this)s 19.421 (case,)s 50.293 (b)s 56.627 (y)s 68.671 (using)s 101.782 (the)s 124.16 (metho)s 157.16 (ds)s 174.272 (of)s 189.649 ([F])s 209.859 (and)s 234.904 ([Y])s 256.28 (one)s 279.991 (can)s 303.702 (get)s 325.413 (en)s 337.08 (trop)s 358.78 (y)s 370.825 (and)s 395.869 (the)s 418.247 (Diric)s 443.78 (hlet)s 215.362 y -5.69 (form)s 22.575 (estimates)s 75.274 (uniform)s 120.206 (in)s 134.105 (the)s 154.671 (v)s 160.671 (olume,)s 199.256 (for)s 217.522 (the)s 238.087 (en)s 249.754 (trop)s 271.454 (y)s 281.686 (of)s 295.252 (pro)s 312.952 (cesses)s 347.05 (ev)s 358.384 (olving)s 393.949 (in)s 407.848 (large)s 437.114 (\257nite)s 232.162 y -5.69 (v)s .31 (olumes)s 40.909 (and)s 64.776 (then)s 92.642 (extend)s 132.175 (them)s 163.375 (b)s 169.708 (y)s 180.574 (lo)s 189.574 (w)s 197.908 (er)s 212.474 (semi-con)s 257.541 (tin)s 271.874 (uit)s 286.207 (y)s 297.074 (to)s 312.273 (the)s 333.473 (in\257nite)s 374.673 (system.)s 420.738 (F)s 427.572 (or)s 10 f 442.805 (\257)s 12 f 454.447 (6)s 1 f 454.447 (=)s 248.962 y -5.69 (0)s 5.766 (pro)s 23.466 (duct)s 52.255 (measures)s 105.211 (are)s 126.7 (no)s 144.823 (more)s 176.312 (in)s 185.979 (v)s 191.646 (arian)s 218.013 (t)s 228.135 (for)s 247.958 (the)s 270.08 (generator,)s 328.634 (but)s 352.09 (it)s 365.546 (is)s 379.068 (p)s 386.068 (ossible)s 425.658 (to)s 441.78 (tak)s 458.447 (e)s 265.762 y -5.69 (adv)s 12.643 (an)s 24.977 (tage)s 52.767 (from)s 82.925 (the)s 105.382 (fact)s 130.839 (that)s 158.63 (the)s 181.088 (pro)s 198.788 (cess)s 224.712 (is)s 238.569 (a)s 250.36 (w)s 258.693 (eak)s 282.15 (p)s 289.15 (erturbation)s 354.341 (of)s 369.799 (the)s 392.256 (exclusion)s 445.78 (one)s 282.562 y -5.69 (\050Lemma)s 42.669 (4.1)s 62.862 (b)s 69.862 (elo)s 84.195 (w\051)s 102.388 (and)s 126.58 (adapt)s 161.44 (the)s 182.965 (F)s 189.799 (ritz\047s)s 220.758 (approac)s 261.791 (h)s 273.317 (to)s 288.843 (that)s 315.702 (case)s 341.962 (without)s 387.488 (considering)s 451.114 (an)s 299.362 y -5.69 (appro)s 24.01 (ximation)s 75.092 (of)s 89.508 (the)s 110.924 (in\257nite)s 152.34 (v)s 158.34 (olume)s 194.422 (dynamics.)s 254.403 (Notice)s 292.819 (that)s 319.568 (from)s 348.684 (\0504.2\051)s 378.1 (there)s 409.549 (is)s 422.365 (no)s 439.78 (need)s 316.162 y -5.69 (for)s 12.677 (an)s 29.343 (initial)s 64.01 (condition)s 116.677 (on)s 133.343 (the)s 154.01 (en)s 165.677 (trop)s 187.377 (y)s 197.71 (in)s 211.71 (Theorem)s 262.41 (3.1.)s 0 f 351.427 y -5.69 (Lemma)s 43.243 (4.1)s 17 f 69.476 (F)s 76.389 (or)s 91.876 (any)s 10 f 114.876 (i)s 12 f 122.343 (2)s 10 f 133.676 (Z)s 136.727 (Z)s 11 f 346.193 y 147.777 (d)s 17 f 351.427 y 153.372 (,)s 161.345 (unit)s 186.492 (ve)s 196.918 (ctor)s 10 f 221.911 (e)s 12 f 230.832 (2)s 10 f 242.165 (Z)s 245.216 (Z)s 11 f 346.193 y 256.266 (d)s 17 f 351.427 y 266.154 (and)s 10 f 289.461 (\276)s 12 f 300.082 (2)s 1 f 311.415 (\255)s 10 f 389.38 y 40.494 (C)s 11 f 384.426 y 49.929 (K)s 58.064 (;\257)s 392.347 y 49.07 (\260)s 1 f 389.38 y 67.387 (\050)s 10 f 72.054 (i;)s 81.521 (i)s 1 f 88.322 (+)s 10 f 100.322 (e)s 1 f 105.909 (;)s 10 f 111.242 (\276)s 1 f 118.53 (\051)s 126.53 (=)s 139.197 (1)s 12 f 147.863 (\241)s 10 f 159.863 (\260)s 166.743 (\257)s 13 f 379.66 y 174.163 (\243)s 10 f 389.38 y 179.163 (\276)s 1 f 186.451 (\050)s 10 f 191.118 (i)s 1 f 197.918 (+)s 10 f 209.918 (e)s 1 f 215.506 (\051)s 12 f 222.839 (\241)s 10 f 234.839 (\276)s 1 f 242.127 (\050)s 10 f 246.793 (i)s 1 f 250.927 (\051)s 13 f 379.66 y 255.594 (\244)s 10 f 389.38 y 260.594 (\260)s 11 f 384.426 y 267.473 (d)s 13 f 377.98 y 279.651 (X)s 11 f 404.92 y 275.069 (\140)s 14 f 279.086 (2)s 11 f 285.552 (Z)s 287.762 (Z)s 15 f 402.147 y 296.528 (d)s 13 f 379.66 y 303.566 (\241)s 10 f 389.38 y 309.066 (e)s 12 f 317.32 (\242)s 323.32 (r)s 10 f 333.32 (J)s 13 f 379.66 y 341.128 (\242)s 1 f 389.38 y 346.628 (\050)s 10 f 351.295 (\260)s 1 f 358.175 (\050)s 10 f 362.841 (i)s 12 f 369.642 (\241)s 10 f 381.642 (\140)s 1 f 386.642 (\051\051)s 10 f 395.975 (\276)s 1 f 403.263 (\050)s 10 f 407.93 (\140)s 1 f 412.93 (\051)s 12 f 427.803 y 149.863 (\241)s 10 f 161.863 (\260)s 11 f 422.848 y 168.743 (d)s 2 f 173.738 (+1)s 10 f 427.803 y 186.488 (\257)s 13 f 418.083 y 193.909 (\243)s 10 f 427.803 y 198.909 (\276)s 1 f 206.197 (\050)s 10 f 210.863 (i)s 1 f 217.664 (+)s 10 f 229.664 (e)s 1 f 235.251 (\051)s 12 f 242.585 (\241)s 10 f 254.585 (\276)s 1 f 261.872 (\050)s 10 f 266.539 (i)s 1 f 270.673 (\051)s 13 f 418.083 y 275.34 (\244)s 2 f 420.569 y 280.34 (2)s 13 f 418.083 y 285.723 (\241)s 10 f 427.803 y 291.223 (e)s 12 f 299.477 (\242)s 305.477 (r)s 10 f 315.477 (J)s 13 f 418.083 y 323.286 (\242)s 1 f 427.803 y 328.786 (\0500\051)s 346.786 (+)s 10 f 358.785 (O)s 1 f 368.272 (\050)s 10 f 372.939 (\260)s 2 f 422.848 y 379.818 (2)s 1 f 427.803 y 385.202 (\051)s 448.203 y 126.53 (=)s 139.197 (1)s 147.863 (+)s 10 f 159.863 (\257)s 167.284 (O)s 1 f 176.771 (\050)s 10 f 181.437 (\260)s 1 f 188.317 (\051)s 10 f 192.983 (:)s 17 f 510.688 y -5.69 (Pr)s 6.896 (o)s 12.416 (of.)s 1 f 31.243 (By)s 50.076 (de\257nition)s 103.41 (of)s 10 f 117.076 (H)s 11 f 512.488 y 127.051 (\260)s 1 f 510.688 y 133.209 (,)s 140.542 (for)s 158.909 (all)s 10 f 175.575 (i;)s 185.043 (j)s 12 f 194.005 (2)s 10 f 205.338 (Z)s 208.388 (Z)s 11 f 505.455 y 219.438 (d)s 1 f 510.688 y 229.034 (and)s 10 f 252.367 (\276)s 12 f 262.988 (2)s 1 f 274.321 (\255)s 13 f 540.021 y 60.36 (\241)s 12 f 549.741 y 65.86 (r)s 11 f 551.541 y 75.86 (i;j)s 10 f 549.741 y 87.161 (H)s 11 f 551.541 y 97.136 (\260)s 13 f 540.021 y 103.294 (\242)s 1 f 549.741 y 108.794 (\050)s 10 f 113.46 (\276)s 1 f 120.748 (\051)s 128.748 (=)s 141.414 (2)s 13 f 540.021 y 147.414 (\243)s 10 f 549.741 y 152.414 (\276)s 1 f 159.702 (\050)s 10 f 164.368 (i)s 1 f 168.503 (\051)s 12 f 175.836 (\241)s 10 f 187.836 (\276)s 1 f 195.123 (\050)s 10 f 199.79 (j)s 1 f 205.419 (\051)s 13 f 540.021 y 210.085 (\244)s 10 f 549.741 y 215.085 (\260)s 11 f 544.787 y 221.965 (d)s 13 f 538.341 y 234.142 (X)s 11 f 565.282 y 229.56 (\140)s 14 f 233.577 (2)s 11 f 240.044 (Z)s 242.254 (Z)s 15 f 562.508 y 251.019 (d)s 13 f 540.021 y 258.057 (\243)s 10 f 549.741 y 263.057 (J)s 11 f 551.541 y 269.711 (\260)s 1 f 549.741 y 275.869 (\050)s 10 f 280.535 (i)s 12 f 287.336 (\241)s 10 f 299.336 (\140)s 1 f 304.336 (\051)s 12 f 311.669 (\241)s 10 f 323.669 (J)s 11 f 551.541 y 330.324 (\260)s 1 f 549.741 y 336.481 (\050)s 10 f 341.148 (j)s 12 f 349.443 (\241)s 10 f 361.443 (\140)s 1 f 366.443 (\051)s 13 f 540.021 y 371.109 (\244)s 10 f 549.741 y 376.109 (\276)s 1 f 383.397 (\050)s 10 f 388.064 (\140)s 1 f 393.064 (\051)s 588.164 y 140.081 (+)s 152.081 (2)s 13 f 578.444 y 158.081 (\243)s 10 f 588.164 y 163.081 (\276)s 1 f 170.369 (\050)s 10 f 175.035 (i)s 1 f 179.169 (\051)s 12 f 186.503 (\241)s 10 f 198.503 (\276)s 1 f 205.79 (\050)s 10 f 210.457 (j)s 1 f 216.085 (\051)s 13 f 578.444 y 220.752 (\244)s 2 f 580.931 y 225.752 (2)s 10 f 588.164 y 231.135 (\260)s 11 f 583.209 y 238.015 (d)s 13 f 578.444 y 243.61 (\243)s 10 f 588.164 y 248.61 (J)s 11 f 589.964 y 255.264 (\260)s 1 f 588.164 y 261.422 (\050)s 10 f 266.088 (i)s 12 f 272.889 (\241)s 10 f 284.889 (j)s 1 f 290.518 (\051)s 12 f 297.851 (\241)s 10 f 309.851 (J)s 11 f 589.964 y 316.505 (\260)s 1 f 588.164 y 322.662 (\0500\051)s 13 f 578.444 y 337.996 (\244)s 10 f 588.164 y 342.996 (:)s 1 f 567.753 y 439.114 (\0504)s 10 f 449.78 (:)s 1 f 453.114 (3\051)s 625.111 y 8.71 (T)s 16.376 (o)s 27.105 (pro)s 44.138 (v)s 50.138 (e)s 60.199 (the)s 81.594 (lemma,)s 124.504 (it)s 137.232 (is)s 150.027 (enough)s 192.089 (to)s 207.483 (remark)s 249.278 (that)s 276.006 (the)s 297.401 (conditions)s 355.529 (imp)s 375.863 (osed)s 403.324 (on)s 420.719 (\251)s 434.113 (imply)s 641.911 y -5.69 (that)s 20.31 (\251)s 14 f 637.556 y 28.977 (0)s 1 f 641.911 y 32.343 (\0500\051)s 51.01 (=)s 12 f 63.676 (\241)s 2 f 637.186 y 74.45 (1)s 4.783 .48 74.45 639.151 r 646.049 y 74.45 (2)s 1 f 641.911 y 84.673 (\050cf.)s 107.007 ([GL]\051)s 139.257 (and)s 162.59 (to)s 177.257 (use)s 197.99 (T)s 205.657 (a)s 211.323 (ylor)s 235.69 (expansion.)s 8.16 .48 301.424 635.311 r .48 7.2 301.424 642.511 r .48 7.2 309.104 642.511 r 8.16 .48 301.424 642.991 r 677.176 y 8.71 (W)s 20.043 (e)s 29.376 (get)s 49.376 (the)s 70.043 (follo)s 92.043 (wing)s 120.71 (estimate)s 168.777 (for)s 187.143 (the)s 207.81 (Diric)s 233.343 (hlet)s 257.344 (form)s 285.71 (in)s 299.71 (the)s 320.377 (in\257nite)s 361.044 (v)s 367.044 (olume:)s 705.976 y 223.045 (17)s do-end end endp %%Page: 18 18 %%BeginPageSetup initializepage (Raffaele Esposito; page: 18 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f0_12 sf ( )S -996 -1000 :M f1_12 sf ( )S -993 -1000 :M f2_12 sf ( )S -989 -1000 :M f10_12 sf ( )S -981 -1000 :M f11_12 sf ( )S -972 -1000 :M f12_12 sf ( )S -960 -1000 :M f13_12 sf ( )S -951 -1000 :M f14_12 sf ( )S -937 -1000 :M f15_12 sf ( )S -926 -1000 :M f16_12 sf ( )S -921 -1000 :M f17_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 1200 1000 div mul /CMBX10 findfont fdef 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 16 5 1200 1000 div mul /CMR5 findfont fdef 17 10 1200 1000 div mul /CMTI10 findfont fdef 58 60 translate 72 72.27 div dup scale 0 f 6.31 y -5.69 (Theorem)s 52.627 (4.2)s 17 f 78.333 (Ther)s 103.019 (e)s 112.607 (exists)s 145.241 (a)s 155.442 (p)s 160.962 (ositive)s 198.456 (\257nite)s 229.203 (c)s 234.11 (onstant)s 10 f 276.817 (C)s 2 f 8.11 y 285.394 (1)s 17 f 6.31 y 294.845 (that)s 319.152 (dep)s 336.325 (ends)s 363.699 (on)s 10 f 380.647 (P)s 17 f 390.018 (,)s 10 f 397.81 (t)s 17 f 406.211 (and)s 10 f 429.292 (\257)s 17 f 440.78 (such)s 23.11 y -5.69 (that)s 13 f 30.11 y 145.242 (Z)s 11 f 33.076 y 157.243 (t)s 2 f 57.377 y 151.909 (0)s 12 f 46.443 y 163.467 (D)s 13 f 36.723 y 173.058 (\241)s 10 f 46.443 y 178.558 (\271)s 11 f 41.489 y 185.788 (K)s 193.923 (;\257)s 1 f 46.443 y 203.246 (\050)s 10 f 207.913 (\277)s 1 f 214.517 (\051)s 12 f 219.184 (j)s 10 f 222.517 (\272)s 11 f 48.243 y 228.445 (P)s 13 f 36.723 y 236.446 (\242)s 10 f 46.443 y 241.946 (d\277)s 12 f 258.129 (\267)s 10 f 270.796 (C)s 2 f 48.243 y 279.373 (1)s 10 f 46.443 y 284.756 (\260)s 2 f 41.489 y 291.635 (2)s 14 f 296.419 (\241)s 11 f 303.919 (d)s 10 f 46.443 y 309.514 (:)s 1 f 103.32 y 8.71 (The)s 33.936 (strategy)s 80.929 (of)s 95.156 (the)s 116.382 (pro)s 134.082 (of)s 148.309 (is)s 160.935 (to)s 176.162 (in)s 185.828 (tro)s 201.528 (duce)s 230.088 (suitable)s 275.381 (en)s 287.048 (trop)s 308.748 (y)s 319.641 (and)s 343.534 (Diric)s 369.068 (hlet)s 393.627 (form)s 422.554 (in)s 437.114 (\257nite)s 120.12 y -5.69 (v)s .31 (olume)s 36.935 (and)s 61.56 (b)s 68.56 (ound)s 99.852 (the)s 121.811 (corresp)s 159.611 (onding)s 200.236 (en)s 211.903 (trop)s 233.603 (y)s 245.228 (pro)s 262.928 (duction)s 307.554 (in)s 322.846 (terms)s 357.571 (of)s 372.53 (the)s 394.488 (\257nite)s 426.447 (v)s 432.447 (olume)s 136.92 y -5.69 (Diric)s 19.843 (hlet)s 44.17 (form)s 72.863 (times)s 10 f 105.256 (\260)s 2 f 132.566 y 112.136 (2)s 1 f 136.92 y 121.846 (uniformly)s 176.872 (in)s 191.199 (the)s 212.192 (v)s 218.192 (olume)s 253.852 (\050Lemma)s 301.679 (4.2\051.)s 331.325 (Then,)s 366.4 (the)s 387.394 (a)s 397.72 (priori)s 430.78 (b)s 437.78 (ound)s 153.72 y -5.69 (on)s 10.977 (the)s 31.643 (en)s 43.31 (trop)s 65.01 (y)s 75.343 (\0504.2\051)s 104.01 (allo)s 122.343 (ws)s 139.743 (to)s 154.41 (get)s 174.41 (the)s 195.077 (estimate.)s 170.64 y 8.71 (Fix)s 30.83 (a)s 41.451 (measure)s 10 f 88.838 (\271)s 1 f 100.689 (on)s 117.976 (\255)s 131.263 (and)s 155.217 (a)s 165.837 (c)s 170.837 (hemical)s 215.458 (p)s 222.458 (oten)s 244.791 (tial)s 10 f 266.745 (P)s 1 f 276.116 (.)s 286.643 (F)s 293.477 (or)s 308.797 (all)s 10 f 326.084 (t)s 12 f 334.785 (\270)s 1 f 348.486 (0)s 359.106 (and)s 383.06 (p)s 390.06 (ositiv)s 418.126 (e)s 428.08 (in)s 437.747 (teger)s 10 f 187.44 y -5.69 (n)s 1 f 1.513 (,)s 9.899 (denote)s 49.409 (b)s 55.742 (y)s 10 f 66.918 (f)s 11 f 183.086 y 74.085 (t)s 190.407 y 72.793 (n)s 1 f 187.44 y 84.168 (the)s 105.678 (probabilit)s 156.711 (y)s 167.887 (densit)s 198.954 (y)s 210.13 (of)s 13 f 177.72 y 224.639 (\241)s 10 f 187.44 y 230.14 (\271)s 11 f 183.086 y 237.37 (K)s 245.505 (;\257)s 1 f 187.44 y 254.828 (\050)s 10 f 259.495 (t)s 1 f 263.828 (\051)s 13 f 177.72 y 268.495 (\242)s 11 f 192.24 y 273.995 (n)s 1 f 187.44 y 285.37 (with)s 313.546 (resp)s 335.312 (ect)s 355.489 (to)s 10 f 370.998 (\272)s 11 f 189.24 y 376.926 (P)s 383.294 (;n)s 1 f 187.44 y 392.676 (.)s 403.871 (T)s 411.537 (o)s 422.38 (simplify)s 204.24 y -5.69 (the)s 15.105 (notation,)s 66.598 (w)s 74.932 (e)s 84.393 (denote)s 123.188 (resp)s 144.955 (ectiv)s 169.621 (ely)s 188.75 (b)s 195.083 (y)s 10 f 205.545 (s)s 11 f 206.04 y 211.17 (n)s 1 f 204.24 y 217.702 (\050)s 10 f 222.368 (f)s 11 f 199.886 y 229.535 (t)s 207.207 y 228.243 (n)s 1 f 204.24 y 234.775 (\051)s 243.57 (and)s 10 f 267.032 (D)s 11 f 206.04 y 276.967 (n)s 1 f 204.24 y 283.499 (\050)s 10 f 288.165 (f)s 11 f 199.886 y 295.332 (t)s 207.207 y 294.04 (n)s 1 f 204.24 y 300.572 (\051)s 309.367 (the)s 330.162 (en)s 341.829 (trop)s 363.529 (y)s 373.99 (and)s 397.452 (the)s 418.247 (Diric)s 443.78 (hlet)s 221.04 y -5.69 (form)s 22.789 (of)s 13 f 211.32 y 36.569 (\241)s 10 f 221.04 y 42.069 (\271)s 11 f 216.686 y 49.299 (K)s 57.434 (;\257)s 1 f 221.04 y 66.757 (\050)s 10 f 71.424 (t)s 1 f 75.757 (\051)s 13 f 211.32 y 80.424 (\242)s 11 f 225.84 y 85.924 (n)s 1 f 221.04 y 96.569 (with)s 124.015 (resp)s 145.781 (ect)s 165.227 (to)s 10 f 180.007 (\272)s 11 f 222.84 y 185.934 (P)s 192.302 (;n)s 1 f 221.04 y 201.684 (.)s 210.689 (F)s 217.522 (or)s 232.335 (all)s 249.114 (p)s 256.114 (ositiv)s 284.181 (e)s 293.627 (in)s 303.294 (teger)s 10 f 333.44 (M)s 1 f 346.39 (,)s 353.864 (let)s 10 f 371.31 (M)s 11 f 222.84 y 382.951 (\260)s 1 f 221.04 y 393.221 (b)s 400.221 (e)s 409.667 (de\257ned)s 451.113 (b)s 457.447 (y)s 10 f 237.84 y -5.69 (M)s 11 f 239.64 y 5.951 (\260)s 1 f 237.84 y 15.588 (=)s 10 f 28.401 (N)s 2 f 233.486 y 39.351 (2)s 11 f 240.807 y 38.043 (\260)s 1 f 237.84 y 47.459 (+)s 10 f 59.518 (M)s 1 f 72.468 (,)s 79.911 (where)s 10 f 114.698 (N)s 11 f 239.64 y 124.34 (\260)s 1 f 237.84 y 133.977 (=)s 146.79 ([)s 148.123 ([)s 10 f 151.456 (\260)s 14 f 233.486 y 158.336 (\241)s 2 f 165.836 (1)s 1 f 237.84 y 171.219 (])s 172.552 (])s 179.973 (stands)s 217.528 (for)s 235.982 (the)s 256.737 (in)s 266.403 (teger)s 296.524 (part)s 322.645 (of)s 10 f 336.4 (\260)s 14 f 233.486 y 343.279 (\241)s 2 f 350.779 (1)s 1 f 237.84 y 356.163 (.)s 365.092 (De\257ne)s 402.347 (resp)s 424.113 (ectiv)s 448.78 (ely)s 254.64 y -5.69 (the)s 14.976 (en)s 26.643 (trop)s 48.343 (y)s 12 f 58.677 (S)s 11 f 256.44 y 65.943 (M)s 15 f 257.64 y 75.094 (\260)s 1 f 254.64 y 81.192 (\050)s 10 f 85.859 (:)s 1 f 89.192 (\051)s 97.859 (and)s 121.192 (the)s 141.859 (Diric)s 167.392 (hlet)s 191.392 (form)s 12 f 219.759 (D)s 11 f 256.44 y 229.016 (M)s 15 f 257.64 y 238.167 (\260)s 1 f 254.64 y 244.265 (\050)s 10 f 248.931 (:)s 1 f 252.265 (\051)s 260.931 (with)s 288.265 (\257nite)s 318.932 (sum)s 344.332 (b)s 350.665 (y)s 12 f 296.039 y 129.634 (S)s 11 f 297.839 y 136.901 (M)s 15 f 299.039 y 146.052 (\260)s 13 f 286.319 y 152.15 (\241)s 10 f 296.039 y 157.65 (\271)s 11 f 291.084 y 164.88 (K)s 173.015 (;\257)s 1 f 296.039 y 182.338 (\050)s 10 f 187.005 (t)s 1 f 191.338 (\051)s 12 f 196.005 (j)s 10 f 199.338 (\272)s 11 f 297.839 y 205.266 (P)s 13 f 286.319 y 213.267 (\242)s 1 f 296.039 y 222.101 (=)s 10 f 234.767 (\260)s 11 f 279.739 y 245.363 (M)s 15 f 280.939 y 254.514 (\260)s 13 f 284.639 y 244.021 (X)s 11 f 310.052 y 243.647 (n)s 2 f 249.579 (=1)s 10 f 296.039 y 263.729 (s)s 11 f 297.839 y 269.354 (n)s 1 f 296.039 y 275.886 (\050)s 10 f 280.552 (f)s 11 f 291.084 y 287.719 (t)s 299.005 y 286.427 (n)s 1 f 296.039 y 292.959 (\051)s 10 f 297.626 (e)s 14 f 291.084 y 303.213 (\241)s 11 f 310.714 (n\260)s 10 f 296.039 y 322.803 (;)s 12 f 342.892 y 127.644 (D)s 11 f 344.692 y 136.901 (M)s 15 f 345.892 y 146.052 (\260)s 13 f 333.172 y 152.15 (\241)s 10 f 342.892 y 157.65 (\271)s 11 f 337.938 y 164.88 (K)s 173.015 (;\257)s 1 f 342.892 y 182.338 (\050)s 10 f 187.005 (t)s 1 f 191.338 (\051)s 12 f 196.005 (j)s 10 f 199.338 (\272)s 11 f 344.692 y 205.266 (P)s 13 f 333.172 y 213.267 (\242)s 1 f 342.892 y 222.101 (=)s 10 f 234.767 (\260)s 11 f 326.592 y 245.363 (M)s 15 f 327.792 y 254.514 (\260)s 13 f 331.492 y 244.021 (X)s 11 f 356.906 y 243.647 (n)s 2 f 249.579 (=1)s 10 f 342.892 y 263.729 (D)s 11 f 344.692 y 273.664 (n)s 1 f 342.892 y 280.196 (\050)s 10 f 284.862 (f)s 11 f 337.938 y 292.029 (t)s 345.859 y 290.737 (n)s 1 f 342.892 y 297.269 (\051)s 10 f 301.936 (e)s 14 f 337.938 y 307.523 (\241)s 11 f 315.024 (n\260)s 10 f 342.892 y 327.113 (:)s 0 f 397.623 y -5.69 (Lemma)s 42.885 (4.3)s 17 f 68.448 (Ther)s 93.135 (e)s 102.662 (exist)s 130.328 (p)s 135.848 (ositive)s 173.282 (and)s 196.302 (\257nite)s 226.988 (c)s 231.895 (onstants)s 10 f 279.448 (A)s 2 f 399.423 y 288.448 (0)s 17 f 397.623 y 297.838 (and)s 10 f 320.858 (A)s 2 f 399.423 y 329.858 (1)s 17 f 397.623 y 339.248 (that)s 363.495 (dep)s 380.668 (end)s 403.075 (on)s 10 f 419.962 (P)s 17 f 433.339 (and)s 10 f 456.359 (\257)s 17 f 414.423 y -5.69 (such)s 21.603 (that,)s 49.816 (for)s 68.983 (al)s 78.796 (l)s 86.156 (p)s 91.676 (ositive)s 10 f 129.396 (M)s 440.414 y 77.7 (@)s 11 f 442.214 y 84.071 (t)s 12 f 440.414 y 88.296 (S)s 11 f 442.214 y 95.562 (M)s 15 f 443.414 y 104.713 (\260)s 13 f 430.694 y 110.811 (\241)s 10 f 440.414 y 116.311 (\271)s 11 f 435.46 y 123.542 (K)s 131.677 (;\257)s 1 f 440.414 y 141 (\050)s 10 f 145.667 (t)s 1 f 150 (\051)s 12 f 154.667 (j)s 10 f 158 (\272)s 11 f 442.214 y 163.928 (P)s 13 f 430.694 y 171.929 (\242)s 12 f 440.414 y 180.762 (\267)s 193.429 (\241)s 10 f 202.762 (\260)s 14 f 435.46 y 209.642 (\241)s 2 f 217.142 (2)s 10 f 440.414 y 222.525 (A)s 2 f 442.214 y 231.525 (0)s 12 f 440.414 y 236.909 (D)s 11 f 442.214 y 246.165 (M)s 15 f 443.414 y 255.316 (\260)s 13 f 430.694 y 261.414 (\241)s 10 f 440.414 y 266.914 (\271)s 11 f 435.46 y 274.145 (K)s 282.28 (;\257)s 1 f 440.414 y 291.603 (\050)s 10 f 296.27 (t)s 1 f 300.603 (\051)s 12 f 305.27 (j)s 10 f 308.603 (\272)s 11 f 442.214 y 314.531 (P)s 13 f 430.694 y 322.532 (\242)s 1 f 440.414 y 330.699 (+)s 10 f 342.699 (A)s 2 f 442.214 y 351.699 (1)s 10 f 440.414 y 357.082 (\260)s 14 f 435.46 y 363.961 (\241)s 11 f 371.461 (d)s 10 f 440.414 y 377.057 (:)s 1 f 439.114 (\0504)s 10 f 449.78 (:)s 1 f 453.114 (4\051)s 503.419 y 8.71 (Before)s 46.243 (pro)s 63.277 (ving)s 89.61 (the)s 110.277 (Lemma)s 153.11 (w)s 161.443 (e)s 170.777 (conclude)s 220.11 (the)s 240.777 (pro)s 258.477 (of)s 272.144 (of)s 285.81 (Theorem)s 336.51 (4.2.)s 17 f 520.339 y -5.69 (Pr)s 6.896 (o)s 12.416 (of)s 26.523 (of)s 40.629 (The)s 60.256 (or)s 70.836 (em)s 90.462 (4.2.)s 1 f 115.422 (In)s 126.089 (tegrate)s 166.789 (\0504.4\051)s 195.456 (from)s 223.823 (0)s 233.823 (to)s 10 f 248.489 (t)s 1 f 252.823 (,)s 260.156 (let)s 10 f 277.489 (M)s 12 f 293.772 (\042)s 303.106 (1)s 1 f 319.106 (and)s 342.439 (use)s 363.172 (\0504.2\051.)s 8.16 .48 401.839 513.739 r .48 7.2 401.839 520.939 r .48 7.2 409.519 520.939 r 8.16 .48 401.839 521.419 r 17 f 552.366 y -5.69 (Pr)s 6.896 (o)s 12.416 (of)s 27.328 (of)s 42.24 (L)s 49.154 (emma)s 85.532 (4.3.)s 1 f 113.118 (W)s 124.452 (e)s 134.661 (drop)s 163.569 (the)s 185.112 (indices)s 225.387 (in)s 240.263 (I)s 242.436 (L)s 11 f 547.133 y 249.936 (K)s 258.071 (;\257)s 555.333 y 249.936 (\260)s 1 f 552.366 y 272.269 (and)s 296.478 (denote)s 336.02 (the)s 357.563 (generator)s 411.838 (simply)s 451.114 (b)s 457.447 (y)s 569.166 y -5.69 (I)s -3.517 (L)s 3.983 (,)s 12.096 (F)s 18.929 (or)s 34.253 (all)s 51.543 (p)s 58.543 (ositiv)s 86.609 (e)s 96.566 (in)s 106.233 (teger)s 10 f 136.89 (k)s 1 f 148.138 (denote)s 187.428 (b)s 193.762 (y)s 204.718 (I)s 206.892 (L)s 11 f 570.966 y 214.392 (k)s 1 f 569.166 y 224.919 (the)s 246.209 (restriction)s 304.3 (of)s 318.59 (the)s 339.88 (generator)s 393.903 (I)s 396.077 (L)s 408.2 (to)s 423.49 (the)s 444.78 (b)s 451.78 (o)s 457.447 (x)s 585.966 y -5.69 (\244)s 11 f 587.766 y 2.643 (k)s 1 f 585.966 y 8.547 (.)s 17.26 (F)s 24.093 (or)s 38.808 (a)s 48.824 (subset)s 10 f 85.639 (A)s 12 f 97.998 (\275)s 1 f 110.69 (\244)s 123.038 (of)s 10 f 136.72 (Z)s 139.77 (Z)s 11 f 580.733 y 150.82 (d)s 1 f 585.966 y 156.416 (,)s 163.768 (and)s 187.117 (a)s 197.132 (function)s 10 f 244.147 (h)s 1 f 255.076 (in)s 10 f 269.092 (L)s 2 f 581.611 y 277.258 (1)s 1 f 585.966 y 282.642 (\050)s 10 f 287.308 (\272)s 11 f 587.766 y 293.236 (P)s 299.604 (;)s 2 f 302.454 (\244)s 1 f 585.966 y 309.621 (\051,)s 321.64 (let)s 12 f 338.988 (h)s 10 f 343.655 (h)s 12 f 350.569 (i)s 11 f 589.566 y 355.236 (A)s 1 f 585.966 y 367.068 (b)s 374.068 (e)s 383.416 (the)s 404.098 (function)s 451.113 (on)s 12 f 602.766 y -5.69 (f\241)s 1 f 9.643 (1)s 10 f 15.643 (;)s 1 f 20.976 (0)s 10 f 26.977 (;)s 1 f 32.31 (1)s 12 f 38.31 (g)s 2 f 598.411 y 44.31 (\244)s 14 f 50.877 (n)s 11 f 55.793 (A)s 1 f 602.766 y 67.248 (obtained)s 116.219 (b)s 122.552 (y)s 132.523 (in)s 142.19 (tegrating)s 10 f 193.194 (h)s 1 f 203.746 (o)s 209.412 (v)s 215.412 (er)s 229.083 (the)s 249.388 (co)s 261.055 (ordinates)s 12 f 312.792 (f)s 10 f 318.792 (\276)s 1 f 326.08 (\050)s 10 f 330.746 (x)s 1 f 337.605 (\051)s 349.242 (:)s 10 f 359.547 (x)s 12 f 369.738 (2)s 10 f 381.072 (A)s 12 f 390.072 (g)s 1 f 399.709 (with)s 426.68 (resp)s 448.447 (ect)s 619.566 y -5.69 (to)s 10 f 8.976 (\272)s 11 f 621.366 y 14.904 (P)s 21.272 (;)s 2 f 24.122 (\244)s 1 f 619.566 y 31.289 (.)s 39.956 (When)s 10 f 74.956 (A)s 1 f 87.289 (=)s 99.956 (\244)s 11 f 621.366 y 108.289 (n)s 2 f 114.221 (+)s 11 f 121.588 (m)s 2 f 130.103 (+1)s 12 f 619.566 y 145.52 (\241)s 1 f 157.52 (\244)s 11 f 621.366 y 165.853 (n)s 1 f 619.566 y 172.385 (,)s 179.718 (w)s 188.052 (e)s 197.385 (shall)s 225.452 (denote)s 264.118 (this)s 287.518 (exp)s 306.185 (ectation)s 352.185 (simply)s 390.585 (b)s 396.919 (y)s 13 f 609.846 y 407.252 (\255)s 10 f 619.566 y 412.919 (h)s 13 f 609.846 y 419.832 (\256)s 2 f 624.366 y 425.499 (\244)s 15 f 620.745 y 432.066 (m)s 626.766 y 432.066 (n)s 1 f 619.566 y 440.634 (.)s 641.207 y 8.71 (With)s 39.71 (this)s 63.11 (notation,)s 114.443 (w)s 122.777 (e)s 132.11 (can)s 154.11 (v)s 160.11 (erify)s 187.477 (that)s 10 f 213.477 (f)s 11 f 636.853 y 220.644 (t)s 644.174 y 219.352 (n)s 1 f 641.207 y 229.884 (satisfy)s 267.351 (the)s 288.017 (equation)s 10 f 671.966 y 137.086 (@)s 11 f 673.766 y 143.457 (t)s 10 f 671.966 y 147.682 (f)s 11 f 667.011 y 154.849 (t)s 674.933 y 153.557 (n)s 1 f 671.966 y 163.422 (=)s 10 f 176.089 (\260)s 14 f 667.011 y 182.968 (\241)s 2 f 190.468 (2)s 13 f 658.646 y 197.852 (D)s 12 f 671.966 y 205.185 (L)s 14 f 667.011 y 213.462 (\244)s 11 f 674.933 y 213.462 (n)s 2 f 219.394 (+1)s 10 f 671.966 y 232.144 (f)s 11 f 667.011 y 239.311 (t)s 674.933 y 238.019 (n)s 2 f 243.951 (+)s 11 f 251.318 (N)s 15 f 676.133 y 258.918 (\260)s 2 f 674.933 y 264.417 (+1)s 13 f 658.646 y 277.167 (E)s 2 f 680.366 y 284.5 (\244)s 15 f 675.106 y 291.067 (n)s 16 f 296.351 (+)s 15 f 302.518 (N)s 676.306 y 308.972 (\260)s 681.976 y 291.067 (n)s 10 f 671.966 y 317.67 (;)s 1 f 439.114 (\0504)s 10 f 449.78 (:)s 1 f 453.114 (5\051)s 705.976 y 223.045 (18)s do-end end endp %%Page: 19 19 %%BeginPageSetup initializepage (Raffaele Esposito; page: 19 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f1_12 sf ( )S -997 -1000 :M f2_12 sf ( )S -993 -1000 :M f10_12 sf ( )S -985 -1000 :M f11_12 sf ( )S -976 -1000 :M f12_12 sf ( )S -964 -1000 :M f13_12 sf ( )S -954 -1000 :M f14_12 sf ( )S -941 -1000 :M f15_12 sf ( )S -930 -1000 :M f16_12 sf ( )S -925 -1000 :M f17_12 sf ( )S -922 -1000 :M f18_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 16 5 1200 1000 div mul /CMR5 findfont fdef 17 10 1200 1000 div mul /CMTI10 findfont fdef 18 5 1200 1000 div mul /CMSY5 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 6.31 y -5.69 (where)s 29.248 (for)s 47.853 (a)s 58.091 (p)s 65.091 (ositiv)s 93.158 (e)s 102.729 (in)s 112.396 (teger)s 10 f 142.667 (k)s 1 f 149.292 (,)s 12 f 156.923 (L)s 14 f 1.955 y 165.2 (\244)s 11 f 9.708 y 165.2 (k)s 1 f 6.31 y 175.342 (represen)s 218.476 (ts)s 232.114 (the)s 253.019 (adjoin)s 285.019 (t)s 293.924 (op)s 306.924 (erator)s 342.562 (of)s 12 f 356.467 (L)s 11 f 8.11 y 364.744 (k)s 1 f 6.31 y 374.886 (in)s 10 f 389.124 (L)s 2 f 1.955 y 397.291 (2)s 1 f 6.31 y 402.674 (\050)s 10 f 407.341 (\272)s 11 f 8.11 y 413.269 (P)s 419.636 (;)s 2 f 422.486 (\244)s 15 f 9.383 y 429.053 (k)s 1 f 6.31 y 434.899 (\051.)s 448.947 (By)s 23.11 y -5.69 (relation)s 38.343 (\0504.5\051)s 67.01 (and)s 90.343 (the)s 111.01 (explicit)s 153.343 (form)s 177.377 (ula)s 197.377 (for)s 215.744 (the)s 236.41 (en)s 248.077 (trop)s 269.777 (y)s 280.11 (w)s 288.444 (e)s 297.777 (ha)s 310.11 (v)s 316.11 (e)s 325.444 (that)s 10 f 57.775 y 83.24 (@)s 11 f 59.575 y 89.61 (t)s 10 f 57.775 y 93.835 (s)s 11 f 59.575 y 99.46 (n)s 1 f 57.775 y 105.992 (\050)s 10 f 110.659 (f)s 11 f 52.82 y 117.826 (t)s 60.742 y 116.534 (n)s 1 f 57.775 y 123.066 (\051)s 131.066 (=)s 10 f 143.733 (\260)s 14 f 52.82 y 150.612 (\241)s 2 f 158.112 (2)s 13 f 41.442 y 165.495 (Z)s 10 f 57.775 y 179.495 (f)s 11 f 52.82 y 186.662 (t)s 60.742 y 185.37 (n)s 2 f 191.302 (+)s 11 f 198.669 (N)s 15 f 61.942 y 206.27 (\260)s 2 f 60.742 y 211.768 (+1)s 1 f 57.775 y 224.518 (I)s 226.691 (L)s 11 f 59.575 y 234.191 (n)s 1 f 57.775 y 242.723 (log)s 13 f 48.055 y 260.223 (\241)s 10 f 57.775 y 265.723 (f)s 11 f 52.82 y 272.89 (t)s 60.742 y 271.598 (n)s 13 f 48.055 y 278.13 (\242)s 10 f 57.775 y 283.63 (d\272)s 11 f 59.575 y 295.804 (P)s 302.172 (;n)s 2 f 310.954 (+)s 11 f 318.321 (N)s 15 f 60.775 y 325.922 (\260)s 2 f 59.575 y 331.42 (+1)s 1 f 92.842 y 133.733 (+)s 10 f 145.733 (\260)s 14 f 87.887 y 152.612 (\241)s 2 f 160.112 (2)s 13 f 76.509 y 167.495 (Z)s 10 f 92.842 y 181.495 (f)s 11 f 87.887 y 188.662 (t)s 95.809 y 187.37 (n)s 2 f 193.302 (+)s 11 f 200.669 (N)s 15 f 97.009 y 208.27 (\260)s 2 f 95.809 y 213.768 (+1)s 13 f 83.122 y 226.518 (\241)s 10 f 92.842 y 232.018 (@)s 239.056 (L)s 11 f 94.642 y 247.222 (n)s 2 f 253.154 (+1)s 13 f 83.122 y 265.904 (\242)s 1 f 92.842 y 273.404 (log)s 13 f 83.122 y 290.904 (\241)s 10 f 92.842 y 296.404 (f)s 11 f 87.887 y 303.571 (t)s 95.809 y 302.279 (n)s 13 f 83.122 y 308.811 (\242)s 10 f 92.842 y 314.311 (d\272)s 11 f 94.642 y 326.485 (P)s 332.853 (;n)s 2 f 341.635 (+)s 11 f 349.002 (N)s 15 f 95.842 y 356.602 (\260)s 2 f 94.642 y 362.1 (+1)s 1 f 121.944 y 137.733 (:=)s 153.732 (\255)s 2 f 116.989 y 162.399 (1)s 11 f 124.91 y 162.399 (n)s 1 f 121.944 y 171.598 (+)s 183.598 (\255)s 2 f 116.989 y 192.264 (2)s 11 f 124.91 y 192.264 (n)s 10 f 121.944 y 198.796 (:)s 1 f 86.793 y 439.114 (\0504)s 10 f 449.78 (:)s 1 f 453.114 (6\051)s 151.243 y -5.69 (The)s 18.25 (\257rst)s 42.29 (term)s 70.263 (\255)s 2 f 146.889 y 78.93 (1)s 11 f 154.21 y 78.93 (n)s 1 f 151.243 y 88.735 (in)s 102.008 (the)s 121.948 (righ)s 142.315 (t)s 150.254 (hand)s 179.528 (side)s 202.868 (of)s 215.807 (the)s 235.747 (last)s 257.754 (inequalit)s 303.087 (y)s 312.694 (corresp)s 350.494 (onds)s 377.834 (to)s 391.774 (the)s 411.714 (exc)s 428.38 (hanges)s 168.043 y -5.69 (in)s 8.141 (the)s 28.64 (in)s 38.306 (terior)s 70.871 (of)s 84.37 (\244)s 11 f 169.843 y 92.703 (n)s 1 f 168.043 y 99.235 (,)s 106.434 (while)s 137.598 (the)s 158.097 (second)s 196.662 (term)s 225.193 (\255)s 2 f 163.689 y 233.86 (2)s 11 f 171.01 y 233.86 (n)s 1 f 168.043 y 244.224 (is)s 256.122 (asso)s 277.922 (ciated)s 313.087 (to)s 327.585 (exc)s 344.252 (hange)s 378.75 (at)s 393.248 (the)s 413.747 (b)s 420.747 (oundary)s 13 f 190.422 y 98.627 (\241)s 10 f 200.142 y 104.127 (@)s 111.164 (L)s 11 f 201.942 y 119.331 (n)s 2 f 125.263 (+1)s 13 f 190.422 y 138.013 (\242)s 1 f 200.142 y 143.513 (\050)s 10 f 148.18 (f)s 1 f 155.347 (\051)s 163.347 (=)s 13 f 188.742 y 190.722 (X)s 15 f 213.242 y 177.453 (i)s 18 f 180.655 (2)s 16 f 186.321 (\244)s 15 f 214.442 y 191.788 (n)s 213.242 y 197.673 (;j)s 205.176 (=)s 18 f 204.306 (2)s 16 f 209.973 (\244)s 15 f 214.442 y 215.439 (n)s 18 f 220.382 y 184.721 (j)s 15 f 187.471 (i)s 18 f 190.673 (\241)s 15 f 197.173 (j)s 18 f 201.056 (j)s 16 f 203.806 (=1)s 10 f 200.142 y 224.764 (C)s 11 f 195.187 y 234.199 (K)s 242.334 (;\257)s 203.108 y 233.341 (\260)s 1 f 200.142 y 251.657 (\050)s 10 f 256.324 (i;)s 265.791 (j)s 1 f 271.42 (;)s 10 f 276.753 (\276)s 1 f 284.041 (\051)s 13 f 186.822 y 288.707 (h)s 190.422 y 294.374 (\241)s 12 f 200.142 y 299.874 (r)s 11 f 201.942 y 309.874 (i;j)s 10 f 200.142 y 321.176 (f)s 13 f 190.422 y 328.342 (\242)s 1 f 200.142 y 333.842 (\050)s 10 f 338.509 (\276)s 1 f 345.796 (\051)s 13 f 186.822 y 350.463 (i)s 10 f 200.142 y 356.13 (:)s 1 f 248.302 y 8.71 (The)s 33.645 (pro)s 51.345 (of)s 65.281 (is)s 77.616 (divided)s 120.218 (in)s 134.487 (three)s 165.456 (steps.)s 201.062 (In)s 216.331 (the)s 237.266 (\257rst)s 262.302 (t)s 266.635 (w)s 274.968 (o)s 285.237 (steps)s 315.639 (w)s 323.972 (e)s 333.574 (estimate)s 381.91 (\255)s 2 f 243.947 y 390.577 (1)s 11 f 251.268 y 390.577 (n)s 1 f 248.302 y 401.377 (and)s 424.979 (\255)s 2 f 243.947 y 433.646 (2)s 11 f 251.268 y 433.646 (n)s 1 f 248.302 y 444.447 (and)s 265.102 y -5.69 (in)s 8.31 (the)s 28.977 (third)s 59.01 (one)s 81.01 (w)s 89.343 (e)s 98.677 (pro)s 115.71 (v)s 121.71 (e)s 131.043 (\0504.4\051)s 159.71 (.)s 17 f 288.362 y 8.71 (First)s 38.47 (step)s 1 f 63.016 (\050)s 17 f 67.683 (b)s 72.589 (ound)s 102.336 (of)s 1 f 116.442 (\255)s 2 f 284.007 y 125.109 (1)s 11 f 291.329 y 125.109 (n)s 1 f 288.362 y 131.641 (\051.)s 305.282 y 8.71 (Fix)s 29.707 (a)s 39.204 (b)s 46.204 (ond)s 69.035 (\050)s 10 f 73.701 (i;)s 83.169 (j)s 1 f 88.797 (\051)s 12 f 96.797 (2)s 1 f 108.13 (\244)s 11 f 307.082 y 116.464 (n)s 12 f 305.282 y 124.657 (\243)s 1 f 135.651 (\244)s 11 f 307.082 y 143.984 (n)s 1 f 305.282 y 154.013 (suc)s 170.413 (h)s 180.577 (that)s 12 f 206.074 (j)s 10 f 209.407 (i)s 12 f 215.202 (\241)s 10 f 226.197 (j)s 12 f 231.825 (j)s 1 f 238.492 (=)s 251.158 (1,)s 264.089 (denote)s 302.253 (b)s 308.587 (y)s 318.417 (I)s 320.59 (L)s 11 f 307.082 y 328.09 (i;j)s 1 f 305.282 y 342.889 (the)s 363.053 (one)s 384.55 (b)s 391.55 (ond)s 414.38 (generator)s 322.082 y -5.69 (corresp)s 32.11 (onding)s 72.274 (to)s 87.772 (the)s 109.27 (exc)s 125.937 (hange)s 161.435 (of)s 175.933 (spins)s 206.897 (b)s 213.897 (et)s 223.564 (w)s 231.897 (een)s 10 f 254.062 (i)s 1 f 263.027 (and)s 10 f 287.192 (j)s 1 f 297.652 (and)s 321.816 (let)s 10 f 339.981 (F)s 11 f 317.727 y 349.364 (i;j)s 325.049 y 347.698 (n)s 1 f 322.082 y 360.666 (\050)s 10 f 365.332 (\276)s 1 f 372.62 (\051)s 382.118 (b)s 389.118 (e)s 399.282 (the)s 420.78 (function)s 344.957 y -5.69 (de\257ned)s 35.643 (b)s 41.977 (y)s 10 f 52.31 (F)s 11 f 340.602 y 61.693 (i;j)s 347.923 y 60.027 (n)s 1 f 344.957 y 72.995 (\050)s 10 f 77.661 (\276)s 1 f 84.949 (\051)s 92.949 (=)s 13 f 335.237 y 105.615 (\255)s 11 f 337.67 y 112.722 (C)s 15 f 334.049 y 120.193 (K)s 127.018 (;\257)s 340.07 y 119.605 (\260)s 2 f 337.67 y 135.42 (\050)s 11 f 139.17 (i;j)s 2 f 149.872 (;)s 14 f 152.589 (\242)s 2 f 155.439 (\051)s 46.467 .48 112.722 342.197 r 11 f 349.095 y 123.992 (f)s 15 f 346.695 y 129.613 (t)s 351.495 y 128.671 (n)s 2 f 349.095 y 134.556 (\050)s 11 f 138.306 (\276)s 2 f 144.168 (\051)s 10 f 344.957 y 160.629 (f)s 11 f 340.602 y 167.795 (t)s 348.262 y 166.504 (n)s 2 f 172.436 (+)s 11 f 179.802 (N)s 15 f 349.462 y 187.403 (\260)s 2 f 348.262 y 192.901 (+1)s 1 f 344.957 y 205.651 (\050)s 12 f 210.318 (\242)s 1 f 213.651 (\051)s 13 f 335.237 y 218.318 (\256)s 2 f 350.183 y 223.985 (\244)s 15 f 344.923 y 230.551 (n)s 16 f 235.836 (+)s 15 f 242.003 (N)s 346.123 y 248.457 (\260)s 351.793 y 230.551 (n)s 1 f 344.957 y 255.155 (.)s 263.822 (W)s 275.155 (e)s 284.489 (ha)s 296.822 (v)s 302.822 (e)s 10 f 385.156 y 28.157 (\260)s 14 f 380.201 y 35.036 (\241)s 2 f 42.536 (2)s 13 f 368.823 y 49.92 (Z)s 10 f 385.156 y 63.919 (f)s 11 f 380.201 y 71.086 (t)s 388.123 y 69.795 (n)s 2 f 75.727 (+)s 11 f 83.093 (N)s 15 f 389.323 y 90.694 (\260)s 2 f 388.123 y 96.192 (+1)s 1 f 385.156 y 108.942 (I)s 111.116 (L)s 11 f 386.956 y 118.616 (i;j)s 1 f 385.156 y 131.917 (log)s 13 f 375.436 y 149.417 (\241)s 10 f 385.156 y 154.917 (f)s 11 f 380.201 y 162.084 (t)s 388.123 y 160.792 (n)s 13 f 375.436 y 167.324 (\242)s 10 f 385.156 y 172.824 (d\272)s 11 f 386.956 y 184.998 (P)s 1 f 385.156 y 196.332 (=)s 10 f 208.999 (\260)s 14 f 380.201 y 215.878 (\241)s 2 f 223.378 (2)s 13 f 368.823 y 230.761 (Z)s 10 f 385.156 y 244.761 (F)s 11 f 380.201 y 254.145 (i;j)s 388.123 y 252.478 (n)s 1 f 385.156 y 265.446 (\050)s 10 f 270.113 (\276)s 1 f 277.4 (\051)s 10 f 282.067 (f)s 11 f 380.201 y 289.234 (t)s 388.123 y 287.942 (n)s 1 f 385.156 y 294.474 (\050)s 10 f 299.141 (\276)s 1 f 306.428 (\051)s 313.095 (log)s 13 f 371.836 y 330.595 (n)s 10 f 377.038 y 340.035 (f)s 11 f 372.683 y 347.202 (t)s 380.005 y 345.91 (n)s 1 f 377.038 y 352.442 (\050)s 10 f 357.109 (\276)s 11 f 372.683 y 364.396 (i;j)s 1 f 377.038 y 375.698 (\051)s 40.329 .48 340.035 382.396 r 10 f 393.388 y 345.686 (f)s 11 f 389.921 y 352.852 (t)s 396.354 y 351.561 (n)s 1 f 393.388 y 358.093 (\050)s 10 f 362.759 (\276)s 1 f 370.047 (\051)s 13 f 371.836 y 381.804 (o)s 10 f 385.156 y 389.804 (d\272)s 11 f 386.956 y 401.978 (P)s 1 f 385.156 y 409.979 (\050)s 10 f 414.646 (\276)s 1 f 421.933 (\051)s 10 f 426.6 (:)s 1 f 420.053 y -5.69 (Using)s 28.043 (the)s 48.71 (basic)s 78.777 (inequalit)s 124.11 (y)s 10 f 447.384 y 118.942 (a)s 13 f 437.664 y 125.285 (\241)s 1 f 447.384 y 132.785 (log)s 10 f 150.285 (b)s 12 f 158.102 (\241)s 1 f 170.102 (log)s 10 f 187.602 (a)s 13 f 437.664 y 193.945 (\242)s 12 f 447.384 y 202.778 (\267)s 215.445 (\241)s 13 f 437.664 y 224.778 (\241)s 12 f 438.155 y 230.278 (p)s 6.343 .48 240.278 438.155 r 10 f 447.384 y 240.278 (a)s 12 f 249.288 (\241)s 436.572 y 261.288 (p)s 5.15 .48 271.288 436.572 r 10 f 447.384 y 271.288 (b)s 13 f 437.664 y 276.438 (\242)s 2 f 440.151 y 281.938 (2)s 1 f 447.384 y 289.988 (+)s 13 f 437.664 y 301.988 (\241)s 10 f 447.384 y 307.488 (b)s 12 f 315.305 (\241)s 10 f 327.305 (a)s 13 f 437.664 y 333.648 (\242)s 1 f 447.384 y 439.114 (\0504)s 10 f 449.78 (:)s 1 f 453.114 (7\051)s 474.716 y -5.69 (for)s 12.677 (p)s 19.677 (ositiv)s 47.743 (e)s 10 f 57.077 (a)s 1 f 67.42 (and)s 10 f 90.753 (b)s 1 f 95.903 (,)s 103.236 (the)s 123.903 (righ)s 144.27 (t)s 152.936 (hand)s 182.937 (side)s 207.003 (of)s 220.67 (the)s 241.337 (last)s 264.07 (expression)s 321.903 (is)s 333.97 (b)s 340.97 (ounded)s 382.97 (b)s 389.304 (y)s 12 f 508.715 y .31 (\241)s 10 f 9.643 (\260)s 14 f 503.76 y 16.523 (\241)s 2 f 24.023 (2)s 13 f 492.381 y 31.406 (Z)s 10 f 508.715 y 45.406 (F)s 11 f 503.76 y 54.789 (i;j)s 511.681 y 53.123 (n)s 1 f 508.715 y 66.091 (\050)s 10 f 70.757 (\276)s 1 f 78.045 (\051)s 13 f 495.395 y 82.712 (h)s 498.036 y 88.378 (p)s 12.407 .48 100.378 498.036 r 10 f 508.715 y 100.378 (f)s 11 f 505.248 y 107.545 (t)s 511.681 y 106.253 (n)s 1 f 508.715 y 112.785 (\050)s 10 f 117.452 (\276)s 11 f 503.76 y 124.739 (i;j)s 1 f 508.715 y 136.041 (\051)s 12 f 143.188 (\241)s 13 f 498.036 y 155.003 (p)s 12.407 .48 167.003 498.036 r 10 f 508.715 y 167.003 (f)s 11 f 505.248 y 174.17 (t)s 511.681 y 172.878 (n)s 1 f 508.715 y 179.41 (\050)s 10 f 184.077 (\276)s 1 f 191.364 (\051)s 13 f 495.395 y 196.031 (i)s 2 f 497.881 y 201.697 (2)s 10 f 508.715 y 207.081 (d\272)s 11 f 510.515 y 219.254 (P)s 1 f 508.715 y 229.737 (+)s 10 f 241.551 (\260)s 14 f 503.76 y 248.43 (\241)s 2 f 255.93 (2)s 13 f 492.381 y 263.314 (Z)s 10 f 508.715 y 277.314 (F)s 11 f 503.76 y 286.697 (i;j)s 511.681 y 285.03 (n)s 1 f 508.715 y 297.999 (\050)s 10 f 302.665 (\276)s 1 f 309.953 (\051)s 13 f 495.395 y 314.619 (h)s 10 f 508.715 y 320.286 (f)s 11 f 503.76 y 327.453 (t)s 511.681 y 326.161 (n)s 1 f 508.715 y 332.693 (\050)s 10 f 337.36 (\276)s 11 f 503.76 y 344.647 (i;j)s 1 f 508.715 y 355.949 (\051)s 12 f 363.096 (\241)s 10 f 374.911 (f)s 11 f 503.76 y 382.077 (t)s 511.681 y 380.786 (n)s 1 f 508.715 y 387.318 (\050)s 10 f 391.984 (\276)s 1 f 399.272 (\051)s 13 f 495.395 y 403.939 (i)s 10 f 508.715 y 409.605 (d\272)s 11 f 510.515 y 421.779 (P)s 10 f 508.715 y 429.78 (:)s 1 f 439.114 (\0504)s 10 f 449.78 (:)s 1 f 453.114 (8\051)s 544.58 y -5.69 (Observ)s 31.077 (e)s 41.02 (that)s 67.63 (for)s 86.607 (all)s 103.884 (function)s 10 f 151.495 (h)s 1 f 163.019 (and)s 186.962 (p)s 193.962 (ositiv)s 222.029 (e)s 231.973 (in)s 241.639 (tegers)s 10 f 277.016 (n)s 1 f 288.829 (and)s 10 f 312.773 (m)s 1 f 323.309 (,)s 13 f 534.86 y 331.405 (\255)s 10 f 544.58 y 337.072 (h)s 11 f 546.38 y 343.986 (n)s 2 f 349.918 (+)s 11 f 357.285 (m)s 2 f 365.8 (+1)s 13 f 534.86 y 378.55 (\256)s 2 f 549.38 y 384.217 (\244)s 15 f 545.759 y 390.783 (n)s 16 f 396.068 (+)s 15 f 402.235 (m)s 551.78 y 390.783 (n)s 1 f 544.58 y 415.153 (=)s 10 f 428.837 (h)s 11 f 546.38 y 435.751 (n)s 1 f 544.58 y 442.283 (.)s 452.78 (In)s 561.38 y -5.69 (particular,)s 53.043 (using)s 84.443 (Lemma)s 127.277 (4.1)s 146.61 (w)s 154.943 (e)s 164.277 (ha)s 176.61 (v)s 182.61 (e)s 191.943 (that)s 13 f 574.912 y 178.101 (\257)s 582.112 y 178.101 (\257)s 589.312 y 178.101 (\257)s 10 f 588.712 y 182.101 (F)s 11 f 583.757 y 191.484 (i;j)s 591.679 y 189.817 (n)s 1 f 588.712 y 202.785 (\050)s 10 f 207.452 (\276)s 1 f 214.739 (\051)s 12 f 222.073 (\241)s 1 f 234.073 (1)s 13 f 574.912 y 240.073 (\257)s 582.112 y 240.073 (\257)s 589.312 y 240.073 (\257)s 12 f 588.712 y 247.406 (\267)s 10 f 260.073 (B)s 269.777 (\260)s 276.656 (:)s 1 f 620.844 y -5.69 (With)s 25.137 (this)s 48.364 (remark,)s 92.626 (and)s 115.786 (since)s 145.013 (the)s 165.507 (measure)s 10 f 212.1 (\272)s 11 f 622.644 y 218.028 (P)s 1 f 620.844 y 229.856 (is)s 241.75 (in)s 251.417 (v)s 257.083 (arian)s 283.45 (t)s 291.944 (for)s 310.137 (the)s 330.631 (exclusion)s 382.192 (pro)s 399.892 (cess,)s 427.22 (\0504.8\051)s 455.714 (is)s 637.644 y -5.69 (b)s 1.31 (ounded)s 43.31 (ab)s 56.31 (o)s 61.977 (v)s 67.977 (e)s 77.31 (b)s 83.643 (y)s 12 f 671.642 y 22.915 (\241)s 10 f 32.248 (\260)s 14 f 666.688 y 39.128 (\241)s 2 f 46.628 (2)s 1 f 671.642 y 52.011 (\0501)s 12 f 65.344 (\241)s 10 f 77.344 (B)s 87.048 (\260)s 1 f 93.928 (\051)s 13 f 655.309 y 100.595 (Z)s 658.322 y 114.594 (h)s 660.963 y 120.261 (p)s 12.407 .48 132.261 660.963 r 10 f 671.642 y 132.261 (f)s 11 f 668.176 y 139.428 (t)s 674.609 y 138.136 (n)s 1 f 671.642 y 144.668 (\050)s 10 f 149.335 (\276)s 11 f 666.688 y 156.622 (i;j)s 1 f 671.642 y 167.924 (\051)s 12 f 175.257 (\241)s 13 f 660.963 y 187.257 (p)s 12.407 .48 199.257 660.963 r 10 f 671.642 y 199.257 (f)s 11 f 668.176 y 206.424 (t)s 674.609 y 205.132 (n)s 1 f 671.642 y 211.664 (\050)s 10 f 216.331 (\276)s 1 f 223.618 (\051)s 13 f 658.322 y 228.285 (i)s 2 f 660.809 y 233.952 (2)s 10 f 671.642 y 239.335 (d\272)s 11 f 673.442 y 251.509 (P)s 1 f 671.642 y 262.176 (+)s 10 f 274.176 (B)s 283.881 (\260)s 14 f 666.688 y 290.76 (\241)s 2 f 298.26 (1)s 13 f 655.309 y 305.643 (Z)s 657.842 y 319.643 (\257)s 665.042 y 319.643 (\257)s 672.242 y 319.643 (\257)s 10 f 671.642 y 323.643 (f)s 11 f 666.688 y 330.81 (t)s 674.609 y 329.518 (n)s 1 f 671.642 y 336.05 (\050)s 10 f 340.717 (\276)s 11 f 666.688 y 348.004 (i;j)s 1 f 671.642 y 359.306 (\051)s 12 f 366.639 (\241)s 10 f 378.639 (f)s 11 f 666.688 y 385.806 (t)s 674.609 y 384.514 (n)s 1 f 671.642 y 391.046 (\050)s 10 f 395.713 (\276)s 1 f 403 (\051)s 13 f 657.842 y 407.667 (\257)s 665.042 y 407.667 (\257)s 672.242 y 407.667 (\257)s 10 f 671.642 y 411.667 (d\272)s 11 f 673.442 y 423.841 (P)s 10 f 671.642 y 431.842 (:)s 1 f 705.976 y 223.045 (19)s do-end end endp %%Page: 20 20 %%BeginPageSetup initializepage (Raffaele Esposito; page: 20 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f0_12 sf ( )S -996 -1000 :M f1_12 sf ( )S -993 -1000 :M f2_12 sf ( )S -989 -1000 :M f10_12 sf ( )S -981 -1000 :M f11_12 sf ( )S -972 -1000 :M f12_12 sf ( )S -960 -1000 :M f13_12 sf ( )S -951 -1000 :M f14_12 sf ( )S -937 -1000 :M f15_12 sf ( )S -926 -1000 :M f17_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 1200 1000 div mul /CMBX10 findfont fdef 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 17 10 1200 1000 div mul /CMTI10 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 6.31 y -5.69 (Using)s 27.541 (the)s 47.705 (elemen)s 83.372 (tary)s 108.57 (inequalit)s 153.903 (y)s 163.735 (2)s 10 f 169.735 (ab)s 12 f 184.561 (\267)s 10 f 197.227 (A)s 14 f 1.955 y 206.228 (\241)s 2 f 213.728 (1)s 10 f 6.31 y 219.111 (a)s 2 f 1.955 y 225.454 (2)s 1 f 6.31 y 232.499 (+)s 10 f 243.495 (Ab)s 2 f 1.955 y 257.645 (2)s 1 f 6.31 y 263.028 (,)s 269.96 (the)s 290.124 (second)s 328.356 (term)s 356.553 (of)s 369.718 (the)s 389.882 (last)s 412.113 (inequalit)s 457.447 (y)s 23.11 y -5.69 (is)s 6.376 (b)s 13.376 (ounded)s 55.377 (b)s 61.71 (y)s 10 f 55.059 y 34.811 (A)s 9 .48 34.811 60.417 r 1 f 71.408 y 36.311 (2)s 10 f 63.177 y 45.251 (\260)s 14 f 58.222 y 52.13 (\241)s 2 f 59.63 (2)s 10 f 63.177 y 65.014 (I)s 11 f 64.977 y 70.289 (i;j)s 1 f 63.177 y 81.59 (\050)s 10 f 86.257 (f)s 11 f 58.222 y 93.423 (t)s 66.143 y 92.132 (n)s 1 f 63.177 y 98.664 (\051)s 105.997 (+)s 10 f 55.059 y 122.085 (B)s 15 .48 119.437 60.417 r 1 f 71.408 y 119.437 (2)s 10 f 125.437 (A)s 13 f 46.843 y 137.877 (Z)s 49.857 y 151.877 (h)s 52.497 y 157.544 (p)s 12.407 .48 169.544 52.497 r 10 f 63.177 y 169.544 (f)s 11 f 59.71 y 176.71 (t)s 66.143 y 175.419 (n)s 1 f 63.177 y 181.951 (\050)s 10 f 186.617 (\276)s 11 f 58.222 y 193.905 (i;j)s 1 f 63.177 y 205.206 (\051)s 212.54 (+)s 13 f 52.497 y 224.54 (p)s 12.407 .48 236.54 52.497 r 10 f 63.177 y 236.54 (f)s 11 f 59.71 y 243.706 (t)s 66.143 y 242.415 (n)s 1 f 63.177 y 248.947 (\050)s 10 f 253.613 (\276)s 1 f 260.901 (\051)s 13 f 49.857 y 265.567 (i)s 2 f 52.343 y 271.234 (2)s 10 f 63.177 y 276.617 (d\272)s 11 f 64.977 y 288.791 (P)s 12 f 63.177 y 300.126 (\267)s 10 f 55.059 y 314.232 (A)s 9 .48 314.232 60.417 r 1 f 71.408 y 315.732 (2)s 10 f 63.177 y 324.672 (\260)s 14 f 58.222 y 331.552 (\241)s 2 f 339.052 (2)s 10 f 63.177 y 344.435 (I)s 11 f 64.977 y 349.71 (i;j)s 1 f 63.177 y 361.011 (\050)s 10 f 365.678 (f)s 11 f 58.222 y 372.845 (t)s 66.143 y 371.553 (n)s 1 f 63.177 y 378.085 (\051)s 385.418 (+)s 397.418 (2)s 10 f 55.059 y 404.858 (B)s 2 f 50.704 y 414.563 (2)s 15.088 .48 404.858 60.417 r 10 f 71.408 y 407.902 (A)s 63.177 y 421.386 (;)s 1 f 102.879 y -5.69 (where)s 30.898 (w)s 39.231 (e)s 50.453 (used)s 79.741 (in)s 95.63 (the)s 118.185 (last)s 142.806 (inequalit)s 188.14 (y)s 193.473 (,)s 203.167 (Sc)s 214.833 (h)s 221.167 (w)s 229.5 (artz)s 256.088 (inequalit)s 301.422 (y)s 313.643 (and)s 338.865 (the)s 361.42 (fact)s 386.975 (that)s 10 f 414.863 (f)s 11 f 98.524 y 422.03 (t)s 105.846 y 420.738 (n)s 1 f 102.879 y 433.159 (is)s 447.114 (the)s 119.679 y -5.69 (probabilit)s 45.343 (y)s 55.025 (densit)s 86.092 (y)s 95.773 (with)s 122.455 (resp)s 144.222 (ect)s 162.903 (to)s 10 f 176.918 (\272)s 11 f 121.479 y 182.846 (P)s 1 f 119.679 y 190.847 (.)s 199.297 (Cho)s 220.963 (osing)s 10 f 251.045 (A)s 1 f 263.393 (small)s 294.142 (enough,)s 338.287 (and)s 360.969 (taking)s 397.317 (the)s 417.332 (sum)s 442.08 (o)s 447.747 (v)s 453.747 (er)s 136.479 y -5.69 (all)s 10 f 10.977 (i;)s 20.444 (j)s 12 f 29.406 (2)s 1 f 40.739 (\244)s 11 f 138.279 y 49.072 (n)s 1 f 136.479 y 59.604 (suc)s 76.004 (h)s 86.671 (that)s 12 f 112.671 (j)s 10 f 116.004 (i)s 12 f 122.805 (\241)s 10 f 134.805 (j)s 12 f 140.434 (j)s 1 f 147.1 (=)s 159.767 (1,)s 173.1 (w)s 181.434 (e)s 190.767 (get)s 168.327 y 161.983 (\255)s 2 f 163.372 y 170.65 (1)s 11 f 171.293 y 170.65 (n)s 12 f 168.327 y 180.515 (\267)s 193.182 (\241)s 10 f 202.515 (C)s 2 f 170.127 y 211.092 (0)s 10 f 168.327 y 216.475 (D)s 11 f 170.127 y 226.41 (n)s 1 f 168.327 y 232.942 (\050)s 10 f 237.609 (f)s 11 f 163.372 y 244.775 (t)s 171.293 y 243.484 (n)s 1 f 168.327 y 250.016 (\051)s 257.349 (+)s 10 f 269.349 (C)s 14 f 163.372 y 278.784 (0)s 2 f 171.293 y 277.925 (0)s 10 f 168.327 y 283.309 (n)s 11 f 163.372 y 290.512 (d)s 1 f 168.327 y 439.114 (\0504)s 10 f 449.78 (:)s 1 f 453.114 (9\051)s 200.174 y -5.69 (for)s 12.677 (some)s 42.743 (p)s 49.743 (ositiv)s 77.81 (e)s 87.143 (constan)s 126.877 (ts)s 10 f 140.277 (C)s 2 f 201.974 y 148.853 (0)s 1 f 200.174 y 158.237 (and)s 10 f 181.57 (C)s 14 f 195.819 y 191.005 (0)s 2 f 203.153 y 190.147 (0)s 1 f 200.174 y 195.53 (.)s 17 f 224.942 y 8.71 (Se)s 20.363 (c)s 25.27 (ond)s 48.576 (step)s 1 f 73.123 (\050)s 17 f 77.789 (b)s 82.696 (ound)s 112.442 (of)s 1 f 126.549 (\255)s 2 f 220.587 y 135.216 (2)s 11 f 227.908 y 135.216 (n)s 1 f 224.942 y 141.748 (\051.)s 242.077 y 8.71 (Fix)s 30.21 (a)s 40.21 (b)s 47.21 (ond)s 70.543 (\050)s 10 f 75.21 (i;)s 84.677 (j)s 1 f 90.306 (\051)s 12 f 98.306 (2)s 1 f 109.639 (\244)s 11 f 243.877 y 117.973 (n)s 12 f 242.077 y 127.171 (\243)s 1 f 139.171 (\244)s 11 f 237.723 y 147.504 (c)s 245.044 y 147.504 (n)s 1 f 242.077 y 154.036 (,)s 161.37 (suc)s 177.77 (h)s 188.436 (that)s 12 f 214.437 (j)s 10 f 217.77 (i)s 12 f 224.571 (\241)s 10 f 236.571 (j)s 12 f 242.199 (j)s 1 f 248.866 (=)s 261.532 (1)s 271.532 (and)s 294.866 (decomp)s 335.199 (ose)s 355.266 (I)s 357.439 (L)s 11 f 243.877 y 364.939 (i;j)s 1 f 242.077 y 380.241 (in)s 394.241 (three)s 424.941 (terms,)s 273.925 y 141.439 (I)s 143.613 (L)s 11 f 275.725 y 151.113 (i;j)s 1 f 273.925 y 165.747 (=)s 178.414 (I)s 180.587 (L)s 2 f 267.692 y 188.087 (\0500)s 11 f 196.621 (;)s 2 f 199.471 (1\051)s 11 f 277.27 y 188.087 (i;j)s 1 f 273.925 y 211.271 (+)s 223.271 (I)s 225.444 (L)s 2 f 267.692 y 232.944 (\050)s 14 f 236.694 (\241)s 2 f 244.194 (1)s 11 f 248.977 (;)s 2 f 251.827 (0\051)s 11 f 277.27 y 232.944 (i;j)s 1 f 273.925 y 263.627 (+)s 275.627 (I)s 277.801 (L)s 2 f 267.692 y 285.301 (\050)s 14 f 289.051 (\241)s 2 f 296.551 (1)s 11 f 301.334 (;)s 2 f 304.184 (1\051)s 11 f 277.27 y 285.301 (i;j)s 10 f 273.925 y 313.317 (;)s 1 f 433.113 (\0504)s 10 f 443.78 (:)s 1 f 447.114 (10\051)s 311.284 y -5.69 (where)s 29.01 (for)s 47.377 (\050)s 10 f 52.043 (l)s 55.86 (;)s 61.193 (m)s 1 f 71.729 (\051)s 12 f 79.729 (2)s 91.063 (f)s 1 f 97.063 (\0500)s 10 f 107.729 (;)s 1 f 113.063 (1\051)s 10 f 123.729 (;)s 1 f 129.063 (\050)s 12 f 133.729 (\241)s 1 f 143.063 (1)s 10 f 149.063 (;)s 1 f 154.396 (0\051)s 10 f 165.063 (;)s 1 f 170.396 (\050)s 12 f 175.063 (\241)s 1 f 184.396 (1)s 10 f 190.396 (;)s 1 f 195.729 (1\051)s 12 f 206.396 (g)s 1 f 212.396 (,)s 219.729 (I)s 221.903 (L)s 2 f 305.051 y 229.403 (\050)s 11 f 233.153 (l)s 236.236 (;m)s 2 f 247.601 (\051)s 11 f 314.629 y 229.403 (i;j)s 1 f 311.284 y 255.951 (is)s 268.018 (giv)s 283.351 (en)s 299.351 (b)s 305.685 (y)s 13 f 340.19 y 74.192 (\241)s 1 f 349.91 y 79.692 (I)s 81.866 (L)s 2 f 343.676 y 89.366 (\050)s 11 f 93.116 (l)s 96.199 (;m)s 2 f 107.564 (\051)s 11 f 353.255 y 89.366 (i;j)s 10 f 349.91 y 111.914 (g)s 13 f 340.19 y 118.069 (\242)s 1 f 349.91 y 123.569 (\050)s 10 f 128.235 (\276)s 1 f 135.523 (\051)s 143.523 (=)s 10 f 156.189 (r)s 2 f 343.676 y 161.937 (\050)s 11 f 165.687 (l)s 168.77 (;m)s 2 f 180.135 (\051)s 11 f 353.255 y 161.603 (i;j)s 1 f 349.91 y 184.485 (\050)s 10 f 189.152 (\276)s 1 f 196.439 (\051)s 10 f 201.106 (C)s 11 f 344.955 y 210.541 (K)s 218.676 (;\257)s 352.876 y 209.683 (\260)s 1 f 349.91 y 227.999 (\050)s 10 f 232.666 (i;)s 242.133 (j)s 1 f 247.762 (;)s 10 f 253.095 (\276)s 1 f 260.383 (\051)s 13 f 336.59 y 267.049 (h)s 10 f 349.91 y 272.716 (g)s 1 f 278.87 (\050)s 0 f 283.537 (T)s 11 f 344.143 y 293.137 (j)s 297.076 (;i)s 353.53 y 293.137 (m)s 14 f 301.652 (\241)s 11 f 309.152 (l)s 10 f 349.91 y 312.835 (\276)s 1 f 320.123 (\051)s 12 f 327.456 (\241)s 10 f 339.456 (g)s 1 f 345.61 (\050)s 10 f 350.277 (\276)s 1 f 357.564 (\051)s 13 f 336.59 y 362.231 (i)s 1 f 379.91 y 154.856 (+)s 10 f 166.856 (r)s 2 f 373.677 y 172.603 (\050)s 11 f 176.353 (l)s 179.437 (;m)s 2 f 190.802 (\051)s 11 f 383.255 y 172.27 (j)s 176.21 (;i)s 1 f 379.91 y 195.152 (\050)s 10 f 199.819 (\276)s 1 f 207.106 (\051)s 10 f 211.773 (C)s 11 f 374.955 y 221.208 (K)s 229.343 (;\257)s 382.876 y 220.349 (\260)s 1 f 379.91 y 238.666 (\050)s 10 f 243.332 (i;)s 252.8 (j)s 1 f 258.429 (;)s 10 f 263.762 (\276)s 1 f 271.049 (\051)s 13 f 366.59 y 277.716 (h)s 10 f 379.91 y 283.383 (g)s 1 f 289.537 (\050)s 0 f 294.203 (T)s 11 f 374.143 y 303.803 (i;j)s 383.53 y 303.803 (m)s 14 f 312.319 (\241)s 11 f 319.819 (l)s 10 f 379.91 y 323.502 (\276)s 1 f 330.79 (\051)s 12 f 338.123 (\241)s 10 f 350.123 (g)s 1 f 356.277 (\050)s 10 f 360.944 (\276)s 1 f 368.231 (\051)s 13 f 366.59 y 372.898 (i)s 10 f 379.91 y 380.564 (:)s 1 f 418.624 y -5.69 (Here)s 23.439 (for)s 10 f 42.568 (\266)s 1 f 51.42 (=)s 65.357 (1)s 10 f 71.357 (;)s 1 f 76.691 (2,)s 90.977 (\050)s 10 f 95.644 (i;)s 105.112 (j)s 1 f 110.74 (\051)s 12 f 120.011 (2)s 10 f 132.615 (Z)s 135.665 (Z)s 11 f 413.391 y 146.715 (d)s 12 f 418.624 y 155.486 (\243)s 10 f 167.994 (Z)s 171.044 (Z)s 11 f 413.391 y 182.094 (d)s 1 f 418.624 y 192.452 (and)s 216.548 (a)s 227.311 (con\257guration)s 10 f 300.774 (\276)s 1 f 308.061 (,)s 0 f 316.348 (T)s 11 f 414.269 y 325.948 (i;j)s 421.591 y 325.948 (\266)s 10 f 418.624 y 337.249 (\276)s 1 f 349.299 (is)s 362.128 (de\257ned)s 404.224 (b)s 410.558 (y)s 0 f 421.654 (T)s 11 f 414.269 y 431.254 (i;j)s 421.591 y 431.254 (\266)s 10 f 418.624 y 442.555 (\276)s 1 f 454.447 (=)s 10 f 435.424 y -5.69 (\276)s 12 f 2.485 (\241)s 10 f 12.706 (\266\261)s 11 f 437.224 y 22.286 (i)s 1 f 435.424 y 27.169 (+)s 10 f 37.39 (\266\261)s 11 f 437.224 y 46.971 (j)s 1 f 435.424 y 52.027 (,)s 58.649 (and)s 10 f 81.093 (r)s 2 f 429.191 y 86.84 (\050)s 11 f 90.59 (l)s 93.673 (;m)s 2 f 105.039 (\051)s 11 f 438.769 y 86.507 (i;j)s 1 f 435.424 y 109.389 (\050)s 10 f 114.055 (\276)s 1 f 121.343 (\051)s 129.343 (=)s 142.009 (1)s 14 f 437.591 y 148.009 (f)s 11 f 152.926 (\276)s 2 f 158.788 (\050)s 11 f 162.538 (i)s 2 f 165.933 (\051=)s 11 f 177.05 (l)s 180.133 (;\276)s 2 f 188.846 (\050)s 11 f 192.596 (j)s 2 f 197.052 (\051=)s 11 f 208.169 (m)s 14 f 216.684 (g)s 1 f 435.424 y 222.201 (.)s 230.571 (F)s 237.404 (or)s 10 f 251.215 (k)s 12 f 261.173 (2)s 10 f 272.506 (Z)s 275.556 (Z)s 11 f 430.191 y 286.606 (d)s 1 f 435.424 y 292.202 (,)s 10 f 298.823 (\261)s 11 f 437.224 y 304.157 (k)s 1 f 435.424 y 313.171 (is)s 324.349 (the)s 344.126 (con\257guration)s 415.936 (with)s 442.38 (spin)s 452.224 y -5.69 (1)s 3.892 (at)s 18.14 (site)s 10 f 39.789 (k)s 1 f 49.996 (and)s 72.911 (none)s 101.159 (elsewhere,)s 157.592 (and)s 180.507 (addition)s 227.422 (of)s 240.671 (t)s 245.004 (w)s 253.337 (o)s 262.919 (con\257gurations)s 339.934 (is)s 351.583 (de\257ned)s 392.498 (co)s 404.165 (ordinate)s 451.114 (b)s 457.447 (y)s 469.024 y -5.69 (co)s 5.976 (ordinate.)s 486.16 y 8.71 (The)s 34.522 (term)s 64.367 (\255)s 2 f 481.805 y 73.034 (2)s 11 f 489.127 y 73.034 (n)s 1 f 486.16 y 84.711 (in)s 99.856 (\0504.6\051)s 129.668 (can)s 152.814 (b)s 159.814 (e)s 170.292 (written)s 213.471 (as)s 229.35 (a)s 240.495 (sum)s 267.04 (of)s 281.852 (terms)s 316.431 (\255)s 2 f 481.805 y 325.097 (2)s 11 f 489.283 y 325.097 (i;j)s 1 f 486.16 y 341.544 (asso)s 363.344 (ciated)s 399.823 (to)s 415.635 (the)s 437.447 (b)s 444.447 (ond)s 502.96 y -5.69 (\050)s 10 f -1.024 (i;)s 8.444 (j)s 1 f 14.073 (\051.)s 28.88 (The)s 54.038 (decomp)s 94.372 (osition)s 133.597 (\0504.10\051)s 168.755 (induces)s 211.98 (an)s 229.138 (analogous)s 285.03 (decomp)s 325.363 (osition)s 364.588 (for)s 383.446 (\255)s 2 f 498.605 y 392.113 (2)s 11 f 506.083 y 392.113 (i;j)s 1 f 502.96 y 403.414 (.)s 413.555 (W)s 424.889 (e)s 434.713 (study)s 525.05 y -5.69 (explicitly)s 45.746 (only)s 71.516 (the)s 91.619 (one)s 113.055 (corresp)s 150.855 (onding)s 189.625 (to)s 203.728 (I)s 205.901 (L)s 2 f 518.817 y 213.401 (\050)s 14 f 217.151 (\241)s 2 f 224.651 (1)s 11 f 229.435 (;)s 2 f 232.285 (1\051)s 11 f 528.395 y 213.401 (i;j)s 1 f 525.05 y 241.418 (,)s 248.3 (that)s 273.737 (w)s 282.07 (e)s 290.839 (denote)s 328.942 (b)s 335.276 (y)s 345.045 (\255)s 2 f 518.817 y 353.712 (\050)s 14 f 357.462 (\241)s 2 f 364.962 (1)s 11 f 369.745 (;)s 2 f 372.595 (1\051)s 11 f 528.395 y 353.712 (i;j)s 1 f 525.05 y 381.729 (.)s 390.208 (The)s 414.311 (other)s 445.114 (t)s 449.447 (w)s 457.78 (o)s 541.85 y -5.69 (terms)s 27.743 (are)s 47.777 (dealt)s 77.777 (with)s 105.11 (in)s 119.11 (the)s 139.777 (same)s 169.843 (w)s 178.177 (a)s 183.843 (y)s 189.177 (.)s 580.364 y 93.637 (\255)s 2 f 574.131 y 102.304 (\050)s 14 f 106.054 (\241)s 2 f 113.554 (1)s 11 f 118.337 (;)s 2 f 121.187 (1\051)s 11 f 583.709 y 102.304 (i;j)s 1 f 580.364 y 133.654 (=)s 10 f 146.32 (\260)s 14 f 575.41 y 153.2 (\241)s 2 f 160.7 (2)s 13 f 564.031 y 168.083 (Z)s 10 f 580.364 y 182.083 (f)s 11 f 575.41 y 189.25 (t)s 583.331 y 187.958 (n)s 2 f 193.89 (+)s 11 f 201.257 (N)s 15 f 584.531 y 208.858 (\260)s 2 f 583.331 y 214.356 (+1)s 1 f 580.364 y 227.106 (\050)s 10 f 231.773 (\276)s 1 f 239.06 (\051I)s 245.9 (L)s 2 f 574.131 y 253.4 (\050)s 14 f 257.15 (\241)s 2 f 264.65 (1)s 11 f 269.433 (;)s 2 f 272.283 (1\051)s 11 f 583.709 y 253.4 (i;j)s 1 f 580.364 y 283.417 (log)s 13 f 570.644 y 300.917 (\241)s 10 f 580.364 y 306.417 (f)s 11 f 575.41 y 313.584 (t)s 583.331 y 312.292 (n)s 1 f 580.364 y 318.824 (\050)s 10 f 323.491 (\276)s 1 f 330.778 (\051)s 13 f 570.644 y 335.445 (\242)s 10 f 580.364 y 340.945 (d\272)s 11 f 582.164 y 353.118 (P)s 10 f 580.364 y 361.12 (:)s 1 f 621.87 y -5.69 (Let)s 10 f 15.81 (F)s 11 f 616.104 y 25.193 (i;j)s 2 f 625.07 y 23.526 (1)s 1 f 621.87 y 40.495 (and)s 10 f 63.828 (F)s 11 f 616.104 y 73.211 (i;j)s 2 f 625.07 y 71.545 (2)s 1 f 621.87 y 88.513 (b)s 95.513 (e)s 104.846 (de\257ned)s 146.179 (b)s 152.513 (y)s 10 f 656.243 y 103.947 (F)s 11 f 650.476 y 113.33 (i;j)s 2 f 659.442 y 111.663 (1)s 1 f 656.243 y 124.631 (\050)s 10 f 129.298 (\276)s 1 f 136.586 (\051)s 144.585 (=)s 157.252 (1)s 14 f 658.409 y 163.252 (f)s 11 f 168.169 (\276)s 2 f 174.031 (\050)s 11 f 177.781 (j)s 2 f 182.237 (\051=1)s 14 f 198.137 (g)s 10 f 656.243 y 203.654 (C)s 11 f 651.288 y 213.089 (K)s 221.224 (;\257)s 659.209 y 212.231 (\260)s 1 f 656.243 y 230.547 (\050)s 10 f 235.214 (i;)s 244.681 (j)s 1 f 250.31 (;)s 10 f 255.643 (\276)s 1 f 262.93 (\051)s 10 f 267.597 (f)s 11 f 651.288 y 274.764 (t)s 659.209 y 273.472 (n)s 2 f 279.404 (+)s 11 f 286.771 (N)s 15 f 660.409 y 294.372 (\260)s 2 f 659.209 y 299.87 (+1)s 1 f 656.243 y 312.62 (\050)s 10 f 317.287 (\276)s 1 f 324.574 (\051)s 10 f 329.241 (;)s 676.643 y 103.947 (F)s 11 f 670.876 y 113.33 (i;j)s 2 f 679.842 y 111.663 (2)s 1 f 676.643 y 124.631 (\050)s 10 f 129.298 (\276)s 1 f 136.586 (\051)s 144.585 (=)s 157.252 (1)s 14 f 678.809 y 163.252 (f)s 11 f 168.169 (\276)s 2 f 174.031 (\050)s 11 f 177.781 (j)s 2 f 182.237 (\051=1)s 14 f 198.137 (g)s 10 f 676.643 y 203.654 (C)s 11 f 671.688 y 213.089 (K)s 221.224 (;\257)s 679.609 y 212.231 (\260)s 1 f 676.643 y 230.547 (\050)s 10 f 235.214 (i;)s 244.681 (j)s 1 f 250.31 (;)s 10 f 255.643 (\276)s 11 f 671.688 y 262.93 (j)s 266.87 (;i)s 1 f 676.643 y 273.715 (\051)s 10 f 278.382 (f)s 11 f 671.688 y 285.549 (t)s 679.609 y 284.257 (n)s 2 f 290.189 (+)s 11 f 297.556 (N)s 15 f 680.809 y 305.156 (\260)s 2 f 679.609 y 310.655 (+1)s 1 f 676.643 y 323.405 (\050)s 10 f 328.071 (\276)s 11 f 671.688 y 335.359 (j)s 339.298 (;i)s 1 f 676.643 y 346.143 (\051)s 10 f 350.81 (:)s 1 f 705.976 y 223.045 (20)s do-end end endp %%Page: 21 21 %%BeginPageSetup initializepage (Raffaele Esposito; page: 21 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f1_12 sf ( )S -997 -1000 :M f2_12 sf ( )S -993 -1000 :M f10_12 sf ( )S -985 -1000 :M f11_12 sf ( )S -976 -1000 :M f12_12 sf ( )S -964 -1000 :M f13_12 sf ( )S -954 -1000 :M f14_12 sf ( )S -941 -1000 :M f15_12 sf ( )S -930 -1000 :M f16_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 16 5 1200 1000 div mul /CMR5 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 6.843 y -5.69 (By)s 13.143 (c)s 18.143 (hanging)s 63.477 (v)s 69.143 (ariables,)s 116.577 (\255)s 2 f .61 y 125.243 (\050)s 14 f 128.993 (\241)s 2 f 136.493 (1)s 11 f 141.277 (;)s 2 f 144.127 (1\051)s 11 f 10.188 y 125.243 (i;j)s 1 f 6.843 y 157.26 (can)s 179.26 (b)s 186.26 (e)s 195.594 (rewritten)s 247.66 (as)s 10 f 42.507 y 5.501 (\260)s 14 f 37.552 y 12.38 (\241)s 2 f 19.881 (2)s 13 f 26.174 y 27.264 (Z)s 1 f 42.507 y 41.264 (1)s 14 f 44.674 y 47.264 (f)s 11 f 52.18 (\276)s 2 f 58.043 (\050)s 11 f 61.793 (i)s 2 f 65.188 (\051=)s 14 f 76.304 (\241)s 2 f 83.805 (1)s 14 f 88.588 (g)s 13 f 29.187 y 94.105 (n)s 32.787 y 102.105 (\255)s 10 f 42.507 y 107.771 (F)s 11 f 36.74 y 117.155 (i;j)s 2 f 45.707 y 115.488 (1)s 1 f 42.507 y 128.456 (\050)s 10 f 133.123 (\276)s 1 f 140.41 (\051)s 13 f 32.787 y 145.077 (\256)s 2 f 47.734 y 150.744 (\244)s 15 f 42.474 y 157.31 (n)s 16 f 162.595 (+)s 15 f 168.762 (N)s 43.674 y 175.216 (\260)s 49.344 y 157.31 (n)s 12 f 42.507 y 184.581 (\241)s 13 f 32.787 y 196.581 (\255)s 10 f 42.507 y 202.247 (F)s 11 f 36.74 y 211.631 (i;j)s 2 f 45.707 y 209.964 (2)s 1 f 42.507 y 222.932 (\050)s 10 f 227.599 (\276)s 1 f 234.886 (\051)s 13 f 32.787 y 239.553 (\256)s 2 f 47.734 y 245.22 (\244)s 15 f 42.474 y 251.786 (n)s 16 f 257.071 (+)s 15 f 263.238 (N)s 43.674 y 269.692 (\260)s 49.344 y 251.786 (n)s 13 f 29.187 y 276.39 (o)s 1 f 42.507 y 286.39 (log)s 13 f 29.187 y 303.89 (n)s 10 f 34.389 y 313.33 (f)s 11 f 30.034 y 320.497 (t)s 37.356 y 319.205 (n)s 1 f 34.389 y 325.737 (\050)s 10 f 330.404 (\276)s 1 f 340.358 (+)s 352.358 (2)s 10 f 358.358 (\261)s 11 f 36.189 y 363.691 (i)s 1 f 34.389 y 367.686 (\051)s 59.023 .48 313.33 39.747 r 10 f 50.738 y 328.328 (f)s 11 f 47.272 y 335.494 (t)s 53.705 y 334.203 (n)s 1 f 50.738 y 340.735 (\050)s 10 f 345.401 (\276)s 1 f 352.689 (\051)s 13 f 29.187 y 373.793 (o)s 10 f 42.507 y 381.793 (d\272)s 11 f 44.307 y 393.967 (P)s 1 f 42.507 y 401.968 (\050)s 10 f 406.635 (\276)s 1 f 413.922 (\051)s 10 f 418.589 (:)s 1 f 433.113 (\0504)s 10 f 443.78 (:)s 1 f 447.114 (11\051)s 76.985 y -5.69 (Since)s 25.244 (w)s 33.577 (e)s 42.511 (ha)s 54.844 (v)s 60.844 (e)s 69.778 (that)s 95.379 (\050)s 10 f 100.046 (a)s 12 f 108.256 (\241)s 10 f 119.457 (b)s 1 f 124.607 (\051)s 13 f 67.265 y 129.274 (\241)s 1 f 76.985 y 136.774 (log)s 10 f 154.274 (c)s 12 f 161.335 (\241)s 1 f 172.536 (log)s 10 f 190.036 (d)s 13 f 67.265 y 196.282 (\242)s 1 f 76.985 y 205.382 (is)s 217.05 (negativ)s 255.05 (e)s 263.984 (for)s 10 f 281.951 (a)s 1 f 288.294 (,)s 10 f 295.308 (b)s 1 f 300.458 (,)s 10 f 307.472 (c)s 1 f 316.265 (and)s 10 f 339.199 (d)s 1 f 349.046 (p)s 356.046 (ositiv)s 384.112 (e)s 393.046 (real)s 416.014 (n)s 422.347 (um)s 438.68 (b)s 445.68 (ers,)s 93.785 y -5.69 (unless)s 10 f 30.778 (a)s 12 f 42.125 (\270)s 10 f 56.461 (b)s 1 f 66.613 (and)s 10 f 90.949 (c)s 12 f 101.145 (\270)s 10 f 115.482 (d)s 1 f 126.729 (or)s 10 f 142.431 (a)s 12 f 153.778 (\267)s 10 f 168.114 (b)s 1 f 178.266 (and)s 10 f 202.602 (c)s 12 f 212.798 (\267)s 10 f 227.134 (d)s 1 f 233.38 (,)s 241.966 (w)s 250.299 (e)s 260.635 (ma)s 276.301 (y)s 287.637 (in)s 297.303 (tro)s 313.004 (duce)s 342.006 (in)s 357.008 (the)s 378.676 (last)s 402.412 (in)s 412.078 (tegral)s 447.114 (the)s 110.585 y -5.69 (indicator)s 45.01 (function)s 92.01 (of)s 105.677 (the)s 126.343 (set)s 10 f 145.077 (E)s 2 f 106.23 y 154.627 (1)s 11 f 113.551 y 153.935 (n)s 12 f 110.585 y 163.134 ([)s 10 f 173.8 (E)s 2 f 106.23 y 183.35 (2)s 11 f 113.551 y 182.659 (n)s 1 f 110.585 y 189.191 (,)s 196.524 (where)s 10 f 140.398 y 45.872 (E)s 2 f 135.443 y 55.422 (1)s 11 f 143.364 y 54.73 (n)s 1 f 140.398 y 64.595 (=)s 13 f 127.078 y 77.262 (n)s 10 f 140.398 y 85.262 (\276)s 1 f 99.216 (:)s 13 f 130.678 y 109.216 (\255)s 10 f 140.398 y 114.882 (F)s 11 f 134.631 y 124.266 (i;j)s 2 f 143.598 y 122.599 (1)s 1 f 140.398 y 135.567 (\050)s 10 f 140.234 (\276)s 1 f 147.521 (\051)s 13 f 130.678 y 152.188 (\256)s 2 f 145.624 y 157.855 (\244)s 15 f 140.364 y 164.421 (n)s 16 f 169.706 (+)s 15 f 175.873 (N)s 141.564 y 182.327 (\260)s 147.234 y 164.421 (n)s 12 f 140.398 y 192.358 (\270)s 13 f 130.678 y 205.025 (\255)s 10 f 140.398 y 210.692 (F)s 11 f 134.631 y 220.075 (i;j)s 2 f 143.598 y 218.408 (2)s 1 f 140.398 y 231.377 (\050)s 10 f 236.043 (\276)s 1 f 243.331 (\051)s 13 f 130.678 y 247.997 (\256)s 2 f 145.624 y 253.664 (\244)s 15 f 140.364 y 260.231 (n)s 16 f 265.516 (+)s 15 f 271.682 (N)s 141.564 y 278.137 (\260)s 147.234 y 260.231 (n)s 10 f 140.398 y 284.835 (;)s 296.834 (f)s 11 f 135.443 y 304.001 (t)s 143.364 y 302.709 (n)s 1 f 140.398 y 309.241 (\050)s 10 f 313.908 (\276)s 1 f 323.862 (+)s 335.862 (2)s 10 f 341.862 (\261)s 11 f 142.198 y 347.196 (i)s 1 f 140.398 y 351.191 (\051)s 12 f 359.191 (\270)s 10 f 371.857 (f)s 11 f 135.443 y 379.024 (t)s 143.364 y 377.732 (n)s 1 f 140.398 y 384.264 (\050)s 10 f 388.931 (\276)s 1 f 396.218 (\051)s 13 f 127.078 y 400.885 (o)s 10 f 140.398 y 408.885 (;)s 170.398 y 45.872 (E)s 2 f 165.443 y 55.422 (2)s 11 f 173.365 y 54.73 (n)s 1 f 170.398 y 64.595 (=)s 13 f 157.078 y 77.262 (n)s 10 f 170.398 y 85.262 (\276)s 1 f 99.216 (:)s 13 f 160.678 y 109.216 (\255)s 10 f 170.398 y 114.882 (F)s 11 f 164.631 y 124.266 (i;j)s 2 f 173.598 y 122.599 (1)s 1 f 170.398 y 135.567 (\050)s 10 f 140.234 (\276)s 1 f 147.521 (\051)s 13 f 160.678 y 152.188 (\256)s 2 f 175.625 y 157.855 (\244)s 15 f 170.365 y 164.421 (n)s 16 f 169.706 (+)s 15 f 175.873 (N)s 171.565 y 182.327 (\260)s 177.235 y 164.421 (n)s 12 f 170.398 y 192.358 (\267)s 13 f 160.678 y 205.025 (\255)s 10 f 170.398 y 210.692 (F)s 11 f 164.631 y 220.075 (i;j)s 2 f 173.598 y 218.408 (2)s 1 f 170.398 y 231.377 (\050)s 10 f 236.043 (\276)s 1 f 243.331 (\051)s 13 f 160.678 y 247.997 (\256)s 2 f 170.398 y 253.664 (\244)s 15 f 165.138 y 260.231 (n)s 16 f 265.516 (+)s 15 f 271.682 (N)s 166.338 y 278.137 (\260)s 172.008 y 260.231 (n)s 10 f 170.398 y 284.235 (;)s 296.234 (f)s 11 f 165.443 y 303.401 (t)s 173.365 y 302.109 (n)s 1 f 170.398 y 308.641 (\050)s 10 f 313.308 (\276)s 1 f 323.262 (+)s 335.262 (2)s 10 f 341.262 (\261)s 11 f 172.198 y 346.596 (i)s 1 f 170.398 y 350.591 (\051)s 12 f 358.591 (\267)s 10 f 371.257 (f)s 11 f 165.443 y 378.424 (t)s 173.365 y 377.132 (n)s 1 f 170.398 y 383.664 (\050)s 10 f 388.331 (\276)s 1 f 395.618 (\051)s 13 f 157.078 y 400.285 (o)s 10 f 170.398 y 408.285 (:)s 1 f 201.012 y -5.69 (W)s 5.643 (e)s 15.809 (shall)s 44.708 (consider)s 92.307 (separately)s 150.239 (the)s 171.738 (in)s 181.405 (tegral)s 216.271 (on)s 10 f 233.77 (E)s 2 f 196.658 y 243.319 (1)s 11 f 203.979 y 242.628 (n)s 1 f 201.012 y 253.992 (and)s 10 f 278.158 (E)s 2 f 196.658 y 287.708 (2)s 11 f 203.979 y 287.016 (n)s 1 f 201.012 y 293.548 (,)s 301.922 (and)s 326.087 (w)s 334.421 (e)s 344.586 (call)s 367.419 (\255)s 2 f 202.812 y 376.085 (4)s 1 f 201.012 y 386.301 (\050resp.)s 423.565 (\255)s 2 f 202.812 y 432.231 (5)s 1 f 201.012 y 437.615 (\051)s 447.114 (the)s 217.812 y -5.69 (in)s 3.976 (tegral)s 38.362 (on)s 55.381 (the)s 76.4 (set)s 10 f 95.486 (E)s 2 f 213.458 y 105.036 (1)s 11 f 220.779 y 104.344 (n)s 1 f 217.812 y 115.229 (\050resp.)s 10 f 151.052 (E)s 2 f 213.458 y 160.602 (2)s 11 f 220.779 y 159.911 (n)s 1 f 217.812 y 166.443 (\051.)s 180.833 (W)s 192.166 (e)s 201.852 (consider)s 248.971 (\257rst)s 274.09 (the)s 295.109 (in)s 304.776 (tegral)s 339.162 (on)s 10 f 356.181 (E)s 2 f 213.458 y 365.731 (1)s 11 f 220.779 y 365.039 (n)s 1 f 217.812 y 375.923 (and)s 399.609 (rewrite)s 440.695 (it)s 453.047 (as)s 234.612 y -5.69 (the)s 14.976 (sum)s 40.377 (of)s 54.043 (t)s 58.377 (w)s 66.71 (o)s 76.71 (other)s 108.077 (terms)s 265.298 y -2.289 (\255)s 2 f 267.098 y 6.378 (4)s 1 f 265.298 y 15.095 (=)s 10 f 27.761 (\260)s 14 f 260.343 y 34.641 (\241)s 2 f 42.141 (2)s 13 f 248.965 y 49.524 (Z)s 1 f 265.298 y 63.524 (1)s 14 f 267.465 y 69.524 (f)s 11 f 74.441 (\276)s 2 f 80.303 (\050)s 11 f 84.053 (i)s 2 f 87.448 (\051=)s 14 f 98.565 (\241)s 2 f 106.065 (1)s 14 f 110.848 (g)s 13 f 251.978 y 116.365 (n)s 255.578 y 124.365 (\255)s 10 f 265.298 y 130.031 (F)s 11 f 259.531 y 139.415 (i;j)s 2 f 268.498 y 137.748 (1)s 1 f 265.298 y 150.716 (\050)s 10 f 155.383 (\276)s 1 f 162.67 (\051)s 13 f 255.578 y 167.337 (\256)s 2 f 270.525 y 173.004 (\244)s 15 f 265.265 y 179.57 (n)s 16 f 184.855 (+)s 15 f 191.022 (N)s 266.465 y 197.476 (\260)s 272.135 y 179.57 (n)s 12 f 265.298 y 206.841 (\241)s 13 f 255.578 y 218.841 (\255)s 10 f 265.298 y 224.507 (F)s 11 f 259.531 y 233.891 (i;j)s 2 f 268.498 y 232.224 (3)s 1 f 265.298 y 245.192 (\050)s 10 f 249.859 (\276)s 1 f 257.146 (\051)s 13 f 255.578 y 261.813 (\256)s 2 f 270.525 y 267.48 (\244)s 15 f 265.265 y 274.046 (n)s 16 f 279.331 (+)s 15 f 285.498 (N)s 266.465 y 291.952 (\260)s 272.135 y 274.046 (n)s 13 f 251.978 y 298.65 (o)s 1 f 265.298 y 308.65 (log)s 13 f 251.978 y 326.15 (n)s 10 f 257.18 y 335.59 (f)s 11 f 252.825 y 342.757 (t)s 260.147 y 341.465 (n)s 1 f 257.18 y 347.997 (\050)s 10 f 352.664 (\276)s 1 f 362.618 (+)s 374.618 (2)s 10 f 380.618 (\261)s 11 f 258.98 y 385.951 (i)s 1 f 257.18 y 389.947 (\051)s 59.023 .48 335.59 262.538 r 10 f 273.529 y 350.588 (f)s 11 f 270.063 y 357.755 (t)s 276.496 y 356.463 (n)s 1 f 273.529 y 362.995 (\050)s 10 f 367.662 (\276)s 1 f 374.949 (\051)s 13 f 251.978 y 396.053 (o)s 1 f 265.298 y 404.053 (1)s 11 f 267.431 y 410.053 (E)s 16 f 265.031 y 417.56 (1)s 15 f 269.831 y 417.098 (n)s 10 f 265.298 y 423.583 (d\272)s 11 f 267.098 y 435.757 (P)s 1 f 265.298 y 443.758 (\050)s 10 f 448.425 (\276)s 1 f 455.712 (\051)s 302.569 y 3.711 (+)s 10 f 15.711 (\260)s 14 f 297.614 y 22.591 (\241)s 2 f 30.091 (2)s 13 f 286.236 y 37.474 (Z)s 1 f 302.569 y 51.474 (1)s 14 f 304.736 y 57.474 (f)s 11 f 62.391 (\276)s 2 f 68.253 (\050)s 11 f 72.003 (i)s 2 f 75.398 (\051=)s 14 f 86.514 (\241)s 2 f 94.015 (1)s 14 f 98.798 (g)s 13 f 289.249 y 104.315 (n)s 292.849 y 112.315 (\255)s 10 f 302.569 y 117.981 (F)s 11 f 296.802 y 127.365 (i;j)s 2 f 305.769 y 125.698 (3)s 1 f 302.569 y 138.666 (\050)s 10 f 143.333 (\276)s 1 f 150.62 (\051)s 13 f 292.849 y 155.287 (\256)s 2 f 307.796 y 160.954 (\244)s 15 f 302.536 y 167.52 (n)s 16 f 172.805 (+)s 15 f 178.972 (N)s 303.736 y 185.426 (\260)s 309.406 y 167.52 (n)s 12 f 302.569 y 194.791 (\241)s 13 f 292.849 y 206.791 (\255)s 10 f 302.569 y 212.457 (F)s 11 f 296.802 y 221.841 (i;j)s 2 f 305.769 y 220.174 (2)s 1 f 302.569 y 233.142 (\050)s 10 f 237.809 (\276)s 1 f 245.096 (\051)s 13 f 292.849 y 249.763 (\256)s 2 f 307.796 y 255.43 (\244)s 15 f 302.536 y 261.996 (n)s 16 f 267.281 (+)s 15 f 273.448 (N)s 303.736 y 279.902 (\260)s 309.406 y 261.996 (n)s 13 f 289.249 y 286.6 (o)s 1 f 302.569 y 296.6 (log)s 13 f 289.249 y 314.1 (n)s 10 f 294.451 y 323.54 (f)s 11 f 290.096 y 330.707 (t)s 297.417 y 329.415 (n)s 1 f 294.451 y 335.947 (\050)s 10 f 340.614 (\276)s 1 f 350.568 (+)s 362.568 (2)s 10 f 368.568 (\261)s 11 f 296.251 y 373.901 (i)s 1 f 294.451 y 377.896 (\051)s 59.023 .48 323.54 299.809 r 10 f 310.8 y 338.538 (f)s 11 f 307.334 y 345.704 (t)s 313.767 y 344.413 (n)s 1 f 310.8 y 350.945 (\050)s 10 f 355.611 (\276)s 1 f 362.899 (\051)s 13 f 289.249 y 384.003 (o)s 1 f 302.569 y 392.003 (1)s 11 f 304.702 y 398.003 (E)s 16 f 302.302 y 405.51 (1)s 15 f 307.102 y 405.048 (n)s 10 f 302.569 y 411.533 (d\272)s 11 f 304.369 y 423.707 (P)s 1 f 302.569 y 431.708 (\050)s 10 f 436.375 (\276)s 1 f 443.662 (\051)s 10 f 448.329 (:)s 1 f 338.172 y -5.69 (where)s 10 f 29.01 (F)s 11 f 332.405 y 38.393 (i;j)s 2 f 341.372 y 36.726 (3)s 1 f 338.172 y 53.695 (is)s 65.761 (de\257ned)s 107.095 (b)s 113.428 (y)s 10 f 363.218 y 109.339 (F)s 11 f 357.451 y 118.722 (i;j)s 2 f 366.418 y 117.056 (3)s 1 f 363.218 y 130.024 (\050)s 10 f 134.69 (\276)s 1 f 141.978 (\051)s 149.978 (=)s 162.644 (1)s 14 f 365.385 y 168.644 (f)s 11 f 173.561 (\276)s 2 f 179.423 (\050)s 11 f 183.173 (j)s 2 f 187.63 (\051=1)s 14 f 203.53 (g)s 10 f 363.218 y 209.046 (C)s 11 f 358.263 y 218.481 (K)s 226.616 (;\257)s 366.184 y 217.623 (\260)s 1 f 363.218 y 235.939 (\050)s 10 f 240.606 (i;)s 250.073 (j)s 1 f 255.702 (;)s 10 f 261.035 (\276)s 11 f 358.263 y 268.323 (j)s 272.262 (;i)s 1 f 363.218 y 279.108 (\051)s 10 f 283.774 (f)s 11 f 358.263 y 290.941 (t)s 366.184 y 289.649 (n)s 2 f 295.581 (+)s 11 f 302.948 (N)s 15 f 367.384 y 310.549 (\260)s 2 f 366.184 y 316.047 (+1)s 1 f 363.218 y 328.797 (\050)s 10 f 333.464 (\276)s 1 f 340.751 (\051)s 10 f 345.418 (:)s 1 f 388.264 y -5.69 (Applying)s 46.361 (Lemma)s 89.246 (4.1)s 108.631 (b)s 115.631 (elo)s 129.965 (w,)s 146.029 (w)s 154.362 (e)s 163.747 (obtain)s 201.132 (that)s 227.183 (the)s 247.902 (\257rst)s 272.72 (line)s 295.438 (of)s 309.156 (the)s 329.874 (last)s 352.659 (expression)s 410.544 (is)s 422.662 (of)s 436.38 (order)s 10 f 405.064 y -5.69 (\260)s 14 f 400.709 y 1.189 (\241)s 2 f 8.689 (1)s 1 f 405.064 y 14.073 (.)s 22.739 (Indeed,)s 65.073 (observ)s 98.506 (e)s 107.839 (that)s 133.839 (w)s 142.173 (e)s 151.506 (ha)s 163.839 (v)s 169.839 (e)s 179.173 (for)s 197.54 (all)s 214.206 (con\257gurations)s 10 f 291.64 (\276)s 431.769 y 41.962 (\260)s 14 f 426.814 y 48.841 (\241)s 2 f 56.341 (2)s 13 f 422.049 y 61.725 (\255)s 10 f 431.769 y 67.391 (F)s 11 f 426.002 y 76.775 (i;j)s 2 f 434.969 y 75.108 (1)s 1 f 431.769 y 88.076 (\050)s 10 f 92.743 (\276)s 1 f 100.03 (\051)s 13 f 422.049 y 104.697 (\256)s 2 f 436.995 y 110.364 (\244)s 15 f 431.735 y 116.93 (n)s 16 f 122.215 (+)s 15 f 128.382 (N)s 432.935 y 134.836 (\260)s 438.605 y 116.93 (n)s 12 f 431.769 y 144.201 (\241)s 13 f 422.049 y 156.201 (\255)s 10 f 431.769 y 161.867 (F)s 11 f 426.002 y 171.251 (i;j)s 2 f 434.969 y 169.584 (3)s 1 f 431.769 y 182.552 (\050)s 10 f 187.219 (\276)s 1 f 194.506 (\051)s 13 f 422.049 y 199.173 (\256)s 2 f 436.995 y 204.84 (\244)s 15 f 431.735 y 211.406 (n)s 16 f 216.691 (+)s 15 f 222.858 (N)s 432.935 y 229.312 (\260)s 438.605 y 211.406 (n)s 1 f 457.793 y 69.295 (=)s 10 f 81.962 (\260)s 14 f 452.839 y 88.841 (\241)s 2 f 96.341 (2)s 13 f 448.073 y 101.725 (\255)s 1 f 457.793 y 107.391 (1)s 14 f 459.96 y 113.391 (f)s 11 f 118.308 (\276)s 2 f 124.17 (\050)s 11 f 127.92 (j)s 2 f 132.376 (\051=1)s 14 f 148.276 (g)s 13 f 448.073 y 153.793 (\243)s 10 f 457.793 y 158.793 (C)s 11 f 452.839 y 168.228 (K)s 176.363 (;\257)s 460.76 y 167.37 (\260)s 1 f 457.793 y 185.686 (\050)s 10 f 190.353 (i;)s 199.82 (j)s 1 f 205.449 (;)s 10 f 210.782 (\276)s 1 f 218.07 (\051)s 12 f 225.403 (\241)s 10 f 237.403 (C)s 11 f 452.839 y 246.838 (K)s 254.973 (;\257)s 460.76 y 245.979 (\260)s 1 f 457.793 y 264.296 (\050)s 10 f 268.962 (i;)s 278.43 (j)s 1 f 284.059 (;)s 10 f 289.392 (\276)s 11 f 452.839 y 296.679 (i;j)s 1 f 457.793 y 307.981 (\051)s 13 f 448.073 y 312.647 (\244)s 10 f 457.793 y 317.647 (f)s 11 f 452.839 y 324.814 (t)s 460.76 y 323.522 (n)s 2 f 329.454 (+)s 11 f 336.821 (N)s 15 f 461.96 y 344.422 (\260)s 2 f 460.76 y 349.92 (+1)s 1 f 457.793 y 362.67 (\050)s 10 f 367.337 (\276)s 1 f 374.624 (\051)s 13 f 448.073 y 379.291 (\256)s 2 f 463.02 y 384.958 (\244)s 15 f 457.76 y 391.524 (n)s 16 f 396.809 (+)s 15 f 402.976 (N)s 458.96 y 409.43 (\260)s 464.63 y 391.524 (n)s 12 f 483.398 y 75.962 (\267)s 10 f 88.628 (C)s 2 f 485.198 y 97.205 (2)s 10 f 483.398 y 102.588 (\260)s 14 f 478.443 y 109.468 (\241)s 2 f 116.968 (1)s 13 f 473.678 y 122.351 (\255)s 10 f 483.398 y 128.018 (f)s 11 f 478.443 y 135.184 (t)s 486.364 y 133.893 (n)s 2 f 139.825 (+)s 11 f 147.191 (N)s 15 f 487.564 y 154.792 (\260)s 2 f 486.364 y 160.29 (+1)s 1 f 483.398 y 173.04 (\050)s 10 f 177.707 (\276)s 1 f 184.995 (\051)s 13 f 473.678 y 189.661 (\256)s 2 f 488.624 y 195.328 (\244)s 15 f 483.365 y 201.895 (n)s 16 f 207.179 (+)s 15 f 213.346 (N)s 484.565 y 219.8 (\260)s 490.234 y 201.895 (n)s 1 f 483.398 y 229.832 (=)s 10 f 242.498 (C)s 2 f 485.198 y 251.075 (2)s 10 f 483.398 y 256.458 (\260)s 14 f 478.443 y 263.338 (\241)s 2 f 270.838 (1)s 10 f 483.398 y 276.221 (f)s 11 f 478.443 y 283.388 (t)s 486.364 y 282.096 (n)s 1 f 483.398 y 288.628 (\050)s 10 f 293.295 (\276)s 1 f 300.582 (\051)s 513.049 y -5.69 (for)s 11.836 (some)s 41.062 (p)s 48.062 (ositiv)s 76.129 (e)s 84.622 (constan)s 124.355 (t)s 10 f 132.182 (C)s 2 f 514.849 y 140.758 (2)s 1 f 513.049 y 146.142 (,)s 152.803 (and)s 175.296 (on)s 191.122 (the)s 210.948 (set)s 10 f 228.841 (E)s 2 f 508.694 y 238.391 (1)s 11 f 516.015 y 237.7 (n)s 1 f 513.049 y 244.232 (,)s 250.893 (w)s 259.226 (e)s 267.719 (ha)s 280.052 (v)s 286.052 (e)s 294.545 (that)s 10 f 319.705 (f)s 11 f 508.694 y 326.871 (t)s 516.015 y 325.58 (n)s 1 f 513.049 y 332.112 (\050)s 10 f 336.778 (\276)s 1 f 345.052 (+)s 355.371 (2)s 10 f 361.371 (\261)s 11 f 514.849 y 366.704 (i)s 1 f 513.049 y 370.699 (\051)s 12 f 378.699 (\270)s 10 f 391.366 (f)s 11 f 508.694 y 398.533 (t)s 516.015 y 397.241 (n)s 1 f 513.049 y 403.773 (\050)s 10 f 408.44 (\276)s 1 f 415.727 (\051.)s 428.78 (Hence,)s 529.849 y -5.69 (from)s 22.593 (inequalit)s 67.926 (y)s 78.176 (\0504.7\051,)s 110.109 (the)s 130.692 (c)s 135.692 (hange)s 170.276 (of)s 183.859 (v)s 189.525 (ariables)s 233.542 (and)s 256.792 (the)s 277.375 (fact)s 300.958 (that)s 10 f 326.874 (f)s 11 f 525.494 y 334.041 (t)s 532.815 y 332.749 (n)s 1 f 529.849 y 343.198 (is)s 355.181 (a)s 365.097 (probabilit)s 416.131 (y)s 426.38 (densit)s 457.447 (y)s 546.649 y -5.69 (with)s 21.643 (resp)s 43.41 (ect)s 62.743 (to)s 10 f 77.41 (\272)s 11 f 548.449 y 83.338 (P)s 1 f 546.649 y 91.339 (,)s 98.672 (the)s 119.339 (\257rst)s 144.106 (term)s 172.806 (of)s 186.472 (\255)s 2 f 548.449 y 195.139 (4)s 1 f 546.649 y 204.522 (is)s 216.589 (b)s 223.589 (ounded)s 265.589 (b)s 271.923 (y)s 10 f 578.362 y 79.145 (C)s 2 f 580.162 y 87.722 (2)s 10 f 578.362 y 93.105 (\260)s 14 f 573.407 y 99.985 (\241)s 2 f 107.485 (1)s 13 f 562.028 y 114.868 (Z)s 1 f 578.362 y 128.868 (1)s 14 f 580.528 y 134.868 (f)s 11 f 139.785 (\276)s 2 f 145.647 (\050)s 11 f 149.397 (i)s 2 f 152.792 (\051=)s 14 f 163.909 (\241)s 2 f 171.409 (1)s 14 f 176.192 (g)s 13 f 568.162 y 181.709 (\257)s 575.362 y 181.709 (\257)s 10 f 578.362 y 185.709 (f)s 11 f 573.407 y 192.876 (t)s 581.328 y 191.584 (n)s 1 f 578.362 y 198.116 (\050)s 10 f 202.783 (\276)s 1 f 212.737 (+)s 224.737 (2)s 10 f 230.737 (\261)s 11 f 580.162 y 236.07 (i)s 1 f 578.362 y 240.065 (\051)s 12 f 247.398 (\241)s 10 f 259.398 (f)s 11 f 573.407 y 266.565 (t)s 581.328 y 265.273 (n)s 1 f 578.362 y 271.805 (\050)s 10 f 276.472 (\276)s 1 f 283.76 (\051)s 13 f 568.162 y 288.426 (\257)s 575.362 y 288.426 (\257)s 10 f 578.362 y 292.426 (d\272)s 11 f 580.162 y 304.6 (P)s 1 f 578.362 y 312.601 (\050)s 10 f 317.268 (\276)s 1 f 324.555 (\051)s 12 f 332.555 (\267)s 10 f 345.222 (C)s 14 f 573.407 y 354.657 (0)s 2 f 581.328 y 353.798 (2)s 10 f 578.362 y 359.182 (\260)s 14 f 573.407 y 366.061 (\241)s 2 f 373.561 (1)s 1 f 610.763 y -5.69 (for)s 12.062 (some)s 41.515 (p)s 48.515 (ositiv)s 76.582 (e)s 85.301 (constan)s 125.035 (t)s 10 f 133.087 (C)s 14 f 606.408 y 142.522 (0)s 2 f 613.741 y 141.664 (2)s 1 f 610.763 y 150.433 (that)s 175.819 (dep)s 194.819 (ends)s 221.605 (on)s 10 f 237.658 (P)s 1 f 250.415 (and)s 10 f 273.134 (\257)s 1 f 280.555 (.)s 289.017 (W)s 300.35 (e)s 309.069 (estimate)s 356.522 (no)s 368.856 (w)s 380.908 (the)s 400.961 (second)s 439.08 (term)s 627.563 y -5.69 (of)s 7.602 (\255)s 2 f 629.363 y 16.268 (4)s 1 f 627.563 y 21.652 (.)s 30.194 (Since)s 61.152 (on)s 10 f 77.444 (E)s 2 f 623.208 y 86.994 (1)s 11 f 630.529 y 86.302 (n)s 1 f 627.563 y 96.46 (w)s 104.793 (e)s 113.751 (ha)s 126.085 (v)s 132.085 (e)s 10 f 141.043 (f)s 11 f 623.208 y 148.21 (t)s 630.529 y 146.918 (n)s 1 f 627.563 y 153.45 (\050)s 10 f 158.117 (\276)s 1 f 167.322 (+)s 178.572 (2)s 10 f 184.572 (\261)s 11 f 629.363 y 189.905 (i)s 1 f 627.563 y 193.901 (\051)s 12 f 201.901 (\270)s 10 f 214.567 (f)s 11 f 623.208 y 221.734 (t)s 630.529 y 220.442 (n)s 1 f 627.563 y 226.974 (\050)s 10 f 231.641 (\276)s 1 f 238.928 (\051,)s 250.629 (w)s 258.962 (e)s 267.92 (ma)s 283.587 (y)s 293.546 (replace)s 333.871 (the)s 354.163 (indicator)s 404.488 (function)s 451.113 (on)s 10 f 644.363 y -5.69 (E)s 2 f 640.008 y 3.86 (1)s 11 f 647.329 y 3.168 (n)s 1 f 644.363 y 13.7 (b)s 20.033 (y)s 30.367 (the)s 51.034 (indicator)s 101.734 (function)s 148.734 (on)s 165.4 (the)s 186.067 (set)s 10 f 204.8 (E)s 2 f 640.008 y 214.35 (3)s 11 f 647.329 y 213.659 (n)s 1 f 644.363 y 224.191 (de\257ned)s 265.524 (b)s 271.858 (y)s 10 f 674.176 y 45.872 (E)s 2 f 669.221 y 55.422 (3)s 11 f 677.142 y 54.73 (n)s 1 f 674.176 y 64.595 (=)s 13 f 660.856 y 77.262 (n)s 10 f 674.176 y 85.262 (\276)s 1 f 99.216 (:)s 13 f 664.456 y 109.216 (\255)s 10 f 674.176 y 114.882 (F)s 11 f 668.409 y 124.266 (i;j)s 2 f 677.376 y 122.599 (3)s 1 f 674.176 y 135.567 (\050)s 10 f 140.234 (\276)s 1 f 147.521 (\051)s 13 f 664.456 y 152.188 (\256)s 2 f 679.402 y 157.855 (\244)s 15 f 674.143 y 164.421 (n)s 16 f 169.706 (+)s 15 f 175.873 (N)s 675.343 y 182.327 (\260)s 681.012 y 164.421 (n)s 12 f 674.176 y 192.358 (\270)s 13 f 664.456 y 205.025 (\255)s 10 f 674.176 y 210.692 (F)s 11 f 668.409 y 220.075 (i;j)s 2 f 677.376 y 218.408 (2)s 1 f 674.176 y 231.377 (\050)s 10 f 236.043 (\276)s 1 f 243.331 (\051)s 13 f 664.456 y 247.997 (\256)s 2 f 679.402 y 253.664 (\244)s 15 f 674.143 y 260.231 (n)s 16 f 265.516 (+)s 15 f 271.682 (N)s 675.343 y 278.137 (\260)s 681.012 y 260.231 (n)s 10 f 674.176 y 284.835 (;)s 296.834 (f)s 11 f 669.221 y 304.001 (t)s 677.142 y 302.709 (n)s 1 f 674.176 y 309.241 (\050)s 10 f 313.908 (\276)s 1 f 323.862 (+)s 335.862 (2)s 10 f 341.862 (\261)s 11 f 675.976 y 347.196 (i)s 1 f 674.176 y 351.191 (\051)s 12 f 359.191 (\270)s 10 f 371.857 (f)s 11 f 669.221 y 379.024 (t)s 677.142 y 377.732 (n)s 1 f 674.176 y 384.264 (\050)s 10 f 388.931 (\276)s 1 f 396.218 (\051)s 13 f 660.856 y 400.885 (o)s 10 f 674.176 y 408.885 (:)s 1 f 705.976 y 223.045 (21)s do-end end endp %%Page: 22 22 %%BeginPageSetup initializepage (Raffaele Esposito; page: 22 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f1_12 sf ( )S -997 -1000 :M f2_12 sf ( )S -993 -1000 :M f10_12 sf ( )S -985 -1000 :M f11_12 sf ( )S -976 -1000 :M f12_12 sf ( )S -964 -1000 :M f13_12 sf ( )S -954 -1000 :M f14_12 sf ( )S -941 -1000 :M f15_12 sf ( )S -930 -1000 :M f16_12 sf ( )S -925 -1000 :M f18_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 16 5 1200 1000 div mul /CMR5 findfont fdef 18 5 1200 1000 div mul /CMSY5 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 6.31 y -5.69 (Since)s 27.656 (for)s 48.037 (all)s 66.717 (p)s 73.717 (ositiv)s 101.783 (e)s 10 f 113.13 (x)s 1 f 119.988 (,)s 129.838 (log)s 10 f 147.338 (x)s 12 f 160.885 (\267)s 1 f 176.907 (2\050)s 12 f -2.334 y 187.574 (p)s 6.858 .48 197.574 -2.334 r 10 f 6.31 y 197.574 (x)s 12 f 208.441 (\241)s 1 f 221.783 (1\051)s 238.463 (,)s 248.313 (and)s 273.66 (since)s 305.073 (on)s 323.753 (the)s 346.433 (set)s 10 f 367.18 (E)s 2 f 1.955 y 376.73 (3)s 11 f 9.276 y 376.038 (n)s 1 f 6.31 y 382.57 (,)s 392.42 (w)s 400.754 (e)s 412.1 (ha)s 424.434 (v)s 430.434 (e)s 441.78 (that)s 13 f 13.39 y -5.69 (\255)s 10 f 23.11 y -.024 (F)s 11 f 17.343 y 9.36 (i;j)s 2 f 26.31 y 7.693 (3)s 1 f 23.11 y 20.661 (\050)s 10 f 25.328 (\276)s 1 f 32.615 (\051)s 13 f 13.39 y 37.282 (\256)s 2 f 28.336 y 42.949 (\244)s 15 f 23.076 y 49.515 (n)s 16 f 54.8 (+)s 15 f 60.967 (N)s 24.276 y 67.421 (\260)s 29.946 y 49.515 (n)s 12 f 23.11 y 79.238 (\270)s 13 f 13.39 y 93.77 (\255)s 10 f 23.11 y 99.436 (F)s 11 f 17.343 y 108.82 (i;j)s 2 f 26.31 y 107.153 (2)s 1 f 23.11 y 120.121 (\050)s 10 f 124.788 (\276)s 1 f 132.075 (\051)s 13 f 13.39 y 136.742 (\256)s 2 f 28.336 y 142.409 (\244)s 15 f 23.076 y 148.975 (n)s 16 f 154.26 (+)s 15 f 160.427 (N)s 24.276 y 166.881 (\260)s 29.946 y 148.975 (n)s 1 f 23.11 y 173.579 (,)s 182.311 (the)s 204.097 (second)s 243.949 (in)s 253.616 (tegral)s 288.768 (of)s 303.554 (\255)s 2 f 24.91 y 312.221 (4)s 1 f 23.11 y 322.723 (with)s 351.175 (indicator)s 402.994 (function)s 451.114 (on)s 10 f 39.91 y -5.69 (E)s 2 f 35.555 y 3.86 (3)s 11 f 42.876 y 3.168 (n)s 1 f 39.91 y 13.7 (is)s 25.767 (less)s 47.9 (than)s 75.9 (or)s 90.6 (equal)s 122.267 (to)s 81 y 1.486 (2)s 10 f 7.486 (\260)s 14 f 76.045 y 14.366 (\241)s 2 f 21.866 (2)s 13 f 64.666 y 29.249 (Z)s 1 f 81 y 43.249 (1)s 14 f 83.166 y 49.249 (f)s 11 f 54.166 (\276)s 2 f 60.028 (\050)s 11 f 63.778 (i)s 2 f 67.173 (\051=)s 14 f 78.29 (\241)s 2 f 85.79 (1)s 14 f 90.573 (g)s 13 f 67.679 y 96.09 (n)s 71.28 y 104.09 (\255)s 10 f 81 y 109.756 (F)s 11 f 75.233 y 119.14 (i;j)s 2 f 84.2 y 117.473 (3)s 1 f 81 y 130.441 (\050)s 10 f 135.108 (\276)s 1 f 142.395 (\051)s 13 f 71.28 y 147.062 (\256)s 2 f 86.226 y 152.729 (\244)s 15 f 80.966 y 159.295 (n)s 16 f 164.58 (+)s 15 f 170.747 (N)s 82.166 y 177.201 (\260)s 87.836 y 159.295 (n)s 12 f 81 y 186.566 (\241)s 13 f 71.28 y 198.566 (\255)s 10 f 81 y 204.232 (F)s 11 f 75.233 y 213.616 (i;j)s 2 f 84.2 y 211.949 (2)s 1 f 81 y 224.917 (\050)s 10 f 229.584 (\276)s 1 f 236.871 (\051)s 13 f 71.28 y 241.538 (\256)s 2 f 86.226 y 247.205 (\244)s 15 f 80.966 y 253.771 (n)s 16 f 259.056 (+)s 15 f 265.223 (N)s 82.166 y 271.677 (\260)s 87.836 y 253.771 (n)s 13 f 67.679 y 278.375 (o)s 286.375 (n)s 62.4 y 295.815 (p)s 59.023 .48 307.815 62.4 r 10 f 72.66 y 307.815 (f)s 11 f 69.193 y 314.982 (t)s 75.626 y 313.69 (n)s 1 f 72.66 y 320.222 (\050)s 10 f 324.889 (\276)s 1 f 334.843 (+)s 346.843 (2)s 10 f 352.843 (\261)s 11 f 74.46 y 358.177 (i)s 1 f 72.66 y 362.172 (\051)s 71.023 .48 295.815 78.24 r 13 f 80.639 y 310.813 (p)s 29.028 .48 322.813 80.639 r 10 f 90.9 y 322.813 (f)s 11 f 87.433 y 329.98 (t)s 93.866 y 328.688 (n)s 1 f 90.9 y 335.22 (\050)s 10 f 339.887 (\276)s 1 f 347.174 (\051)s 12 f 81 y 370.945 (\241)s 1 f 382.945 (1)s 13 f 67.679 y 388.945 (o)s 1 f 81 y 396.945 (1)s 11 f 83.133 y 402.945 (E)s 16 f 80.733 y 410.452 (3)s 15 f 85.533 y 409.99 (n)s 10 f 81 y 416.475 (d\272)s 11 f 82.8 y 428.648 (P)s 1 f 81 y 436.65 (\050)s 10 f 441.316 (\276)s 1 f 448.604 (\051)s 10 f 453.271 (:)s 1 f 126.097 y -5.69 (By)s 12.482 (the)s 32.487 (elemen)s 68.154 (tary)s 93.192 (inequalit)s 138.526 (y)s 148.198 (2)s 10 f 154.198 (xy)s 12 f 170.703 (\267)s 11 f 120.744 y 184.81 (\260)s 18 f 117.123 y 190.367 (\241)s 16 f 196.867 (1)s 16.741 .48 184.81 123.337 r 11 f 130.236 y 190.061 (\256)s 10 f 126.097 y 202.99 (x)s 2 f 121.743 y 209.849 (2)s 1 f 126.097 y 216.576 (+)s 11 f 121.373 y 233.944 (\256)s 16.741 .48 228.693 123.337 r 130.236 y 228.693 (\260)s 18 f 127.836 y 234.25 (\241)s 16 f 240.75 (1)s 10 f 126.097 y 246.874 (y)s 2 f 121.743 y 253.188 (2)s 1 f 126.097 y 261.909 (and)s 284.581 (since)s 313.32 (\050)s 10 f 317.987 (A)s 12 f 328.33 (\241)s 10 f 339.007 (B)s 1 f 348.712 (\051)s 356.711 (=)s 369.378 (\050)s 12 f 115.938 y 374.045 (p)s 9 .48 384.045 115.938 r 10 f 126.097 y 384.045 (A)s 12 f 394.389 (\241)s 115.938 y 405.066 (p)s 9.704 .48 415.066 115.938 r 10 f 126.097 y 415.066 (B)s 1 f 424.77 (\051\050)s 12 f 115.938 y 434.103 (p)s 9 .48 444.103 115.938 r 10 f 126.097 y 444.103 (A)s 1 f 454.447 (+)s 12 f 137.629 y -5.69 (p)s 9.704 .48 4.31 137.629 r 10 f 147.789 y 4.31 (B)s 1 f 14.014 (\051)s 22.681 (w)s 31.014 (e)s 40.347 (ha)s 52.681 (v)s 58.681 (e)s 68.014 (that)s 94.014 (for)s 112.381 (ev)s 123.714 (ery)s 144.081 (p)s 151.081 (ositiv)s 179.148 (e)s 10 f 188.481 (A;)s 202.814 (B)s 212.518 (;)s 217.852 (a;)s 229.528 (b)s 1 f 238.678 (and)s 262.011 (for)s 280.378 (ev)s 291.711 (ery)s 312.078 (p)s 319.078 (ositiv)s 347.145 (e)s 10 f 356.478 (\256)s 1 f 364.199 (,)s 187.238 y 31.611 (2)s 13 f 173.918 y 37.611 (\263)s 10 f 187.238 y 44.778 (A)s 12 f 56.445 (\241)s 10 f 68.445 (B)s 13 f 173.918 y 78.149 (\264)s 177.518 y 85.315 (\241)s 1 f 187.238 y 90.815 (\050)s 10 f 95.482 (b=a)s 1 f 112.975 (\051)s 12 f 120.309 (\241)s 1 f 132.308 (1)s 13 f 177.518 y 138.308 (\242)s 12 f 187.238 y 147.142 (\267)s 10 f 179.12 y 161.248 (\260)s 14 f 174.765 y 168.128 (\241)s 2 f 175.628 (1)s 19.763 .48 161.248 184.478 r 10 f 195.47 y 167.269 (\256)s 13 f 177.518 y 182.451 (\241)s 12 f 176.492 y 187.951 (p)s 9 .48 197.951 176.492 r 10 f 187.238 y 197.951 (A)s 12 f 209.618 (\241)s 176.492 y 221.618 (p)s 9.704 .48 231.618 176.492 r 10 f 187.238 y 231.618 (B)s 13 f 177.518 y 241.322 (\242)s 2 f 180.005 y 246.822 (2)s 1 f 187.238 y 254.872 (+)s 10 f 179.12 y 274.333 (\256)s 19.763 .48 268.312 184.478 r 195.47 y 268.312 (\260)s 14 f 192.003 y 275.191 (\241)s 2 f 282.691 (1)s 13 f 177.518 y 289.515 (\241)s 12 f 176.492 y 295.015 (p)s 9 .48 305.015 176.492 r 10 f 187.238 y 305.015 (A)s 1 f 316.681 (+)s 12 f 176.492 y 328.681 (p)s 9.704 .48 338.681 176.492 r 10 f 187.238 y 338.681 (B)s 13 f 177.518 y 348.386 (\242)s 2 f 180.005 y 353.886 (2)s 13 f 177.518 y 359.269 (\241)s 1 f 187.238 y 364.769 (\050)s 10 f 369.436 (b=a)s 1 f 386.929 (\051)s 12 f 394.262 (\241)s 1 f 406.262 (1)s 13 f 177.518 y 412.262 (\242)s 2 f 180.005 y 417.762 (2)s 10 f 187.238 y 423.145 (:)s 1 f 224.699 y -5.69 (In)s 9.31 (particular)s 64.71 (the)s 85.377 (last)s 108.11 (in)s 117.777 (tegral)s 151.81 (is)s 163.877 (b)s 170.877 (ounded)s 212.877 (ab)s 225.877 (o)s 231.544 (v)s 237.544 (e)s 246.877 (b)s 253.21 (y)s 10 f 255.364 y 41.178 (\260)s 14 f 251.009 y 48.057 (\241)s 2 f 55.557 (3)s 19.763 .48 41.178 260.722 r 10 f 271.713 y 47.198 (\256)s 13 f 247.149 y 64.38 (Z)s 1 f 263.482 y 78.38 (1)s 14 f 265.649 y 84.38 (f)s 11 f 89.297 (\276)s 2 f 95.159 (\050)s 11 f 98.909 (i)s 2 f 102.304 (\051=)s 14 f 113.421 (\241)s 2 f 120.921 (1)s 14 f 125.704 (g)s 13 f 250.162 y 131.221 (n)s 249.792 y 139.221 (q)s 79.81 .48 151.221 249.792 r 253.762 y 151.221 (\255)s 10 f 263.482 y 156.888 (F)s 11 f 257.715 y 166.271 (i;j)s 2 f 266.682 y 164.604 (3)s 1 f 263.482 y 177.572 (\050)s 10 f 182.239 (\276)s 1 f 189.527 (\051)s 13 f 253.762 y 194.193 (\256)s 2 f 268.709 y 199.86 (\244)s 15 f 263.449 y 206.427 (n)s 16 f 211.711 (+)s 15 f 217.878 (N)s 264.649 y 224.332 (\260)s 270.319 y 206.427 (n)s 12 f 263.482 y 233.697 (\241)s 13 f 249.792 y 245.697 (q)s 79.81 .48 257.697 249.792 r 253.762 y 257.697 (\255)s 10 f 263.482 y 263.364 (F)s 11 f 257.715 y 272.747 (i;j)s 2 f 266.682 y 271.08 (2)s 1 f 263.482 y 284.049 (\050)s 10 f 288.715 (\276)s 1 f 296.003 (\051)s 13 f 253.762 y 300.669 (\256)s 2 f 268.709 y 306.336 (\244)s 15 f 263.449 y 312.903 (n)s 16 f 318.188 (+)s 15 f 324.354 (N)s 264.649 y 330.809 (\260)s 270.319 y 312.903 (n)s 13 f 250.162 y 337.507 (o)s 2 f 252.649 y 345.507 (2)s 10 f 263.482 y 350.89 (d\272)s 11 f 265.282 y 363.064 (P)s 1 f 263.482 y 371.065 (\050)s 10 f 375.732 (\276)s 1 f 383.019 (\051)s 298.549 y 45.737 (+)s 10 f 57.737 (\256)s 65.458 (\260)s 14 f 293.594 y 72.338 (\241)s 2 f 79.838 (1)s 13 f 282.215 y 87.221 (Z)s 1 f 298.549 y 101.221 (1)s 14 f 300.716 y 107.221 (f)s 11 f 112.138 (\276)s 2 f 118 (\050)s 11 f 121.75 (i)s 2 f 125.145 (\051=)s 14 f 136.262 (\241)s 2 f 143.762 (1)s 14 f 148.545 (g)s 13 f 285.229 y 154.062 (n)s 284.859 y 162.062 (q)s 79.81 .48 174.062 284.859 r 288.829 y 174.062 (\255)s 10 f 298.549 y 179.728 (F)s 11 f 292.782 y 189.112 (i;j)s 2 f 301.749 y 187.445 (3)s 1 f 298.549 y 200.413 (\050)s 10 f 205.08 (\276)s 1 f 212.367 (\051)s 13 f 288.829 y 217.034 (\256)s 2 f 303.776 y 222.701 (\244)s 15 f 298.516 y 229.267 (n)s 16 f 234.552 (+)s 15 f 240.719 (N)s 299.716 y 247.173 (\260)s 305.386 y 229.267 (n)s 1 f 298.549 y 256.538 (+)s 13 f 284.859 y 268.538 (q)s 79.81 .48 280.538 284.859 r 288.829 y 280.538 (\255)s 10 f 298.549 y 286.204 (F)s 11 f 292.782 y 295.588 (i;j)s 2 f 301.749 y 293.921 (2)s 1 f 298.549 y 306.889 (\050)s 10 f 311.556 (\276)s 1 f 318.843 (\051)s 13 f 288.829 y 323.51 (\256)s 2 f 303.776 y 329.177 (\244)s 15 f 298.516 y 335.743 (n)s 16 f 341.028 (+)s 15 f 347.195 (N)s 299.716 y 353.649 (\260)s 305.386 y 335.743 (n)s 13 f 285.229 y 360.347 (o)s 2 f 287.715 y 368.347 (2)s 12 f 336.842 y 186.404 (\243)s 13 f 323.522 y 198.404 (n)s 318.242 y 207.844 (p)s 59.023 .48 219.844 318.242 r 10 f 328.502 y 219.844 (f)s 11 f 325.036 y 227.011 (t)s 331.469 y 225.719 (n)s 1 f 328.502 y 232.251 (\050)s 10 f 236.918 (\276)s 1 f 246.872 (+)s 258.872 (2)s 10 f 264.872 (\261)s 11 f 330.302 y 270.205 (i)s 1 f 328.502 y 274.201 (\051)s 71.023 .48 207.844 334.082 r 13 f 336.482 y 222.842 (p)s 29.028 .48 234.842 336.482 r 10 f 346.742 y 234.842 (f)s 11 f 343.276 y 242.009 (t)s 349.709 y 240.717 (n)s 1 f 346.742 y 247.249 (\050)s 10 f 251.916 (\276)s 1 f 259.203 (\051)s 12 f 336.842 y 282.974 (\241)s 1 f 294.974 (1)s 13 f 323.522 y 300.974 (o)s 2 f 326.009 y 308.974 (2)s 1 f 336.842 y 314.357 (1)s 11 f 338.976 y 320.357 (E)s 16 f 336.576 y 327.864 (3)s 15 f 341.376 y 327.402 (n)s 10 f 336.842 y 333.887 (d\272)s 11 f 338.642 y 346.061 (P)s 1 f 336.842 y 354.062 (\050)s 10 f 358.729 (\276)s 1 f 366.016 (\051)s 10 f 370.683 (:)s 1 f 300.999 y 433.113 (\0504)s 10 f 443.78 (:)s 1 f 447.114 (12\051)s 377.419 y 8.71 (The)s 33.357 (\257rst)s 58.104 (line)s 80.752 (of)s 94.399 (this)s 117.78 (expression)s 175.594 (is)s 187.641 (b)s 194.641 (ounded)s 236.622 (ab)s 249.622 (o)s 255.289 (v)s 261.289 (e)s 270.603 (b)s 276.936 (y)s 287.25 (the)s 307.897 (one)s 329.878 (b)s 336.878 (ond)s 360.192 (Diric)s 385.725 (hlet)s 409.706 (form.)s 442.733 (It)s 455.714 (is)s 394.219 y -5.69 (equal)s 25.977 (to)s 10 f 430.237 y 16.419 (\260)s 14 f 425.883 y 23.299 (\241)s 2 f 30.799 (3)s 23.52 .48 14.541 435.596 r 10 f 446.587 y 14.541 (N)s 11 f 448.387 y 24.183 (\260)s 10 f 446.587 y 30.34 (\256)s 11 f 422.056 y 53.125 (n)s 2 f 59.057 (+2)s 11 f 71.207 (N)s 15 f 423.256 y 78.808 (\260)s 13 f 426.956 y 60.049 (X)s 11 f 452.696 y 41.501 (m)s 2 f 50.016 (=)s 11 f 57.383 (n)s 2 f 63.315 (+)s 11 f 70.681 (N)s 15 f 453.896 y 78.282 (\260)s 2 f 452.696 y 83.78 (+1)s 13 f 422.022 y 97.93 (Z)s 425.035 y 111.93 (n)s 420.643 y 119.93 (r)s 194.494 .48 131.93 420.643 r 428.636 y 131.93 (\255)s 10 f 438.356 y 137.597 (r)s 2 f 432.122 y 143.344 (\050)s 14 f 147.094 (\241)s 2 f 154.594 (1)s 11 f 159.378 (;)s 2 f 162.228 (1\051)s 11 f 441.7 y 143.011 (i;j)s 1 f 438.356 y 171.361 (\050)s 10 f 176.028 (\276)s 1 f 183.315 (\051)s 10 f 187.982 (C)s 11 f 432.589 y 197.417 (K)s 205.552 (;\257)s 439.759 y 196.559 (\260)s 1 f 438.356 y 214.875 (\050)s 10 f 219.542 (i;)s 229.009 (j)s 1 f 234.638 (;)s 10 f 239.971 (\276)s 11 f 434.889 y 247.258 (i;j)s 1 f 438.356 y 258.56 (\051)s 10 f 263.226 (f)s 11 f 434.889 y 270.393 (t)s 441.322 y 269.102 (m)s 1 f 438.356 y 278.217 (\050)s 10 f 282.884 (\276)s 11 f 434.889 y 290.171 (j)s 294.111 (;i)s 1 f 438.356 y 300.956 (\051)s 13 f 428.636 y 305.622 (\256)s 2 f 443.156 y 311.289 (\244)s 15 f 439.534 y 317.856 (m)s 445.556 y 317.856 (n)s 12 f 483.335 y 183.768 (\241)s 13 f 465.622 y 195.768 (r)s 183.709 .48 207.768 465.622 r 473.615 y 207.768 (\255)s 10 f 483.335 y 213.434 (r)s 2 f 477.102 y 219.182 (\050)s 14 f 222.932 (\241)s 2 f 230.432 (1)s 11 f 235.215 (;)s 2 f 238.065 (1\051)s 11 f 486.68 y 218.848 (i;j)s 1 f 483.335 y 247.198 (\050)s 10 f 251.865 (\276)s 1 f 259.153 (\051)s 10 f 263.819 (C)s 11 f 477.568 y 273.254 (K)s 281.389 (;\257)s 484.738 y 272.396 (\260)s 1 f 483.335 y 290.712 (\050)s 10 f 295.379 (i;)s 304.846 (j)s 1 f 310.475 (;)s 10 f 315.808 (\276)s 11 f 479.868 y 323.096 (i;j)s 1 f 483.335 y 334.397 (\051)s 10 f 339.064 (f)s 11 f 479.868 y 346.231 (t)s 486.301 y 344.939 (m)s 1 f 483.335 y 354.054 (\050)s 10 f 358.721 (\276)s 1 f 366.008 (\051)s 13 f 473.615 y 370.675 (\256)s 2 f 488.135 y 376.342 (\244)s 15 f 484.514 y 382.909 (m)s 490.535 y 382.909 (n)s 13 f 470.015 y 391.477 (o)s 2 f 472.501 y 399.477 (2)s 10 f 483.335 y 404.86 (d\272)s 11 f 485.135 y 417.034 (P)s 1 f 483.335 y 425.035 (\050)s 10 f 429.702 (\276)s 1 f 436.989 (\051)s 10 f 441.656 (;)s 1 f 520.839 y -5.69 (whic)s 17.976 (h,)s 31.977 (b)s 38.31 (y)s 48.643 (Sc)s 60.31 (h)s 66.643 (w)s 74.977 (artz)s 99.677 (inequalit)s 145.01 (y)s 150.343 (,)s 157.677 (is)s 169.743 (b)s 176.743 (ounded)s 218.744 (b)s 225.077 (y)s 10 f 556.858 y 22.474 (\260)s 14 f 552.503 y 29.353 (\241)s 2 f 36.853 (3)s 23.52 .48 20.595 562.216 r 10 f 573.207 y 20.595 (N)s 11 f 575.007 y 30.237 (\260)s 10 f 573.207 y 36.394 (\256)s 11 f 548.676 y 59.179 (n)s 2 f 65.111 (+2)s 11 f 77.261 (N)s 15 f 549.876 y 84.862 (\260)s 13 f 553.576 y 66.103 (X)s 11 f 579.316 y 47.555 (m)s 2 f 56.07 (=)s 11 f 63.437 (n)s 2 f 69.369 (+)s 11 f 76.736 (N)s 15 f 580.516 y 84.336 (\260)s 2 f 579.316 y 89.834 (+1)s 13 f 548.642 y 103.984 (Z)s 555.256 y 117.984 (\255)s 10 f 564.976 y 123.651 (r)s 2 f 558.742 y 129.398 (\050)s 14 f 133.148 (\241)s 2 f 140.648 (1)s 11 f 145.432 (;)s 2 f 148.282 (1\051)s 11 f 568.321 y 129.065 (i;j)s 1 f 564.976 y 157.415 (\050)s 10 f 162.082 (\276)s 1 f 169.369 (\051)s 10 f 174.036 (C)s 11 f 560.021 y 183.471 (K)s 191.606 (;\257)s 567.942 y 182.613 (\260)s 1 f 564.976 y 200.929 (\050)s 10 f 205.596 (i;)s 215.063 (j)s 1 f 220.692 (;)s 10 f 226.025 (\276)s 11 f 560.021 y 233.312 (i;j)s 1 f 564.976 y 244.614 (\051)s 13 f 555.256 y 249.281 (\251)s 554.117 y 256.281 (p)s 42.396 .48 268.281 554.117 r 10 f 564.976 y 268.281 (f)s 11 f 561.509 y 275.447 (t)s 567.942 y 274.156 (m)s 1 f 564.976 y 283.271 (\050)s 10 f 287.938 (\276)s 11 f 561.509 y 295.225 (j)s 299.165 (;i)s 1 f 564.976 y 306.01 (\051)s 12 f 313.343 (\241)s 13 f 554.13 y 325.343 (p)s 31.611 .48 337.343 554.13 r 10 f 564.976 y 337.343 (f)s 11 f 561.509 y 344.51 (t)s 567.942 y 343.218 (m)s 1 f 564.976 y 352.334 (\050)s 10 f 357 (\276)s 1 f 364.288 (\051)s 13 f 555.256 y 368.954 (\252)s 2 f 557.742 y 375.954 (2)s 13 f 555.256 y 381.338 (\256)s 2 f 569.776 y 387.004 (\244)s 15 f 566.154 y 393.571 (m)s 572.176 y 393.571 (n)s 10 f 564.976 y 402.139 (d\272)s 11 f 566.776 y 414.313 (P)s 1 f 564.976 y 422.314 (\050)s 10 f 426.981 (\276)s 1 f 434.268 (\051)s 12 f 614.522 y 25.822 (\267)s 10 f 38.488 (C)s 2 f 616.322 y 47.065 (4)s 10 f 606.404 y 53.888 (\260)s 14 f 602.05 y 60.768 (\241)s 2 f 68.268 (2)s 19.763 .48 53.888 611.762 r 10 f 622.754 y 59.909 (\256)s 11 f 598.222 y 88.715 (n)s 2 f 94.647 (+2)s 11 f 106.797 (N)s 15 f 599.422 y 114.398 (\260)s 13 f 603.122 y 95.639 (X)s 11 f 628.863 y 77.091 (m)s 2 f 85.606 (=)s 11 f 92.973 (n)s 2 f 98.905 (+)s 11 f 106.272 (N)s 15 f 630.063 y 113.873 (\260)s 2 f 628.863 y 119.371 (+1)s 13 f 598.189 y 133.521 (Z)s 604.802 y 147.521 (\255)s 10 f 614.522 y 153.187 (r)s 2 f 608.289 y 158.934 (\050)s 14 f 162.685 (\241)s 2 f 170.185 (1)s 11 f 174.968 (;)s 2 f 177.818 (1\051)s 11 f 617.867 y 158.601 (i;j)s 1 f 614.522 y 186.951 (\050)s 10 f 191.618 (\276)s 1 f 198.905 (\051)s 13 f 604.802 y 203.572 (\251)s 603.664 y 210.572 (p)s 42.396 .48 222.572 603.664 r 10 f 614.522 y 222.572 (f)s 11 f 611.056 y 229.739 (t)s 617.489 y 228.447 (m)s 1 f 614.522 y 237.563 (\050)s 10 f 242.229 (\276)s 11 f 611.056 y 249.517 (j)s 253.456 (;i)s 1 f 614.522 y 260.301 (\051)s 12 f 267.635 (\241)s 13 f 603.677 y 279.635 (p)s 31.611 .48 291.635 603.677 r 10 f 614.522 y 291.635 (f)s 11 f 611.056 y 298.801 (t)s 617.489 y 297.51 (m)s 1 f 614.522 y 306.625 (\050)s 10 f 311.292 (\276)s 1 f 318.579 (\051)s 13 f 604.802 y 323.246 (\252)s 2 f 607.289 y 330.246 (2)s 13 f 604.802 y 335.629 (\256)s 2 f 619.322 y 341.296 (\244)s 15 f 615.701 y 347.863 (m)s 621.722 y 347.863 (n)s 10 f 614.522 y 356.431 (d\272)s 11 f 616.322 y 368.604 (P)s 1 f 614.522 y 376.606 (\050)s 10 f 381.272 (\276)s 1 f 388.56 (\051)s 664.069 y 34.488 (=)s 10 f 47.155 (C)s 2 f 665.869 y 55.732 (4)s 10 f 655.951 y 62.555 (\260)s 14 f 651.596 y 69.434 (\241)s 2 f 76.934 (2)s 19.763 .48 62.555 661.309 r 10 f 672.301 y 68.576 (\256)s 11 f 647.769 y 97.382 (n)s 2 f 103.314 (+2)s 11 f 115.464 (N)s 15 f 648.969 y 123.065 (\260)s 13 f 652.669 y 104.306 (X)s 11 f 678.409 y 85.758 (m)s 2 f 94.273 (=)s 11 f 101.64 (n)s 2 f 107.572 (+)s 11 f 114.938 (N)s 15 f 679.609 y 122.539 (\260)s 2 f 678.409 y 128.037 (+1)s 13 f 647.736 y 142.187 (Z)s 10 f 664.069 y 156.187 (r)s 2 f 657.836 y 161.935 (\050)s 14 f 165.685 (\241)s 2 f 173.185 (1)s 11 f 177.968 (;)s 2 f 180.818 (1\051)s 11 f 667.414 y 161.601 (i;j)s 1 f 664.069 y 189.951 (\050)s 10 f 194.618 (\276)s 1 f 201.906 (\051)s 13 f 654.349 y 206.572 (\251)s 653.211 y 213.572 (p)s 42.396 .48 225.572 653.211 r 10 f 664.069 y 225.572 (f)s 11 f 660.603 y 232.739 (t)s 667.036 y 231.447 (m)s 1 f 664.069 y 240.563 (\050)s 10 f 245.229 (\276)s 11 f 660.603 y 252.517 (j)s 256.456 (;i)s 1 f 664.069 y 263.302 (\051)s 12 f 270.635 (\241)s 13 f 653.223 y 282.635 (p)s 31.611 .48 294.635 653.223 r 10 f 664.069 y 294.635 (f)s 11 f 660.603 y 301.802 (t)s 667.036 y 300.51 (m)s 1 f 664.069 y 309.625 (\050)s 10 f 314.292 (\276)s 1 f 321.579 (\051)s 13 f 654.349 y 326.246 (\252)s 2 f 656.836 y 333.246 (2)s 10 f 664.069 y 338.629 (d\272)s 11 f 665.869 y 350.803 (P)s 1 f 664.069 y 358.804 (\050)s 10 f 363.471 (\276)s 1 f 370.758 (\051)s 10 f 375.425 (;)s 1 f 705.976 y 223.045 (22)s do-end end endp %%Page: 23 23 %%BeginPageSetup initializepage (Raffaele Esposito; page: 23 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f1_12 sf ( )S -997 -1000 :M f2_12 sf ( )S -993 -1000 :M f10_12 sf ( )S -985 -1000 :M f11_12 sf ( )S -976 -1000 :M f12_12 sf ( )S -964 -1000 :M f13_12 sf ( )S -954 -1000 :M f14_12 sf ( )S -941 -1000 :M f15_12 sf ( )S -930 -1000 :M f16_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 16 5 1200 1000 div mul /CMR5 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 6.31 y -5.69 (where)s 29.121 (w)s 37.454 (e)s 46.898 (used)s 74.41 (the)s 95.187 (fact)s 118.965 (that)s 145.076 (there)s 175.887 (exists)s 209.131 (a)s 219.242 (p)s 226.242 (ositiv)s 254.309 (e)s 263.753 (constan)s 303.487 (t)s 10 f 312.265 (C)s 2 f 8.11 y 320.841 (4)s 1 f 6.31 y 326.225 (,)s 333.697 (suc)s 350.097 (h)s 360.874 (that)s 10 f 386.985 (C)s 11 f 1.955 y 396.42 (K)s 404.555 (;\257)s 9.276 y 395.562 (\260)s 1 f 6.31 y 413.878 (\050)s 10 f 418.545 (i;)s 428.013 (j)s 1 f 433.641 (;)s 10 f 438.974 (\276)s 1 f 446.262 (\051)s 12 f 454.447 (\267)s 10 f 23.11 y -5.69 (C)s 2 f 24.91 y 2.886 (4)s 1 f 23.11 y 8.27 (,)s 15.603 (for)s 33.97 (all)s 50.637 (con\257guration)s 10 f 123.337 (\276)s 1 f 130.624 (.)s 40.03 y 8.71 (Finally)s 49.543 (the)s 70.21 (second)s 108.943 (term)s 137.643 (of)s 151.31 (\0504.12\051)s 185.977 (is)s 198.043 (b)s 205.044 (ounded)s 247.044 (b)s 253.377 (y)s 77.657 y 42.733 (4)s 10 f 48.733 (\260)s 14 f 72.703 y 55.612 (\241)s 2 f 63.112 (1)s 10 f 77.657 y 68.496 (\256)s 13 f 61.324 y 78.217 (Z)s 1 f 77.657 y 92.216 (1)s 14 f 79.824 y 98.216 (f)s 11 f 103.133 (\276)s 2 f 108.995 (\050)s 11 f 112.745 (i)s 2 f 116.14 (\051=)s 14 f 127.257 (\241)s 2 f 134.757 (1)s 14 f 139.541 (g)s 13 f 56.421 y 146.497 (\255)s 10 f 66.141 y 152.164 (F)s 11 f 60.374 y 161.547 (i;j)s 2 f 69.341 y 159.881 (3)s 1 f 66.141 y 172.849 (\050)s 10 f 177.515 (\276)s 1 f 184.803 (\051)s 13 f 56.421 y 189.47 (\256)s 2 f 71.368 y 195.136 (\244)s 15 f 66.108 y 201.703 (n)s 16 f 206.988 (+)s 15 f 213.154 (N)s 67.308 y 219.609 (\260)s 72.978 y 201.703 (n)s 79.81 .48 146.497 74.897 r 10 f 85.889 y 171.888 (f)s 11 f 82.422 y 179.055 (t)s 88.855 y 177.763 (n)s 1 f 85.889 y 184.295 (\050)s 10 f 188.962 (\276)s 1 f 196.249 (\051)s 13 f 67.937 y 227.747 (\251)s 66.812 y 234.747 (p)s 59.023 .48 246.747 66.812 r 10 f 77.657 y 246.747 (f)s 11 f 74.191 y 253.914 (t)s 80.624 y 252.622 (n)s 1 f 77.657 y 259.154 (\050)s 10 f 263.821 (\276)s 1 f 273.775 (+)s 285.775 (2)s 10 f 291.775 (\261)s 11 f 79.457 y 297.108 (i)s 1 f 77.657 y 301.103 (\051)s 12 f 308.436 (\241)s 13 f 66.812 y 320.436 (p)s 29.028 .48 332.436 66.812 r 10 f 77.657 y 332.436 (f)s 11 f 74.191 y 339.603 (t)s 80.624 y 338.311 (n)s 1 f 77.657 y 344.843 (\050)s 10 f 349.51 (\276)s 1 f 356.798 (\051)s 13 f 67.937 y 361.464 (\252)s 2 f 70.424 y 368.464 (2)s 10 f 77.657 y 373.848 (d\272)s 11 f 79.457 y 386.021 (P)s 1 f 77.657 y 394.022 (\050)s 10 f 398.689 (\276)s 1 f 405.977 (\051)s 12 f 113.622 y 46.066 (\267)s 1 f 58.733 (4)s 10 f 64.733 (C)s 2 f 115.422 y 73.309 (4)s 10 f 113.622 y 78.693 (\260)s 14 f 108.668 y 85.572 (\241)s 2 f 93.072 (1)s 10 f 113.622 y 98.456 (\256)s 13 f 97.289 y 108.176 (Z)s 1 f 113.622 y 122.176 (1)s 14 f 115.789 y 128.176 (f)s 11 f 133.093 (\276)s 2 f 138.955 (\050)s 11 f 142.705 (i)s 2 f 146.1 (\051=)s 14 f 157.217 (\241)s 2 f 164.717 (1)s 14 f 169.5 (g)s 13 f 103.902 y 175.017 (\251)s 102.776 y 182.017 (p)s 59.023 .48 194.017 102.776 r 10 f 113.622 y 194.017 (f)s 11 f 110.156 y 201.184 (t)s 116.589 y 199.892 (n)s 1 f 113.622 y 206.424 (\050)s 10 f 211.091 (\276)s 1 f 221.045 (+)s 233.045 (2)s 10 f 239.045 (\261)s 11 f 115.422 y 244.378 (i)s 1 f 113.622 y 248.373 (\051)s 12 f 255.707 (\241)s 13 f 102.776 y 267.707 (p)s 29.028 .48 279.707 102.776 r 10 f 113.622 y 279.707 (f)s 11 f 110.156 y 286.873 (t)s 116.589 y 285.582 (n)s 1 f 113.622 y 292.114 (\050)s 10 f 296.78 (\276)s 1 f 304.068 (\051)s 13 f 103.902 y 308.735 (\252)s 2 f 106.389 y 315.735 (2)s 10 f 113.622 y 321.118 (d\272)s 11 f 115.422 y 333.292 (P)s 1 f 113.622 y 341.293 (\050)s 10 f 345.959 (\276)s 1 f 353.247 (\051)s 12 f 361.247 (\267)s 10 f 373.914 (C)s 2 f 115.422 y 382.49 (5)s 10 f 113.622 y 387.874 (\260)s 14 f 108.668 y 394.753 (\241)s 2 f 402.253 (1)s 10 f 113.622 y 407.636 (\256)s 1 f 144.075 y -5.69 (for)s 13.427 (some)s 44.244 (p)s 51.244 (ositiv)s 79.311 (e)s 89.394 (constan)s 129.128 (t)s 10 f 138.545 (C)s 2 f 145.875 y 147.121 (5)s 1 f 144.075 y 157.255 (that)s 184.006 (dep)s 203.006 (ends)s 231.156 (on)s 10 f 248.573 (P)s 1 f 257.944 (.)s 268.862 (W)s 280.195 (e)s 290.279 (ha)s 302.612 (v)s 308.612 (e)s 318.696 (c)s 323.696 (hanged)s 365.779 (v)s 371.446 (ariables)s 416.297 (and)s 440.38 (used)s 160.875 y -5.69 (the)s 14.976 (fact)s 38.643 (that)s 10 f 64.643 (f)s 11 f 156.521 y 71.81 (t)s 163.842 y 70.518 (n)s 1 f 160.875 y 81.05 (is)s 93.117 (a)s 103.117 (probabilit)s 154.15 (y)s 164.484 (densit)s 195.551 (y)s 205.884 (with)s 233.217 (resp)s 254.984 (ect)s 274.317 (to)s 10 f 288.984 (\272)s 11 f 162.675 y 294.912 (P)s 1 f 160.875 y 302.913 (.)s 177.795 y 8.71 (Collecting)s 64.915 (the)s 85.119 (ab)s 98.119 (o)s 103.786 (v)s 109.786 (e)s 118.657 (inequalities,)s 184.688 (w)s 193.021 (e)s 201.892 (get)s 221.43 (the)s 241.635 (follo)s 263.635 (wing)s 291.84 (b)s 298.84 (ound)s 328.378 (for)s 346.283 (\255)s 2 f 179.595 y 354.949 (4)s 1 f 177.795 y 360.333 (.)s 368.845 (F)s 375.679 (or)s 389.917 (an)s 402.25 (y)s 412.121 (p)s 419.121 (ositiv)s 447.188 (e)s 10 f 456.059 (\256)s 1 f 202.283 y 31.885 (\255)s 2 f 204.083 y 40.552 (4)s 12 f 202.283 y 49.268 (\267)s 10 f 61.935 (\260)s 14 f 197.328 y 68.814 (\241)s 2 f 76.314 (1)s 1 f 202.283 y 81.698 (\050)s 10 f 86.364 (C)s 14 f 197.328 y 95.799 (0)s 2 f 205.25 y 94.941 (2)s 1 f 202.283 y 102.991 (+)s 10 f 114.991 (C)s 2 f 204.083 y 123.568 (5)s 10 f 202.283 y 128.951 (\256)s 1 f 136.672 (\051)s 238.123 y 51.935 (+)s 10 f 63.935 (C)s 2 f 239.923 y 72.511 (4)s 10 f 230.005 y 79.335 (\260)s 14 f 225.65 y 86.214 (\241)s 2 f 93.714 (2)s 19.763 .48 79.335 235.363 r 10 f 246.354 y 85.356 (\256)s 11 f 221.823 y 114.162 (n)s 2 f 120.094 (+2)s 11 f 132.244 (N)s 15 f 223.023 y 139.845 (\260)s 13 f 226.723 y 121.086 (X)s 11 f 252.463 y 102.538 (m)s 2 f 111.053 (=)s 11 f 118.42 (n)s 2 f 124.352 (+)s 11 f 131.718 (N)s 15 f 253.663 y 139.319 (\260)s 2 f 252.463 y 144.817 (+1)s 13 f 221.79 y 158.967 (Z)s 10 f 238.123 y 172.967 (r)s 2 f 231.89 y 178.714 (\050)s 14 f 182.464 (\241)s 2 f 189.964 (1)s 11 f 194.748 (;)s 2 f 197.598 (1\051)s 11 f 241.468 y 178.381 (i;j)s 1 f 238.123 y 206.731 (\050)s 10 f 211.398 (\276)s 1 f 218.685 (\051)s 13 f 228.403 y 223.352 (\251)s 227.265 y 230.352 (p)s 42.396 .48 242.352 227.265 r 10 f 238.123 y 242.352 (f)s 11 f 234.656 y 249.519 (t)s 241.09 y 248.227 (m)s 1 f 238.123 y 257.342 (\050)s 10 f 262.009 (\276)s 11 f 234.656 y 269.297 (j)s 273.236 (;i)s 1 f 238.123 y 280.081 (\051)s 12 f 287.415 (\241)s 13 f 227.277 y 299.415 (p)s 31.611 .48 311.415 227.277 r 10 f 238.123 y 311.415 (f)s 11 f 234.656 y 318.581 (t)s 241.09 y 317.29 (m)s 1 f 238.123 y 326.405 (\050)s 10 f 331.072 (\276)s 1 f 338.359 (\051)s 13 f 228.403 y 343.026 (\252)s 2 f 230.89 y 350.026 (2)s 10 f 238.123 y 355.409 (d\272)s 11 f 239.923 y 367.583 (P)s 1 f 238.123 y 375.584 (\050)s 10 f 380.251 (\276)s 1 f 387.538 (\051)s 10 f 392.205 (:)s 1 f 226.972 y 433.113 (\0504)s 10 f 443.78 (:)s 1 f 447.114 (13\051)s 276.269 y 8.71 (The)s 33.376 (term)s 62.077 (\255)s 2 f 278.069 y 70.743 (5)s 1 f 276.269 y 80.127 (will)s 102.793 (b)s 109.793 (e)s 119.127 (handled)s 164.46 (in)s 178.46 (an)s 195.127 (analogous)s 250.527 (w)s 258.86 (a)s 264.527 (y)s 269.86 (.)s 278.527 (It)s 291.527 (can)s 313.527 (b)s 320.527 (e)s 329.86 (rewritten)s 381.927 (as)s 308.028 y -2.289 (\255)s 2 f 309.828 y 6.378 (5)s 1 f 308.028 y 15.095 (=)s 10 f 27.761 (\260)s 14 f 303.074 y 34.641 (\241)s 2 f 42.141 (2)s 13 f 291.695 y 49.524 (Z)s 1 f 308.028 y 63.524 (1)s 14 f 310.195 y 69.524 (f)s 11 f 74.441 (\276)s 2 f 80.303 (\050)s 11 f 84.053 (i)s 2 f 87.448 (\051=)s 14 f 98.565 (\241)s 2 f 106.065 (1)s 14 f 110.848 (g)s 13 f 294.708 y 116.365 (n)s 298.308 y 124.365 (\255)s 10 f 308.028 y 130.031 (F)s 11 f 302.262 y 139.415 (i;j)s 2 f 311.228 y 137.748 (2)s 1 f 308.028 y 150.716 (\050)s 10 f 155.383 (\276)s 1 f 162.67 (\051)s 13 f 298.308 y 167.337 (\256)s 2 f 313.255 y 173.004 (\244)s 15 f 307.995 y 179.57 (n)s 16 f 184.855 (+)s 15 f 191.022 (N)s 309.195 y 197.476 (\260)s 314.865 y 179.57 (n)s 12 f 308.028 y 206.841 (\241)s 13 f 298.308 y 218.841 (\255)s 10 f 308.028 y 224.507 (F)s 11 f 302.262 y 233.891 (i;j)s 2 f 311.228 y 232.224 (4)s 1 f 308.028 y 245.192 (\050)s 10 f 249.859 (\276)s 1 f 257.146 (\051)s 13 f 298.308 y 261.813 (\256)s 2 f 313.255 y 267.48 (\244)s 15 f 307.995 y 274.046 (n)s 16 f 279.331 (+)s 15 f 285.498 (N)s 309.195 y 291.952 (\260)s 314.865 y 274.046 (n)s 13 f 294.708 y 298.65 (o)s 1 f 308.028 y 308.65 (log)s 13 f 294.708 y 326.15 (n)s 10 f 299.91 y 350.588 (f)s 11 f 295.556 y 357.755 (t)s 302.877 y 356.463 (n)s 1 f 299.91 y 362.995 (\050)s 10 f 367.662 (\276)s 1 f 374.949 (\051)s 59.023 .48 335.59 305.268 r 10 f 316.26 y 335.59 (f)s 11 f 312.793 y 342.757 (t)s 319.226 y 341.465 (n)s 1 f 316.26 y 347.997 (\050)s 10 f 352.664 (\276)s 1 f 362.618 (+)s 374.618 (2)s 10 f 380.618 (\261)s 11 f 318.06 y 385.951 (i)s 1 f 316.26 y 389.947 (\051)s 13 f 294.708 y 396.053 (o)s 1 f 308.028 y 404.053 (1)s 11 f 310.162 y 410.053 (E)s 16 f 307.762 y 417.56 (2)s 15 f 312.562 y 417.098 (n)s 10 f 308.028 y 423.583 (d\272)s 11 f 309.828 y 435.757 (P)s 1 f 308.028 y 443.758 (\050)s 10 f 448.425 (\276)s 1 f 455.712 (\051)s 345.299 y 3.711 (+)s 10 f 15.711 (\260)s 14 f 340.345 y 22.591 (\241)s 2 f 30.091 (2)s 13 f 328.966 y 37.474 (Z)s 1 f 345.299 y 51.474 (1)s 14 f 347.466 y 57.474 (f)s 11 f 62.391 (\276)s 2 f 68.253 (\050)s 11 f 72.003 (i)s 2 f 75.398 (\051=)s 14 f 86.514 (\241)s 2 f 94.015 (1)s 14 f 98.798 (g)s 13 f 331.979 y 104.315 (n)s 335.579 y 112.315 (\255)s 10 f 345.299 y 117.981 (F)s 11 f 339.533 y 127.365 (i;j)s 2 f 348.499 y 125.698 (4)s 1 f 345.299 y 138.666 (\050)s 10 f 143.333 (\276)s 1 f 150.62 (\051)s 13 f 335.579 y 155.287 (\256)s 2 f 350.526 y 160.954 (\244)s 15 f 345.266 y 167.52 (n)s 16 f 172.805 (+)s 15 f 178.972 (N)s 346.466 y 185.426 (\260)s 352.136 y 167.52 (n)s 12 f 345.299 y 194.791 (\241)s 13 f 335.579 y 206.791 (\255)s 10 f 345.299 y 212.457 (F)s 11 f 339.533 y 221.841 (i;j)s 2 f 348.499 y 220.174 (1)s 1 f 345.299 y 233.142 (\050)s 10 f 237.809 (\276)s 1 f 245.096 (\051)s 13 f 335.579 y 249.763 (\256)s 2 f 350.526 y 255.43 (\244)s 15 f 345.266 y 261.996 (n)s 16 f 267.281 (+)s 15 f 273.448 (N)s 346.466 y 279.902 (\260)s 352.136 y 261.996 (n)s 13 f 331.979 y 286.6 (o)s 1 f 345.299 y 296.6 (log)s 13 f 331.979 y 314.1 (n)s 10 f 337.181 y 338.538 (f)s 11 f 332.827 y 345.704 (t)s 340.148 y 344.413 (n)s 1 f 337.181 y 350.945 (\050)s 10 f 355.611 (\276)s 1 f 362.899 (\051)s 59.023 .48 323.54 342.539 r 10 f 353.531 y 323.54 (f)s 11 f 350.064 y 330.707 (t)s 356.497 y 329.415 (n)s 1 f 353.531 y 335.947 (\050)s 10 f 340.614 (\276)s 1 f 350.568 (+)s 362.568 (2)s 10 f 368.568 (\261)s 11 f 355.331 y 373.901 (i)s 1 f 353.531 y 377.896 (\051)s 13 f 331.979 y 384.003 (o)s 1 f 345.299 y 392.003 (1)s 11 f 347.433 y 398.003 (E)s 16 f 345.033 y 405.51 (2)s 15 f 349.833 y 405.048 (n)s 10 f 345.299 y 411.533 (d\272)s 11 f 347.099 y 423.707 (P)s 1 f 345.299 y 431.708 (\050)s 10 f 436.375 (\276)s 1 f 443.662 (\051)s 376.65 y -5.69 (with)s 10 f 393.45 y 117.649 (F)s 11 f 387.684 y 127.033 (i;j)s 2 f 396.65 y 125.366 (4)s 1 f 393.45 y 141.667 (=)s 154.334 (1)s 14 f 395.617 y 160.334 (f)s 11 f 165.251 (\276)s 2 f 171.113 (\050)s 11 f 174.863 (j)s 2 f 179.319 (\051=1)s 14 f 195.219 (g)s 10 f 393.45 y 200.736 (C)s 11 f 388.496 y 210.171 (K)s 218.306 (;\257)s 396.417 y 209.313 (\260)s 1 f 393.45 y 227.629 (\050)s 10 f 232.296 (i;)s 241.763 (j)s 1 f 247.392 (;)s 10 f 252.725 (\276)s 1 f 260.012 (\051)s 10 f 264.679 (f)s 11 f 388.496 y 271.846 (t)s 396.417 y 270.554 (n)s 2 f 276.486 (+)s 11 f 283.853 (N)s 15 f 397.617 y 291.454 (\260)s 2 f 396.417 y 296.952 (+1)s 1 f 393.45 y 309.702 (\050)s 10 f 314.368 (\276)s 11 f 388.496 y 321.656 (j)s 325.596 (;i)s 1 f 393.45 y 332.441 (\051)s 10 f 337.107 (:)s 1 f 415.475 y 8.71 (By)s 27.216 (the)s 47.556 (same)s 77.295 (argumen)s 122.329 (ts)s 135.402 (used)s 162.474 (to)s 176.814 (estimate)s 224.554 (\255)s 2 f 417.275 y 233.22 (4)s 1 f 415.475 y 238.604 (,)s 245.675 (w)s 254.009 (e)s 263.015 (obtain)s 300.021 (b)s 306.355 (y)s 316.361 (exc)s 333.027 (hanging)s 378.034 (the)s 398.373 (role)s 421.413 (of)s 10 f 434.753 (f)s 11 f 411.121 y 441.919 (t)s 418.442 y 440.628 (n)s 1 f 415.475 y 447.16 (\050)s 10 f 451.826 (\276)s 1 f 459.114 (\051)s 432.275 y -5.69 (and)s 10 f 17.643 (f)s 11 f 427.921 y 24.81 (t)s 435.242 y 23.518 (n)s 1 f 432.275 y 30.05 (\050)s 10 f 34.717 (\276)s 1 f 44.671 (+)s 56.671 (2)s 10 f 62.671 (\261)s 11 f 434.075 y 68.004 (i)s 1 f 432.275 y 71.999 (\051,)s 457.43 y 48.627 (\255)s 2 f 459.23 y 57.293 (5)s 12 f 457.43 y 66.01 (\267)s 10 f 78.677 (\260)s 14 f 452.475 y 85.556 (\241)s 2 f 93.056 (1)s 1 f 457.43 y 98.439 (\050)s 10 f 103.106 (C)s 14 f 452.475 y 112.541 (0)s 2 f 460.396 y 111.683 (2)s 1 f 457.43 y 119.733 (+)s 10 f 131.733 (C)s 2 f 459.23 y 140.309 (5)s 10 f 457.43 y 145.693 (\256)s 1 f 153.413 (\051)s 493.27 y 68.677 (+)s 10 f 80.677 (C)s 2 f 495.07 y 89.253 (4)s 10 f 485.152 y 96.077 (\260)s 14 f 480.797 y 102.956 (\241)s 2 f 110.456 (2)s 19.763 .48 96.077 490.51 r 10 f 501.501 y 102.098 (\256)s 11 f 476.97 y 130.904 (n)s 2 f 136.836 (+2)s 11 f 148.986 (N)s 15 f 478.17 y 156.587 (\260)s 13 f 481.87 y 137.827 (X)s 11 f 507.61 y 119.279 (m)s 2 f 127.795 (=)s 11 f 135.161 (n)s 2 f 141.093 (+)s 11 f 148.46 (N)s 15 f 508.81 y 156.061 (\260)s 2 f 507.61 y 161.559 (+1)s 13 f 476.936 y 175.709 (Z)s 10 f 493.27 y 189.709 (r)s 2 f 487.036 y 195.456 (\050)s 14 f 199.206 (\241)s 2 f 206.706 (1)s 11 f 211.49 (;)s 2 f 214.34 (1\051)s 11 f 496.615 y 195.123 (j)s 199.062 (;i)s 1 f 493.27 y 223.473 (\050)s 10 f 228.14 (\276)s 1 f 235.427 (\051)s 13 f 483.55 y 240.094 (\251)s 482.411 y 247.094 (p)s 42.913 .48 259.094 482.411 r 10 f 493.27 y 259.094 (f)s 11 f 489.803 y 266.261 (t)s 496.236 y 264.969 (m)s 1 f 493.27 y 274.084 (\050)s 10 f 278.751 (\276)s 11 f 489.803 y 286.038 (i;j)s 1 f 493.27 y 297.34 (\051)s 12 f 304.673 (\241)s 13 f 482.424 y 316.673 (p)s 31.611 .48 328.673 482.424 r 10 f 493.27 y 328.673 (f)s 11 f 489.803 y 335.84 (t)s 496.236 y 334.548 (m)s 1 f 493.27 y 343.663 (\050)s 10 f 348.33 (\276)s 1 f 355.618 (\051)s 13 f 483.55 y 360.284 (\252)s 2 f 486.036 y 367.284 (2)s 10 f 493.27 y 372.668 (d\272)s 11 f 495.07 y 384.841 (P)s 1 f 493.27 y 392.843 (\050)s 10 f 397.509 (\276)s 1 f 404.797 (\051)s 531.963 y -5.69 (for)s 12.541 (all)s 29.073 (p)s 36.073 (ositiv)s 64.139 (e)s 10 f 73.338 (\256)s 1 f 81.058 (.)s 89.68 (Therefore,)s 147.305 (taking)s 184.17 (adv)s 202.503 (an)s 214.837 (tage)s 240.702 (of)s 254.233 (this)s 277.498 (last)s 300.096 (inequalit)s 345.429 (y)s 355.627 (and)s 378.826 (of)s 392.357 (\0504.13\051,)s 430.249 (w)s 438.582 (e)s 447.78 (get)s 10 f 572.549 y 6.31 (\260)s 14 f 567.594 y 13.189 (\241)s 2 f 20.689 (2)s 13 f 556.215 y 28.073 (Z)s 10 f 572.549 y 42.073 (f)s 11 f 567.594 y 49.239 (t)s 575.515 y 47.948 (n)s 2 f 53.88 (+)s 11 f 61.246 (N)s 15 f 576.715 y 68.847 (\260)s 2 f 575.515 y 74.345 (+1)s 1 f 572.549 y 87.095 (\050)s 10 f 91.762 (\276)s 1 f 99.049 (\051I)s 105.889 (L)s 2 f 566.316 y 113.389 (\050)s 14 f 117.139 (\241)s 2 f 124.639 (1)s 11 f 129.423 (;)s 2 f 132.273 (1\051)s 11 f 575.894 y 113.389 (i;j)s 1 f 572.549 y 143.406 (log)s 13 f 562.829 y 160.906 (\241)s 10 f 572.549 y 166.406 (f)s 11 f 567.594 y 173.573 (t)s 575.515 y 172.281 (n)s 1 f 572.549 y 178.813 (\050)s 10 f 183.48 (\276)s 1 f 190.767 (\051)s 13 f 562.829 y 195.434 (\242)s 10 f 572.549 y 200.934 (d\272)s 11 f 574.349 y 213.108 (P)s 12 f 572.549 y 224.442 (\267)s 1 f 237.109 (2)s 10 f 243.109 (\260)s 14 f 567.594 y 249.988 (\241)s 2 f 257.488 (1)s 1 f 572.549 y 262.872 (\050)s 10 f 267.538 (C)s 14 f 567.594 y 276.973 (0)s 2 f 575.515 y 276.115 (2)s 1 f 572.549 y 284.165 (+)s 10 f 296.165 (C)s 2 f 574.349 y 304.742 (5)s 10 f 572.549 y 310.125 (\256)s 1 f 317.846 (\051)s 614.522 y 98.843 (+)s 10 f 108.177 (C)s 2 f 616.322 y 116.753 (4)s 10 f 606.404 y 123.577 (\260)s 14 f 602.05 y 130.456 (\241)s 2 f 137.956 (2)s 19.763 .48 123.577 611.762 r 10 f 622.754 y 129.598 (\256)s 11 f 598.222 y 158.404 (n)s 2 f 164.336 (+2)s 11 f 176.486 (N)s 15 f 599.422 y 184.087 (\260)s 13 f 603.122 y 165.328 (X)s 11 f 628.863 y 146.779 (m)s 2 f 155.295 (=)s 11 f 162.661 (n)s 2 f 168.593 (+)s 11 f 175.96 (N)s 15 f 630.063 y 183.561 (\260)s 2 f 628.863 y 189.059 (+1)s 13 f 598.189 y 203.209 (Z)s 10 f 614.522 y 217.209 (r)s 2 f 608.289 y 222.956 (\050)s 14 f 226.706 (\241)s 2 f 234.206 (1)s 11 f 238.99 (;)s 2 f 241.84 (1\051)s 11 f 617.867 y 222.623 (i;j)s 1 f 614.522 y 250.973 (\050)s 10 f 255.64 (\276)s 1 f 262.927 (\051)s 13 f 604.802 y 267.594 (\251)s 603.664 y 274.594 (p)s 42.396 .48 286.594 603.664 r 10 f 614.522 y 286.594 (f)s 11 f 611.056 y 293.761 (t)s 617.489 y 292.469 (m)s 1 f 614.522 y 301.584 (\050)s 10 f 306.251 (\276)s 11 f 611.056 y 313.539 (j)s 317.478 (;i)s 1 f 614.522 y 324.323 (\051)s 12 f 331.657 (\241)s 13 f 603.677 y 343.657 (p)s 31.611 .48 355.657 603.677 r 10 f 614.522 y 355.657 (f)s 11 f 611.056 y 362.823 (t)s 617.489 y 361.532 (m)s 1 f 614.522 y 370.647 (\050)s 10 f 375.314 (\276)s 1 f 382.601 (\051)s 13 f 604.802 y 387.268 (\252)s 2 f 607.289 y 394.268 (2)s 10 f 614.522 y 399.651 (d\272)s 11 f 616.322 y 411.825 (P)s 1 f 614.522 y 419.826 (\050)s 10 f 424.493 (\276)s 1 f 431.78 (\051)s 10 f 436.447 (:)s 1 f 664.069 y 110.327 (+)s 10 f 119.66 (C)s 2 f 665.869 y 128.237 (4)s 10 f 655.951 y 135.06 (\260)s 14 f 651.596 y 141.939 (\241)s 2 f 149.44 (2)s 19.763 .48 135.06 661.309 r 10 f 672.301 y 141.081 (\256)s 11 f 647.769 y 169.887 (n)s 2 f 175.819 (+2)s 11 f 187.969 (N)s 15 f 648.969 y 195.57 (\260)s 13 f 652.669 y 176.811 (X)s 11 f 678.409 y 158.263 (m)s 2 f 166.778 (=)s 11 f 174.145 (n)s 2 f 180.077 (+)s 11 f 187.444 (N)s 15 f 679.609 y 195.044 (\260)s 2 f 678.409 y 200.542 (+1)s 13 f 647.736 y 214.692 (Z)s 10 f 664.069 y 228.692 (r)s 2 f 657.836 y 234.44 (\050)s 14 f 238.19 (\241)s 2 f 245.69 (1)s 11 f 250.473 (;)s 2 f 253.323 (1\051)s 11 f 667.414 y 234.106 (j)s 238.046 (;i)s 1 f 664.069 y 262.456 (\050)s 10 f 267.123 (\276)s 1 f 274.411 (\051)s 13 f 654.349 y 279.077 (\251)s 653.211 y 286.077 (p)s 42.913 .48 298.077 653.211 r 10 f 664.069 y 298.077 (f)s 11 f 660.603 y 305.244 (t)s 667.036 y 303.952 (m)s 1 f 664.069 y 313.068 (\050)s 10 f 317.734 (\276)s 11 f 660.603 y 325.022 (i;j)s 1 f 664.069 y 336.323 (\051)s 12 f 343.657 (\241)s 13 f 653.223 y 355.657 (p)s 31.611 .48 367.657 653.223 r 10 f 664.069 y 367.657 (f)s 11 f 660.603 y 374.823 (t)s 667.036 y 373.532 (m)s 1 f 664.069 y 382.647 (\050)s 10 f 387.314 (\276)s 1 f 394.601 (\051)s 13 f 654.349 y 399.268 (\252)s 2 f 656.836 y 406.268 (2)s 10 f 664.069 y 411.651 (d\272)s 11 f 665.869 y 423.825 (P)s 1 f 664.069 y 431.826 (\050)s 10 f 436.493 (\276)s 1 f 443.78 (\051)s 10 f 448.447 (:)s 1 f 705.976 y 223.045 (23)s do-end end endp %%Page: 24 24 %%BeginPageSetup initializepage (Raffaele Esposito; page: 24 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f0_12 sf ( )S -996 -1000 :M f1_12 sf ( )S -993 -1000 :M f2_12 sf ( )S -989 -1000 :M f10_12 sf ( )S -981 -1000 :M f11_12 sf ( )S -972 -1000 :M f12_12 sf ( )S -960 -1000 :M f13_12 sf ( )S -951 -1000 :M f14_12 sf ( )S -937 -1000 :M f15_12 sf ( )S -926 -1000 :M f17_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 1200 1000 div mul /CMBX10 findfont fdef 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 17 10 1200 1000 div mul /CMTI10 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 6.31 y -5.69 (T)s 1.976 (o)s 11.928 (conclude)s 61.212 (this)s 84.563 (step,)s 113.257 (w)s 121.591 (e)s 130.875 (ha)s 143.209 (v)s 149.209 (e)s 158.493 (just)s 182.177 (to)s 196.795 (sum)s 222.146 (o)s 227.813 (v)s 233.813 (er)s 12 f 247.797 (f)s 1 f 253.798 (\0500)s 10 f 264.464 (;)s 1 f 269.798 (1\051)s 10 f 280.464 (;)s 1 f 285.798 (\050)s 12 f 290.464 (\241)s 1 f 299.798 (1)s 10 f 305.798 (;)s 1 f 311.131 (0\051)s 10 f 321.798 (;)s 1 f 327.131 (\050)s 12 f 331.798 (\241)s 1 f 341.131 (1)s 10 f 347.131 (;)s 1 f 352.464 (1\051)s 12 f 363.131 (g)s 1 f 373.082 (and)s 396.366 (o)s 402.033 (v)s 408.033 (er)s 12 f 422.018 (f)s 1 f 428.018 (\050)s 10 f 432.684 (i;)s 442.152 (j)s 1 f 447.78 (\051)s 12 f 455.78 (2)s 1 f 23.11 y -5.69 (\244)s 11 f 24.91 y 2.643 (n)s 12 f 23.11 y 11.842 (\243)s 1 f 23.842 (\244)s 11 f 18.755 y 32.175 (c)s 26.076 y 32.175 (n)s 1 f 23.11 y 45.374 (:)s 12 f 55.373 (j)s 10 f 58.707 (i)s 12 f 65.507 (\241)s 10 f 77.507 (j)s 12 f 83.136 (j)s 1 f 89.803 (=)s 102.469 (1)s 12 f 108.469 (g)s 1 f 114.469 (.)s 123.136 (W)s 134.469 (e)s 143.803 (obtain)s 63.227 y 88.979 (\255)s 2 f 58.272 y 97.645 (2)s 11 f 66.194 y 97.645 (n)s 12 f 63.227 y 107.511 (\267)s 1 f 120.177 (6)s 10 f 126.177 (n)s 11 f 58.272 y 133.38 (d)s 14 f 138.375 (\241)s 2 f 145.875 (1)s 10 f 63.227 y 151.259 (\260)s 14 f 58.272 y 158.138 (\241)s 2 f 165.638 (1)s 1 f 63.227 y 171.022 (\050)s 10 f 175.688 (C)s 14 f 58.272 y 185.123 (0)s 2 f 66.194 y 184.265 (2)s 1 f 63.227 y 192.315 (+)s 10 f 204.315 (C)s 2 f 65.027 y 212.891 (5)s 10 f 63.227 y 218.275 (\256)s 1 f 225.996 (\051)s 233.329 (+)s 10 f 245.329 (C)s 2 f 65.027 y 253.906 (4)s 10 f 55.109 y 260.729 (\260)s 14 f 50.754 y 267.608 (\241)s 2 f 275.108 (2)s 19.763 .48 260.729 60.467 r 10 f 71.459 y 266.75 (\256)s 11 f 46.927 y 289.481 (n)s 2 f 295.413 (+2)s 11 f 307.563 (N)s 15 f 48.127 y 315.164 (\260)s 13 f 51.827 y 296.405 (X)s 11 f 77.567 y 283.932 (m)s 2 f 292.447 (=)s 11 f 299.814 (n)s 2 f 305.746 (+)s 11 f 313.112 (N)s 15 f 78.767 y 320.713 (\260)s 10 f 63.227 y 328.211 (I)s 11 f 65.027 y 333.486 (i;j)s 1 f 63.227 y 344.788 (\050)s 10 f 349.454 (f)s 11 f 58.272 y 356.621 (t)s 66.194 y 355.329 (m)s 1 f 63.227 y 364.445 (\051)s 433.113 (\0504)s 10 f 443.78 (:)s 1 f 447.114 (14\051)s 103.344 y -5.69 (for)s 12.677 (an)s 25.01 (y)s 35.343 (p)s 42.343 (ositiv)s 70.41 (e)s 10 f 79.743 (\256)s 1 f 87.464 (.)s 17 f 126.282 y 8.71 (Thir)s 31.556 (d)s 41.983 (step)s 1 f 66.529 (\050)s 17 f 71.196 (Pr)s 83.783 (o)s 89.303 (of)s 103.409 (of)s 117.516 (\0504.4\051)s 1 f 143.276 (\051.)s 143.202 y 8.71 (F)s 15.543 (rom)s 40.243 (\0504.6\051,)s 72.243 (\0504.9\051)s 100.91 (and)s 124.243 (\0504.14\051,)s 162.244 (for)s 180.61 (all)s 197.277 (p)s 204.277 (ositiv)s 232.344 (e)s 10 f 241.677 (n)s 170.867 y 88.797 (@)s 11 f 172.667 y 95.167 (t)s 10 f 170.867 y 99.392 (s)s 11 f 172.667 y 105.017 (n)s 1 f 170.867 y 111.549 (\050)s 10 f 116.216 (t)s 1 f 120.549 (\051)s 12 f 128.549 (\267)s 141.216 (\241)s 10 f 150.549 (C)s 2 f 172.667 y 159.126 (0)s 10 f 170.867 y 164.509 (D)s 11 f 172.667 y 174.444 (n)s 1 f 170.867 y 180.976 (\050)s 10 f 185.643 (f)s 11 f 165.912 y 192.81 (t)s 173.834 y 191.518 (n)s 1 f 170.867 y 198.05 (\051)s 205.383 (+)s 10 f 217.383 (C)s 14 f 165.912 y 226.818 (0)s 2 f 173.834 y 225.96 (0)s 10 f 170.867 y 231.343 (n)s 11 f 165.912 y 238.546 (d)s 1 f 170.867 y 246.808 (+)s 258.808 (6)s 10 f 264.808 (n)s 11 f 165.912 y 272.011 (d)s 14 f 277.006 (\241)s 2 f 284.507 (1)s 10 f 170.867 y 289.89 (\260)s 14 f 165.912 y 296.769 (\241)s 2 f 304.269 (1)s 1 f 170.867 y 309.653 (\050)s 10 f 314.319 (C)s 14 f 165.912 y 323.754 (0)s 2 f 173.834 y 322.896 (2)s 1 f 170.867 y 330.946 (+)s 10 f 342.946 (C)s 2 f 172.667 y 351.523 (5)s 10 f 170.867 y 356.906 (\256)s 1 f 364.627 (\051)s 206.707 y 151.883 (+)s 10 f 163.883 (C)s 2 f 208.507 y 172.459 (4)s 10 f 198.589 y 179.283 (\260)s 14 f 194.234 y 186.162 (\241)s 2 f 193.662 (2)s 19.763 .48 179.283 203.947 r 10 f 214.938 y 185.304 (\256)s 13 f 195.307 y 222.354 (X)s 2 f 221.607 y 202.486 (\050)s 11 f 206.236 (i;j)s 2 f 216.937 (\051)s 14 f 220.687 (2)s 2 f 227.154 (\244)s 15 f 222.807 y 233.72 (n)s 14 f 221.607 y 239.605 (\243)s 2 f 247.105 (\244)s 15 f 219.207 y 253.672 (c)s 224.007 y 253.672 (n)s 11 f 190.407 y 273.181 (n)s 2 f 279.113 (+2)s 11 f 291.263 (N)s 15 f 191.607 y 298.864 (\260)s 13 f 195.307 y 280.105 (X)s 11 f 221.047 y 261.557 (m)s 2 f 270.072 (=)s 11 f 277.439 (n)s 2 f 283.371 (+)s 11 f 290.737 (N)s 15 f 222.247 y 298.338 (\260)s 2 f 221.047 y 303.836 (+1)s 10 f 206.707 y 317.986 (I)s 11 f 208.507 y 323.261 (i;j)s 1 f 206.707 y 334.563 (\050)s 10 f 339.229 (f)s 11 f 201.752 y 346.396 (t)s 209.674 y 345.104 (m)s 1 f 206.707 y 354.22 (\051)s 10 f 358.886 (:)s 1 f 248.639 y -5.69 (Multiply)s 44.8 (b)s 51.8 (oth)s 74.291 (sides)s 104.248 (of)s 119.072 (this)s 143.629 (inequalit)s 188.963 (y)s 200.453 (b)s 206.787 (y)s 10 f 218.277 (e)s 14 f 244.284 y 223.865 (\241)s 11 f 231.365 (n\260)s 1 f 248.639 y 243.454 (,)s 252.234 (sum)s 278.791 (o)s 284.458 (v)s 290.458 (er)s 305.648 (1)s 12 f 316.91 (\267)s 10 f 331.505 (n)s 12 f 343.97 (\267)s 10 f 358.565 (M)s 11 f 250.439 y 370.207 (\260)s 1 f 248.639 y 381.521 (and)s 406.012 (for)s 10 f 425.536 (\256)s 1 f 438.414 (large)s 265.439 y -5.69 (enough.)s 40.31 (W)s 51.643 (e)s 60.977 (get)s 80.977 (for)s 99.343 (some)s 129.41 (p)s 136.41 (ositiv)s 164.477 (e)s 173.81 (constan)s 213.544 (ts)s 10 f 226.944 (A)s 2 f 267.239 y 235.944 (0)s 1 f 265.439 y 245.327 (and)s 10 f 268.66 (A)s 2 f 267.239 y 277.66 (1)s 10 f 292.438 y 43.564 (@)s 11 f 294.238 y 49.935 (t)s 12 f 292.438 y 54.16 (S)s 11 f 294.238 y 61.427 (M)s 1 f 292.438 y 72.079 (\050)s 10 f 76.745 (t)s 1 f 81.079 (\051)s 12 f 89.079 (\267)s 101.745 (\241)s 10 f 111.079 (A)s 2 f 294.238 y 120.079 (0)s 12 f 292.438 y 125.462 (D)s 11 f 294.238 y 134.719 (n)s 1 f 292.438 y 141.251 (\050)s 10 f 145.917 (f)s 11 f 287.483 y 153.084 (t)s 295.404 y 151.792 (n)s 1 f 292.438 y 158.324 (\051)s 165.658 (+)s 10 f 177.658 (A)s 2 f 294.238 y 186.658 (1)s 10 f 292.438 y 192.041 (\260)s 14 f 287.483 y 198.92 (\241)s 11 f 206.42 (d)s 1 f 328.278 y 112.412 (+)s 10 f 124.412 (C)s 14 f 323.323 y 133.847 (0)s 2 f 331.244 y 132.989 (4)s 10 f 328.278 y 138.372 (\260)s 14 f 323.323 y 145.251 (\241)s 2 f 152.751 (2)s 11 f 311.978 y 185.55 (M)s 15 f 313.178 y 194.701 (\260)s 13 f 316.878 y 184.208 (X)s 11 f 342.618 y 160.135 (n)s 2 f 166.067 (=)s 11 f 173.433 (M)s 15 f 343.818 y 182.584 (\260)s 14 f 342.618 y 188.082 (\241)s 2 f 195.582 (2)s 11 f 200.366 (N)s 15 f 343.818 y 207.967 (\260)s 2 f 342.618 y 213.465 (+1)s 10 f 328.278 y 227.615 (e)s 14 f 323.323 y 233.202 (\241)s 11 f 240.702 (n\260)s 311.978 y 258.575 (N)s 15 f 313.178 y 266.176 (\260)s 13 f 316.878 y 256.457 (X)s 11 f 342.291 y 254.791 (m)s 2 f 263.307 (=1)s 13 f 316.878 y 297.326 (X)s 2 f 343.178 y 277.457 (\050)s 11 f 281.207 (i;j)s 2 f 291.908 (\051)s 14 f 295.658 (2)s 2 f 302.125 (\244)s 15 f 344.378 y 308.692 (n)s 14 f 343.178 y 314.576 (\243)s 2 f 322.076 (\244)s 15 f 340.778 y 328.643 (c)s 345.578 y 328.643 (n)s 10 f 328.278 y 336.528 (I)s 11 f 330.078 y 341.803 (i;j)s 1 f 328.278 y 353.104 (\050)s 10 f 357.771 (f)s 11 f 323.323 y 364.938 (t)s 331.244 y 363.646 (m)s 2 f 372.161 (+)s 11 f 379.528 (n)s 2 f 385.46 (+)s 11 f 392.827 (N)s 15 f 332.444 y 400.428 (\260)s 1 f 328.278 y 406.526 (\051)s 10 f 411.192 (:)s 1 f 369.108 y 8.71 (T)s 16.376 (o)s 26.803 (conclude)s 76.564 (the)s 97.657 (pro)s 115.357 (of)s 129.451 (of)s 143.544 (Lemma)s 186.805 (4.3,)s 210.005 (it)s 222.432 (remains)s 267.625 (to)s 282.719 (observ)s 316.152 (e)s 325.912 (that)s 352.339 (the)s 373.433 (third)s 403.893 (term)s 433.02 (of)s 447.114 (the)s 385.908 y -5.69 (righ)s 14.677 (t)s 23.343 (hand)s 53.343 (side)s 77.41 (of)s 91.077 (the)s 111.743 (last)s 134.477 (inequalit)s 179.81 (y)s 190.143 (is)s 202.21 (b)s 209.21 (ounded)s 251.21 (b)s 257.544 (y)s 10 f 267.877 (C)s 277.312 (onst:\260)s 14 f 381.554 y 310.503 (\241)s 11 f 318.003 (d)s 1 f 385.908 y 323.598 (.)s 8.16 .48 337.598 379.308 r .48 7.2 337.598 386.508 r .48 7.2 345.278 386.508 r 8.16 .48 337.598 386.988 r 0 f 419.9 y -5.69 (Corollary)s 55.701 (4.4)s 17 f 81.934 (F)s 88.848 (or)s 104.334 (al)s 114.147 (l)s 10 f 121.507 (K)s 135.891 (\076)s 1 f 148.557 (0)s 17 f 154.557 (,)s 13 f 438.311 y 132.231 (Z)s 11 f 441.277 y 144.231 (t)s 2 f 465.578 y 138.898 (0)s 10 f 454.644 y 150.456 (D)s 11 f 456.444 y 160.391 (K)s 169.043 (N)s 15 f 457.644 y 176.644 (\260)s 13 f 444.924 y 182.742 (\241)s 10 f 454.644 y 188.242 (f)s 11 f 449.689 y 195.409 (\277)s 457.611 y 194.117 (K)s 202.769 (N)s 15 f 458.811 y 210.37 (\260)s 13 f 444.924 y 216.468 (\242)s 10 f 454.644 y 221.968 (d\277)s 12 f 238.151 (\267)s 1 f 250.818 (2)s 10 f 256.818 (C)s 2 f 456.444 y 265.394 (1)s 10 f 454.644 y 270.778 (e)s 11 f 449.689 y 276.365 (K)s 2 f 285.017 (+1)s 10 f 454.644 y 297.767 (\260)s 2 f 449.689 y 304.646 (2)s 14 f 309.43 (\241)s 11 f 316.93 (d)s 10 f 454.644 y 322.525 (:)s 17 f 514.513 y -5.69 (Pr)s 6.896 (o)s 12.416 (of.)s 1 f 32.899 (Fix)s 10 f 54.951 (K)s 70.254 (\076)s 1 f 83.84 (0)s 94.392 (and)s 10 f 118.277 (\277)s 12 f 129.135 (2)s 1 f 141.388 ([0)s 10 f 150.721 (;)s 156.054 (t)s 1 f 160.388 (],)s 171.744 (since)s 201.696 (b)s 208.029 (y)s 218.915 (Sc)s 230.581 (h)s 236.915 (w)s 245.248 (artz)s 270.5 (inequalit)s 315.833 (y)s 10 f 326.719 (n)s 12 f 338.175 (7\241)s 345.508 (!)s 10 f 361.761 (D)s 11 f 516.313 y 371.696 (n)s 1 f 514.513 y 378.228 (\050)s 10 f 382.895 (f)s 11 f 510.158 y 390.061 (\277)s 517.48 y 388.77 (n)s 1 f 514.513 y 396.058 (\051)s 405.276 (is)s 417.895 (a)s 428.447 (nonde-)s 531.313 y -5.69 (creasing)s 40.41 (function)s 87.41 (w)s 95.743 (e)s 105.077 (ha)s 117.41 (v)s 123.41 (e)s 10 f 570.764 y 64.629 (D)s 11 f 572.564 y 74.564 (K)s 83.216 (N)s 15 f 573.764 y 90.817 (\260)s 13 f 561.044 y 96.915 (\241)s 10 f 570.764 y 102.415 (f)s 11 f 565.809 y 109.582 (\277)s 573.73 y 108.29 (K)s 116.942 (N)s 15 f 574.93 y 124.543 (\260)s 13 f 561.044 y 130.641 (\242)s 12 f 570.764 y 139.474 (\267)s 1 f 562.646 y 158.48 (1)s 15.799 .48 153.581 568.004 r 10 f 578.995 y 153.581 (N)s 11 f 580.795 y 163.222 (\260)s 554.464 y 176.603 (N)s 15 f 555.664 y 184.204 (\260)s 13 f 559.364 y 174.486 (X)s 11 f 584.777 y 172.82 (m)s 2 f 181.335 (=1)s 10 f 570.764 y 195.485 (D)s 11 f 572.564 y 205.42 (K)s 214.072 (N)s 15 f 573.764 y 221.673 (\260)s 2 f 572.564 y 227.171 (+)s 11 f 234.537 (m)s 13 f 561.044 y 243.653 (\241)s 10 f 570.764 y 249.153 (f)s 11 f 565.809 y 256.319 (\277)s 573.73 y 255.028 (K)s 263.679 (N)s 15 f 574.93 y 271.28 (\260)s 2 f 573.73 y 276.778 (+)s 11 f 284.145 (m)s 13 f 561.044 y 293.26 (\242)s 12 f 617.617 y 142.807 (\267)s 10 f 155.474 (e)s 11 f 612.663 y 161.062 (K)s 2 f 169.713 (+1)s 1 f 609.499 y 188.803 (1)s 15.799 .48 183.903 614.857 r 10 f 625.849 y 183.903 (N)s 11 f 627.649 y 193.545 (\260)s 601.317 y 206.925 (N)s 15 f 602.517 y 214.526 (\260)s 13 f 606.217 y 204.808 (X)s 11 f 631.631 y 203.142 (m)s 2 f 211.658 (=1)s 10 f 617.617 y 225.808 (D)s 11 f 619.417 y 235.743 (K)s 244.394 (N)s 15 f 620.617 y 251.995 (\260)s 2 f 619.417 y 257.493 (+)s 11 f 264.86 (m)s 13 f 607.897 y 273.975 (\241)s 10 f 617.617 y 279.475 (f)s 11 f 612.663 y 286.642 (\277)s 620.584 y 285.35 (K)s 294.002 (N)s 15 f 621.784 y 301.603 (\260)s 2 f 620.584 y 307.101 (+)s 11 f 314.468 (m)s 13 f 607.897 y 323.583 (\242)s 10 f 617.617 y 329.083 (e)s 14 f 612.663 y 334.671 (\241)s 2 f 342.171 (\050)s 11 f 345.921 (K)s 354.572 (N)s 15 f 613.863 y 362.173 (\260)s 2 f 612.663 y 367.671 (+)s 11 f 375.038 (m)s 2 f 383.553 (\051)s 11 f 387.303 (\260)s 12 f 652.019 y 142.807 (\267)s 1 f 155.474 (2)s 10 f 161.474 (e)s 11 f 647.064 y 167.062 (K)s 2 f 175.713 (+1)s 12 f 652.019 y 188.463 (D)s 13 f 642.299 y 198.053 (\241)s 10 f 652.019 y 203.553 (\271)s 11 f 647.064 y 210.784 (K)s 218.919 (;\257)s 1 f 652.019 y 228.242 (\050)s 10 f 232.909 (\277)s 1 f 239.513 (\051)s 12 f 244.18 (j)s 10 f 247.513 (\272)s 11 f 653.819 y 253.441 (P)s 13 f 642.299 y 261.442 (\242)s 10 f 652.019 y 266.942 (:)s 8.16 .48 455.62 670.576 r .48 7.2 455.62 677.776 r .48 7.2 463.3 677.776 r 8.16 .48 455.62 678.256 r 1 f 705.976 y 223.045 (24)s do-end end endp %%Page: 25 25 %%BeginPageSetup initializepage (Raffaele Esposito; page: 25 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f0_12 sf ( )S -996 -1000 :M f1_12 sf ( )S -993 -1000 :M f2_12 sf ( )S -989 -1000 :M f10_12 sf ( )S -981 -1000 :M f11_12 sf ( )S -972 -1000 :M f12_12 sf ( )S -960 -1000 :M f13_12 sf ( )S -951 -1000 :M f14_12 sf ( )S -937 -1000 :M f15_12 sf ( )S -926 -1000 :M f17_12 sf ( )S -923 -1000 :M f21_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 1200 1000 div mul /CMBX10 findfont fdef 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 17 10 1200 1000 div mul /CMTI10 findfont fdef 22 10 1200 1000 div mul /CMSL10 findfont fdef 58 60 translate 72 72.27 div dup scale 0 f 6.31 y -5.69 (5.)s 11.176 (Hydro)s 49.893 (dynamic)s 105.284 (limits)s 143.694 (for)s 165.094 (Ka)s 182.235 (w)s 191.819 (asaki)s 226.395 (and)s 253.037 (Glaub)s 290.145 (er)s 306.753 (dynamics.)s 1 f 31.416 y 8.71 (In)s 23.733 (this)s 47.155 (section)s 87.245 (w)s 95.578 (e)s 104.934 (pro)s 121.968 (v)s 127.968 (e)s 137.324 (Theorem)s 188.047 (3.1.)s 212.115 (Let)s 12 f 233.638 (C)s 11 f 33.216 y 239.956 (K)s 1 f 31.416 y 249.208 (\050I)s 256.048 (R)s 11 f 26.182 y 264.881 (d)s 1 f 31.416 y 270.477 (\051)s 279.166 (denote)s 317.856 (the)s 338.545 (space)s 370.635 (of)s 384.324 (real)s 407.714 (con)s 425.38 (tin)s 439.714 (uous)s 48.216 y -5.69 (functions)s 46.304 (\050with)s 78.566 (compact)s 126.827 (supp)s 151.894 (ort\051)s 176.188 (and)s 199.783 (denote)s 238.711 (b)s 245.044 (y)s 12 f 255.639 (M)s 1 f 274.311 (the)s 295.239 (space)s 327.567 (of)s 341.494 (signed)s 378.489 (measures)s 430.25 (on)s 447.178 (I)s 449.351 (R)s 11 f 42.982 y 458.185 (d)s 1 f 65.016 y -5.69 (with)s 21.675 (total)s 50.374 (v)s 56.04 (ariation)s 100.772 (b)s 107.772 (ounded)s 149.804 (b)s 156.138 (y)s 166.503 (1)s 176.535 (equipp)s 211.868 (ed)s 227.9 (with)s 255.265 (the)s 275.964 (w)s 284.297 (eak)s 14 f 59.649 y 301.964 (\244)s 1 f 65.016 y 311.512 (top)s 329.179 (ology)s 360.878 (induced)s 405.576 (b)s 411.909 (y)s 12 f 422.275 (C)s 11 f 66.816 y 428.593 (K)s 1 f 65.016 y 437.845 (\050I)s 444.685 (R)s 11 f 59.782 y 453.518 (d)s 1 f 65.016 y 459.114 (\051)s 81.816 y -5.69 (via)s 13 f 72.096 y 13.977 (\255)s 10 f 81.816 y 19.643 (\271;)s 32.207 (U)s 13 f 72.096 y 41.709 (\256)s 1 f 81.816 y 50.709 (=)s 13 f 72.149 y 63.375 (R)s 10 f 81.816 y 73.375 (U)s 82.877 (d\271)s 1 f 96.353 (.)s 99.064 y 8.71 (Giv)s 27.46 (en)s 43.734 (a)s 54.008 (con\257guration)s 10 f 126.982 (\276)s 1 f 134.27 (\050)s 10 f 138.936 (t;)s 148.603 (:)s 1 f 151.936 (\051,)s 164.279 (w)s 172.612 (e)s 182.219 (de\257ne)s 217.16 (the)s 238.101 (empirical)s 290.408 (measures)s 10 f 342.182 (\274)s 2 f 94.71 y 349.453 (1)s 11 f 354.237 (;\260)s 1 f 99.064 y 363.244 (\050)s 10 f 367.911 (\276)s 1 f 375.198 (\050)s 10 f 379.865 (t;)s 389.531 (:)s 1 f 392.865 (\051\051)s 405.988 (=)s 10 f 419.111 (\274)s 2 f 93.298 y 426.382 (1)s 11 f 431.166 (;\260)s 102.017 y 425.952 (t)s 1 f 99.064 y 444.447 (and)s 10 f 115.864 y -5.69 (\274)s 2 f 111.51 y 1.581 (2)s 11 f 6.364 (;\260)s 1 f 115.864 y 15.371 (\050)s 10 f 20.038 (\276)s 1 f 27.325 (\050)s 10 f 31.992 (t;)s 41.659 (:)s 1 f 44.992 (\051\051)s 57.659 (=)s 10 f 70.325 (\274)s 2 f 110.098 y 77.596 (2)s 11 f 82.38 (;\260)s 118.817 y 77.166 (t)s 1 f 115.864 y 95.387 (b)s 101.72 (y)s 13 f 143.13 y 81.134 (\241)s 10 f 152.85 y 86.634 (\274)s 2 f 147.083 y 93.905 (1)s 11 f 98.688 (;\260)s 155.803 y 93.475 (t)s 10 f 152.85 y 107.696 (;)s 113.029 (\274)s 2 f 147.083 y 120.3 (2)s 11 f 125.083 (;\260)s 155.803 y 119.869 (t)s 13 f 143.13 y 134.091 (\242)s 1 f 152.85 y 142.924 (=)s 13 f 139.53 y 155.59 (\263)s 10 f 152.85 y 162.757 (\260)s 11 f 147.895 y 169.637 (d)s 13 f 141.45 y 181.503 (X)s 11 f 168.39 y 177.232 (i)s 14 f 180.627 (2)s 11 f 187.094 (Z)s 189.304 (Z)s 15 f 165.617 y 198.069 (d)s 10 f 152.85 y 205.107 (\276)s 1 f 212.395 (\050)s 10 f 217.062 (t;)s 226.728 (i)s 1 f 230.862 (\051)s 10 f 235.529 (\261)s 11 f 154.65 y 240.862 (\260)s 246.42 (i)s 10 f 152.85 y 253.748 (;)s 262.415 (\260)s 11 f 147.895 y 269.294 (d)s 13 f 141.45 y 281.161 (X)s 11 f 168.39 y 276.889 (i)s 14 f 280.285 (2)s 11 f 286.751 (Z)s 288.961 (Z)s 15 f 165.617 y 297.727 (d)s 13 f 143.13 y 304.765 (\241)s 10 f 152.85 y 310.265 (\276)s 1 f 317.553 (\050)s 10 f 322.219 (t;)s 331.886 (i)s 1 f 336.02 (\051)s 13 f 143.13 y 340.687 (\242)s 2 f 145.617 y 346.187 (2)s 10 f 152.85 y 351.57 (\261)s 11 f 154.65 y 356.903 (\260)s 362.461 (i)s 13 f 139.53 y 366.456 (\264)s 10 f 152.85 y 373.623 (;)s 1 f 199.412 y -5.69 (where)s 10 f 28.301 (\261)s 11 f 201.212 y 33.634 (\260)s 39.191 (i)s 1 f 199.412 y 46.477 (is)s 57.835 (the)s 77.792 (Dirac)s 109.616 (mass)s 138.374 (at)s 152.331 (the)s 172.288 (macroscopic)s 239.013 (site)s 10 f 260.37 (\260)s 267.25 (i)s 1 f 271.384 (.)s 279.814 (W)s 291.147 (e)s 299.771 (shall)s 327.129 (denote)s 365.086 (in)s 378.377 (the)s 398.335 (sequel)s 10 f 433.359 (\276)s 1 f 440.646 (\050)s 10 f 445.313 (t;)s 454.98 (i)s 1 f 459.114 (\051)s 216.212 y -5.69 (b)s .643 (y)s 10 f 10.977 (\276)s 11 f 218.012 y 17.833 (t)s 1 f 216.212 y 22.058 (\050)s 10 f 26.725 (i)s 1 f 30.859 (\051)s 39.526 (and)s 13 f 206.492 y 62.859 (\241)s 10 f 216.212 y 68.359 (\276)s 1 f 75.647 (\050)s 10 f 80.314 (t;)s 89.98 (i)s 1 f 94.114 (\051)s 13 f 206.492 y 98.781 (\242)s 2 f 208.978 y 104.281 (2)s 1 f 216.212 y 113.664 (b)s 119.998 (y)s 10 f 130.331 (\276)s 1 f 137.619 (\050)s 10 f 142.285 (t;)s 151.952 (i)s 1 f 156.086 (\051)s 2 f 211.857 y 160.753 (2)s 1 f 216.212 y 166.136 (.)s 22 f 249.175 y 8.71 (Ka)s 23.71 (w)s 32.043 (asaki)s 62.443 (dynamics.)s 1 f 266.423 y 8.71 (First)s 38.597 (of)s 52.883 (all,)s 73.658 (in)s 88.278 (order)s 120.298 (to)s 135.585 (pro)s 152.618 (v)s 158.618 (e)s 168.572 (\0503.4\051)s 197.858 (it)s 210.478 (is)s 223.165 (enough)s 265.118 (to)s 280.405 (sho)s 297.472 (w)s 310.758 (that,)s 340.867 (for)s 359.853 (an)s 372.187 (y)s 383.14 (p)s 390.14 (ositiv)s 418.207 (e)s 428.16 (time)s 10 f 456.114 (t)s 1 f 460.447 (,)s 283.223 y -5.69 (an)s 6.643 (y)s 16.977 (functions)s 10 f 68.71 (U)s 76.878 (;)s 82.212 (V)s 12 f 95.211 (2)s 106.545 (C)s 11 f 285.023 y 112.863 (K)s 13 f 273.503 y 122.115 (\241)s 1 f 283.223 y 127.615 (I)s 129.788 (R)s 11 f 277.99 y 138.621 (d)s 13 f 273.503 y 144.217 (\242)s 1 f 283.223 y 153.717 (and)s 10 f 177.05 (\261)s 186.171 (\076)s 1 f 198.838 (0,)s 323.943 y -4.07 (lim)s 11 f 331.356 y -5.69 (\260)s 14 f -.133 (!)s 2 f 9.434 (0)s 0 f 323.943 y 16.217 (P)s 2 f 317.709 y 25.65 (\050)s 11 f 29.4 (K)s 2 f 38.052 (\051)s 11 f 41.802 (;\257)s 326.712 y 25.65 (\271)s 15 f 324.313 y 31.485 (\260)s 13 f 310.622 y 51.125 (n)s 310.142 y 59.125 (\257)s 317.343 y 59.125 (\257)s 324.543 y 59.125 (\257)s 314.223 y 63.125 (\255)s 10 f 323.943 y 68.792 (\274)s 2 f 318.176 y 76.063 (1)s 11 f 80.846 (;\260)s 326.896 y 75.632 (t)s 10 f 323.943 y 89.853 (;)s 95.187 (U)s 13 f 314.223 y 104.688 (\256)s 1 f 323.943 y 112.761 (+)s 13 f 314.223 y 124.5 (\255)s 10 f 323.943 y 130.167 (\274)s 2 f 318.176 y 137.438 (2)s 11 f 142.221 (;\260)s 326.896 y 137.007 (t)s 10 f 323.943 y 151.228 (;)s 156.562 (V)s 13 f 314.223 y 166.228 (\256)s 12 f 323.943 y 174.301 (\241)s 13 f 307.609 y 186.041 (Z)s 2 f 334.876 y 192.707 (I)s 194.014 (R)s 15 f 332.103 y 200.981 (d)s 13 f 310.622 y 208.619 (\263)s 10 f 323.943 y 215.785 (m)s 2 f 318.988 y 226.322 (\050)s 11 f 230.072 (K)s 2 f 238.723 (\051)s 1 f 323.943 y 243.073 (\050)s 10 f 247.74 (t;)s 257.407 (x)s 1 f 264.265 (\051)s 10 f 268.932 (U)s 1 f 278.433 (\050)s 10 f 283.1 (x)s 1 f 289.958 (\051)s 297.031 (+)s 10 f 308.77 (\301)s 2 f 318.988 y 315.92 (\050)s 11 f 319.67 (K)s 2 f 328.322 (\051)s 1 f 323.943 y 332.672 (\050)s 10 f 337.339 (t;)s 347.005 (x)s 1 f 353.864 (\051)s 10 f 358.53 (V)s 1 f 368.197 (\050)s 10 f 372.864 (x)s 1 f 379.722 (\051)s 13 f 310.622 y 384.389 (\264)s 10 f 323.943 y 391.556 (dx)s 13 f 310.142 y 404.66 (\257)s 317.343 y 404.66 (\257)s 324.543 y 404.66 (\257)s 10 f 323.943 y 411.993 (\076)s 424.66 (\261)s 13 f 310.622 y 430.447 (o)s 1 f 323.943 y 441.78 (=)s 454.447 (0)s 10 f 460.447 (:)s 1 f 365.717 y -5.69 (where)s 13 f 355.996 y 29.01 (\241)s 10 f 365.717 y 34.51 (m)s 2 f 361.362 y 45.046 (\050)s 11 f 48.796 (K)s 2 f 57.448 (\051)s 1 f 365.717 y 61.798 (\050)s 10 f 66.464 (:;)s 75.131 (:)s 1 f 78.464 (\051)s 10 f 83.131 (;)s 88.464 (\301)s 2 f 361.362 y 95.614 (\050)s 11 f 99.364 (K)s 2 f 108.016 (\051)s 1 f 365.717 y 112.366 (\050)s 10 f 117.033 (:;)s 125.699 (:)s 1 f 129.033 (\051)s 13 f 355.996 y 133.7 (\242)s 1 f 365.717 y 143.2 (is)s 155.266 (a)s 165.266 (w)s 173.6 (eak)s 195.266 (solution)s 240.666 (of)s 254.333 (the)s 275 (h)s 281.333 (ydro)s 305.367 (dynamic)s 353.7 (equations)s 407.433 (\0503.5\051.)s 382.965 y 8.71 (Fix)s 30.391 (a)s 40.571 (parameter)s 10 f 98.152 (\257)s 109.208 (\076)s 1 f 122.176 (0)s 132.356 (and)s 155.87 (consider)s 202.818 (the)s 223.665 (Ka)s 238.665 (w)s 246.999 (asaki)s 277.58 (dynamics)s 330.827 (at)s 10 f 345.675 (\257)s 1 f 357.276 (p)s 364.276 (ositiv)s 392.343 (e.)s 406.885 (F)s 413.719 (or)s 428.599 (a)s 438.78 (\257xed)s 399.765 y -5.69 (time)s 22.572 (in)s 32.239 (terv)s 52.606 (al)s 66.868 ([0)s 10 f 76.201 (;)s 81.535 (T)s 1 f 90.214 (],)s 102.042 (w)s 110.375 (e)s 120.638 (denote)s 160.233 (b)s 166.567 (y)s 0 f 177.829 (P)s 2 f 393.532 y 187.262 (\050)s 11 f 191.012 (K)s 2 f 199.664 (\051)s 11 f 402.535 y 187.262 (\271)s 15 f 400.135 y 193.097 (\260)s 1 f 399.765 y 208.943 (the)s 230.539 (la)s 239.539 (w)s 253.135 (of)s 267.731 (the)s 289.326 (pro)s 307.026 (cess)s 332.089 (\050)s 10 f 336.755 (\276)s 11 f 401.565 y 343.612 (t)s 1 f 399.765 y 347.837 (\051)s 11 f 401.932 y 352.504 (t)s 14 f 356.129 (2)s 2 f 362.596 ([0)s 11 f 370.096 (;T)s 2 f 379.905 (])s 1 f 399.765 y 388.151 (accelerated)s 451.114 (b)s 457.447 (y)s 10 f 421.502 y -5.69 (\260)s 14 f 417.147 y 1.189 (\241)s 2 f 8.689 (2)s 1 f 421.502 y 19.438 (on)s 37.47 (the)s 59.502 (space)s 10 f 92.934 (D)s 1 f 103.202 (\050[0)s 10 f 117.202 (;)s 122.535 (T)s 1 f 131.215 (])s 10 f 134.548 (;)s 1 f 139.881 (\255\051)s 158.58 (and)s 183.279 (b)s 189.612 (y)s 10 f 201.31 (Q)s 2 f 415.268 y 210.797 (\050)s 11 f 214.547 (K)s 2 f 223.199 (\051)s 11 f 424.272 y 210.797 (\271)s 15 f 421.872 y 216.632 (\260)s 1 f 421.502 y 232.914 (the)s 254.946 (la)s 263.946 (w)s 277.978 (of)s 293.01 (the)s 315.042 (pro)s 332.742 (cess)s 358.241 (\050)s 10 f 362.907 (\274)s 2 f 415.735 y 370.178 (1)s 11 f 374.962 (;\260)s 424.455 y 369.748 (t)s 10 f 421.502 y 383.969 (;)s 389.302 (\274)s 2 f 415.735 y 396.573 (2)s 11 f 401.356 (;\260)s 424.455 y 396.142 (t)s 1 f 421.502 y 410.364 (\051)s 11 f 423.668 y 415.03 (t)s 14 f 418.655 (2)s 2 f 425.122 ([0)s 11 f 432.622 (;T)s 2 f 442.432 (])s 1 f 421.502 y 451.114 (on)s 438.302 y -5.69 (the)s 15.817 (space)s 10 f 48.724 (D)s 13 f 428.582 y 58.992 (\241)s 1 f 438.302 y 64.492 ([0)s 10 f 73.826 (;)s 79.159 (T)s 1 f 87.838 (])s 10 f 91.172 (;)s 12 f 96.505 (M)s 2 f 433.947 y 110.916 (2)s 13 f 428.582 y 116.299 (\242)s 1 f 438.302 y 126.64 (with)s 154.813 (initial)s 190.321 (distribution)s 10 f 256.595 (\271)s 11 f 433.947 y 263.825 (\260)s 1 f 438.302 y 269.983 (.)s 281.171 (The)s 306.678 (la)s 315.678 (ws)s 333.918 (of)s 348.425 (large)s 378.633 (n)s 384.966 (um)s 401.299 (b)s 408.299 (ers)s 427.906 (for)s 447.114 (the)s 455.102 y -5.69 (empirical)s 45.967 (measures)s 10 f 97.091 (\274)s 2 f 449.335 y 104.361 (1)s 11 f 109.145 (;\260)s 458.055 y 103.931 (t)s 1 f 455.102 y 121.776 (and)s 10 f 144.733 (\274)s 2 f 449.335 y 152.004 (2)s 11 f 156.787 (;\260)s 458.055 y 151.573 (t)s 1 f 455.102 y 169.418 (follo)s 191.418 (ws)s 208.442 (\050[GPV])s 249.982 (\051)s 258.271 (from)s 286.262 (the)s 306.552 (w)s 314.885 (eak)s 336.176 (con)s 353.842 (v)s 359.843 (ergence)s 402.166 (of)s 415.456 (the)s 435.747 (prob-)s 471.902 y -5.69 (abilit)s 21.31 (y)s 31.788 (measures)s 10 f 83.433 (Q)s 2 f 465.668 y 92.92 (\050)s 11 f 96.67 (K)s 2 f 105.321 (\051)s 11 f 474.672 y 92.92 (\271)s 15 f 472.272 y 98.754 (\260)s 1 f 471.902 y 113.816 (to)s 128.628 (a)s 138.772 (probabilit)s 189.806 (y)s 10 f 200.284 (Q)s 2 f 467.547 y 209.771 (\050)s 11 f 213.521 (K)s 2 f 222.173 (\051)s 1 f 471.902 y 230.667 (concen)s 265.667 (trated)s 301.846 (on)s 318.657 (the)s 339.469 (deterministic)s 411.714 (tra)s 427.747 (jectory)s 13 f 478.982 y -5.69 (\241)s 10 f 488.702 y -.19 (\274)s 2 f 484.347 y 7.081 (1)s 1 f 488.702 y 12.464 (\050)s 10 f 17.131 (t;)s 26.797 (dx)s 1 f 39.902 (\051)s 10 f 44.568 (;)s 49.901 (\274)s 2 f 484.347 y 57.172 (2)s 1 f 488.702 y 62.556 (\050)s 10 f 67.222 (t;)s 76.889 (dx)s 1 f 89.993 (\051)s 13 f 478.982 y 94.66 (\242)s 1 f 488.702 y 103.493 (=)s 13 f 478.982 y 116.16 (\241)s 10 f 488.702 y 121.66 (m)s 2 f 484.347 y 132.196 (\050)s 11 f 135.946 (K)s 2 f 144.598 (\051)s 1 f 488.702 y 148.948 (\050)s 10 f 153.614 (t;)s 163.281 (x)s 1 f 170.139 (\051)s 10 f 174.806 (dx;)s 193.243 (\301)s 2 f 484.347 y 200.393 (\050)s 11 f 204.144 (K)s 2 f 212.795 (\051)s 1 f 488.702 y 217.145 (\050)s 10 f 221.812 (t;)s 231.479 (x)s 1 f 238.337 (\051)s 10 f 243.004 (dx)s 13 f 478.982 y 256.108 (\242)s 1 f 488.702 y 261.608 (,)s 268.588 (where)s 13 f 478.982 y 302.847 (\241)s 10 f 488.702 y 308.347 (m)s 2 f 484.347 y 318.883 (\050)s 11 f 322.633 (K)s 2 f 331.285 (\051)s 1 f 488.702 y 335.635 (\050)s 10 f 340.302 (:;)s 348.968 (:)s 1 f 352.302 (\051)s 10 f 356.968 (;)s 362.302 (\301)s 2 f 484.347 y 369.452 (\050)s 11 f 373.202 (K)s 2 f 381.853 (\051)s 1 f 488.702 y 386.203 (\050)s 10 f 390.87 (:;)s 399.537 (:)s 1 f 402.87 (\051)s 13 f 478.982 y 407.537 (\242)s 1 f 488.702 y 416.596 (is)s 428.221 (a)s 437.78 (w)s 446.114 (eak)s 505.502 y -5.69 (solution)s 39.889 (of)s 53.734 (the)s 74.58 (h)s 80.913 (ydro)s 104.946 (dynamic)s 153.459 (equations)s 207.371 (\0503.5\051.)s 241.241 (The)s 266.086 (pro)s 283.786 (of)s 297.632 (of)s 311.477 (this)s 335.056 (result)s 368.668 (requires)s 413.98 (tigh)s 434.314 (tness,)s 522.302 y -5.69 (iden)s 15.977 (ti\257cation)s 66.643 (of)s 80.31 (the)s 100.977 (limit)s 129.643 (and)s 152.977 (uniqueness)s 213.444 (of)s 227.11 (the)s 247.777 (w)s 256.11 (eak)s 277.777 (solution)s 323.177 (of)s 336.844 (the)s 357.51 (limiting)s 402.177 (equation.)s 0 f 556.622 y -5.69 (Lemma)s 43.636 (5.1)s 1 f 74.945 (Tigh)s 99.278 (tness.)s 17 f 135.103 (The)s 159.95 (se)s 169.764 (quenc)s 198.897 (e)s 13 f 546.902 y 209.024 (\241)s 10 f 556.622 y 214.524 (Q)s 2 f 550.389 y 224.011 (\050)s 11 f 227.761 (K)s 2 f 236.413 (\051)s 11 f 559.392 y 224.011 (\271)s 15 f 556.992 y 229.846 (\260)s 13 f 546.902 y 240.763 (\242)s 11 f 561.422 y 246.263 (\260)s 17 f 556.622 y 257.028 (is)s 270.222 (a)s 280.963 (tight)s 308.877 (family)s 345.684 (and)s 369.305 (al)s 379.118 (l)s 386.792 (its)s 403.973 (limit)s 432.807 (p)s 438.327 (oints)s 10 f 573.422 y -5.69 (Q)s 14 f 569.067 y 3.796 (\244)s 17 f 573.422 y 13.606 (ar)s 24.186 (e)s 34 (such)s 61.293 (that)s 10 f 609.741 y 50.181 (Q)s 14 f 604.786 y 59.668 (\244)s 13 f 596.421 y 65.184 (n)s 1 f 609.741 y 73.184 (\050)s 10 f 77.851 (\274)s 2 f 604.786 y 85.122 (1)s 10 f 609.741 y 90.505 (;)s 95.839 (\274)s 2 f 604.786 y 103.109 (2)s 1 f 609.741 y 108.493 (\051)s 119.826 (:)s 13 f 600.021 y 129.826 (\241)s 10 f 609.741 y 135.326 (\274)s 2 f 604.786 y 142.597 (1)s 1 f 609.741 y 147.98 (\050)s 10 f 152.647 (t;)s 162.313 (dx)s 1 f 175.418 (\051)s 10 f 180.084 (;)s 185.418 (\274)s 2 f 604.786 y 192.688 (2)s 1 f 609.741 y 198.072 (\050)s 10 f 202.738 (t;)s 212.405 (dx)s 1 f 225.509 (\051)s 13 f 600.021 y 230.176 (\242)s 1 f 609.741 y 239.009 (=)s 13 f 600.021 y 251.676 (\241)s 10 f 609.741 y 257.176 (\274)s 2 f 604.786 y 264.447 (1)s 1 f 609.741 y 269.83 (\050)s 10 f 274.497 (t;)s 284.163 (x)s 1 f 291.022 (\051)s 10 f 295.688 (dx;)s 314.126 (\274)s 2 f 604.786 y 321.397 (2)s 1 f 609.741 y 326.78 (\050)s 10 f 331.447 (t;)s 341.113 (x)s 1 f 347.972 (\051)s 10 f 352.638 (dx)s 13 f 600.021 y 365.743 (\242)s 596.421 y 371.243 (o)s 1 f 609.741 y 382.576 (=)s 395.242 (1)s 10 f 404.576 (;)s 639.741 y 50.181 (Q)s 14 f 634.787 y 59.668 (\244)s 13 f 626.421 y 65.184 (n)s 1 f 639.741 y 73.184 (\050)s 10 f 77.851 (\274)s 2 f 634.787 y 85.122 (1)s 10 f 639.741 y 90.505 (;)s 95.839 (\274)s 2 f 634.787 y 103.109 (2)s 1 f 639.741 y 108.493 (\051)s 119.826 (:)s 12 f 129.826 (\241)s 1 f 139.159 (1)s 12 f 148.492 (\267)s 10 f 161.159 (\274)s 2 f 634.787 y 168.43 (1)s 1 f 639.741 y 173.813 (\050)s 10 f 178.48 (t;)s 188.147 (x)s 1 f 195.005 (\051)s 12 f 203.005 (\267)s 1 f 215.671 (1)s 10 f 221.671 (;)s 1 f 230.338 (0)s 12 f 239.671 (\267)s 10 f 252.338 (\274)s 2 f 634.787 y 259.609 (2)s 1 f 639.741 y 264.992 (\050)s 10 f 269.659 (t;)s 279.325 (x)s 1 f 286.184 (\051)s 12 f 294.184 (\267)s 1 f 306.85 (1)s 13 f 626.421 y 312.85 (o)s 1 f 639.741 y 324.184 (=)s 336.85 (1)s 10 f 346.184 (:)s 1 f 677.176 y 8.71 (The)s 33.376 (pro)s 51.077 (of)s 64.743 (of)s 78.41 (5.1)s 97.743 (is)s 109.81 (v)s 115.81 (ery)s 136.177 (simple)s 173.577 (since)s 202.977 (sup)s 11 f 680.109 y 221.043 (\276)s 1 f 677.176 y 229.506 (sup)s 11 f 680.109 y 247.572 (i)s 12 f 677.176 y 253.567 (j)s 10 f 256.901 (\276)s 1 f 264.188 (\050)s 10 f 268.855 (i)s 1 f 272.989 (\051)s 12 f 277.656 (j)s 10 f 284.322 (\074)s 12 f 296.989 (1)s 1 f 312.989 (and)s 336.322 (therefore)s 386.722 (is)s 398.789 (omitted.)s 705.976 y 223.045 (25)s do-end end endp %%Page: 26 26 %%BeginPageSetup initializepage (Raffaele Esposito; page: 26 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f0_12 sf ( )S -996 -1000 :M f1_12 sf ( )S -993 -1000 :M f2_12 sf ( )S -989 -1000 :M f10_12 sf ( )S -981 -1000 :M f11_12 sf ( )S -972 -1000 :M f12_12 sf ( )S -960 -1000 :M f13_12 sf ( )S -951 -1000 :M f14_12 sf ( )S -937 -1000 :M f15_12 sf ( )S -926 -1000 :M f17_12 sf ( )S -923 -1000 :M f21_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 1200 1000 div mul /CMBX10 findfont fdef 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 17 10 1200 1000 div mul /CMTI10 findfont fdef 22 10 1200 1000 div mul /CMSL10 findfont fdef 58 60 translate 72 72.27 div dup scale 0 f 6.843 y -5.69 (Lemma)s 43.323 (5.2)s 17 f 69.706 (A)s 78.32 (l)s 82 (l)s 89.424 (limit)s 118.008 (p)s 123.528 (oints)s 10 f 153.338 (Q)s 14 f 2.488 y 162.825 (\244)s 17 f 6.843 y 172.699 (of)s 186.87 (the)s 206.867 (se)s 216.681 (quenc)s 245.814 (e)s 13 f -2.877 y 255.691 (\241)s 10 f 6.843 y 261.191 (Q)s 2 f .61 y 270.678 (\050)s 11 f 274.428 (K)s 2 f 283.08 (\051)s 11 f 9.613 y 270.678 (\271)s 15 f 7.213 y 276.513 (\260)s 13 f -2.877 y 287.43 (\242)s 11 f 11.643 y 292.93 (\260)s 17 f 6.843 y 303.445 (ar)s 314.024 (e)s 323.902 (c)s 328.809 (onc)s 346.595 (entr)s 367.295 (ate)s 382.321 (d)s 392.812 (on)s 410.05 (we)s 422.93 (ak)s 438.94 (solu-)s 23.643 y -5.69 (tions)s 24.056 (of)s 38.163 (e)s 43.069 (quation)s 1 f 85.709 (\0503.5\051.)s 57.635 y 8.71 (Finally)s 44.543 (,)s 52.736 (the)s 74.091 (la)s 83.091 (w)s 96.446 (of)s 110.8 (large)s 140.855 (n)s 147.188 (um)s 163.522 (b)s 170.522 (ers)s 189.976 (follo)s 211.976 (ws)s 230.064 (from)s 259.119 (the)s 280.474 (uniqueness)s 341.628 (of)s 355.983 (the)s 377.338 (w)s 385.671 (eak)s 408.025 (solution)s 454.114 (of)s 74.435 y -5.69 (equations)s 48.043 (\0503.5\051,)s 80.043 (whose)s 115.443 (pro)s 133.143 (of)s 146.81 (is)s 158.877 (giv)s 174.21 (en)s 190.21 (in)s 204.21 (Lemma)s 247.044 (5.4)s 266.377 (b)s 273.377 (elo)s 287.71 (w.)s 22 f 101.611 y -5.69 (Pro)s 13.51 (of)s 27.202 (of)s 40.894 (Lemma)s 83.752 (5.2.)s 1 f 107.828 (Denote)s 149.02 (b)s 155.353 (y)s 12 f 165.712 (C)s 2 f 95.845 y 172.73 (1)s 11 f 177.514 (;)s 2 f 180.364 (2)s 11 f 105.138 y 172.03 (K)s 1 f 101.611 y 185.747 (\050[0)s 10 f 199.747 (;)s 205.08 (T)s 1 f 213.759 (])s 12 f 219.776 (\243)s 1 f 231.793 (I)s 233.966 (R)s 11 f 96.378 y 242.8 (d)s 1 f 101.611 y 248.395 (\051)s 257.087 (the)s 277.779 (space)s 309.871 (of)s 323.563 (compact)s 371.588 (supp)s 396.655 (ort)s 416.047 (functions)s 10 f 118.411 y -5.69 (V)s 1 f 7.31 (:)s 13.976 ([0)s 10 f 23.31 (;)s 28.643 (T)s 1 f 37.322 (])s 12 f 41.217 (\243)s 1 f 51.113 (I)s 53.286 (R)s 11 f 113.178 y 62.119 (d)s 12 f 118.411 y 71.048 (\241)s 78.381 (!)s 1 f 93.715 (I)s 95.888 (R)s 104.721 (,)s 111.213 (t)s 115.546 (wice)s 141.161 (con)s 158.827 (tin)s 173.161 (uously)s 209.842 (di\256eren)s 248.542 (tiable)s 280.823 (on)s 296.437 (space)s 327.451 (with)s 353.732 (con)s 371.399 (tin)s 385.732 (uous)s 412.747 (deriv)s 438.447 (ativ)s 458.447 (e)s 135.211 y -5.69 (in)s 8.991 (time.)s 43.036 (Fix)s 65.217 (a)s 75.899 (function)s 10 f 123.58 (U)s 1 f 137.551 (=)s 151.353 (\050)s 10 f 156.02 (U)s 2 f 130.856 y 165.522 (1)s 10 f 135.211 y 170.905 (;)s 176.238 (U)s 2 f 130.856 y 185.74 (2)s 1 f 135.211 y 191.123 (\051)s 200.471 (suc)s 216.871 (h)s 228.22 (that)s 10 f 254.901 (U)s 2 f 130.856 y 264.403 (1)s 1 f 135.211 y 269.786 (\050)s 10 f 274.453 (t;)s 284.119 (x)s 1 f 290.978 (\051)s 300.113 (=)s 10 f 313.916 (U)s 2 f 130.856 y 323.417 (1)s 11 f 138.178 y 322.109 (t)s 1 f 135.211 y 328.801 (\050)s 10 f 333.468 (x)s 1 f 340.326 (\051)s 349.674 (and)s 10 f 373.689 (U)s 2 f 130.856 y 383.19 (2)s 1 f 135.211 y 388.574 (\050)s 10 f 393.241 (t;)s 402.907 (x)s 1 f 409.765 (\051)s 418.901 (=)s 10 f 432.704 (U)s 2 f 130.856 y 442.205 (2)s 11 f 138.178 y 440.897 (t)s 1 f 135.211 y 447.589 (\050)s 10 f 452.255 (x)s 1 f 459.114 (\051)s 152.011 y -5.69 (are)s 14.343 (in)s 12 f 28.343 (C)s 2 f 146.245 y 35.362 (1)s 11 f 40.145 (;)s 2 f 42.995 (2)s 11 f 155.538 y 34.662 (K)s 1 f 152.011 y 48.378 (\050[0)s 10 f 62.378 (;)s 67.712 (T)s 1 f 76.391 (])s 12 f 82.391 (\243)s 1 f 94.391 (I)s 96.564 (R)s 11 f 146.778 y 105.397 (d)s 1 f 152.011 y 110.993 (\051,)s 122.993 (and)s 146.326 (consider)s 193.093 (the)s 213.76 (martingale)s 10 f 273.793 (M)s 11 f 147.656 y 286.743 (U)s 154.978 y 285.435 (t)s 1 f 152.011 y 298.781 (de\257ned)s 340.114 (b)s 346.448 (y)s 10 f 187.028 y 9.233 (M)s 11 f 182.073 y 22.183 (U)s 189.995 y 20.875 (t)s 1 f 187.028 y 33.554 (=)s 2 f 172.028 y 52.87 (2)s 13 f 175.628 y 46.595 (X)s 11 f 201.041 y 46.221 (n)s 2 f 52.153 (=1)s 13 f 166.508 y 66.303 (\050)s 10 f 187.028 y 79.303 (\074)s 91.97 (\274)s 11 f 181.261 y 99.24 (n;\260)s 189.981 y 98.81 (t)s 10 f 187.028 y 114.18 (;)s 119.513 (U)s 11 f 182.073 y 129.015 (n)s 189.995 y 127.706 (t)s 10 f 187.028 y 138.88 (\076)s 12 f 151.547 (\241)s 10 f 164.213 (\074)s 176.88 (\274)s 11 f 181.261 y 184.151 (n;\260)s 2 f 190.228 y 183.72 (0)s 10 f 187.028 y 199.09 (;)s 204.423 (U)s 11 f 182.073 y 213.925 (n)s 2 f 189.995 y 212.617 (0)s 10 f 187.028 y 223.79 (\076)s 12 f 236.457 (\241)s 13 f 170.695 y 247.79 (Z)s 11 f 173.661 y 259.79 (t)s 2 f 197.962 y 254.457 (0)s 13 f 173.708 y 266.015 (\263)s 10 f 187.028 y 273.182 (@)s 11 f 188.828 y 279.552 (s)s 1 f 187.028 y 287.348 (+)s 10 f 299.348 (\260)s 14 f 182.073 y 306.228 (\241)s 2 f 313.728 (2)s 1 f 187.028 y 319.111 (I)s 321.284 (L)s 11 f 181.795 y 328.784 (K)s 336.919 (;\257)s 189.995 y 328.784 (\260)s 13 f 177.308 y 346.242 (\242)s 10 f 187.028 y 355.076 (\074)s 367.742 (\274)s 11 f 182.073 y 375.013 (n;\260)s 189.995 y 374.583 (s)s 10 f 187.028 y 389.952 (;)s 395.286 (U)s 11 f 182.073 y 404.787 (n)s 189.995 y 403.479 (s)s 10 f 187.028 y 414.653 (\076)s 427.319 (ds)s 13 f 166.508 y 439.19 (\051)s 1 f 222.213 y -5.69 (with)s 21.643 (the)s 42.31 (quadratic)s 96.01 (v)s 101.677 (ariation)s 12 f 146.377 (N)s 11 f 217.858 y 157.991 (U)s 225.18 y 156.223 (t)s 1 f 222.213 y 170.029 (giv)s 185.362 (en)s 201.362 (b)s 207.696 (y)s 12 f 256.55 y 18.31 (N)s 11 f 251.595 y 29.924 (U)s 259.517 y 28.156 (t)s 1 f 256.55 y 41.295 (=)s 13 f 246.83 y 53.962 (\241)s 10 f 256.55 y 59.462 (M)s 11 f 251.595 y 72.412 (U)s 259.517 y 71.103 (t)s 13 f 246.83 y 80.45 (\242)s 2 f 248.822 y 85.95 (2)s 12 f 256.55 y 94 (\241)s 13 f 240.217 y 106 (Z)s 11 f 243.183 y 118 (t)s 2 f 267.484 y 112.666 (0)s 13 f 236.03 y 124.225 (\050)s 10 f 256.55 y 133.891 (\260)s 14 f 251.595 y 140.771 (\241)s 2 f 148.271 (2)s 1 f 256.55 y 153.654 (I)s 155.827 (L)s 11 f 251.317 y 163.327 (K)s 171.462 (;\257)s 259.517 y 163.327 (\260)s 13 f 243.23 y 180.785 (\263)s 2 f 241.55 y 196.601 (2)s 13 f 245.15 y 190.326 (X)s 11 f 270.563 y 189.952 (n)s 2 f 195.884 (=1)s 10 f 256.55 y 211.367 (\074)s 224.034 (\274)s 11 f 251.595 y 231.305 (n;\260)s 259.517 y 230.874 (s)s 10 f 256.55 y 246.244 (;)s 251.577 (U)s 11 f 251.595 y 261.079 (n)s 259.517 y 259.771 (s)s 10 f 256.55 y 270.944 (\076)s 13 f 243.23 y 283.611 (\264)s 2 f 245.717 y 290.778 (2)s 12 f 301.777 y 132.698 (\241)s 1 f 142.031 (2)s 13 f 288.457 y 148.031 (\263)s 2 f 286.777 y 163.847 (2)s 13 f 290.377 y 157.572 (X)s 11 f 315.79 y 157.198 (n)s 2 f 163.13 (=1)s 10 f 301.777 y 178.613 (\074)s 191.279 (\274)s 11 f 296.822 y 198.55 (n;\260)s 304.743 y 198.12 (s)s 10 f 301.777 y 213.49 (;)s 218.823 (U)s 11 f 296.822 y 228.324 (n)s 304.743 y 227.016 (s)s 10 f 301.777 y 238.19 (\076)s 13 f 288.457 y 250.856 (\264)s 10 f 301.777 y 258.023 (\260)s 14 f 296.822 y 264.902 (\241)s 2 f 272.402 (2)s 1 f 301.777 y 277.786 (I)s 279.959 (L)s 11 f 296.544 y 287.459 (K)s 295.594 (;\257)s 304.743 y 287.459 (\260)s 13 f 288.457 y 304.917 (\263)s 2 f 286.777 y 320.733 (2)s 13 f 290.377 y 314.458 (X)s 11 f 315.79 y 314.084 (n)s 2 f 320.016 (=1)s 10 f 301.777 y 335.499 (\074)s 348.166 (\274)s 11 f 296.822 y 355.437 (n;\260)s 304.743 y 355.006 (s)s 10 f 301.777 y 370.376 (;)s 375.709 (U)s 11 f 296.822 y 385.211 (n)s 304.743 y 383.902 (s)s 10 f 301.777 y 395.076 (\076)s 13 f 288.457 y 407.743 (\264)s 281.257 y 414.909 (\051)s 10 f 301.777 y 424.576 (ds:)s 1 f 337.934 y -5.69 (Denote)s 36.766 (b)s 43.099 (y)s 12 f 54.722 (f)s 10 f 60.722 (e)s 2 f 339.734 y 66.31 (1)s 10 f 337.934 y 71.693 (;)s 12 f 77.026 (\242)s 82.36 (\242)s 87.693 (\242)s 10 f 93.026 (;)s 98.36 (e)s 11 f 339.734 y 103.947 (d)s 12 f 337.934 y 109.543 (g)s 1 f 120.832 (the)s 142.788 (orthonormal)s 212.811 (basis)s 243.568 (of)s 258.524 (I)s 260.697 (R)s 11 f 332.701 y 269.53 (d)s 1 f 337.934 y 275.126 (,)s 284.071 (and)s 308.694 (observ)s 342.127 (e)s 352.75 (that)s 380.04 (for)s 399.696 (all)s 10 f 417.652 (i)s 12 f 427.269 (2)s 10 f 440.751 (Z)s 443.802 (Z)s 11 f 332.701 y 454.851 (d)s 1 f 337.934 y 460.447 (,)s 10 f 354.734 y -5.69 (\276)s 12 f 5.035 (2)s 1 f 16.473 (\255)s 29.203 (and)s 10 f 52.599 (k)s 1 f 62.662 (=)s 75.433 (1)s 10 f 81.433 (;)s 12 f 86.766 (\242)s 92.099 (\242)s 97.433 (\242)s 10 f 102.766 (;)s 108.099 (d)s 1 f 118.408 (w)s 126.741 (e)s 136.137 (ha)s 148.471 (v)s 154.471 (e)s 10 f 163.867 (C)s 11 f 350.379 y 173.302 (K)s 181.437 (;\257)s 357.7 y 172.444 (\260)s 1 f 354.734 y 190.76 (\050)s 10 f 195.427 (i)s 1 f 202.269 (+)s 10 f 214.311 (e)s 11 f 356.534 y 219.899 (k)s 10 f 354.734 y 225.803 (;)s 231.136 (i)s 1 f 235.27 (;)s 10 f 240.603 (\276)s 1 f 247.891 (\051)s 255.995 (=)s 10 f 268.767 (\277)s 11 f 356.534 y 274.013 (e)s 15 f 357.807 y 278.566 (k)s 10 f 354.734 y 284.411 (C)s 11 f 350.379 y 293.846 (K)s 301.981 (;\257)s 357.7 y 292.988 (\260)s 1 f 354.734 y 311.304 (\050)s 10 f 315.971 (i;)s 325.439 (i)s 12 f 332.281 (\241)s 10 f 344.323 (e)s 11 f 356.534 y 349.91 (k)s 1 f 354.734 y 355.815 (;)s 10 f 361.148 (\276)s 1 f 368.435 (\051,)s 380.514 (where)s 10 f 415.277 (\277)s 11 f 356.534 y 420.523 (e)s 15 f 357.807 y 425.076 (k)s 1 f 354.734 y 434.984 (is)s 447.114 (the)s 371.534 y -5.69 (space)s 26.053 (shift)s 52.797 (b)s 59.13 (y)s 10 f 69.141 (e)s 11 f 373.334 y 74.728 (k)s 1 f 371.534 y 84.309 (acting)s 119.987 (on)s 136.33 (\255.)s 153.556 (Hence,)s 192.297 (a)s 201.974 (spatial)s 240.385 (summation)s 302.129 (b)s 308.462 (y)s 318.472 (parts)s 348.916 (p)s 355.916 (ermits)s 392.36 (to)s 406.703 (rewrite)s 447.114 (the)s 388.334 y -5.69 (in)s 3.976 (tegral)s 38.01 (term)s 66.71 (of)s 10 f 80.377 (M)s 11 f 383.979 y 93.327 (U)s 391.3 y 92.018 (t)s 1 f 388.334 y 105.364 (as)s 2 f 407.791 y 26.223 (2)s 13 f 411.391 y 19.948 (X)s 11 f 436.804 y 19.574 (n)s 2 f 25.505 (=1)s 13 f 406.457 y 39.656 (Z)s 11 f 409.424 y 51.656 (t)s 2 f 433.724 y 46.322 (0)s 13 f 413.071 y 57.88 (\255)s 10 f 422.791 y 63.547 (\274)s 11 f 417.836 y 70.818 (n;\260)s 425.757 y 70.387 (s)s 10 f 422.791 y 85.757 (;)s 91.091 (@)s 11 f 424.591 y 97.461 (s)s 10 f 422.791 y 102.591 (U)s 11 f 417.836 y 112.092 (n)s 425.757 y 110.784 (s)s 13 f 413.071 y 118.624 (\256)s 10 f 422.791 y 124.291 (ds)s 12 f 468.438 y 32.24 (\241)s 2 f 453.438 y 50.889 (2)s 13 f 457.037 y 44.614 (X)s 11 f 482.451 y 44.24 (n)s 2 f 50.172 (=1)s 13 f 452.104 y 64.322 (Z)s 11 f 455.071 y 76.322 (t)s 2 f 479.371 y 70.989 (0)s 10 f 468.438 y 82.547 (\260)s 11 f 463.483 y 89.427 (d)s 14 f 94.422 (\241)s 2 f 101.922 (1)s 13 f 457.037 y 113.576 (X)s 11 f 483.978 y 109.305 (i)s 14 f 112.7 (2)s 11 f 119.167 (Z)s 121.377 (Z)s 15 f 481.204 y 130.143 (d)s 11 f 453.438 y 143.41 (d)s 13 f 457.037 y 137.241 (X)s 11 f 482.871 y 137.181 (k)s 2 f 142.485 (=1)s 10 f 468.438 y 156.635 (C)s 11 f 463.483 y 166.07 (K)s 174.205 (;\257)s 471.404 y 165.212 (\260)s 1 f 468.438 y 183.528 (\050)s 10 f 188.195 (i)s 1 f 194.996 (+)s 10 f 206.995 (e)s 11 f 470.238 y 212.583 (k)s 10 f 468.438 y 218.487 (;)s 223.82 (i)s 1 f 227.955 (;)s 10 f 233.288 (\276)s 11 f 470.238 y 240.145 (s)s 1 f 468.438 y 245.274 (\051)s 13 f 458.717 y 249.941 (\243)s 10 f 468.438 y 254.941 (\276)s 11 f 470.238 y 261.798 (s)s 1 f 468.438 y 266.927 (\050)s 10 f 271.594 (i)s 1 f 278.394 (+)s 10 f 290.394 (e)s 11 f 470.238 y 295.982 (k)s 1 f 468.438 y 301.886 (\051)s 11 f 463.483 y 306.553 (n)s 12 f 468.438 y 315.751 (\241)s 10 f 327.751 (\276)s 11 f 470.238 y 334.608 (s)s 1 f 468.438 y 339.737 (\050)s 10 f 344.404 (i)s 1 f 348.538 (\051)s 11 f 463.483 y 353.205 (n)s 13 f 458.717 y 359.737 (\244)s 364.737 (\241)s 10 f 468.438 y 370.237 (@)s 11 f 462.671 y 377.274 (\260)s 472.057 y 376.608 (k)s 10 f 468.438 y 383.432 (U)s 11 f 463.483 y 392.933 (n)s 471.404 y 391.625 (s)s 13 f 458.717 y 399.465 (\242)s 1 f 468.438 y 404.965 (\050)s 10 f 409.632 (\260)s 416.512 (i)s 1 f 420.646 (\051)s 10 f 425.312 (ds:)s 1 f 505.074 y -5.69 (Here)s 10 f 22.676 (@)s 11 f 499.307 y 29.714 (\260)s 508.693 y 29.047 (k)s 1 f 505.074 y 39.871 (represen)s 83.005 (ts)s 96.405 (the)s 117.071 (discrete)s 161.171 (deriv)s 186.871 (ativ)s 206.871 (e)s 216.205 (in)s 230.205 (the)s 10 f 250.872 (k)s 1 f 257.497 (-th)s 276.83 (direction:)s 13 f 517.23 y 122.3 (\241)s 10 f 526.95 y 127.8 (@)s 11 f 521.184 y 134.838 (\260)s 530.57 y 134.171 (k)s 10 f 526.95 y 140.995 (V)s 13 f 517.23 y 150.662 (\242)s 1 f 526.95 y 156.162 (\050)s 10 f 160.828 (\260)s 167.708 (i)s 1 f 171.842 (\051)s 179.842 (=)s 10 f 192.508 (\260)s 14 f 521.996 y 199.388 (\241)s 2 f 206.888 (1)s 13 f 517.23 y 212.271 (\243)s 10 f 526.95 y 217.271 (V)s 1 f 226.938 (\050)s 10 f 231.605 (\260)s 1 f 238.484 (\050)s 10 f 243.151 (i)s 1 f 249.951 (+)s 10 f 261.951 (e)s 11 f 528.75 y 267.539 (k)s 1 f 526.95 y 273.443 (\051\051)s 12 f 285.443 (\241)s 10 f 297.443 (V)s 1 f 307.11 (\050)s 10 f 311.776 (\260)s 318.656 (i)s 1 f 322.79 (\051)s 13 f 517.23 y 327.457 (\244)s 10 f 526.95 y 332.457 (:)s 1 f 548.947 y 8.71 (Notice)s 48.376 (that)s 76.375 (the)s 99.041 (conditions)s 158.44 (imp)s 178.774 (osed)s 207.506 (on)s 226.172 (\251)s 240.838 (imply)s 276.504 (that)s 304.503 (\251)s 14 f 544.593 y 313.17 (0)s 1 f 548.947 y 316.537 (\0500\051)s 338.535 (=)s 12 f 354.534 (\241)s 1 f 363.867 (1)s 10 f 369.867 (=)s 1 f 375.867 (2)s 387.867 (\050cf.)s 416.198 ([GL]\051,)s 453.78 (in)s 565.747 y -5.69 (particular,)s 52.6 (using)s 83.447 (Lemma)s 125.726 (4.1)s 144.506 (and)s 167.286 (a)s 176.732 (second)s 214.912 (summation)s 276.425 (b)s 282.758 (y)s 292.538 (parts,)s 326.195 (w)s 334.528 (e)s 343.308 (ma)s 358.975 (y)s 368.754 (rewrite)s 408.934 (the)s 429.047 (second)s 582.547 y -5.69 (term)s 23.01 (of)s 36.677 (the)s 57.343 (last)s 80.077 (in)s 89.743 (tegral)s 123.777 (as)s 2 f 601.791 y 18.933 (2)s 13 f 605.391 y 12.658 (X)s 11 f 630.804 y 12.284 (n)s 2 f 18.216 (=1)s 13 f 596.271 y 32.366 (\050)s 10 f 616.791 y 42.032 (\260)s 11 f 611.836 y 48.912 (d)s 13 f 605.391 y 60.778 (X)s 11 f 632.331 y 56.507 (i)s 14 f 59.902 (2)s 11 f 66.369 (Z)s 68.579 (Z)s 15 f 629.558 y 77.345 (d)s 11 f 601.791 y 90.612 (d)s 13 f 605.391 y 84.443 (X)s 11 f 631.224 y 84.383 (k)s 2 f 89.687 (=1)s 13 f 600.458 y 103.837 (Z)s 11 f 603.424 y 115.837 (t)s 2 f 627.725 y 110.504 (0)s 10 f 616.791 y 122.062 (ds)s 13 f 603.471 y 133.933 (n)s 607.071 y 141.933 (\241)s 10 f 616.791 y 147.433 (\276)s 11 f 618.591 y 154.29 (s)s 1 f 616.791 y 159.419 (\050)s 10 f 164.086 (i)s 1 f 168.22 (\051)s 11 f 611.836 y 172.887 (n)s 13 f 607.071 y 179.419 (\242)s 10 f 616.791 y 184.919 (\260)s 14 f 611.836 y 191.798 (\241)s 2 f 199.298 (2)s 13 f 607.071 y 204.681 (\243)s 10 f 616.791 y 209.681 (U)s 11 f 611.836 y 219.183 (n)s 619.758 y 217.875 (s)s 1 f 616.791 y 225.715 (\050)s 10 f 230.382 (\260)s 1 f 237.261 (\050)s 10 f 241.928 (i)s 1 f 248.729 (+)s 10 f 260.729 (e)s 11 f 618.591 y 266.316 (k)s 1 f 616.791 y 272.22 (\051\051)s 284.22 (+)s 10 f 296.22 (U)s 11 f 611.836 y 305.722 (n)s 619.758 y 304.414 (s)s 1 f 616.791 y 312.254 (\050)s 10 f 316.92 (\260)s 1 f 323.8 (\050)s 10 f 328.467 (i)s 12 f 335.267 (\241)s 10 f 347.267 (e)s 11 f 618.591 y 352.855 (k)s 1 f 616.791 y 358.759 (\051\051)s 12 f 370.759 (\241)s 1 f 382.759 (2)s 10 f 388.759 (U)s 11 f 611.836 y 398.261 (n)s 619.758 y 396.952 (s)s 1 f 616.791 y 404.793 (\050)s 10 f 409.459 (\260)s 416.339 (i)s 1 f 420.473 (\051)s 13 f 607.071 y 425.14 (\244)s 603.471 y 430.14 (o)s 596.271 y 438.14 (\051)s 1 f 664.6 y 24.95 (+)s 10 f 656.482 y 38.39 (\257)s 7.421 .48 38.39 661.84 r 1 f 672.832 y 39.101 (2)s 2 f 649.6 y 55.9 (2)s 13 f 653.2 y 49.625 (X)s 11 f 678.614 y 49.251 (n)s 2 f 55.183 (=1)s 13 f 644.08 y 69.333 (\050)s 10 f 664.6 y 79 (\260)s 11 f 659.645 y 85.879 (d)s 13 f 653.2 y 97.746 (X)s 11 f 680.14 y 93.475 (i)s 14 f 96.87 (2)s 11 f 103.336 (Z)s 105.546 (Z)s 15 f 677.367 y 114.312 (d)s 11 f 649.6 y 127.58 (d)s 13 f 653.2 y 121.411 (X)s 11 f 679.034 y 121.35 (k)s 2 f 126.654 (=1)s 13 f 648.267 y 140.804 (Z)s 11 f 651.233 y 152.804 (t)s 2 f 675.534 y 147.471 (0)s 10 f 664.6 y 159.029 (ds)s 13 f 651.28 y 170.9 (n)s 1 f 664.6 y 178.9 (\050)s 10 f 183.567 (@)s 11 f 658.834 y 190.604 (\260)s 668.22 y 189.938 (k)s 10 f 664.6 y 196.762 (U)s 11 f 659.645 y 206.263 (n)s 667.567 y 204.955 (s)s 1 f 664.6 y 212.795 (\051\050)s 10 f 222.129 (\260)s 229.008 (i)s 1 f 233.142 (\051)s 13 f 654.88 y 237.809 (\241)s 10 f 664.6 y 243.309 (\277)s 11 f 666.4 y 248.555 (i)s 10 f 664.6 y 252.55 (g)s 11 f 659.645 y 258.704 (n)s 1 f 664.6 y 265.236 (\050)s 10 f 269.903 (\276)s 1 f 277.19 (\051)s 13 f 654.88 y 281.857 (\242)s 287.357 (\241)s 10 f 664.6 y 292.857 (\274)s 2 f 659.645 y 300.128 (1)s 11 f 304.911 (;\260)s 667.567 y 299.697 (s)s 12 f 664.6 y 316.585 (\244)s 10 f 325.252 (@)s 11 f 658.834 y 332.289 (\260)s 668.22 y 331.623 (k)s 10 f 664.6 y 338.447 (J)s 13 f 654.88 y 346.255 (\242)s 1 f 664.6 y 351.755 (\050)s 10 f 356.422 (\260)s 363.301 (i)s 1 f 367.435 (\051)s 13 f 651.28 y 372.102 (o)s 644.08 y 380.102 (\051)s 1 f 664.6 y 392.435 (+)s 10 f 404.435 (o)s 11 f 666.4 y 410.252 (\260)s 1 f 664.6 y 416.409 (\0501\051)s 10 f 431.742 (;)s 1 f 705.976 y 223.045 (26)s do-end end endp %%Page: 27 27 %%BeginPageSetup initializepage (Raffaele Esposito; page: 27 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f0_12 sf ( )S -996 -1000 :M f1_12 sf ( )S -993 -1000 :M f2_12 sf ( )S -989 -1000 :M f10_12 sf ( )S -981 -1000 :M f11_12 sf ( )S -972 -1000 :M f12_12 sf ( )S -960 -1000 :M f13_12 sf ( )S -951 -1000 :M f14_12 sf ( )S -937 -1000 :M f15_12 sf ( )S -926 -1000 :M f17_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 1200 1000 div mul /CMBX10 findfont fdef 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 17 10 1200 1000 div mul /CMTI10 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 6.31 y -5.69 (where)s 10 f 27.805 (o)s 11 f 8.11 y 33.622 (\260)s 1 f 6.31 y 39.779 (\0501\051)s 57.907 (is)s 68.769 (a)s 77.564 (random)s 120.393 (v)s 126.059 (ariable)s 164.221 (that)s 189.016 (con)s 206.683 (v)s 212.683 (erges)s 241.578 (to)s 255.04 (0)s 263.835 (with)s 10 f 289.963 (\260)s 1 f 299.638 (and)s 12 f 321.766 (\244)s 1 f 330.561 (stands)s 366.823 (for)s 383.985 (the)s 403.447 (con)s 421.113 (v)s 427.113 (olution)s 23.11 y -5.69 (in)s 8.31 (the)s 28.977 (spatial)s 67.71 (v)s 73.377 (ariable.)s 117.41 (F)s 124.243 (or)s 10 f 138.943 (n)s 1 f 149.479 (=)s 162.146 (1)s 10 f 168.146 (;)s 1 f 173.479 (2,)s 186.813 (the)s 207.479 (functions)s 10 f 259.213 (g)s 11 f 18.755 y 265.367 (n)s 1 f 23.11 y 275.899 (are)s 295.932 (de\257ned)s 337.266 (b)s 343.599 (y)s 10 f 46.341 y 122.793 (g)s 11 f 41.387 y 128.947 (n)s 1 f 46.341 y 135.479 (\050)s 10 f 140.146 (\276)s 1 f 147.433 (\051)s 155.433 (=)s 13 f 36.621 y 168.1 (\243)s 10 f 46.341 y 173.1 (\276)s 1 f 180.387 (\050)s 10 f 185.054 (e)s 11 f 48.141 y 190.641 (k)s 1 f 46.341 y 196.546 (\051)s 12 f 203.879 (\241)s 10 f 215.879 (\276)s 1 f 223.166 (\0500\051)s 13 f 36.621 y 238.5 (\244)s 243.5 (\243)s 10 f 46.341 y 248.5 (\276)s 1 f 255.787 (\050)s 10 f 260.454 (e)s 11 f 48.141 y 266.042 (k)s 1 f 46.341 y 271.946 (\051)s 11 f 41.387 y 276.612 (n)s 12 f 46.341 y 285.811 (\241)s 10 f 297.811 (\276)s 1 f 305.098 (\0500\051)s 11 f 41.387 y 320.432 (n)s 13 f 36.621 y 326.964 (\244)s 10 f 46.341 y 331.964 (:)s 1 f 69.693 y 8.71 (This)s 37.089 (time,)s 68.98 (ho)s 81.314 (w)s 89.647 (ev)s 100.981 (er,)s 119.572 (it)s 132.551 (is)s 145.597 (not)s 167.91 (the)s 189.556 (densit)s 220.623 (y)s 231.936 (\257elds)s 263.649 (themselv)s 309.716 (es)s 324.762 (that)s 351.741 (app)s 371.408 (ear)s 392.421 (in)s 407.401 (the)s 429.047 (second)s 86.493 y -5.69 (term)s 23.163 (of)s 36.984 (the)s 57.804 (last)s 80.691 (expression)s 138.678 (but)s 160.831 (another)s 205.018 (lo)s 214.685 (cal)s 233.505 (function)s 280.659 (of)s 294.479 (the)s 315.299 (con\257guration.)s 393.126 (F)s 399.96 (ollo)s 418.293 (wing)s 447.113 (the)s 103.293 y -5.69 (metho)s 27.31 (ds)s 43.784 (of)s 58.524 (Guo-P)s 92.441 (apanicolaou-V)s 166.441 (aradhan)s 214.214 ([GPV],)s 255.871 (the)s 277.612 (main)s 308.686 (step)s 335.159 (in)s 350.233 (pro)s 367.266 (ving)s 394.673 (the)s 416.414 (h)s 422.747 (ydro)s 446.78 (dy-)s 120.093 y -5.69 (namic)s 29.934 (equations)s 83.958 (is)s 96.315 (to)s 111.273 (replace)s 152.263 (this)s 175.954 (lo)s 185.621 (cal)s 204.578 (function)s 251.869 (b)s 258.202 (y)s 268.826 (another)s 313.151 (function)s 360.441 (of)s 374.399 (the)s 395.356 (densit)s 426.423 (y)s 437.047 (\257elds)s 136.893 y -5.69 (in)s 8.284 (order)s 39.658 (to)s 54.299 (close)s 83.007 (the)s 103.648 (equations.)s 162.04 (F)s 168.873 (or)s 183.547 (a)s 193.521 (cylinder)s 239.196 (function)s 286.17 (\252,)s 302.816 (w)s 311.15 (e)s 320.457 (denote)s 359.098 (its)s 375.806 (exp)s 394.473 (ectation)s 440.447 (with)s 153.693 y -5.69 (resp)s 16.076 (ect)s 35.41 (to)s 50.077 (the)s 70.743 (measure)s 10 f 117.51 (\272)s 2 f 155.86 y 123.438 (\050)s 11 f 127.188 (m;\301)s 2 f 144.323 (\051)s 1 f 153.693 y 152.006 (=)s 10 f 164.673 (\272)s 11 f 155.493 y 170.601 (P)s 1 f 153.693 y 182.602 (de\257ned)s 223.935 (in)s 237.935 (\0503.2\051)s 266.602 (b)s 272.936 (y)s 13 f 150.66 y 284.602 (e)s 1 f 153.693 y 283.269 (\252)s 292.602 (\050)s 10 f 297.269 (m;)s 313.138 (\301)s 1 f 320.288 (\051:)s 13 f 182.491 y 163.16 (e)s 1 f 185.525 y 161.827 (\252)s 171.16 (\050)s 10 f 175.827 (m;)s 191.697 (\301)s 1 f 198.847 (\051)s 206.847 (=)s 13 f 169.191 y 219.513 (Z)s 1 f 185.525 y 233.513 (\252\050)s 10 f 247.513 (\276)s 1 f 254.801 (\051)s 10 f 259.467 (d\272)s 11 f 187.325 y 271.641 (P)s 1 f 185.525 y 279.642 (\050)s 10 f 284.309 (\276)s 1 f 291.596 (\051)s 218.156 y -5.69 (and)s 17.848 (for)s 36.419 (a)s 46.624 (p)s 53.624 (ositiv)s 81.69 (e)s 91.228 (in)s 100.895 (teger)s 10 f 131.133 (\140)s 1 f 140.338 (and)s 10 f 163.876 (i)s 12 f 171.684 (2)s 10 f 183.358 (Z)s 186.408 (Z)s 11 f 212.923 y 197.458 (d)s 1 f 218.156 y 203.054 (,)s 210.643 (denote)s 249.514 (the)s 270.386 (empirical)s 322.624 (mean)s 354.828 (densities)s 403.833 (on)s 420.704 (a)s 430.909 (b)s 437.909 (o)s 443.576 (x)s 454.114 (of)s 234.956 y -5.69 (size)s 13 f 225.236 y 17.043 (\241)s 1 f 234.956 y 22.543 (2)s 10 f 28.543 (\140)s 1 f 36.21 (+)s 48.21 (1)s 13 f 225.236 y 54.21 (\242)s 11 f 227.723 y 59.71 (d)s 1 f 234.956 y 69.305 (cen)s 86.305 (tered)s 117.005 (at)s 10 f 131.672 (i)s 1 f 139.806 (b)s 146.139 (y)s 13 f 225.236 y 156.473 (\241)s 0 f 234.956 y 161.973 (A)s 2 f 230.602 y 172.406 (1)s 11 f 177.19 (;\140)s 10 f 234.956 y 184.656 (\276)s 13 f 225.236 y 191.944 (\242)s 1 f 234.956 y 197.444 (\050)s 10 f 202.11 (i)s 1 f 206.245 (\051)s 214.911 (and)s 13 f 225.236 y 238.245 (\241)s 0 f 234.956 y 243.745 (A)s 2 f 230.602 y 254.178 (2)s 11 f 258.961 (;\140)s 10 f 234.956 y 266.428 (\276)s 13 f 225.236 y 273.715 (\242)s 1 f 234.956 y 279.216 (\050)s 10 f 283.882 (i)s 1 f 288.016 (\051:)s 13 f 254.468 y 22.622 (\303)s 265.268 y 32.122 (\241)s 0 f 274.988 y 37.622 (A)s 2 f 270.034 y 48.055 (1)s 11 f 52.839 (;\140)s 10 f 274.988 y 60.306 (\276)s 13 f 265.268 y 67.593 (\242)s 1 f 274.988 y 73.093 (\050)s 10 f 77.76 (i)s 1 f 81.894 (\051)s 10 f 86.561 (;)s 13 f 265.268 y 91.894 (\241)s 0 f 274.988 y 97.394 (A)s 2 f 270.034 y 107.827 (2)s 11 f 112.611 (;\140)s 10 f 274.988 y 120.077 (\276)s 13 f 265.268 y 127.365 (\242)s 1 f 274.988 y 132.865 (\050)s 10 f 137.531 (i)s 1 f 141.666 (\051)s 13 f 254.468 y 146.332 (!)s 1 f 274.988 y 159.166 (=)s 13 f 250.868 y 171.832 (0)s 272.468 y 171.832 (@)s 1 f 266.87 y 204.903 (1)s 48.262 .48 183.772 272.228 r 13 f 277.015 y 183.772 (\241)s 1 f 286.735 y 189.272 (2)s 10 f 195.272 (\140)s 1 f 202.939 (+)s 214.939 (1)s 13 f 277.015 y 220.939 (\242)s 11 f 279.501 y 226.439 (d)s 13 f 263.588 y 243.092 (X)s 14 f 289.888 y 235.474 (j)s 11 f 238.324 (i)s 14 f 241.719 (\241)s 11 f 249.219 (j)s 14 f 253.676 (j\267)s 11 f 264.026 (\140)s 10 f 274.988 y 270.042 (\276)s 1 f 277.33 (\050)s 10 f 281.997 (j)s 1 f 287.625 (\051)s 10 f 295.625 (;)s 1 f 266.87 y 323.529 (1)s 48.262 .48 302.398 272.228 r 13 f 277.015 y 302.398 (\241)s 1 f 286.735 y 307.898 (2)s 10 f 313.898 (\140)s 1 f 321.565 (+)s 333.565 (1)s 13 f 277.015 y 339.565 (\242)s 11 f 279.501 y 345.065 (d)s 13 f 263.588 y 361.718 (X)s 14 f 289.888 y 354.1 (j)s 11 f 356.95 (i)s 14 f 360.346 (\241)s 11 f 367.846 (j)s 14 f 372.302 (j\267)s 11 f 382.652 (\140)s 10 f 274.988 y 388.669 (\276)s 1 f 395.956 (\050)s 10 f 400.623 (j)s 1 f 406.251 (\051)s 2 f 270.034 y 410.918 (2)s 13 f 250.868 y 419.635 (1)s 272.468 y 419.635 (A)s 10 f 274.988 y 432.135 (:)s 0 f 333.078 y -5.69 (Lemma)s 44.45 (5.3)s 17 f 72.941 (F)s 79.854 (or)s 96.307 (al)s 106.12 (l)s 114.446 (cylinder)s 161.258 (function)s 1 f 209.451 (\252)s 17 f 224.043 (and)s 248.316 (al)s 258.129 (l)s 10 f 266.455 (V)s 1 f 281.205 (:)s 289.621 ([0)s 10 f 298.955 (;)s 304.288 (T)s 1 f 312.967 (])s 12 f 319.667 (\243)s 1 f 332.367 (I)s 334.54 (R)s 11 f 327.845 y 343.374 (d)s 12 f 333.078 y 354.052 (\241)s 361.386 (!)s 1 f 378.469 (I)s 380.642 (R)s 17 f 394.735 (with)s 421.767 (c)s 426.674 (omp)s 448.14 (act)s 349.878 y -5.69 (supp)s 17.31 (ort)s 1 f 384.323 y 6.31 (lim)s 24.976 (sup)s 11 f 394.07 y 15.235 (\042)s 14 f 19.768 (!)s 2 f 29.335 (0)s 1 f 384.323 y 45.043 (lim)s 63.71 (sup)s 11 f 394.07 y 53.456 (\260)s 14 f 59.013 (!)s 2 f 68.58 (0)s 0 f 384.323 y 83.776 (E)s 2 f 378.09 y 92.843 (\050)s 11 f 96.593 (K)s 2 f 105.245 (\051)s 11 f 387.093 y 92.843 (\271)s 15 f 384.693 y 98.678 (\260)s 13 f 363.803 y 109.595 (\042)s 10 f 384.323 y 116.595 (\260)s 11 f 379.369 y 123.474 (d)s 13 f 372.923 y 135.341 (X)s 11 f 399.863 y 131.07 (i)s 14 f 134.465 (2)s 11 f 140.932 (Z)s 143.142 (Z)s 15 f 397.09 y 151.907 (d)s 13 f 367.99 y 158.945 (Z)s 11 f 370.957 y 170.945 (T)s 2 f 395.257 y 165.612 (0)s 10 f 384.323 y 180.505 (ds)s 13 f 374.123 y 192.376 (\257)s 381.323 y 192.376 (\257)s 10 f 384.323 y 196.376 (V)s 11 f 386.123 y 203.376 (s)s 1 f 384.323 y 208.505 (\050)s 10 f 213.171 (\260)s 220.051 (i)s 1 f 224.185 (\051)s 13 f 374.123 y 228.852 (\257)s 381.323 y 228.852 (\257)s 363.803 y 232.852 (\050)s 363.323 y 242.518 (\257)s 370.523 y 242.518 (\257)s 377.723 y 242.518 (\257)s 384.923 y 242.518 (\257)s 392.124 y 242.518 (\257)s 374.603 y 246.518 (\241)s 1 f 384.323 y 252.018 (2)s 10 f 258.018 (\042N)s 11 f 386.123 y 273.256 (\260)s 1 f 384.323 y 282.08 (+)s 294.08 (1)s 13 f 374.603 y 300.08 (\242)s 14 f 377.09 y 305.58 (\241)s 11 f 313.08 (d)s 13 f 372.923 y 335.101 (X)s 14 f 399.223 y 320.675 (j)s 11 f 323.525 (j)s 14 f 327.982 (\241)s 11 f 335.482 (i)s 14 f 338.877 (j\267)s 11 f 349.227 (\042N)s 15 f 400.423 y 361.361 (\260)s 10 f 384.323 y 368.859 (\277)s 11 f 386.123 y 374.105 (j)s 1 f 384.323 y 379.162 (\252\050)s 10 f 393.162 (\276)s 11 f 386.123 y 400.018 (s)s 1 f 384.323 y 405.148 (\051)s 12 f 432.19 y 217.274 (\241)s 13 f 429.157 y 227.941 (e)s 1 f 432.19 y 226.607 (\252)s 13 f 411.67 y 235.941 (\303)s 422.47 y 245.441 (\241)s 0 f 432.19 y 250.941 (A)s 2 f 427.236 y 261.374 (1)s 11 f 266.158 (;\042N)s 15 f 428.436 y 281.142 (\260)s 10 f 432.19 y 287.24 (\276)s 11 f 433.99 y 294.097 (s)s 13 f 422.47 y 299.226 (\242)s 1 f 432.19 y 304.726 (\050)s 10 f 309.393 (i)s 1 f 313.527 (\051)s 10 f 318.194 (;)s 13 f 422.47 y 323.527 (\241)s 0 f 432.19 y 329.027 (A)s 2 f 427.236 y 339.461 (2)s 11 f 344.244 (;\042N)s 15 f 428.436 y 359.229 (\260)s 10 f 432.19 y 365.327 (\276)s 11 f 433.99 y 372.184 (s)s 13 f 422.47 y 377.313 (\242)s 1 f 432.19 y 382.813 (\050)s 10 f 387.479 (i)s 1 f 391.614 (\051)s 13 f 411.67 y 396.28 (!)s 411.19 y 405.78 (\257)s 418.39 y 405.78 (\257)s 425.59 y 405.78 (\257)s 432.79 y 405.78 (\257)s 439.99 y 405.78 (\257)s 411.67 y 409.78 (\051)s 419.447 (#)s 1 f 432.19 y 429.78 (=)s 442.447 (0)s 10 f 448.447 (;)s 17 f 468.19 y -5.69 (wher)s 18.383 (e)s 10 f 28.196 (N)s 11 f 469.99 y 37.838 (\260)s 17 f 468.19 y 48.288 (is)s 61.168 (the)s 81.102 (inte)s 100.421 (ger)s 120.815 (p)s 126.334 (art)s 145.808 (of)s 10 f 159.914 (\260)s 14 f 463.835 y 166.794 (\241)s 2 f 174.294 (1)s 1 f 468.19 y 179.677 (.)s 502.182 y 8.71 (Since)s 39.193 (the)s 59.01 (supp)s 84.077 (ort)s 102.593 (of)s 115.41 (the)s 135.227 (function)s 10 f 181.377 (V)s 1 f 194.193 (is)s 205.41 (compact,)s 256.063 (b)s 262.397 (y)s 271.88 (corollary)s 320.763 (4.4)s 339.247 (the)s 359.063 (pro)s 376.763 (of)s 389.58 (of)s 402.397 (this)s 424.947 (Lemma)s 518.982 y -5.69 (is)s 5.705 (v)s 11.705 (ery)s 31.4 (similar)s 70.162 (to)s 84.157 (the)s 104.152 (one)s 125.48 (usually)s 165.875 (used)s 192.604 (in)s 205.932 (\257nite)s 235.927 (v)s 241.927 (olume.)s 281.704 (Nev)s 302.037 (ertheless,)s 353.666 (w)s 362 (e)s 370.662 (shall)s 398.057 (giv)s 413.39 (e)s 422.052 (a)s 431.38 (sk)s 442.113 (etc)s 457.113 (h)s 535.782 y -5.69 (of)s 7.977 (its)s 24.71 (pro)s 42.41 (of)s 56.077 (at)s 70.743 (the)s 91.41 (end)s 114.077 (of)s 127.743 (this)s 151.143 (subsection.)s 552.702 y 8.71 (Let)s 30.394 (us)s 45.979 (go)s 62.164 (on)s 79.015 (with)s 106.533 (the)s 127.384 (pro)s 145.085 (of)s 158.936 (of)s 172.787 (Lemma)s 215.805 (5.2.)s 240.359 (No)s 255.026 (w,)s 271.257 (b)s 277.59 (y)s 288.108 (Lemma)s 331.126 (5.3)s 350.644 (and)s 374.162 (T)s 381.829 (a)s 387.496 (ylor)s 412.047 (expansion)s 569.502 y -5.69 (applied)s 37.163 (to)s 52.682 (the)s 74.201 (functions)s 10 f 126.788 (U)s 2 f 565.147 y 136.289 (1)s 1 f 569.502 y 141.673 (,)s 10 f 150.072 (U)s 2 f 565.147 y 159.574 (2)s 1 f 569.502 y 169.81 (and)s 10 f 193.996 (J)s 1 f 201.804 (,)s 210.203 (the)s 231.723 (in)s 241.39 (tegral)s 276.276 (term)s 305.828 (of)s 320.348 (the)s 341.867 (martingale)s 10 f 402.754 (M)s 11 f 565.147 y 415.704 (U)s 572.468 y 414.395 (t)s 1 f 569.502 y 428.594 (can)s 451.447 (b)s 458.447 (e)s 586.302 y -5.69 (written)s 36.343 (as)s 2 f 604.567 y 10.956 (2)s 13 f 608.167 y 4.681 (X)s 11 f 633.58 y 4.307 (n)s 2 f 10.239 (=1)s 11 f 604.567 y 30.618 (d)s 13 f 608.167 y 24.449 (X)s 11 f 634 y 24.389 (k)s 2 f 29.693 (=1)s 13 f 603.233 y 43.843 (Z)s 11 f 606.2 y 55.843 (t)s 2 f 630.5 y 50.51 (0)s 10 f 619.567 y 62.068 (ds)s 13 f 599.047 y 73.939 (\050)s 609.847 y 83.606 (\255)s 10 f 619.567 y 89.272 (\274)s 11 f 614.612 y 96.543 (n;\260)s 622.533 y 96.113 (s)s 10 f 619.567 y 111.482 (;)s 13 f 609.847 y 116.816 (\241)s 10 f 619.567 y 122.316 (@)s 11 f 621.367 y 128.687 (s)s 10 f 619.567 y 133.816 (U)s 11 f 614.612 y 143.317 (n)s 622.533 y 142.009 (s)s 1 f 619.567 y 152.516 (+)s 10 f 164.516 (@)s 2 f 614.612 y 171.553 (2)s 11 f 622.533 y 170.887 (k)s 10 f 619.567 y 176.937 (U)s 11 f 614.612 y 186.438 (n)s 622.533 y 185.13 (s)s 13 f 609.847 y 192.97 (\242)s 198.47 (\256)s 1 f 664.6 y 16.973 (+)s 10 f 656.482 y 30.413 (\257)s 7.421 .48 30.413 661.84 r 1 f 672.832 y 31.124 (2)s 13 f 653.2 y 45.545 (X)s 11 f 680.14 y 41.274 (i)s 14 f 44.669 (2)s 11 f 51.136 (Z)s 53.346 (Z)s 15 f 677.367 y 62.112 (d)s 13 f 644.08 y 69.15 (\042)s 1 f 664.6 y 76.15 (\050)s 10 f 80.816 (@)s 11 f 666.4 y 87.187 (k)s 10 f 664.6 y 93.092 (U)s 11 f 659.646 y 102.593 (n)s 667.567 y 101.285 (s)s 1 f 664.6 y 109.125 (\051\050)s 10 f 118.459 (\260)s 125.338 (i)s 1 f 129.472 (\051)s 13 f 654.88 y 134.139 (\241)s 10 f 664.6 y 139.639 (\274)s 2 f 659.646 y 146.91 (1)s 11 f 151.693 (;\260)s 667.567 y 146.479 (s)s 12 f 664.6 y 163.367 (\244)s 10 f 172.034 (@)s 11 f 666.4 y 178.404 (k)s 10 f 664.6 y 184.309 (J)s 13 f 654.88 y 192.117 (\242)s 1 f 664.6 y 197.617 (\050)s 10 f 202.284 (\260)s 209.163 (i)s 1 f 213.297 (\051)s 13 f 662.684 y 218.307 (f)s 10 f 664.6 y 217.964 (g)s 11 f 661.134 y 224.118 (n)s 13 f 651.28 y 230.65 (\263)s 654.88 y 237.817 (\241)s 0 f 664.6 y 243.317 (A)s 2 f 659.646 y 253.75 (1)s 11 f 258.533 (;\042N)s 15 f 660.846 y 273.518 (\260)s 10 f 664.6 y 279.616 (\276)s 13 f 654.88 y 286.904 (\242)s 1 f 664.6 y 292.404 (\050)s 10 f 297.07 (i)s 1 f 301.204 (\051)s 10 f 305.871 (;)s 13 f 654.88 y 311.204 (\241)s 0 f 664.6 y 316.704 (A)s 2 f 659.646 y 327.138 (2)s 11 f 331.921 (;\042N)s 15 f 660.846 y 346.906 (\260)s 10 f 664.6 y 353.004 (\276)s 13 f 654.88 y 360.291 (\242)s 1 f 664.6 y 365.791 (\050)s 10 f 370.458 (i)s 1 f 374.592 (\051)s 13 f 651.28 y 379.259 (\264)s 644.08 y 386.425 (#)s 393.426 (\051)s 1 f 664.6 y 405.759 (+)s 10 f 417.759 (o)s 11 f 666.4 y 423.575 (\260)s 429.133 (;\042)s 1 f 664.6 y 437.117 (\0501\051)s 10 f 452.45 (;)s 1 f 705.976 y 223.045 (27)s do-end end endp %%Page: 28 28 %%BeginPageSetup initializepage (Raffaele Esposito; page: 28 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f0_12 sf ( )S -996 -1000 :M f1_12 sf ( )S -993 -1000 :M f2_12 sf ( )S -989 -1000 :M f10_12 sf ( )S -981 -1000 :M f11_12 sf ( )S -972 -1000 :M f12_12 sf ( )S -960 -1000 :M f13_12 sf ( )S -951 -1000 :M f14_12 sf ( )S -937 -1000 :M f15_12 sf ( )S -926 -1000 :M f16_12 sf ( )S -921 -1000 :M f18_12 sf ( )S -905 -1000 :M f21_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 1200 1000 div mul /CMBX10 findfont fdef 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 16 5 1200 1000 div mul /CMR5 findfont fdef 18 5 1200 1000 div mul /CMSY5 findfont fdef 22 10 1200 1000 div mul /CMSL10 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 6.31 y -5.69 (where)s 10 f 29.382 (@)s 11 f 8.11 y 35.753 (k)s 1 f 6.31 y 46.03 (and)s 10 f 69.736 (@)s 2 f 1.955 y 76.774 (2)s 11 f 9.708 y 76.107 (k)s 1 f 6.31 y 86.529 (represen)s 129.663 (t)s 138.702 (the)s 159.741 (\257rst)s 184.881 (and)s 208.587 (the)s 229.626 (second)s 268.732 (deriv)s 294.432 (ativ)s 314.432 (es)s 328.871 (in)s 343.244 (the)s 10 f 364.283 (k)s 1 f 370.908 (-th)s 390.614 (direction,)s 444.447 (and)s 10 f 23.11 y -5.69 (o)s 11 f 24.91 y .126 (\260)s 5.684 (;\042)s 1 f 23.11 y 13.668 (\0501\051)s 33.001 (is)s 45.068 (a)s 55.068 (random)s 99.101 (v)s 104.768 (ariable)s 144.134 (that)s 170.135 (con)s 187.801 (v)s 193.801 (erges)s 223.901 (to)s 238.568 (0)s 248.568 (when)s 10 f 279.901 (\260)s 12 f 290.114 (!)s 1 f 305.447 (0)s 315.447 (and)s 10 f 338.781 (\042)s 12 f 347.71 (!)s 1 f 363.043 (0.)s 40.03 y 8.71 (Moreo)s 41.41 (v)s 47.41 (er,)s 64.777 (remark)s 105.843 (that)s 13 f 68.047 y 44.245 (e)s 10 f 71.76 y 41.809 (g)s 2 f 68.294 y 47.963 (1)s 13 f 58.44 y 53.347 (\263)s 62.04 y 60.513 (\241)s 0 f 71.76 y 66.013 (A)s 2 f 66.806 y 76.447 (1)s 11 f 81.23 (;\042N)s 15 f 68.006 y 96.215 (\260)s 10 f 71.76 y 102.313 (\276)s 13 f 62.04 y 109.6 (\242)s 1 f 71.76 y 115.1 (\050)s 10 f 119.767 (i)s 1 f 123.901 (\051)s 10 f 128.568 (;)s 13 f 62.04 y 133.901 (\241)s 0 f 71.76 y 139.401 (A)s 2 f 66.806 y 149.834 (2)s 11 f 154.618 (;\042N)s 15 f 68.006 y 169.602 (\260)s 10 f 71.76 y 175.7 (\276)s 13 f 62.04 y 182.988 (\242)s 1 f 71.76 y 188.488 (\050)s 10 f 193.155 (i)s 1 f 197.289 (\051)s 13 f 58.44 y 201.956 (\264)s 1 f 71.76 y 212.455 (=)s 225.122 (2)s 13 f 58.44 y 231.122 (h)s 62.04 y 236.789 (\241)s 0 f 71.76 y 242.289 (A)s 2 f 66.806 y 252.722 (2)s 11 f 257.505 (;\042N)s 15 f 68.006 y 272.49 (\260)s 10 f 71.76 y 278.588 (\276)s 13 f 62.04 y 285.876 (\242)s 1 f 71.76 y 291.376 (\050)s 10 f 296.042 (i)s 1 f 300.176 (\051)s 12 f 307.51 (\241)s 13 f 58.44 y 319.51 (\263)s 62.04 y 326.676 (\241)s 0 f 71.76 y 332.176 (A)s 2 f 66.806 y 342.61 (1)s 11 f 347.393 (;\042N)s 15 f 68.006 y 362.378 (\260)s 10 f 71.76 y 368.476 (\276)s 13 f 62.04 y 375.763 (\242)s 1 f 71.76 y 381.263 (\050)s 10 f 385.93 (i)s 1 f 390.064 (\051)s 13 f 58.44 y 394.731 (\264)s 2 f 60.927 y 401.897 (2)s 13 f 58.44 y 407.281 (i)s 10 f 71.76 y 412.948 (;)s 13 f 98.047 y 44.245 (e)s 10 f 101.761 y 41.809 (g)s 2 f 98.294 y 47.963 (2)s 13 f 88.44 y 53.347 (\263)s 92.041 y 60.513 (\241)s 0 f 101.761 y 66.013 (A)s 2 f 96.806 y 76.447 (1)s 11 f 81.23 (;\042N)s 15 f 98.006 y 96.215 (\260)s 10 f 101.761 y 102.313 (\276)s 13 f 92.041 y 109.6 (\242)s 1 f 101.761 y 115.1 (\050)s 10 f 119.767 (i)s 1 f 123.901 (\051)s 10 f 128.568 (;)s 13 f 92.041 y 133.901 (\241)s 0 f 101.761 y 139.401 (A)s 2 f 96.806 y 149.834 (2)s 11 f 154.618 (;\042N)s 15 f 98.006 y 169.602 (\260)s 10 f 101.761 y 175.7 (\276)s 13 f 92.041 y 182.988 (\242)s 1 f 101.761 y 188.488 (\050)s 10 f 193.155 (i)s 1 f 197.289 (\051)s 13 f 88.44 y 201.956 (\264)s 1 f 101.761 y 212.455 (=)s 225.122 (2)s 13 f 92.041 y 231.122 (\241)s 0 f 101.761 y 236.622 (A)s 2 f 96.806 y 247.055 (1)s 11 f 251.839 (;\042N)s 15 f 98.006 y 266.823 (\260)s 10 f 101.761 y 272.921 (\276)s 13 f 92.041 y 280.209 (\242)s 1 f 101.761 y 285.709 (\050)s 10 f 290.376 (i)s 1 f 294.51 (\051)s 13 f 88.44 y 299.176 (h)s 1 f 101.761 y 304.843 (1)s 12 f 313.51 (\241)s 13 f 92.041 y 325.51 (\241)s 0 f 101.761 y 331.01 (A)s 2 f 96.806 y 341.443 (2)s 11 f 346.226 (;\042N)s 15 f 98.006 y 361.211 (\260)s 10 f 101.761 y 367.309 (\276)s 13 f 92.041 y 374.597 (\242)s 1 f 101.761 y 380.097 (\050)s 10 f 384.763 (i)s 1 f 388.897 (\051)s 13 f 88.44 y 393.564 (i)s 10 f 101.761 y 399.231 (:)s 1 f 131.044 y -5.69 (On)s 14.483 (the)s 35.323 (other)s 66.863 (hand,)s 100.413 (a)s 110.587 (simple)s 148.16 (computation)s 218.333 (sho)s 235.4 (ws)s 252.973 (that)s 279.147 (the)s 299.987 (quadratic)s 353.86 (v)s 359.527 (ariation)s 404.4 (of)s 418.24 (the)s 439.08 (mar-)s 147.844 y -5.69 (tingale)s 10 f 33.643 (M)s 11 f 143.49 y 46.593 (U)s 150.811 y 45.285 (t)s 1 f 147.844 y 58.631 (is)s 70.698 (equal)s 102.364 (to)s 12 f 184.842 y 6.31 (N)s 11 f 179.887 y 17.924 (U)s 187.808 y 16.156 (t)s 1 f 184.842 y 29.295 (=)s 13 f 175.122 y 41.962 (\241)s 10 f 184.842 y 47.462 (M)s 11 f 179.887 y 60.412 (U)s 187.808 y 59.103 (t)s 13 f 175.122 y 68.45 (\242)s 2 f 177.114 y 73.95 (2)s 12 f 184.842 y 82 (\241)s 10 f 94 (\260)s 2 f 179.887 y 100.879 (2)s 11 f 105.662 (d)s 13 f 173.442 y 120.698 (X)s 15 f 197.441 y 124.448 (i;j)s 18 f 204.547 y 114.698 (j)s 15 f 117.448 (i)s 18 f 120.649 (\241)s 15 f 127.149 (j)s 18 f 131.032 (j)s 16 f 133.782 (=1)s 13 f 168.508 y 147.472 (Z)s 11 f 171.475 y 159.472 (t)s 2 f 195.775 y 154.139 (0)s 13 f 164.321 y 165.697 (\050)s 10 f 184.842 y 175.364 (C)s 11 f 179.887 y 184.799 (K)s 192.934 (;\257)s 187.808 y 183.941 (\260)s 1 f 184.842 y 202.257 (\050)s 10 f 206.924 (i;)s 216.391 (j)s 1 f 222.02 (;)s 10 f 227.353 (\276)s 11 f 186.642 y 234.21 (s)s 1 f 184.842 y 239.339 (\051)s 12 f 237.261 y 182.293 (\243)s 13 f 223.94 y 191.627 (\263)s 2 f 222.26 y 207.443 (2)s 13 f 225.86 y 201.168 (X)s 11 f 251.274 y 200.793 (n)s 2 f 206.725 (=1)s 10 f 237.261 y 220.875 (\260)s 14 f 232.306 y 227.755 (\241)s 2 f 235.255 (1)s 13 f 227.54 y 240.638 (\243)s 10 f 237.261 y 245.638 (U)s 11 f 232.306 y 255.14 (n)s 240.227 y 253.832 (s)s 1 f 237.261 y 261.672 (\050)s 10 f 266.339 (\260)s 273.218 (i)s 1 f 277.352 (\051)s 12 f 284.685 (\241)s 10 f 296.685 (U)s 11 f 232.306 y 306.187 (n)s 240.227 y 304.879 (s)s 1 f 237.261 y 312.719 (\050)s 10 f 317.386 (\260)s 324.265 (j)s 1 f 329.894 (\051)s 13 f 227.54 y 334.56 (\244)s 339.56 (\243)s 10 f 237.261 y 344.56 (\276)s 11 f 239.061 y 351.417 (s)s 1 f 237.261 y 356.547 (\050)s 10 f 361.213 (i)s 1 f 365.347 (\051)s 11 f 232.306 y 370.014 (n)s 12 f 237.261 y 379.213 (\241)s 10 f 391.213 (\276)s 11 f 239.061 y 398.07 (s)s 1 f 237.261 y 403.199 (\050)s 10 f 407.865 (j)s 1 f 413.494 (\051)s 11 f 232.306 y 418.161 (n)s 13 f 227.54 y 424.693 (\244)s 223.94 y 429.693 (\264)s 2 f 226.427 y 436.859 (2)s 13 f 216.74 y 442.243 (\051)s 10 f 237.261 y 451.909 (ds)s 1 f 273.958 y -5.69 (and)s 17.643 (then)s 44.977 (it)s 56.977 (v)s 62.643 (anishes)s 104.11 (as)s 10 f 118.843 (\260)s 1 f 129.723 (go)s 142.056 (es)s 156.123 (to)s 170.789 (0.)s 185.456 (By)s 204.29 (Do)s 219.79 (ob\047s)s 244.523 (inequalit)s 289.856 (y)s 295.19 (,)s 302.523 (for)s 320.89 (ev)s 332.223 (ery)s 10 f 352.59 (\261)s 361.711 (\076)s 1 f 374.377 (0,)s 299.108 y 143.381 (lim)s 11 f 306.521 y 141.761 (\260)s 14 f 147.318 (!)s 2 f 156.885 (0)s 0 f 299.108 y 163.668 (P)s 2 f 292.875 y 173.101 (\050)s 11 f 176.851 (K)s 2 f 185.503 (\051)s 11 f 301.878 y 173.101 (\271)s 15 f 299.478 y 178.936 (\260)s 13 f 285.788 y 189.853 (n)s 1 f 299.108 y 206.004 (sup)s 2 f 309.199 y 199.853 (0)s 14 f 204.636 (\267)s 11 f 212.136 (t)s 14 f 215.761 (\267)s 11 f 223.261 (T)s 13 f 288.908 y 232.221 (\257)s 296.108 y 232.221 (\257)s 10 f 299.108 y 236.221 (M)s 11 f 294.153 y 249.171 (U)s 302.075 y 247.863 (t)s 13 f 288.908 y 257.209 (\257)s 296.108 y 257.209 (\257)s 10 f 299.108 y 264.542 (\076)s 277.209 (\261)s 13 f 285.788 y 282.996 (o)s 1 f 299.108 y 294.329 (=)s 306.996 (0)s 10 f 312.996 (:)s 1 f 333.441 y -5.69 (Therefore,)s 51.836 (collecting)s 104.91 (the)s 125.318 (ab)s 138.318 (o)s 143.985 (v)s 149.985 (e)s 159.059 (argumen)s 204.093 (ts)s 217.234 (and)s 240.308 (using)s 271.449 (Lemma)s 314.023 (5.1,)s 336.483 (w)s 344.816 (e)s 353.89 (obtain)s 390.965 (that)s 416.706 (an)s 429.039 (y)s 439.114 (limit)s 350.241 y -5.69 (p)s 1.31 (oin)s 16.977 (t)s 10 f 25.643 (Q)s 14 f 345.886 y 35.13 (\244)s 1 f 350.241 y 44.647 (of)s 58.313 (the)s 78.98 (sequence)s 13 f 340.521 y 128.713 (\241)s 10 f 350.241 y 134.213 (Q)s 2 f 344.008 y 143.7 (\050)s 11 f 147.45 (K)s 2 f 156.102 (\051)s 11 f 353.011 y 143.7 (\271)s 15 f 350.611 y 149.535 (\260)s 13 f 340.521 y 160.452 (\242)s 11 f 355.041 y 165.952 (\260)s 1 f 350.241 y 176.109 (is)s 188.176 (suc)s 204.576 (h)s 215.242 (that)s 10 f 401.192 y .976 (Q)s 14 f 396.237 y 10.463 (\244)s 13 f 380.672 y 17.98 (\050)s 1 f 401.192 y 27.646 (\050)s 10 f 32.313 (m;)s 48.182 (\301)s 1 f 55.332 (\051)s 66.666 (:)s 13 f 380.192 y 76.665 (\257)s 387.392 y 76.665 (\257)s 394.592 y 76.665 (\257)s 401.792 y 76.665 (\257)s 408.992 y 76.665 (\257)s 391.472 y 80.665 (\255)s 10 f 401.192 y 86.332 (m)s 11 f 402.992 y 96.868 (T)s 10 f 401.192 y 104.428 (;)s 109.761 (U)s 11 f 402.992 y 117.955 (T)s 13 f 391.472 y 125.514 (\256)s 12 f 401.192 y 133.847 (\241)s 13 f 391.472 y 145.847 (\255)s 10 f 401.192 y 151.514 (m)s 2 f 402.992 y 162.05 (0)s 10 f 401.192 y 167.434 (;)s 172.767 (U)s 2 f 402.992 y 180.96 (0)s 13 f 391.472 y 186.344 (\256)s 12 f 401.192 y 194.677 (\241)s 13 f 384.858 y 206.677 (Z)s 11 f 387.825 y 218.677 (T)s 2 f 412.125 y 213.343 (0)s 13 f 387.872 y 228.236 (D)s 10 f 401.192 y 235.57 (m)s 11 f 402.992 y 246.106 (s)s 10 f 401.192 y 251.235 (;)s 13 f 391.472 y 256.568 (\241)s 10 f 401.192 y 262.068 (@)s 11 f 402.992 y 268.439 (s)s 10 f 401.192 y 273.568 (U)s 11 f 402.992 y 281.762 (s)s 1 f 401.192 y 289.557 (+)s 301.557 (\242)s 10 f 311.557 (U)s 11 f 402.992 y 319.751 (s)s 13 f 391.472 y 324.88 (\242)s 387.872 y 330.38 (E)s 10 f 401.192 y 337.713 (ds)s 1 f 443.699 y 79.385 (+)s 13 f 433.979 y 88.718 (\255)s 10 f 443.699 y 94.385 (\301)s 11 f 445.499 y 101.535 (T)s 10 f 443.699 y 109.095 (;)s 114.428 (V)s 11 f 445.499 y 121.428 (T)s 13 f 433.979 y 128.987 (\256)s 12 f 443.699 y 137.321 (\241)s 13 f 433.979 y 149.321 (\255)s 10 f 443.699 y 154.987 (\301)s 2 f 445.499 y 162.137 (0)s 10 f 443.699 y 167.521 (;)s 172.854 (V)s 2 f 445.499 y 179.854 (0)s 13 f 433.979 y 185.237 (\256)s 12 f 443.699 y 193.571 (\241)s 13 f 427.365 y 205.571 (Z)s 11 f 430.332 y 217.571 (T)s 2 f 454.632 y 212.237 (0)s 13 f 430.379 y 227.13 (D)s 10 f 443.699 y 234.463 (\301)s 11 f 445.499 y 241.613 (s)s 10 f 443.699 y 246.743 (;)s 13 f 433.979 y 252.076 (\241)s 10 f 443.699 y 257.576 (@)s 11 f 445.499 y 263.947 (s)s 10 f 443.699 y 269.076 (V)s 11 f 445.499 y 276.076 (s)s 1 f 443.699 y 283.872 (+)s 295.872 (\242)s 10 f 305.872 (V)s 11 f 445.499 y 312.872 (s)s 13 f 433.979 y 318.001 (\242)s 430.379 y 323.501 (E)s 10 f 443.699 y 330.834 (ds)s 12 f 485.066 y 68.412 (\241)s 10 f 77.745 (\257)s 11 f 470.066 y 93.395 (d)s 13 f 473.666 y 87.226 (X)s 11 f 499.499 y 87.166 (k)s 2 f 92.47 (=1)s 13 f 468.732 y 106.62 (Z)s 11 f 471.699 y 118.62 (T)s 2 f 495.999 y 113.287 (0)s 13 f 471.746 y 128.18 (D)s 135.513 (\263)s 10 f 485.066 y 142.68 (m)s 11 f 486.866 y 153.216 (s)s 12 f 485.066 y 161.012 (\244)s 13 f 475.346 y 169.678 (\241)s 10 f 485.066 y 175.178 (@)s 11 f 486.866 y 181.549 (k)s 10 f 485.066 y 187.453 (J)s 13 f 475.346 y 195.262 (\242)s 471.746 y 200.762 (\264)s 207.928 (\263)s 475.346 y 215.095 (\241)s 10 f 485.066 y 220.595 (\301)s 11 f 486.866 y 227.745 (s)s 12 f 485.066 y 235.541 (\244)s 10 f 244.208 (\256)s 11 f 486.866 y 251.884 (\042)s 13 f 475.346 y 257.018 (\242)s 12 f 485.066 y 265.184 (\241)s 13 f 475.346 y 277.184 (\241)s 10 f 485.066 y 282.684 (m)s 11 f 486.866 y 293.221 (s)s 12 f 485.066 y 301.016 (\244)s 10 f 309.683 (\256)s 11 f 486.866 y 317.359 (\042)s 13 f 475.346 y 322.493 (\242)s 2 f 477.832 y 327.993 (2)s 13 f 471.746 y 333.376 (\264)s 10 f 485.066 y 340.543 (;)s 13 f 475.346 y 345.876 (\241)s 10 f 485.066 y 351.376 (@)s 11 f 486.866 y 357.747 (k)s 10 f 485.066 y 363.652 (U)s 11 f 486.866 y 371.845 (s)s 13 f 475.346 y 376.974 (\242)s 471.746 y 382.474 (E)s 10 f 485.066 y 389.807 (ds)s 12 f 531.132 y 63.637 (\241)s 10 f 72.97 (\257)s 11 f 516.132 y 88.62 (d)s 13 f 519.732 y 82.451 (X)s 11 f 545.566 y 82.391 (k)s 2 f 87.695 (=1)s 13 f 514.799 y 101.845 (Z)s 11 f 517.766 y 113.845 (T)s 2 f 542.066 y 108.512 (0)s 13 f 517.812 y 123.405 (D)s 130.738 (\263)s 10 f 531.132 y 137.905 (m)s 11 f 532.932 y 148.441 (s)s 12 f 531.132 y 156.237 (\244)s 13 f 521.412 y 164.903 (\241)s 10 f 531.132 y 170.403 (@)s 11 f 532.932 y 176.774 (k)s 10 f 531.132 y 182.678 (J)s 13 f 521.412 y 190.487 (\242)s 517.812 y 195.987 (\264)s 203.153 (\263)s 10 f 531.132 y 210.32 (m)s 11 f 532.932 y 220.856 (s)s 12 f 531.132 y 228.652 (\244)s 10 f 237.319 (\256)s 11 f 532.932 y 244.995 (\042)s 13 f 517.812 y 250.129 (\264)s 257.295 (\263)s 1 f 531.132 y 264.462 (1)s 12 f 273.129 (\241)s 13 f 521.412 y 285.129 (\241)s 10 f 531.132 y 290.629 (\301)s 11 f 532.932 y 297.779 (s)s 12 f 531.132 y 305.575 (\244)s 10 f 314.241 (\256)s 11 f 532.932 y 321.918 (\042)s 13 f 521.412 y 327.051 (\242)s 517.812 y 332.551 (\264)s 10 f 531.132 y 339.718 (;)s 13 f 521.412 y 345.051 (\241)s 10 f 531.132 y 350.551 (@)s 11 f 532.932 y 356.922 (k)s 10 f 531.132 y 362.826 (V)s 11 f 532.932 y 369.826 (s)s 13 f 521.412 y 374.956 (\242)s 517.812 y 380.456 (E)s 10 f 531.132 y 387.789 (ds)s 13 f 510.132 y 399.66 (\257)s 517.332 y 399.66 (\257)s 524.532 y 399.66 (\257)s 531.732 y 399.66 (\257)s 538.932 y 399.66 (\257)s 10 f 531.132 y 406.993 (\076)s 419.66 (\261)s 13 f 510.612 y 425.447 (\051)s 1 f 531.132 y 438.447 (=)s 451.114 (0)s 572.983 y -5.69 (for)s 11.431 (an)s 23.765 (y)s 10 f 32.853 (\261)s 41.973 (\076)s 1 f 54.64 (0)s 63.395 (and)s 10 f 85.483 (U)s 93.651 (;)s 98.984 (V)s 12 f 111.984 (2)s 123.317 (C)s 2 f 567.216 y 130.336 (1)s 11 f 135.119 (;)s 2 f 137.969 (2)s 11 f 576.51 y 129.636 (K)s 13 f 563.263 y 143.352 (\241)s 1 f 572.983 y 148.852 ([0)s 10 f 158.186 (;)s 163.519 (T)s 1 f 172.198 (])s 12 f 175.708 (\243)s 1 f 185.217 (I)s 187.39 (R)s 11 f 567.75 y 196.224 (d)s 13 f 563.263 y 201.819 (\242)s 1 f 572.983 y 207.319 (,)s 213.656 (where)s 10 f 247.111 (\256)s 11 f 574.783 y 254.787 (\042)s 1 f 572.983 y 262.676 (is)s 273.497 (de\257ned)s 313.585 (as)s 10 f 327.073 (\256)s 11 f 574.783 y 334.749 (\042)s 1 f 572.983 y 339.883 (\050)s 10 f 344.55 (x)s 1 f 351.408 (\051)s 359.408 (=)s 13 f 563.263 y 372.075 (\241)s 1 f 572.983 y 377.575 (2)s 10 f 383.575 (\042)s 13 f 563.263 y 389.171 (\242)s 14 f 565.75 y 394.671 (\241)s 11 f 402.171 (d)s 1 f 572.983 y 407.766 (1)s 2 f 575.416 y 413.766 ([)s 14 f 416.483 (\241)s 11 f 423.983 (\042;\042)s 2 f 435.9 (])s 15 f 573.016 y 438.617 (d)s 1 f 572.983 y 444.255 (\050)s 10 f 448.922 (x)s 1 f 455.78 (\051.)s 589.783 y -5.69 (Let)s 10 f 15.81 (\042)s 1 f 25.406 (go)s 41.406 (to)s 56.072 (0)s 66.072 (and)s 89.406 (b)s 95.739 (y)s 106.072 (arbitrariness)s 175.639 (of)s 10 f 189.306 (\261)s 1 f 199.093 (w)s 207.427 (e)s 216.76 (obtain)s 254.094 (the)s 274.76 (statemen)s 321.827 (t)s 330.494 (of)s 344.16 (Lemma)s 386.994 (5.2.)s 8.16 .48 416.327 583.183 r .48 7.2 416.327 590.383 r .48 7.2 424.007 590.383 r 8.16 .48 416.327 590.863 r 22 f 612.559 y -5.69 (Pro)s 13.51 (of)s 27.121 (of)s 40.733 (Lemma)s 83.511 (5.3)s 1 f 98.845 (.)s 107.493 (T)s 115.16 (o)s 125.105 (simplify)s 170.45 (the)s 191.061 (notation,)s 242.351 (for)s 10 f 260.662 (\276)s 12 f 271.283 (2)s 1 f 282.616 (\255,)s 298.572 (denote)s 337.184 (b)s 343.517 (y)s 0 f 353.795 (V)s 11 f 608.204 y 364.42 (N)s 15 f 609.404 y 372.021 (\260)s 11 f 608.204 y 377.519 (;\042)s 1 f 612.559 y 385.503 (\050)s 10 f 390.17 (\276)s 1 f 397.457 (\051)s 406.069 (the)s 426.68 (expres-)s 629.359 y -5.69 (sion)s 0 f 663.509 y 30.737 (V)s 11 f 658.555 y 41.362 (N)s 15 f 659.755 y 48.963 (\260)s 11 f 658.555 y 54.461 (;\042)s 1 f 663.509 y 62.445 (\050)s 10 f 67.112 (\276)s 1 f 74.399 (\051)s 82.399 (=)s 655.391 y 125.834 (1)s 64.657 .48 96.506 660.749 r 13 f 665.536 y 96.506 (\241)s 1 f 675.256 y 102.006 (2)s 10 f 108.006 (\042N)s 11 f 677.056 y 123.243 (\260)s 1 f 675.256 y 132.067 (+)s 144.067 (1)s 13 f 665.536 y 150.067 (\242)s 11 f 668.022 y 155.567 (d)s 13 f 642.509 y 162.603 (\257)s 649.709 y 162.603 (\257)s 656.909 y 162.603 (\257)s 664.109 y 162.603 (\257)s 671.309 y 162.603 (\257)s 652.109 y 177.58 (X)s 14 f 678.409 y 168.602 (j)s 11 f 171.452 (j)s 14 f 175.909 (j\267)s 11 f 186.259 (\042N)s 15 f 679.609 y 198.393 (\260)s 1 f 663.509 y 205.891 (\252\050)s 10 f 219.891 (\276)s 1 f 227.179 (\051)s 12 f 234.512 (\241)s 13 f 660.476 y 247.846 (e)s 1 f 663.509 y 246.512 (\252)s 13 f 642.989 y 255.846 (\303)s 653.789 y 265.346 (\241)s 0 f 663.509 y 270.846 (A)s 2 f 658.555 y 281.279 (1)s 11 f 286.062 (;\042N)s 15 f 659.755 y 301.047 (\260)s 10 f 663.509 y 307.145 (\276)s 13 f 653.789 y 314.432 (\242)s 1 f 663.509 y 319.932 (\0500\051)s 10 f 335.266 (;)s 13 f 653.789 y 340.599 (\241)s 0 f 663.509 y 346.099 (A)s 2 f 658.555 y 356.532 (2)s 11 f 361.316 (;\042N)s 15 f 659.755 y 376.3 (\260)s 10 f 663.509 y 382.399 (\276)s 13 f 653.789 y 389.686 (\242)s 1 f 663.509 y 395.186 (\0500\051)s 13 f 642.989 y 410.519 (!)s 642.509 y 420.019 (\257)s 649.709 y 420.019 (\257)s 656.909 y 420.019 (\257)s 664.109 y 420.019 (\257)s 671.309 y 420.019 (\257)s 10 f 663.509 y 424.019 (:)s 1 f 705.976 y 223.045 (28)s do-end end endp %%Page: 29 29 %%BeginPageSetup initializepage (Raffaele Esposito; page: 29 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f0_12 sf ( )S -996 -1000 :M f1_12 sf ( )S -993 -1000 :M f2_12 sf ( )S -989 -1000 :M f10_12 sf ( )S -981 -1000 :M f11_12 sf ( )S -972 -1000 :M f12_12 sf ( )S -960 -1000 :M f13_12 sf ( )S -951 -1000 :M f14_12 sf ( )S -937 -1000 :M f15_12 sf ( )S -926 -1000 :M f17_12 sf ( )S -923 -1000 :M f21_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 1200 1000 div mul /CMBX10 findfont fdef 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 17 10 1200 1000 div mul /CMTI10 findfont fdef 22 10 1200 1000 div mul /CMSL10 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 6.31 y -5.69 (Fix)s 10 f 15.81 (M)s 32.093 (\076)s 1 f 44.76 (0)s 54.76 (suc)s 71.16 (h)s 81.826 (that)s 107.826 ([)s 12 f 111.16 (\241)s 10 f 120.493 (M)s 132.776 (;)s 138.11 (M)s 1 f 151.06 (])s 11 f 1.955 y 154.393 (d)s 1 f 6.31 y 163.989 (con)s 181.655 (tains)s 211.055 (the)s 231.722 (supp)s 256.789 (ort)s 276.155 (of)s 10 f 289.822 (V)s 11 f 8.11 y 296.822 (s)s 1 f 6.31 y 305.951 (for)s 324.318 (all)s 10 f 340.985 (s)s 12 f 349.943 (2)s 1 f 361.276 ([0)s 10 f 370.61 (;)s 375.943 (T)s 1 f 384.622 (].)s 396.622 (W)s 407.955 (e)s 417.289 (ha)s 429.622 (v)s 435.622 (e)s 0 f 55.663 y -5.375 (E)s 2 f 49.43 y 3.691 (\050)s 11 f 7.441 (K)s 2 f 16.093 (\051)s 11 f 58.433 y 3.691 (\271)s 15 f 56.033 y 9.526 (\260)s 13 f 31.543 y 22.443 (2)s 53.143 y 22.443 (4)s 10 f 55.663 y 30.443 (\260)s 11 f 50.709 y 37.322 (d)s 13 f 44.263 y 49.189 (X)s 11 f 71.203 y 44.918 (i)s 14 f 48.313 (2)s 11 f 54.78 (Z)s 56.99 (Z)s 15 f 68.43 y 65.755 (d)s 13 f 39.33 y 72.793 (Z)s 11 f 42.296 y 84.793 (T)s 2 f 66.597 y 79.46 (0)s 13 f 45.463 y 94.353 (\257)s 52.663 y 94.353 (\257)s 10 f 55.663 y 98.353 (V)s 11 f 57.463 y 105.353 (s)s 1 f 55.663 y 110.482 (\050)s 10 f 115.149 (\260)s 122.028 (i)s 1 f 126.162 (\051)s 13 f 45.463 y 130.829 (\257)s 52.663 y 130.829 (\257)s 10 f 55.663 y 134.829 (\277)s 11 f 57.463 y 140.075 (i)s 0 f 55.663 y 144.07 (V)s 11 f 50.709 y 154.695 (N)s 15 f 51.909 y 162.296 (\260)s 11 f 50.709 y 167.794 (;\042)s 1 f 55.663 y 175.778 (\050)s 10 f 180.444 (\276)s 11 f 57.463 y 187.301 (s)s 1 f 55.663 y 192.43 (\051)s 10 f 197.097 (ds)s 13 f 31.543 y 208.968 (3)s 53.143 y 208.968 (5)s 12 f 55.663 y 220.301 (\267)s 232.968 (k)s 10 f 238.968 (V)s 12 f 248.635 (k)s 14 f 57.463 y 254.635 (1)s 0 f 55.663 y 264.801 (E)s 2 f 49.43 y 273.868 (\050)s 11 f 277.618 (K)s 2 f 286.27 (\051)s 11 f 58.433 y 273.868 (\271)s 15 f 56.033 y 279.703 (\260)s 13 f 31.543 y 292.62 (2)s 53.143 y 292.62 (4)s 10 f 55.663 y 300.62 (\260)s 11 f 50.709 y 307.499 (d)s 13 f 44.263 y 325.097 (X)s 11 f 70.003 y 315.094 (i)s 14 f 318.49 (2)s 2 f 324.956 (\244)s 15 f 71.21 y 331.523 (M)s 339.881 (N)s 72.41 y 346.336 (\260)s 13 f 39.33 y 354.434 (Z)s 11 f 42.296 y 366.434 (T)s 2 f 66.597 y 361.1 (0)s 10 f 55.663 y 375.993 (\277)s 11 f 57.463 y 381.239 (i)s 0 f 55.663 y 385.234 (V)s 11 f 50.709 y 395.859 (N)s 15 f 51.909 y 403.46 (\260)s 11 f 50.709 y 408.958 (;\042)s 1 f 55.663 y 416.942 (\050)s 10 f 421.608 (\276)s 11 f 57.463 y 428.465 (s)s 1 f 55.663 y 433.595 (\051)s 10 f 438.261 (ds)s 13 f 31.543 y 450.132 (3)s 53.143 y 450.132 (5)s 10 f 55.663 y 460.132 (:)s 1 f 110.037 y -5.69 (Denote)s 7.167 .48 36.413 100.263 r 10 f 110.037 y 36.413 (f)s 11 f 102.27 y 43.58 (T)s 1 f 110.037 y 56.034 (=)s 2 f 105.312 y 72.791 (1)s 6.96 .48 71.702 107.277 r 11 f 114.175 y 71.702 (T)s 13 f 100.37 y 82.102 (R)s 11 f 103.336 y 90.102 (T)s 2 f 114.303 y 87.769 (0)s 10 f 110.037 y 99.662 (f)s 11 f 105.682 y 106.828 (s)s 2 f 113.902 y 105.537 (\050)s 11 f 109.287 (M)s 2 f 119.338 (+2\051)s 11 f 135.238 (N)s 15 f 115.102 y 142.839 (\260)s 10 f 110.037 y 148.937 (ds)s 1 f 160.808 (,)s 169.313 (where)s 10 f 204.949 (f)s 11 f 105.682 y 212.116 (s)s 2 f 113.902 y 210.825 (\050)s 11 f 214.575 (M)s 2 f 224.626 (+2\051)s 11 f 240.526 (N)s 15 f 115.102 y 248.127 (\260)s 1 f 110.037 y 259.162 (is)s 272.166 (the)s 293.769 (probabilit)s 344.803 (y)s 356.073 (densit)s 387.14 (y)s 398.41 (with)s 426.68 (resp)s 448.447 (ect)s 133.308 y -5.69 (to)s 10 f 10.077 (\272)s 11 f 135.475 y 16.004 (P)s 22.372 (;)s 2 f 25.222 (\050)s 11 f 28.972 (M)s 2 f 39.024 (+2\051)s 11 f 54.924 (N)s 15 f 136.675 y 62.525 (\260)s 1 f 133.308 y 73.79 (=)s 10 f 88.29 (\272)s 11 f 126.808 y 94.981 (M)s 104.516 (;N)s 15 f 128.008 y 114.967 (\260)s 11 f 136.835 y 94.217 (P)s 1 f 133.308 y 126.165 (of)s 140.932 (the)s 162.699 (restriction)s 221.265 (of)s 236.032 (the)s 257.799 (measure)s 10 f 305.666 (\271)s 11 f 128.954 y 312.896 (K)s 321.031 (;\257)s 1 f 133.308 y 330.354 (\050)s 10 f 335.021 (s)s 1 f 340.646 (\051)s 350.413 (to)s 366.179 (the)s 387.946 (b)s 394.946 (o)s 400.613 (x)s 412.046 (\244)s 2 f 135.475 y 420.38 (\050)s 11 f 424.13 (M)s 2 f 434.181 (+2\051)s 11 f 450.081 (N)s 15 f 136.675 y 457.682 (\260)s 1 f 150.108 y -5.69 (\050see)s 19.077 (section)s 59.844 (3\051.)s 81.279 (Since)s 113.313 (the)s 134.68 (function)s 13 f 141.108 y 182.381 (P)s 11 f 153.708 y 195.048 (i)s 14 f 198.443 (2)s 2 f 204.91 (\244)s 15 f 154.915 y 211.476 (M)s 219.835 (N)s 156.115 y 226.289 (\260)s 10 f 150.108 y 234.987 (\277)s 11 f 151.908 y 240.233 (i)s 0 f 150.108 y 244.228 (V)s 11 f 145.754 y 254.853 (N)s 15 f 146.954 y 262.454 (\260)s 11 f 145.754 y 267.952 (;\042)s 1 f 150.108 y 275.936 (\050)s 10 f 280.602 (\276)s 1 f 287.89 (\051)s 297.257 (dep)s 316.257 (ends)s 344.358 (on)s 361.725 (the)s 383.092 (con\257guration)s 10 f 456.493 (\276)s 1 f 172.282 y -5.69 (only)s 21.235 (through)s 67.193 (the)s 88.452 (v)s 94.118 (ariables)s 13 f 162.562 y 138.81 (\251)s 10 f 172.282 y 145.81 (\276)s 1 f 153.098 (\050)s 10 f 157.764 (k)s 1 f 164.389 (\051)s 175.375 (:)s 10 f 185.028 (k)s 12 f 195.972 (2)s 1 f 208.292 (\244)s 2 f 174.449 y 216.625 (\050)s 11 f 220.375 (M)s 2 f 230.427 (+1\051)s 11 f 246.327 (N)s 15 f 175.649 y 253.928 (\260)s 13 f 162.562 y 260.026 (\252)s 1 f 172.282 y 267.026 (,)s 275.099 (b)s 281.432 (y)s 292.357 (F)s 299.19 (ubini\047s)s 338.515 (theorem,)s 389.288 (Diric)s 414.822 (hlet)s 439.414 (form)s 189.082 y -5.69 (con)s 11.976 (v)s 17.977 (exit)s 37.31 (y)s 47.612 (and)s 70.913 (Corollary)s 123.949 (4.4,)s 146.59 (there)s 177.258 (exists)s 210.36 (a)s 220.329 (p)s 227.329 (ositiv)s 255.395 (e)s 264.697 (constan)s 304.431 (t)s 10 f 313.066 (C)s 1 f 326.469 (that)s 352.437 (dep)s 371.437 (ends)s 398.806 (on)s 10 f 415.441 (M)s 427.724 (;)s 433.058 (\257)s 1 f 444.447 (and)s 10 f 205.882 y -5.69 (P)s 1 f 7.681 (suc)s 24.081 (h)s 34.747 (that)s 60.747 (the)s 81.414 (righ)s 101.781 (t)s 110.447 (hand)s 140.448 (side)s 164.514 (of)s 178.181 (the)s 198.848 (last)s 221.581 (inequalit)s 266.914 (y)s 277.248 (is)s 289.314 (b)s 296.314 (ounded)s 338.315 (b)s 344.648 (y)s 13 f 229.968 y 10.641 (8)s 240.769 y 10.641 (\074)s 262.369 y 10.641 (:)s 10 f 254.569 y 21.308 (T)s 12 f 29.987 (k)s 10 f 35.987 (V)s 12 f 45.654 (k)s 14 f 256.369 y 51.654 (1)s 13 f 238.235 y 63.821 (Z)s 10 f 254.569 y 77.821 (\260)s 11 f 249.614 y 84.7 (d)s 13 f 243.169 y 102.298 (X)s 11 f 268.909 y 92.295 (i)s 14 f 95.691 (2)s 2 f 102.157 (\244)s 15 f 270.115 y 108.724 (M)s 117.082 (N)s 271.315 y 123.537 (\260)s 10 f 254.569 y 131.635 (\277)s 11 f 256.369 y 136.88 (i)s 0 f 254.569 y 140.876 (V)s 11 f 249.614 y 151.501 (N)s 15 f 250.814 y 159.101 (\260)s 11 f 249.614 y 164.599 (;\042)s 1 f 254.569 y 172.583 (\050)s 10 f 177.25 (\276)s 1 f 184.537 (\051)s 7.167 .48 189.204 244.795 r 10 f 254.569 y 189.204 (f)s 11 f 246.802 y 196.371 (T)s 1 f 254.569 y 203.93 (\050)s 10 f 208.597 (\276)s 1 f 215.885 (\051)s 10 f 220.551 (d\272)s 11 f 248.069 y 233.489 (M)s 243.024 (;N)s 15 f 249.269 y 253.475 (\260)s 11 f 258.095 y 232.725 (P)s 1 f 254.569 y 259.573 (\050)s 10 f 264.239 (\276)s 1 f 271.527 (\051)s 12 f 278.86 (\241)s 10 f 290.86 (A\260)s 11 f 249.614 y 306.74 (d)s 14 f 311.735 (\241)s 2 f 319.235 (2)s 10 f 254.569 y 324.618 (D)s 2 f 256.735 y 334.553 (\050)s 11 f 338.303 (M)s 2 f 348.355 (+2\051)s 11 f 364.255 (N)s 15 f 257.935 y 371.856 (\260)s 13 f 244.849 y 377.954 (\241)s 7.167 .48 383.454 244.795 r 10 f 254.569 y 383.454 (f)s 11 f 246.802 y 390.621 (T)s 13 f 244.849 y 398.18 (\242)s 229.968 y 403.68 (9)s 240.769 y 403.68 (=)s 262.369 y 403.68 (;)s 1 f 254.569 y 417.014 (+)s 10 f 429.014 (AC)s 1 f 303.769 y -5.69 (for)s 12.886 (all)s 29.762 (p)s 36.762 (ositiv)s 64.828 (e)s 10 f 74.371 (A)s 1 f 83.371 (.)s 92.665 (It)s 105.874 (follo)s 127.874 (ws)s 145.484 (that,)s 175.079 (in)s 189.288 (order)s 220.897 (to)s 235.773 (pro)s 252.806 (v)s 258.806 (e)s 268.349 (Lemma)s 311.391 (5.3)s 330.934 (it)s 343.143 (is)s 355.419 (enough)s 396.962 (to)s 411.838 (sho)s 428.904 (w)s 441.78 (that)s 320.569 y -5.69 (for)s 12.677 (eac)s 29.01 (h)s 39.677 (p)s 46.677 (ositiv)s 74.743 (e)s 10 f 84.077 (A)s 1 f 369.256 y -5.425 (lim)s 13.241 (sup)s 11 f 379.002 y 3.5 (\042)s 14 f 8.033 (!)s 2 f 17.6 (0)s 1 f 369.256 y 33.308 (lim)s 51.975 (sup)s 11 f 379.002 y 41.721 (\260)s 14 f 47.278 (!)s 2 f 56.845 (0)s 1 f 369.256 y 72.041 (sup)s 13 f 344.655 y 92.108 (8)s 355.455 y 92.108 (\074)s 377.056 y 92.108 (:)s 352.922 y 102.775 (Z)s 10 f 369.256 y 116.775 (\260)s 11 f 364.301 y 123.654 (d)s 13 f 357.855 y 141.252 (X)s 11 f 383.596 y 131.25 (i)s 14 f 134.645 (2)s 2 f 141.111 (\244)s 15 f 384.802 y 147.678 (M)s 156.036 (N)s 386.002 y 162.491 (\260)s 10 f 369.256 y 170.589 (\277)s 11 f 371.056 y 175.835 (i)s 0 f 369.256 y 179.83 (V)s 11 f 364.301 y 190.455 (N)s 15 f 365.501 y 198.056 (\260)s 11 f 364.301 y 203.554 (;\042)s 1 f 369.256 y 211.537 (\050)s 10 f 216.204 (\276)s 1 f 223.492 (\051)s 10 f 228.158 (f)s 1 f 235.325 (\050)s 10 f 239.992 (\276)s 1 f 247.279 (\051)s 10 f 251.946 (d\272)s 11 f 362.756 y 264.883 (M)s 274.418 (;N)s 15 f 363.956 y 284.869 (\260)s 11 f 372.782 y 264.119 (P)s 1 f 369.256 y 290.967 (\050)s 10 f 295.634 (\276)s 1 f 302.921 (\051)s 12 f 310.255 (\241)s 10 f 322.255 (A\260)s 11 f 364.301 y 338.134 (d)s 14 f 343.13 (\241)s 2 f 350.63 (2)s 10 f 369.256 y 356.013 (D)s 2 f 371.422 y 365.948 (\050)s 11 f 369.698 (M)s 2 f 379.75 (+2\051)s 11 f 395.65 (N)s 15 f 372.622 y 403.251 (\260)s 13 f 359.535 y 409.349 (\241)s 10 f 369.256 y 414.849 (f)s 13 f 359.535 y 422.015 (\242)s 344.655 y 427.515 (9)s 355.455 y 427.515 (=)s 377.056 y 427.515 (;)s 1 f 369.256 y 441.515 (=)s 454.182 (0)s 10 f 460.182 (;)s 1 f 422.362 y -5.69 (where)s 29.01 (the)s 49.677 (suprem)s 87.443 (um)s 108.11 (is)s 120.177 (carried)s 160.243 (o)s 165.91 (v)s 171.91 (er)s 185.943 (all)s 202.61 (probabilit)s 253.644 (y)s 263.977 (densities)s 10 f 312.777 (f)s 1 f 323.944 (with)s 351.277 (resp)s 373.044 (ect)s 392.377 (to)s 10 f 407.044 (\272)s 11 f 415.862 y 413.735 (M)s 423.27 (;N)s 15 f 417.062 y 433.721 (\260)s 11 f 425.889 y 412.972 (P)s 1 f 422.362 y 439.819 (.)s 440.133 y 8.71 (The)s 33.728 (pro)s 51.428 (of)s 65.445 (of)s 79.463 (this)s 103.214 (limit)s 132.232 (relies)s 163.35 (on)s 180.368 (the)s 201.386 (usual)s 233.137 (one)s 255.488 (and)s 279.173 (t)s 283.506 (w)s 291.839 (o)s 302.19 (blo)s 318.524 (c)s 323.524 (ks)s 338.942 (estimates)s 392.093 (\050cf.)s 415.48 ([GPV])s 453.08 (or)s 456.933 y -5.69 ([K)s 6.643 (O)s 15.643 (V]\051)s 36.643 (and)s 59.977 (therefore)s 110.377 (is)s 122.443 (omitted.)s 8.16 .48 177.11 450.333 r .48 7.2 177.11 457.533 r .48 7.2 184.79 457.533 r 8.16 .48 177.11 458.013 r 0 f 491.776 y -5.69 (Lemma)s 42.804 (5.4)s 1 f 68.217 (\050Uniqueness\051.)s 17 f 144.89 (F)s 151.803 (or)s 166.939 (any)s 10 f 189.588 (T)s 201.6 (\076)s 1 f 214.267 (0)s 17 f 220.267 (,)s 227.959 (the)s 247.541 (e)s 252.448 (quation)s 295.03 (\0503.5\051)s 324.732 (has)s 345.848 (a)s 355.923 (unique)s 394.212 (we)s 407.092 (ak)s 422.687 (solution)s 508.576 y -5.69 (in)s 9.03 (the)s 28.963 (class)s 10 f 57.789 (L)s 14 f 504.221 y 65.956 (1)s 13 f 498.856 y 76.123 (\241)s 1 f 508.576 y 81.623 ([0)s 10 f 90.956 (;)s 96.289 (T)s 1 f 104.969 (])s 13 f 498.856 y 108.302 (\242)s 12 f 508.576 y 116.469 (\243)s 1 f 128.469 (I)s 130.642 (R)s 11 f 503.343 y 139.475 (d)s 13 f 498.856 y 145.071 (\242)s 12 f 508.576 y 153.237 (\243)s 10 f 165.237 (L)s 14 f 504.221 y 173.404 (1)s 13 f 498.856 y 183.571 (\241)s 1 f 508.576 y 189.071 ([0)s 10 f 198.404 (;)s 203.737 (T)s 1 f 212.417 (])s 13 f 498.856 y 215.75 (\242)s 12 f 508.576 y 223.916 (\243)s 1 f 235.916 (I)s 238.09 (R)s 11 f 503.343 y 246.923 (d)s 13 f 498.856 y 252.519 (\242)s 1 f 508.576 y 258.019 (.)s 22 f 535.249 y -5.69 (Pro)s 13.51 (of.)s 1 f 32.658 (The)s 57.596 (pro)s 75.296 (of)s 89.234 (follo)s 111.234 (ws)s 128.906 (the)s 149.844 (argumen)s 194.877 (ts)s 208.549 (in)s 222.82 ([GL])s 250.675 (adapted)s 296.946 (to)s 311.884 (the)s 332.823 (in\257nite)s 373.761 (v)s 379.761 (olume)s 415.366 (case.)s 446.247 (F)s 453.08 (or)s 552.049 y -5.69 (a)s 4.31 (p)s 11.31 (ositiv)s 39.377 (e)s 48.71 (time)s 10 f 76.043 (t)s 83.71 (\076)s 1 f 96.376 (0,)s 10 f 109.71 (f)s 12 f 120.21 (2)s 131.543 (C)s 11 f 553.849 y 137.861 (K)s 1 f 552.049 y 147.113 (\050I)s 153.953 (R)s 11 f 546.816 y 162.787 (d)s 1 f 552.049 y 168.382 (\051)s 177.049 (and)s 10 f 200.382 (\042)s 209.311 (\076)s 1 f 221.978 (0,)s 235.311 (let)s 12 f 252.644 (H)s 11 f 546.283 y 262.894 (f)s 555.003 y 262.779 (t;\042)s 1 f 552.049 y 277.721 (:)s 284.387 ([0)s 10 f 293.721 (;)s 299.054 (t)s 1 f 303.387 (])s 12 f 309.387 (\243)s 1 f 321.387 (I)s 323.56 (R)s 11 f 546.816 y 332.394 (d)s 12 f 552.049 y 341.322 (\241)s 348.656 (!)s 1 f 363.989 (I)s 366.163 (R)s 378.996 (b)s 385.996 (e)s 395.329 (de\257ned)s 436.663 (b)s 442.996 (y)s 12 f 585.803 y 154.552 (H)s 11 f 580.036 y 164.802 (f)s 588.756 y 164.686 (t;\042)s 1 f 585.803 y 176.295 (\050)s 10 f 180.961 (s;)s 191.92 (x)s 1 f 198.778 (\051)s 206.778 (=)s 13 f 576.083 y 219.445 (\241)s 10 f 585.803 y 224.945 (f)s 12 f 234.778 (\244)s 10 f 243.445 (h)s 11 f 587.603 y 250.359 (t)s 2 f 253.984 (+)s 11 f 261.35 (\042)s 14 f 265.884 (\241)s 11 f 273.384 (s)s 13 f 576.083 y 278.513 (\242)s 1 f 585.803 y 284.013 (\050)s 10 f 288.68 (x)s 1 f 295.538 (\051)s 10 f 300.205 (;)s 1 f 619.556 y -5.69 (where)s 10 f 29.01 (h)s 11 f 621.356 y 35.924 (t)s 2 f 39.549 (+)s 11 f 46.915 (\042)s 14 f 51.449 (\241)s 11 f 58.949 (s)s 1 f 619.556 y 64.078 (\050)s 10 f 68.745 (:)s 1 f 72.078 (\051)s 80.745 (is)s 92.812 (the)s 113.478 (heat)s 140.145 (k)s 146.145 (ernel)s 175.512 (giv)s 190.845 (en)s 206.845 (b)s 213.179 (y)s 10 f 666.343 y 59.088 (h)s 11 f 668.143 y 66.002 (t)s 2 f 69.627 (+)s 11 f 76.993 (\042)s 14 f 81.527 (\241)s 11 f 89.027 (s)s 1 f 666.343 y 94.156 (\050)s 10 f 98.823 (x)s 1 f 105.681 (\051)s 113.681 (=)s 13 f 656.623 y 126.348 (\241)s 1 f 666.343 y 131.848 (2)s 10 f 137.848 (\274)s 1 f 145.119 (\050)s 10 f 149.785 (t)s 1 f 156.785 (+)s 10 f 168.785 (\042)s 12 f 177.048 (\241)s 10 f 189.048 (s)s 1 f 194.673 (\051)s 13 f 656.623 y 199.339 (\242)s 14 f 659.109 y 204.839 (\241)s 11 f 212.339 (d=)s 2 f 222.252 (2)s 1 f 666.343 y 229.635 (exp)s 13 f 645.822 y 249.968 (\050)s 12 f 666.343 y 262.302 (\241)s 1 f 658.225 y 303.685 (1)s 61.887 .48 275.741 663.583 r 675.223 y 275.741 (4)s 13 f 665.502 y 281.742 (\241)s 10 f 675.223 y 287.242 (t)s 1 f 294.241 (+)s 10 f 306.241 (\042)s 12 f 314.504 (\241)s 10 f 326.504 (s)s 13 f 665.502 y 332.129 (\242)s 11 f 651.343 y 347.298 (d)s 13 f 654.943 y 341.129 (X)s 11 f 680.776 y 341.069 (k)s 2 f 346.373 (=1)s 1 f 666.343 y 358.523 (\050)s 10 f 363.19 (x)s 11 f 668.143 y 370.048 (k)s 1 f 666.343 y 375.952 (\051)s 2 f 661.388 y 380.619 (2)s 13 f 645.822 y 386.002 (\051)s 10 f 666.343 y 395.669 (:)s 1 f 705.976 y 223.045 (29)s do-end end endp %%Page: 30 30 %%BeginPageSetup initializepage (Raffaele Esposito; page: 30 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f1_12 sf ( )S -997 -1000 :M f2_12 sf ( )S -993 -1000 :M f10_12 sf ( )S -985 -1000 :M f11_12 sf ( )S -976 -1000 :M f12_12 sf ( )S -964 -1000 :M f13_12 sf ( )S -954 -1000 :M f14_12 sf ( )S -941 -1000 :M f15_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 6.31 y -5.69 (In)s 10.036 (the)s 31.429 (App)s 54.095 (endix)s 87.155 (it)s 99.881 (is)s 112.674 (pro)s 129.707 (v)s 135.707 (en)s 152.433 (that)s 12 f 179.16 (H)s 11 f .543 y 189.41 (f)s 9.263 y 189.294 (t;\042)s 1 f 6.31 y 205.629 (solv)s 225.695 (es)s 240.488 (the)s 261.881 (equation)s 10 f 311.607 (@)s 11 f 8.11 y 317.978 (t)s 10 f 6.31 y 322.203 (\275)s 1 f 332.951 (=)s 346.828 (\242)s 10 f 356.828 (\275)s 1 f 367.758 (on)s 385.151 ([0)s 10 f 394.484 (;)s 399.817 (t)s 1 f 404.151 (])s 12 f 410.635 (\243)s 1 f 423.119 (I)s 425.292 (R)s 11 f 1.076 y 434.125 (d)s 1 f 6.31 y 444.447 (and)s 23.11 y -5.69 (that)s 11 f 34.943 y 105.827 (d)s 13 f 38.543 y 99.658 (X)s 11 f 64.377 y 99.598 (k)s 2 f 104.902 (=1)s 13 f 33.61 y 119.052 (Z)s 11 f 36.576 y 131.052 (t)s 2 f 60.877 y 125.719 (0)s 13 f 36.143 y 137.277 (\257)s 43.343 y 137.277 (\257)s 50.543 y 137.277 (\257)s 40.223 y 141.277 (\255)s 10 f 49.943 y 146.944 (@)s 11 f 51.743 y 153.314 (k)s 12 f 49.943 y 159.219 (H)s 11 f 44.177 y 169.469 (f)s 52.896 y 169.353 (t;\042)s 1 f 49.943 y 180.962 (\050)s 10 f 185.628 (s;)s 196.587 (:)s 1 f 199.92 (\051)s 13 f 40.223 y 204.587 (\256)s 36.143 y 210.253 (\257)s 43.343 y 210.253 (\257)s 50.543 y 210.253 (\257)s 10 f 49.943 y 216.253 (ds)s 12 f 231.457 (\267)s 10 f 244.124 (C)s 2 f 51.743 y 252.701 (1)s 13 f 40.223 y 258.084 (\241)s 12 f 40.107 y 263.584 (p)s 24.596 .48 273.584 40.107 r 10 f 49.943 y 273.584 (t)s 1 f 280.584 (+)s 10 f 292.584 (\042)s 12 f 300.846 (\241)s 40.714 y 312.846 (p)s 5.596 .48 322.846 40.714 r 10 f 49.943 y 322.846 (\042)s 13 f 40.223 y 328.442 (\242)s 12 f 49.943 y 333.942 (k)s 10 f 339.942 (f)s 12 f 347.109 (k)s 2 f 51.743 y 353.109 (1)s 12 f 85.273 y 231.457 (\267)s 10 f 244.124 (C)s 2 f 87.073 y 252.701 (1)s 12 f 74.936 y 258.084 (p)s 4.333 .48 268.084 74.936 r 10 f 85.273 y 268.084 (t)s 12 f 272.417 (k)s 10 f 278.417 (f)s 12 f 285.584 (k)s 2 f 87.073 y 291.584 (1)s 10 f 85.273 y 296.967 (;)s 1 f 61.691 y 439.114 (\0505)s 10 f 449.78 (:)s 1 f 453.114 (1\051)s 106.476 y -5.69 (where)s 10 f 29.865 (C)s 2 f 108.276 y 38.441 (1)s 1 f 106.476 y 48.679 (is)s 61.601 (a)s 72.455 (p)s 79.455 (ositiv)s 107.522 (e)s 117.71 (constan)s 157.444 (t)s 166.965 (that)s 193.82 (dep)s 212.82 (ends)s 241.075 (on)s 10 f 258.596 (d)s 1 f 269.697 (and)s 10 f 293.885 (@)s 11 f 108.276 y 300.256 (k)s 1 f 106.476 y 311.015 (is)s 323.936 (the)s 345.457 (\257rst)s 371.079 (deriv)s 396.779 (ativ)s 416.779 (e)s 426.967 (in)s 10 f 441.822 (k)s 1 f 448.447 (-th)s 123.276 y -5.69 (direction.)s 140.196 y 8.71 (Let)s 31.745 (us)s 48.681 (consider)s 96.983 (\050)s 10 f 101.65 (m;)s 117.519 (\301)s 1 f 124.669 (\051)s 134.872 (and)s 159.74 (\050)s 13 f 166.342 (e)s 10 f 164.407 (m)s 174.943 (;)s 13 f 137.03 y 181.518 (e)s 10 f 140.196 y 180.277 (\301)s 1 f 187.427 (\051)s 197.629 (t)s 201.962 (w)s 210.296 (o)s 221.831 (w)s 230.164 (eak)s 253.367 (solutions)s 305.036 (of)s 320.238 (\0503.5\051)s 350.44 (with)s 379.309 (the)s 401.511 (same)s 433.114 (initial)s 156.996 y -5.69 (datum.)s 37.481 (Set)s 10.536 .48 58.316 150.39 r 10 f 156.996 y 58.316 (m)s 1 f 72.465 (=)s 10 f 85.412 (m)s 12 f 98.727 (\241)s 13 f 112.774 (e)s 10 f 110.839 (m)s 1 f 121.375 (,)s 7.15 .48 128.919 147.223 r 10 f 156.996 y 128.919 (\301)s 1 f 139.682 (=)s 10 f 152.629 (\301)s 12 f 162.558 (\241)s 13 f 153.83 y 175.911 (e)s 10 f 156.996 y 174.67 (\301)s 1 f 185.988 (and)s 10 f 209.489 (W)s 1 f 226.103 (=)s 12 f 239.049 (j)s 10.536 .48 242.383 150.39 r 10 f 156.996 y 242.383 (m)s 12 f 252.919 (j)s 1 f 259.031 (+)s 12 f 271.143 (j)s 7.15 .48 274.476 147.223 r 10 f 156.996 y 274.476 (\301)s 12 f 281.626 (j)s 1 f 284.96 (.)s 294.131 (T)s 301.797 (o)s 311.966 (k)s 317.966 (eep)s 339.467 (the)s 360.302 (notation)s 408.47 (simple,)s 449.414 (for)s 173.796 y -5.69 (\050)s 10 f -1.024 (s;)s 9.935 (x)s 1 f 16.793 (\051)s 12 f 25.125 (2)s 1 f 36.789 (I)s 38.963 (R)s 2 f 175.596 y 47.796 (+)s 12 f 173.796 y 58.562 (\243)s 1 f 70.695 (I)s 72.868 (R)s 11 f 168.563 y 81.701 (d)s 1 f 173.796 y 87.297 (,)s 94.879 (w)s 103.212 (e)s 112.744 (shall)s 141.01 (denote)s 10.536 .48 179.876 167.19 r 10 f 173.796 y 179.876 (m)s 11 f 175.596 y 190.412 (s)s 1 f 173.796 y 195.541 (\050)s 10 f 200.208 (x)s 1 f 207.066 (\051)s 215.398 (=)s 10.536 .48 228.396 167.19 r 10 f 173.796 y 228.396 (m)s 1 f 238.932 (\050)s 10 f 243.599 (s;)s 254.557 (x)s 1 f 261.415 (\051)s 270.281 (and)s 7.15 .48 293.813 164.023 r 10 f 173.796 y 293.813 (\301)s 11 f 176.73 y 300.963 (s)s 1 f 173.796 y 309.757 (=)s 7.15 .48 322.755 164.023 r 10 f 173.796 y 322.755 (\301)s 1 f 329.905 (\050)s 10 f 334.572 (s;)s 345.53 (x)s 1 f 352.389 (\051.)s 366.319 (F)s 373.152 (or)s 388.051 (1)s 12 f 397.716 (\267)s 10 f 410.714 (k)s 12 f 421.004 (\267)s 10 f 434.002 (d)s 1 f 444.447 (and)s 10 f 190.596 y -5.69 (s)s 3.268 (\076)s 1 f 15.935 (0,)s 29.268 (let)s 10 f 46.601 (M)s 11 f 192.396 y 58.243 (k)s 1 f 190.596 y 68.147 (and)s 10 f 91.481 (F)s 11 f 192.396 y 99.197 (k)s 1 f 190.596 y 109.101 (b)s 116.102 (e)s 125.435 (de\257ned)s 166.768 (b)s 173.102 (y)s 10 f 212.306 y 130.453 (M)s 11 f 214.106 y 142.095 (k)s 1 f 212.306 y 147.999 (\050)s 10 f 152.666 (m)s 11 f 214.106 y 163.202 (s)s 10 f 212.306 y 168.331 (;)s 173.664 (\301)s 11 f 214.106 y 180.815 (s)s 1 f 212.306 y 185.944 (\051)s 193.944 (=)s 13 f 202.586 y 206.61 (\241)s 10 f 212.306 y 212.11 (\301)s 11 f 214.106 y 219.26 (s)s 12 f 212.306 y 227.056 (\241)s 10 f 239.056 (m)s 2 f 207.351 y 249.592 (2)s 11 f 215.272 y 249.592 (s)s 13 f 202.586 y 254.976 (\242)s 260.476 (\241)s 10 f 212.306 y 265.976 (@)s 11 f 214.106 y 272.346 (k)s 10 f 212.306 y 278.251 (J)s 12 f 288.726 (\244)s 10 f 297.392 (m)s 11 f 214.106 y 307.928 (s)s 13 f 202.586 y 313.058 (\242)s 10 f 212.306 y 318.558 (;)s 232.706 y 134.378 (F)s 11 f 234.506 y 142.095 (k)s 1 f 232.706 y 147.999 (\050)s 10 f 152.666 (m)s 11 f 234.506 y 163.202 (s)s 10 f 232.706 y 168.331 (;)s 173.664 (\301)s 11 f 234.506 y 180.815 (s)s 1 f 232.706 y 185.944 (\051)s 193.944 (=)s 10 f 206.61 (m)s 11 f 234.506 y 217.146 (s)s 13 f 222.986 y 222.276 (\241)s 1 f 232.706 y 227.776 (1)s 12 f 236.442 (\241)s 10 f 248.442 (\301)s 11 f 234.506 y 255.592 (s)s 13 f 222.986 y 260.721 (\242)s 266.221 (\241)s 10 f 232.706 y 271.721 (@)s 11 f 234.506 y 278.092 (k)s 10 f 232.706 y 283.997 (J)s 12 f 294.471 (\244)s 10 f 303.138 (m)s 11 f 234.506 y 313.674 (s)s 13 f 222.986 y 318.803 (\242)s 10 f 232.706 y 324.303 (:)s 1 f 254.914 y -5.69 (Observ)s 31.077 (e)s 40.41 (that)s 66.41 (for)s 84.777 (all)s 10 f 101.443 (s)s 12 f 110.402 (2)s 1 f 121.735 ([0)s 10 f 131.068 (;)s 136.402 (t)s 1 f 140.735 (],)s 10 f 278.755 y 63.376 (M)s 11 f 280.555 y 75.018 (k)s 1 f 278.755 y 80.922 (\050)s 10 f 85.589 (m)s 11 f 280.555 y 96.125 (s)s 10 f 278.755 y 101.254 (;)s 106.587 (\301)s 11 f 280.555 y 113.737 (s)s 1 f 278.755 y 118.867 (\051)s 12 f 126.2 (\241)s 10 f 138.2 (M)s 11 f 280.555 y 149.842 (k)s 1 f 278.755 y 155.746 (\050)s 13 f 162.347 (e)s 10 f 160.412 (m)s 11 f 280.555 y 170.949 (s)s 10 f 278.755 y 176.078 (;)s 13 f 275.588 y 182.653 (e)s 10 f 278.755 y 181.411 (\301)s 11 f 280.555 y 188.561 (s)s 1 f 278.755 y 193.69 (\051)s 201.69 (=)s 13 f 269.035 y 211.024 (\241)s 10 f 278.755 y 216.524 (@)s 11 f 280.555 y 222.894 (k)s 10 f 278.755 y 228.799 (J)s 12 f 239.274 (\244)s 10.536 .48 247.94 272.149 r 10 f 278.755 y 247.94 (m)s 11 f 280.555 y 258.476 (s)s 13 f 269.035 y 263.606 (\242)s 269.106 (\241)s 275.588 y 275.847 (e)s 10 f 278.755 y 274.606 (\301)s 11 f 280.555 y 281.756 (s)s 12 f 278.755 y 289.551 (\241)s 13 f 303.486 (e)s 10 f 301.551 (m)s 2 f 273.8 y 312.087 (2)s 11 f 281.722 y 312.087 (s)s 13 f 269.035 y 317.471 (\242)s 1 f 305.155 y 213.69 (+)s 13 f 295.435 y 225.69 (\241)s 10 f 305.155 y 231.19 (@)s 11 f 306.955 y 237.561 (k)s 10 f 305.155 y 243.465 (J)s 12 f 253.94 (\244)s 10 f 262.607 (m)s 11 f 306.955 y 273.143 (s)s 13 f 295.435 y 278.272 (\242)s 291.835 y 283.772 (h)s 7.15 .48 289.439 295.382 r 10 f 305.155 y 289.439 (\301)s 11 f 308.089 y 296.589 (s)s 12 f 305.155 y 304.385 (\241)s 10.536 .48 316.385 298.549 r 10 f 305.155 y 316.385 (m)s 11 f 306.955 y 326.921 (s)s 13 f 295.435 y 332.05 (\241)s 10 f 305.155 y 337.55 (m)s 11 f 306.955 y 348.086 (s)s 1 f 305.155 y 355.882 (+)s 13 f 369.817 (e)s 10 f 367.882 (m)s 11 f 306.955 y 378.418 (s)s 13 f 295.435 y 383.547 (\242)s 291.835 y 389.047 (i)s 1 f 330.297 y -5.69 (and)s 10 f 346.93 y 65.828 (F)s 11 f 348.73 y 73.544 (k)s 1 f 346.93 y 79.448 (\050)s 10 f 84.115 (m)s 11 f 348.73 y 94.651 (s)s 10 f 346.93 y 99.78 (;)s 105.114 (\301)s 11 f 348.73 y 112.264 (s)s 1 f 346.93 y 117.393 (\051)s 12 f 124.726 (\241)s 10 f 136.726 (F)s 11 f 348.73 y 144.443 (k)s 1 f 346.93 y 150.347 (\050)s 13 f 156.949 (e)s 10 f 155.014 (m)s 11 f 348.73 y 165.55 (s)s 10 f 346.93 y 170.679 (;)s 13 f 343.763 y 177.254 (e)s 10 f 346.93 y 176.012 (\301)s 11 f 348.73 y 183.162 (s)s 1 f 346.93 y 188.292 (\051)s 196.292 (=)s 13 f 337.21 y 205.625 (\241)s 10 f 346.93 y 211.125 (@)s 11 f 348.73 y 217.496 (k)s 10 f 346.93 y 223.4 (J)s 12 f 233.875 (\244)s 10.536 .48 242.542 340.323 r 10 f 346.93 y 242.542 (m)s 11 f 348.73 y 253.078 (s)s 13 f 337.21 y 258.207 (\242)s 10 f 346.93 y 263.707 (m)s 11 f 348.73 y 274.243 (s)s 13 f 337.21 y 279.372 (\241)s 1 f 346.93 y 284.872 (1)s 12 f 293.539 (\241)s 10 f 305.539 (\301)s 11 f 348.73 y 312.689 (s)s 13 f 337.21 y 317.818 (\242)s 1 f 367.33 y 208.292 (+)s 13 f 357.61 y 220.291 (\241)s 10 f 367.33 y 225.792 (@)s 11 f 369.13 y 232.162 (k)s 10 f 367.33 y 238.067 (J)s 12 f 248.541 (\244)s 13 f 259.143 (e)s 10 f 257.208 (m)s 11 f 369.13 y 267.744 (s)s 13 f 357.61 y 272.873 (\242)s 278.373 (\243)s 10.536 .48 283.374 360.723 r 10 f 367.33 y 283.374 (m)s 11 f 369.13 y 293.91 (s)s 1 f 367.33 y 299.039 (\0501)s 12 f 312.372 (\241)s 10 f 324.372 (\301)s 11 f 369.13 y 331.522 (s)s 1 f 367.33 y 336.651 (\051)s 12 f 343.985 (\241)s 13 f 357.919 (e)s 10 f 355.985 (m)s 11 f 369.13 y 366.521 (s)s 7.15 .48 371.65 357.557 r 10 f 367.33 y 371.65 (\301)s 11 f 370.263 y 378.8 (s)s 13 f 357.61 y 383.929 (\244)s 10 f 367.33 y 388.929 (:)s 1 f 389.2 y -5.69 (It)s 9.045 (follo)s 31.045 (ws)s 50.18 (that)s 77.915 (there)s 110.35 (exists)s 145.218 (a)s 156.953 (p)s 163.953 (ositiv)s 192.02 (e)s 203.088 (constan)s 242.822 (t)s 10 f 253.223 (C)s 2 f 391 y 261.8 (2)s 1 f 389.2 y 272.918 (that)s 300.653 (dep)s 319.653 (ends)s 348.788 (on)s 12 f 367.19 (k)s 10 f 373.19 (m)s 12 f 383.726 (k)s 14 f 391 y 389.726 (1)s 1 f 389.2 y 399.893 (,)s 12 f 409.395 (k)s 10 f 415.395 (\301)s 12 f 422.545 (k)s 14 f 391 y 428.545 (1)s 1 f 389.2 y 444.447 (and)s 406 y -5.69 (sup)s 2 f 408.934 y 12.376 (1)s 14 f 17.16 (\267)s 11 f 24.66 (k)s 14 f 29.964 (\267)s 11 f 37.464 (d)s 12 f 406 y 45.059 (k)s 10 f 51.06 (@)s 11 f 407.8 y 57.43 (k)s 10 f 406 y 63.335 (J)s 12 f 71.143 (k)s 1 f 81.143 (suc)s 97.543 (h)s 108.21 (that,)s 137.543 (for)s 155.91 (almost)s 194.643 (ev)s 205.976 (ery)s 226.343 (\050)s 10 f 231.01 (s;)s 241.968 (x)s 1 f 248.826 (\051)s 12 f 256.826 (2)s 1 f 268.16 ([0)s 10 f 277.493 (;)s 282.826 (t)s 1 f 287.16 (])s 12 f 293.16 (\243)s 1 f 305.16 (I)s 307.333 (R)s 11 f 400.767 y 316.166 (d)s 1 f 406 y 321.762 (,)s 13 f 421.133 y 129.473 (\257)s 428.333 y 129.473 (\257)s 10 f 431.333 y 133.473 (M)s 11 f 433.133 y 145.114 (k)s 1 f 431.333 y 151.018 (\050)s 10 f 155.685 (m)s 11 f 433.133 y 166.221 (s)s 10 f 431.333 y 171.351 (;)s 176.684 (\301)s 11 f 433.133 y 183.834 (s)s 1 f 431.333 y 188.963 (\051)s 12 f 196.296 (\241)s 10 f 208.296 (M)s 11 f 433.133 y 219.938 (k)s 1 f 431.333 y 225.842 (\050)s 13 f 232.444 (e)s 10 f 230.509 (m)s 11 f 433.133 y 241.045 (s)s 10 f 431.333 y 246.174 (;)s 13 f 428.166 y 252.749 (e)s 10 f 431.333 y 251.507 (\301)s 11 f 433.133 y 258.657 (s)s 1 f 431.333 y 263.787 (\051)s 13 f 421.133 y 268.453 (\257)s 428.333 y 268.453 (\257)s 12 f 431.333 y 275.787 (\267)s 10 f 288.453 (C)s 2 f 433.133 y 297.03 (2)s 10 f 431.333 y 302.413 (R)s 1 f 311.617 (\050)s 10 f 316.284 (t)s 1 f 320.617 (\051)s 10 f 325.284 (;)s 13 f 441.533 y 137.323 (\257)s 448.733 y 137.323 (\257)s 10 f 451.733 y 141.323 (F)s 11 f 453.533 y 149.039 (k)s 1 f 451.733 y 154.944 (\050)s 10 f 159.61 (m)s 11 f 453.533 y 170.146 (s)s 10 f 451.733 y 175.276 (;)s 180.609 (\301)s 11 f 453.533 y 187.759 (s)s 1 f 451.733 y 192.888 (\051)s 12 f 200.221 (\241)s 10 f 212.221 (F)s 11 f 453.533 y 219.938 (k)s 1 f 451.733 y 225.842 (\050)s 13 f 232.444 (e)s 10 f 230.509 (m)s 11 f 453.533 y 241.045 (s)s 10 f 451.733 y 246.174 (;)s 13 f 448.566 y 252.749 (e)s 10 f 451.733 y 251.507 (\301)s 11 f 453.533 y 258.657 (s)s 1 f 451.733 y 263.787 (\051)s 13 f 441.533 y 268.453 (\257)s 448.733 y 268.453 (\257)s 12 f 451.733 y 275.787 (\267)s 10 f 288.453 (C)s 2 f 453.533 y 297.03 (2)s 10 f 451.733 y 302.413 (R)s 1 f 311.617 (\050)s 10 f 316.284 (t)s 1 f 320.617 (\051)s 10 f 325.284 (:)s 1 f 476.008 y -5.69 (Here)s 10 f 22.676 (R)s 1 f 31.881 (\050)s 10 f 36.547 (t)s 1 f 40.881 (\051)s 49.547 (stands)s 87.014 (for)s 105.381 (the)s 126.047 (essen)s 152.514 (tial)s 173.848 (sup)s 195.914 (of)s 10 f 209.581 (W)s 1 f 226.581 (in)s 240.581 ([0)s 10 f 249.914 (;)s 255.248 (t)s 1 f 259.581 (])s 12 f 265.581 (\243)s 1 f 277.581 (I)s 279.754 (R)s 11 f 470.774 y 288.588 (d)s 1 f 476.008 y 294.183 (:)s 10 f 497.016 y 144.883 (R)s 1 f 154.087 (\050)s 10 f 158.754 (t)s 1 f 163.087 (\051)s 171.087 (=)s 183.754 (ess)s 202.554 (sup)s 2 f 499.949 y 220.62 ([0)s 11 f 228.12 (;t)s 2 f 234.595 (])s 14 f 237.312 (\243)s 2 f 244.812 (I)s 246.119 (R)s 15 f 497.176 y 253.086 (d)s 13 f 487.296 y 258.724 (\241)s 10 f 497.016 y 264.224 (W)s 1 f 277.224 (\050)s 10 f 281.89 (s;)s 292.849 (x)s 1 f 299.707 (\051)s 13 f 487.296 y 304.374 (\242)s 10 f 497.016 y 309.874 (:)s 1 f 523.01 y 8.71 (Since)s 40.156 (\050)s 10 f 44.823 (m;)s 60.692 (\301)s 1 f 67.842 (\051)s 76.621 (and)s 100.067 (\050)s 13 f 106.669 (e)s 10 f 104.734 (m)s 115.27 (;)s 13 f 519.844 y 121.845 (e)s 10 f 523.01 y 120.604 (\301)s 1 f 127.754 (\051)s 136.533 (are)s 156.679 (t)s 161.012 (w)s 169.346 (o)s 179.458 (w)s 187.792 (eak)s 209.571 (solutions)s 259.817 (of)s 273.596 (\0503.5\051,)s 305.737 (w)s 314.071 (e)s 323.517 (obtain)s 360.963 (b)s 367.296 (y)s 377.742 (\0505.1\051)s 406.521 (that)s 432.634 (for)s 451.114 (all)s 539.81 y -5.69 (0)s 12 f 3.643 (\267)s 10 f 16.31 (\277)s 12 f 26.247 (\267)s 10 f 38.914 (t)s 13 f 558.683 y 17.864 (\257)s 565.883 y 17.864 (\257)s 573.083 y 17.864 (\257)s 562.763 y 21.864 (\255)s 10.536 .48 27.531 565.877 r 10 f 572.483 y 27.531 (m)s 1 f 38.067 (\050)s 10 f 42.733 (\277)s 48.671 (;)s 54.004 (:)s 1 f 57.338 (\051)s 10 f 62.004 (;)s 12 f 67.337 (H)s 11 f 567.529 y 77.588 (f)s 575.45 y 77.472 (\277)s 82.351 (;\042)s 1 f 572.483 y 90.335 (\050)s 10 f 95.002 (\277)s 100.939 (;)s 106.273 (:)s 1 f 109.606 (\051)s 13 f 562.763 y 114.273 (\256)s 558.683 y 119.939 (\257)s 565.883 y 119.939 (\257)s 573.083 y 119.939 (\257)s 1 f 572.483 y 127.273 (=)s 10 f 139.939 (\257)s 13 f 558.683 y 147.36 (\257)s 565.883 y 147.36 (\257)s 573.083 y 147.36 (\257)s 11 f 557.483 y 159.589 (d)s 13 f 561.083 y 153.42 (X)s 11 f 586.917 y 153.36 (k)s 2 f 158.664 (=1)s 13 f 556.15 y 172.814 (Z)s 11 f 559.116 y 184.814 (\277)s 2 f 583.417 y 179.481 (0)s 13 f 559.163 y 192.81 (D)s 200.144 (\263)s 10 f 572.483 y 207.31 (M)s 11 f 574.283 y 218.952 (k)s 1 f 572.483 y 224.856 (\050)s 10 f 229.523 (m)s 11 f 574.283 y 240.059 (s)s 10 f 572.483 y 245.188 (;)s 250.522 (\301)s 11 f 574.283 y 257.672 (s)s 1 f 572.483 y 262.801 (\051)s 12 f 270.134 (\241)s 10 f 282.134 (M)s 11 f 574.283 y 293.776 (k)s 1 f 572.483 y 299.68 (\050)s 13 f 306.281 (e)s 10 f 304.347 (m)s 11 f 574.283 y 314.883 (s)s 10 f 572.483 y 320.012 (;)s 13 f 569.317 y 326.587 (e)s 10 f 572.483 y 325.345 (\301)s 11 f 574.283 y 332.495 (s)s 1 f 572.483 y 337.624 (\051)s 13 f 559.163 y 342.291 (\264)s 10 f 572.483 y 349.458 (;)s 354.791 (@)s 11 f 574.283 y 361.162 (k)s 12 f 572.483 y 367.066 (H)s 11 f 567.529 y 377.316 (f)s 575.45 y 377.2 (\277)s 382.08 (;\042)s 1 f 572.483 y 390.064 (\050)s 10 f 394.73 (s;)s 405.689 (:)s 1 f 409.022 (\051)s 13 f 559.163 y 413.689 (E)s 10 f 572.483 y 421.022 (ds)s 13 f 558.683 y 432.893 (\257)s 565.883 y 432.893 (\257)s 573.083 y 432.893 (\257)s 10 f 572.483 y 436.893 (;)s 12 f 607.813 y 127.273 (\267)s 10 f 139.939 (C)s 2 f 609.613 y 148.516 (3)s 12 f 597.477 y 153.899 (p)s 4.333 .48 163.899 597.477 r 10 f 607.813 y 163.899 (t)s 168.233 (R)s 1 f 177.437 (\050)s 10 f 182.103 (t)s 1 f 186.437 (\051)s 12 f 191.103 (k)s 10 f 197.103 (f)s 12 f 204.27 (k)s 2 f 609.613 y 210.27 (1)s 10 f 607.813 y 215.653 (;)s 13 f 628.646 y 21.25 (\257)s 635.846 y 21.25 (\257)s 643.046 y 21.25 (\257)s 632.726 y 25.25 (\255)s 7.15 .48 30.917 632.673 r 10 f 642.446 y 30.917 (\301)s 1 f 38.067 (\050)s 10 f 42.733 (\277)s 48.671 (;)s 54.004 (:)s 1 f 57.338 (\051)s 10 f 62.004 (;)s 12 f 67.337 (H)s 11 f 637.492 y 77.588 (f)s 645.413 y 77.472 (\277)s 82.351 (;\042)s 1 f 642.446 y 90.335 (\050)s 10 f 95.002 (\277)s 100.939 (;)s 106.273 (:)s 1 f 109.606 (\051)s 13 f 632.726 y 114.273 (\256)s 628.646 y 119.939 (\257)s 635.846 y 119.939 (\257)s 643.046 y 119.939 (\257)s 1 f 642.446 y 127.273 (=)s 10 f 139.939 (\257)s 13 f 628.646 y 147.36 (\257)s 635.846 y 147.36 (\257)s 643.046 y 147.36 (\257)s 11 f 627.446 y 159.589 (d)s 13 f 631.046 y 153.42 (X)s 11 f 656.88 y 153.36 (k)s 2 f 158.664 (=1)s 13 f 626.113 y 172.814 (Z)s 11 f 629.079 y 184.814 (\277)s 2 f 653.38 y 179.481 (0)s 13 f 629.126 y 192.81 (D)s 200.144 (\263)s 10 f 642.446 y 207.31 (F)s 11 f 644.246 y 215.027 (k)s 1 f 642.446 y 220.931 (\050)s 10 f 225.598 (m)s 11 f 644.246 y 236.134 (s)s 10 f 642.446 y 241.263 (;)s 246.597 (\301)s 11 f 644.246 y 253.747 (s)s 1 f 642.446 y 258.876 (\051)s 12 f 266.209 (\241)s 10 f 278.209 (F)s 11 f 644.246 y 285.926 (k)s 1 f 642.446 y 291.83 (\050)s 13 f 298.431 (e)s 10 f 296.497 (m)s 11 f 644.246 y 307.033 (s)s 10 f 642.446 y 312.162 (;)s 13 f 639.28 y 318.737 (e)s 10 f 642.446 y 317.495 (\301)s 11 f 644.246 y 324.645 (s)s 1 f 642.446 y 329.774 (\051)s 13 f 629.126 y 334.441 (\264)s 10 f 642.446 y 341.608 (;)s 346.941 (@)s 11 f 644.246 y 353.312 (k)s 12 f 642.446 y 359.216 (H)s 11 f 637.492 y 369.466 (f)s 645.413 y 369.35 (\277)s 374.23 (;\042)s 1 f 642.446 y 382.214 (\050)s 10 f 386.88 (s;)s 397.839 (:)s 1 f 401.172 (\051)s 13 f 629.126 y 405.839 (E)s 10 f 642.446 y 413.172 (ds)s 13 f 628.646 y 425.043 (\257)s 635.846 y 425.043 (\257)s 643.046 y 425.043 (\257)s 12 f 677.776 y 127.273 (\267)s 10 f 139.939 (C)s 2 f 679.576 y 148.516 (3)s 12 f 667.44 y 153.899 (p)s 4.333 .48 163.899 667.44 r 10 f 677.776 y 163.899 (t)s 168.233 (R)s 1 f 177.437 (\050)s 10 f 182.103 (t)s 1 f 186.437 (\051)s 12 f 191.103 (k)s 10 f 197.103 (f)s 12 f 204.27 (k)s 2 f 679.576 y 210.27 (1)s 10 f 677.776 y 215.653 (;)s 1 f 705.976 y 223.045 (30)s do-end end endp %%Page: 31 31 %%BeginPageSetup initializepage (Raffaele Esposito; page: 31 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f0_12 sf ( )S -996 -1000 :M f1_12 sf ( )S -993 -1000 :M f2_12 sf ( )S -989 -1000 :M f10_12 sf ( )S -981 -1000 :M f11_12 sf ( )S -972 -1000 :M f12_12 sf ( )S -960 -1000 :M f13_12 sf ( )S -951 -1000 :M f14_12 sf ( )S -937 -1000 :M f15_12 sf ( )S -926 -1000 :M f21_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 1200 1000 div mul /CMBX10 findfont fdef 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 22 10 1200 1000 div mul /CMSL10 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 6.31 y -5.69 (for)s 13.136 (some)s 43.663 (p)s 50.663 (ositiv)s 78.73 (e)s 88.523 (constan)s 128.256 (t)s 10 f 137.383 (C)s 2 f 8.11 y 145.96 (3)s 1 f 6.31 y 151.343 (.)s 161.389 (By)s 180.682 (observing)s 234.909 (that)s 10 f 261.369 (h)s 11 f 8.11 y 268.283 (\042)s 1 f 6.31 y 277.877 (is)s 290.403 (an)s 307.53 (appro)s 337.23 (ximate)s 377.356 (iden)s 399.023 (tit)s 411.356 (y)s 422.15 (in)s 10 f 436.61 (\042)s 1 f 442.205 (,)s 450.114 (w)s 458.447 (e)s 23.11 y -5.69 (obtain)s 31.643 (that)s 13 f 27.91 y 148.368 (\257)s 35.11 y 148.368 (\257)s 42.31 y 148.368 (\257)s 31.99 y 152.368 (\255)s 10.536 .48 158.034 35.103 r 10 f 41.71 y 158.034 (m)s 1 f 168.571 (\050)s 10 f 173.237 (\277)s 179.175 (;)s 184.508 (:)s 1 f 187.841 (\051)s 10 f 192.508 (;)s 197.841 (f)s 13 f 31.99 y 205.008 (\256)s 27.91 y 210.675 (\257)s 35.11 y 210.675 (\257)s 42.31 y 210.675 (\257)s 12 f 41.71 y 218.008 (\267)s 10 f 230.675 (C)s 2 f 43.51 y 239.251 (3)s 12 f 31.374 y 244.635 (p)s 4.333 .48 254.635 31.374 r 10 f 41.71 y 254.635 (t)s 258.968 (R)s 1 f 268.172 (\050)s 10 f 272.839 (t)s 1 f 277.172 (\051)s 12 f 281.839 (k)s 10 f 287.839 (f)s 12 f 295.006 (k)s 2 f 43.51 y 301.006 (1)s 10 f 41.71 y 306.389 (;)s 13 f 57.91 y 151.754 (\257)s 65.11 y 151.754 (\257)s 72.31 y 151.754 (\257)s 61.99 y 155.754 (\255)s 7.15 .48 161.421 61.937 r 10 f 71.71 y 161.421 (\301)s 1 f 168.571 (\050)s 10 f 173.237 (\277)s 179.175 (;)s 184.508 (:)s 1 f 187.841 (\051)s 10 f 192.508 (;)s 197.841 (f)s 13 f 61.99 y 205.008 (\256)s 57.91 y 210.675 (\257)s 65.11 y 210.675 (\257)s 72.31 y 210.675 (\257)s 12 f 71.71 y 218.008 (\267)s 10 f 230.675 (C)s 2 f 73.51 y 239.251 (3)s 12 f 61.374 y 244.635 (p)s 4.333 .48 254.635 61.374 r 10 f 71.71 y 254.635 (t)s 258.968 (R)s 1 f 268.172 (\050)s 10 f 272.839 (t)s 1 f 277.172 (\051)s 12 f 281.839 (k)s 10 f 287.839 (f)s 12 f 295.006 (k)s 2 f 73.51 y 301.006 (1)s 1 f 103.362 y -5.69 (for)s 14.042 (all)s 10 f 32.075 (f)s 12 f 44.851 (2)s 58.461 (C)s 11 f 105.162 y 64.78 (K)s 1 f 103.362 y 74.031 (\050I)s 80.871 (R)s 11 f 98.128 y 89.705 (d)s 1 f 103.362 y 95.3 (\051)s 105.333 (and)s 130.032 (then)s 158.731 (for)s 178.464 (all)s 10 f 196.496 (f)s 12 f 209.273 (2)s 10 f 222.883 (L)s 2 f 99.007 y 231.049 (1)s 1 f 103.362 y 236.433 (\050I)s 243.273 (R)s 11 f 98.128 y 252.106 (d)s 1 f 103.362 y 257.702 (\051.)s 275.133 (It)s 289.499 (follo)s 311.499 (ws)s 330.264 (that,)s 361.305 (for)s 381.038 (0)s 12 f 392.648 (\267)s 10 f 407.591 (\277)s 12 f 419.805 (\267)s 10 f 434.748 (t)s 1 f 444.447 (and)s 10 f 120.162 y -5.69 (f)s 12 f 4.81 (2)s 10 f 16.143 (L)s 2 f 115.807 y 24.31 (1)s 1 f 120.162 y 29.693 (\050I)s 36.533 (R)s 11 f 114.928 y 45.366 (d)s 1 f 120.162 y 50.962 (\051,)s 13 f 129.538 y 148.368 (\255)s 129.058 y 154.034 (\257)s 136.258 y 154.034 (\257)s 10.536 .48 158.034 132.651 r 10 f 139.258 y 158.034 (m)s 1 f 168.571 (\050)s 10 f 173.237 (\277)s 179.175 (;)s 184.508 (:)s 1 f 187.841 (\051)s 13 f 129.058 y 192.508 (\257)s 136.258 y 192.508 (\257)s 10 f 139.258 y 196.508 (;)s 201.841 (f)s 13 f 129.538 y 209.008 (\256)s 12 f 139.258 y 218.008 (\267)s 10 f 230.675 (C)s 2 f 141.058 y 239.251 (3)s 12 f 128.921 y 244.635 (p)s 4.333 .48 254.635 128.921 r 10 f 139.258 y 254.635 (t)s 258.968 (R)s 1 f 268.172 (\050)s 10 f 272.839 (t)s 1 f 277.172 (\051)s 12 f 281.839 (k)s 10 f 287.839 (f)s 12 f 295.006 (k)s 2 f 141.058 y 301.006 (1)s 10 f 139.258 y 306.389 (;)s 13 f 149.938 y 151.754 (\255)s 149.458 y 157.421 (\257)s 156.658 y 157.421 (\257)s 7.15 .48 161.421 149.885 r 10 f 159.658 y 161.421 (\301)s 1 f 168.571 (\050)s 10 f 173.237 (\277)s 179.175 (;)s 184.508 (:)s 1 f 187.841 (\051)s 13 f 149.458 y 192.508 (\257)s 156.658 y 192.508 (\257)s 10 f 159.658 y 196.508 (;)s 201.841 (f)s 13 f 149.938 y 209.008 (\256)s 12 f 159.658 y 218.008 (\267)s 10 f 230.675 (C)s 2 f 161.458 y 239.251 (3)s 12 f 149.321 y 244.635 (p)s 4.333 .48 254.635 149.321 r 10 f 159.658 y 254.635 (t)s 258.968 (R)s 1 f 268.172 (\050)s 10 f 272.839 (t)s 1 f 277.172 (\051)s 12 f 281.839 (k)s 10 f 287.839 (f)s 12 f 295.006 (k)s 2 f 161.458 y 301.006 (1)s 10 f 159.658 y 306.389 (:)s 1 f 187.709 y -5.69 (Therefore,)s 52.043 (for)s 70.41 (all)s 87.077 (0)s 12 f 96.41 (\267)s 10 f 109.076 (\277)s 12 f 119.014 (\267)s 10 f 131.681 (t)s 1 f 140.014 (and)s 10 f 163.347 (f)s 12 f 173.847 (2)s 10 f 185.18 (L)s 2 f 183.354 y 193.347 (1)s 1 f 187.709 y 198.731 (\050I)s 205.571 (R)s 11 f 182.476 y 214.404 (d)s 1 f 187.709 y 219.999 (\051,)s 13 f 208.255 y 148.136 (\255)s 10 f 217.975 y 153.802 (W)s 1 f 166.802 (\050)s 10 f 171.469 (\277)s 177.407 (;)s 182.74 (:)s 1 f 186.073 (\051)s 10 f 190.74 (;)s 196.073 (f)s 13 f 208.255 y 203.24 (\256)s 12 f 217.975 y 212.24 (\267)s 1 f 224.907 (2)s 10 f 230.907 (C)s 2 f 219.775 y 239.483 (3)s 12 f 207.638 y 244.867 (p)s 4.333 .48 254.867 207.638 r 10 f 217.975 y 254.867 (t)s 259.2 (R)s 1 f 268.404 (\050)s 10 f 273.071 (t)s 1 f 277.404 (\051)s 12 f 282.071 (k)s 10 f 288.071 (f)s 12 f 295.238 (k)s 2 f 219.775 y 301.238 (1)s 10 f 217.975 y 306.621 (;)s 1 f 439.114 (\0505)s 10 f 449.78 (:)s 1 f 453.114 (2\051)s 248.24 y -5.69 (whic)s 17.976 (h)s 28.643 (implies)s 69.377 (that,)s 98.71 (for)s 117.077 (all)s 10 f 133.743 (\277)s 12 f 143.681 (2)s 1 f 155.014 ([0)s 10 f 164.347 (;)s 169.681 (t)s 1 f 174.014 (])s 181.347 (\050see)s 205.414 (App)s 228.081 (endix\051,)s 10 f 278.506 y 99.641 (W)s 1 f 112.641 (\050)s 10 f 117.308 (\277)s 123.245 (;)s 128.579 (:)s 1 f 131.912 (\051)s 12 f 139.912 (2)s 10 f 151.245 (L)s 14 f 273.551 y 159.412 (1)s 1 f 278.506 y 169.578 (\050I)s 176.418 (R)s 11 f 273.272 y 185.252 (d)s 1 f 278.506 y 190.847 (\051)s 199.514 (and)s 12 f 222.847 (k)s 10 f 228.847 (W)s 1 f 241.847 (\050)s 10 f 246.514 (\277)s 252.452 (;)s 257.785 (:)s 1 f 261.118 (\051)s 12 f 265.785 (k)s 14 f 280.305 y 271.785 (1)s 12 f 278.506 y 285.285 (\267)s 1 f 297.951 (2)s 10 f 303.951 (C)s 2 f 280.305 y 312.528 (3)s 12 f 268.169 y 317.911 (p)s 4.333 .48 327.911 268.169 r 10 f 278.506 y 327.911 (t)s 332.245 (R)s 1 f 341.449 (\050)s 10 f 346.116 (t)s 1 f 350.449 (\051)s 10 f 355.116 (:)s 1 f 439.114 (\0505)s 10 f 449.78 (:)s 1 f 453.114 (3\051)s 308.891 y 8.71 (On)s 28.71 (the)s 49.377 (other)s 80.743 (hand,)s 114.077 (pro)s 131.777 (ceeding)s 174.443 (as)s 189.177 (in)s 203.177 (the)s 223.844 (pro)s 241.544 (of)s 255.21 (of)s 268.877 (\0505.2\051,)s 300.877 (w)s 309.21 (e)s 318.544 (obtain)s 13 f 329.436 y 160.411 (\255)s 10 f 339.156 y 166.078 (W)s 1 f 179.078 (\050)s 10 f 183.744 (\277)s 189.682 (;)s 195.015 (:)s 1 f 198.348 (\051)s 10 f 203.015 (;)s 208.348 (f)s 13 f 329.436 y 215.515 (\256)s 12 f 339.156 y 224.515 (\267)s 1 f 237.182 (2)s 10 f 243.182 (C)s 2 f 340.956 y 251.758 (3)s 12 f 328.82 y 257.142 (p)s 4.333 .48 267.142 328.82 r 10 f 339.156 y 267.142 (t)s 13 f 336.123 y 273.744 (e)s 10 f 339.156 y 271.475 (R)s 1 f 280.679 (\050)s 10 f 285.346 (t)s 1 f 289.679 (\051)s 10 f 294.346 (;)s 1 f 369.422 y -5.69 (where)s 13 f 366.389 y 31.279 (e)s 10 f 369.422 y 29.01 (R)s 1 f 38.214 (\050)s 10 f 42.881 (t)s 1 f 47.214 (\051)s 55.881 (is)s 67.947 (giv)s 83.281 (en)s 99.281 (b)s 105.614 (y)s 13 f 383.189 y 165.847 (e)s 10 f 386.222 y 163.578 (R)s 1 f 172.783 (\050)s 10 f 177.449 (t)s 1 f 181.783 (\051)s 189.782 (=)s 207.385 (sup)s 2 f 396.313 y 202.449 (0)s 14 f 207.232 (\267)s 11 f 214.732 (s)s 14 f 219.262 (\267)s 11 f 226.762 (t)s 12 f 386.222 y 232.387 (k)s 10 f 238.387 (W)s 1 f 251.387 (\050)s 10 f 256.053 (s;)s 267.012 (:)s 1 f 270.345 (\051)s 12 f 275.012 (k)s 14 f 388.022 y 281.012 (1)s 10 f 386.222 y 291.178 (:)s 1 f 420.189 y -5.69 (This)s 21.71 (implies)s 62.443 (that)s 13 f 433.956 y 181.63 (e)s 10 f 436.989 y 179.361 (R)s 1 f 188.565 (\050)s 10 f 193.232 (t)s 1 f 197.565 (\051)s 12 f 205.565 (\267)s 1 f 218.232 (2)s 10 f 224.232 (C)s 2 f 438.789 y 232.808 (3)s 12 f 426.653 y 238.192 (p)s 4.333 .48 248.192 426.653 r 10 f 436.989 y 248.192 (t)s 13 f 433.956 y 254.794 (e)s 10 f 436.989 y 252.525 (R)s 1 f 261.729 (\050)s 10 f 266.396 (t)s 1 f 270.729 (\051)s 10 f 275.396 (:)s 1 f 461.774 y -5.69 (Cho)s 15.977 (osing)s 10 f 46.852 (t)s 1 f 54.756 (=)s 10 f 67.66 (t)s 2 f 463.574 y 71.993 (0)s 1 f 461.774 y 81.519 (suc)s 97.919 (h)s 108.728 (that)s 134.87 (2)s 10 f 140.87 (C)s 2 f 463.574 y 149.447 (3)s 12 f 452.923 y 154.83 (p)s 9.717 .48 164.83 452.923 r 10 f 461.774 y 164.83 (t)s 2 f 463.574 y 169.164 (0)s 10 f 461.774 y 178.118 (\074)s 1 f 191.021 (1,)s 204.533 (this)s 228.075 (giv)s 243.409 (es)s 257.618 (uniqueness)s 318.227 (in)s 332.369 ([0)s 10 f 341.702 (;)s 347.036 (t)s 2 f 463.574 y 351.369 (0)s 1 f 461.774 y 356.752 (])s 12 f 362.847 (\243)s 1 f 374.942 (I)s 377.115 (R)s 11 f 456.54 y 385.949 (d)s 1 f 461.774 y 391.544 (.)s 400.638 (T)s 408.305 (o)s 418.447 (conclude)s 478.574 y -5.69 (the)s 16.618 (pro)s 34.318 (of)s 49.627 (w)s 57.96 (e)s 68.935 (ha)s 81.268 (v)s 87.268 (e)s 98.244 (just)s 123.619 (to)s 139.927 (rep)s 156.96 (eat)s 178.602 (the)s 200.911 (same)s 232.619 (argumen)s 277.652 (ts)s 292.694 (in)s 308.336 ([)s 10 f 311.669 (t)s 2 f 480.374 y 316.003 (0)s 10 f 478.574 y 321.386 (;)s 1 f 326.719 (2)s 10 f 332.719 (t)s 2 f 480.374 y 337.053 (0)s 1 f 478.574 y 342.436 (],)s 355.155 (and)s 380.13 (in)s 395.772 (eac)s 412.105 (h)s 424.413 (in)s 434.08 (terv)s 454.447 (al)s 495.374 y -5.69 ([)s 10 f -2.357 (k)s 4.268 (t)s 2 f 497.174 y 8.601 (0)s 10 f 495.374 y 13.985 (;)s 1 f 19.318 (\050)s 10 f 23.985 (k)s 1 f 33.276 (+)s 45.276 (1\051)s 10 f 55.943 (t)s 2 f 497.174 y 60.276 (0)s 1 f 495.374 y 65.66 (],)s 10 f 76.326 (k)s 12 f 86.285 (2)s 10 f 97.618 (N)s 1 f 108.568 (,)s 10 f 115.901 (k)s 125.86 (\076)s 1 f 138.526 (1.)s 8.16 .48 158.526 488.774 r .48 7.2 158.526 495.974 r .48 7.2 166.206 495.974 r 8.16 .48 158.526 496.454 r 22 f 519.286 y -5.69 (Glaub)s 26.727 (er)s 40.76 (dynamics.)s 1 f 536.206 y 8.71 (The)s 34.806 (pro)s 52.506 (of)s 67.603 (of)s 82.699 (the)s 104.795 (h)s 111.129 (ydro)s 135.162 (dynamical)s 194.259 (limit)s 224.355 (in)s 239.785 (the)s 261.881 (Glaub)s 294.298 (er)s 309.761 (case)s 336.591 (is)s 350.087 (based)s 384.917 (on)s 403.013 (martingales)s 553.006 y -5.69 (argumen)s 39.343 (ts)s 54.015 (and)s 78.62 (do)s 91.62 (es)s 106.958 (not)s 129.563 (require)s 171.235 (Diric)s 196.768 (hlet)s 222.04 (form)s 251.678 (estimates.)s 312.96 (F)s 319.793 (ollo)s 338.127 (w)s 352.065 (the)s 374.004 (same)s 405.342 (strategy)s 453.047 (as)s 569.806 y -5.69 (in)s 10.275 (the)s 32.907 (Ka)s 47.907 (w)s 56.241 (asaki)s 88.606 (case)s 115.972 (w)s 124.305 (e)s 135.604 (pro)s 152.637 (vide)s 180.269 (the)s 202.901 (analogous)s 260.267 (of)s 275.899 (Lemma)s 320.698 (5.1,)s 345.821 (5.2)s 367.12 (and)s 392.419 (5.4.)s 422.315 (Fixed)s 457.78 (a)s 586.606 y -5.69 (parameter)s 10 f 52.433 (\257)s 64.391 (\076)s 1 f 78.263 (0)s 88.986 (and)s 113.042 (the)s 134.431 (time)s 162.487 (in)s 172.154 (terv)s 192.521 (al)s 206.577 ([0)s 10 f 215.91 (;)s 221.244 (T)s 1 f 229.923 (],)s 241.493 (w)s 249.826 (e)s 259.883 (denote)s 299.272 (b)s 305.605 (y)s 0 f 316.662 (P)s 2 f 580.373 y 326.095 (\050)s 11 f 329.845 (G)s 2 f 337.316 (\051)s 11 f 589.376 y 326.095 (\271)s 15 f 586.976 y 331.93 (\260)s 1 f 586.606 y 346.389 (the)s 367.778 (la)s 376.778 (w)s 390.168 (of)s 404.557 (the)s 425.947 (pro)s 443.647 (cess)s 608.343 y -5.69 (\050)s 10 f -1.024 (\276)s 1 f 6.264 (\050)s 10 f 10.931 (t;)s 20.597 (:)s 1 f 23.931 (\051\051)s 11 f 610.509 y 33.264 (t)s 14 f 36.889 (2)s 2 f 43.356 ([0)s 11 f 50.856 (;T)s 2 f 60.665 (])s 1 f 608.343 y 68.01 (\050without)s 117.371 (acceleration\051)s 188.098 (on)s 204.793 (the)s 225.487 (space)s 10 f 257.581 (D)s 1 f 267.85 (\050[0)s 10 f 281.85 (;)s 287.183 (T)s 1 f 295.862 (])s 10 f 299.195 (;)s 1 f 304.529 (\255\051)s 321.89 (and)s 345.251 (b)s 351.584 (y)s 10 f 361.945 (Q)s 2 f 602.109 y 371.432 (\050)s 11 f 375.182 (G)s 2 f 382.653 (\051)s 11 f 611.112 y 371.432 (\271)s 15 f 608.712 y 377.266 (\260)s 1 f 608.343 y 391.031 (the)s 411.725 (la)s 420.725 (w)s 433.419 (of)s 447.113 (the)s 625.143 y -5.69 (pro)s 12.01 (cess)s 35.417 (\050)s 10 f 40.083 (\274)s 2 f 619.376 y 47.354 (1)s 11 f 52.138 (;\260)s 628.096 y 46.924 (t)s 10 f 625.143 y 61.145 (;)s 66.478 (\274)s 2 f 619.376 y 73.749 (2)s 11 f 78.532 (;\260)s 628.096 y 73.318 (t)s 1 f 625.143 y 87.54 (\051)s 11 f 627.309 y 92.206 (t)s 14 f 95.831 (2)s 2 f 102.298 ([0)s 11 f 109.798 (;T)s 2 f 119.608 (])s 1 f 625.143 y 126.198 (on)s 142.138 (the)s 162.078 (space)s 10 f 193.418 (D)s 13 f 615.422 y 203.687 (\241)s 1 f 625.143 y 209.187 ([0)s 10 f 218.52 (;)s 223.853 (T)s 1 f 232.532 (])s 10 f 235.866 (;)s 12 f 241.199 (M)s 2 f 620.788 y 255.61 (2)s 13 f 615.422 y 260.993 (\242)s 1 f 625.143 y 269.767 (with)s 296.374 (initial)s 330.314 (distribution)s 10 f 395.021 (\271)s 11 f 620.788 y 402.251 (\260)s 1 f 625.143 y 408.409 (.)s 416.833 (As)s 433.84 (in)s 447.113 (the)s 641.943 y -5.69 (Ka)s 9.31 (w)s 17.643 (asaki)s 47.639 (case)s 72.635 (the)s 92.897 (pro)s 110.598 (of)s 123.86 (of)s 137.123 (the)s 157.385 (analogous)s 212.381 (of)s 225.644 (Lemma)s 268.073 (5.1)s 287.002 (is)s 298.665 (simple)s 335.661 (and)s 358.59 (is)s 370.252 (omitted.)s 419.451 (W)s 430.784 (e)s 439.714 (shall)s 658.743 y -5.69 (giv)s 9.643 (e)s 19.725 (only)s 46.808 (the)s 68.224 (pro)s 85.924 (of)s 100.339 (of)s 114.755 (the)s 136.171 (analogous)s 192.32 (of)s 206.736 (Lemma)s 250.318 (5.2:)s 275.816 (All)s 296.232 (limit)s 325.647 (p)s 332.647 (oin)s 348.314 (ts)s 10 f 362.463 (Q)s 14 f 654.388 y 371.95 (\244)s 1 f 658.743 y 382.215 (of)s 396.631 (the)s 418.047 (sequence)s 13 f 665.822 y -5.69 (\241)s 10 f 675.543 y -.19 (Q)s 2 f 669.309 y 9.296 (\050)s 11 f 13.047 (G)s 2 f 20.518 (\051)s 11 f 678.312 y 9.296 (\271)s 15 f 675.912 y 15.131 (\260)s 13 f 665.822 y 24.868 (\242)s 11 f 680.343 y 30.368 (\260)s 1 f 675.543 y 41.604 (are)s 62.717 (concen)s 97.717 (trated)s 134.829 (on)s 152.575 (w)s 160.909 (eak)s 183.654 (solutions)s 234.867 (of)s 249.613 (equation)s 299.692 (\0503.7\051.)s 336.263 (Finally)s 378.176 (the)s 399.922 (pro)s 417.622 (of)s 432.368 (of)s 447.114 (the)s 705.976 y 223.045 (31)s do-end end endp %%Page: 32 32 %%BeginPageSetup initializepage (Raffaele Esposito; page: 32 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f1_12 sf ( )S -997 -1000 :M f2_12 sf ( )S -993 -1000 :M f10_12 sf ( )S -985 -1000 :M f11_12 sf ( )S -976 -1000 :M f12_12 sf ( )S -964 -1000 :M f13_12 sf ( )S -954 -1000 :M f14_12 sf ( )S -941 -1000 :M f15_12 sf ( )S -930 -1000 :M f16_12 sf ( )S -925 -1000 :M f18_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 16 5 1200 1000 div mul /CMR5 findfont fdef 18 5 1200 1000 div mul /CMSY5 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 6.31 y -5.69 (uniqueness)s 54.866 (of)s 68.621 (the)s 89.377 (equation)s 138.466 (\0503.7\051)s 167.222 (go)s 179.555 (es)s 193.711 (on)s 210.467 (along)s 242.556 (the)s 263.312 (same)s 293.468 (lines)s 320.957 (as)s 335.779 (in)s 349.868 (the)s 370.624 (Ka)s 385.624 (w)s 393.957 (asaki)s 424.446 (case.)s 454.78 (It)s 23.11 y -5.69 (is)s 6.376 (easier,)s 43.143 (since)s 72.543 (w)s 80.877 (e)s 90.21 (do)s 106.877 (not)s 128.21 (need)s 156.21 (to)s 170.877 (use)s 191.61 (prop)s 215.977 (erties)s 248.077 (of)s 261.743 (the)s 282.41 (heat)s 309.077 (k)s 315.077 (ernel.)s 40.03 y 8.71 (Denote)s 49.007 (b)s 55.34 (y)s 12 f 64.804 (C)s 2 f 34.263 y 71.822 (1)s 11 f 76.605 (;)s 2 f 79.455 (0)s 11 f 43.556 y 71.122 (K)s 13 f 30.31 y 84.839 (\241)s 1 f 40.03 y 90.339 ([0)s 10 f 99.672 (;)s 105.005 (T)s 1 f 113.685 (])s 12 f 117.945 (\243)s 1 f 128.206 (I)s 130.379 (R)s 11 f 34.796 y 139.212 (d)s 13 f 30.31 y 144.808 (\242)s 1 f 40.03 y 153.438 (the)s 173.235 (space)s 204.432 (of)s 217.229 (con)s 234.895 (tin)s 249.229 (uous)s 276.426 (functions)s 327.289 (with)s 353.753 (compact)s 400.883 (supp)s 425.95 (ort)s 444.447 (and)s 56.83 y -5.69 (with)s 20.622 (deriv)s 46.322 (ativ)s 66.322 (e)s 74.634 (con)s 92.301 (tin)s 106.634 (uous)s 133.68 (in)s 146.659 (time.)s 178.318 (Let)s 10 f 198.797 (U)s 1 f 211.632 (=)s 224.299 (\050)s 10 f 228.965 (U)s 2 f 52.475 y 238.467 (1)s 10 f 56.83 y 243.85 (;)s 249.184 (U)s 2 f 52.475 y 258.685 (2)s 1 f 56.83 y 264.069 (\051)s 12 f 272.069 (2)s 283.402 (C)s 2 f 51.063 y 290.42 (1)s 11 f 295.204 (;)s 2 f 298.054 (0)s 11 f 60.356 y 289.72 (K)s 1 f 56.83 y 303.437 (\050[0)s 10 f 317.437 (;)s 322.77 (T)s 1 f 331.449 (])s 12 f 335.407 (\243)s 1 f 345.365 (I)s 347.538 (R)s 11 f 51.596 y 356.371 (d)s 1 f 56.83 y 361.967 (\051)s 12 f 367.258 (\243)s 377.215 (C)s 2 f 51.063 y 384.234 (1)s 11 f 389.017 (;)s 2 f 391.867 (0)s 11 f 60.356 y 383.534 (K)s 1 f 56.83 y 397.25 (\050[0)s 10 f 411.25 (;)s 416.584 (T)s 1 f 425.263 (])s 12 f 429.221 (\243)s 1 f 439.178 (I)s 441.351 (R)s 11 f 51.596 y 450.185 (d)s 1 f 56.83 y 455.78 (\051,)s 73.63 y -5.69 (and)s 17.643 (consider)s 64.41 (the)s 85.077 (martingale)s 10 f 145.11 (M)s 2 f 67.396 y 158.06 (\050)s 11 f 161.81 (G)s 2 f 169.281 (\051)s 11 f 173.031 (;U)s 76.583 y 156.752 (t)s 1 f 73.63 y 187.919 (de\257ned)s 229.253 (b)s 235.586 (y)s 10 f 115.474 y 18.052 (M)s 2 f 109.241 y 31.002 (\050)s 11 f 34.752 (G)s 2 f 42.223 (\051)s 11 f 45.973 (;U)s 118.427 y 29.694 (t)s 1 f 115.474 y 60.194 (=)s 2 f 100.474 y 79.136 (2)s 13 f 104.074 y 72.861 (X)s 11 f 129.487 y 73.677 (\266)s 2 f 77.228 (=1)s 13 f 102.154 y 92.194 (n)s 10 f 115.474 y 103.528 (\074)s 116.194 (\274)s 11 f 109.707 y 123.465 (\266;\260)s 118.427 y 123.035 (t)s 10 f 115.474 y 136.024 (;)s 141.357 (U)s 11 f 110.519 y 150.859 (\266)s 118.44 y 149.55 (t)s 10 f 115.474 y 158.343 (\076)s 12 f 171.01 (\241)s 10 f 183.677 (\074)s 196.343 (\274)s 11 f 109.707 y 203.614 (\266;\260)s 2 f 118.674 y 203.184 (0)s 10 f 115.474 y 216.173 (;)s 221.506 (U)s 11 f 110.519 y 231.008 (\266)s 2 f 118.44 y 229.699 (0)s 10 f 115.474 y 238.492 (\076)s 12 f 251.159 (\241)s 13 f 99.14 y 262.492 (Z)s 11 f 102.107 y 274.492 (t)s 2 f 126.407 y 269.159 (0)s 13 f 102.154 y 280.717 (\263)s 10 f 115.474 y 287.884 (@)s 11 f 117.274 y 294.255 (s)s 1 f 115.474 y 302.051 (+)s 314.051 (I)s 316.224 (L)s 11 f 110.241 y 323.724 (G;\257)s 118.44 y 323.724 (\260)s 13 f 105.754 y 340.518 (\242)s 10 f 115.474 y 349.351 (\074)s 362.018 (\274)s 11 f 110.519 y 369.289 (\266;\260)s 118.44 y 368.858 (s)s 10 f 115.474 y 381.848 (;)s 387.181 (U)s 11 f 110.519 y 396.682 (\266)s 118.44 y 395.374 (s)s 10 f 115.474 y 404.167 (\076)s 416.834 (ds)s 13 f 102.154 y 428.705 (o)s 10 f 115.474 y 436.705 (:)s 1 f 159.031 y -5.69 (Observ)s 31.077 (e)s 41.671 (that)s 68.931 (since)s 99.592 (for)s 119.22 (all)s 10 f 137.147 (\276)s 12 f 149.869 (2)s 1 f 163.303 (\255)s 177.231 (and)s 10 f 201.825 (i)s 12 f 211.393 (2)s 10 f 224.828 (Z)s 227.878 (Z)s 11 f 153.798 y 238.928 (d)s 1 f 159.031 y 244.523 (,)s 10 f 253.432 (\276)s 1 f 260.72 (\050)s 10 f 265.387 (i)s 1 f 269.521 (\051)s 12 f 279.622 (2)s 293.056 (f\241)s 1 f 308.39 (1)s 10 f 314.39 (;)s 1 f 319.723 (0)s 10 f 325.723 (;)s 1 f 331.056 (1)s 12 f 337.056 (g)s 1 f 348.317 (w)s 356.65 (e)s 367.244 (ha)s 379.578 (v)s 385.578 (e)s 396.172 (1)s 14 f 161.198 y 402.172 (f)s 11 f 407.088 (\276)s 2 f 412.951 (\050)s 11 f 416.701 (i)s 2 f 420.096 (\051=)s 14 f 431.212 (\241)s 2 f 438.712 (1)s 14 f 443.496 (g)s 1 f 159.031 y 454.447 (=)s 175.831 y -5.69 (\0501)s 10 f 4.977 (=)s 1 f 10.977 (2\051)s 10 f 21.643 (\276)s 1 f 28.931 (\050)s 10 f 33.597 (i)s 1 f 37.732 (\051\050)s 10 f 47.065 (\276)s 1 f 54.352 (\050)s 10 f 59.019 (i)s 1 f 63.153 (\051)s 12 f 70.708 (\241)s 1 f 82.93 (1\051,)s 101.346 (1)s 14 f 177.998 y 107.346 (f)s 11 f 112.263 (\276)s 2 f 118.125 (\050)s 11 f 121.875 (i)s 2 f 125.27 (\051=0)s 14 f 141.17 (g)s 1 f 175.831 y 150.575 (=)s 163.796 (\0501)s 12 f 177.351 (\241)s 1 f 189.573 (\050)s 10 f 194.24 (\276)s 1 f 201.528 (\050)s 10 f 206.194 (i)s 1 f 210.328 (\051\051)s 2 f 171.477 y 219.662 (2)s 1 f 175.831 y 225.045 (\051)s 234.045 (and)s 257.711 (1)s 14 f 177.998 y 263.711 (f)s 11 f 268.627 (\276)s 2 f 274.49 (\050)s 11 f 278.24 (i)s 2 f 281.635 (\051=1)s 14 f 297.535 (g)s 1 f 175.831 y 306.939 (=)s 320.161 (\0501)s 10 f 330.827 (=)s 1 f 336.827 (2\051)s 10 f 347.494 (\276)s 1 f 354.782 (\050)s 10 f 359.448 (i)s 1 f 363.583 (\051\050)s 10 f 372.916 (\276)s 1 f 380.203 (\050)s 10 f 384.87 (i)s 1 f 389.004 (\051)s 396.559 (+)s 408.781 (1\051)s 423.781 (w)s 432.114 (e)s 441.78 (ma)s 457.447 (y)s 192.631 y -5.69 (th)s 5.31 (us)s 20.71 (rewrite)s 61.443 (the)s 82.11 (generator)s 135.51 (I)s 137.683 (L)s 2 f 187.398 y 145.183 (\050)s 11 f 148.933 (G)s 2 f 156.405 (\051)s 11 f 160.155 (;\257)s 195.598 y 145.183 (\260)s 1 f 192.631 y 173.478 (as)s 221.909 y 158.324 (I)s 160.498 (L)s 2 f 216.675 y 167.998 (\050)s 11 f 171.748 (G)s 2 f 179.219 (\051)s 11 f 182.969 (;\257)s 224.875 y 167.998 (\260)s 1 f 221.909 y 195.625 (=)s 208.292 (I)s 210.465 (L)s 2 f 216.675 y 217.965 (\050)s 11 f 221.715 (f)s 2 f 227.336 (\051)s 1 f 221.909 y 234.353 (+)s 246.352 (I)s 248.526 (L)s 14 f 216.675 y 256.026 (\241)s 1 f 221.909 y 266.792 (+)s 278.792 (I)s 280.966 (L)s 2 f 216.675 y 288.466 (+)s 10 f 221.909 y 296.432 (;)s 1 f 251.186 y -5.69 (with)s 13 f 280.11 y 12.115 (\241)s 1 f 289.83 y 17.615 (I)s 19.788 (L)s 2 f 284.596 y 27.288 (\050)s 11 f 31.038 (f)s 2 f 36.659 (\051)s 10 f 289.83 y 41.009 (g)s 13 f 280.11 y 47.163 (\242)s 1 f 289.83 y 52.663 (\050)s 10 f 57.33 (\276)s 1 f 64.618 (\051)s 72.618 (=)s 281.712 y 86.724 (1)s 6 .48 86.724 287.07 r 298.061 y 86.724 (2)s 13 f 278.43 y 100.435 (X)s 11 f 305.37 y 96.164 (i)s 14 f 99.559 (2)s 11 f 106.026 (Z)s 108.236 (Z)s 15 f 302.596 y 117.002 (d)s 10 f 281.712 y 130.899 (e)s 14 f 277.357 y 136.486 (\241)s 15 f 273.37 y 145.426 (\257)s 5.052 .48 145.426 275.497 r 16 f 280.248 y 145.911 (2)s 2 f 277.357 y 151.918 (\050)s 14 f 155.668 (r)s 16 f 272.964 y 163.685 (\050)s 15 f 166.935 (f)s 16 f 171.748 (\051)s 15 f 280.382 y 163.685 (i)s 11 f 277.357 y 175.598 (H)s 15 f 278.557 y 183.457 (\260)s 2 f 277.357 y 188.955 (\051\050)s 11 f 196.455 (\276)s 2 f 202.317 (\051)s 86.606 .48 125.48 287.07 r 1 f 301.043 y 125.48 (2c)s 136.48 (h)s 13 f 291.323 y 143.146 (\241)s 11 f 295.69 y 150.086 (\257)s 5.873 .48 150.086 298.283 r 2 f 305.181 y 150.631 (2)s 1 f 301.043 y 157.399 (\050)s 12 f 162.066 (r)s 2 f 294.81 y 172.066 (\050)s 11 f 175.816 (f)s 2 f 181.437 (\051)s 11 f 304.388 y 172.066 (i)s 10 f 301.043 y 185.787 (H)s 11 f 302.843 y 195.762 (\260)s 1 f 301.043 y 201.919 (\051)s 13 f 291.323 y 206.586 (\242)s 276.51 y 213.526 (h)s 280.11 y 219.193 (\241)s 12 f 289.83 y 224.693 (r)s 2 f 283.596 y 234.693 (\050)s 11 f 238.443 (f)s 2 f 244.064 (\051)s 11 f 293.175 y 234.693 (i)s 10 f 289.83 y 248.414 (g)s 13 f 280.11 y 254.568 (\242)s 1 f 289.83 y 260.068 (\050)s 10 f 264.735 (\276)s 1 f 272.022 (\051)s 13 f 276.51 y 276.689 (i)s 10 f 289.83 y 282.355 (;)s 13 f 326.886 y 17.736 (\241)s 1 f 336.606 y 23.236 (I)s 25.409 (L)s 14 f 331.372 y 32.909 (\250)s 10 f 336.606 y 41.009 (g)s 13 f 326.886 y 47.163 (\242)s 1 f 336.606 y 52.663 (\050)s 10 f 57.33 (\276)s 1 f 64.618 (\051)s 72.618 (=)s 328.488 y 86.724 (1)s 6 .48 86.724 333.846 r 344.837 y 86.724 (2)s 13 f 325.206 y 100.435 (X)s 11 f 352.146 y 96.164 (i)s 14 f 99.559 (2)s 11 f 106.026 (Z)s 108.236 (Z)s 15 f 349.372 y 117.002 (d)s 10 f 328.488 y 130.494 (e)s 14 f 324.133 y 136.082 (\241)s 15 f 320.146 y 145.022 (\257)s 5.052 .48 145.022 322.273 r 16 f 327.024 y 145.506 (2)s 2 f 324.133 y 151.514 (\050)s 14 f 155.264 (r)s 18 f 320.239 y 163.281 (\250)s 15 f 327.158 y 163.281 (i)s 11 f 324.133 y 170.381 (H)s 15 f 325.333 y 178.24 (\260)s 2 f 324.133 y 183.738 (\051\050)s 11 f 191.238 (\276)s 2 f 197.1 (\051)s 80.985 .48 125.48 333.846 r 1 f 346.472 y 125.48 (2c)s 136.48 (h)s 13 f 336.752 y 143.146 (\241)s 11 f 341.119 y 150.086 (\257)s 5.873 .48 150.086 343.712 r 2 f 350.61 y 150.631 (2)s 1 f 346.472 y 157.399 (\050)s 12 f 162.066 (r)s 14 f 341.339 y 172.066 (\250)s 11 f 349.817 y 172.066 (i)s 10 f 346.472 y 180.166 (H)s 11 f 348.272 y 190.141 (\260)s 1 f 346.472 y 196.298 (\051)s 13 f 336.752 y 200.965 (\242)s 316.085 y 209.905 (\303)s 326.886 y 219.405 (\241)s 1 f 336.606 y 224.905 (1)s 12 f 233.572 (\241)s 10 f 245.572 (\276)s 1 f 252.859 (\050)s 10 f 257.526 (i)s 1 f 261.66 (\051)s 2 f 331.651 y 266.327 (2)s 13 f 326.886 y 271.71 (\242)s 1 f 336.606 y 279.877 (+)s 10 f 327.726 y 293.317 (\276)s 1 f 300.604 (\050)s 10 f 305.271 (i)s 1 f 309.405 (\051)s 13 f 318.006 y 314.072 (\241)s 10 f 327.726 y 319.572 (\276)s 1 f 326.859 (\050)s 10 f 331.526 (i)s 1 f 335.66 (\051)s 12 f 342.993 (\247)s 1 f 354.993 (1)s 13 f 318.006 y 360.993 (\242)s 73.177 .48 293.317 333.846 r 1 f 344.837 y 326.905 (2)s 13 f 316.085 y 367.933 (!)s 323.286 y 379.433 (h)s 326.886 y 385.1 (\241)s 12 f 336.606 y 390.6 (r)s 14 f 331.472 y 400.6 (\250)s 11 f 339.951 y 400.6 (i)s 10 f 336.606 y 408.7 (g)s 13 f 326.886 y 414.854 (\242)s 1 f 336.606 y 420.354 (\050)s 10 f 425.021 (\276)s 1 f 432.308 (\051)s 13 f 323.286 y 436.975 (i)s 10 f 336.606 y 442.642 (;)s 1 f 383.792 y -5.69 (where)s 29.01 (for)s 47.377 (a)s 57.377 (cylinder)s 103.077 (function)s 10 f 150.077 (F)s 1 f 159.46 (,)s 13 f 374.072 y 166.793 (\241)s 12 f 383.792 y 172.293 (r)s 2 f 377.559 y 182.293 (\050)s 11 f 186.044 (f)s 2 f 191.664 (\051)s 11 f 387.137 y 182.293 (i)s 10 f 383.792 y 196.014 (F)s 13 f 374.072 y 205.398 (\242)s 1 f 383.792 y 210.898 (\050)s 10 f 215.564 (\276)s 1 f 222.852 (\051)s 231.519 (is)s 243.585 (de\257ned)s 284.919 (b)s 291.252 (y)s 13 f 408.083 y 145.695 (\241)s 12 f 417.803 y 151.195 (r)s 2 f 411.57 y 161.195 (\050)s 11 f 164.945 (f)s 2 f 170.566 (\051)s 11 f 421.148 y 161.195 (i)s 10 f 417.803 y 174.916 (F)s 13 f 408.083 y 184.3 (\242)s 1 f 417.803 y 189.8 (\050)s 10 f 194.466 (\276)s 1 f 201.754 (\051)s 209.754 (=)s 10 f 222.42 (F)s 1 f 231.804 (\050)s 10 f 236.47 (\276)s 2 f 412.848 y 243.758 (\050)s 11 f 247.508 (f)s 2 f 253.129 (\051)s 11 f 256.879 (;i)s 1 f 417.803 y 263.724 (\051)s 12 f 271.057 (\241)s 10 f 283.057 (F)s 1 f 292.441 (\050)s 10 f 297.107 (\276)s 1 f 304.395 (\051)s 10 f 309.061 (:)s 1 f 447.08 y -5.69 (F)s 1.143 (or)s 10 f 15.843 (i)s 12 f 23.311 (2)s 10 f 34.644 (Z)s 37.694 (Z)s 11 f 441.847 y 48.744 (d)s 1 f 447.08 y 54.339 (,)s 10 f 61.673 (\276)s 2 f 442.726 y 68.96 (\050)s 11 f 72.71 (f)s 2 f 78.331 (\051)s 11 f 82.081 (;i)s 1 f 447.08 y 92.926 (is)s 104.993 (a)s 114.993 (con\257guration)s 187.693 (obtained)s 237.027 (from)s 10 f 265.393 (\276)s 1 f 276.681 (b)s 283.014 (y)s 293.348 (\260)s 300.014 (ipping)s 336.681 (the)s 357.348 (v)s 363.014 (alue)s 388.348 (at)s 10 f 403.014 (i)s 13 f 470.771 y 141.604 (\263)s 10 f 484.091 y 148.77 (\276)s 2 f 479.137 y 156.058 (\050)s 11 f 159.808 (f)s 2 f 165.429 (\051)s 11 f 169.179 (;i)s 13 f 470.771 y 176.024 (\264)s 1 f 484.091 y 185.191 (\050)s 10 f 189.857 (l)s 1 f 193.674 (\051)s 201.674 (=)s 13 f 467.171 y 214.341 (\275)s 10 f 476.891 y 225.341 (\276)s 1 f 232.628 (\050)s 10 f 237.295 (l)s 1 f 241.111 (\051)s 267.429 (if)s 10 f 278.429 (l)s 12 f 285.579 (6)s 1 f 285.579 (=)s 10 f 298.245 (i)s 12 f 491.291 y 225.341 (\241)s 10 f 234.674 (\276)s 1 f 241.961 (\050)s 10 f 246.628 (i)s 1 f 250.762 (\051)s 267.429 (if)s 10 f 278.429 (l)s 1 f 285.579 (=)s 10 f 298.245 (i)s 1 f 306.38 (.)s 523.835 y -5.69 (On)s 14.31 (the)s 34.977 (other)s 66.343 (hand,)s 99.677 (for)s 118.043 (all)s 10 f 134.71 (\276)s 12 f 145.331 (2)s 1 f 156.664 (\255)s 169.331 (and)s 10 f 192.664 (i)s 12 f 200.132 (2)s 10 f 211.465 (Z)s 214.515 (Z)s 11 f 518.602 y 225.565 (d)s 1 f 523.835 y 235.16 (w)s 243.494 (e)s 252.827 (ha)s 265.16 (v)s 271.16 (e)s 559.898 y 13.3 (exp)s 13 f 546.578 y 33.633 (\263)s 12 f 559.898 y 43.466 (\241)s 10 f 551.78 y 56.906 (\257)s 7.421 .48 56.906 557.138 r 1 f 568.129 y 57.617 (2)s 559.898 y 65.767 (\050)s 12 f 70.434 (r)s 2 f 553.664 y 80.434 (\050)s 11 f 84.184 (f)s 2 f 89.805 (\051)s 11 f 563.243 y 80.434 (i)s 10 f 559.898 y 94.155 (H)s 11 f 561.698 y 104.13 (\260)s 1 f 559.898 y 110.287 (\051\050)s 10 f 119.621 (\276)s 1 f 126.908 (\051)s 13 f 546.578 y 131.575 (\264)s 1 f 559.898 y 142.075 (=)s 154.741 (exp)s 13 f 546.578 y 175.075 (\263)s 12 f 559.898 y 184.908 (\241)s 10 f 196.908 (\257)s 204.329 (\276)s 1 f 211.616 (\050)s 10 f 216.283 (i)s 1 f 220.417 (\051)s 10 f 225.084 (\256)s 11 f 554.943 y 232.804 (h)s 16 f 556.143 y 238.423 (1)s 1 f 559.898 y 243.706 (\050)s 10 f 248.373 (\260)s 255.252 (i)s 1 f 259.386 (\051)s 13 f 546.578 y 264.053 (\264)s 1 f 559.898 y 273.22 (exp)s 13 f 546.578 y 293.553 (\263)s 1 f 559.898 y 300.72 (2)s 10 f 306.72 (\260)s 11 f 554.943 y 313.599 (d)s 10 f 559.898 y 319.194 (J)s 11 f 561.698 y 325.849 (\260)s 1 f 559.898 y 332.006 (\0500\051)s 13 f 546.578 y 347.339 (\264)s 10 f 559.898 y 354.506 (;)s 1 f 592.98 y 18.921 (exp)s 13 f 579.66 y 39.254 (\263)s 12 f 592.98 y 49.087 (\241)s 10 f 584.862 y 62.527 (\257)s 7.421 .48 62.527 590.22 r 1 f 601.212 y 63.238 (2)s 592.98 y 71.388 (\050)s 12 f 76.055 (r)s 14 f 587.847 y 86.055 (\250)s 11 f 596.325 y 86.055 (i)s 10 f 592.98 y 94.155 (H)s 11 f 594.78 y 104.13 (\260)s 1 f 592.98 y 110.287 (\051\050)s 10 f 119.621 (\276)s 1 f 126.908 (\051)s 13 f 579.66 y 131.575 (\264)s 1 f 592.98 y 142.075 (=)s 154.741 (exp)s 13 f 579.66 y 175.075 (\263)s 12 f 592.98 y 184.908 (\250)s 10 f 584.862 y 198.348 (\257)s 7.421 .48 198.348 590.22 r 1 f 601.212 y 199.058 (2)s 13 f 583.26 y 207.209 (\243)s 10 f 592.98 y 212.209 (\256)s 11 f 588.026 y 219.929 (h)s 16 f 589.226 y 225.548 (1)s 1 f 592.98 y 230.831 (\050)s 10 f 235.498 (\260)s 242.377 (i)s 1 f 246.511 (\051)s 253.845 (+)s 13 f 589.814 y 265.635 (e)s 10 f 592.98 y 265.844 (h)s 11 f 587.214 y 272.758 (\260)s 2 f 596.18 y 272.758 (2)s 13 f 583.26 y 278.916 (\241)s 1 f 592.98 y 284.416 (2)s 10 f 290.416 (\276)s 1 f 297.703 (\050)s 10 f 302.37 (i)s 1 f 306.504 (\051)s 12 f 313.837 (\250)s 1 f 325.837 (1)s 13 f 583.26 y 331.837 (\242)s 337.337 (\244)s 579.66 y 342.337 (\264)s 1 f 592.98 y 351.504 (exp)s 13 f 579.66 y 371.837 (\263)s 12 f 592.98 y 381.671 (\241)s 10 f 393.671 (\260)s 11 f 588.026 y 400.55 (d)s 10 f 592.98 y 406.145 (J)s 11 f 594.78 y 412.8 (\260)s 1 f 592.98 y 418.957 (\0500\051)s 13 f 579.66 y 434.29 (\264)s 10 f 592.98 y 441.457 (;)s 1 f 630.323 y -5.69 (where)s 10 f 29.01 (\256)s 11 f 625.968 y 36.731 (h)s 16 f 627.168 y 42.349 (1)s 1 f 630.323 y 51.632 (and)s 13 f 627.156 y 74.756 (e)s 10 f 630.323 y 74.966 (h)s 11 f 624.556 y 81.879 (\260)s 2 f 633.523 y 81.879 (2)s 1 f 630.323 y 92.037 (are)s 112.07 (de\257ned)s 153.403 (b)s 159.737 (y)s 10 f 664.6 y 69 (\256)s 11 f 659.645 y 76.721 (h)s 16 f 660.845 y 82.339 (1)s 1 f 664.6 y 87.622 (\050)s 10 f 92.289 (\260)s 99.168 (i)s 1 f 103.303 (\051)s 111.303 (=)s 123.969 (2)s 13 f 654.88 y 129.969 (\241)s 10 f 664.6 y 135.469 (\274)s 2 f 659.645 y 142.74 (1)s 11 f 147.523 (;\260)s 12 f 664.6 y 159.197 (\244)s 10 f 167.864 (J)s 13 f 654.88 y 175.672 (\242)s 1 f 664.6 y 181.172 (\050)s 10 f 185.839 (\260)s 192.718 (i)s 1 f 196.853 (\051)s 204.186 (+)s 10 f 216.186 (h)s 2 f 666.4 y 223.1 (1)s 10 f 664.6 y 231.816 (;)s 13 f 661.433 y 240.273 (e)s 10 f 664.6 y 240.483 (h)s 11 f 658.833 y 247.397 (\260)s 2 f 667.8 y 247.397 (2)s 1 f 664.6 y 256.887 (=)s 13 f 651.28 y 269.554 (\263)s 10 f 664.6 y 276.721 (h)s 2 f 666.4 y 283.635 (2)s 12 f 664.6 y 291.684 (\241)s 10 f 303.684 (\260)s 11 f 659.645 y 310.564 (d)s 13 f 653.2 y 323.385 (X)s 11 f 680.14 y 318.159 (k)s 14 f 323.463 (2)s 11 f 329.93 (Z)s 332.14 (Z)s 15 f 677.367 y 340.906 (d)s 10 f 664.6 y 347.944 (J)s 1 f 355.752 (\050)s 10 f 360.419 (\260)s 367.298 (k)s 1 f 373.923 (\051)s 13 f 651.28 y 378.59 (\264)s 10 f 664.6 y 385.757 (;)s 1 f 705.976 y 223.045 (32)s do-end end endp %%Page: 33 33 %%BeginPageSetup initializepage (Raffaele Esposito; page: 33 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f0_12 sf ( )S -996 -1000 :M f1_12 sf ( )S -993 -1000 :M f2_12 sf ( )S -989 -1000 :M f10_12 sf ( )S -981 -1000 :M f11_12 sf ( )S -972 -1000 :M f12_12 sf ( )S -960 -1000 :M f13_12 sf ( )S -951 -1000 :M f14_12 sf ( )S -937 -1000 :M f15_12 sf ( )S -926 -1000 :M f16_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 1200 1000 div mul /CMBX10 findfont fdef 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 16 5 1200 1000 div mul /CMR5 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 6.31 y -5.69 (for)s 10 f 12.677 (s)s 12 f 21.635 (2)s 1 f 32.968 ([0)s 10 f 42.301 (;)s 47.635 (T)s 1 f 56.314 (],)s 66.981 (w)s 75.314 (e)s 84.647 (shall)s 112.714 (denote)s 10 f 36.371 y 147.637 (\256)s 11 f 31.416 y 155.358 (h)s 16 f 32.616 y 160.976 (1)s 11 f 39.338 y 155.313 (s)s 1 f 36.371 y 166.259 (\050)s 10 f 170.926 (\260)s 177.805 (i)s 1 f 181.939 (\051)s 189.939 (=)s 202.606 (2)s 13 f 26.651 y 208.606 (\241)s 10 f 36.371 y 214.106 (\274)s 2 f 31.416 y 221.377 (1)s 11 f 226.16 (;\260)s 39.338 y 220.946 (s)s 12 f 36.371 y 237.834 (\244)s 10 f 246.501 (J)s 13 f 26.651 y 254.309 (\242)s 1 f 36.371 y 259.809 (\050)s 10 f 264.476 (\260)s 271.355 (i)s 1 f 275.489 (\051)s 282.823 (+)s 10 f 294.823 (h)s 2 f 38.171 y 301.737 (1)s 10 f 36.371 y 307.12 (:)s 1 f 71.286 y 8.71 (By)s 27.052 (using)s 57.961 (the)s 78.137 (relation)s 10 f 121.679 (e)s 11 f 66.931 y 127.267 (b)s 1 f 71.286 y 135.42 (=)s 13 f 61.566 y 148.087 (\241)s 1 f 71.286 y 153.587 (c)s 158.587 (h)s 165.254 (\050)s 10 f 169.92 (b)s 1 f 175.07 (\051)s 181.422 (+)s 192.44 (sh)s 203.84 (\050)s 10 f 208.506 (b)s 1 f 213.656 (\051)s 13 f 61.566 y 218.323 (\242)s 1 f 71.286 y 227.332 (it)s 238.841 (is)s 250.417 (easy)s 276.326 (to)s 290.502 (sho)s 307.568 (w)s 319.744 (that)s 345.253 (the)s 365.429 (martingale)s 10 f 424.971 (M)s 2 f 65.052 y 437.921 (\050)s 11 f 441.671 (G)s 2 f 449.142 (\051)s 11 f 452.892 (;U)s 74.239 y 436.613 (t)s 1 f 88.086 y -5.69 (can)s 16.31 (b)s 23.31 (e)s 32.643 (written)s 74.677 (as)s 10 f 104.886 y 153.32 (M)s 2 f 98.652 y 166.27 (\050)s 11 f 170.02 (G)s 2 f 177.492 (\051)s 11 f 181.242 (;U)s 107.839 y 164.962 (t)s 1 f 104.886 y 195.463 (=)s 10 f 208.129 (M)s 2 f 99.931 y 221.079 (1)s 11 f 107.852 y 219.771 (t)s 1 f 104.886 y 229.129 (+)s 10 f 241.129 (M)s 2 f 99.931 y 254.079 (2)s 11 f 107.852 y 252.771 (t)s 1 f 104.886 y 262.129 (+)s 10 f 274.129 (o)s 11 f 106.686 y 279.946 (\260)s 1 f 104.886 y 286.103 (\0501\051)s 10 f 301.436 (;)s 1 f 129.58 y -5.69 (where)s 10 f 29.01 (M)s 2 f 125.225 y 41.96 (1)s 11 f 132.546 y 40.652 (t)s 1 f 129.58 y 51.343 (and)s 10 f 74.677 (M)s 2 f 125.225 y 87.627 (2)s 11 f 132.546 y 86.318 (t)s 1 f 129.58 y 97.01 (are)s 117.043 (the)s 137.71 (martingales)s 202.477 (giv)s 217.81 (en)s 233.81 (b)s 240.143 (y)s 10 f 169.141 y 16.758 (M)s 2 f 164.186 y 29.708 (1)s 11 f 172.108 y 28.4 (t)s 1 f 169.141 y 38.425 (=)s 10 f 47.758 (\074)s 60.425 (\274)s 2 f 163.374 y 67.695 (1)s 11 f 72.479 (;\260)s 172.094 y 67.265 (t)s 10 f 169.141 y 81.486 (;)s 86.819 (U)s 2 f 164.186 y 96.321 (1)s 11 f 172.108 y 95.013 (t)s 10 f 169.141 y 105.038 (\076)s 12 f 117.704 (\241)s 10 f 130.371 (\074)s 143.038 (\274)s 2 f 163.374 y 150.308 (1)s 11 f 155.092 (;\260)s 2 f 172.341 y 149.878 (0)s 10 f 169.141 y 164.099 (;)s 169.432 (U)s 2 f 164.186 y 178.934 (1)s 172.108 y 177.626 (0)s 10 f 169.141 y 187.651 (\076)s 12 f 200.317 (\241)s 13 f 152.807 y 211.65 (Z)s 11 f 155.774 y 223.651 (t)s 2 f 180.074 y 218.317 (0)s 13 f 159.421 y 229.875 (\255)s 10 f 169.141 y 235.542 (\274)s 2 f 164.186 y 242.813 (1)s 11 f 247.596 (;\260)s 172.108 y 242.382 (s)s 10 f 169.141 y 256.604 (;)s 261.937 (@)s 11 f 170.941 y 268.308 (s)s 10 f 169.141 y 273.437 (U)s 2 f 164.186 y 282.939 (1)s 11 f 172.108 y 281.63 (s)s 13 f 159.421 y 288.322 (\256)s 10 f 169.141 y 293.989 (ds)s 12 f 207.008 y 31.425 (\241)s 1 f 198.89 y 44.865 (1)s 6 .48 44.865 204.248 r 215.239 y 44.865 (2)s 13 f 190.674 y 54.305 (Z)s 11 f 193.641 y 66.305 (t)s 2 f 217.941 y 60.971 (0)s 13 f 193.688 y 72.53 (n)s 197.288 y 80.53 (\255)s 12 f 207.008 y 88.863 (\241)s 10 f 100.863 (\274)s 2 f 202.053 y 108.134 (1)s 11 f 112.917 (;\260)s 209.974 y 107.703 (s)s 10 f 207.008 y 121.924 (;)s 127.258 (U)s 2 f 202.053 y 136.759 (1)s 11 f 209.974 y 135.451 (s)s 13 f 197.288 y 142.143 (\256)s 1 f 207.008 y 150.476 (+)s 13 f 197.288 y 162.476 (\255)s 10 f 207.008 y 168.143 (\274)s 2 f 202.053 y 175.413 (2)s 11 f 180.197 (;\260)s 209.974 y 174.983 (s)s 10 f 207.008 y 189.204 (;)s 194.537 (U)s 2 f 202.053 y 204.039 (1)s 11 f 209.974 y 202.731 (s)s 1 f 207.008 y 209.422 (\050)s 10 f 214.089 (:)s 1 f 217.422 (\051tanh)s 13 f 197.288 y 246.089 (\241)s 10 f 207.008 y 251.589 (\257)s 259.01 (\256)s 11 f 202.053 y 266.731 (h)s 16 f 203.253 y 272.349 (1)s 11 f 209.974 y 266.686 (s)s 1 f 207.008 y 277.632 (\050)s 10 f 282.299 (:)s 1 f 285.632 (\051)s 13 f 197.288 y 290.299 (\242)s 295.799 (\256)s 193.688 y 301.466 (o)s 10 f 207.008 y 309.466 (ds)s 12 f 244.875 y 31.425 (\241)s 1 f 236.757 y 44.865 (1)s 6 .48 44.865 242.115 r 253.106 y 44.865 (4)s 10 f 244.875 y 52.305 (\260)s 11 f 239.92 y 59.184 (d)s 13 f 233.475 y 71.051 (X)s 11 f 260.415 y 66.779 (i)s 14 f 70.175 (2)s 11 f 76.641 (Z)s 78.851 (Z)s 15 f 257.642 y 87.617 (d)s 13 f 228.541 y 94.655 (Z)s 11 f 231.508 y 106.655 (t)s 2 f 255.808 y 101.322 (0)s 10 f 244.875 y 112.88 (U)s 2 f 239.92 y 122.382 (1)s 11 f 247.841 y 121.073 (s)s 1 f 244.875 y 127.765 (\050)s 10 f 132.432 (\260)s 139.311 (i)s 1 f 143.445 (\051)s 13 f 231.555 y 148.112 (n)s 1 f 244.875 y 156.112 (tanh)s 13 f 231.555 y 180.112 (\263)s 10 f 236.757 y 188.719 (\257)s 7.421 .48 188.719 242.115 r 1 f 253.106 y 189.429 (2)s 13 f 235.155 y 197.58 (\243)s 10 f 244.875 y 202.58 (\256)s 11 f 239.92 y 210.3 (h)s 16 f 241.12 y 215.918 (1)s 11 f 247.841 y 210.256 (s)s 1 f 244.875 y 221.202 (\050)s 10 f 225.869 (\260)s 232.748 (i)s 1 f 236.882 (\051)s 244.215 (+)s 13 f 241.708 y 256.006 (e)s 10 f 244.875 y 256.215 (h)s 11 f 239.108 y 263.129 (\260)s 2 f 248.075 y 263.129 (2)s 13 f 235.155 y 269.287 (\244)s 231.555 y 274.287 (\264)s 1 f 244.875 y 284.12 (+)s 296.12 (tanh)s 13 f 231.555 y 320.12 (\263)s 10 f 236.757 y 328.727 (\257)s 7.421 .48 328.727 242.115 r 1 f 253.106 y 329.437 (2)s 13 f 235.155 y 337.587 (\243)s 10 f 244.875 y 342.587 (\256)s 11 f 239.92 y 350.308 (h)s 16 f 241.12 y 355.926 (1)s 11 f 247.841 y 350.264 (s)s 1 f 244.875 y 361.21 (\050)s 10 f 365.876 (\260)s 372.756 (i)s 1 f 376.89 (\051)s 12 f 384.223 (\241)s 13 f 241.708 y 396.014 (e)s 10 f 244.875 y 396.223 (h)s 11 f 239.108 y 403.137 (\260)s 2 f 248.075 y 403.137 (2)s 13 f 235.155 y 409.294 (\244)s 231.555 y 414.294 (\264)s 421.461 (o)s 10 f 244.875 y 429.461 (ds)s 12 f 289.184 y 31.425 (\241)s 1 f 281.066 y 44.865 (1)s 6 .48 44.865 286.424 r 297.415 y 44.865 (8)s 13 f 272.851 y 54.305 (Z)s 11 f 275.817 y 66.305 (t)s 2 f 300.118 y 60.971 (0)s 13 f 275.864 y 72.53 (D)s 10 f 289.184 y 79.863 (\274)s 2 f 284.229 y 87.134 (1)s 11 f 91.917 (;\260)s 292.151 y 86.703 (s)s 10 f 289.184 y 100.924 (;)s 106.258 (U)s 2 f 284.229 y 115.759 (1)s 11 f 292.151 y 114.451 (s)s 1 f 289.184 y 121.143 (\050)s 10 f 125.809 (:)s 1 f 129.143 (\051)s 13 f 275.864 y 133.809 (n)s 1 f 289.184 y 141.809 (tanh)s 13 f 275.864 y 165.81 (\263)s 10 f 281.066 y 174.416 (\257)s 7.421 .48 174.416 286.424 r 1 f 297.415 y 175.127 (2)s 13 f 279.464 y 183.277 (\243)s 10 f 289.184 y 188.277 (\256)s 11 f 284.229 y 195.998 (h)s 16 f 285.429 y 201.616 (1)s 11 f 292.151 y 195.953 (s)s 1 f 289.184 y 206.899 (\050)s 10 f 211.566 (:)s 1 f 214.899 (\051)s 222.233 (+)s 13 f 286.017 y 234.023 (e)s 10 f 289.184 y 234.233 (h)s 11 f 283.417 y 241.147 (\260)s 2 f 292.384 y 241.147 (2)s 13 f 279.464 y 247.304 (\244)s 275.864 y 252.304 (\264)s 12 f 289.184 y 262.137 (\241)s 1 f 274.137 (tanh)s 13 f 275.864 y 298.137 (\263)s 10 f 281.066 y 306.744 (\257)s 7.421 .48 306.744 286.424 r 1 f 297.415 y 307.454 (2)s 13 f 279.464 y 315.605 (\243)s 10 f 289.184 y 320.605 (\256)s 11 f 284.229 y 328.326 (h)s 16 f 285.429 y 333.944 (1)s 11 f 292.151 y 328.281 (s)s 1 f 289.184 y 339.227 (\050)s 10 f 343.894 (:)s 1 f 347.227 (\051)s 12 f 354.56 (\241)s 13 f 286.017 y 366.351 (e)s 10 f 289.184 y 366.56 (h)s 11 f 283.417 y 373.474 (\260)s 2 f 292.384 y 373.474 (2)s 13 f 279.464 y 379.631 (\244)s 275.864 y 384.632 (\264)s 12 f 289.184 y 394.465 (\241)s 1 f 406.465 (2)s 13 f 275.864 y 412.465 (o)s 420.465 (E)s 10 f 289.184 y 427.798 (ds)s 12 f 327.051 y 31.425 (\241)s 1 f 318.933 y 44.865 (1)s 6 .48 44.865 324.291 r 335.282 y 44.865 (8)s 13 f 310.718 y 54.305 (Z)s 11 f 313.684 y 66.305 (t)s 2 f 337.985 y 60.971 (0)s 13 f 313.731 y 72.53 (D)s 12 f 327.051 y 82.53 (\241)s 10 f 94.529 (\274)s 2 f 322.096 y 101.8 (2)s 11 f 106.584 (;\260)s 330.018 y 101.37 (s)s 10 f 327.051 y 115.591 (;)s 120.924 (U)s 2 f 322.096 y 130.426 (1)s 11 f 330.018 y 129.118 (s)s 1 f 327.051 y 135.809 (\050)s 10 f 140.476 (:)s 1 f 143.809 (\051)s 13 f 313.731 y 148.476 (n)s 1 f 327.051 y 156.476 (tanh)s 13 f 313.731 y 180.476 (\263)s 10 f 318.933 y 189.083 (\257)s 7.421 .48 189.083 324.291 r 1 f 335.282 y 189.793 (2)s 13 f 317.331 y 197.944 (\243)s 10 f 327.051 y 202.944 (\256)s 11 f 322.096 y 210.664 (h)s 16 f 323.296 y 216.283 (1)s 11 f 330.018 y 210.62 (s)s 1 f 327.051 y 221.566 (\050)s 10 f 226.233 (:)s 1 f 229.566 (\051)s 236.899 (+)s 13 f 323.884 y 248.689 (e)s 10 f 327.051 y 248.899 (h)s 11 f 321.284 y 255.813 (\260)s 2 f 330.251 y 255.813 (2)s 13 f 317.331 y 261.97 (\244)s 313.731 y 266.97 (\264)s 1 f 327.051 y 276.804 (+)s 288.804 (tanh)s 13 f 313.731 y 312.804 (\263)s 10 f 318.933 y 321.41 (\257)s 7.421 .48 321.41 324.291 r 1 f 335.282 y 322.121 (2)s 13 f 317.331 y 330.271 (\243)s 10 f 327.051 y 335.271 (\256)s 11 f 322.096 y 342.992 (h)s 16 f 323.296 y 348.61 (1)s 11 f 330.018 y 342.948 (s)s 1 f 327.051 y 353.894 (\050)s 10 f 358.56 (:)s 1 f 361.894 (\051)s 12 f 369.227 (\241)s 13 f 323.884 y 381.017 (e)s 10 f 327.051 y 381.227 (h)s 11 f 321.284 y 388.141 (\260)s 2 f 330.251 y 388.141 (2)s 13 f 317.331 y 394.298 (\244)s 313.731 y 399.298 (\264)s 406.465 (o)s 414.465 (E)s 10 f 327.051 y 421.798 (ds)s 1 f 364.379 y -5.69 (and)s 10 f 400.974 y 6.425 (M)s 2 f 396.019 y 19.375 (2)s 11 f 403.94 y 18.066 (t)s 1 f 400.974 y 28.091 (=)s 10 f 37.425 (\074)s 50.091 (\274)s 2 f 395.207 y 57.362 (2)s 11 f 62.146 (;\260)s 403.927 y 56.932 (t)s 10 f 400.974 y 71.153 (;)s 76.486 (U)s 2 f 396.019 y 85.988 (2)s 11 f 403.94 y 84.679 (t)s 10 f 400.974 y 94.704 (\076)s 12 f 107.371 (\241)s 10 f 120.038 (\074)s 132.704 (\274)s 2 f 395.207 y 139.975 (2)s 11 f 144.758 (;\260)s 2 f 404.174 y 139.545 (0)s 10 f 400.974 y 153.766 (;)s 159.099 (U)s 2 f 396.019 y 168.601 (2)s 403.94 y 167.292 (0)s 10 f 400.974 y 177.317 (\076)s 12 f 189.984 (\241)s 13 f 384.64 y 201.317 (Z)s 11 f 387.607 y 213.317 (t)s 2 f 411.907 y 207.984 (0)s 13 f 391.254 y 219.542 (\255)s 10 f 400.974 y 225.209 (\274)s 2 f 396.019 y 232.48 (2)s 11 f 237.263 (;\260)s 403.94 y 232.049 (s)s 10 f 400.974 y 246.27 (;)s 251.604 (@)s 11 f 402.774 y 257.974 (s)s 10 f 400.974 y 263.104 (U)s 2 f 396.019 y 272.605 (2)s 11 f 403.94 y 271.297 (s)s 13 f 391.254 y 277.989 (\256)s 10 f 400.974 y 283.655 (ds)s 12 f 438.841 y 21.091 (\241)s 1 f 430.723 y 34.531 (1)s 6 .48 34.531 436.081 r 447.072 y 34.531 (4)s 10 f 438.841 y 41.971 (\260)s 11 f 433.886 y 48.851 (d)s 13 f 427.441 y 60.717 (X)s 11 f 454.381 y 56.446 (i)s 14 f 59.841 (2)s 11 f 66.308 (Z)s 68.518 (Z)s 15 f 451.608 y 77.284 (d)s 13 f 422.507 y 84.322 (Z)s 11 f 425.474 y 96.322 (t)s 2 f 449.774 y 90.988 (0)s 10 f 438.841 y 102.547 (U)s 2 f 433.886 y 112.048 (2)s 11 f 441.807 y 110.74 (s)s 1 f 438.841 y 117.432 (\050)s 10 f 122.098 (\260)s 128.978 (i)s 1 f 133.112 (\051)s 13 f 425.521 y 137.779 (n)s 1 f 438.841 y 145.779 (tanh)s 13 f 425.521 y 169.779 (\263)s 10 f 430.723 y 178.385 (\257)s 7.421 .48 178.385 436.081 r 1 f 447.072 y 179.096 (2)s 13 f 429.121 y 187.246 (\243)s 10 f 438.841 y 192.246 (\256)s 11 f 433.886 y 199.967 (h)s 16 f 435.086 y 205.585 (1)s 11 f 441.807 y 199.923 (s)s 1 f 438.841 y 210.869 (\050)s 10 f 215.535 (\260)s 222.415 (i)s 1 f 226.549 (\051)s 233.882 (+)s 13 f 435.674 y 245.672 (e)s 10 f 438.841 y 245.882 (h)s 11 f 433.074 y 252.796 (\260)s 2 f 442.041 y 252.796 (2)s 13 f 429.121 y 258.953 (\244)s 425.521 y 263.953 (\264)s 12 f 438.841 y 273.787 (\241)s 1 f 285.787 (tanh)s 13 f 425.521 y 309.787 (\263)s 10 f 430.723 y 318.393 (\257)s 7.421 .48 318.393 436.081 r 1 f 447.072 y 319.104 (2)s 13 f 429.121 y 327.254 (\243)s 10 f 438.841 y 332.254 (\256)s 11 f 433.886 y 339.975 (h)s 16 f 435.086 y 345.593 (1)s 11 f 441.807 y 339.931 (s)s 1 f 438.841 y 350.876 (\050)s 10 f 355.543 (\260)s 362.423 (i)s 1 f 366.557 (\051)s 12 f 373.89 (\241)s 13 f 435.674 y 385.68 (e)s 10 f 438.841 y 385.89 (h)s 11 f 433.074 y 392.804 (\260)s 2 f 442.041 y 392.804 (2)s 13 f 429.121 y 398.961 (\244)s 425.521 y 403.961 (\264)s 1 f 438.841 y 413.794 (+)s 425.794 (2)s 13 f 425.521 y 431.794 (o)s 10 f 438.841 y 439.794 (ds)s 12 f 483.15 y 21.091 (\241)s 1 f 475.032 y 34.531 (1)s 6 .48 34.531 480.39 r 491.381 y 34.531 (8)s 13 f 466.817 y 43.971 (Z)s 11 f 469.783 y 55.971 (t)s 2 f 494.083 y 50.638 (0)s 13 f 469.83 y 62.196 (D)s 12 f 483.15 y 72.196 (\241)s 10 f 84.196 (\274)s 2 f 478.195 y 91.467 (2)s 11 f 96.25 (;\260)s 486.117 y 91.037 (s)s 10 f 483.15 y 105.258 (;)s 110.591 (U)s 2 f 478.195 y 120.093 (2)s 11 f 486.117 y 118.784 (s)s 1 f 483.15 y 125.476 (\050)s 10 f 130.143 (:)s 1 f 133.476 (\051)s 13 f 469.83 y 138.143 (n)s 1 f 483.15 y 146.143 (tanh)s 13 f 469.83 y 170.143 (\263)s 10 f 475.032 y 178.749 (\257)s 7.421 .48 178.749 480.39 r 1 f 491.381 y 179.46 (2)s 13 f 473.43 y 187.61 (\243)s 10 f 483.15 y 192.61 (\256)s 11 f 478.195 y 200.331 (h)s 16 f 479.395 y 205.949 (1)s 11 f 486.117 y 200.287 (s)s 1 f 483.15 y 211.233 (\050)s 10 f 215.899 (:)s 1 f 219.233 (\051)s 226.566 (+)s 13 f 479.983 y 238.356 (e)s 10 f 483.15 y 238.566 (h)s 11 f 477.383 y 245.48 (\260)s 2 f 486.35 y 245.48 (2)s 13 f 473.43 y 251.637 (\244)s 469.83 y 256.637 (\264)s 12 f 483.15 y 266.47 (\241)s 1 f 278.47 (tanh)s 13 f 469.83 y 302.47 (\263)s 10 f 475.032 y 311.077 (\257)s 7.421 .48 311.077 480.39 r 1 f 491.381 y 311.788 (2)s 13 f 473.43 y 319.938 (\243)s 10 f 483.15 y 324.938 (\256)s 11 f 478.195 y 332.659 (h)s 16 f 479.395 y 338.277 (1)s 11 f 486.117 y 332.614 (s)s 1 f 483.15 y 343.56 (\050)s 10 f 348.227 (:)s 1 f 351.56 (\051)s 12 f 358.894 (\241)s 13 f 479.983 y 370.684 (e)s 10 f 483.15 y 370.894 (h)s 11 f 477.383 y 377.807 (\260)s 2 f 486.35 y 377.807 (2)s 13 f 473.43 y 383.965 (\244)s 469.83 y 388.965 (\264)s 1 f 483.15 y 398.798 (+)s 410.798 (6)s 13 f 469.83 y 416.798 (o)s 424.798 (E)s 10 f 483.15 y 432.131 (ds)s 12 f 521.017 y 21.091 (\241)s 1 f 512.899 y 34.531 (1)s 6 .48 34.531 518.257 r 529.248 y 34.531 (8)s 13 f 504.684 y 43.971 (Z)s 11 f 507.65 y 55.971 (t)s 2 f 531.95 y 50.638 (0)s 13 f 507.697 y 62.196 (D)s 10 f 521.017 y 69.53 (\274)s 2 f 516.062 y 76.8 (1)s 11 f 81.584 (;\260)s 523.984 y 76.37 (s)s 10 f 521.017 y 90.591 (;)s 95.924 (U)s 2 f 516.062 y 105.426 (2)s 11 f 523.984 y 104.118 (s)s 1 f 521.017 y 110.809 (\050)s 10 f 115.476 (:)s 1 f 118.809 (\051)s 13 f 507.697 y 123.476 (n)s 1 f 521.017 y 131.476 (tanh)s 13 f 507.697 y 155.476 (\263)s 10 f 512.899 y 164.083 (\257)s 7.421 .48 164.083 518.257 r 1 f 529.248 y 164.793 (2)s 13 f 511.297 y 172.944 (\243)s 10 f 521.017 y 177.944 (\256)s 11 f 516.062 y 185.665 (h)s 16 f 517.262 y 191.283 (1)s 11 f 523.984 y 185.62 (s)s 1 f 521.017 y 196.566 (\050)s 10 f 201.233 (:)s 1 f 204.566 (\051)s 211.899 (+)s 13 f 517.85 y 223.69 (e)s 10 f 521.017 y 223.899 (h)s 11 f 515.25 y 230.813 (\260)s 2 f 524.217 y 230.813 (2)s 13 f 511.297 y 236.971 (\244)s 507.697 y 241.971 (\264)s 1 f 521.017 y 251.804 (+)s 263.804 (tanh)s 13 f 507.697 y 287.804 (\263)s 10 f 512.899 y 296.411 (\257)s 7.421 .48 296.411 518.257 r 1 f 529.248 y 297.121 (2)s 13 f 511.297 y 305.271 (\243)s 10 f 521.017 y 310.271 (\256)s 11 f 516.062 y 317.992 (h)s 16 f 517.262 y 323.61 (1)s 11 f 523.984 y 317.948 (s)s 1 f 521.017 y 328.894 (\050)s 10 f 333.56 (:)s 1 f 336.894 (\051)s 12 f 344.227 (\241)s 13 f 517.85 y 356.017 (e)s 10 f 521.017 y 356.227 (h)s 11 f 515.25 y 363.141 (\260)s 2 f 524.217 y 363.141 (2)s 13 f 511.297 y 369.298 (\244)s 507.697 y 374.298 (\264)s 381.465 (o)s 389.465 (E)s 10 f 521.017 y 396.798 (ds:)s 1 f 560.786 y 8.71 (On)s 29.713 (the)s 51.382 (other)s 83.752 (hand,)s 118.339 (a)s 129.341 (simple)s 167.744 (computation)s 238.747 (sho)s 255.814 (ws)s 274.217 (that)s 301.22 (the)s 322.889 (quadratic)s 377.592 (v)s 383.259 (ariation)s 12 f 428.962 (N)s 2 f 556.432 y 440.576 (\050)s 11 f 444.326 (G)s 2 f 451.797 (\051)s 11 f 455.547 (;)s 2 f 458.397 (1)s 1 f 577.586 y -5.69 (\050resp.)s 12 f 32.626 (N)s 2 f 573.232 y 44.24 (\050)s 11 f 47.99 (G)s 2 f 55.462 (\051)s 11 f 59.212 (;)s 2 f 62.062 (2)s 1 f 577.586 y 67.445 (\051)s 77.295 (of)s 92.145 (the)s 113.995 (martingale)s 10 f 175.212 (M)s 2 f 573.232 y 188.162 (1)s 11 f 580.553 y 186.853 (t)s 1 f 577.586 y 198.728 (\050resp.)s 10 f 237.045 (M)s 2 f 573.232 y 249.995 (2)s 11 f 580.553 y 248.686 (t)s 1 f 577.586 y 255.378 (\051)s 265.228 (v)s 270.895 (anishes)s 313.545 (as)s 10 f 329.461 (\260)s 12 f 341.646 (!)s 1 f 358.951 (0.)s 377.168 (Therefore,)s 436.38 (using)s 594.386 y -5.69 (Cheb)s 21.31 (yc)s 32.643 (hev\047s)s 63.043 (inequalit)s 108.377 (y)s 118.71 (and)s 142.043 (Do)s 157.543 (ob\047s)s 182.277 (inequalit)s 227.61 (y)s 232.944 (,)s 240.277 (w)s 248.61 (e)s 257.944 (obtain)s 635.781 y 101.044 (lim)s 11 f 643.194 y 99.423 (\260)s 14 f 104.981 (!)s 2 f 114.547 (0)s 0 f 635.781 y 121.331 (P)s 2 f 629.548 y 130.764 (\050)s 11 f 134.514 (G)s 2 f 141.985 (\051)s 11 f 638.551 y 130.764 (\271)s 15 f 636.151 y 136.599 (\260)s 13 f 615.261 y 146.335 (\050)s 622.461 y 156.002 (h)s 1 f 635.781 y 170.271 (sup)s 2 f 645.872 y 163.669 (0)s 14 f 168.452 (\267)s 11 f 175.952 (s)s 14 f 180.481 (\267)s 11 f 187.981 (T)s 13 f 625.581 y 196.941 (\257)s 632.781 y 196.941 (\257)s 10 f 635.781 y 200.941 (M)s 2 f 630.826 y 213.891 (1)s 11 f 638.748 y 212.582 (s)s 13 f 625.581 y 219.274 (\257)s 632.781 y 219.274 (\257)s 1 f 635.781 y 225.941 (+)s 244.543 (sup)s 2 f 645.872 y 237.941 (0)s 14 f 242.724 (\267)s 11 f 250.224 (s)s 14 f 254.753 (\267)s 11 f 262.253 (T)s 13 f 625.581 y 271.213 (\257)s 632.781 y 271.213 (\257)s 10 f 635.781 y 275.213 (M)s 2 f 630.826 y 288.163 (2)s 11 f 638.748 y 286.854 (s)s 13 f 625.581 y 293.546 (\257)s 632.781 y 293.546 (\257)s 622.461 y 299.546 (i)s 10 f 635.781 y 308.546 (\076)s 321.213 (\261)s 13 f 615.261 y 327 (\051)s 1 f 635.781 y 340 (=)s 352.667 (0)s 677.176 y -5.69 (for)s 12.677 (an)s 25.01 (y)s 35.343 (p)s 42.343 (ositiv)s 70.41 (e)s 10 f 79.743 (\261)s 1 f 85.531 (.)s 705.976 y 223.045 (33)s do-end end endp %%Page: 34 34 %%BeginPageSetup initializepage (Raffaele Esposito; page: 34 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f0_12 sf ( )S -996 -1000 :M f1_12 sf ( )S -993 -1000 :M f2_12 sf ( )S -989 -1000 :M f10_12 sf ( )S -981 -1000 :M f11_12 sf ( )S -972 -1000 :M f12_12 sf ( )S -960 -1000 :M f13_12 sf ( )S -951 -1000 :M f14_12 sf ( )S -937 -1000 :M f15_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 1200 1000 div mul /CMBX10 findfont fdef 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 6.31 y 8.71 (T)s 16.376 (o)s 26.731 (conclude)s 76.419 (the)s 97.441 (pro)s 115.141 (of)s 129.162 (w)s 137.495 (e)s 147.183 (ha)s 159.517 (v)s 165.517 (e)s 175.205 (just)s 199.293 (to)s 214.314 (let)s 10 f 232.002 (\260)s 12 f 242.806 (!)s 1 f 258.73 (0)s 269.085 (and)s 292.773 (to)s 307.794 (follo)s 329.795 (w)s 342.816 (the)s 363.837 (same)s 394.259 (argumen)s 439.292 (ts)s 453.047 (as)s 23.11 y -5.69 (in)s 8.31 (the)s 28.977 (Ka)s 43.977 (w)s 52.31 (asaki)s 82.71 (case.)s 8.16 .48 118.11 16.51 r .48 7.2 118.11 23.71 r .48 7.2 125.79 23.71 r 8.16 .48 118.11 24.19 r 0 f 68.482 y -5.69 (6.)s 11.176 (Non)s 41.143 (gradien)s 85.543 (t)s 95.509 (dynamics.)s 1 f 92.4 y 8.71 (In)s 22.815 (this)s 45.32 (section,)s 88.005 (w)s 96.338 (e)s 104.777 (consider)s 150.649 (a)s 159.754 (di\256eren)s 198.454 (t)s 206.226 (kind)s 232.331 (of)s 245.103 (dynamics)s 297.275 (rev)s 313.309 (ersible)s 349.848 (for)s 367.319 (the)s 387.091 (Gibbs)s 421.013 (measure)s 109.2 y -5.69 (asso)s 16.11 (ciated)s 50.212 (to)s 63.648 (the)s 83.084 (Hamiltonian)s 150.854 (\0501.1\051)s 178.29 (\050with)s 10 f 209.059 (h)s 2 f 111 y 215.973 (2)s 1 f 109.2 y 224.69 (=)s 237.356 (1\051)s 250.792 (whic)s 274.459 (h)s 283.895 (is)s 294.731 (of)s 307.167 (the)s 326.603 (so)s 340.105 (called)s 372.875 (non)s 394.977 (gradien)s 433.344 (t)s 440.78 (t)s 445.113 (yp)s 458.447 (e)s 126 y -5.69 ([KL].)s 24.235 (W)s 35.568 (e)s 43.994 (consider)s 89.852 (a)s 98.944 (system)s 137.836 (of)s 10 f 150.595 (N)s 1 f 164.637 (spins)s 193.862 (on)s 209.621 (a)s 218.713 (d-dimensional)s 294.538 (torus)s 324.397 (I)s 323.57 (T)s 11 f 120.767 y 332.237 (d)s 1 f 126 y 337.832 (.)s 346.196 (A)s 354.863 (t)s 362.621 (times)s 393.78 (exp)s 412.447 (onen)s 436.78 (tially)s 142.8 y -5.69 (distributed)s 57.307 (eac)s 73.64 (h)s 85.87 (b)s 92.87 (ond)s 117.767 (\050)s 10 f 122.434 (i;)s 131.901 (j)s 1 f 137.53 (\051)s 12 f 148.135 (2)s 1 f 162.074 (I)s 161.248 (T)s 11 f 137.567 y 169.914 (d)s 12 f 142.8 y 179.219 (\243)s 1 f 192.261 (I)s 191.434 (T)s 11 f 137.567 y 200.101 (d)s 10 f 142.8 y 205.697 (;)s 12 f 211.03 (j)s 10 f 214.363 (i)s 12 f 222.206 (\241)s 10 f 235.248 (j)s 12 f 240.877 (j)s 1 f 250.149 (=)s 265.422 (1)s 276.985 (c)s 281.985 (hange)s 318.215 (its)s 336.512 (con\257guration)s 410.776 (\050)s 10 f 415.442 (\276)s 1 f 422.73 (\050)s 10 f 427.397 (i)s 1 f 431.531 (\051)s 10 f 436.197 (;)s 441.531 (\276)s 1 f 448.818 (\050)s 10 f 453.485 (j)s 1 f 459.114 (\051)s 159.6 y -5.69 (indip)s 21.31 (enden)s 51.643 (tly)s 69.846 (of)s 83.382 (the)s 103.918 (others)s 139.887 (\050or)s 159.123 (sta)s 174.19 (ys)s 189.126 (unc)s 207.459 (hanged\051)s 253.329 (to)s 267.865 (the)s 288.401 (new)s 312.937 (con\257guration)s 385.506 (\050)s 10 f 390.173 (\276)s 14 f 155.245 y 397.461 (0)s 1 f 159.6 y 400.827 (\050)s 10 f 405.494 (i)s 1 f 409.628 (\051)s 10 f 414.295 (;)s 419.628 (\276)s 14 f 155.245 y 426.916 (0)s 1 f 159.6 y 430.282 (\050)s 10 f 434.949 (j)s 1 f 440.577 (\051\051)s 453.78 (in)s 176.4 y -5.69 (suc)s 10.71 (h)s 21.486 (a)s 31.596 (w)s 39.929 (a)s 45.596 (y)s 56.039 (that)s 12 f 82.149 (j)s 10 f 85.482 (\276)s 1 f 92.769 (\050)s 10 f 97.436 (i)s 1 f 101.57 (\051)s 12 f 108.977 (\241)s 10 f 121.05 (\276)s 1 f 128.337 (\050)s 10 f 133.004 (i)s 1 f 137.138 (\051)s 14 f 172.045 y 141.805 (0)s 12 f 176.4 y 145.171 (j)s 1 f 152.021 (=)s 164.87 (1,)s 12 f 178.341 (j)s 10 f 181.674 (\276)s 1 f 188.962 (\050)s 10 f 193.628 (j)s 1 f 199.257 (\051)s 12 f 206.663 (\241)s 10 f 218.736 (\276)s 14 f 172.045 y 226.024 (0)s 1 f 176.4 y 229.39 (\050)s 10 f 234.057 (j)s 1 f 239.686 (\051)s 12 f 244.352 (j)s 1 f 251.202 (=)s 264.051 (1)s 274.161 (and)s 10 f 297.604 (\276)s 1 f 304.891 (\050)s 10 f 309.558 (i)s 1 f 313.692 (\051)s 321.099 (+)s 10 f 333.172 (\276)s 1 f 340.459 (\050)s 10 f 345.126 (j)s 1 f 350.754 (\051)s 358.937 (=)s 10 f 371.787 (\276)s 14 f 172.045 y 379.074 (0)s 1 f 176.4 y 382.441 (\050)s 10 f 387.107 (i)s 1 f 391.242 (\051)s 398.648 (+)s 10 f 410.721 (\276)s 14 f 172.045 y 418.009 (0)s 1 f 176.4 y 421.375 (\050)s 10 f 426.042 (j)s 1 f 431.671 (\051)s 440.447 (with)s 193.2 y -5.69 (jump)s 25.31 (rates)s 54.743 (c)s 59.743 (hosen)s 93.143 (to)s 107.81 (satisfy)s 145.277 (the)s 165.943 (detailed)s 211.277 (balance)s 254.61 (condition)s 307.277 (with)s 334.61 (resp)s 356.377 (ect)s 375.71 (the)s 396.377 (Hamiltonian)s 10 f 223.49 y 138.314 (H)s 11 f 225.29 y 148.289 (\260)s 1 f 223.49 y 154.446 (\050)s 10 f 159.113 (\264)s 1 f 165.502 (\051)s 173.502 (=)s 12 f 186.168 (\241)s 13 f 212.09 y 202.516 (X)s 11 f 239.03 y 197.501 (i;j)s 14 f 208.203 (2)s 2 f 214.67 (I)s 212.976 (T)s 15 f 236.257 y 219.826 (d)s 10 f 223.49 y 226.864 (J)s 11 f 225.29 y 233.519 (\260)s 1 f 223.49 y 239.676 (\050)s 10 f 244.343 (i)s 12 f 251.143 (\241)s 10 f 263.143 (j)s 1 f 268.772 (\051)s 10 f 273.439 (\276)s 1 f 280.726 (\050)s 10 f 285.393 (i)s 1 f 289.527 (\051)s 10 f 294.194 (\276)s 1 f 301.481 (\050)s 10 f 306.148 (j)s 1 f 311.776 (\051)s 10 f 316.443 (;)s 1 f 269.153 y -5.69 (In)s 9.31 (other)s 40.677 (w)s 49.01 (ords,)s 78.443 (the)s 99.11 (transitions)s 158.61 (allo)s 176.943 (w)s 185.277 (ed)s 201.277 (for)s 219.643 (a)s 229.643 (b)s 236.644 (ond)s 259.977 (\050)s 10 f 264.644 (i;)s 274.111 (j)s 1 f 279.74 (\051)s 288.406 (are)s 300.643 y 126.045 (\0500)s 10 f 136.712 (;)s 12 f 142.045 (\241)s 1 f 151.378 (1\051)s 12 f 162.045 (\050)s 172.045 (\051)s 1 f 184.045 (\050)s 12 f 188.712 (\241)s 1 f 198.045 (1)s 10 f 204.045 (;)s 1 f 209.378 (0\051)s 10 f 220.045 (;)s 1 f 247.378 (\0501)s 10 f 258.045 (;)s 1 f 263.378 (0\051)s 12 f 274.045 (\050)s 284.045 (\051)s 1 f 296.045 (\0500)s 10 f 306.712 (;)s 1 f 312.045 (1\051)s 321.043 y 127.378 (\0501)s 10 f 138.045 (;)s 12 f 143.378 (\241)s 1 f 152.712 (1\051)s 12 f 163.378 (\050)s 173.378 (\051)s 1 f 185.378 (\0500)s 10 f 196.045 (;)s 1 f 201.378 (0\051)s 10 f 212.045 (;)s 1 f 247.378 (\0500)s 10 f 258.045 (;)s 1 f 263.378 (0\051)s 12 f 274.045 (\050)s 284.045 (\051)s 1 f 296.045 (\050)s 12 f 300.712 (\241)s 1 f 310.045 (1)s 10 f 316.045 (;)s 1 f 321.379 (1\051)s 351.986 y 8.71 (W)s 20.043 (e)s 30.556 (remark)s 72.803 (that)s 99.982 (the)s 121.829 (di\256erence)s 176.709 (b)s 183.709 (et)s 193.375 (w)s 201.709 (een)s 224.222 (the)s 246.068 (n)s 252.402 (um)s 268.735 (b)s 275.735 (er)s 290.948 (of)s 305.794 (p)s 312.794 (ositiv)s 340.861 (e)s 351.374 (and)s 375.887 (negativ)s 413.888 (e)s 424.401 (spins)s 455.714 (is)s 368.786 y -5.69 (conserv)s 33.077 (ed)s 49.461 (b)s 55.794 (y)s 66.511 (this)s 90.296 (dynamics,)s 147.176 (while)s 178.893 (the)s 199.944 (n)s 206.278 (um)s 222.611 (b)s 229.611 (er)s 244.028 (of)s 258.079 (zero)s 283.83 (spins)s 314.348 (is)s 326.798 (not,)s 351.945 (b)s 358.945 (ecause)s 396.729 (negativ)s 434.729 (e)s 444.447 (and)s 385.586 y -5.69 (p)s 1.31 (ositiv)s 29.377 (e)s 38.446 (neigh)s 66.113 (b)s 73.113 (ouring)s 110.216 (spins)s 140.085 (can)s 161.821 (annihilate)s 217.558 (to)s 231.96 (create)s 267.063 (t)s 271.397 (w)s 279.73 (o)s 289.466 (spins)s 319.336 (with)s 346.405 (zero)s 371.508 (v)s 377.175 (alue)s 402.244 (or)s 416.68 (vicev)s 443.014 (ersa)s 402.386 y -5.69 (t)s -1.357 (w)s 6.976 (o)s 16.976 (zero)s 42.343 (spins)s 72.477 (can)s 94.477 (disapp)s 128.877 (ear)s 148.91 (to)s 163.577 (giv)s 178.91 (e)s 188.243 (rise)s 210.343 (to)s 225.01 (a)s 235.01 (couple)s 272.344 (of)s 286.01 (spins)s 12 f 316.144 (\247)s 1 f 325.477 (1.)s 419.306 y 8.71 (This)s 38.085 (dynamics,)s 96.953 (when)s 130.261 (reform)s 164.328 (ulated)s 202.969 (as)s 219.677 (a)s 231.652 (lattice)s 270.294 (gas,)s 296.829 (turns)s 330.237 (out)s 353.545 (to)s 370.186 (b)s 377.186 (e)s 388.494 (at)s 10 f 405.136 (\257)s 1 f 419.181 (=)s 435.139 (0)s 447.113 (the)s 436.106 y -5.69 (generalized)s 56.557 (exclusion)s 108.505 (pro)s 126.205 (cess)s 150.552 (in)s 160.219 (tro)s 175.919 (duced)s 210.8 (in)s 225.014 ([KLO].)s 265.395 (T)s 273.062 (o)s 283.276 (matc)s 308.943 (h)s 319.823 (the)s 340.704 (notations)s 393.652 (in)s 407.866 (that)s 434.08 (pap)s 453.747 (er)s 452.906 y -5.69 (w)s 2.643 (e)s 11.508 (prefer)s 45.439 (to)s 59.637 (use)s 79.902 (in)s 93.434 (this)s 116.365 (section)s 155.963 (the)s 176.161 (represen)s 219.295 (tation)s 254.16 (of)s 267.358 (the)s 287.556 (system)s 326.887 (in)s 340.419 (terms)s 373.384 (of)s 386.582 (the)s 406.78 (o)s 413.113 (ccupation)s 469.706 y -5.69 (n)s .643 (um)s 16.977 (b)s 23.977 (er)s 10 f 39.661 (\264)s 1 f 46.05 (\050)s 10 f 50.716 (i)s 1 f 54.85 (\051)s 65.602 (=)s 81.019 (0)s 10 f 87.019 (;)s 1 f 92.353 (1)s 10 f 98.353 (;)s 1 f 103.686 (2)s 115.337 (instead)s 158.388 (of)s 173.705 (the)s 196.023 (spin)s 223.073 (v)s 228.74 (ariable)s 10 f 269.758 (\276)s 1 f 277.045 (\050)s 10 f 281.712 (i)s 1 f 285.846 (\051)s 296.597 (=)s 12 f 312.015 (\241)s 1 f 321.348 (1)s 10 f 327.348 (;)s 1 f 332.682 (0)s 10 f 338.682 (;)s 1 f 344.015 (1,)s 359.412 (their)s 389.763 (relation)s 435.447 (b)s 442.447 (eing)s 10 f 486.506 y -5.69 (\276)s 1 f 1.597 (\050)s 10 f 6.264 (i)s 1 f 10.398 (\051)s 18.398 (=)s 10 f 31.065 (\264)s 1 f 37.454 (\050)s 10 f 42.12 (i)s 1 f 46.254 (\051)s 12 f 53.322 (\241)s 1 f 65.057 (1.)s 79.68 (In)s 94.547 (eac)s 110.88 (h)s 121.414 (site)s 143.348 (of)s 156.882 (the)s 177.416 (torus)s 208.051 (I)s 207.224 (T)s 11 f 481.273 y 215.891 (d)s 1 f 486.506 y 225.353 (there)s 255.921 (are)s 275.821 (at)s 290.355 (most)s 319.623 (2)s 329.49 (particles.)s 382.213 (A)s 395.08 (con\257guration)s 503.306 y -5.69 (of)s 8.278 (the)s 29.246 (system)s 69.347 (is)s 81.715 (an)s 98.682 (elemen)s 134.349 (t)s 10 f 143.317 (\264)s 1 f 154.007 (of)s 167.975 (X)s 169.775 (X)s 11 f 505.106 y 178.775 (N)s 1 f 503.306 y 191.712 (=)s 12 f 204.88 (f)s 1 f 210.88 (0)s 10 f 216.88 (;)s 1 f 222.214 (1)s 10 f 228.214 (;)s 1 f 233.547 (2)s 12 f 239.547 (g)s 2 f 498.951 y 245.547 (I)s 243.854 (T)s 15 f 495.33 y 250.704 (d)s 1 f 503.306 y 256.342 (,)s 264.052 (where)s 10 f 299.053 (N)s 1 f 314.304 (is)s 326.672 (the)s 347.64 (n)s 353.973 (um)s 370.307 (b)s 377.307 (er)s 391.641 (of)s 405.609 (sites)s 432.71 (in)s 447.011 (I)s 446.185 (T)s 11 f 498.073 y 454.851 (d)s 1 f 503.306 y 460.447 (.)s 520.106 y -5.69 (P)s 2.143 (articles)s 42.971 (mo)s 58.638 (v)s 64.638 (e)s 73.365 (on)s 89.426 (the)s 109.488 (torus)s 139.649 (in)s 153.043 (the)s 173.104 (follo)s 195.104 (wing)s 223.165 (w)s 231.499 (a)s 237.165 (y)s 242.499 (.)s 250.964 (A)s 263.357 (particle)s 306.118 (in)s 10 f 319.513 (i)s 1 f 327.041 (jumps)s 362.169 (with)s 388.897 (a)s 398.291 (giv)s 413.625 (en)s 429.019 (rate)s 453.114 (to)s 536.906 y -5.69 (the)s 14.762 (nearest)s 55.98 (neigh)s 83.647 (b)s 90.647 (our)s 10 f 111.798 (j)s 1 f 121.212 (if)s 131.997 (in)s 10 f 145.782 (j)s 1 f 155.196 (there)s 185.681 (is)s 197.533 (at)s 211.984 (most)s 241.169 (one)s 262.954 (particle.)s 310.916 (W)s 322.25 (e)s 331.368 (call)s 10 f 353.153 (\264)s 11 f 532.551 y 359.542 (i;j)s 1 f 536.906 y 374.628 (the)s 395.08 (con\257guration)s 553.706 y -5.69 (obtained)s 43.643 (from)s 10 f 72.01 (\264)s 1 f 82.399 (letting)s 120.399 (one)s 142.399 (particle)s 185.766 (jump)s 216.766 (from)s 10 f 245.133 (i)s 1 f 253.267 (to)s 10 f 267.933 (j)s 1 f 273.562 (:)s 13 f 589.209 y 133.133 (\241)s 10 f 598.929 y 138.633 (\264)s 11 f 593.975 y 145.022 (i;j)s 13 f 589.209 y 156.324 (\242)s 1 f 598.929 y 163.824 (\050)s 10 f 168.49 (k)s 1 f 175.115 (\051)s 183.115 (=)s 13 f 574.329 y 195.782 (8)s 585.129 y 195.782 (\074)s 606.73 y 195.782 (:)s 10 f 584.529 y 208.449 (\264)s 1 f 214.837 (\050)s 10 f 219.504 (k)s 1 f 226.129 (\051)s 263.462 (if)s 10 f 274.462 (k)s 12 f 284.421 (6)s 1 f 284.421 (=)s 10 f 297.087 (i;)s 306.555 (j)s 1 f 316.183 (,)s 10 f 598.929 y 208.449 (\264)s 1 f 214.837 (\050)s 10 f 219.504 (k)s 1 f 226.129 (\051)s 12 f 233.462 (\241)s 1 f 245.462 (1)s 263.462 (if)s 10 f 274.462 (k)s 1 f 284.421 (=)s 10 f 297.087 (i)s 1 f 301.222 (,)s 10 f 613.329 y 208.449 (\264)s 1 f 214.837 (\050)s 10 f 219.504 (k)s 1 f 226.129 (\051)s 233.462 (+)s 245.462 (1)s 263.462 (if)s 10 f 274.462 (k)s 1 f 284.421 (=)s 10 f 297.087 (j)s 1 f 302.716 (.)s 646.886 y -5.69 (F)s 1.143 (or)s 15.843 (\050)s 10 f 20.51 (i;)s 29.977 (j)s 1 f 35.606 (\051)s 12 f 43.606 (2)s 1 f 54.939 (I)s 54.112 (T)s 11 f 641.653 y 62.779 (d)s 1 f 646.886 y 72.375 (and)s 95.708 (ev)s 107.041 (ery)s 127.408 (cylindric)s 176.441 (function)s 10 f 223.442 (F)s 1 f 236.158 (:)s 242.825 (X)s 244.625 (X)s 11 f 648.686 y 253.625 (N)s 12 f 646.886 y 266.06 (\241)s 273.393 (!)s 1 f 288.726 (I)s 290.9 (R)s 299.733 (,)s 307.066 (de\257ne)s 13 f 637.166 y 341.733 (\241)s 12 f 646.886 y 347.233 (r)s 11 f 648.686 y 357.233 (i;j)s 10 f 646.886 y 368.535 (F)s 13 f 637.166 y 377.918 (\242)s 1 f 646.886 y 383.418 (\050)s 10 f 388.085 (\264)s 1 f 394.474 (\051)s 403.14 (b)s 409.474 (y)s 13 f 667.456 y 127.367 (\241)s 12 f 677.176 y 132.867 (r)s 11 f 678.976 y 142.867 (i;j)s 10 f 677.176 y 154.168 (F)s 13 f 667.456 y 163.551 (\242)s 1 f 677.176 y 169.051 (\050)s 10 f 173.718 (\264)s 1 f 180.107 (\051)s 188.107 (=)s 10 f 200.773 (r)s 11 f 678.976 y 206.187 (i;j)s 1 f 677.176 y 217.489 (\050)s 10 f 222.155 (\264)s 1 f 228.544 (\051)s 13 f 667.456 y 235.211 (\251)s 10 f 677.176 y 242.211 (F)s 1 f 251.594 (\050)s 10 f 256.261 (\264)s 11 f 672.221 y 262.65 (i;j)s 1 f 677.176 y 273.951 (\051)s 12 f 281.285 (\241)s 10 f 293.285 (F)s 1 f 302.668 (\050)s 10 f 307.335 (\264)s 1 f 313.724 (\051)s 13 f 667.456 y 318.39 (\252)s 10 f 677.176 y 327.39 (:)s 1 f 705.976 y 223.045 (34)s do-end end endp %%Page: 35 35 %%BeginPageSetup initializepage (Raffaele Esposito; page: 35 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f1_12 sf ( )S -997 -1000 :M f2_12 sf ( )S -993 -1000 :M f10_12 sf ( )S -985 -1000 :M f11_12 sf ( )S -976 -1000 :M f12_12 sf ( )S -964 -1000 :M f13_12 sf ( )S -954 -1000 :M f14_12 sf ( )S -941 -1000 :M f15_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 6.31 y -5.69 (where)s 10 f 23.11 y 143.89 (r)s 11 f 24.91 y 149.303 (i;j)s 1 f 23.11 y 160.605 (\050)s 10 f 165.272 (\264)s 1 f 171.66 (\051)s 182.994 (=)s 198.994 (1)s 12 f 204.994 (f)s 10 f 210.994 (\264)s 1 f 217.382 (\050)s 10 f 222.049 (i)s 1 f 226.183 (\051)s 10 f 234.183 (\076)s 1 f 246.85 (0)s 10 f 252.85 (;)s 258.183 (\264)s 1 f 264.572 (\050)s 10 f 269.239 (j)s 1 f 274.867 (\051)s 10 f 282.867 (\074)s 1 f 295.534 (2)s 12 f 301.534 (g)s 10 f 310.867 (;)s 1 f 47.982 y -5.69 (The)s 18.976 (jump)s 49.977 (rates)s 79.41 (are)s 10 f 64.782 y 122.022 (C)s 11 f 59.827 y 131.457 (\257)s 67.748 y 130.599 (\260)s 1 f 64.782 y 137.93 (\050)s 10 f 142.597 (i;)s 152.064 (j)s 1 f 157.693 (;)s 10 f 163.026 (\264)s 1 f 169.415 (\051)s 177.415 (=)s 190.081 (\251)s 13 f 55.062 y 200.748 (\251)s 10 f 64.782 y 207.748 (\257)s 13 f 55.062 y 217.169 (\241)s 10 f 64.782 y 222.669 (H)s 11 f 66.582 y 232.644 (N)s 1 f 64.782 y 241.746 (\050)s 10 f 246.412 (\264)s 11 f 59.827 y 252.801 (i;j)s 1 f 64.782 y 264.103 (\051)s 12 f 271.436 (\241)s 10 f 283.436 (H)s 11 f 66.582 y 293.411 (N)s 1 f 64.782 y 302.512 (\050)s 10 f 307.179 (\264)s 1 f 313.568 (\051)s 13 f 55.062 y 318.235 (\242)s 323.735 (\252)s 10 f 64.782 y 332.735 (;)s 1 f 89.654 y -5.69 (with)s 10 f 106.454 y 139.212 (H)s 11 f 108.254 y 149.187 (\260)s 1 f 106.454 y 155.345 (\050)s 10 f 160.011 (\264)s 1 f 166.4 (\051)s 174.4 (=)s 12 f 187.067 (\241)s 13 f 95.054 y 203.415 (X)s 11 f 121.994 y 198.4 (i;j)s 14 f 209.101 (2)s 2 f 215.568 (I)s 213.875 (T)s 15 f 119.221 y 220.725 (d)s 10 f 106.454 y 227.763 (J)s 11 f 108.254 y 234.417 (\260)s 1 f 106.454 y 240.574 (\050)s 10 f 245.241 (i)s 12 f 252.042 (\241)s 10 f 264.042 (j)s 1 f 269.67 (\051)s 10 f 274.337 (\264)s 1 f 280.726 (\050)s 10 f 285.393 (i)s 1 f 289.527 (\051)s 10 f 294.194 (\264)s 1 f 300.582 (\050)s 10 f 305.249 (j)s 1 f 310.878 (\051)s 10 f 315.544 (;)s 1 f 439.114 (\0506)s 10 f 449.78 (:)s 1 f 453.114 (1\051)s 146.033 y -5.69 (where)s 10 f 29.722 (J)s 11 f 147.833 y 36.376 (\260)s 1 f 146.033 y 47.245 (is)s 60.024 (the)s 81.402 (Kac)s 106.781 (p)s 113.781 (oten)s 136.114 (tial)s 158.159 (de\257ned)s 200.205 (in)s 214.917 (section)s 255.695 (2)s 266.407 (and)s 290.452 (\251)s 303.639 (:)s 311.492 (I)s 313.665 (R)s 12 f 327.018 (\241)s 334.351 (!)s 1 f 350.871 (I)s 353.044 (R)s 2 f 147.833 y 361.878 (+)s 1 f 146.033 y 374.556 (is)s 387.335 (a)s 398.047 (con)s 415.714 (tin)s 430.047 (uously)s 162.833 y -5.69 (di\256eren)s 33.01 (tiable)s 66.482 (function)s 113.622 (in)s 127.761 (a)s 137.9 (neigh)s 165.567 (b)s 172.567 (orho)s 196.267 (o)s 202.6 (d)s 213.406 (of)s 227.212 (0,)s 240.719 (suc)s 257.119 (h)s 267.925 (that)s 294.064 (\251\0500\051)s 321.629 (=)s 334.528 (1,)s 348.035 (satisfying)s 401.641 (the)s 422.447 (detailed)s 179.633 y -5.69 (balance)s 37.643 (condition)s 196.433 y 155.887 (\251\050)s 10 f 169.22 (E)s 1 f 178.77 (\051)s 186.77 (=)s 199.437 (exp)s 13 f 186.712 y 219.77 (\241)s 12 f 196.433 y 227.937 (\241)s 10 f 239.937 (E)s 13 f 186.712 y 249.487 (\242)s 1 f 196.433 y 254.987 (\251)s 13 f 186.712 y 263.653 (\241)s 12 f 196.433 y 271.82 (\241)s 10 f 283.82 (E)s 13 f 186.712 y 293.37 (\242)s 10 f 196.433 y 298.87 (:)s 1 f 439.114 (\0506)s 10 f 449.78 (:)s 1 f 453.114 (2\051)s 221.305 y -5.69 (The)s 18.976 (generator)s 72.377 (of)s 86.043 (this)s 109.443 (jump)s 140.443 (Mark)s 168.143 (o)s 173.81 (v)s 184.143 (pro)s 201.844 (cess)s 225.977 (\050)s 10 f 230.644 (\264)s 11 f 223.105 y 236.602 (t)s 1 f 221.305 y 240.827 (\051)s 11 f 223.105 y 245.494 (t)s 14 f 249.119 (\270)s 2 f 256.619 (0)s 1 f 221.305 y 266.002 (is)s 278.069 (giv)s 293.402 (en)s 309.402 (b)s 315.735 (y)s 13 f 243.605 y 92.81 (\263)s 1 f 256.925 y 99.977 (I)s 102.15 (L)s 11 f 251.691 y 109.65 (\257)s 259.891 y 109.65 (\260)s 10 f 256.925 y 116.123 (f)s 13 f 243.605 y 123.29 (\264)s 1 f 256.925 y 132.456 (\050)s 10 f 137.123 (\264)s 1 f 143.512 (\051)s 151.512 (=)s 164.178 (\0501)s 10 f 174.845 (=)s 1 f 180.845 (2\051)s 13 f 245.525 y 202.886 (X)s 11 f 273.313 y 197.871 (i;j)s 14 f 208.572 (2)s 2 f 215.039 (I)s 213.346 (T)s 15 f 269.691 y 220.196 (d)s 14 f 282.686 y 194.952 (j)s 11 f 197.802 (i)s 14 f 201.197 (\241)s 11 f 208.697 (j)s 14 f 213.153 (j)s 2 f 216.003 (=1)s 10 f 256.925 y 231.593 (C)s 11 f 251.158 y 241.028 (\257)s 260.451 y 240.17 (N)s 1 f 256.925 y 249.272 (\050)s 10 f 253.938 (i;)s 263.406 (j)s 1 f 269.034 (;)s 10 f 274.368 (\264)s 1 f 280.756 (\051)s 13 f 247.205 y 287.423 (\251)s 294.423 (\241)s 12 f 256.925 y 299.923 (r)s 11 f 258.725 y 309.923 (i;j)s 10 f 256.925 y 321.225 (f)s 13 f 247.205 y 328.391 (\242)s 1 f 256.925 y 333.891 (\050)s 10 f 338.558 (\264)s 1 f 344.947 (\051)s 13 f 247.205 y 349.614 (\252)s 10 f 256.925 y 361.947 (:)s 1 f 312.781 y -5.69 (where)s 29.01 (w)s 37.343 (e)s 46.676 (ha)s 59.01 (v)s 65.01 (e)s 74.343 (made)s 106.343 (explicit)s 148.677 (the)s 169.343 (dep)s 188.343 (endence)s 233.677 (on)s 250.343 (the)s 271.01 (parameter)s 10 f 328.41 (\257)s 12 f 339.164 (\270)s 1 f 351.831 (0.)s 329.701 y 8.71 (Lemma)s 52.058 (6.9)s 71.907 (sho)s 88.974 (ws)s 106.889 (that)s 133.404 (the)s 154.586 (dynamics)s 208.168 (with)s 236.017 (parameter)s 10 f 293.932 (\257)s 305.545 (\076)s 1 f 319.07 (0)s 329.586 (is)s 342.168 (a)s 352.683 (w)s 361.016 (eak)s 383.198 (p)s 390.198 (erturbation)s 454.113 (of)s 346.501 y -5.69 (the)s 15.306 (generalized)s 77.669 (simple)s 115.398 (exclusion)s 167.461 (pro)s 185.161 (cess)s 209.623 (GSEP)s 246.369 (in)s 260.698 ([KLO])s 297.861 (and)s 321.523 (reduces)s 364.619 (to)s 379.615 (it)s 391.945 (at)s 10 f 406.941 (\257)s 1 f 418.244 (=)s 431.459 (0.)s 447.114 (W)s 458.447 (e)s 363.301 y -5.69 (shall)s 22.377 (denote)s 61.043 (the)s 81.71 (generator)s 135.11 (of)s 148.777 (GSEP)s 185.193 (b)s 191.527 (y)s 201.86 (I)s 204.033 (L)s 2 f 358.068 y 211.534 (0)s 11 f 366.268 y 211.534 (N)s 1 f 363.301 y 220.635 (.)s 380.221 y 8.71 (F)s 15.543 (or)s 10 f 30.243 (\047)s 12 f 41.426 (\270)s 1 f 54.093 (0,)s 67.426 (de\257ne)s 102.772 (\271)s 10 f 102.093 (\272)s 11 f 375.867 y 108.785 (N)s 383.188 y 108.021 (\047)s 1 f 380.221 y 121.886 (as)s 136.62 (the)s 157.286 (pro)s 174.987 (duct)s 202.32 (measure)s 249.087 (on)s 265.753 (X)s 267.553 (X)s 11 f 382.021 y 276.553 (N)s 1 f 380.221 y 289.655 (with)s 316.988 (marginals)s 371.755 (giv)s 387.089 (en)s 403.089 (b)s 409.422 (y)s 419.373 y 108.238 (\271)s 10 f 107.559 (\272)s 11 f 414.418 y 114.25 (N)s 422.339 y 113.487 (\047)s 12 f 419.373 y 123.352 (f)s 10 f 129.352 (\264)s 1 f 135.741 (\0500\051)s 154.408 (=)s 10 f 167.074 (r)s 12 f 172.822 (g)s 1 f 185.488 (=)s 10 f 411.255 y 224.554 (\047)s 11 f 406.9 y 232.404 (r)s 56.417 .48 202.928 416.613 r 1 f 427.604 y 202.928 (1)s 211.595 (+)s 10 f 223.594 (\047)s 1 f 234.111 (+)s 10 f 246.111 (\047)s 2 f 424.137 y 253.961 (2)s 10 f 419.373 y 264.118 (;)s 293.451 (r)s 1 f 302.531 (=)s 315.198 (0)s 10 f 321.198 (;)s 1 f 326.531 (1)s 10 f 332.531 (;)s 1 f 337.865 (2)s 10 f 347.198 (:)s 1 f 458.494 y -5.69 (Let)s 10 f 15.81 (R)s 1 f 25.014 (\050)s 10 f 29.681 (\047)s 1 f 37.531 (\051)s 46.197 (b)s 53.197 (e)s 62.531 (the)s 83.197 (mean)s 115.197 (o)s 121.531 (ccupation)s 176.198 (n)s 182.531 (um)s 198.864 (b)s 205.864 (er)s 219.898 (of)s 233.564 (particles)s 281.664 (under)s 316.377 (\271)s 10 f 315.698 (\272)s 11 f 454.14 y 322.39 (N)s 461.461 y 321.626 (\047)s 1 f 458.494 y 335.491 (:)s 10 f 488.956 y 175.722 (R)s 1 f 184.926 (\050)s 10 f 189.592 (\047)s 1 f 197.442 (\051)s 208.776 (=)s 10 f 224.775 (E)s 2 f 491.323 y 234.186 (\271)s 11 f 233.634 (\272)s 15 f 488.923 y 239.005 (N)s 493.723 y 238.445 (\047)s 1 f 488.956 y 247.313 ([)s 10 f 250.646 (\264)s 1 f 257.035 (\0500\051])s 10 f 279.035 (:)s 1 f 519.418 y -5.69 (The)s 19.646 (function)s 10 f 67.317 (R)s 1 f 76.521 (:)s 81.854 (I)s 84.027 (R)s 2 f 521.218 y 92.861 (+)s 12 f 519.418 y 105.277 (!)s 1 f 121.727 ([0)s 10 f 131.06 (;)s 1 f 136.394 (2\051)s 151.73 (is)s 164.467 (a)s 175.137 (bijection)s 224.807 (and)s 248.81 (w)s 257.144 (e)s 267.147 (denote)s 306.484 (b)s 312.817 (y)s 10 f 323.82 (\303)s 1 f 332.067 (:)s 337.401 ([0)s 10 f 346.734 (;)s 1 f 352.067 (2\051)s 12 f 367.184 (!)s 1 f 383.634 (I)s 385.807 (R)s 2 f 521.218 y 394.64 (+)s 1 f 519.418 y 407.277 (its)s 424.68 (in)s 434.347 (v)s 440.347 (erse.)s 536.218 y -5.69 (F)s 1.143 (or)s 16.377 (ev)s 27.71 (ery)s 10 f 48.61 (\256)s 1 f 60.865 (in)s 75.399 ([0)s 10 f 84.732 (;)s 1 f 90.065 (2\051,)s 108.732 (w)s 117.066 (e)s 126.932 (denote)s 166.133 (b)s 172.466 (y)s 10 f 183.333 (\272)s 11 f 531.864 y 190.025 (N)s 539.185 y 189.261 (\256)s 1 f 536.218 y 203.66 (the)s 224.86 (pro)s 242.56 (duct)s 270.427 (measure)s 318.407 (\271)s 10 f 317.728 (\272)s 11 f 531.864 y 324.419 (N)s 540.083 y 323.655 (\303)s 2 f 330.307 (\050)s 11 f 334.057 (\256)s 2 f 340.295 (\051)s 1 f 536.218 y 349.179 (so)s 364.446 (that)s 390.98 (the)s 412.18 (densit)s 443.247 (y)s 454.114 (of)s 553.018 y -5.69 (particles)s 42.41 (on)s 59.077 (eac)s 75.41 (h)s 86.077 (site)s 108.143 (is)s 10 f 120.21 (\256)s 1 f 131.931 (:)s 10 f 583.48 y 148.729 (E)s 11 f 585.847 y 157.587 (\272)s 15 f 583.447 y 162.958 (N)s 588.247 y 162.398 (\256)s 1 f 583.48 y 171.267 ([)s 10 f 174.6 (\264)s 1 f 180.989 (\050)s 10 f 185.655 (x)s 1 f 192.514 (\051])s 207.18 (=)s 10 f 223.18 (\256)s 1 f 242.901 (for)s 10 f 261.268 (x)s 1 f 272.126 (in)s 286.126 (X)s 287.926 (X)s 11 f 585.28 y 296.926 (N)s 10 f 583.48 y 306.028 (:)s 1 f 613.942 y -5.69 (W)s 5.643 (e)s 14.757 (will)s 37.204 (use)s 57.717 (the)s 78.164 (notation)s 10 f 125.944 (\272)s 11 f 615.742 y 131.872 (\256)s 1 f 613.942 y 142.491 (for)s 160.638 (the)s 181.085 (pro)s 198.785 (duct)s 225.898 (measure)s 272.445 (on)s 288.892 (the)s 309.339 (in\257nite)s 349.786 (v)s 355.786 (olume)s 390.9 (pro)s 408.6 (duct)s 435.713 (space)s 630.742 y -5.69 (X)s -3.89 (X)s 8.815 (=)s 12 f 21.853 (f)s 1 f 27.853 (0)s 10 f 33.853 (;)s 1 f 39.186 (1)s 10 f 45.186 (;)s 1 f 50.519 (2)s 12 f 56.519 (g)s 11 f 626.388 y 62.52 (Z)s 64.73 (Z)s 15 f 622.766 y 73.495 (d)s 1 f 630.742 y 83.356 (and)s 10 f 106.913 (\074)s 119.951 (f)s 130.822 (\076)s 11 f 632.542 y 140.156 (\256)s 1 f 630.742 y 151.217 (for)s 169.807 (the)s 190.696 (exp)s 209.363 (ectation)s 255.586 (of)s 269.476 (a)s 279.699 (cylinder)s 325.622 (function)s 10 f 372.845 (f)s 1 f 384.234 (with)s 411.791 (resp)s 433.557 (ect)s 453.114 (to)s 10 f 647.542 y -5.69 (\272)s 11 f 649.342 y .238 (\256)s 1 f 647.542 y 11.076 (or)s 10 f 25.776 (\272)s 11 f 643.188 y 32.468 (N)s 650.509 y 31.704 (\256)s 1 f 647.542 y 45.569 (:)s 10 f 671.642 y 160.564 (\074)s 173.231 (f)s 183.731 (\076)s 11 f 673.442 y 193.064 (\256)s 1 f 671.642 y 203.236 (=)s 13 f 655.309 y 219.236 (Z)s 10 f 671.642 y 233.236 (f)s 1 f 240.403 (\050)s 10 f 245.069 (\264)s 1 f 251.458 (\051)s 10 f 256.125 (\272)s 11 f 673.442 y 262.053 (\256)s 1 f 671.642 y 268.891 (\050)s 10 f 273.558 (d\264)s 1 f 286.193 (\051)s 10 f 294.192 (:)s 1 f 439.114 (\0506)s 10 f 449.78 (:)s 1 f 453.114 (3\051)s 705.976 y 223.045 (35)s do-end end endp %%Page: 36 36 %%BeginPageSetup initializepage (Raffaele Esposito; page: 36 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f0_12 sf ( )S -996 -1000 :M f1_12 sf ( )S -993 -1000 :M f2_12 sf ( )S -989 -1000 :M f10_12 sf ( )S -981 -1000 :M f11_12 sf ( )S -972 -1000 :M f12_12 sf ( )S -960 -1000 :M f13_12 sf ( )S -951 -1000 :M f14_12 sf ( )S -937 -1000 :M f15_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 1200 1000 div mul /CMBX10 findfont fdef 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef fonts 20 get /CharDefs get dup 90[6.642 1 0 7 7 6 7 -1 0 {}]put pop 58 60 translate 72 72.27 div dup scale 1 f 6.31 y 8.71 (The)s 33.183 (one-parameter)s 112.39 (family)s 148.863 (\050)s 10 f 153.53 (\272)s 11 f 1.955 y 160.221 (N)s 9.276 y 159.457 (\256)s 1 f 6.31 y 169.323 (\051)s 11 f 8.11 y 173.99 (\256)s 1 f 6.31 y 184.635 (of)s 198.108 (probabilit)s 249.141 (y)s 259.281 (measures)s 310.588 (is)s 322.461 (rev)s 338.494 (ersible)s 375.734 (for)s 393.907 (the)s 414.38 (generator)s 23.11 y -5.69 (I)s -3.517 (L)s 2 f 17.876 y 3.983 (0)s 11 f 26.076 y 3.983 (N)s 1 f 23.11 y 16.296 (\050GSEP\051)s 61.257 (and)s 83.802 (for)s 10 f 101.38 (\257)s 112.134 (\076)s 1 f 124.8 (0)s 134.012 (the)s 153.89 (one-parameter)s 232.501 (family)s 268.38 (of)s 281.258 (probabilit)s 332.291 (y)s 341.836 (measures)s 392.547 (\050)s 10 f 397.214 (\272)s 11 f 18.755 y 403.906 (\257)s 409.779 (;N)s 26.076 y 403.142 (\256)s 1 f 23.11 y 421.73 (\051)s 11 f 24.91 y 426.397 (\256)s 1 f 23.11 y 436.447 (giv)s 451.78 (en)s 39.91 y -5.69 (b)s .643 (y)s 10 f 64.161 y 142.785 (\272)s 11 f 59.207 y 149.476 (\257)s 155.349 (;N)s 67.128 y 148.713 (\256)s 1 f 64.161 y 167.301 (\050)s 10 f 171.968 (\264)s 1 f 178.357 (\051)s 186.357 (=)s 56.043 y 200.463 (exp)s 12 f 218.797 (f\241)s 10 f 234.13 (\257)s 241.551 (H)s 11 f 57.843 y 251.526 (N)s 1 f 56.043 y 260.627 (\050)s 10 f 265.294 (\264)s 1 f 271.683 (\051)s 12 f 276.35 (g)s 81.887 .48 200.463 61.401 r 10 f 74.441 y 233.645 (Z)s 11 f 68.674 y 242.695 (\257)s 75.844 y 241.837 (\256)s 10 f 64.161 y 283.79 (\272)s 11 f 59.207 y 290.481 (N)s 67.128 y 289.718 (\256)s 1 f 64.161 y 299.583 (\050)s 10 f 304.25 (\264)s 1 f 310.639 (\051)s 96.999 y -5.69 (is)s 6.376 (rev)s 22.41 (ersible)s 59.843 (for)s 78.21 (the)s 98.877 (dynamics)s 151.943 (with)s 10 f 179.277 (\257)s 190.031 (\076)s 1 f 202.697 (0.)s 217.364 (Here)s 10 f 245.731 (Z)s 11 f 92.644 y 254.781 (\257)s 99.966 y 253.923 (\256)s 1 f 96.999 y 265.254 (is)s 277.32 (the)s 297.987 (normalization)s 374.021 (constan)s 413.754 (t.)s 113.919 y 8.71 (W)s 20.043 (e)s 29.545 (no)s 41.878 (w)s 54.713 (c)s 59.713 (ho)s 72.713 (ose)s 10 f 92.948 (N)s 1 f 107.512 (=)s 10 f 120.459 (\260)s 14 f 109.564 y 127.338 (\241)s 2 f 134.838 (1)s 1 f 113.919 y 144.39 (and)s 167.892 (sp)s 179.625 (eed)s 201.127 (up)s 218.628 (the)s 239.464 (generator)s 293.032 (as)s 10 f 307.934 (\260)s 14 f 109.564 y 314.813 (\241)s 2 f 322.313 (2)s 1 f 113.919 y 327.696 (,)s 335.24 (as)s 350.142 (in)s 364.31 (the)s 385.145 (Ka)s 400.145 (w)s 408.478 (asaki)s 439.047 (case,)s 130.719 y -5.69 (and)s 18.313 (study)s 52.05 (the)s 73.386 (limit)s 10 f 102.723 (N)s 12 f 118.122 (!)s 134.572 (1)s 1 f 146.572 (.)s 157.248 (In)s 172.918 (this)s 196.987 (Section)s 239.657 (w)s 247.991 (e)s 257.994 (sho)s 275.06 (w)s 288.397 (that,)s 318.568 (starting)s 364.004 (from)s 393.041 (a)s 403.71 (sequence)s 454.114 (of)s 147.519 y -5.69 (measures)s 45.38 (on)s 61.618 (X)s 63.418 (X)s 11 f 149.319 y 72.418 (N)s 1 f 147.519 y 85.09 (asso)s 106.89 (ciated)s 141.794 (to)s 156.031 (the)s 176.269 (same)s 205.906 (initial)s 240.143 (pro\257le)s 10 f 276.414 (\275)s 2 f 149.319 y 282.618 (0)s 1 f 147.519 y 288.001 (,)s 294.991 (the)s 315.228 (densit)s 346.295 (y)s 356.199 (\257eld)s 381.77 (con)s 399.436 (v)s 405.436 (erges,)s 438.526 (as)s 10 f 452.83 (N)s 1 f 164.319 y -5.69 (increases)s 44.408 (to)s 59.006 (in\257nit)s 90.006 (y)s 95.34 (,)s 102.618 (to)s 117.216 (the)s 137.814 (w)s 146.148 (eak)s 167.746 (solution)s 213.077 (of)s 226.675 (the)s 247.274 (nonlinear)s 299.905 (parab)s 330.272 (olic)s 352.203 (equation)s 401.135 (\0506.5\051,)s 433.08 (where)s 181.119 y -5.69 (the)s 14.976 (di\256usion)s 63.377 (matrix)s 10 f 102.41 (D)s 1 f 116.678 (is)s 128.745 (giv)s 144.078 (en)s 160.078 ([KLO])s 196.912 (b)s 203.245 (y)s 213.579 (\0506.4\051)s 242.245 (b)s 249.245 (elo)s 263.579 (w.)s 198.039 y 8.71 (It)s 23.337 (has)s 46.365 (b)s 53.365 (een)s 76.326 (pro)s 93.359 (v)s 99.359 (ed)s 116.986 (in)s 132.614 ([KLO])s 171.073 (that)s 198.701 (the)s 220.995 (co)s 232.661 (e\261cien)s 268.328 (ts)s 10 f 283.356 (D)s 11 f 199.839 y 293.291 (k)s 298.595 (;m)s 1 f 198.039 y 310.56 (\050)s 10 f 315.227 (\275)s 1 f 321.431 (\051)s 331.725 (are)s 353.386 (nonlinear)s 407.713 (con)s 425.38 (tin)s 439.713 (uous)s 214.839 y -5.69 (functions)s 45.463 (of)s 10 f 58.55 (\275)s 1 f 68.175 (and)s 90.928 (that)s 10 f 116.349 (D)s 1 f 130.037 (is)s 141.524 (strictly)s 182.044 (elliptic.)s 225.851 (That)s 255.272 (is)s 266.759 (not)s 287.512 (enough)s 328.266 (to)s 342.353 (pro)s 359.386 (v)s 365.386 (e)s 374.14 (the)s 394.227 (uniqueness)s 454.114 (of)s 231.639 y -5.69 (w)s 2.643 (eak)s 24.33 (solutions)s 74.483 (of)s 88.17 (\0506.5\051,)s 120.194 (whic)s 143.861 (h)s 154.548 (is)s 166.634 (easy)s 193.054 (to)s 207.741 (pro)s 224.774 (v)s 230.774 (e)s 240.127 (instead)s 281.547 (if)s 292.567 (the)s 313.254 (di\256usion)s 361.674 (co)s 373.34 (e\261cien)s 409.007 (t)s 417.694 (is)s 429.78 (kno)s 448.447 (wn)s 248.439 y -5.69 (to)s 8.976 (b)s 15.977 (e)s 25.31 (lo)s 34.977 (cally)s 63.31 (Lipsc)s 90.543 (hitz)s 114.543 (con)s 132.21 (tin)s 146.543 (uous)s 174.61 (\050for)s 197.644 (example)s 244.644 (b)s 250.977 (y)s 261.31 (the)s 281.977 (metho)s 314.977 (d)s 325.644 (in)s 339.644 ([LMS]\051.)s 265.359 y 8.71 (In)s 24.346 (order)s 56.383 (to)s 71.686 (de\257ne)s 106.989 (the)s 128.292 (di\256usion)s 177.329 (co)s 188.996 (e\261cien)s 224.662 (t,)s 237.458 (w)s 245.791 (e)s 255.761 (need)s 284.398 (to)s 299.701 (establish)s 349.804 (some)s 380.507 (notation)s 429.144 (and)s 453.114 (to)s 282.159 y -5.69 (consider)s 41.077 (the)s 61.743 (generalized)s 123.777 (exclusion)s 175.51 (pro)s 193.21 (cess)s 217.343 (in)s 231.343 (the)s 252.01 (in\257nite)s 292.677 (v)s 298.677 (olume)s 334.01 (space)s 366.077 (X)s 367.877 (X)s 376.877 (.)s 299.079 y 8.71 (F)s 15.543 (or)s 10 f 29.932 (i)s 1 f 37.755 (in)s 10 f 51.444 (Z)s 54.494 (Z)s 11 f 294.724 y 65.544 (d)s 1 f 299.079 y 71.14 (,)s 78.224 (let)s 10 f 95.246 (\277)s 11 f 300.879 y 100.492 (i)s 1 f 299.079 y 108.176 (denote)s 146.532 (the)s 166.888 (space)s 198.643 (shift)s 225.399 (b)s 231.732 (y)s 10 f 241.755 (i)s 1 f 249.578 (units)s 279.333 (on)s 295.689 (X)s 297.489 (X)s 306.489 (.)s 315.052 (F)s 321.885 (or)s 336.274 (a)s 345.963 (cylinder)s 391.352 (function)s 10 f 438.041 (F)s 1 f 451.114 (on)s 315.879 y -5.69 (X)s -3.89 (X)s 5.11 (,)s 12.443 (de\257ne)s 47.11 (the)s 67.777 (formal)s 105.477 (sum)s 332.679 y 167.773 (\241)s 11 f 334.479 y 175.273 (F)s 1 f 332.679 y 183.251 (\050)s 10 f 187.917 (\264)s 1 f 194.306 (\051)s 202.306 (=)s 13 f 321.279 y 219.774 (X)s 11 f 348.219 y 214.973 (j)s 14 f 219.429 (2)s 11 f 225.896 (Z)s 228.106 (Z)s 15 f 345.446 y 236.871 (d)s 13 f 322.959 y 243.909 (\241)s 10 f 332.679 y 249.409 (\277)s 11 f 334.479 y 254.655 (j)s 10 f 332.679 y 259.711 (F)s 13 f 322.959 y 269.095 (\242)s 1 f 332.679 y 274.595 (\050)s 10 f 279.262 (\264)s 1 f 285.65 (\051)s 371.019 y -5.69 (whic)s 17.976 (h)s 29.487 (do)s 42.487 (es)s 57.398 (not)s 79.576 (mak)s 101.576 (e)s 111.753 (sense)s 143.397 (but)s 166.241 (for)s 185.452 (whic)s 209.119 (h)s 220.63 (the)s 242.14 (quan)s 267.474 (tities)s 12 f 298.385 (fr)s 2 f 372.819 y 314.385 (0)s 11 f 319.168 (;e)s 15 f 374.093 y 326.571 (k)s 1 f 371.019 y 332.417 (\241)s 11 f 372.819 y 339.917 (F)s 10 f 371.019 y 347.894 (;)s 1 f 355.228 (1)s 12 f 365.968 (\267)s 10 f 380.041 (k)s 12 f 391.406 (\267)s 10 f 405.48 (d)s 12 f 411.725 (g)s 1 f 422.569 (are)s 443.447 (w)s 451.78 (ell)s 387.819 y -5.69 (de\257ned.)s 41.108 (Here)s 12 f 69.74 (f)s 10 f 75.74 (e)s 2 f 389.619 y 81.328 (1)s 10 f 387.819 y 86.711 (;)s 12 f 92.044 (\242)s 97.378 (\242)s 102.711 (\242)s 10 f 108.044 (;)s 113.378 (e)s 11 f 389.619 y 118.965 (d)s 12 f 387.819 y 124.561 (g)s 1 f 134.827 (are)s 155.126 (the)s 176.058 (unitary)s 218.691 (v)s 224.691 (ectors)s 259.724 (in)s 273.99 (the)s 294.922 (co)s 306.589 (ordinate)s 354.222 (directions)s 409.254 (of)s 20 f 423.187 (Z)s 11 f 383.465 y 431.187 (d)s 1 f 387.819 y 436.782 (.)s 446.247 (F)s 453.08 (or)s 404.619 y -5.69 (eac)s 10.643 (h)s 10 f 21.307 (\256)s 1 f 33.024 (in)s 47.021 ([0)s 10 f 56.354 (;)s 1 f 61.688 (2],)s 78.352 (let)s 10 f 95.682 (D)s 1 f 105.95 (\050)s 10 f 110.617 (\256)s 1 f 118.338 (\051)s 126.337 (=)s 12 f 139.004 (f)s 10 f 145.004 (D)s 11 f 406.419 y 154.939 (k)s 160.243 (;m)s 1 f 404.619 y 172.209 (\050)s 10 f 176.875 (\256)s 1 f 184.596 (\051)s 10 f 189.263 (;)s 1 f 198.593 (1)s 12 f 207.926 (\267)s 10 f 220.593 (k)s 227.218 (;)s 232.551 (m)s 12 f 246.42 (\267)s 10 f 259.087 (d)s 12 f 265.333 (g)s 1 f 275.33 (b)s 282.33 (e)s 291.66 (the)s 312.323 (symmetric)s 370.753 (matrix)s 409.783 (de\257ned)s 451.114 (b)s 457.447 (y)s 421.419 y -5.69 (the)s 14.976 (follo)s 36.977 (wing)s 65.643 (v)s 71.31 (ariational)s 125.343 (form)s 149.377 (ula)s 10 f 459.961 y 86.747 (a)s 12 f 95.756 (\242)s 10 f 101.756 (D)s 1 f 112.025 (\050)s 10 f 116.691 (\256)s 1 f 124.412 (\051)s 10 f 129.079 (a)s 1 f 142.089 (=)s 451.843 y 171.81 (1)s 30.563 .48 159.528 457.201 r 468.193 y 159.528 (2)s 10 f 165.528 (\302)s 1 f 173.037 (\050)s 10 f 177.703 (\256)s 1 f 185.424 (\051)s 459.961 y 193.531 (inf)s 11 f 467.701 y 197.142 (F)s 444.961 y 216.36 (d)s 13 f 448.561 y 210.191 (X)s 11 f 474.395 y 210.131 (k)s 2 f 215.435 (=1)s 13 f 446.641 y 229.585 (D)s 236.918 (\263)s 10 f 459.961 y 244.085 (a)s 11 f 461.761 y 250.428 (k)s 10 f 459.961 y 256.332 (r)s 2 f 461.761 y 261.746 (0)s 11 f 266.53 (;e)s 15 f 463.035 y 273.933 (k)s 1 f 459.961 y 282.445 (+)s 12 f 294.445 (r)s 2 f 461.761 y 304.445 (0)s 11 f 309.228 (;e)s 15 f 463.035 y 316.631 (k)s 1 f 459.961 y 322.477 (\241)s 11 f 461.761 y 329.977 (F)s 13 f 446.641 y 337.955 (\264)s 2 f 449.128 y 345.121 (2)s 13 f 446.641 y 350.505 (E)s 11 f 468.361 y 357.838 (\256)s 10 f 459.961 y 368.01 (;)s 1 f 439.114 (\0506)s 10 f 449.78 (:)s 1 f 453.114 (4\051)s 500.837 y -5.69 (for)s 12.677 (an)s 25.01 (y)s 35.343 (v)s 41.343 (ector)s 10 f 71.377 (a)s 1 f 81.72 (in)s 95.72 (I)s 97.893 (R)s 11 f 495.603 y 106.726 (d)s 1 f 500.837 y 112.322 (.)s 120.988 (In)s 135.988 (this)s 159.389 (form)s 183.422 (ula)s 10 f 203.422 (\302)s 1 f 210.93 (\050)s 10 f 215.597 (\256)s 1 f 223.318 (\051)s 231.984 (is)s 244.051 (the)s 264.718 (static)s 297.451 (compressibilit)s 369.285 (y)s 379.618 (de\257ned)s 420.951 (b)s 427.285 (y)s 10 f 527.012 y 83.361 (\302)s 1 f 90.869 (\050)s 10 f 95.536 (\256)s 1 f 103.257 (\051)s 114.59 (=)s 13 f 517.292 y 130.59 (\255)s 10 f 527.012 y 136.256 (\264)s 1 f 142.645 (\0500\051)s 2 f 522.057 y 157.979 (2)s 13 f 517.292 y 163.362 (\256)s 11 f 531.812 y 169.029 (\256)s 12 f 527.012 y 181.867 (\241)s 13 f 517.292 y 197.2 (\255)s 10 f 527.012 y 202.867 (\264)s 1 f 209.256 (\0500\051)s 13 f 517.292 y 224.589 (\256)s 2 f 519.779 y 230.256 (2)s 11 f 531.812 y 230.256 (\256)s 1 f 527.012 y 243.761 (=)s 13 f 517.292 y 259.761 (\255)s 10 f 527.012 y 265.427 (\276)s 1 f 272.715 (\0500\051)s 2 f 522.057 y 288.048 (2)s 13 f 517.292 y 293.432 (\256)s 11 f 531.812 y 299.098 (\256)s 12 f 527.012 y 311.937 (\241)s 13 f 517.292 y 327.27 (\255)s 10 f 527.012 y 332.937 (\276)s 1 f 340.224 (\0500\051)s 13 f 517.292 y 355.557 (\256)s 2 f 519.779 y 361.224 (2)s 11 f 531.812 y 361.224 (\256)s 10 f 527.012 y 371.396 (:)s 1 f 553.307 y 8.71 (F)s 15.543 (or)s 31.946 (a)s 43.648 (measure)s 10 f 92.118 (\271)s 1 f 105.051 (on)s 123.42 (X)s 125.22 (X)s 11 f 555.107 y 134.22 (N)s 1 f 553.307 y 143.322 (,)s 152.784 (denote)s 193.153 (b)s 199.486 (y)s 10 f 211.522 (P)s 11 f 555.107 y 219.227 (\271)s 1 f 553.307 y 231.364 (the)s 253.733 (probabilit)s 304.767 (y)s 316.803 (measure)s 365.272 (on)s 383.642 (the)s 406.011 (path)s 435.714 (space)s 10 f 570.107 y -5.69 (D)s 1 f 4.578 (\050I)s 11.418 (R)s 2 f 571.907 y 20.251 (+)s 10 f 570.107 y 28.218 (;)s 1 f 33.551 (X)s 35.352 (X)s 11 f 571.907 y 44.352 (N)s 1 f 570.107 y 53.453 (\051)s 62.454 (corresp)s 100.254 (onding)s 139.922 (to)s 154.923 (the)s 175.923 (Mark)s 203.623 (o)s 209.29 (v)s 219.958 (pro)s 237.658 (cess)s 262.125 (\050)s 10 f 266.792 (\264)s 11 f 571.907 y 272.75 (t)s 1 f 570.107 y 276.975 (\051)s 285.976 (with)s 313.644 (generator)s 367.378 (sp)s 379.111 (eeded)s 412.779 (up)s 430.446 (b)s 436.779 (y)s 10 f 447.447 (N)s 2 f 565.753 y 458.397 (2)s 1 f 586.907 y -5.69 (and)s 17.643 (starting)s 62.41 (from)s 10 f 90.777 (\271)s 1 f 98.007 (,)s 105.341 (and)s 128.674 (b)s 135.007 (y)s 0 f 145.341 (E)s 11 f 588.707 y 154.407 (P)s 15 f 589.907 y 160.517 (\271)s 1 f 586.907 y 170.816 (the)s 191.482 (exp)s 210.149 (ectation)s 256.149 (with)s 283.482 (resp)s 305.249 (ect)s 324.582 (to)s 10 f 339.249 (P)s 11 f 588.707 y 346.953 (\271)s 1 f 586.907 y 353.388 (.)s 603.827 y 8.71 (Let)s 12 f 30.036 (M)s 1 f 47.78 (=)s 12 f 60.447 (M)s 1 f 74.858 (\050I)s 78.698 (T)s 11 f 598.594 y 87.364 (d)s 1 f 603.827 y 92.96 (\051)s 101.453 (b)s 108.453 (e)s 117.613 (the)s 138.106 (space)s 169.999 (of)s 183.492 (p)s 190.492 (ositiv)s 218.559 (e)s 227.719 (measures)s 279.045 (on)s 295.539 (the)s 316.032 (d-dimensional)s 392.592 (torus)s 423.185 (I)s 422.358 (T)s 11 f 598.594 y 431.025 (d)s 1 f 603.827 y 440.447 (with)s 620.627 y -5.69 (total)s 23.242 (mass)s 52.974 (b)s 59.974 (ounded)s 102.24 (b)s 108.573 (y)s 119.172 (2)s 10 f 125.172 (d)s 1 f 131.418 (.)s 140.881 (F)s 147.715 (or)s 162.68 (eac)s 179.014 (h)s 189.946 (con\257guration)s 10 f 262.912 (\264)s 1 f 269.3 (,)s 276.966 (denote)s 315.898 (b)s 322.231 (y)s 10 f 332.83 (\274)s 11 f 616.273 y 340.101 (N)s 1 f 620.627 y 352.979 (=)s 10 f 366.088 (\274)s 11 f 616.273 y 373.359 (N)s 1 f 620.627 y 382.46 (\050)s 10 f 387.127 (\264)s 1 f 393.516 (\051)s 402.448 (the)s 423.38 (p)s 430.38 (ositiv)s 458.447 (e)s 637.427 y -5.69 (measure)s 41.077 (obtained)s 90.41 (assigning)s 141.877 (mass)s 10 f 171.343 (N)s 14 f 633.073 y 182.293 (\241)s 11 f 189.793 (d)s 1 f 637.427 y 199.389 (to)s 214.056 (eac)s 230.389 (h)s 241.056 (particle)s 284.422 (of)s 10 f 298.089 (\264)s 1 f 308.478 (:)s 10 f 663.603 y 159.623 (\274)s 11 f 658.648 y 166.894 (N)s 1 f 663.603 y 181.329 (=)s 10 f 195.995 (N)s 14 f 658.648 y 206.945 (\241)s 11 f 214.445 (d)s 13 f 652.202 y 223.933 (X)s 11 f 679.143 y 222.041 (j)s 14 f 226.497 (2)s 2 f 232.964 (I)s 231.27 (T)s 15 f 676.369 y 238.12 (d)s 10 f 663.603 y 245.158 (\264)s 1 f 251.547 (\050)s 10 f 256.214 (j)s 1 f 261.843 (\051)s 10 f 268.509 (\261)s 11 f 665.769 y 273.843 (j)s 278.299 (=)s 282.699 (N)s 10 f 663.603 y 295.134 (;)s 1 f 705.976 y 223.045 (36)s do-end end endp %%Page: 37 37 %%BeginPageSetup initializepage (Raffaele Esposito; page: 37 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f0_12 sf ( )S -996 -1000 :M f1_12 sf ( )S -993 -1000 :M f2_12 sf ( )S -989 -1000 :M f10_12 sf ( )S -981 -1000 :M f11_12 sf ( )S -972 -1000 :M f12_12 sf ( )S -960 -1000 :M f13_12 sf ( )S -951 -1000 :M f14_12 sf ( )S -937 -1000 :M f17_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 1200 1000 div mul /CMBX10 findfont fdef 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 17 10 1200 1000 div mul /CMTI10 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 6.31 y -5.69 (where)s 10 f 29.114 (\261)s 11 f 8.11 y 34.448 (x)s 1 f 6.31 y 44.594 (is)s 56.765 (the)s 77.536 (Dirac)s 110.174 (measure)s 157.045 (concen)s 192.045 (trated)s 228.183 (on)s 10 f 244.954 (x)s 1 f 251.813 (.)s 260.793 (F)s 267.626 (or)s 282.431 (eac)s 298.764 (h)s 10 f 309.535 (t)s 12 f 317.376 (\270)s 1 f 330.217 (0,)s 343.681 (denote)s 382.452 (b)s 388.785 (y)s 10 f 399.223 (\274)s 11 f 8.11 y 406.063 (t)s 1 f 6.31 y 413.796 (=)s 10 f 426.637 (\274)s 11 f 1.955 y 433.908 (N)s 9.276 y 433.477 (t)s 1 f 6.31 y 447.114 (the)s 23.11 y -5.69 (empirical)s 46.259 (measure)s 92.941 (at)s 107.523 (time)s 10 f 134.772 (t)s 1 f 143.02 (:)s 10 f 151.645 (\274)s 11 f 24.91 y 158.485 (t)s 1 f 23.11 y 166.043 (=)s 10 f 178.71 (\274)s 11 f 18.755 y 185.981 (N)s 1 f 23.11 y 195.083 (\050)s 10 f 199.749 (\264)s 11 f 24.91 y 205.708 (t)s 1 f 23.11 y 209.933 (\051.)s 223.238 (F)s 230.071 (or)s 244.687 (a)s 254.602 (con)s 272.269 (tin)s 286.602 (uous)s 314.584 (function)s 10 f 361.5 (U)s 1 f 374.917 (and)s 10 f 398.166 (\274)s 1 f 409.352 (in)s 12 f 423.267 (M)s 1 f 437.678 (\050I)s 441.518 (T)s 11 f 17.876 y 450.185 (d)s 1 f 23.11 y 455.78 (\051,)s 39.91 y -5.69 (w)s 2.643 (e)s 11.766 (shall)s 39.621 (denote)s 78.077 (b)s 84.41 (y)s 10 f 94.533 (\074)s 107.199 (\274)s 114.47 (;)s 119.804 (U)s 132.639 (\076)s 1 f 145.761 (the)s 166.217 (in)s 175.883 (tegral)s 209.706 (of)s 223.162 (the)s 243.617 (function)s 10 f 290.407 (U)s 1 f 303.697 (with)s 330.82 (resp)s 352.586 (ect)s 371.709 (to)s 386.165 (the)s 406.62 (measure)s 10 f 453.176 (\274)s 1 f 460.447 (.)s 57.271 y 8.71 (Fix)s 10 f 30.391 (T)s 42.706 (\076)s 1 f 55.676 (0.)s 70.887 (F)s 77.72 (or)s 92.602 (eac)s 108.935 (h)s 119.783 (probabilit)s 170.817 (y)s 181.332 (measure)s 10 f 228.28 (\271)s 1 f 239.692 (on)s 256.54 (X)s 258.34 (X)s 11 f 59.071 y 267.34 (N)s 1 f 57.271 y 276.442 (,)s 284.002 (denote)s 322.851 (b)s 329.184 (y)s 10 f 339.699 (Q)s 11 f 52.917 y 349.186 (N)s 60.238 y 349.186 (\271)s 1 f 57.271 y 362.469 (the)s 383.317 (measure)s 430.265 (on)s 447.114 (the)s 74.071 y -5.69 (state)s 23.71 (space)s 10 f 55.777 (D)s 1 f 66.045 (\050[0)s 10 f 80.045 (;)s 85.378 (T)s 1 f 94.057 (])s 10 f 97.391 (;)s 12 f 102.724 (M)s 1 f 117.135 (\051)s 125.801 (induced)s 170.468 (b)s 176.802 (y)s 187.135 (the)s 207.802 (Mark)s 235.502 (o)s 241.168 (v)s 251.502 (pro)s 269.202 (cess)s 10 f 293.335 (\274)s 11 f 75.871 y 300.175 (t)s 1 f 74.071 y 308.4 (sp)s 320.134 (eeded)s 353.467 (up)s 370.801 (b)s 377.134 (y)s 10 f 387.467 (N)s 2 f 69.717 y 398.417 (2)s 1 f 74.071 y 407.801 (and)s 10 f 431.134 (\271)s 11 f 69.717 y 438.364 (N)s 1 f 74.071 y 447.466 (.)s 0 f 99.516 y -5.69 (Theorem)s 53.162 (6.1)s 17 f 79.867 (Consider)s 131.129 (a)s 141.757 (se)s 151.571 (quenc)s 180.704 (e)s 190.719 (of)s 205.027 (pr)s 215.607 (ob)s 226.647 (ability)s 263.036 (me)s 277.756 (asur)s 299.682 (es)s 10 f 314.604 (\271)s 11 f 95.161 y 321.834 (N)s 17 f 99.516 y 335.431 (on)s 1 f 352.807 (X)s 354.607 (X)s 11 f 101.316 y 363.607 (N)s 17 f 99.516 y 377.204 (asso)s 398.67 (ciate)s 422.897 (d)s 433.525 (to)s 448.14 (the)s 116.316 y -5.69 (initial)s 29.576 (pr)s 40.156 (o\257le)s 10 f 65.916 (\275)s 2 f 118.116 y 72.12 (0)s 17 f 116.316 y 81.797 (in)s 96.517 (the)s 116.45 (fol)s 129.943 (lowing)s 167.356 (sense)s 199.249 (:)s 1 f 148.841 y 101.328 (lim)s 11 f 156.581 y 95.844 (N)s 14 f 104.346 (!1)s 10 f 148.841 y 125.479 (\271)s 11 f 143.886 y 132.71 (N)s 13 f 135.521 y 141.811 (n)s 135.041 y 151.811 (\257)s 142.241 y 151.811 (\257)s 149.441 y 151.811 (\257)s 139.121 y 157.811 (\255)s 10 f 148.841 y 163.478 (\274)s 11 f 143.886 y 170.749 (N)s 1 f 148.841 y 179.85 (\050)s 10 f 184.517 (\264)s 1 f 190.906 (\051)s 10 f 195.573 (;)s 200.906 (U)s 13 f 139.121 y 210.408 (\256)s 12 f 148.841 y 218.741 (\241)s 230.741 (h)s 10 f 235.407 (\275)s 2 f 150.641 y 241.612 (0)s 1 f 148.841 y 246.995 (\050)s 10 f 251.662 (x)s 1 f 258.52 (\051)s 10 f 265.187 (dx;)s 283.624 (U)s 12 f 293.126 (i)s 13 f 135.041 y 299.792 (\257)s 142.241 y 299.792 (\257)s 149.441 y 299.792 (\257)s 10 f 148.841 y 307.126 (\076)s 319.792 (\261)s 13 f 135.521 y 325.58 (o)s 1 f 148.841 y 340.246 (=)s 356.246 (0)s 17 f 189.372 y -5.69 (for)s 15.073 (every)s 48.41 (c)s 53.317 (ontinuous)s 110.42 (function)s 10 f 159.244 (U)s 1 f 174.972 (:)s 184.532 (I)s 183.705 (T)s 11 f 184.139 y 192.372 (d)s 12 f 189.372 y 204.194 (!)s 1 f 222.421 (I)s 224.594 (R)s 17 f 239.318 (and)s 264.221 (every)s 10 f 297.558 (\261)s 309.572 (\076)s 1 f 325.132 (0)s 17 f 331.132 (.)s 345.124 (Then,)s 382.08 (the)s 403.61 (se)s 413.423 (quenc)s 442.556 (e)s 453.967 (of)s 206.172 y -5.69 (pr)s 4.89 (ob)s 15.93 (ability)s 51.617 (me)s 66.337 (asur)s 88.264 (es)s 13 f 196.452 y 102.485 (\251)s 10 f 206.172 y 109.485 (Q)s 11 f 201.818 y 118.972 (N)s 209.139 y 118.972 (\271)s 10 f 206.172 y 132.367 (;)s 141.993 (N)s 156.277 (\076)s 1 f 168.943 (1)s 13 f 196.452 y 174.943 (\252)s 17 f 206.172 y 185.738 (is)s 198.119 (tight)s 225.221 (and)s 248.028 (al)s 257.842 (l)s 264.703 (its)s 281.071 (limit)s 309.092 (p)s 314.612 (oints)s 10 f 343.86 (Q)s 14 f 201.818 y 353.347 (\244)s 17 f 206.172 y 362.658 (ar)s 373.238 (e)s 382.553 (c)s 387.459 (onc)s 405.246 (entr)s 425.946 (ate)s 440.972 (d)s 450.9 (on)s 222.972 y -5.69 (absolutely)s 48.789 (c)s 53.696 (ontinuous)s 108.788 (p)s 114.308 (aths)s 10 f 139.347 (\274)s 1 f 146.618 (\050)s 10 f 151.285 (t;)s 160.951 (dx)s 1 f 174.056 (\051)s 182.056 (=)s 10 f 194.722 (\275)s 1 f 200.926 (\050)s 10 f 205.593 (t;)s 215.26 (x)s 1 f 222.118 (\051)s 10 f 226.785 (dx)s 17 f 243.768 (whose)s 278.314 (density)s 10 f 318.993 (\275)s 17 f 329.077 (is)s 341.543 (the)s 361.062 (we)s 373.942 (ak)s 389.475 (solution)s 434.448 (of)s 448.14 (the)s 239.772 y -5.69 (e)s -.784 (quation)s 13 f 250.48 y 77.346 (8)s 261.28 y 77.346 (\076)s 264.88 y 77.346 (\076)s 268.48 y 77.346 (\074)s 290.081 y 77.346 (\076)s 293.681 y 77.346 (\076)s 297.281 y 77.346 (:)s 10 f 270.264 y 90.012 (@)s 11 f 272.064 y 96.383 (t)s 10 f 270.264 y 100.608 (\275)s 1 f 113.479 (=)s 11 f 255.264 y 141.391 (d)s 13 f 258.864 y 135.222 (X)s 11 f 284.697 y 129.479 (k)s 134.783 (;m)s 2 f 146.148 (=1)s 10 f 270.264 y 160.298 (@)s 11 f 272.064 y 166.669 (k)s 13 f 256.944 y 172.573 (n)s 10 f 270.264 y 180.573 (D)s 11 f 272.064 y 190.508 (k)s 195.813 (;m)s 1 f 270.264 y 207.778 (\050)s 10 f 212.445 (\275)s 1 f 218.649 (\051)s 13 f 256.944 y 223.315 (n)s 10 f 270.264 y 231.315 (@)s 11 f 272.064 y 237.686 (m)s 10 f 270.264 y 246.802 (\275)s 12 f 255.672 (\241)s 1 f 267.672 (2)s 10 f 273.672 (\257)s 281.093 (\302)s 1 f 288.602 (\050)s 10 f 293.268 (\275)s 1 f 299.472 (\051)s 13 f 260.544 y 304.139 (\241)s 10 f 270.264 y 309.639 (@)s 11 f 272.064 y 316.01 (m)s 10 f 270.264 y 325.125 (J)s 12 f 335.6 (\244)s 10 f 344.267 (\275)s 13 f 260.544 y 350.471 (\242)s 256.944 y 355.971 (o)s 363.971 (o)s 10 f 270.264 y 373.971 (;)s 306.131 y 90.012 (\275)s 1 f 96.217 (\0500)s 10 f 106.883 (;)s 12 f 112.217 (\242)s 1 f 115.55 (\051)s 126.883 (=)s 10 f 142.883 (\275)s 2 f 307.931 y 149.087 (0)s 1 f 306.131 y 154.47 (\050)s 12 f 159.137 (\242)s 1 f 162.47 (\051)s 10 f 167.137 (:)s 1 f 282.281 y 439.114 (\0506)s 10 f 449.78 (:)s 1 f 453.114 (5\051)s 17 f 338.655 y -5.69 (and)s 17.507 (b)s 22.414 (elongs)s 58.491 (to)s 10 f 72.795 (L)s 2 f 334.301 y 80.961 (2)s 13 f 325.335 y 88.345 (\263)s 1 f 338.655 y 95.511 ([0)s 10 f 104.845 (;)s 110.178 (T)s 1 f 118.857 (])s 10 f 122.191 (;)s 127.524 (H)s 2 f 340.455 y 137.499 (1)s 1 f 338.655 y 142.882 (\050I)s 146.722 (T)s 11 f 333.422 y 155.389 (d)s 1 f 338.655 y 160.984 (\051)s 13 f 325.335 y 165.651 (\264)s 17 f 338.655 y 172.818 (.)s 181.981 (Mor)s 203.321 (e)s 208.228 (over)s 234.645 (if)s 246.189 (the)s 266.013 (di\256usion)s 315.277 (matrix)s 10 f 353.7 (D)s 17 f 368.153 (is)s 380.923 (lo)s 389.51 (c)s 394.417 (al)s 404.23 (ly)s 417.307 (Lipschitz)s 355.455 y -5.69 (c)s -.784 (ontinuous,)s 58.397 (then)s 85.069 (the)s 104.995 (empiric)s 143.788 (al)s 157.273 (me)s 171.993 (asur)s 193.92 (es)s 208.632 (c)s 213.539 (onver)s 241.905 (ge)s 257.231 (in)s 271.943 (the)s 291.869 (limit)s 10 f 320.381 (N)s 12 f 334.664 (!)s 349.998 (1)s 17 f 366.283 (to)s 380.689 (the)s 400.615 (unique)s 439.247 (we)s 452.127 (ak)s 372.255 y -5.69 (solution)s 39.696 (of)s 53.803 (e)s 58.709 (quation)s 101.642 (\0506.5\051.)s 1 f 416.027 y 8.71 (Since)s 10 f 39.696 (\275)s 1 f 45.9 (\050)s 10 f 50.567 (x)s 1 f 57.425 (\051)s 65.425 (=)s 10 f 78.092 (m)s 1 f 88.628 (\050)s 10 f 93.294 (x)s 1 f 100.153 (\051)s 106.791 (+)s 118.097 (1)s 127.749 (the)s 148.069 (equation)s 196.722 (for)s 214.741 (the)s 235.06 (magnetization)s 312.713 (is)s 324.432 (the)s 344.752 (same)s 374.471 (as)s 388.857 (\0506.5\051.)s 422.075 (It)s 434.727 (is)s 446.447 (not)s 432.827 y -5.69 (di\261cult)s 38.31 (to)s 52.977 (see)s 72.377 (that)s 98.377 (it)s 110.377 (can)s 132.377 (b)s 139.377 (e)s 148.71 (put)s 170.71 (in)s 184.71 (the)s 205.377 (form)s 10 f 476.685 y 172.711 (@)s 11 f 478.485 y 179.081 (t)s 10 f 476.685 y 183.306 (m)s 1 f 197.176 (=)s 12 f 209.843 (r)s 222.509 (\242)s 13 f 456.165 y 228.509 (\303)s 1 f 476.685 y 238.009 (\247)s 12 f 246.676 (r)s 10 f 468.567 y 259.459 (\261)s 12 f 265.246 (G)s 16.324 .48 258.116 473.925 r 10 f 484.916 y 258.116 (\261)s 263.903 (m)s 13 f 456.165 y 275.879 (!)s 1 f 476.685 y 439.114 (\0506)s 10 f 449.78 (:)s 1 f 453.114 (6\051)s 520.543 y -5.69 (with)s 21.643 (the)s 42.31 (energy)s 80.677 (functional)s 12 f 559.735 y 68.82 (G)s 1 f 76.67 (\050)s 10 f 81.337 (m)s 1 f 91.873 (\050)s 10 f 96.54 (r)s 1 f 102.287 (\051\051)s 114.954 (:=)s 13 f 543.401 y 130.954 (Z)s 10 f 559.735 y 144.954 (dr)s 156.947 (g)s 2 f 554.78 y 163.101 (0)s 13 f 550.015 y 168.484 (\241)s 10 f 559.735 y 173.984 (m)s 1 f 184.52 (\050)s 10 f 189.187 (r)s 1 f 194.934 (\051)s 13 f 550.015 y 199.601 (\242)s 1 f 559.735 y 207.768 (+)s 551.617 y 221.208 (1)s 6 .48 221.208 556.975 r 567.966 y 221.208 (2)s 13 f 543.401 y 230.648 (Z)s 10 f 559.735 y 244.647 (dr)s 13 f 543.401 y 258.641 (Z)s 10 f 559.735 y 272.64 (dr)s 14 f 554.78 y 284.634 (0)s 10 f 559.735 y 288 (J)s 1 f 295.809 (\050)s 10 f 300.475 (r)s 12 f 308.889 (\241)s 10 f 320.889 (r)s 14 f 554.78 y 326.636 (0)s 1 f 559.735 y 330.003 (\051)s 10 f 334.67 (m)s 1 f 345.206 (\050)s 10 f 349.872 (r)s 1 f 355.62 (\051)s 10 f 360.286 (m)s 1 f 370.823 (\050)s 10 f 375.489 (r)s 14 f 554.78 y 381.236 (0)s 1 f 559.735 y 384.603 (\051)s 439.114 (\0506)s 10 f 449.78 (:)s 1 f 453.114 (7\051)s 598.926 y -5.69 (where)s 10 f 617.051 y 144.639 (g)s 2 f 612.096 y 150.794 (0)s 1 f 617.051 y 156.177 (\050)s 10 f 160.844 (m)s 1 f 171.38 (\051)s 179.38 (:=)s 12 f 195.38 (\241)s 10 f 204.713 (m)s 2 f 612.096 y 215.249 (2)s 12 f 617.051 y 223.299 (\241)s 10 f 235.299 (\257)s 14 f 612.096 y 242.72 (\241)s 2 f 250.22 (1)s 10 f 617.051 y 255.603 (s)s 1 f 261.228 (\050)s 10 f 265.895 (m;)s 281.764 (\301)s 1 f 288.914 (\050)s 10 f 293.581 (m)s 1 f 304.117 (\051\051)s 439.114 (\0506)s 10 f 449.78 (:)s 1 f 453.114 (8\051)s 643.576 y -5.69 (and)s 10 f 17.634 (\301)s 1 f 24.784 (\050)s 10 f 29.451 (m)s 1 f 39.987 (\051)s 47.987 (=)s 10 f 57.32 (\074)s 69.987 (\276)s 2 f 639.221 y 77.274 (2)s 10 f 643.576 y 85.991 (\076)s 11 f 645.376 y 95.324 (m)s 1 f 643.576 y 104.44 (,)s 111.766 (where)s 10 f 146.457 (\074)s 12 f 159.124 (\242)s 10 f 165.79 (\076)s 11 f 645.376 y 175.124 (m)s 1 f 643.576 y 188.23 (is)s 200.288 (de\257ned)s 241.612 (in)s 255.603 (\0506.3\051.)s 288.934 (The)s 313.591 (mobilit)s 350.591 (y)s 360.916 (is)s 372.974 (giv)s 388.307 (en)s 404.298 (b)s 410.631 (y)s 420.956 (the)s 441.614 (Ein-)s 660.376 y -5.69 (stein)s 22.915 (relation)s 66.819 (\247)s 78.819 (=)s 10 f 91.486 (D)s 1 f 101.754 (\050)s 10 f 106.421 (m)s 1 f 116.957 (\051)s 10 f 121.624 (\302)s 1 f 129.132 (\050)s 10 f 133.799 (m)s 1 f 144.335 (\051.)s 157.625 (Moreo)s 190.325 (v)s 196.325 (er)s 210.23 (the)s 230.768 (energy)s 269.006 (functional)s 12 f 325.211 (G)s 1 f 336.932 (is)s 348.871 (a)s 358.742 (Liapuno)s 401.242 (v)s 411.447 (functional)s 677.176 y -5.69 (for)s 12.677 (\0506.5\051.)s 705.976 y 223.045 (37)s do-end end endp %%Page: 38 38 %%BeginPageSetup initializepage (Raffaele Esposito; page: 38 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f0_12 sf ( )S -996 -1000 :M f1_12 sf ( )S -993 -1000 :M f2_12 sf ( )S -989 -1000 :M f10_12 sf ( )S -981 -1000 :M f11_12 sf ( )S -972 -1000 :M f12_12 sf ( )S -960 -1000 :M f13_12 sf ( )S -951 -1000 :M f14_12 sf ( )S -937 -1000 :M f15_12 sf ( )S -926 -1000 :M f17_12 sf ( )S -923 -1000 :M f18_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 1200 1000 div mul /CMBX10 findfont fdef 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 17 10 1200 1000 div mul /CMTI10 findfont fdef 18 5 1200 1000 div mul /CMSY5 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 6.31 y 8.71 (The)s 33.602 (stationary)s 90.928 (homogeneous)s 164.554 (solutions)s 214.914 (of)s 228.806 (\0506.6\051)s 257.699 (are)s 277.958 (giv)s 293.291 (en)s 309.517 (b)s 315.851 (y)s 326.41 (the)s 347.302 (solutions)s 397.662 (of)s 411.554 (\0502.8\051)s 440.447 (with)s 10 f 23.11 y -5.69 (h)s 2 f 24.91 y 1.224 (1)s 1 f 23.11 y 10.076 (=)s 22.878 (0)s 32.959 (and)s 10 f 56.374 (h)s 2 f 24.91 y 63.288 (2)s 1 f 23.11 y 72.14 (=)s 84.942 (1.)s 99.852 (Notice)s 137.6 (that)s 163.682 (for)s 182.13 (these)s 212.944 (v)s 218.611 (alues)s 248.759 (of)s 262.507 (the)s 283.255 (parameters)s 345.47 (the)s 366.218 (second)s 405.032 (equation)s 454.114 (of)s 39.91 y -5.69 (\0502.8\051)s 22.977 (determines)s 83.743 (the)s 104.41 (function)s 10 f 151.41 (\301)s 1 f 158.56 (\050)s 10 f 163.227 (m)s 1 f 173.763 (\051)s 182.43 (de\257ned)s 223.763 (ab)s 236.763 (o)s 242.43 (v)s 248.43 (e)s 257.763 (as)s 10 f 81.548 y 169.75 (\301)s 1 f 176.9 (\050)s 10 f 181.567 (m)s 1 f 192.103 (\051)s 200.103 (=)s 73.43 y 224.543 (cosh)s 249.276 (2)s 10 f 255.276 (\257)s 262.697 (m)s 69.357 .48 214.21 78.788 r 1 f 89.78 y 214.21 (1)s 222.876 (+)s 234.876 (cosh)s 259.61 (2)s 10 f 265.61 (\257)s 273.03 (m)s 81.548 y 285.007 (:)s 1 f 124.068 y -5.69 (F)s 1.143 (or)s 10 f 16.164 (\257)s 27.453 (\076)s 1 f 40.655 (3)s 10 f 46.655 (=)s 1 f 52.655 (4)s 62.976 (the)s 83.964 (function)s 10 f 131.285 (g)s 2 f 119.713 y 137.439 (0)s 1 f 124.068 y 142.822 (\050)s 10 f 147.489 (m)s 1 f 158.025 (\051)s 167.013 (has)s 188.734 (t)s 193.067 (w)s 201.401 (o)s 211.722 (symmetric)s 270.476 (minima)s 12 f 314.131 (\247)s 10 f 323.464 (m)s 11 f 125.868 y 334 (s)s 1 f 124.068 y 343.45 (determined)s 406.471 (b)s 412.805 (y)s 423.459 (the)s 444.447 (non)s 140.868 y -5.69 (v)s -.024 (anishing)s 47.377 (solutions)s 97.51 (of)s 10 f 167.44 y 180.325 (m)s 1 f 194.195 (=)s 159.322 y 218.635 (sinh)s 242.035 (2)s 10 f 248.035 (\257)s 255.455 (m)s 68.024 .48 208.301 164.68 r 1 f 175.671 y 208.301 (1)s 216.968 (+)s 228.968 (sinh)s 252.368 (2)s 10 f 258.368 (\257)s 265.789 (m)s 0 f 213.884 y -5.69 (Pro)s 16.71 (of)s 32.426 (of)s 48.143 (Theorem)s 106.743 (6.1.)s 1 f 231.799 y 8.71 (F)s 15.543 (ollo)s 33.877 (wing)s 62.767 (the)s 83.658 (strategy)s 130.316 (adopted)s 176.54 (in)s 190.764 (Section)s 232.988 (4)s 243.212 (for)s 261.803 (the)s 282.694 (Ka)s 297.694 (w)s 306.027 (asaki)s 336.652 (dynamics,)s 393.332 (w)s 401.665 (e)s 411.223 (divide)s 447.114 (the)s 248.599 y -5.69 (pro)s 12.01 (of)s 25.961 (of)s 39.911 (Theorem)s 90.896 (6.1)s 110.513 (in)s 124.797 (three)s 155.781 (steps:)s 191.149 (Tigh)s 215.483 (tness,)s 249.304 (iden)s 270.971 (ti\257cation)s 321.922 (of)s 335.873 (the)s 356.824 (limit,)s 389.179 (and)s 412.796 (under)s 447.114 (the)s 265.399 y -5.69 (assumption)s 57.415 (that)s 83.054 (the)s 103.359 (di\256usion)s 151.398 (matrix)s 190.07 (is)s 201.776 (lo)s 211.442 (cally)s 239.414 (Lipsc)s 266.648 (hitz)s 290.286 (con)s 307.953 (tin)s 322.286 (uous,)s 353.397 (the)s 373.703 (uniqueness)s 433.808 (of)s 447.114 (the)s 282.199 y -5.69 (h)s .643 (ydro)s 24.677 (dynamic)s 73.01 (equation.)s 300.115 y 8.71 (The)s 32.988 (pro)s 50.688 (of)s 63.967 (of)s 77.246 (the)s 97.524 (tigh)s 117.858 (tness)s 147.603 (is)s 159.282 (essen)s 185.748 (tially)s 216.36 (the)s 236.639 (same)s 266.318 (as)s 280.663 (the)s 300.942 (one)s 322.554 (giv)s 337.887 (en)s 353.499 (in)s 367.111 (Section)s 408.723 (6)s 418.335 (in)s 431.947 ([LMS])s 316.915 y -5.69 (and)s 16.959 (therefore)s 66.676 (is)s 78.059 (omitted.)s 127.164 (Notice)s 164.147 (ho)s 176.48 (w)s 184.814 (ev)s 196.147 (er,)s 212.967 (that)s 238.283 (in)s 251.599 (the)s 271.582 (presen)s 304.682 (t)s 312.665 (case)s 337.381 (of)s 350.364 (p)s 357.364 (erturb)s 390.431 (ed)s 405.747 (generalized)s 333.715 y -5.69 (simple)s 30.638 (exclusion)s 81.3 (pro)s 99 (cess)s 122.062 (the)s 141.657 (in)s 151.324 (v)s 156.99 (arian)s 183.357 (t)s 190.952 (measures)s 241.381 (are)s 260.343 (not)s 280.604 (pro)s 298.304 (duct)s 324.566 (while)s 354.828 (the)s 374.423 (pro)s 392.123 (of)s 404.718 (of)s 417.313 (tigh)s 437.647 (tness)s 350.515 y -5.69 (in)s 8.31 ([KLO])s 45.143 (use)s 65.877 (explicitly)s 117.877 (the)s 138.543 (fact)s 162.21 (that)s 188.21 (the)s 208.877 (pro)s 226.577 (duct)s 253.91 (measures)s 305.41 (\050)s 10 f 310.077 (\272)s 11 f 346.16 y 316.769 (N)s 353.482 y 316.005 (\256)s 1 f 350.515 y 325.87 (\051)s 11 f 352.315 y 330.537 (\256)s 1 f 350.515 y 341.376 (are)s 361.409 (in)s 371.076 (v)s 376.742 (arian)s 403.109 (t.)s 368.431 y 8.71 (F)s 15.543 (or)s 31.646 (the)s 53.715 (uniqueness)s 115.585 (of)s 130.654 (w)s 138.988 (eak)s 162.057 (solutions)s 213.594 (of)s 228.663 (the)s 250.732 (h)s 257.066 (ydro)s 281.099 (dynamic)s 330.835 (equation)s 381.238 (w)s 389.572 (e)s 400.308 (need)s 429.711 (an)s 447.78 (en-)s 385.231 y -5.69 (ergy)s 22.127 (estimate)s 71.645 (whic)s 95.312 (h)s 107.429 (states)s 143.014 (that)s 170.465 (ev)s 181.798 (ery)s 203.616 (limit)s 233.733 (p)s 240.733 (oin)s 256.4 (t)s 10 f 266.518 (Q)s 14 f 380.876 y 276.004 (\244)s 1 f 385.231 y 286.972 (of)s 302.089 (the)s 324.207 (sequence)s 13 f 375.511 y 375.391 (\251)s 10 f 385.231 y 382.391 (Q)s 11 f 380.876 y 391.878 (N)s 388.197 y 391.878 (\271)s 10 f 385.231 y 400.98 (;)s 410.313 (N)s 424.596 (\076)s 1 f 437.263 (1)s 13 f 375.511 y 443.263 (\252)s 1 f 385.231 y 455.714 (is)s 408.431 y -5.69 (concen)s 29.31 (trated)s 65.343 (on)s 82.01 (paths)s 114.743 (whose)s 150.143 (densit)s 181.21 (y)s 10 f 191.543 (\275)s 1 f 201.748 (b)s 208.748 (elongs)s 244.814 (to)s 10 f 259.481 (L)s 2 f 404.076 y 267.648 (2)s 13 f 395.111 y 275.031 (\263)s 1 f 408.431 y 282.198 ([0)s 10 f 291.531 (;)s 296.864 (T)s 1 f 305.544 (])s 10 f 308.877 (;)s 314.21 (H)s 2 f 410.231 y 324.185 (1)s 1 f 408.431 y 329.569 (\050I)s 333.409 (T)s 11 f 403.197 y 342.075 (d)s 1 f 408.431 y 347.671 (\051)s 13 f 395.111 y 352.337 (\264)s 1 f 408.431 y 359.504 (.)s 0 f 432.241 y -5.69 (Prop)s 24.376 (osition)s 68.919 (6.2)s 17 f 95.153 (L)s 102.066 (et)s 10 f 115.866 (Q)s 14 f 427.886 y 125.352 (\244)s 17 f 432.241 y 135.162 (b)s 140.069 (e)s 149.882 (a)s 160.309 (limit)s 188.829 (p)s 194.349 (oint)s 219.188 (of)s 233.295 (the)s 253.228 (se)s 263.041 (quenc)s 292.175 (e)s 12 f 301.988 (f)s 10 f 307.988 (Q)s 11 f 427.886 y 317.474 (N)s 435.208 y 317.474 (\271)s 10 f 432.241 y 326.576 (;)s 333.909 (N)s 348.193 (\076)s 1 f 360.859 (1)s 12 f 366.859 (g)s 17 f 372.859 (.)s 382.059 (Then,)s 10 f 478.135 y 116.829 (E)s 11 f 479.935 y 125.687 (Q)s 18 f 477.535 y 133.245 (\244)s 13 f 464.815 y 138.861 (h)s 461.801 y 146.528 (Z)s 11 f 464.768 y 158.528 (T)s 2 f 489.068 y 153.195 (0)s 10 f 478.135 y 168.087 (ds)s 13 f 464.815 y 179.958 (\263)s 461.801 y 189.125 (Z)s 2 f 489.068 y 195.792 (I)s 194.098 (T)s 15 f 486.295 y 200.948 (d)s 12 f 478.135 y 209.92 (k)s 219.253 (r)s 10 f 229.253 (\275)s 1 f 235.457 (\050)s 10 f 240.124 (s;)s 251.082 (x)s 1 f 257.941 (\051)s 12 f 265.941 (k)s 2 f 473.18 y 271.941 (2)s 10 f 478.135 y 280.657 (dx)s 13 f 464.815 y 293.761 (\264)s 300.928 (i)s 10 f 478.135 y 309.928 (\074)s 12 f 322.595 (1)s 10 f 337.928 (:)s 1 f 530.238 y 8.71 (The)s 34.579 (pro)s 52.279 (of)s 67.148 (of)s 82.017 (this)s 106.619 (prop)s 130.986 (osition)s 170.921 (is)s 184.19 (similar)s 224.826 (to)s 240.695 (the)s 262.564 (pro)s 280.264 (of)s 295.133 (of)s 310.002 (Prop)s 335.869 (osition)s 375.804 (A.1.1.)s 415.745 (in)s 430.947 ([KLO])s 547.038 y -5.69 (and)s 17.866 (is)s 30.156 (therefore)s 80.779 (omitted.)s 130.782 (The)s 155.672 (pro)s 173.372 (of)s 187.262 (of)s 201.151 (the)s 222.041 (uniqueness)s 282.731 (of)s 296.621 (w)s 304.954 (eak)s 326.844 (solutions)s 377.2 (follo)s 399.201 (ws)s 416.824 (the)s 437.713 (same)s 563.838 y -5.69 (lines)s 21.93 (as)s 36.884 (in)s 51.105 ([VY])s 79.992 (or)s 94.912 (in)s 109.133 ([LMS].)s 148.52 (It)s 161.741 (is)s 174.028 (here)s 200.282 (that)s 226.503 (w)s 234.836 (e)s 244.39 (need)s 272.61 (the)s 293.498 (di\256usion)s 342.118 (co)s 353.785 (e\261cien)s 389.452 (t)s 398.339 (to)s 413.226 (b)s 420.226 (e)s 429.78 (lo)s 439.447 (cally)s 580.638 y -5.69 (Lipsc)s 21.543 (hitz.)s 598.553 y 8.71 (The)s 32.696 (iden)s 54.363 (ti\257cation)s 104.35 (of)s 117.336 (the)s 137.322 (limit)s 165.309 (is)s 176.695 (not)s 197.349 (trivial)s 232.369 (and)s 255.022 (is)s 266.408 (the)s 286.395 (main)s 315.714 (step)s 340.434 (of)s 353.421 (the)s 373.407 (pro)s 391.107 (of)s 404.094 (of)s 417.08 (Theorem)s 615.353 y -5.69 (6.1.)s 0 f 633.269 y -5.69 (Lemma)s 43.497 (6.3)s 17 f 70.205 (A)s 78.818 (l)s 82.498 (l)s 90.062 (limit)s 118.785 (p)s 124.305 (oints)s 10 f 154.254 (Q)s 14 f 628.914 y 163.741 (\244)s 17 f 633.269 y 173.754 (of)s 188.064 (the)s 208.201 (se)s 218.014 (quenc)s 247.147 (e)s 13 f 623.549 y 257.163 (\251)s 10 f 633.269 y 264.163 (Q)s 11 f 628.914 y 273.65 (N)s 636.236 y 273.65 (\271)s 10 f 633.269 y 287.045 (;)s 296.672 (N)s 310.955 (\076)s 1 f 323.621 (1)s 13 f 623.549 y 329.621 (\252)s 17 f 633.269 y 341.118 (ar)s 351.698 (e)s 361.714 (c)s 366.621 (onc)s 384.408 (entr)s 405.107 (ate)s 420.134 (d)s 430.764 (on)s 448.14 (the)s 650.069 y -5.69 (p)s -.17 (ath)s 10 f 20.376 (\275)s 1 f 26.58 (\050)s 10 f 31.247 (t;)s 40.914 (x)s 1 f 47.772 (\051)s 10 f 52.439 (dx)s 17 f 69.836 (whose)s 104.796 (density)s 10 f 145.889 (\275)s 17 f 156.387 (is)s 169.266 (the)s 189.2 (we)s 202.08 (ak)s 218.026 (solution)s 263.412 (of)s 277.519 (e)s 282.426 (quation)s 325.359 (\0506.5\051.)s 677.176 y -5.69 (Pr)s 6.896 (o)s 12.416 (of.)s 1 f 35.511 (Fix)s 58.434 (a)s 69.857 (function)s 10 f 118.28 (U)s 1 f 133.204 (in)s 12 f 148.627 (C)s 2 f 672.821 y 155.645 (1)s 11 f 160.429 (;)s 2 f 163.279 (2)s 1 f 677.176 y 168.662 (\050[0)s 10 f 182.662 (;)s 187.995 (T)s 1 f 196.675 (])s 12 f 203.623 (\243)s 1 f 216.572 (I)s 215.745 (T)s 11 f 671.943 y 224.412 (d)s 1 f 677.176 y 230.007 (\051.)s 247.609 (Consider)s 299.132 (the)s 321.221 (martingales)s 10 f 387.411 (M)s 11 f 672.821 y 400.361 (U)s 680.143 y 399.052 (t)s 1 f 677.176 y 414.103 (=)s 10 f 429.141 (M)s 11 f 671.409 y 442.091 (U)s 448.495 (;N)s 680.129 y 440.782 (t)s 1 f 677.176 y 460.447 (,)s 705.976 y 223.045 (38)s do-end end endp %%Page: 39 39 %%BeginPageSetup initializepage (Raffaele Esposito; page: 39 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f1_12 sf ( )S -997 -1000 :M f2_12 sf ( )S -993 -1000 :M f10_12 sf ( )S -985 -1000 :M f11_12 sf ( )S -976 -1000 :M f12_12 sf ( )S -964 -1000 :M f13_12 sf ( )S -954 -1000 :M f14_12 sf ( )S -941 -1000 :M f15_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 58 60 translate 72 72.27 div dup scale 10 f 6.31 y -5.69 (N)s 11 f 1.955 y 5.26 (U)s 9.276 y 3.951 (t)s 1 f 6.31 y 16.631 (=)s 10 f 29.297 (N)s 11 f .543 y 40.247 (U)s 46.652 (;N)s 9.263 y 38.939 (t)s 1 f 6.31 y 62.604 (de\257ned)s 103.937 (b)s 110.27 (y)s 10 f 45.887 y 28.155 (M)s 11 f 40.932 y 41.105 (U)s 48.854 y 39.797 (t)s 1 f 45.887 y 55.809 (=)s 10 f 68.476 (\074)s 81.143 (\274)s 11 f 40.932 y 88.413 (N)s 48.854 y 87.983 (t)s 10 f 45.887 y 97.515 (;)s 102.848 (U)s 11 f 47.687 y 111.042 (t)s 10 f 45.887 y 118.6 (\076)s 12 f 131.267 (\241)s 10 f 143.933 (\074)s 156.6 (\274)s 11 f 40.932 y 163.871 (N)s 2 f 48.854 y 163.44 (0)s 10 f 45.887 y 172.972 (;)s 178.306 (U)s 2 f 47.687 y 186.499 (0)s 10 f 45.887 y 195.216 (\076)s 12 f 207.882 (\241)s 13 f 29.554 y 219.216 (Z)s 11 f 32.52 y 231.216 (t)s 2 f 56.821 y 225.882 (0)s 13 f 36.167 y 237.441 (\241)s 10 f 45.887 y 242.941 (@)s 11 f 47.687 y 249.311 (s)s 1 f 45.887 y 257.107 (+)s 10 f 269.107 (N)s 2 f 40.932 y 280.057 (2)s 1 f 45.887 y 285.44 (I)s 287.614 (L)s 11 f 40.121 y 295.114 (\257)s 49.414 y 295.114 (N)s 13 f 36.167 y 304.216 (\242)s 10 f 45.887 y 313.049 (\074)s 325.715 (\274)s 11 f 40.932 y 332.986 (N)s 48.854 y 332.556 (s)s 10 f 45.887 y 342.088 (;)s 347.421 (U)s 11 f 47.687 y 355.615 (s)s 10 f 45.887 y 364.077 (\076)s 378.744 (ds)s 393.948 (;)s 78.362 y 40.155 (N)s 11 f 73.407 y 51.105 (U)s 81.329 y 49.797 (t)s 1 f 78.362 y 65.809 (=)s 13 f 68.642 y 81.809 (\241)s 10 f 78.362 y 87.309 (M)s 11 f 73.407 y 100.259 (U)s 81.329 y 98.951 (t)s 13 f 68.642 y 108.297 (\242)s 2 f 70.634 y 113.797 (2)s 12 f 109.496 y 54.822 (\241)s 13 f 93.162 y 70.155 (Z)s 11 f 96.129 y 82.155 (t)s 2 f 120.429 y 76.822 (0)s 13 f 96.175 y 88.38 (n)s 10 f 109.496 y 96.38 (N)s 2 f 104.541 y 107.33 (2)s 1 f 109.496 y 112.713 (I)s 114.887 (L)s 11 f 103.729 y 122.387 (\257)s 113.022 y 122.387 (N)s 13 f 99.776 y 131.488 (\241)s 10 f 109.496 y 140.322 (\074)s 152.988 (\274)s 11 f 104.541 y 160.259 (N)s 112.462 y 159.828 (s)s 10 f 109.496 y 169.361 (;)s 174.694 (U)s 11 f 111.296 y 182.887 (s)s 10 f 109.496 y 191.35 (\076)s 13 f 99.776 y 204.016 (\242)s 2 f 102.262 y 209.516 (2)s 12 f 109.496 y 217.566 (\241)s 1 f 229.566 (2)s 10 f 238.9 (\074)s 251.566 (\274)s 11 f 104.541 y 258.837 (N)s 112.462 y 258.407 (s)s 10 f 109.496 y 267.939 (;)s 273.272 (U)s 11 f 111.296 y 281.465 (s)s 10 f 109.496 y 289.928 (\076)s 302.594 (N)s 2 f 104.541 y 313.544 (2)s 1 f 109.496 y 318.928 (I)s 321.101 (L)s 11 f 103.729 y 328.601 (\257)s 113.022 y 328.601 (N)s 10 f 109.496 y 341.036 (\074)s 353.703 (\274)s 11 f 104.541 y 360.973 (N)s 112.462 y 360.543 (s)s 10 f 109.496 y 370.075 (;)s 375.408 (U)s 11 f 111.296 y 383.602 (s)s 10 f 109.496 y 392.064 (\076)s 13 f 96.175 y 401.398 (o)s 10 f 109.496 y 411.398 (ds)s 426.602 (:)s 1 f 149.573 y -5.69 (In)s 9.61 (these)s 40.643 (form)s 64.676 (ulas,)s 93.117 (for)s 111.784 (a)s 122.084 (con)s 139.75 (tin)s 154.084 (uous)s 182.45 (function)s 10 f 229.75 (U)s 1 f 243.552 (and)s 10 f 267.185 (\274)s 1 f 278.755 (in)s 12 f 293.055 (M)s 1 f 307.466 (\050I)s 311.306 (T)s 11 f 144.34 y 319.973 (d)s 1 f 149.573 y 325.568 (\051,)s 10 f 337.943 (\074)s 351.109 (\274)s 358.38 (;)s 363.713 (U)s 377.048 (\076)s 1 f 390.681 (stands)s 428.447 (for)s 447.114 (the)s 166.373 y -5.69 (in)s 3.976 (tegral)s 38.01 (of)s 51.677 (the)s 72.343 (function)s 10 f 119.343 (U)s 1 f 132.845 (with)s 160.178 (resp)s 181.945 (ect)s 201.278 (to)s 215.945 (the)s 236.612 (measure)s 10 f 283.379 (\274)s 1 f 290.649 (.)s 183.293 y 8.71 (A)s 22.791 (simple)s 61.273 (computation)s 132.355 (of)s 147.104 (the)s 168.853 (in)s 178.52 (tegral)s 213.635 (term)s 243.417 (of)s 10 f 258.166 (N)s 11 f 178.938 y 269.116 (U)s 186.26 y 267.808 (t)s 1 f 183.293 y 282.236 (sho)s 299.303 (ws)s 317.785 (that)s 344.867 (the)s 366.616 (exp)s 385.283 (ectation)s 432.365 (of)s 447.114 (the)s 200.093 y -5.69 (quadratic)s 49.775 (v)s 55.441 (ariation)s 101.906 (of)s 117.338 (the)s 139.769 (martingale)s 10 f 201.567 (M)s 11 f 195.738 y 214.517 (U)s 203.06 y 213.209 (t)s 1 f 200.093 y 228.32 (v)s 233.987 (anishes)s 277.218 (as)s 10 f 293.716 (N)s 12 f 310.941 (\042)s 323.215 (1)s 1 f 335.215 (.)s 349.176 (Therefore,)s 409.115 (b)s 415.449 (y)s 427.547 (Do)s 443.047 (ob\047s)s 216.893 y -5.69 (inequalit)s 39.643 (y)s 44.977 (,)s 52.31 (for)s 70.677 (ev)s 82.01 (ery)s 10 f 102.377 (\261)s 111.497 (\076)s 1 f 124.164 (0,)s 246.97 y 143.55 (lim)s 11 f 254.71 y 138.066 (N)s 14 f 146.567 (!1)s 10 f 246.97 y 167.701 (P)s 11 f 249.337 y 175.405 (\271)s 15 f 246.937 y 181.24 (N)s 13 f 233.65 y 189.548 (h)s 1 f 246.97 y 203.365 (sup)s 2 f 257.062 y 197.215 (0)s 14 f 201.998 (\267)s 11 f 209.498 (t)s 14 f 213.123 (\267)s 11 f 220.623 (T)s 12 f 246.97 y 229.583 (j)s 10 f 232.916 (M)s 11 f 242.016 y 245.866 (U)s 249.937 y 244.558 (t)s 12 f 246.97 y 253.904 (j)s 10 f 260.57 (\076)s 273.237 (\261)s 13 f 233.65 y 279.025 (i)s 1 f 246.97 y 291.358 (=)s 307.358 (0)s 10 f 316.691 (:)s 1 f 439.114 (\0506)s 10 f 449.78 (:)s 1 f 453.114 (9\051)s 288.111 y 8.71 (W)s 20.043 (e)s 30.586 (no)s 42.919 (w)s 56.795 (turn)s 84.705 (to)s 100.581 (the)s 122.457 (martingale)s 10 f 183.7 (M)s 11 f 283.757 y 196.65 (U)s 291.078 y 195.341 (t)s 1 f 288.111 y 204.687 (.)s 216.982 (A)s 231.19 (summation)s 294.466 (b)s 300.8 (y)s 312.343 (parts)s 344.319 (p)s 351.319 (ermits)s 389.295 (to)s 405.171 (rewrite)s 447.113 (the)s 304.911 y -5.69 (in)s 3.976 (tegral)s 38.01 (term)s 66.71 (of)s 80.377 (the)s 101.043 (martingale)s 10 f 161.077 (M)s 11 f 300.557 y 174.027 (U)s 307.878 y 172.718 (t)s 1 f 304.911 y 186.065 (as)s 13 f 331.655 y 36.444 (Z)s 11 f 334.622 y 48.444 (t)s 2 f 358.922 y 43.11 (0)s 10 f 347.989 y 56.002 (\074)s 68.669 (\274)s 11 f 343.034 y 75.94 (N)s 350.955 y 75.509 (s)s 10 f 347.989 y 85.041 (;)s 90.375 (@)s 11 f 349.789 y 96.745 (s)s 10 f 347.989 y 101.875 (U)s 11 f 349.789 y 110.068 (s)s 10 f 347.989 y 118.53 (\076)s 131.197 (ds)s 1 f 149.068 (+)s 13 f 331.655 y 164.401 (Z)s 11 f 334.622 y 176.401 (t)s 2 f 358.922 y 171.068 (0)s 10 f 347.989 y 182.626 (ds)s 196.497 (N)s 14 f 343.034 y 207.447 (\241)s 11 f 214.947 (d)s 2 f 219.942 (+1)s 11 f 332.989 y 240.921 (d)s 13 f 336.589 y 234.752 (X)s 11 f 362.422 y 234.692 (k)s 2 f 239.996 (=1)s 13 f 336.589 y 255.508 (X)s 11 f 363.529 y 254.146 (i)s 14 f 257.541 (2)s 2 f 264.008 (I)s 262.315 (T)s 15 f 360.755 y 269.165 (d)s 13 f 338.269 y 276.203 (\241)s 10 f 347.989 y 281.703 (@)s 11 f 343.034 y 288.74 (N)s 350.955 y 288.074 (k)s 10 f 347.989 y 297.842 (U)s 13 f 338.269 y 307.344 (\242)s 1 f 347.989 y 312.844 (\050)s 10 f 317.511 (s;)s 328.469 (i=)s 337.936 (N)s 1 f 348.886 (\051W)s 354.653 (W)s 11 f 342.222 y 367.153 (\257)s 373.026 (;N)s 351.334 y 367.153 (i;i)s 2 f 376.793 (+)s 11 f 384.16 (e)s 15 f 352.607 y 388.713 (k)s 1 f 347.989 y 394.559 (\050)s 10 f 399.225 (\264)s 11 f 349.789 y 405.184 (s)s 1 f 347.989 y 410.313 (\051)s 10 f 418.313 (;)s 1 f 395.042 y -5.69 (where)s 29.01 (W)s 30.11 (W)s 11 f 389.275 y 42.61 (\257)s 48.483 (;N)s 398.387 y 42.61 (i;i)s 2 f 52.25 (+)s 11 f 59.617 (e)s 15 f 399.66 y 64.17 (k)s 1 f 395.042 y 70.016 (\050)s 10 f 74.682 (\264)s 1 f 81.071 (\051)s 89.738 (is)s 101.805 (the)s 122.471 (curren)s 155.538 (t)s 164.205 (o)s 169.871 (v)s 175.871 (er)s 189.905 (the)s 210.571 (b)s 217.571 (ond)s 12 f 240.905 (f)s 10 f 246.905 (i;)s 256.372 (i)s 1 f 263.173 (+)s 10 f 275.173 (e)s 11 f 396.842 y 280.76 (k)s 12 f 395.042 y 286.665 (g)s 1 f 296.665 (:)s 433.949 y 93.414 (W)s 94.514 (W)s 11 f 428.182 y 107.014 (\257)s 112.887 (;N)s 437.293 y 107.014 (i;i)s 2 f 116.654 (+)s 11 f 124.021 (e)s 15 f 438.567 y 128.574 (k)s 1 f 433.949 y 134.42 (\050)s 10 f 139.086 (\264)s 1 f 145.475 (\051)s 153.475 (=)s 425.83 y 167.582 (1)s 6 .48 167.582 431.189 r 442.18 y 167.582 (2)s 13 f 420.628 y 177.022 (n)s 10 f 433.949 y 185.022 (C)s 11 f 428.182 y 194.457 (\257)s 437.475 y 193.599 (N)s 1 f 433.949 y 202.7 (\050)s 10 f 207.367 (i;)s 216.834 (i)s 1 f 223.635 (+)s 10 f 235.635 (e)s 11 f 435.749 y 241.223 (k)s 1 f 433.949 y 247.127 (;)s 10 f 252.46 (\264)s 1 f 258.849 (\051)s 12 f 266.182 (\241)s 10 f 278.182 (C)s 11 f 428.182 y 287.617 (\257)s 437.475 y 286.759 (N)s 1 f 433.949 y 295.861 (\050)s 10 f 300.527 (i)s 1 f 307.328 (+)s 10 f 319.328 (e)s 11 f 435.749 y 324.916 (k)s 10 f 433.949 y 330.82 (;)s 336.153 (i)s 1 f 340.287 (;)s 10 f 345.62 (\264)s 1 f 352.009 (\051)s 13 f 420.628 y 356.676 (o)s 1 f 470.457 y -5.69 (and)s 13 f 460.737 y 17.643 (\241)s 10 f 470.457 y 23.143 (@)s 11 f 466.103 y 30.181 (N)s 473.856 y 29.514 (k)s 10 f 470.457 y 39.282 (U)s 13 f 460.737 y 48.784 (\242)s 1 f 470.457 y 58.284 (is)s 70.351 (the)s 91.017 (discrete)s 135.117 (gradien)s 173.484 (t)s 182.151 (de\257ned)s 223.484 (b)s 229.818 (y)s 13 f 490.814 y 108.043 (\241)s 10 f 500.535 y 113.543 (@)s 11 f 495.58 y 120.58 (N)s 503.501 y 119.914 (k)s 10 f 500.535 y 129.682 (U)s 13 f 490.814 y 139.184 (\242)s 1 f 500.535 y 144.684 (\050)s 10 f 149.35 (i=)s 158.818 (N)s 1 f 169.768 (\051)s 181.101 (=)s 10 f 197.101 (N)s 1 f 208.051 ([)s 10 f 211.384 (U)s 1 f 220.886 (\050\050)s 10 f 230.219 (i)s 1 f 237.02 (+)s 10 f 249.02 (e)s 11 f 502.335 y 254.607 (k)s 1 f 500.535 y 260.512 (\051)s 10 f 265.178 (=)s 270.512 (N)s 1 f 281.462 (\051)s 12 f 288.795 (\241)s 10 f 300.795 (U)s 1 f 310.296 (\050)s 10 f 314.963 (i=)s 324.431 (N)s 1 f 335.381 (\051])s 10 f 346.714 (:)s 1 f 530.612 y -5.69 (Remark)s 39.92 (that)s 66.33 (w)s 74.663 (e)s 84.406 (ma)s 100.073 (y)s 110.816 (write)s 141.926 (the)s 163.003 (curren)s 196.069 (t)s 205.146 (W)s 206.246 (W)s 11 f 524.845 y 218.746 (\257)s 224.619 (;N)s 533.957 y 218.746 (i;i)s 2 f 228.386 (+)s 11 f 235.753 (e)s 15 f 535.23 y 240.306 (k)s 1 f 530.612 y 250.562 (as)s 265.705 (the)s 286.782 (sum)s 312.592 (of)s 326.668 (the)s 347.745 (curren)s 380.811 (t)s 10 f 389.888 (W)s 11 f 532.412 y 401.221 (i;i)s 2 f 410.862 (+)s 11 f 418.228 (e)s 15 f 533.685 y 422.781 (k)s 1 f 530.612 y 433.037 (of)s 447.114 (the)s 547.412 y -5.69 (GSEP)s 30.727 (\050I)s 37.567 (L)s 11 f 549.212 y 45.067 (N)s 53.052 (;)s 2 f 55.902 (0)s 1 f 547.412 y 61.285 (\051)s 69.952 (and)s 93.285 (a)s 103.285 (term)s 131.985 (coming)s 173.318 (from)s 201.685 (the)s 222.352 (p)s 229.352 (erturbation:)s 585.374 y 2.057 (W)s 3.157 (W)s 11 f 579.607 y 15.657 (\257)s 21.53 (;N)s 588.719 y 15.657 (i;i)s 2 f 25.297 (+)s 11 f 32.664 (e)s 15 f 589.992 y 37.217 (k)s 1 f 585.374 y 43.063 (\050)s 10 f 47.729 (\264)s 1 f 54.118 (\051)s 62.118 (=)s 10 f 74.785 (W)s 11 f 587.174 y 86.118 (i;i)s 2 f 95.758 (+)s 11 f 103.125 (e)s 15 f 588.447 y 107.678 (k)s 1 f 585.374 y 113.524 (\050)s 10 f 118.191 (\264)s 1 f 124.579 (\051)s 131.913 (+)s 10 f 577.256 y 145.353 (\257)s 7.421 .48 145.353 582.614 r 1 f 593.605 y 146.063 (2)s 10 f 585.374 y 154.214 (N)s 14 f 580.419 y 165.164 (\241)s 2 f 172.664 (1)s 13 f 575.654 y 180.047 (\241)s 10 f 585.374 y 185.547 (@)s 11 f 587.174 y 191.918 (k)s 10 f 585.374 y 197.822 (J)s 12 f 208.297 (\244)s 10 f 216.963 (\274)s 11 f 580.419 y 224.234 (N)s 1 f 585.374 y 233.336 (\050)s 10 f 238.003 (\264)s 1 f 244.392 (\051)s 13 f 575.654 y 249.058 (\242)s 1 f 585.374 y 256.558 (\050)s 10 f 261.225 (i=)s 270.692 (N)s 1 f 281.642 (\051)s 12 f 291.642 (f)s 10 f 297.642 (r)s 11 f 587.174 y 303.056 (i;i)s 2 f 312.696 (+)s 11 f 320.063 (e)s 15 f 588.447 y 324.616 (k)s 1 f 585.374 y 333.129 (+)s 10 f 345.129 (r)s 11 f 587.174 y 350.542 (i)s 2 f 353.938 (+)s 11 f 361.304 (e)s 15 f 588.447 y 365.857 (k)s 11 f 587.174 y 371.103 (;i)s 12 f 585.374 y 377.948 (g)s 1 f 386.615 (+)s 10 f 398.615 (N)s 14 f 580.419 y 409.565 (\241)s 2 f 417.065 (1)s 10 f 585.374 y 422.448 (o)s 11 f 587.174 y 428.265 (N)s 1 f 585.374 y 437.367 (\0501\051)s 10 f 452.7 (;)s 1 f 620.683 y -5.69 (where)s 10 f 29.311 (o)s 11 f 622.483 y 35.128 (N)s 1 f 620.683 y 44.229 (\0501\051)s 63.864 (is)s 76.232 (a)s 86.533 (random)s 130.868 (v)s 136.534 (ariable)s 176.202 (whic)s 199.869 (h)s 210.837 (is)s 223.205 (b)s 230.205 (ounded)s 272.506 (in)s 286.807 (absolute)s 334.508 (v)s 340.175 (alue)s 365.81 (b)s 372.143 (y)s 382.778 (a)s 393.079 (constan)s 432.812 (t)s 441.78 (that)s 637.483 y -5.69 (con)s 11.976 (v)s 17.977 (erges)s 48.077 (to)s 62.743 (0)s 72.743 (as)s 10 f 87.477 (N)s 12 f 101.76 (\042)s 111.093 (1)s 1 f 127.093 (and)s 10 f 673.745 y 123.833 (W)s 11 f 675.545 y 135.166 (i;i)s 2 f 144.806 (+)s 11 f 152.173 (e)s 15 f 676.818 y 156.726 (k)s 1 f 673.745 y 162.572 (\050)s 10 f 167.238 (\264)s 1 f 173.627 (\051)s 181.627 (=)s 665.626 y 195.734 (1)s 6 .48 195.734 670.985 r 681.976 y 195.734 (2)s 12 f 673.745 y 205.174 (f)s 10 f 211.174 (r)s 11 f 675.545 y 216.588 (i;i)s 2 f 226.228 (+)s 11 f 233.595 (e)s 15 f 676.818 y 238.148 (k)s 1 f 673.745 y 243.993 (\050)s 10 f 248.66 (\264)s 1 f 255.049 (\051)s 12 f 262.382 (\241)s 10 f 274.382 (r)s 11 f 675.545 y 279.796 (i)s 2 f 283.191 (+)s 11 f 290.558 (e)s 15 f 676.818 y 295.111 (k)s 11 f 675.545 y 300.357 (;i)s 1 f 673.745 y 307.202 (\050)s 10 f 311.869 (\264)s 1 f 318.258 (\051)s 12 f 322.924 (g)s 10 f 330.924 (:)s 1 f 705.976 y 223.045 (39)s do-end end endp %%Page: 40 40 %%BeginPageSetup initializepage (Raffaele Esposito; page: 40 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f0_12 sf ( )S -996 -1000 :M f1_12 sf ( )S -993 -1000 :M f2_12 sf ( )S -989 -1000 :M f10_12 sf ( )S -981 -1000 :M f11_12 sf ( )S -972 -1000 :M f12_12 sf ( )S -960 -1000 :M f13_12 sf ( )S -951 -1000 :M f14_12 sf ( )S -937 -1000 :M f15_12 sf ( )S -926 -1000 :M f17_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 1200 1000 div mul /CMBX10 findfont fdef 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 17 10 1200 1000 div mul /CMTI10 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 6.31 y -5.69 (W)s 5.643 (e)s 14.976 (will)s 37.643 (often)s 67.977 (omit)s 95.977 (the)s 116.643 (dep)s 135.643 (endence)s 180.977 (of)s 10 f 194.643 (W)s 11 f 8.11 y 205.977 (i;i)s 2 f 215.617 (+)s 11 f 222.984 (e)s 15 f 9.383 y 227.537 (k)s 1 f 6.31 y 237.383 (and)s 260.716 (W)s 261.816 (W)s 11 f .543 y 274.316 (\257)s 280.189 (;N)s 9.655 y 274.316 (i;i)s 2 f 283.956 (+)s 11 f 291.323 (e)s 15 f 10.928 y 295.876 (k)s 1 f 6.31 y 305.722 (on)s 10 f 322.388 (\264)s 1 f 332.777 (and)s 10 f 356.111 (N)s 1 f 367.061 (.)s 23.23 y 8.71 (F)s 15.543 (ollo)s 33.877 (wing)s 62.56 (the)s 83.244 (non)s 106.594 (gradien)s 144.961 (t)s 153.644 (metho)s 186.644 (d)s 197.328 (of)s 211.012 (V)s 219.012 (aradhan)s 265.729 ([V])s 285.412 (and)s 308.762 (the)s 329.446 (en)s 341.113 (trop)s 362.813 (y)s 373.163 (metho)s 406.163 (d)s 416.847 (of)s 430.53 ([GPV])s 40.03 y -5.69 (w)s 2.643 (e)s 10.904 (no)s 23.237 (w)s 34.831 (replace)s 74.458 (the)s 94.052 (curren)s 127.119 (t)s 134.713 (W)s 135.813 (W)s 11 f 34.263 y 148.313 (\257)s 154.186 (;N)s 43.375 y 148.313 (i;i)s 2 f 157.953 (+)s 11 f 165.32 (e)s 15 f 44.648 y 169.873 (k)s 1 f 40.03 y 178.646 (app)s 198.313 (earing)s 233.274 (in)s 246.201 (the)s 265.795 (in)s 275.462 (tegral)s 308.422 (term)s 336.05 (of)s 348.644 (the)s 368.238 (martingale)s 10 f 427.198 (M)s 11 f 35.675 y 440.148 (U)s 42.996 y 438.84 (t)s 1 f 40.03 y 451.113 (b)s 457.447 (y)s 63.608 y -5.69 (a)s 3.514 (linear)s 36.084 (com)s 57.084 (bination)s 103.621 (of)s 116.492 (the)s 136.362 (gradien)s 174.729 (t)s 13 f 50.288 y 182.599 (n)s 10 f 63.608 y 190.599 (\264)s 1 f 196.988 (\050)s 10 f 201.655 (i)s 1 f 206.863 (+)s 10 f 217.271 (e)s 11 f 65.408 y 222.858 (m)s 1 f 63.608 y 231.974 (\051)s 12 f 237.715 (\241)s 10 f 248.122 (\264)s 1 f 254.511 (\050)s 10 f 259.178 (i)s 1 f 263.312 (\051)s 13 f 50.288 y 267.978 (o)s 1 f 63.608 y 279.182 (and)s 13 f 50.288 y 301.719 (n)s 10 f 63.608 y 309.719 (\257)s 317.14 (N)s 14 f 59.253 y 328.09 (\241)s 2 f 335.59 (1)s 13 f 53.888 y 342.974 (\241)s 10 f 63.608 y 348.474 (@)s 11 f 65.408 y 354.844 (m)s 10 f 63.608 y 363.96 (J)s 12 f 374.435 (\244)s 10 f 383.101 (\274)s 11 f 59.253 y 390.372 (N)s 1 f 63.608 y 399.474 (\050)s 10 f 404.141 (\264)s 1 f 410.529 (\051)s 13 f 53.888 y 415.196 (\242)s 1 f 63.608 y 422.696 (\050)s 10 f 427.363 (i=)s 436.83 (N)s 1 f 447.78 (\051)s 13 f 50.288 y 452.447 (o)s 1 f 63.608 y 460.447 (.)s 87.275 y -5.69 (This)s 21.297 (requires)s 66.018 (some)s 95.672 (notation.)s 148.201 (F)s 155.034 (or)s 10 f 169.321 (\140)s 12 f 177.655 (\267)s 10 f 190.321 (N)s 1 f 204.858 (and)s 10 f 227.779 (i)s 1 f 235.5 (in)s 249.088 (I)s 248.261 (T)s 11 f 82.042 y 256.928 (d)s 1 f 87.275 y 262.523 (,)s 269.526 (let)s 10 f 286.447 (\264)s 11 f 82.92 y 292.836 (\140)s 1 f 87.275 y 297.452 (\050)s 10 f 302.119 (x)s 1 f 308.977 (\051)s 317.231 (stands)s 354.285 (for)s 372.239 (the)s 392.493 (mean)s 424.08 (n)s 430.414 (um)s 446.747 (b)s 453.747 (er)s 104.075 y -5.69 (of)s 7.977 (particles)s 56.077 (in)s 70.077 (a)s 80.077 (cub)s 99.077 (e)s 108.41 (of)s 122.077 (size)s 144.81 (2)s 10 f 150.81 (\140)s 1 f 158.477 (+)s 170.477 (1)s 180.477 (cen)s 197.477 (tered)s 228.177 (in)s 10 f 242.177 (i)s 1 f 250.311 (:)s 10 f 139.423 y 148.445 (\264)s 11 f 134.468 y 154.834 (\140)s 1 f 139.423 y 159.45 (\050)s 10 f 164.117 (i)s 1 f 168.251 (\051)s 179.584 (=)s 131.305 y 217.322 (1)s 46.595 .48 197.024 136.663 r 147.654 y 197.024 (\0502)s 10 f 207.691 (\140)s 1 f 215.358 (+)s 227.358 (1\051)s 11 f 144.188 y 238.024 (d)s 13 f 128.023 y 254.677 (X)s 14 f 154.323 y 247.06 (j)s 11 f 249.91 (j)s 14 f 254.366 (\241)s 11 f 261.866 (i)s 14 f 265.261 (j\267)s 11 f 275.611 (\140)s 10 f 139.423 y 281.628 (\264)s 1 f 288.017 (\050)s 10 f 292.683 (j)s 1 f 298.312 (\051)s 10 f 306.312 (:)s 1 f 185.853 y -5.69 (F)s 1.143 (or)s 10 f 15.843 (k)s 1 f 25.801 (=)s 38.468 (1)s 10 f 44.468 (;)s 12 f 49.801 (\242)s 55.135 (\242)s 60.468 (\242)s 10 f 65.801 (;)s 71.135 (d)s 1 f 77.38 (,)s 10 f 84.714 (N)s 12 f 98.997 (\270)s 1 f 111.664 (1,)s 10 f 124.997 (\042)s 133.926 (\076)s 1 f 146.593 (0)s 156.593 (and)s 179.926 (a)s 189.926 (smo)s 210.993 (oth)s 232.326 (function)s 10 f 279.326 (G)s 1 f 292.094 (:)s 298.761 (I)s 297.934 (T)s 11 f 180.619 y 306.601 (d)s 12 f 185.853 y 315.53 (!)s 1 f 330.863 (I)s 333.036 (R)s 341.87 (,)s 349.203 (let)s 10 f 215.016 y 111.893 (X)s 11 f 210.061 y 122.776 (k)s 217.982 y 121.835 (N)s 129.82 (;\042)s 1 f 215.016 y 137.804 (\050)s 10 f 142.47 (G;)s 157.238 (\264)s 1 f 163.627 (\051)s 174.961 (=)s 10 f 190.96 (N)s 14 f 210.061 y 201.91 (\241)s 11 f 209.41 (d)s 2 f 214.406 (+1)s 13 f 203.616 y 230.518 (X)s 11 f 230.556 y 229.156 (i)s 14 f 232.551 (2)s 2 f 239.018 (I)s 237.324 (T)s 15 f 227.783 y 244.174 (d)s 10 f 215.016 y 251.213 (G)s 1 f 260.648 (\050)s 10 f 265.314 (i=)s 274.782 (N)s 1 f 285.732 (\051)s 10 f 290.398 (\277)s 11 f 216.816 y 295.644 (i)s 1 f 215.016 y 299.639 (V)s 301.006 (V)s 11 f 209.782 y 310.173 (N)s 318.674 (\042)s 217.982 y 310.173 (k)s 1 f 215.016 y 323.808 (\050)s 10 f 328.475 (\264)s 1 f 334.864 (\051)s 10 f 342.864 (;)s 1 f 257.888 y -5.69 (where)s 296.965 y -5.69 (V)s -4.324 (V)s 11 f 291.731 y 4.843 (N)s 13.345 (\042)s 299.931 y 4.843 (k)s 1 f 296.965 y 18.479 (\050)s 10 f 23.145 (\264)s 1 f 29.534 (\051)s 40.867 (=)s 56.867 (W)s 57.967 (W)s 2 f 298.765 y 70.467 (0)s 11 f 75.251 (;e)s 15 f 300.038 y 82.654 (k)s 1 f 296.965 y 91.166 (+)s 11 f 281.964 y 111.001 (d)s 13 f 285.564 y 104.832 (X)s 11 f 310.978 y 103.166 (m)s 2 f 111.681 (=1)s 10 f 296.965 y 125.831 (D)s 11 f 298.765 y 135.766 (k)s 141.07 (;m)s 13 f 287.244 y 155.036 (\241)s 10 f 296.965 y 160.536 (\264)s 11 f 292.01 y 166.925 (N)s 175.426 (\042)s 1 f 296.965 y 180.56 (\0500\051)s 13 f 287.244 y 195.894 (\242)s 276.444 y 203.393 (\050)s 283.644 y 213.06 (h)s 10 f 296.965 y 218.727 (\264)s 11 f 292.01 y 225.116 (N)s 233.617 (\042)s 1 f 296.965 y 238.751 (\050)s 10 f 243.418 (e)s 11 f 298.765 y 249.005 (m)s 1 f 296.965 y 258.121 (\051)s 12 f 265.454 (\241)s 10 f 277.454 (\264)s 11 f 292.01 y 283.843 (N)s 292.345 (\042)s 1 f 296.965 y 297.478 (\0500\051)s 13 f 283.644 y 312.812 (i)s 12 f 341.578 y 247.938 (\241)s 1 f 257.271 (2)s 10 f 263.271 (\257)s 270.692 (N)s 14 f 336.623 y 281.642 (\241)s 2 f 289.142 (1)s 10 f 341.578 y 294.525 (\302)s 13 f 331.858 y 304.033 (\241)s 10 f 341.578 y 309.533 (\264)s 11 f 336.623 y 315.922 (N)s 324.424 (\042)s 1 f 341.578 y 329.558 (\0500\051)s 13 f 331.858 y 344.891 (\242)s 352.391 (\241)s 10 f 341.578 y 357.891 (@)s 11 f 343.378 y 364.262 (m)s 10 f 341.578 y 373.377 (J)s 12 f 383.852 (\244)s 10 f 392.519 (\274)s 11 f 336.623 y 399.79 (N)s 1 f 341.578 y 408.891 (\050)s 10 f 413.558 (\264)s 1 f 419.947 (\051\0500\051)s 13 f 331.858 y 439.947 (\242)s 321.058 y 447.447 (\051)s 10 f 341.578 y 460.447 (:)s 1 f 382.195 y 8.71 (Next)s 38.477 (theorem)s 85.61 (is)s 98.11 (the)s 119.211 (main)s 149.644 (step)s 175.478 (in)s 189.911 (the)s 211.012 (pro)s 228.712 (of)s 242.812 (of)s 256.912 (Lemma)s 300.179 (6.3)s 319.946 (and)s 343.713 (therefore)s 394.546 (of)s 408.647 (the)s 429.747 (h)s 436.08 (ydro-)s 398.995 y -5.69 (dynamic)s 42.643 (limit.)s 0 f 415.915 y -5.69 (Theorem)s 52.91 (6.4)s 17 f 79.143 (F)s 86.056 (or)s 101.543 (every)s 133.282 (smo)s 153.522 (oth)s 174.069 (function)s 10 f 221.295 (G)s 1 f 234.063 (:)s 240.73 ([0)s 10 f 250.063 (;)s 255.397 (T)s 1 f 264.076 (])s 12 f 270.076 (\243)s 1 f 282.076 (I)s 281.249 (T)s 11 f 410.681 y 289.916 (d)s 12 f 415.915 y 298.844 (!)s 1 f 314.178 (I)s 316.351 (R)s 17 f 325.184 (,)s 1 f 455.185 y 101.328 (lim)s 119.995 (sup)s 11 f 464.931 y 110.253 (\042)s 14 f 114.787 (!)s 2 f 124.353 (0)s 1 f 455.185 y 140.061 (lim)s 158.728 (sup)s 11 f 465.258 y 144.611 (N)s 14 f 153.112 (!1)s 10 f 455.185 y 178.795 (E)s 11 f 456.985 y 187.653 (P)s 15 f 459.958 y 193.763 (\271)s 458.191 y 198.861 (N)s 13 f 441.865 y 207.77 (h)s 441.385 y 215.436 (\257)s 448.585 y 215.436 (\257)s 455.785 y 215.436 (\257)s 438.851 y 221.436 (Z)s 11 f 441.818 y 233.436 (T)s 2 f 466.118 y 228.103 (0)s 10 f 455.185 y 242.996 (X)s 11 f 450.23 y 253.879 (k)s 458.151 y 252.938 (N)s 260.923 (;\042)s 1 f 455.185 y 268.906 (\050)s 10 f 273.573 (G)s 11 f 456.985 y 283.008 (s)s 10 f 455.185 y 288.137 (;)s 293.47 (\264)s 11 f 456.985 y 299.429 (s)s 1 f 455.185 y 304.558 (\051)s 10 f 311.225 (ds)s 13 f 441.385 y 323.095 (\257)s 448.585 y 323.095 (\257)s 455.785 y 323.095 (\257)s 441.865 y 329.095 (i)s 1 f 455.185 y 338.095 (=)s 350.762 (0)s 17 f 491.955 y -5.69 (for)s 10 f 13.476 (k)s 1 f 23.435 (=)s 36.101 (1)s 10 f 42.101 (;)s 12 f 47.435 (\242)s 52.768 (\242)s 58.101 (\242)s 10 f 63.434 (;)s 68.768 (d)s 17 f 75.014 (.)s 1 f 508.875 y 8.71 (The)s 33.873 (pro)s 51.573 (of)s 65.736 (of)s 79.899 (this)s 103.796 (theorem)s 150.992 (is)s 163.556 (p)s 170.556 (ostp)s 192.956 (oned)s 222.119 (to)s 237.282 (the)s 258.445 (end)s 281.608 (of)s 295.772 (this)s 319.668 (section.)s 365.891 (W)s 377.224 (e)s 387.054 (sho)s 404.121 (w)s 417.284 (no)s 429.617 (w)s 442.78 (ho)s 455.114 (w)s 525.675 y -5.69 (Theorem)s 46.401 (6.4)s 67.126 (allo)s 85.459 (ws)s 104.251 (to)s 120.309 (conclude)s 171.033 (the)s 193.091 (pro)s 210.792 (of)s 225.85 (of)s 240.908 (Theorem)s 292.999 (equ\050th-ng\051.)s 361.507 (F)s 368.34 (or)s 384.431 (1)s 12 f 396.083 (\267)s 10 f 411.069 (k)s 417.694 (;)s 423.027 (m)s 12 f 439.216 (\267)s 10 f 454.201 (d)s 1 f 460.447 (,)s 542.475 y -5.69 (denote)s 32.977 (b)s 39.31 (y)s 10 f 49.643 (d)s 11 f 544.275 y 55.889 (k)s 61.193 (;m)s 1 f 542.475 y 77.159 (the)s 97.825 (in)s 107.492 (tegral)s 141.525 (of)s 10 f 155.192 (D)s 11 f 544.275 y 165.127 (k)s 170.431 (;m)s 1 f 542.475 y 186.397 (:)s 10 f 580.055 y 117.369 (d)s 11 f 581.855 y 123.615 (k)s 128.919 (;m)s 1 f 580.055 y 140.885 (\050)s 10 f 145.551 (\256)s 1 f 153.272 (\051)s 161.272 (=)s 13 f 563.721 y 173.939 (Z)s 11 f 566.688 y 185.939 (\256)s 2 f 590.988 y 180.605 (0)s 10 f 580.055 y 194.777 (D)s 11 f 581.855 y 204.712 (k)s 210.016 (;m)s 1 f 580.055 y 221.982 (\050)s 10 f 226.648 (u)s 1 f 233.518 (\051)s 10 f 238.185 (du)s 255.3 (;)s 1 f 272.633 (for)s 10 f 291 (\256)s 12 f 302.054 (2)s 1 f 313.387 ([0)s 10 f 322.721 (;)s 1 f 328.054 (2[)s 10 f 337.387 (:)s 1 f 616.484 y -5.69 (Since)s 10 f 25.643 (D)s 11 f 618.284 y 35.578 (k)s 40.882 (;m)s 1 f 616.484 y 56.848 (is)s 68.914 (a)s 78.914 (con)s 96.581 (tin)s 110.914 (uous)s 138.981 (function,)s 189.315 (b)s 195.648 (y)s 205.981 (T)s 213.648 (a)s 219.315 (ylor)s 243.681 (expansion,)s 10 f 647.776 y 65.048 (d)s 11 f 649.576 y 71.294 (k)s 76.598 (;m)s 1 f 647.776 y 88.563 (\050)s 10 f 93.23 (\264)s 11 f 642.821 y 99.619 (N)s 108.121 (\042)s 1 f 647.776 y 113.254 (\050)s 10 f 117.921 (e)s 11 f 649.576 y 123.509 (m)s 1 f 647.776 y 132.624 (\051\051)s 12 f 147.957 (\241)s 10 f 163.29 (d)s 11 f 649.576 y 169.536 (k)s 174.84 (;m)s 1 f 647.776 y 186.806 (\050)s 10 f 191.472 (\264)s 11 f 642.821 y 197.861 (N)s 206.363 (\042)s 1 f 647.776 y 211.497 (\0500\051\051)s 674.176 y 92.381 (=)s 10 f 108.381 (D)s 11 f 675.976 y 118.316 (k)s 123.62 (;m)s 13 f 664.456 y 137.586 (\241)s 10 f 674.176 y 143.086 (\264)s 11 f 669.221 y 149.475 (N)s 157.976 (\042)s 1 f 674.176 y 163.11 (\0500\051)s 13 f 664.456 y 178.443 (\242)s 660.856 y 185.943 (n)s 10 f 674.176 y 193.943 (\264)s 11 f 669.221 y 200.332 (N)s 208.834 (\042)s 1 f 674.176 y 213.968 (\050)s 10 f 218.634 (e)s 11 f 675.976 y 224.222 (m)s 1 f 674.176 y 233.337 (\051)s 12 f 240.671 (\241)s 10 f 252.67 (\264)s 11 f 669.221 y 259.059 (N)s 267.561 (\042)s 1 f 674.176 y 272.695 (\0500\051)s 13 f 660.856 y 288.028 (o)s 1 f 674.176 y 302.028 (+)s 317.361 (\050)s 10 f 322.028 (N)s 332.978 (\042)s 1 f 338.574 (\051)s 14 f 669.221 y 343.24 (\241)s 2 f 350.74 (1)s 10 f 674.176 y 356.124 (o)s 11 f 675.976 y 361.94 (N)s 1 f 674.176 y 371.042 (\0501\051)s 10 f 389.709 (:)s 1 f 705.976 y 223.045 (40)s do-end end endp %%Page: 41 41 %%BeginPageSetup initializepage (Raffaele Esposito; page: 41 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f0_12 sf ( )S -996 -1000 :M f1_12 sf ( )S -993 -1000 :M f2_12 sf ( )S -989 -1000 :M f10_12 sf ( )S -981 -1000 :M f11_12 sf ( )S -972 -1000 :M f12_12 sf ( )S -960 -1000 :M f13_12 sf ( )S -951 -1000 :M f14_12 sf ( )S -937 -1000 :M f15_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 1200 1000 div mul /CMBX10 findfont fdef 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 6.31 y -5.69 (It)s 7.31 (follo)s 29.31 (ws)s 46.71 (therefore)s 97.11 (from)s 125.477 (Theorem)s 176.177 (6.4)s 195.51 (that)s 44.641 y 97.266 (lim)s 115.932 (sup)s 11 f 54.388 y 106.19 (\042)s 14 f 110.724 (!)s 2 f 120.291 (0)s 1 f 44.641 y 135.999 (lim)s 154.666 (sup)s 11 f 54.714 y 140.548 (N)s 14 f 149.05 (!1)s 10 f 44.641 y 174.732 (E)s 11 f 46.441 y 183.591 (P)s 15 f 49.414 y 189.7 (\271)s 47.648 y 194.799 (N)s 13 f 31.321 y 203.707 (h)s 30.841 y 211.374 (\257)s 38.041 y 211.374 (\257)s 45.241 y 211.374 (\257)s 28.307 y 217.374 (Z)s 11 f 31.274 y 229.374 (T)s 2 f 55.574 y 224.041 (0)s 1 f 44.641 y 238.933 (Y)s 241.033 (Y)s 11 f 39.408 y 250.333 (k)s 47.608 y 250.333 (N)s 258.318 (;\042)s 1 f 44.641 y 266.302 (\050)s 10 f 270.969 (G)s 11 f 46.441 y 280.404 (s)s 10 f 44.641 y 285.533 (;)s 290.866 (\264)s 11 f 46.441 y 296.825 (s)s 1 f 44.641 y 301.954 (\051)s 10 f 308.621 (ds)s 13 f 30.841 y 320.491 (\257)s 38.041 y 320.491 (\257)s 45.241 y 320.491 (\257)s 31.321 y 326.491 (i)s 1 f 44.641 y 335.491 (=)s 348.158 (0)s 10 f 357.491 (;)s 1 f 83.472 y -5.69 (where)s 100.296 y 118.047 (Y)s 120.147 (Y)s 11 f 95.063 y 129.447 (k)s 103.263 y 129.447 (N)s 137.432 (;\042)s 1 f 100.296 y 145.416 (\050)s 10 f 150.083 (G;)s 164.851 (\264)s 1 f 171.24 (\051)s 182.573 (=)s 10 f 198.573 (N)s 2 f 95.342 y 209.523 (1)s 14 f 214.306 (\241)s 11 f 221.806 (d)s 13 f 88.896 y 230.763 (X)s 11 f 115.836 y 229.402 (i)s 14 f 232.797 (2)s 2 f 239.263 (I)s 237.57 (T)s 15 f 113.063 y 244.42 (d)s 10 f 100.296 y 251.458 (G)s 1 f 260.893 (\050)s 10 f 265.56 (i=)s 275.028 (N)s 1 f 285.977 (\051)s 10 f 290.644 (\277)s 11 f 102.096 y 295.89 (i)s 1 f 100.296 y 299.885 (U)s 301.685 (U)s 11 f 95.063 y 310.685 (N)s 319.187 (\042)s 103.263 y 310.685 (k)s 1 f 100.296 y 324.321 (\050)s 10 f 328.987 (\264)s 1 f 335.376 (\051)s 139.23 y -5.69 (and)s 166.087 y 41.764 (U)s 43.564 (U)s 11 f 160.854 y 52.564 (N)s 61.066 (\042)s 169.054 y 52.564 (k)s 1 f 166.087 y 66.2 (\050)s 10 f 70.867 (\264)s 1 f 77.255 (\051)s 85.255 (=)s 97.922 (W)s 99.022 (W)s 2 f 167.887 y 111.522 (0)s 11 f 116.305 (;e)s 15 f 169.161 y 123.708 (k)s 1 f 166.087 y 132.221 (+)s 11 f 151.087 y 152.056 (d)s 13 f 154.687 y 145.887 (X)s 11 f 180.101 y 144.221 (m)s 2 f 152.736 (=1)s 13 f 152.767 y 166.886 (n)s 10 f 166.087 y 174.886 (d)s 11 f 167.887 y 181.132 (k)s 186.436 (;m)s 1 f 166.087 y 198.401 (\050)s 10 f 203.068 (\264)s 11 f 161.133 y 209.457 (N)s 217.959 (\042)s 1 f 166.087 y 223.093 (\050)s 10 f 227.759 (e)s 11 f 167.887 y 233.347 (m)s 1 f 166.087 y 242.462 (\051\051)s 12 f 254.462 (\241)s 10 f 266.462 (d)s 11 f 167.887 y 272.708 (k)s 278.012 (;m)s 1 f 166.087 y 289.977 (\050)s 10 f 294.644 (\264)s 11 f 161.133 y 301.033 (N)s 309.535 (\042)s 1 f 166.087 y 314.668 (\0500\051\051)s 13 f 152.767 y 334.668 (o)s 12 f 211.734 y 92.589 (\241)s 1 f 104.589 (2)s 10 f 110.589 (\257)s 118.01 (N)s 14 f 206.779 y 128.96 (\241)s 2 f 136.46 (1)s 11 f 196.734 y 151.678 (d)s 13 f 200.334 y 145.509 (X)s 11 f 225.748 y 143.843 (m)s 2 f 152.358 (=1)s 13 f 198.414 y 166.508 (n)s 10 f 211.734 y 174.508 (\302)s 13 f 202.014 y 184.016 (\241)s 10 f 211.734 y 189.516 (\264)s 11 f 206.779 y 195.905 (N)s 204.407 (\042)s 1 f 211.734 y 209.541 (\0500\051)s 13 f 202.014 y 224.874 (\242)s 10 f 211.734 y 232.374 (D)s 11 f 213.534 y 242.309 (k)s 247.613 (;m)s 13 f 202.014 y 261.579 (\241)s 10 f 211.734 y 267.079 (\264)s 11 f 206.779 y 273.468 (N)s 281.969 (\042)s 1 f 211.734 y 287.103 (\0500\051)s 13 f 202.014 y 302.436 (\242)s 309.936 (\241)s 10 f 211.734 y 315.436 (@)s 11 f 213.534 y 321.807 (m)s 10 f 211.734 y 330.923 (J)s 12 f 341.398 (\244)s 10 f 350.064 (\274)s 11 f 206.779 y 357.335 (N)s 1 f 211.734 y 366.437 (\050)s 10 f 371.103 (\264)s 1 f 377.492 (\051)s 13 f 202.014 y 382.159 (\242)s 1 f 211.734 y 389.659 (\0500\051)s 13 f 198.414 y 404.992 (o)s 10 f 211.734 y 412.992 (:)s 1 f 250.964 y -5.69 (A)s 7.31 (summation)s 69.377 (b)s 75.71 (y)s 86.043 (parts)s 116.81 (p)s 123.81 (ermits)s 160.577 (to)s 175.243 (rewrite)s 215.977 (the)s 236.644 (second)s 275.377 (term)s 304.077 (of)s 317.744 (Y)s 319.844 (Y)s 11 f 245.73 y 329.144 (i)s 253.93 y 329.144 (N)s 337.129 (;\042)s 1 f 250.964 y 345.112 (\050)s 10 f 349.779 (G;)s 364.547 (\264)s 1 f 370.936 (\051)s 379.603 (as)s 12 f 296.821 y 23.192 (\241)s 10 f 35.192 (N)s 14 f 291.866 y 46.142 (\241)s 11 f 53.642 (d)s 281.821 y 69.073 (d)s 13 f 285.421 y 62.904 (X)s 11 f 310.835 y 61.238 (m)s 2 f 69.753 (=1)s 13 f 285.421 y 85.265 (X)s 11 f 312.361 y 83.903 (i)s 14 f 87.298 (2)s 2 f 93.765 (I)s 92.072 (T)s 15 f 309.588 y 98.922 (d)s 1 f 296.821 y 105.96 (\050)s 10 f 110.626 (@)s 11 f 298.621 y 116.997 (m)s 10 f 296.821 y 126.113 (G)s 1 f 135.548 (\051)s 142.214 (\050)s 10 f 146.881 (i=)s 156.348 (N)s 1 f 167.298 (\051)s 10 f 171.965 (d)s 11 f 298.621 y 178.211 (k)s 183.515 (;m)s 13 f 287.101 y 197.48 (\241)s 10 f 296.821 y 202.98 (\264)s 11 f 291.866 y 209.369 (N)s 217.871 (\042)s 1 f 296.821 y 223.005 (\050)s 10 f 227.671 (i)s 1 f 231.806 (\051)s 13 f 287.101 y 236.472 (\242)s 12 f 344.63 y 31.192 (\241)s 10 f 43.192 (N)s 14 f 339.676 y 54.142 (\241)s 11 f 61.642 (d)s 329.63 y 77.073 (d)s 13 f 333.23 y 70.904 (X)s 11 f 358.644 y 69.238 (m)s 2 f 77.753 (=1)s 13 f 333.23 y 93.265 (X)s 11 f 360.17 y 91.903 (i)s 14 f 95.298 (2)s 2 f 101.765 (I)s 100.072 (T)s 15 f 357.397 y 106.922 (d)s 10 f 344.63 y 113.96 (G)s 1 f 123.395 (\050)s 10 f 128.061 (i=)s 137.529 (N)s 1 f 148.479 (\051)s 13 f 334.91 y 153.146 (\241)s 1 f 344.63 y 158.646 (2)s 10 f 164.646 (\257)s 172.066 (\302D)s 11 f 346.43 y 189.51 (k)s 194.814 (;m)s 13 f 334.91 y 206.779 (\242)s 214.279 (\241)s 10 f 344.63 y 219.779 (\264)s 11 f 339.676 y 226.168 (N)s 234.67 (\042)s 1 f 344.63 y 239.804 (\050)s 10 f 244.47 (i)s 1 f 248.604 (\051)s 13 f 334.91 y 253.271 (\242)s 260.771 (\241)s 10 f 344.63 y 266.271 (@)s 11 f 346.43 y 272.642 (m)s 10 f 344.63 y 281.757 (J)s 12 f 292.232 (\244)s 10 f 300.899 (\274)s 11 f 339.676 y 308.17 (N)s 1 f 344.63 y 317.271 (\050)s 10 f 321.938 (\264)s 1 f 328.327 (\051)s 13 f 334.91 y 332.994 (\242)s 1 f 344.63 y 340.494 (\050)s 10 f 345.16 (i=)s 354.628 (N)s 1 f 365.578 (\051)s 376.244 (+)s 10 f 391.578 (O)s 1 f 401.064 (\050)s 10 f 405.731 (N)s 14 f 339.676 y 416.681 (\241)s 2 f 424.181 (1)s 1 f 344.63 y 429.564 (\051)s 10 f 434.231 (:)s 1 f 389.564 y -5.69 (This)s 21.71 (concludes)s 75.777 (the)s 96.443 (pro)s 114.143 (of)s 127.81 (of)s 141.477 (the)s 162.143 (Theorem.)s 0 f 413.708 y -5.69 (Pro)s 16.71 (of)s 33.263 (of)s 49.816 (Theorem)s 109.252 (6.4)s 1 f 126.885 (.)s 137.734 (W)s 149.067 (e)s 159.128 (\257rst)s 184.622 (in)s 194.288 (tro)s 209.989 (duce)s 238.716 (some)s 269.51 (notations)s 322.971 (and)s 347.031 (recall)s 379.792 (some)s 410.586 (to)s 421.586 (ols)s 440.38 (used)s 430.508 y -5.69 (in)s 9.86 (the)s 32.076 (non)s 56.959 (gradien)s 95.326 (t)s 105.543 (metho)s 138.543 (ds.)s 163.259 (W)s 174.593 (e)s 185.476 (denote)s 225.692 (b)s 232.026 (y)s 243.909 (I)s 246.082 (L)s 2 f 425.275 y 253.582 (0)s 1 f 430.508 y 264.515 (the)s 286.732 (pregenerator)s 358.382 (of)s 373.598 (GSEP)s 411.564 (in)s 427.113 (in\257nite)s 447.308 y -5.69 (v)s .31 (olume)s 35.961 (and)s 59.613 (consider)s 106.698 (the)s 127.683 (family)s 164.668 (\050)s 10 f 169.335 (\272)s 11 f 449.108 y 175.262 (\256)s 1 f 447.308 y 182.101 (\051)s 191.086 (of)s 205.071 (in)s 214.738 (v)s 220.404 (arian)s 246.771 (t)s 255.756 (measures)s 307.574 (for)s 326.259 (I)s 328.432 (L)s 2 f 442.075 y 335.932 (0)s 1 f 447.308 y 341.316 (.)s 350.937 (Let)s 12 f 372.755 (C)s 1 f 384.092 (b)s 391.092 (e)s 400.744 (the)s 421.729 (space)s 454.114 (of)s 464.108 y -5.69 (cylinder)s 39.815 (functions.)s 96.151 (F)s 102.984 (or)s 117.49 (eac)s 133.823 (h)s 144.295 (b)s 151.295 (o)s 156.962 (x)s 167.101 (\244)s 12 f 178.768 (\275)s 10 f 191.434 (Z)s 194.484 (Z)s 11 f 459.753 y 205.534 (d)s 1 f 464.108 y 214.935 (and)s 238.074 (a)s 247.88 (p)s 254.88 (ositiv)s 282.947 (e)s 292.086 (in)s 301.752 (teger)s 10 f 331.591 (\140)s 1 f 336.591 (,)s 343.769 (suc)s 360.169 (h)s 370.641 (that)s 396.447 (0)s 12 f 405.78 (\267)s 10 f 418.447 (\140)s 12 f 426.78 (\267)s 1 f 439.447 (2)s 12 f 445.447 (j)s 1 f 448.78 (\244)s 12 f 457.114 (j)s 1 f 460.447 (,)s 480.908 y -5.69 (w)s 2.643 (e)s 12.431 (denote)s 51.553 (b)s 57.886 (y)s 10 f 68.674 (\272)s 2 f 482.708 y 74.602 (\244)s 11 f 81.168 (;\140)s 1 f 480.908 y 93.09 (the)s 114.211 (canonical)s 167.333 (measure)s 214.554 (on)s 12 f 231.676 (f)s 1 f 237.676 (0)s 10 f 243.676 (;)s 1 f 249.009 (1)s 10 f 255.009 (;)s 1 f 260.342 (2)s 12 f 266.342 (g)s 2 f 476.553 y 272.342 (\244)s 1 f 480.908 y 283.964 (with)s 311.752 (densit)s 342.819 (y)s 10 f 353.607 (\140=)s 12 f 364.607 (j)s 1 f 367.94 (\244)s 12 f 376.273 (j)s 1 f 379.607 (.)s 389.637 (F)s 396.471 (or)s 411.625 (a)s 422.08 (cylinder)s 497.708 y -5.69 (function)s 10 f 41.168 (g)s 12 f 50.655 (2)s 61.988 (C)s 1 f 69.007 (,)s 76.226 (denote)s 114.751 (b)s 121.084 (y)s 131.275 (\244)s 11 f 499.508 y 139.608 (g)s 1 f 497.708 y 149.049 (the)s 169.573 (smallest)s 215.564 (rectangle)s 266.789 (that)s 292.646 (con)s 310.313 (tains)s 339.571 (the)s 360.095 (supp)s 385.162 (ort)s 404.386 (of)s 10 f 417.911 (g)s 1 f 427.923 (and)s 451.114 (b)s 457.447 (y)s 10 f 514.508 y -5.69 (s)s 11 f 516.308 y -.065 (g)s 1 f 514.508 y 9.102 (the)s 29.353 (smallest)s 75.07 (p)s 82.07 (ositiv)s 110.137 (e)s 119.054 (in)s 128.721 (teger)s 10 f 158.339 (s)s 1 f 167.548 (suc)s 183.948 (h)s 194.199 (that)s 219.783 (\244)s 11 f 516.308 y 228.116 (g)s 12 f 514.508 y 237.032 (\275)s 1 f 249.699 (\244)s 11 f 516.308 y 258.032 (s)s 1 f 514.508 y 263.161 (.)s 271.689 (Let)s 12 f 292.774 (C)s 2 f 516.308 y 299.092 (0)s 1 f 514.508 y 308.059 (b)s 315.059 (e)s 323.977 (the)s 344.228 (linear)s 377.179 (space)s 408.829 (of)s 422.08 (cylinder)s 531.308 y -5.69 (functions)s 46.043 (with)s 73.377 (mean)s 105.377 (zero)s 130.743 (with)s 158.077 (resp)s 179.843 (ect)s 199.177 (to)s 213.843 (all)s 230.51 (canonical)s 283.177 (in)s 292.844 (v)s 298.51 (arian)s 324.877 (t)s 333.544 (measures)s 385.044 (for)s 403.41 (I)s 405.584 (L)s 2 f 526.075 y 413.084 (0)s 1 f 531.308 y 422.467 (:)s 12 f 562.532 y 97.399 (C)s 2 f 564.332 y 103.717 (0)s 1 f 562.532 y 112.434 (=)s 13 f 549.212 y 125.1 (n)s 10 f 562.532 y 133.1 (g)s 12 f 142.588 (2)s 153.921 (C)s 1 f 164.939 (;)s 12 f 174.273 (h)s 10 f 178.939 (g)s 12 f 185.094 (i)s 2 f 566.132 y 189.76 (\244)s 15 f 567.332 y 196.327 (g)s 11 f 566.132 y 201.346 (;\140)s 1 f 562.532 y 212.146 (=)s 224.812 (0)s 238.812 (for)s 257.179 (all)s 277.846 (0)s 12 f 287.179 (\267)s 10 f 299.846 (\140)s 12 f 308.179 (\267)s 1 f 320.845 (2)s 12 f 326.845 (j)s 1 f 330.179 (\244)s 2 f 564.332 y 338.512 (g)s 12 f 562.532 y 344.025 (j)s 13 f 549.212 y 347.358 (o)s 10 f 562.532 y 357.358 (:)s 1 f 598.557 y -5.69 (Here)s 12 f 22.081 (h)s 10 f 26.747 (g)s 12 f 32.901 (i)s 2 f 602.157 y 37.568 (\244)s 15 f 603.357 y 44.135 (g)s 11 f 602.157 y 49.154 (;\140)s 1 f 598.557 y 60.025 (stands)s 96.895 (for)s 114.666 (the)s 134.737 (exp)s 153.404 (ectation)s 198.808 (of)s 211.879 (the)s 231.95 (function)s 10 f 278.354 (g)s 1 f 287.913 (with)s 314.65 (resp)s 336.417 (ect)s 355.154 (to)s 369.225 (the)s 389.296 (measure)s 10 f 435.467 (\272)s 2 f 600.357 y 441.395 (\244)s 15 f 601.557 y 447.961 (g)s 11 f 600.357 y 452.98 (;\140)s 1 f 598.557 y 460.447 (.)s 615.485 y 8.71 (F)s 15.543 (or)s 30.737 (a)s 41.23 (p)s 48.23 (ositiv)s 76.297 (e)s 86.123 (densit)s 117.19 (y)s 128.017 (0)s 12 f 138.172 (\267)s 10 f 151.661 (\275)s 12 f 162.021 (\267)s 1 f 175.51 (2,)s 189.46 (de\257ne)s 224.62 (the)s 245.78 (semi-norm)s 12 f 607.907 y 305.04 (p)s 41.067 .48 315.04 607.907 r 10 f 615.485 y 315.04 (\074)s 320.374 (\074)s 329.707 (g)s 335.861 (\076)s 341.195 (\076)s 11 f 617.285 y 350.528 (\275)s 1 f 615.485 y 360.6 (b)s 366.933 (y)s 377.76 (the)s 398.92 (cen)s 415.92 (tral)s 439.114 (limit)s 632.285 y -5.69 (theorem)s 41.01 (v)s 46.677 (ariances)s 10 f 663.509 y 73.553 (\074)s 78.887 (\074)s 88.22 (g)s 94.374 (\076)s 99.708 (\076)s 11 f 665.309 y 109.041 (\275)s 1 f 663.509 y 117.953 (=)s 133.861 (lim)s 11 f 671.343 y 130.62 (\140)s 14 f 134.636 (!1)s 1 f 663.509 y 153.77 (\0502)s 10 f 164.437 (\140)s 1 f 169.437 (\051)s 14 f 658.555 y 174.103 (\241)s 11 f 181.603 (d)s 13 f 650.189 y 187.199 (D)s 653.789 y 196.532 (\241)s 12 f 663.509 y 202.032 (\241)s 1 f 211.365 (I)s 213.539 (L)s 2 f 658.276 y 221.039 (0)s 666.476 y 221.039 (\244)s 15 f 667.749 y 227.605 (\140)s 13 f 653.789 y 232.389 (\242)s 14 f 655.829 y 237.889 (\241)s 2 f 245.389 (1)s 13 f 652.109 y 256.921 (X)s 14 f 678.409 y 252.772 (j)s 11 f 255.622 (i)s 14 f 259.017 (j\267)s 11 f 269.367 (\140)s 15 f 679.609 y 273.384 (g)s 10 f 663.509 y 280.403 (\277)s 11 f 665.309 y 285.649 (i)s 10 f 663.509 y 289.644 (g)s 299.131 (;)s 13 f 652.109 y 311.946 (X)s 14 f 678.409 y 307.798 (j)s 11 f 310.648 (i)s 14 f 314.043 (j\267)s 11 f 324.393 (\140)s 15 f 679.609 y 328.41 (g)s 10 f 663.509 y 335.428 (\277)s 11 f 665.309 y 340.674 (i)s 10 f 663.509 y 344.669 (g)s 13 f 650.189 y 350.823 (E)s 11 f 671.909 y 358.157 (\140;K)s 15 f 673.183 y 373.087 (\140)s 10 f 663.509 y 381.203 (;)s 1 f 705.976 y 223.045 (41)s do-end end endp %%Page: 42 42 %%BeginPageSetup initializepage (Raffaele Esposito; page: 42 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f0_12 sf ( )S -996 -1000 :M f1_12 sf ( )S -993 -1000 :M f2_12 sf ( )S -989 -1000 :M f10_12 sf ( )S -981 -1000 :M f11_12 sf ( )S -972 -1000 :M f12_12 sf ( )S -960 -1000 :M f13_12 sf ( )S -951 -1000 :M f14_12 sf ( )S -937 -1000 :M f15_12 sf ( )S -926 -1000 :M f16_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 1200 1000 div mul /CMBX10 findfont fdef 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 16 5 1200 1000 div mul /CMR5 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 6.31 y -5.69 (for)s 10 f 13.894 (g)s 12 f 25.41 (2)s 38.772 (C)s 2 f 8.11 y 45.09 (0)s 1 f 6.31 y 55.691 (and)s 80.241 (a)s 91.459 (sequence)s 142.409 (of)s 157.293 (p)s 164.293 (ositiv)s 192.36 (e)s 202.911 (in)s 212.577 (tegers)s 10 f 248.561 (K)s 11 f 8.11 y 258.753 (\140)s 1 f 6.31 y 268.587 (suc)s 284.987 (h)s 296.871 (that)s 324.088 (0)s 12 f 335.45 (\267)s 10 f 350.145 (K)s 11 f 8.11 y 360.337 (\140)s 12 f 6.31 y 370.316 (\267)s 1 f 385.011 (2\0502)s 10 f 401.678 (\140)s 1 f 410.156 (+)s 422.967 (1\051)s 11 f 1.955 y 433.634 (d)s 1 f 6.31 y 444.447 (and)s 23.11 y -5.69 (lim)s 11 f 24.91 y 10.977 (\140)s 14 f 14.993 (!1)s 10 f 23.11 y 36.727 (K)s 11 f 24.91 y 46.918 (\140)s 10 f 23.11 y 51.535 (=)s 1 f 57.535 (\0502)s 10 f 68.202 (\140)s 1 f 73.202 (\051)s 11 f 18.755 y 77.868 (d)s 1 f 23.11 y 87.794 (=)s 10 f 101.458 (\275)s 1 f 107.662 (.)s 118.124 (In)s 133.722 (this)s 157.721 (form)s 181.754 (ula)s 10 f 202.352 (\140)s 11 f 24.91 y 207.352 (g)s 1 f 23.11 y 217.266 (=)s 10 f 230.929 (\140)s 12 f 238.995 (\241)s 10 f 251.394 (s)s 11 f 24.91 y 257.019 (g)s 12 f 23.11 y 265.667 (\241)s 1 f 278.066 (1,)s 292.147 (\244)s 11 f 24.91 y 300.481 (\140)s 1 f 23.11 y 309.428 (=)s 12 f 323.092 (f\241)s 10 f 338.425 (\140;)s 12 f 348.758 (\242)s 354.092 (\242)s 359.425 (\242)s 10 f 364.758 (;)s 370.091 (\140)s 12 f 375.091 (g)s 11 f 18.755 y 381.091 (d)s 1 f 23.11 y 391.285 (and)s 415.217 (for)s 434.182 (a)s 444.78 (b)s 451.78 (o)s 457.447 (x)s 39.91 y -5.69 (\244)s 12 f 5.976 (\275)s 10 f 18.643 (Z)s 21.693 (Z)s 11 f 35.555 y 32.743 (d)s 1 f 39.91 y 38.339 (,)s 45.672 (I)s 47.845 (L)s 2 f 34.676 y 55.345 (0)s 42.876 y 55.345 (\244)s 1 f 39.91 y 66.512 (is)s 78.579 (the)s 99.245 (restriction)s 156.712 (of)s 170.379 (I)s 172.552 (L)s 2 f 34.676 y 180.052 (0)s 1 f 39.91 y 189.435 (to)s 204.102 (the)s 224.769 (b)s 231.769 (o)s 237.436 (x)s 247.769 (\244.)s 56.83 y 8.71 (By)s 27.685 (p)s 34.685 (olarization)s 94.194 (w)s 102.527 (e)s 112.003 (ma)s 127.67 (y)s 138.145 (de\257ne)s 172.954 (from)s 10 f 201.463 (\074)s 206.796 (\074)s 12 f 218.891 (\242)s 10 f 224.985 (\076)s 230.319 (\076)s 11 f 58.63 y 239.652 (\275)s 1 f 56.83 y 249.373 (a)s 259.515 (semi-inner)s 317.757 (pro)s 335.457 (duct)s 362.933 (on)s 12 f 379.741 (C)s 2 f 58.63 y 386.06 (0)s 1 f 56.83 y 391.443 (.)s 400.536 (Moreo)s 433.236 (v)s 439.236 (er,)s 456.78 (if)s 73.63 y -5.69 (for)s 12.677 (cylinder)s 58.377 (functions)s 10 f 110.11 (g)s 1 f 120.264 (and)s 10 f 143.598 (h)s 1 f 154.511 (in)s 12 f 168.511 (C)s 2 f 75.43 y 174.83 (0)s 1 f 73.63 y 184.213 (w)s 192.547 (e)s 201.88 (de\257ne)s 10 f 103.046 y 159.628 (\074)s 164.961 (\074)s 174.294 (g)s 180.449 (;)s 185.782 (h\076)s 198.029 (\076)s 11 f 104.846 y 207.363 (\275;)s 2 f 215.191 (0)s 1 f 103.046 y 223.908 (=)s 13 f 91.646 y 236.575 (X)s 11 f 117.205 y 243.544 (i)s 12 f 103.046 y 255.908 (h)s 10 f 260.575 (g)s 266.729 (;)s 272.062 (\277)s 11 f 104.846 y 277.308 (i)s 10 f 103.046 y 281.303 (h)s 12 f 288.217 (i)s 11 f 106.646 y 292.884 (\275)s 1 f 144.821 y -5.69 (w)s 2.643 (e)s 11.429 (obtain)s 48.214 (b)s 54.547 (y)s 64.333 (the)s 84.452 (de\257nition)s 137.237 (of)s 10 f 150.356 (\074)s 155.689 (\074)s 12 f 166.594 (\242)s 10 f 171.498 (\076)s 176.831 (\076)s 11 f 146.621 y 186.165 (\275)s 1 f 144.821 y 195.195 (the)s 215.314 (follo)s 237.314 (wing)s 265.433 (prop)s 289.8 (erties)s 321.352 (\050cf.)s 343.503 ([KL]\051)s 375.121 (:)s 381.906 (F)s 388.74 (or)s 402.892 (all)s 10 f 419.011 (h;)s 431.258 (g)s 12 f 440.745 (2)s 452.079 (C)s 2 f 146.621 y 458.397 (0)s 1 f 161.621 y -5.69 (and)s 17.643 (for)s 36.01 (eac)s 52.343 (h)s 63.01 (0)s 12 f 72.343 (\267)s 10 f 85.01 (k)s 91.635 (;)s 96.968 (m)s 12 f 110.838 (\267)s 10 f 123.504 (d)s 192.017 y 120.586 (\074)s 125.919 (\074)s 135.253 (g)s 141.407 (;)s 1 f 146.74 (I)s 148.914 (L)s 2 f 186.784 y 156.414 (0)s 10 f 192.017 y 161.797 (h\076)s 174.044 (\076)s 11 f 193.817 y 183.378 (\275)s 1 f 192.017 y 195.623 (=)s 12 f 211.623 (\241)s 10 f 220.956 (\074)s 226.29 (\074)s 235.623 (g)s 241.777 (;)s 247.11 (h\076)s 259.358 (\076)s 11 f 193.817 y 268.691 (\275;)s 2 f 276.52 (0)s 10 f 192.017 y 281.903 (;)s 212.417 y 120.586 (\074)s 125.919 (\074)s 135.253 (\264)s 1 f 141.642 (\050)s 10 f 146.308 (e)s 11 f 214.217 y 151.896 (k)s 1 f 212.417 y 157.8 (\051)s 12 f 165.133 (\241)s 10 f 177.133 (\264)s 1 f 183.522 (\0500\051)s 10 f 198.856 (;)s 1 f 204.189 (I)s 206.362 (L)s 2 f 207.184 y 213.862 (0)s 10 f 212.417 y 219.246 (g)s 225.4 (\076)s 230.733 (\076)s 11 f 214.217 y 240.067 (\275)s 1 f 212.417 y 252.312 (=)s 268.312 (0)s 10 f 274.312 (;)s 232.817 y 120.586 (\074)s 125.919 (\074)s 135.253 (\264)s 1 f 141.642 (\050)s 10 f 146.308 (e)s 11 f 234.617 y 151.896 (k)s 1 f 232.817 y 157.8 (\051)s 12 f 165.133 (\241)s 10 f 177.133 (\264)s 1 f 183.522 (\0500\051)s 10 f 198.856 (;)s 204.189 (W)s 2 f 234.617 y 215.522 (0)s 11 f 220.306 (;e)s 15 f 235.817 y 227.709 (m)s 10 f 232.817 y 236.277 (\076)s 241.61 (\076)s 11 f 234.617 y 250.944 (\275)s 1 f 232.817 y 263.189 (=)s 12 f 279.189 (\241)s 10 f 288.522 (\302)s 1 f 296.03 (\050)s 10 f 300.697 (\275)s 1 f 306.901 (\051)s 10 f 311.568 (\261)s 11 f 234.617 y 316.901 (k)s 322.205 (;m)s 10 f 232.817 y 334.171 (;)s 261.269 y 120.586 (\074)s 125.919 (\074)s 135.253 (W)s 2 f 263.069 y 146.586 (0)s 11 f 151.369 (;e)s 15 f 264.342 y 158.772 (k)s 10 f 261.269 y 164.618 (;)s 169.952 (W)s 2 f 263.069 y 181.285 (0)s 11 f 186.068 (;e)s 15 f 264.269 y 193.471 (m)s 10 f 261.269 y 202.039 (\076)s 207.373 (\076)s 11 f 263.069 y 216.706 (\275)s 1 f 261.269 y 228.951 (=)s 253.151 y 246.391 (1)s 6 .48 246.391 258.509 r 269.5 y 246.391 (2)s 12 f 261.269 y 255.831 (h)s 10 f 260.498 (r)s 2 f 263.069 y 265.912 (0)s 11 f 270.695 (;e)s 16 f 264.269 y 278.098 (1)s 12 f 261.269 y 283.382 (i)s 11 f 265.302 y 288.048 (\275)s 10 f 261.269 y 295.627 (\261)s 11 f 263.069 y 300.96 (k)s 306.265 (;m)s 10 f 261.269 y 318.23 (;)s 1 f 228.436 y 433.113 (\0506)s 10 f 443.78 (:)s 1 f 447.114 (10\051)s 295.917 y -5.69 (where)s 10 f 28.916 (\261)s 11 f 297.717 y 34.249 (k)s 39.554 (;m)s 1 f 295.917 y 55.425 (is)s 67.398 (the)s 87.971 (Kro)s 108.337 (enec)s 130.671 (k)s 136.671 (er)s 150.61 (delta.)s 185.246 (Let)s 206.652 (us)s 221.958 (denote)s 260.531 (b)s 266.864 (y)s 12 f 277.104 (F)s 1 f 290.827 (the)s 311.399 (space)s 343.372 (of)s 356.945 (functions)s 10 f 408.585 (F)s 1 f 421.301 (:)s 427.968 ([0)s 10 f 437.301 (;)s 1 f 442.635 (2])s 12 f 454.447 (\243)s 1 f 312.717 y -5.69 (X)s -3.89 (X)s 12 f 8.443 (\241)s 15.776 (!)s 1 f 31.11 (I)s 33.283 (R)s 46.116 (suc)s 62.516 (h)s 73.183 (that)s 329.637 y -5.69 (\050i\051)s 11.261 (for)s 29.913 (eac)s 46.246 (h)s 10 f 57.198 (\275)s 12 f 67.21 (2)s 1 f 79.018 ([0)s 10 f 88.351 (;)s 1 f 93.685 (2],)s 10 f 110.707 (F)s 1 f 120.091 (\050)s 10 f 124.757 (\275;)s 136.295 (:)s 1 f 139.628 (\051)s 148.58 (is)s 160.931 (a)s 171.216 (cylinder)s 217.201 (function)s 264.486 (with)s 292.104 (uniform)s 337.422 (supp)s 362.489 (ort)s 382.141 (i.e.)s 403.662 (there)s 434.647 (exists)s 346.437 y -5.69 (a)s 4.31 (\257nite)s 34.977 (set)s 53.71 (\244)s 12 f 65.376 (\275)s 10 f 78.043 (Z)s 81.093 (Z)s 11 f 341.203 y 92.143 (d)s 1 f 346.437 y 101.739 (that)s 127.739 (con)s 145.405 (tains)s 174.805 (the)s 195.472 (supp)s 220.539 (ort)s 239.906 (of)s 10 f 253.572 (F)s 1 f 262.956 (\050)s 10 f 267.622 (\275;)s 279.16 (:)s 1 f 282.493 (\051)s 291.16 (for)s 309.526 (all)s 10 f 326.193 (\275)s 12 f 335.731 (2)s 1 f 347.064 ([0)s 10 f 356.397 (;)s 1 f 361.731 (2].)s 363.357 y -5.69 (\050ii\051)s 14.31 (F)s 21.143 (or)s 35.843 (eac)s 52.177 (h)s 62.843 (con\257guration)s 10 f 135.543 (\264)s 1 f 141.932 (,)s 10 f 149.266 (F)s 1 f 158.649 (\050)s 10 f 163.316 (:;)s 171.982 (\264)s 1 f 178.371 (\051)s 187.038 (is)s 199.105 (a)s 209.105 (smo)s 230.171 (oth)s 251.505 (function.)s 380.277 y 8.71 (It)s 21.71 (has)s 43.11 (b)s 50.11 (een)s 71.443 (pro)s 88.477 (v)s 94.477 (ed)s 110.477 (in)s 124.477 ([KLO])s 161.31 (and)s 184.643 ([KL])s 212.144 (\050Corollary)s 269.877 (7.5.9)s 298.544 (in)s 312.544 ([KL]\051)s 344.71 (that)s 370.711 (for)s 389.077 (all)s 405.744 (0)s 12 f 415.077 (\267)s 10 f 427.744 (k)s 12 f 437.702 (\267)s 10 f 450.369 (d)s 1 f 456.615 (,)s 422.727 y 49.206 (inf)s 11 f 430.467 y 45.724 (F)s 14 f 53.101 (2F)s 1 f 422.727 y 75.028 (sup)s 2 f 432.818 y 69.289 (0)s 14 f 74.072 (\267)s 11 f 81.572 (\275)s 14 f 86.551 (\267)s 2 f 94.051 (2)s 10 f 422.727 y 100.834 (\074)s 106.168 (\074)s 115.501 (W)s 2 f 424.527 y 126.834 (0)s 11 f 131.618 (;e)s 15 f 425.8 y 139.021 (k)s 1 f 422.727 y 147.533 (+)s 11 f 407.726 y 167.368 (d)s 13 f 411.326 y 161.199 (X)s 11 f 436.74 y 159.533 (m)s 2 f 168.048 (=1)s 10 f 422.727 y 182.198 (D)s 11 f 424.527 y 192.133 (k)s 197.438 (;m)s 1 f 422.727 y 209.403 (\050)s 10 f 214.07 (\275)s 1 f 220.274 (\051)s 226.94 ([)s 10 f 230.274 (\264)s 1 f 236.663 (\050)s 10 f 241.329 (e)s 11 f 424.527 y 246.917 (m)s 1 f 422.727 y 256.032 (\051)s 12 f 263.366 (\241)s 10 f 275.366 (\264)s 1 f 281.754 (\0500\051])s 12 f 303.088 (\241)s 1 f 315.088 (I)s 317.261 (L)s 2 f 417.493 y 324.761 (0)s 10 f 422.727 y 330.144 (F)s 1 f 339.528 (\050)s 10 f 344.194 (\275;)s 355.732 (\264)s 1 f 362.121 (\051)s 10 f 366.787 (\076)s 372.121 (\076)s 11 f 424.527 y 381.454 (\275)s 1 f 422.727 y 390.366 (=)s 403.033 (0)s 10 f 409.033 (:)s 1 f 465.664 y 8.71 (F)s 15.543 (or)s 30.243 (eac)s 46.577 (h)s 57.243 (p)s 64.243 (ositiv)s 92.31 (e)s 101.643 (in)s 111.31 (teger)s 10 f 141.343 (n)s 12 f 151.879 (\270)s 1 f 164.546 (1)s 174.546 (let)s 10 f 191.879 (F)s 11 f 461.31 y 201.263 (k)s 206.567 (;n)s 12 f 465.664 y 219.282 (2)s 230.615 (F)s 1 f 244.432 (suc)s 260.832 (h)s 271.499 (that)s 297.499 (for)s 315.866 (all)s 332.532 (0)s 12 f 341.865 (\267)s 10 f 354.532 (\275)s 12 f 364.07 (\267)s 1 f 376.736 (2,)s 10 f 507.448 y 65.5 (\074)s 70.834 (\074)s 80.167 (W)s 2 f 509.248 y 91.5 (0)s 11 f 96.284 (;e)s 15 f 510.521 y 103.687 (k)s 1 f 507.448 y 112.199 (+)s 11 f 492.447 y 132.034 (d)s 13 f 496.047 y 125.865 (X)s 11 f 521.461 y 124.199 (m)s 2 f 132.714 (=1)s 10 f 507.448 y 146.864 (D)s 11 f 509.248 y 156.799 (k)s 162.103 (;m)s 1 f 507.448 y 174.069 (\050)s 10 f 178.736 (\275)s 1 f 184.94 (\051)s 191.606 ([)s 10 f 194.94 (\264)s 1 f 201.329 (\050)s 10 f 205.995 (e)s 11 f 509.248 y 211.583 (k)s 1 f 507.448 y 217.487 (\051)s 12 f 224.82 (\241)s 10 f 236.82 (\264)s 1 f 243.209 (\0500\051])s 12 f 264.542 (\241)s 1 f 276.542 (I)s 278.716 (L)s 2 f 502.214 y 286.216 (0)s 10 f 507.448 y 291.599 (F)s 11 f 502.493 y 300.982 (k)s 306.287 (;n)s 1 f 507.448 y 315.669 (\050)s 10 f 320.335 (\275;)s 331.873 (\264)s 1 f 338.262 (\051)s 10 f 342.928 (\076)s 348.262 (\076)s 11 f 509.248 y 357.595 (\275)s 12 f 507.448 y 366.507 (\267)s 1 f 499.329 y 381.215 (1)s 7.203 .48 380.614 504.687 r 10 f 515.679 y 380.614 (n)s 507.448 y 389.257 (:)s 1 f 549.197 y 8.71 (It)s 21.71 (is)s 33.776 (easy)s 60.177 (to)s 74.843 (see)s 94.243 (that)s 120.243 (for)s 138.61 (eac)s 154.943 (h)s 10 f 165.61 (n)s 12 f 176.146 (\270)s 1 f 188.813 (1)s 198.813 (\050cf.)s 221.146 (pro)s 238.846 (of)s 252.513 (of)s 266.18 (\0507.1.2\051)s 304.18 (in)s 318.18 ([KL]\051)s 588.721 y 44.091 (lim)s 62.758 (sup)s 11 f 598.794 y 48.641 (N)s 14 f 57.142 (!1)s 0 f 588.721 y 82.825 (E)s 11 f 590.521 y 91.891 (P)s 15 f 593.494 y 98.001 (\271)s 591.727 y 103.1 (N)s 13 f 575.4 y 112.008 (h)s 574.92 y 117.675 (\257)s 582.121 y 117.675 (\257)s 589.321 y 117.675 (\257)s 572.387 y 123.675 (Z)s 11 f 575.354 y 135.675 (T)s 2 f 599.654 y 130.341 (0)s 10 f 588.721 y 145.234 (dsN)s 2 f 583.766 y 168.055 (1)s 14 f 172.838 (\241)s 11 f 180.338 (d)s 13 f 577.321 y 189.296 (X)s 11 f 604.261 y 187.934 (i)s 14 f 191.329 (2)s 2 f 197.796 (I)s 196.102 (T)s 15 f 601.487 y 202.952 (d)s 10 f 588.721 y 209.991 (G)s 1 f 219.426 (\050)s 10 f 224.092 (s;)s 235.05 (i=)s 244.518 (N)s 1 f 255.468 (\051)s 10 f 260.135 (\277)s 11 f 590.521 y 265.38 (i)s 1 f 588.721 y 269.376 (I)s 271.549 (L)s 11 f 582.954 y 279.049 (\257)s 592.247 y 279.049 (N)s 10 f 588.721 y 288.151 (F)s 11 f 583.766 y 297.534 (k)s 302.838 (;n)s 13 f 579.001 y 314.22 (\241)s 10 f 588.721 y 319.72 (\264)s 11 f 583.766 y 326.109 (\042N)s 591.687 y 325.679 (s)s 1 f 588.721 y 339.745 (\0500\051)s 10 f 355.078 (;)s 360.411 (\264)s 11 f 590.521 y 366.37 (s)s 13 f 579.001 y 371.499 (\242)s 574.92 y 378.999 (\257)s 582.121 y 378.999 (\257)s 589.321 y 378.999 (\257)s 575.4 y 382.999 (i)s 1 f 588.721 y 391.999 (=)s 404.665 (0)s 10 f 410.665 (:)s 1 f 631.846 y -5.69 (In)s 9.31 (particular,)s 68.043 (to)s 82.71 (pro)s 99.743 (v)s 105.743 (e)s 115.077 (the)s 135.743 (theorem)s 182.443 (w)s 190.777 (e)s 200.11 (ha)s 212.443 (v)s 218.443 (e)s 227.777 (to)s 242.444 (sho)s 259.51 (w)s 272.177 (that)s 670.703 y 91.025 (lim)s 11 f 677.903 y 86.826 (n)s 14 f 92.758 (!1)s 1 f 670.703 y 113.891 (lim)s 132.558 (sup)s 11 f 680.449 y 122.816 (\042)s 14 f 127.35 (!)s 2 f 136.916 (0)s 1 f 670.703 y 152.624 (lim)s 171.291 (sup)s 11 f 680.776 y 157.173 (N)s 14 f 165.675 (!1)s 0 f 670.703 y 191.358 (E)s 11 f 672.503 y 200.424 (P)s 15 f 675.476 y 206.534 (\271)s 673.709 y 211.632 (N)s 13 f 657.383 y 220.541 (h)s 656.903 y 226.208 (\257)s 664.103 y 226.208 (\257)s 671.303 y 226.208 (\257)s 654.369 y 232.208 (Z)s 11 f 657.336 y 244.208 (T)s 2 f 681.636 y 238.874 (0)s 10 f 670.703 y 253.767 (Z)s 11 f 665.748 y 262.817 (F)s 15 f 662.127 y 270.195 (k)s 274.84 (;n)s 11 f 673.669 y 261.959 (N)s 269.944 (;\042)s 1 f 670.703 y 284.075 (\050)s 10 f 288.742 (G)s 11 f 672.503 y 298.177 (s)s 10 f 670.703 y 303.306 (;)s 308.639 (\264)s 11 f 672.503 y 314.598 (s)s 1 f 670.703 y 319.727 (\051)s 10 f 324.394 (ds)s 13 f 656.903 y 336.265 (\257)s 664.103 y 336.265 (\257)s 671.303 y 336.265 (\257)s 657.383 y 340.265 (i)s 1 f 670.703 y 349.264 (=)s 361.931 (0)s 10 f 367.931 (;)s 1 f 433.113 (\0506)s 10 f 443.78 (:)s 1 f 447.114 (11\051)s 705.976 y 223.045 (42)s do-end end endp %%Page: 43 43 %%BeginPageSetup initializepage (Raffaele Esposito; page: 43 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f0_12 sf ( )S -996 -1000 :M f1_12 sf ( )S -993 -1000 :M f2_12 sf ( )S -989 -1000 :M f10_12 sf ( )S -981 -1000 :M f11_12 sf ( )S -972 -1000 :M f12_12 sf ( )S -960 -1000 :M f13_12 sf ( )S -951 -1000 :M f14_12 sf ( )S -937 -1000 :M f15_12 sf ( )S -926 -1000 :M f17_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 1200 1000 div mul /CMBX10 findfont fdef 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 17 10 1200 1000 div mul /CMTI10 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 6.453 y -5.69 (where)s 10 f 29.01 (Z)s 11 f 2.098 y 38.06 (F)s 15 f -1.524 y 45.437 (k)s 50.083 (;n)s 11 f 9.758 y 37.202 (N)s 45.187 (;\042)s 1 f 6.453 y 59.318 (\050)s 10 f 63.985 (G;)s 78.753 (\264)s 1 f 85.142 (\051)s 93.809 (is)s 105.875 (de\257ned)s 147.209 (b)s 153.542 (y)s 10 f 41.296 y 50.327 (Z)s 11 f 36.341 y 59.377 (F)s 15 f 32.72 y 66.754 (k)s 71.4 (;n)s 11 f 44.262 y 58.519 (N)s 66.504 (;\042)s 1 f 41.296 y 80.635 (\050)s 10 f 85.302 (G;)s 100.07 (\264)s 1 f 106.459 (\051)s 114.459 (=)s 10 f 127.126 (X)s 11 f 36.341 y 138.009 (k)s 44.262 y 137.067 (N)s 145.052 (;\042)s 1 f 41.296 y 153.036 (\050)s 10 f 157.703 (G;)s 172.471 (\264)s 1 f 178.86 (\051)s 12 f 186.193 (\241)s 10 f 198.193 (N)s 2 f 36.341 y 209.143 (1)s 14 f 213.926 (\241)s 11 f 221.426 (d)s 13 f 29.896 y 230.384 (X)s 11 f 56.836 y 229.022 (i)s 14 f 232.417 (2)s 2 f 238.884 (I)s 237.19 (T)s 15 f 54.063 y 244.04 (d)s 10 f 41.296 y 251.079 (G)s 1 f 260.514 (\050)s 10 f 265.18 (i=)s 274.648 (N)s 1 f 285.598 (\051)s 10 f 290.264 (\277)s 11 f 43.096 y 295.51 (i)s 1 f 41.296 y 299.505 (I)s 301.679 (L)s 11 f 35.529 y 309.179 (\257)s 44.822 y 309.179 (N)s 10 f 41.296 y 318.28 (F)s 11 f 36.341 y 327.664 (k)s 332.968 (;n)s 13 f 31.576 y 344.35 (\241)s 10 f 41.296 y 349.85 (\264)s 11 f 36.341 y 356.239 (\042N)s 1 f 41.296 y 369.874 (\0500\051)s 10 f 385.208 (;)s 390.541 (\264)s 13 f 31.576 y 396.93 (\242)s 10 f 41.296 y 404.43 (:)s 1 f 86.142 y 8.71 (On)s 29.554 (the)s 51.064 (other)s 83.275 (hand,)s 117.663 (since)s 10 f 147.907 (F)s 11 f 81.787 y 157.29 (k)s 162.594 (;n)s 1 f 86.142 y 176.82 (is)s 189.731 (a)s 200.574 (cylinder)s 247.118 (function,)s 298.507 (it)s 311.35 (is)s 324.261 (easy)s 351.505 (to)s 367.015 (see)s 387.259 (b)s 393.592 (y)s 404.77 (Lemma)s 448.447 (6.9)s 102.942 y -5.69 (that)s 20.31 (for)s 38.677 (all)s 10 f 55.343 (i)s 12 f 62.811 (2)s 1 f 74.144 (I)s 73.317 (T)s 11 f 97.708 y 81.984 (d)s 10 f 132.173 y 9.486 (\277)s 11 f 133.973 y 14.732 (i)s 1 f 132.173 y 18.727 (I)s 20.9 (L)s 11 f 126.406 y 28.4 (\257)s 135.699 y 28.4 (N)s 10 f 132.173 y 37.502 (F)s 11 f 127.218 y 46.885 (n;k)s 1 f 132.173 y 64.905 (=)s 10 f 77.572 (N)s 14 f 127.218 y 88.521 (\241)s 2 f 96.021 (1)s 10 f 132.173 y 101.405 (o)s 11 f 133.973 y 107.222 (N)s 1 f 132.173 y 116.323 (\0501\051)s 134.323 (+)s 10 f 146.323 (\277)s 11 f 133.973 y 151.569 (i)s 1 f 132.173 y 155.564 (I)s 157.737 (L)s 2 f 126.939 y 165.237 (0)s 11 f 135.139 y 165.237 (N)s 10 f 132.173 y 174.339 (F)s 11 f 127.218 y 183.723 (n;k)s 1 f 166.806 y 67.571 (+)s 10 f 79.571 (N)s 14 f 161.851 y 90.521 (\241)s 2 f 98.021 (1)s 10 f 158.688 y 104.845 (\257)s 7.421 .48 104.845 164.046 r 1 f 175.037 y 105.555 (2)s 11 f 151.806 y 123.541 (d)s 13 f 155.406 y 117.372 (X)s 11 f 180.819 y 115.706 (m)s 2 f 124.221 (=1)s 13 f 157.086 y 138.371 (\241)s 10 f 166.806 y 143.871 (@)s 11 f 168.606 y 150.242 (m)s 10 f 166.806 y 159.357 (J)s 12 f 169.832 (\244)s 10 f 178.499 (\274)s 11 f 161.851 y 185.77 (N)s 1 f 166.806 y 194.871 (\050)s 10 f 199.538 (i=)s 209.005 (N)s 1 f 219.955 (\051)s 13 f 157.086 y 224.622 (\242)s 10 f 166.806 y 232.122 (\277)s 11 f 168.606 y 237.368 (i)s 13 f 153.486 y 241.363 (n)s 155.406 y 253.255 (X)s 11 f 182.346 y 251.363 (j)s 14 f 255.819 (2)s 2 f 262.286 (I)s 260.593 (T)s 15 f 179.573 y 267.443 (d)s 13 f 153.486 y 274.481 (n)s 12 f 166.806 y 282.481 (r)s 11 f 168.606 y 292.481 (j)s 296.42 (;j)s 2 f 303.727 (+)s 11 f 311.093 (e)s 15 f 169.806 y 315.646 (m)s 10 f 166.806 y 324.215 (F)s 11 f 161.851 y 333.598 (n;k)s 12 f 166.806 y 350.951 (\241)s 362.951 (r)s 11 f 168.606 y 372.951 (j)s 2 f 377.407 (+)s 11 f 384.774 (e)s 15 f 169.806 y 389.327 (m)s 11 f 168.606 y 397.295 (;j)s 10 f 166.806 y 405.201 (F)s 11 f 161.851 y 414.584 (n;k)s 13 f 153.486 y 429.271 (o)s 437.271 (o)s 10 f 166.806 y 445.271 (:)s 1 f 216.016 y 8.71 (W)s 20.043 (e)s 29.376 (no)s 41.71 (w)s 54.376 (decomp)s 94.71 (ose)s 10 f 114.777 (Z)s 11 f 211.661 y 123.827 (F)s 15 f 208.04 y 131.204 (k)s 135.85 (;n)s 11 f 219.321 y 122.968 (N)s 130.953 (;\042)s 1 f 216.016 y 149.085 (in)s 163.085 (t)s 167.418 (w)s 175.752 (o)s 185.752 (parts,)s 10 f 219.852 (Z)s 11 f 210.25 y 228.902 (F)s 15 f 206.628 y 236.279 (k)s 240.925 (;n)s 11 f 210.25 y 249.56 (;)s 2 f 252.41 (1)s 11 f 219.543 y 228.043 (N)s 236.028 (;\042)s 1 f 216.016 y 261.793 (and)s 10 f 285.127 (Z)s 11 f 210.25 y 294.177 (F)s 15 f 206.628 y 301.554 (k)s 306.2 (;n)s 11 f 210.25 y 314.835 (;)s 2 f 317.685 (2)s 11 f 219.543 y 293.318 (N)s 301.303 (;\042)s 1 f 216.016 y 327.068 (:)s 10 f 251.893 y 124.574 (Z)s 11 f 246.938 y 133.624 (F)s 15 f 243.317 y 141.001 (k)s 145.647 (;n)s 11 f 254.859 y 132.765 (N)s 140.75 (;\042)s 1 f 251.893 y 158.215 (=)s 10 f 170.882 (Z)s 11 f 246.126 y 179.932 (F)s 15 f 242.505 y 187.309 (k)s 191.955 (;n)s 11 f 246.126 y 200.59 (;)s 2 f 203.44 (1)s 11 f 255.419 y 179.073 (N)s 187.058 (;\042)s 1 f 251.893 y 211.49 (+)s 10 f 223.49 (Z)s 11 f 246.126 y 232.54 (F)s 15 f 242.505 y 239.917 (k)s 244.563 (;n)s 11 f 246.126 y 253.198 (;)s 2 f 256.048 (2)s 11 f 255.419 y 231.682 (N)s 239.667 (;\042)s 1 f 251.893 y 264.098 (+)s 10 f 276.098 (N)s 14 f 246.938 y 287.048 (\241)s 2 f 294.548 (1)s 10 f 251.893 y 299.931 (o)s 11 f 253.693 y 305.748 (N)s 1 f 251.893 y 314.85 (\0501\051)s 10 f 330.183 (;)s 1 f 281.055 y -5.69 (where)s 10 f 320.25 y 5.091 (Z)s 11 f 314.484 y 14.141 (F)s 15 f 310.862 y 21.519 (k)s 26.164 (;n)s 11 f 314.484 y 34.799 (;)s 2 f 37.649 (1)s 11 f 323.777 y 13.283 (N)s 21.268 (;\042)s 1 f 320.25 y 46.366 (=)s 10 f 59.033 (N)s 2 f 315.295 y 69.982 (1)s 14 f 74.766 (\241)s 11 f 82.266 (d)s 13 f 308.85 y 91.223 (X)s 11 f 335.79 y 89.861 (i)s 14 f 93.256 (2)s 2 f 99.723 (I)s 98.03 (T)s 15 f 333.017 y 104.88 (d)s 10 f 320.25 y 111.918 (G)s 1 f 121.353 (\050)s 10 f 126.02 (i=)s 135.487 (N)s 1 f 146.437 (\051)s 10 f 151.104 (\277)s 11 f 322.05 y 156.35 (i)s 13 f 299.73 y 160.345 (\050)s 10 f 320.25 y 170.011 (W)s 2 f 322.05 y 181.345 (0)s 11 f 186.128 (;e)s 15 f 323.324 y 193.531 (k)s 1 f 320.25 y 202.044 (+)s 11 f 305.25 y 221.879 (d)s 13 f 308.85 y 215.71 (X)s 11 f 334.264 y 214.044 (m)s 2 f 222.559 (=1)s 10 f 320.25 y 236.709 (D)s 11 f 322.05 y 246.644 (k)s 251.948 (;m)s 13 f 310.53 y 265.913 (\241)s 10 f 320.25 y 271.413 (\264)s 11 f 315.295 y 277.802 (N)s 286.304 (\042)s 1 f 320.25 y 291.438 (\0500\051)s 13 f 310.53 y 306.771 (\242)s 306.93 y 314.271 (h)s 10 f 320.25 y 319.938 (\264)s 11 f 315.295 y 326.327 (N)s 334.828 (\042)s 1 f 320.25 y 339.962 (\050)s 10 f 344.629 (e)s 11 f 322.05 y 350.216 (m)s 1 f 320.25 y 359.332 (\051)s 12 f 366.665 (\241)s 10 f 378.665 (\264)s 11 f 315.295 y 385.054 (N)s 393.555 (\042)s 1 f 320.25 y 398.689 (\0500\051)s 13 f 306.93 y 414.023 (i)s 299.73 y 419.689 (\051)s 12 f 358.626 y 79.758 (\241)s 10 f 91.758 (N)s 2 f 353.671 y 102.708 (1)s 14 f 107.491 (\241)s 11 f 114.991 (d)s 13 f 347.226 y 123.948 (X)s 11 f 374.166 y 122.586 (i)s 14 f 125.982 (2)s 2 f 132.448 (I)s 130.755 (T)s 15 f 371.393 y 137.605 (d)s 10 f 358.626 y 144.643 (G)s 1 f 154.078 (\050)s 10 f 158.745 (i=)s 168.212 (N)s 1 f 179.162 (\051)s 10 f 183.829 (\277)s 11 f 360.426 y 189.075 (i)s 1 f 358.626 y 193.07 (I)s 195.243 (L)s 2 f 353.393 y 202.743 (0)s 11 f 361.593 y 202.743 (N)s 10 f 358.626 y 211.845 (F)s 11 f 353.671 y 221.228 (n;k)s 13 f 348.906 y 237.915 (\241)s 10 f 358.626 y 243.415 (\264)s 11 f 353.671 y 249.803 (\042N)s 1 f 358.626 y 263.439 (\0500\051)s 10 f 278.772 (;)s 284.106 (\264)s 13 f 348.906 y 290.494 (\242)s 10 f 358.626 y 301.328 (;)s 405.402 y 5.091 (Z)s 11 f 399.635 y 14.141 (F)s 15 f 396.014 y 21.519 (k)s 26.164 (;n)s 11 f 399.635 y 34.799 (;)s 2 f 37.649 (2)s 11 f 408.928 y 13.283 (N)s 21.268 (;\042)s 1 f 405.402 y 46.366 (=)s 10 f 59.033 (\257)s 66.453 (N)s 14 f 400.447 y 77.403 (\241)s 11 f 84.903 (d)s 13 f 394.002 y 93.86 (X)s 11 f 420.942 y 92.499 (i)s 14 f 95.894 (2)s 2 f 102.361 (I)s 100.667 (T)s 15 f 418.169 y 107.517 (d)s 10 f 405.402 y 114.555 (G)s 1 f 123.99 (\050)s 10 f 128.657 (i=)s 138.125 (N)s 1 f 149.075 (\051)s 10 f 153.741 (\277)s 11 f 407.202 y 158.987 (i)s 13 f 384.882 y 162.982 (\050)s 395.682 y 174.649 (\241)s 10 f 405.402 y 180.149 (@)s 11 f 407.202 y 186.52 (k)s 10 f 405.402 y 192.424 (J)s 12 f 202.899 (\244)s 10 f 211.566 (\274)s 11 f 400.447 y 218.836 (N)s 1 f 405.402 y 227.938 (\050)s 10 f 232.605 (\264)s 1 f 238.994 (\051\0500\051)s 13 f 395.682 y 258.994 (\242)s 392.082 y 266.494 (\263)s 10 f 397.284 y 275.1 (r)s 2 f 399.084 y 280.514 (0)s 11 f 285.298 (;e)s 15 f 400.357 y 292.701 (k)s 1 f 397.284 y 301.213 (+)s 10 f 313.213 (r)s 11 f 399.084 y 318.627 (e)s 15 f 400.357 y 323.18 (k)s 11 f 399.084 y 328.426 (;)s 2 f 331.276 (0)s 61.559 .48 275.1 402.642 r 1 f 413.633 y 302.88 (2)s 13 f 392.082 y 338.099 (\264)s 12 f 453.211 y 199.758 (\241)s 1 f 211.758 (2)s 11 f 438.211 y 227.593 (d)s 13 f 441.811 y 221.424 (X)s 11 f 467.224 y 219.758 (m)s 2 f 228.273 (=1)s 1 f 453.211 y 242.423 (\050)s 10 f 247.09 (\302D)s 11 f 455.011 y 264.533 (k)s 269.837 (;m)s 1 f 453.211 y 281.803 (\051)s 13 f 443.491 y 288.469 (\241)s 10 f 453.211 y 293.969 (\264)s 11 f 448.256 y 300.358 (N)s 308.86 (\042)s 1 f 453.211 y 313.994 (\0500\051)s 13 f 443.491 y 329.327 (\242)s 439.891 y 336.827 (\263)s 10 f 453.211 y 343.994 (@)s 11 f 455.011 y 350.365 (m)s 10 f 453.211 y 359.48 (J)s 12 f 369.955 (\244)s 10 f 378.622 (\274)s 11 f 448.256 y 385.892 (N)s 1 f 453.211 y 394.994 (\050)s 10 f 399.661 (\264)s 1 f 406.05 (\051\0500\051)s 13 f 439.891 y 426.05 (\264)s 432.691 y 433.216 (\051)s 12 f 498.858 y 55.758 (\241)s 10 f 67.758 (\257)s 75.179 (N)s 14 f 493.903 y 86.128 (\241)s 11 f 93.629 (d)s 13 f 487.458 y 105.044 (X)s 11 f 514.398 y 101.224 (i)s 14 f 104.619 (2f)s 2 f 116.002 (I)s 114.309 (T)s 15 f 511.624 y 121.159 (d)s 10 f 498.858 y 128.197 (G)s 1 f 137.632 (\050)s 10 f 142.299 (i=)s 151.766 (N)s 1 f 162.716 (\051)s 10 f 167.383 (\277)s 11 f 500.658 y 172.629 (i)s 13 f 478.338 y 176.624 (\050)s 11 f 483.858 y 196.126 (d)s 13 f 487.458 y 189.957 (X)s 11 f 512.871 y 188.291 (m)s 2 f 196.806 (=1)s 13 f 485.538 y 210.956 (\263)s 10 f 498.858 y 218.123 (@)s 11 f 500.658 y 224.494 (m)s 10 f 498.858 y 233.609 (J)s 12 f 244.084 (\244)s 10 f 252.751 (\274)s 11 f 493.903 y 260.021 (N)s 1 f 498.858 y 269.123 (\050)s 10 f 273.79 (\264)s 1 f 280.179 (\051\0500\051)s 13 f 485.538 y 300.179 (\264)s 12 f 498.858 y 307.345 (\243)s 547.098 y 199.758 (\243)s 13 f 533.778 y 211.758 (n)s 535.698 y 223.65 (X)s 11 f 562.638 y 221.758 (j)s 14 f 226.214 (2)s 2 f 232.681 (I)s 230.988 (T)s 15 f 559.865 y 237.838 (d)s 1 f 547.098 y 242.876 (\0501)s 10 f 253.542 (=)s 1 f 259.543 (2\051)s 13 f 537.378 y 272.209 (\241)s 12 f 547.098 y 277.709 (r)s 11 f 548.898 y 287.709 (j)s 291.649 (;j)s 2 f 298.955 (+)s 11 f 306.322 (e)s 15 f 550.098 y 310.875 (m)s 10 f 547.098 y 319.443 (F)s 11 f 542.143 y 328.826 (n;k)s 12 f 547.098 y 346.179 (\241)s 358.179 (r)s 11 f 548.898 y 368.179 (j)s 2 f 372.635 (+)s 11 f 380.002 (e)s 15 f 550.098 y 384.555 (m)s 11 f 548.898 y 392.523 (;j)s 10 f 547.098 y 400.429 (F)s 11 f 542.143 y 409.813 (n;k)s 13 f 537.378 y 424.499 (\242)s 533.778 y 431.999 (o)s 526.578 y 439.999 (\051)s 10 f 547.098 y 449.666 (:)s 1 f 591.633 y -5.69 (Here)s 22.994 (\050)s 10 f 27.661 (\302D)s 11 f 593.433 y 45.104 (k)s 50.408 (;m)s 1 f 591.633 y 62.374 (\051)s 71.358 (represen)s 114.491 (ts)s 128.209 (the)s 149.193 (pro)s 166.894 (duct)s 194.545 (function)s 241.862 (\050)s 10 f 246.529 (\302D)s 11 f 593.433 y 263.972 (k)s 269.277 (;m)s 1 f 591.633 y 281.242 (\051)s 287.909 (\050)s 10 f 292.575 (\256)s 1 f 300.296 (\051)s 308.825 (=)s 10 f 322.022 (\302)s 1 f 329.53 (\050)s 10 f 334.197 (\256)s 1 f 341.917 (\051)s 10 f 346.584 (D)s 11 f 593.433 y 356.519 (k)s 361.823 (;m)s 1 f 591.633 y 373.789 (\050)s 10 f 378.455 (\256)s 1 f 386.176 (\051.)s 400.462 (T)s 408.129 (o)s 418.447 (conclude)s 608.433 y -5.69 (the)s 14.976 (pro)s 32.677 (of)s 46.343 (of)s 60.01 (the)s 80.677 (theorem)s 127.377 (it)s 139.377 (is)s 151.443 (enough)s 192.777 (to)s 207.444 (pro)s 224.477 (v)s 230.477 (e)s 239.81 (the)s 260.477 (follo)s 282.477 (wing)s 311.144 (lemmas)s 354.544 (:)s 0 f 632.1 y -5.69 (Lemma)s 43.243 (6.5)s 17 f 69.476 (F)s 76.389 (or)s 91.876 (e)s 96.782 (ach)s 1 f 118.862 (0)s 12 f 128.196 (\267)s 10 f 140.862 (k)s 12 f 150.82 (\267)s 10 f 163.487 (d)s 17 f 169.733 (,)s 1 f 670.703 y 87.208 (lim)s 11 f 677.903 y 83.009 (n)s 14 f 88.941 (!1)s 1 f 670.703 y 110.074 (lim)s 128.741 (sup)s 11 f 680.449 y 118.999 (\042)s 14 f 123.533 (!)s 2 f 133.1 (0)s 1 f 670.703 y 148.808 (lim)s 167.474 (sup)s 11 f 680.776 y 153.357 (N)s 14 f 161.858 (!1)s 0 f 670.703 y 187.541 (E)s 11 f 672.503 y 196.608 (P)s 15 f 675.476 y 202.717 (\271)s 673.709 y 207.816 (N)s 13 f 657.383 y 216.724 (h)s 656.903 y 222.391 (\257)s 664.103 y 222.391 (\257)s 671.303 y 222.391 (\257)s 654.369 y 228.391 (Z)s 11 f 657.336 y 240.391 (T)s 2 f 681.636 y 235.058 (0)s 10 f 670.703 y 249.95 (Z)s 11 f 664.936 y 259 (F)s 15 f 661.315 y 266.378 (k)s 271.024 (;n)s 11 f 664.936 y 279.659 (;)s 2 f 282.509 (1)s 11 f 674.229 y 258.142 (N)s 266.127 (;\042)s 1 f 670.703 y 287.892 (\050)s 10 f 292.559 (G)s 11 f 672.503 y 301.994 (s)s 10 f 670.703 y 307.123 (;)s 312.456 (\264)s 11 f 672.503 y 318.414 (s)s 1 f 670.703 y 323.544 (\051)s 10 f 328.21 (ds)s 13 f 656.903 y 340.081 (\257)s 664.103 y 340.081 (\257)s 671.303 y 340.081 (\257)s 657.383 y 344.081 (i)s 1 f 670.703 y 353.081 (=)s 365.748 (0)s 10 f 371.748 (:)s 1 f 433.113 (\0506)s 10 f 443.78 (:)s 1 f 447.114 (12\051)s 705.976 y 223.045 (43)s do-end end endp %%Page: 44 44 %%BeginPageSetup initializepage (Raffaele Esposito; page: 44 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f0_12 sf ( )S -996 -1000 :M f1_12 sf ( )S -993 -1000 :M f2_12 sf ( )S -989 -1000 :M f10_12 sf ( )S -981 -1000 :M f11_12 sf ( )S -972 -1000 :M f12_12 sf ( )S -960 -1000 :M f13_12 sf ( )S -951 -1000 :M f14_12 sf ( )S -937 -1000 :M f15_12 sf ( )S -926 -1000 :M f16_12 sf ( )S -921 -1000 :M f17_12 sf ( )S -918 -1000 :M f18_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 1200 1000 div mul /CMBX10 findfont fdef 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 16 5 1200 1000 div mul /CMR5 findfont fdef 17 10 1200 1000 div mul /CMTI10 findfont fdef 18 5 1200 1000 div mul /CMSY5 findfont fdef 58 60 translate 72 72.27 div dup scale 0 f 23.23 y -5.69 (Lemma)s 43.243 (6.6)s 17 f 69.476 (F)s 76.389 (or)s 91.876 (e)s 96.782 (ach)s 1 f 118.862 (0)s 12 f 128.196 (\267)s 10 f 140.862 (k)s 12 f 150.82 (\267)s 10 f 163.487 (d)s 17 f 169.733 (,)s 1 f 58.223 y 87.208 (lim)s 11 f 65.423 y 83.009 (n)s 14 f 88.941 (!1)s 1 f 58.223 y 110.074 (lim)s 128.741 (sup)s 11 f 67.969 y 118.999 (\042)s 14 f 123.533 (!)s 2 f 133.1 (0)s 1 f 58.223 y 148.808 (lim)s 167.474 (sup)s 11 f 68.296 y 153.357 (N)s 14 f 161.858 (!1)s 0 f 58.223 y 187.541 (E)s 11 f 60.023 y 196.608 (P)s 15 f 62.996 y 202.717 (\271)s 61.229 y 207.816 (N)s 13 f 44.903 y 216.724 (h)s 44.423 y 222.391 (\257)s 51.623 y 222.391 (\257)s 58.823 y 222.391 (\257)s 41.889 y 228.391 (Z)s 11 f 44.856 y 240.391 (T)s 2 f 69.156 y 235.058 (0)s 10 f 58.223 y 249.95 (Z)s 11 f 52.456 y 259 (F)s 15 f 48.835 y 266.378 (k)s 271.024 (;n)s 11 f 52.456 y 279.659 (;)s 2 f 282.509 (2)s 11 f 61.749 y 258.142 (N)s 266.127 (;\042)s 1 f 58.223 y 287.892 (\050)s 10 f 292.559 (G)s 11 f 60.023 y 301.994 (s)s 10 f 58.223 y 307.123 (;)s 312.456 (\264)s 11 f 60.023 y 318.414 (s)s 1 f 58.223 y 323.544 (\051)s 10 f 328.21 (ds)s 13 f 44.423 y 340.081 (\257)s 51.623 y 340.081 (\257)s 58.823 y 340.081 (\257)s 44.903 y 344.081 (i)s 1 f 58.223 y 353.081 (=)s 365.748 (0)s 10 f 371.748 (:)s 1 f 433.113 (\0506)s 10 f 443.78 (:)s 1 f 447.114 (13\051)s 17 f 100.696 y -5.69 (Pr)s 6.896 (o)s 12.416 (of)s 27.88 (of)s 43.343 (L)s 50.256 (emma)s 87.186 (6.5)s 1 f 103.132 (.)s 116.223 (Fix)s 139.197 (0)s 12 f 150.988 (\267)s 10 f 166.113 (k)s 12 f 178.528 (\267)s 10 f 193.653 (d)s 1 f 205.373 (and)s 230.181 (denote)s 10 f 270.322 (Z)s 11 f 94.929 y 279.372 (F)s 15 f 91.308 y 286.75 (n;k)s 11 f 94.929 y 300.031 (;)s 2 f 302.881 (1)s 11 f 104.222 y 278.514 (N)s 286.499 (;\042)s 1 f 100.696 y 313.739 (b)s 320.072 (y)s 10 f 331.88 (Z)s 2 f 96.341 y 340.93 (1)s 11 f 104.001 y 340.072 (N)s 348.057 (;\042)s 1 f 100.696 y 356.04 (.)s 369.131 (Since)s 401.939 (the)s 424.08 (en)s 435.747 (trop)s 457.447 (y)s 10 f 117.496 y -5.69 (s)s 13 f 107.776 y 1.935 (\241)s 10 f 117.496 y 7.435 (P)s 11 f 119.862 y 15.139 (\271)s 15 f 117.462 y 20.974 (N)s 12 f 117.496 y 29.282 (j)s 10 f 32.615 (P)s 11 f 119.862 y 40.32 (\272)s 15 f 117.462 y 45.69 (N)s 122.262 y 45.131 (\256)s 13 f 107.776 y 53.999 (\242)s 1 f 117.496 y 63.349 (of)s 10 f 76.866 (P)s 11 f 119.862 y 84.57 (\271)s 15 f 117.462 y 90.405 (N)s 1 f 117.496 y 102.563 (with)s 129.747 (resp)s 151.514 (ect)s 170.697 (to)s 10 f 185.214 (P)s 11 f 119.862 y 192.918 (\272)s 15 f 117.462 y 198.289 (N)s 122.262 y 197.729 (\256)s 1 f 117.496 y 210.448 (is)s 222.364 (equal)s 253.881 (to)s 10 f 268.398 (s)s 13 f 107.776 y 276.023 (\241)s 10 f 117.496 y 281.523 (\271)s 11 f 113.141 y 288.754 (N)s 12 f 117.496 y 297.855 (j)s 10 f 301.189 (\272)s 11 f 113.141 y 307.88 (N)s 120.462 y 307.117 (\256)s 13 f 107.776 y 316.982 (\242)s 1 f 117.496 y 326.332 (whic)s 349.999 (h)s 360.516 (is)s 372.433 (b)s 379.433 (ounded)s 421.283 (b)s 427.616 (y)s 10 f 437.8 (C)s 447.235 (N)s 11 f 113.141 y 458.185 (d)s 1 f 134.296 y -5.69 (for)s 12.677 (some)s 42.743 (p)s 49.743 (ositiv)s 77.81 (e)s 87.143 (constan)s 126.877 (t)s 10 f 135.543 (C)s 1 f 144.978 (,)s 152.312 (b)s 158.645 (y)s 168.978 (the)s 189.645 (en)s 201.312 (trop)s 223.012 (y)s 233.345 (inequalit)s 278.679 (y)s 289.012 (for)s 307.379 (an)s 319.712 (y)s 330.045 (p)s 337.045 (ositiv)s 365.112 (e)s 10 f 374.445 (A)s 0 f 168.715 y 73.207 (E)s 11 f 170.515 y 82.274 (P)s 15 f 173.489 y 88.383 (\271)s 171.722 y 93.482 (N)s 13 f 155.395 y 102.39 (h)s 154.915 y 108.057 (\257)s 162.115 y 108.057 (\257)s 169.315 y 108.057 (\257)s 152.382 y 114.057 (Z)s 11 f 155.348 y 126.057 (t)s 2 f 179.649 y 120.724 (0)s 10 f 168.715 y 132.282 (Z)s 2 f 163.761 y 141.332 (1)s 11 f 171.682 y 140.474 (N)s 148.459 (;\042)s 1 f 168.715 y 158.442 (\050)s 10 f 163.109 (G)s 11 f 170.515 y 172.544 (s)s 10 f 168.715 y 177.673 (;)s 183.007 (\264)s 11 f 170.515 y 188.965 (s)s 1 f 168.715 y 194.094 (\051)s 10 f 200.761 (ds)s 13 f 154.915 y 212.632 (\257)s 162.115 y 212.632 (\257)s 169.315 y 212.632 (\257)s 155.395 y 216.632 (i)s 12 f 168.715 y 225.632 (\267)s 10 f 160.597 y 239.738 (C)s 9.435 .48 239.738 165.955 r 176.947 y 239.956 (A)s 1 f 206.582 y 114.724 (+)s 198.464 y 137.936 (1)s 25.545 .48 128.164 203.822 r 10 f 214.814 y 128.164 (AN)s 11 f 211.347 y 148.114 (d)s 1 f 206.582 y 155.149 (log)s 0 f 170.649 (E)s 11 f 208.382 y 179.716 (P)s 15 f 211.656 y 185.825 (\272)s 209.589 y 190.521 (N)s 214.092 y 190.098 (\256)s 13 f 193.262 y 199.43 (h)s 1 f 206.582 y 207.096 (exp)s 13 f 193.262 y 227.43 (\263)s 10 f 206.582 y 234.596 (AN)s 11 f 201.628 y 254.546 (d)s 13 f 192.782 y 260.142 (\257)s 199.982 y 260.142 (\257)s 207.182 y 260.142 (\257)s 190.249 y 266.142 (Z)s 11 f 193.215 y 278.142 (t)s 2 f 217.516 y 272.808 (0)s 10 f 206.582 y 284.367 (Z)s 2 f 201.628 y 293.417 (1)s 11 f 209.549 y 292.558 (N)s 300.543 (;\042)s 1 f 206.582 y 310.527 (\050)s 10 f 315.194 (G)s 11 f 208.382 y 324.629 (s)s 10 f 206.582 y 329.758 (;)s 335.091 (\264)s 11 f 208.382 y 341.05 (s)s 1 f 206.582 y 346.179 (\051)s 10 f 352.845 (ds)s 13 f 192.782 y 364.716 (\257)s 199.982 y 364.716 (\257)s 207.182 y 364.716 (\257)s 193.262 y 368.716 (\264)s 375.883 (i)s 10 f 206.582 y 381.55 (:)s 1 f 241.723 y -5.69 (Since)s 10 f 25.643 (e)s 14 f 237.369 y 31.231 (j)s 11 f 34.081 (x)s 14 f 39.522 (j)s 12 f 241.723 y 46.306 (\267)s 10 f 58.972 (e)s 11 f 237.369 y 64.56 (x)s 1 f 241.723 y 73.268 (+)s 10 f 85.268 (e)s 14 f 237.369 y 90.856 (\241)s 11 f 98.356 (x)s 1 f 241.723 y 108.397 (and)s 267.276 y 35.097 (lim)s 53.764 (sup)s 10 f 73.831 (N)s 14 f 262.321 y 84.781 (\241)s 11 f 92.281 (d)s 1 f 267.276 y 97.876 (log)s 12 f 115.376 (f)s 10 f 121.376 (a)s 11 f 269.076 y 127.719 (N)s 1 f 267.276 y 139.487 (+)s 10 f 151.487 (b)s 11 f 269.076 y 156.637 (N)s 12 f 267.276 y 165.739 (g)s 175.072 (\267)s 1 f 187.739 (max)s 13 f 257.556 y 212.072 (\251)s 1 f 267.276 y 219.072 (lim)s 237.739 (sup)s 10 f 257.806 (N)s 14 f 262.321 y 268.756 (\241)s 11 f 276.256 (d)s 1 f 267.276 y 281.851 (log)s 10 f 297.351 (a)s 11 f 269.076 y 303.694 (N)s 10 f 267.276 y 312.796 (;)s 1 f 318.129 (lim)s 336.796 (sup)s 10 f 356.862 (N)s 14 f 262.321 y 367.812 (\241)s 11 f 375.312 (d)s 1 f 267.276 y 380.908 (log)s 10 f 396.408 (b)s 11 f 269.076 y 401.558 (N)s 13 f 257.556 y 410.66 (\252)s 10 f 267.276 y 419.659 (;)s 1 f 292.829 y -5.69 (the)s 15.123 (absolute)s 62.67 (v)s 68.337 (alue)s 93.817 (app)s 113.484 (earing)s 149.664 (in)s 163.811 (the)s 184.625 (exp)s 203.291 (onen)s 227.625 (t)s 236.438 (of)s 250.252 (the)s 271.065 (righ)s 291.432 (t)s 300.246 (hand)s 330.392 (side)s 354.606 (of)s 368.42 (the)s 389.233 (last)s 412.113 (inequalit)s 457.447 (y)s 309.629 y -5.69 (can)s 16.31 (b)s 23.31 (e)s 32.643 (eliminated.)s 95.977 (Indeed,)s 138.31 (b)s 144.643 (y)s 154.977 (the)s 175.643 (F)s 182.477 (eynman-Kac)s 252.144 (form)s 276.177 (ula,)s 299.51 (w)s 307.844 (e)s 317.177 (ha)s 329.51 (v)s 335.51 (e)s 344.049 y 63.899 (lim)s 82.565 (sup)s 11 f 353.795 y 72.824 (\042)s 14 f 77.357 (!)s 2 f 86.924 (0)s 1 f 344.049 y 102.632 (lim)s 121.299 (sup)s 11 f 354.122 y 107.181 (N)s 14 f 115.683 (!1)s 1 f 335.93 y 152.578 (1)s 25.545 .48 142.805 341.289 r 10 f 352.28 y 142.805 (AN)s 11 f 348.813 y 162.755 (d)s 1 f 344.049 y 169.791 (log)s 0 f 185.291 (E)s 11 f 345.849 y 194.357 (P)s 15 f 349.122 y 200.467 (\272)s 347.055 y 205.163 (N)s 351.558 y 204.739 (\256)s 13 f 330.728 y 214.071 (h)s 1 f 344.049 y 221.738 (exp)s 13 f 330.728 y 242.071 (\263)s 10 f 344.049 y 249.238 (AN)s 11 f 339.094 y 269.188 (d)s 13 f 330.248 y 274.783 (\257)s 337.449 y 274.783 (\257)s 344.649 y 274.783 (\257)s 327.715 y 280.783 (Z)s 11 f 330.682 y 292.783 (t)s 2 f 354.982 y 287.45 (0)s 10 f 344.049 y 299.008 (Z)s 2 f 339.094 y 308.058 (1)s 11 f 347.015 y 307.2 (N)s 315.185 (;\042)s 1 f 344.049 y 325.169 (\050)s 10 f 329.835 (G)s 11 f 345.849 y 339.27 (s)s 10 f 344.049 y 344.4 (;)s 349.733 (\264)s 11 f 345.849 y 355.691 (s)s 1 f 344.049 y 360.82 (\051)s 10 f 367.487 (ds)s 13 f 330.248 y 379.358 (\257)s 337.449 y 379.358 (\257)s 344.649 y 379.358 (\257)s 330.728 y 383.358 (\264)s 390.525 (i)s 12 f 382.255 y 77.232 (\267)s 1 f 89.899 (lim)s 108.565 (sup)s 11 f 392.002 y 98.823 (\042)s 14 f 103.357 (!)s 2 f 112.924 (0)s 1 f 382.255 y 128.632 (lim)s 147.299 (sup)s 11 f 392.329 y 133.181 (N)s 14 f 141.683 (!1)s 1 f 374.137 y 178.578 (1)s 25.545 .48 168.805 379.495 r 10 f 390.487 y 168.805 (AN)s 11 f 387.02 y 188.755 (d)s 13 f 365.922 y 197.791 (Z)s 11 f 368.889 y 209.791 (t)s 2 f 393.189 y 204.457 (0)s 13 f 368.935 y 216.016 (\263)s 10 f 382.255 y 223.182 (\270)s 11 f 384.055 y 230.182 (N)s 238.167 (;\042)s 1 f 382.255 y 246.151 (\050)s 10 f 250.818 (G)s 11 f 384.055 y 260.253 (s)s 1 f 382.255 y 265.382 (\051)s 272.715 (+)s 10 f 284.715 (\270)s 11 f 384.055 y 291.715 (N)s 299.7 (;\042)s 1 f 382.255 y 307.684 (\050)s 12 f 312.351 (\241)s 10 f 321.684 (G)s 11 f 384.055 y 331.119 (s)s 1 f 382.255 y 336.248 (\051)s 13 f 368.935 y 340.915 (\264)s 10 f 382.255 y 348.082 (ds;)s 1 f 416.082 y -5.69 (where)s 10 f 29.01 (\270)s 11 f 417.882 y 36.01 (N)s 43.995 (;\042)s 1 f 416.082 y 51.979 (\050)s 12 f 56.645 (\247)s 10 f 65.979 (G)s 11 f 417.882 y 75.414 (s)s 1 f 416.082 y 80.543 (\051)s 89.21 (is)s 101.276 (the)s 121.943 (largest)s 160.71 (eigen)s 187.043 (v)s 192.71 (alue)s 218.043 (of)s 231.71 (the)s 252.376 (rev)s 268.41 (ersible)s 305.843 (op)s 318.843 (erator)s 10 f 442.836 y 129.372 (N)s 2 f 438.481 y 140.322 (2)s 16.333 .48 129.372 448.194 r 1 f 459.185 y 134.538 (2)s 13 f 437.634 y 149.145 (\263)s 1 f 450.954 y 156.312 (I)s 158.485 (L)s 11 f 445.187 y 165.985 (\257)s 454.48 y 165.985 (N)s 1 f 450.954 y 177.753 (+)s 189.753 (I)s 191.927 (L)s 11 f 445.187 y 199.427 (\257)s 205.3 (;)s 14 f 208.15 (\244)s 11 f 454.48 y 199.427 (N)s 13 f 437.634 y 213.666 (\264)s 1 f 450.954 y 223.499 (+)s 10 f 235.499 (AN)s 11 f 445.999 y 255.449 (d)s 10 f 450.954 y 261.045 (Z)s 2 f 445.999 y 270.095 (1)s 11 f 453.92 y 269.237 (N)s 277.222 (;\042)s 1 f 450.954 y 285.205 (\050)s 12 f 289.872 (\247)s 10 f 299.205 (G)s 11 f 452.754 y 308.64 (s)s 10 f 450.954 y 313.77 (;)s 319.103 (\264)s 1 f 325.492 (\051)s 476.507 y -5.69 (giv)s 9.643 (en)s 25.643 (b)s 31.977 (y)s 42.31 (the)s 62.977 (v)s 68.643 (ariational)s 122.677 (form)s 146.71 (ula)s 513.393 y 62.55 (sup)s 15 f 522.042 y 63.886 (f)s 18 f 68.698 (\270)s 16 f 75.198 (0)s 13 f 524.798 y 50.895 (R)s 15 f 532.965 y 60.367 (f)s 65.18 (d\272)s 530.898 y 74.314 (N)s 535.401 y 73.89 (a)s 16 f 532.965 y 82.022 (=1)s 13 f 492.873 y 95.712 (\050)s 10 f 513.393 y 105.379 (AN)s 11 f 508.438 y 125.329 (d)s 13 f 497.059 y 132.924 (Z)s 10 f 513.393 y 146.924 (Z)s 2 f 508.438 y 155.974 (1)s 11 f 516.36 y 155.116 (N)s 163.101 (;\042)s 1 f 513.393 y 171.085 (\050)s 12 f 175.752 (\247)s 10 f 185.085 (G)s 11 f 515.193 y 194.52 (s)s 10 f 513.393 y 199.649 (;)s 204.982 (\264)s 1 f 211.371 (\051)s 10 f 216.038 (f)s 1 f 223.205 (\050)s 10 f 227.871 (\264)s 1 f 234.26 (\051)s 10 f 238.927 (d\272)s 11 f 508.438 y 251.864 (N)s 516.36 y 251.101 (\256)s 1 f 513.393 y 260.966 (\050)s 10 f 265.633 (\264)s 1 f 272.022 (\051)s 279.355 (+)s 10 f 291.355 (N)s 2 f 508.438 y 302.305 (2)s 13 f 500.073 y 309.688 (D)s 502.547 y 317.022 (p)s 7.167 .48 329.022 502.547 r 10 f 513.393 y 329.022 (f)s 336.188 (;)s 1 f 341.522 (I)s 343.695 (L)s 11 f 507.626 y 351.195 (\257)s 516.92 y 351.195 (N)s 13 f 502.547 y 360.297 (p)s 7.167 .48 372.297 502.547 r 10 f 513.393 y 372.297 (f)s 13 f 500.073 y 379.463 (E)s 11 f 521.793 y 386.797 (\256)s 13 f 492.873 y 395.635 (\051)s 10 f 513.393 y 405.302 (:)s 1 f 564.484 y -5.69 (Here,)s 26.116 (I)s 28.29 (L)s 11 f 558.718 y 35.79 (\257)s 41.663 (;)s 14 f 44.513 (\244)s 11 f 568.011 y 35.79 (N)s 1 f 564.484 y 54.115 (stands)s 91.667 (for)s 110.119 (the)s 130.871 (adjoin)s 162.871 (t)s 171.623 (op)s 184.623 (erator)s 220.108 (of)s 233.86 (I)s 236.034 (L)s 11 f 558.718 y 243.534 (\257)s 568.011 y 243.534 (N)s 1 f 564.484 y 256.721 (in)s 10 f 270.806 (L)s 2 f 560.13 y 278.973 (2)s 13 f 554.764 y 286.356 (\241)s 10 f 564.484 y 291.856 (\272)s 11 f 560.13 y 298.548 (N)s 567.451 y 297.784 (\256)s 13 f 554.764 y 307.649 (\242)s 1 f 564.484 y 313.149 (.)s 322.072 (F)s 328.905 (rom)s 353.691 (Lemma)s 396.609 (6.8)s 416.028 (b)s 423.028 (elo)s 437.361 (w)s 450.113 (w)s 458.447 (e)s 581.284 y -5.69 (ha)s 6.643 (v)s 12.643 (e,)s 25.31 (for)s 43.677 (all)s 60.343 (p)s 67.343 (ositiv)s 95.41 (e)s 10 f 104.743 (A)s 1 f 607.586 y 22.371 (1)s 25.545 .48 12.599 612.944 r 10 f 623.935 y 12.599 (AN)s 11 f 620.469 y 32.549 (d)s 13 f 599.37 y 41.584 (Z)s 11 f 602.337 y 53.584 (t)s 2 f 626.637 y 48.251 (0)s 10 f 615.704 y 59.809 (\270)s 11 f 617.504 y 66.809 (N)s 74.794 (;\042)s 1 f 615.704 y 84.778 (\050)s 12 f 89.444 (\247)s 10 f 98.778 (G)s 11 f 617.504 y 108.213 (s)s 1 f 615.704 y 113.342 (\051)s 10 f 120.009 (ds)s 12 f 138.546 (\267)s 10 f 607.586 y 152.653 (C)s 2 f 609.386 y 161.229 (1)s 13.96 .48 152.653 612.944 r 10 f 623.935 y 155.133 (A)s 615.704 y 168.053 (t)s 1 f 656.038 y 37.825 (+)s 13 f 639.704 y 49.825 (Z)s 11 f 642.671 y 61.825 (t)s 2 f 666.971 y 56.492 (0)s 10 f 656.038 y 68.05 (ds)s 13 f 635.517 y 79.921 (\050)s 1 f 656.038 y 104.683 (sup)s 15 f 664.687 y 106.018 (f)s 18 f 110.831 (\270)s 16 f 117.331 (0)s 13 f 667.443 y 93.028 (R)s 15 f 675.609 y 102.5 (f)s 107.313 (d\272)s 673.543 y 116.447 (N)s 678.046 y 116.023 (\256)s 16 f 675.609 y 124.155 (=1)s 13 f 642.717 y 137.845 (n)s 639.704 y 147.845 (Z)s 10 f 656.038 y 161.845 (Z)s 2 f 651.083 y 170.895 (1)s 11 f 659.004 y 170.037 (N)s 178.022 (;\042)s 1 f 656.038 y 186.006 (\050)s 12 f 190.672 (\247)s 10 f 200.006 (G)s 11 f 657.837 y 209.441 (s)s 10 f 656.038 y 214.57 (;)s 219.903 (\264)s 1 f 226.292 (\051)s 10 f 230.959 (f)s 1 f 238.125 (\050)s 10 f 242.792 (\264)s 1 f 249.181 (\051)s 10 f 253.848 (d\272)s 11 f 651.083 y 266.785 (N)s 659.004 y 266.021 (\256)s 1 f 656.038 y 275.887 (\050)s 10 f 280.553 (\264)s 1 f 286.942 (\051)s 294.276 (+)s 10 f 647.919 y 307.716 (N)s 2 f 643.565 y 318.666 (2)s 14 f 323.449 (\241)s 11 f 330.949 (d)s 28.829 .48 307.716 653.277 r 10 f 664.269 y 317.63 (A)s 13 f 642.717 y 339.984 (D)s 645.192 y 347.318 (p)s 7.167 .48 359.318 645.192 r 10 f 656.038 y 359.318 (f)s 366.484 (;)s 1 f 371.818 (I)s 373.991 (L)s 2 f 650.804 y 381.491 (0)s 11 f 659.004 y 381.491 (N)s 13 f 645.192 y 390.593 (p)s 7.167 .48 402.593 645.192 r 10 f 656.038 y 402.593 (f)s 13 f 642.717 y 409.759 (E)s 11 f 664.438 y 417.093 (\256)s 13 f 642.717 y 425.931 (o)s 635.517 y 433.931 (\051)s 10 f 656.038 y 443.598 (:)s 1 f 705.976 y 223.045 (44)s do-end end endp %%Page: 45 45 %%BeginPageSetup initializepage (Raffaele Esposito; page: 45 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f0_12 sf ( )S -996 -1000 :M f1_12 sf ( )S -993 -1000 :M f2_12 sf ( )S -989 -1000 :M f10_12 sf ( )S -981 -1000 :M f11_12 sf ( )S -972 -1000 :M f12_12 sf ( )S -960 -1000 :M f13_12 sf ( )S -951 -1000 :M f14_12 sf ( )S -937 -1000 :M f15_12 sf ( )S -926 -1000 :M f16_12 sf ( )S -921 -1000 :M f17_12 sf ( )S -918 -1000 :M f18_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 1200 1000 div mul /CMBX10 findfont fdef 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 16 5 1200 1000 div mul /CMR5 findfont fdef 17 10 1200 1000 div mul /CMTI10 findfont fdef 18 5 1200 1000 div mul /CMSY5 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 6.31 y 8.71 (It)s 22.905 (has)s 45.5 (b)s 52.5 (een)s 75.028 (pro)s 92.062 (v)s 98.062 (en)s 115.257 (in)s 130.452 ([KLO],)s 171.813 ([KL])s 200.507 (that)s 227.702 (for)s 247.264 (an)s 259.597 (y)s 271.126 (p)s 278.126 (ositiv)s 306.192 (e)s 10 f 316.721 (\260)s 1 f 328.795 (and)s 353.323 (an)s 365.657 (y)s 377.185 (smo)s 398.252 (oth)s 420.78 (function)s 10 f 27.91 y -5.69 (G)s 12 f 7.078 (2)s 18.411 (C)s 2 f 23.555 y 25.43 (1)s 11 f 30.213 (;)s 2 f 33.063 (1)s 13 f 14.59 y 40.446 (\263)s 1 f 27.91 y 47.613 ([0)s 10 f 56.946 (;)s 62.28 (T)s 1 f 70.959 (])s 12 f 76.959 (\243)s 1 f 88.959 (I)s 88.132 (T)s 11 f 22.677 y 96.799 (d)s 13 f 14.59 y 102.394 (\264)s 1 f 27.91 y 113.561 (and)s 136.894 (an)s 149.228 (y)s 10 f 159.561 (\256)s 1 f 65.087 y 3.358 (lim)s 11 f 72.287 y -.841 (n)s 14 f 5.091 (!1)s 1 f 65.087 y 26.224 (lim)s 44.891 (sup)s 11 f 74.833 y 35.149 (\042)s 14 f 39.683 (!)s 2 f 49.25 (0)s 1 f 65.087 y 64.958 (lim)s 83.624 (sup)s 11 f 75.16 y 69.507 (N)s 14 f 78.008 (!1)s 13 f 89.427 y 47.159 (Z)s 11 f 92.393 y 59.159 (t)s 2 f 116.694 y 53.826 (0)s 10 f 105.76 y 65.384 (ds)s 13 f 85.24 y 77.255 (\050)s 1 f 105.76 y 102.017 (sup)s 15 f 114.409 y 103.352 (f)s 18 f 108.165 (\270)s 16 f 114.665 (0)s 13 f 117.165 y 90.362 (R)s 15 f 125.332 y 99.834 (f)s 104.646 (d\272)s 123.265 y 113.78 (N)s 127.768 y 113.357 (\256)s 16 f 125.332 y 121.489 (=1)s 13 f 92.44 y 135.179 (n)s 89.427 y 145.179 (Z)s 10 f 105.76 y 159.179 (Z)s 2 f 100.805 y 168.229 (1)s 11 f 108.727 y 167.371 (N)s 175.356 (;\042)s 1 f 105.76 y 183.339 (\050)s 10 f 188.006 (G)s 11 f 107.56 y 197.441 (s)s 10 f 105.76 y 202.57 (;)s 207.903 (\264)s 1 f 214.292 (\051)s 10 f 218.959 (f)s 1 f 226.126 (\050)s 10 f 230.792 (\264)s 1 f 237.181 (\051)s 10 f 241.848 (d\272)s 11 f 100.805 y 254.786 (N)s 108.727 y 254.022 (\256)s 1 f 105.76 y 263.887 (\050)s 10 f 268.554 (\264)s 1 f 274.943 (\051)s 282.276 (+)s 10 f 294.276 (\260)s 301.155 (N)s 2 f 100.805 y 312.105 (2)s 14 f 316.889 (\241)s 11 f 324.389 (d)s 13 f 92.44 y 331.984 (D)s 94.914 y 339.318 (p)s 7.167 .48 351.318 94.914 r 10 f 105.76 y 351.318 (f)s 358.484 (;)s 1 f 363.818 (I)s 365.991 (L)s 2 f 100.527 y 373.491 (0)s 11 f 108.727 y 373.491 (N)s 13 f 94.914 y 382.593 (p)s 7.167 .48 394.593 94.914 r 10 f 105.76 y 394.593 (f)s 13 f 92.44 y 401.759 (E)s 11 f 114.16 y 409.093 (\256)s 13 f 92.44 y 417.931 (o)s 85.24 y 425.931 (\051)s 1 f 105.76 y 438.931 (=)s 451.598 (0)s 10 f 457.598 (:)s 1 f 159.208 y -5.69 (That)s 24.31 (concludes)s 78.377 (the)s 99.043 (pro)s 116.743 (of)s 130.41 (of)s 144.077 (Lemma)s 186.91 (6.5.)s 8.16 .48 455.62 152.609 r .48 7.2 455.62 159.809 r .48 7.2 463.3 159.809 r 8.16 .48 455.62 160.289 r 17 f 176.129 y -5.69 (Pr)s 6.896 (o)s 12.416 (of)s 26.86 (of)s 41.304 (L)s 48.217 (emma)s 84.127 (6.6.)s 1 f 110.186 (Fix)s 132.053 (0)s 12 f 141.997 (\267)s 10 f 155.274 (k)s 12 f 165.843 (\267)s 10 f 179.12 (d)s 1 f 185.366 (.)s 195.132 (T)s 202.799 (o)s 213.165 (simplify)s 258.932 (the)s 279.965 (notation,)s 331.756 (for)s 350.49 (0)s 12 f 360.434 (\267)s 10 f 373.711 (m)s 12 f 388.191 (\267)s 10 f 401.468 (d)s 1 f 412.081 (denote)s 451.114 (b)s 457.447 (y)s 10 f 192.929 y -5.69 (\303)s 2 f 188.574 y 2.557 (1)s 1 f 192.929 y 11.94 (and)s 10 f 35.274 (\303)s 2 f 188.574 y 43.521 (2)s 11 f 48.304 (;m)s 1 f 192.929 y 64.27 (the)s 84.936 (cylinder)s 130.636 (functions)s 182.37 (\252)s 2 f 188.574 y 191.703 (1)s 1 f 192.929 y 200.42 (=)s 10 f 213.087 (r)s 2 f 194.728 y 218.5 (0)s 11 f 223.284 (;e)s 16 f 195.929 y 230.687 (1)s 1 f 192.929 y 239.97 (and)s 229.338 y 92.217 (\252)s 2 f 223.572 y 101.55 (2)s 11 f 106.334 (;m)s 232.958 y 101.55 (k)s 1 f 229.338 y 121.632 (=)s 13 f 216.018 y 134.299 (n)s 217.938 y 146.191 (X)s 11 f 244.879 y 144.299 (j)s 14 f 148.755 (2)s 2 f 155.222 (I)s 153.528 (T)s 15 f 242.105 y 160.378 (d)s 1 f 229.338 y 165.417 (\0501)s 10 f 176.083 (=)s 1 f 182.083 (2\051)s 13 f 219.618 y 194.75 (\241)s 12 f 229.338 y 200.25 (r)s 11 f 231.138 y 210.25 (j)s 214.19 (;j)s 2 f 221.496 (+)s 11 f 228.863 (e)s 15 f 232.338 y 233.416 (m)s 10 f 229.338 y 241.984 (F)s 11 f 224.384 y 251.367 (n;k)s 12 f 229.338 y 268.72 (\241)s 280.72 (r)s 11 f 231.138 y 290.72 (j)s 2 f 295.176 (+)s 11 f 302.543 (e)s 15 f 232.338 y 307.096 (m)s 11 f 231.138 y 315.064 (;j)s 10 f 229.338 y 322.97 (F)s 11 f 224.384 y 332.354 (n;k)s 13 f 219.618 y 347.04 (\242)s 216.018 y 354.54 (o)s 10 f 229.338 y 362.54 (:)s 1 f 278.588 y -5.69 (F)s 1.143 (or)s 16.416 (a)s 26.989 (cylinder)s 73.263 (function)s 120.836 (\252)s 134.743 (and)s 158.649 (a)s 169.222 (p)s 176.222 (ositiv)s 204.289 (e)s 214.195 (densit)s 245.262 (y)s 256.169 (0)s 12 f 266.457 (\267)s 10 f 280.079 (\275)s 12 f 290.572 (\267)s 1 f 304.194 (2,)s 318.243 (w)s 326.577 (e)s 336.483 (shall)s 365.123 (denote)s 404.363 (b)s 410.696 (y)s 13 f 275.555 y 422.936 (e)s 1 f 278.588 y 421.603 (\252)s 430.936 (\050)s 10 f 435.603 (\275)s 1 f 441.807 (\051)s 451.047 (its)s 295.388 y -5.69 (exp)s 12.977 (ectation)s 58.977 (with)s 86.31 (resp)s 108.077 (ect)s 127.41 (to)s 142.077 (the)s 162.743 (measure)s 10 f 209.51 (\272)s 11 f 291.034 y 216.202 (N)s 298.355 y 215.438 (\275)s 1 f 295.388 y 225.303 (.)s 312.308 y 8.71 (Observ)s 45.477 (e)s 55.117 (that)s 81.425 (for)s 100.099 (eac)s 116.432 (h)s 127.406 (0)s 12 f 137.252 (\267)s 10 f 150.431 (m)s 12 f 164.813 (\267)s 10 f 177.992 (d)s 1 f 188.545 (and)s 212.186 (all)s 229.16 (densit)s 260.226 (y)s 270.867 (0)s 12 f 280.713 (\267)s 10 f 293.892 (\275)s 12 f 303.942 (\267)s 1 f 317.121 (2,)s 13 f 309.275 y 332.172 (e)s 1 f 312.308 y 330.838 (\252)s 2 f 306.542 y 340.172 (2)s 11 f 344.955 (;m)s 315.928 y 340.172 (k)s 1 f 312.308 y 356.92 (\050)s 10 f 361.587 (\275)s 1 f 367.791 (\051)s 376.765 (can)s 399.073 (b)s 406.073 (e)s 415.713 (rewritten)s 329.108 y -5.69 (as)s 13 f 342.575 y 139.172 (e)s 1 f 345.608 y 137.839 (\252)s 2 f 339.842 y 147.172 (2)s 11 f 151.955 (;m)s 349.228 y 147.172 (k)s 1 f 345.608 y 163.921 (\050)s 10 f 168.587 (\275)s 1 f 174.792 (\051)s 182.792 (=)s 12 f 198.791 (\241)s 13 f 335.888 y 210.125 (\255)s 1 f 345.608 y 215.791 (2)s 10 f 221.791 (W)s 2 f 347.408 y 233.125 (0)s 11 f 237.908 (;e)s 15 f 348.608 y 245.311 (m)s 10 f 345.608 y 253.879 (;)s 259.213 (F)s 11 f 340.654 y 268.596 (n;k)s 13 f 335.888 y 283.282 (\256)s 11 f 350.408 y 288.949 (\275;)s 2 f 296.778 (0)s 1 f 371.23 y 186.792 (=)s 10 f 199.458 (\074)s 204.792 (\074)s 1 f 214.125 (2)s 10 f 220.125 (W)s 2 f 373.03 y 231.458 (0)s 11 f 236.242 (;e)s 15 f 374.23 y 243.645 (m)s 10 f 371.23 y 252.213 (;)s 1 f 257.546 (I)s 259.719 (L)s 2 f 365.997 y 267.219 (0)s 10 f 371.23 y 272.603 (F)s 11 f 366.275 y 281.986 (n;k)s 10 f 371.23 y 296.672 (\076)s 302.006 (\076)s 11 f 373.03 y 311.339 (\275)s 10 f 371.23 y 316.918 (:)s 1 f 396.953 y -5.69 (In)s 9.31 (particular,)s 68.043 (from)s 96.41 (Lemma)s 139.243 (6.8)s 158.577 (and)s 181.91 (using)s 213.31 (one)s 235.31 (and)s 258.644 (t)s 262.977 (w)s 271.31 (o)s 281.31 (blo)s 297.644 (c)s 302.644 (ks)s 317.71 (estimates,)s 373.844 (w)s 382.177 (e)s 391.511 (obtain)s 13 f 423.769 y 79.664 (\257)s 430.969 y 79.664 (\257)s 438.17 y 79.664 (\257)s 421.236 y 85.663 (Z)s 11 f 424.203 y 97.663 (T)s 2 f 448.503 y 92.33 (0)s 10 f 437.57 y 107.223 (Z)s 11 f 431.803 y 116.273 (F)s 15 f 428.182 y 123.651 (k)s 128.296 (;n)s 11 f 431.803 y 136.931 (;)s 2 f 139.781 (2)s 11 f 441.096 y 115.415 (N)s 123.4 (;\042)s 1 f 437.57 y 145.165 (\050)s 10 f 149.831 (G)s 11 f 439.37 y 159.266 (s)s 10 f 437.57 y 164.395 (;)s 169.729 (\264)s 11 f 439.37 y 175.687 (s)s 1 f 437.57 y 180.816 (\051)s 10 f 185.483 (ds)s 13 f 423.769 y 197.354 (\257)s 430.969 y 197.354 (\257)s 438.17 y 197.354 (\257)s 1 f 437.57 y 204.687 (=)s 13 f 423.769 y 217.354 (\257)s 430.969 y 217.354 (\257)s 438.17 y 217.354 (\257)s 421.236 y 223.354 (Z)s 11 f 424.203 y 235.354 (T)s 2 f 448.503 y 230.02 (0)s 13 f 434.536 y 247.105 (e)s 10 f 437.57 y 244.913 (Z)s 11 f 431.803 y 253.963 (F)s 15 f 428.182 y 261.341 (k)s 265.987 (;n)s 11 f 431.803 y 274.621 (;)s 2 f 277.471 (2)s 11 f 441.096 y 253.105 (N)s 261.09 (;\042)s 1 f 437.57 y 282.855 (\050)s 10 f 287.521 (G)s 11 f 439.37 y 296.956 (s)s 10 f 437.57 y 302.086 (;)s 307.419 (\264)s 11 f 439.37 y 313.377 (s)s 1 f 437.57 y 318.506 (\051)s 10 f 323.173 (ds)s 13 f 423.769 y 335.044 (\257)s 430.969 y 335.044 (\257)s 438.17 y 335.044 (\257)s 1 f 437.57 y 341.711 (+)s 10 f 353.711 (r)s 11 f 439.37 y 359.124 (N)s 367.109 (;\042)s 10 f 437.57 y 375.093 (;)s 1 f 476.013 y -5.69 (where)s 10 f 29.372 (r)s 11 f 477.813 y 34.786 (N)s 42.771 (;\042)s 1 f 476.013 y 55.117 (is)s 67.546 (a)s 77.909 (random)s 122.304 (v)s 127.971 (ariable)s 167.7 (suc)s 184.1 (h)s 195.129 (that)s 221.492 (its)s 238.587 (exp)s 257.254 (ectation)s 303.617 (with)s 331.312 (resp)s 353.079 (ect)s 372.775 (to)s 10 f 387.804 (P)s 11 f 478.38 y 395.508 (\271)s 15 f 475.98 y 401.343 (N)s 1 f 476.013 y 414.014 (con)s 431.68 (v)s 437.68 (erges)s 492.813 y -5.69 (to)s 8.976 (0)s 18.977 (as)s 10 f 33.71 (N)s 12 f 47.993 (\042)s 57.326 (1)s 1 f 73.326 (and)s 10 f 96.66 (\042)s 12 f 105.589 (#)s 1 f 114.922 (0)s 124.922 (and)s 13 f 533.203 y -3.499 (e)s 10 f 536.236 y -5.69 (Z)s 11 f 530.47 y 3.36 (F)s 15 f 526.848 y 10.737 (k)s 15.383 (;n)s 11 f 530.47 y 24.018 (;)s 2 f 26.868 (2)s 11 f 539.763 y 2.501 (N)s 10.486 (;\042)s 1 f 536.236 y 32.251 (\050)s 10 f 36.918 (G;)s 51.686 (\264)s 1 f 58.075 (\051)s 66.075 (=)s 10 f 78.742 (\257)s 86.163 (N)s 14 f 531.281 y 97.113 (\241)s 11 f 104.613 (d)s 13 f 524.836 y 113.57 (X)s 11 f 551.776 y 112.208 (i)s 14 f 115.603 (2)s 2 f 122.07 (I)s 120.377 (T)s 15 f 549.003 y 127.227 (d)s 10 f 536.236 y 134.265 (G)s 1 f 143.7 (\050)s 10 f 148.366 (i=)s 157.834 (N)s 1 f 168.784 (\051)s 13 f 515.716 y 173.451 (\050)s 11 f 521.236 y 192.952 (d)s 13 f 524.836 y 186.783 (X)s 11 f 550.25 y 185.117 (m)s 2 f 193.633 (=1)s 13 f 522.916 y 207.783 (\263)s 10 f 536.236 y 214.949 (@)s 11 f 538.036 y 221.32 (m)s 10 f 536.236 y 230.435 (J)s 12 f 240.91 (\244)s 10 f 249.577 (\274)s 11 f 531.281 y 256.848 (N)s 1 f 536.236 y 265.949 (\050)s 10 f 270.616 (\264)s 1 f 277.005 (\051\050)s 10 f 286.338 (i=)s 295.806 (N)s 1 f 306.756 (\051)s 13 f 522.916 y 311.423 (\264)s 318.589 (n)s 533.203 y 327.923 (e)s 1 f 536.236 y 326.589 (\252)s 2 f 531.281 y 335.923 (1)s 13 f 526.516 y 343.306 (\241)s 10 f 536.236 y 348.806 (\264)s 11 f 531.281 y 355.195 (N)s 363.697 (\042)s 1 f 536.236 y 368.83 (\050)s 10 f 373.497 (i)s 1 f 377.631 (\051)s 13 f 526.516 y 382.298 (\242)s 10 f 536.236 y 389.798 (\261)s 11 f 538.036 y 395.131 (k)s 400.435 (;m)s 12 f 575.812 y 255.335 (\241)s 1 f 264.668 (2)s 272.668 (\050)s 10 f 277.335 (\302D)s 11 f 577.612 y 294.778 (k)s 300.083 (;m)s 1 f 575.812 y 312.048 (\051)s 13 f 566.092 y 318.715 (\241)s 10 f 575.812 y 324.215 (\264)s 11 f 570.857 y 330.603 (N)s 339.105 (\042)s 1 f 575.812 y 344.239 (\050)s 10 f 348.906 (i)s 1 f 353.04 (\051)s 13 f 566.092 y 357.706 (\242)s 12 f 575.812 y 365.873 (\241)s 13 f 572.779 y 379.206 (e)s 1 f 575.812 y 377.873 (\252)s 2 f 570.045 y 387.206 (2)s 11 f 391.99 (;m)s 579.432 y 387.206 (k)s 13 f 566.092 y 405.955 (\241)s 10 f 575.812 y 411.455 (\264)s 11 f 570.857 y 417.844 (N)s 426.346 (\042)s 1 f 575.812 y 431.479 (\050)s 10 f 436.146 (i)s 1 f 440.28 (\051)s 13 f 566.092 y 444.947 (\242)s 562.492 y 452.447 (o)s 10 f 575.812 y 460.447 (:)s 1 f 607.109 y 8.71 (T)s 16.376 (o)s 26.376 (conclude)s 75.71 (the)s 96.377 (pro)s 114.077 (of)s 127.743 (w)s 136.077 (e)s 145.41 (just)s 169.143 (ha)s 181.477 (v)s 187.477 (e)s 196.81 (to)s 211.477 (apply)s 244.477 (Lemma)s 287.31 (6.7)s 306.644 (b)s 313.644 (elo)s 327.977 (w.)s 8.16 .48 455.62 600.509 r .48 7.2 455.62 607.709 r .48 7.2 463.3 607.709 r 8.16 .48 455.62 608.189 r 0 f 631.223 y -5.69 (Lemma)s 43.243 (6.7)s 17 f 69.476 (Ther)s 94.163 (e)s 103.976 (exists)s 136.836 (p)s 142.356 (ositive)s 180.075 (c)s 184.982 (onstant)s 10 f 227.915 (C)s 2 f 633.023 y 236.492 (0)s 17 f 631.223 y 246.168 (such)s 273.461 (that)s 297.994 (for)s 317.161 (e)s 322.068 (ach)s 1 f 344.147 (0)s 12 f 353.481 (\267)s 10 f 366.147 (m)s 12 f 380.017 (\267)s 10 f 392.683 (d)s 1 f 669.051 y 53.814 (sup)s 2 f 679.143 y 48.075 (0)s 14 f 52.858 (\267)s 11 f 60.358 (\275)s 14 f 65.337 (\267)s 2 f 72.837 (2)s 13 f 655.251 y 79.62 (\257)s 662.451 y 79.62 (\257)s 669.651 y 79.62 (\257)s 12 f 669.051 y 85.62 (h)s 10 f 90.287 (r)s 2 f 670.851 y 95.701 (0)s 11 f 100.484 (;e)s 16 f 672.051 y 107.887 (1)s 12 f 669.051 y 113.17 (i)s 11 f 673.085 y 117.837 (\275)s 10 f 669.051 y 125.416 (\261)s 11 f 670.851 y 130.749 (k)s 136.053 (;m)s 12 f 669.051 y 150.685 (\241)s 1 f 162.685 (2)s 10 f 168.685 (\302)s 1 f 176.193 (\050)s 10 f 180.86 (\275)s 1 f 187.064 (\051)s 10 f 191.731 (D)s 11 f 670.851 y 201.666 (k)s 206.97 (;m)s 1 f 669.051 y 218.936 (\050)s 10 f 223.602 (\275)s 1 f 229.806 (\051)s 12 f 237.14 (\241)s 1 f 249.14 (2)s 10 f 255.14 (\074)s 260.473 (\074)s 269.806 (W)s 2 f 670.851 y 281.14 (0)s 11 f 285.923 (;e)s 15 f 672.051 y 293.326 (m)s 10 f 669.051 y 301.894 (;)s 1 f 307.228 (I)s 309.401 (L)s 2 f 663.818 y 316.901 (0)s 10 f 669.051 y 322.284 (F)s 11 f 664.097 y 331.668 (k)s 336.972 (;n)s 10 f 669.051 y 346.354 (\076)s 351.687 (\076)s 11 f 670.851 y 361.021 (\275)s 13 f 655.251 y 366.599 (\257)s 662.451 y 366.599 (\257)s 669.651 y 366.599 (\257)s 12 f 669.051 y 373.933 (\267)s 10 f 660.933 y 389.661 (C)s 2 f 662.733 y 398.237 (0)s 17.203 .48 388.039 666.291 r 12 f 668.691 y 388.039 (p)s 7.203 .48 398.039 668.691 r 10 f 677.335 y 398.039 (n)s 669.051 y 406.682 (:)s 1 f 705.976 y 223.045 (45)s do-end end endp %%Page: 46 46 %%BeginPageSetup initializepage (Raffaele Esposito; page: 46 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f0_12 sf ( )S -996 -1000 :M f1_12 sf ( )S -993 -1000 :M f2_12 sf ( )S -989 -1000 :M f10_12 sf ( )S -981 -1000 :M f11_12 sf ( )S -972 -1000 :M f12_12 sf ( )S -960 -1000 :M f13_12 sf ( )S -951 -1000 :M f14_12 sf ( )S -937 -1000 :M f15_12 sf ( )S -926 -1000 :M f16_12 sf ( )S -921 -1000 :M f17_12 sf ( )S -918 -1000 :M f18_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 1200 1000 div mul /CMBX10 findfont fdef 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 16 5 1200 1000 div mul /CMR5 findfont fdef 17 10 1200 1000 div mul /CMTI10 findfont fdef 18 5 1200 1000 div mul /CMSY5 findfont fdef 58 60 translate 72 72.27 div dup scale 17 f 23.23 y -5.69 (Pr)s 6.896 (o)s 12.416 (of.)s 1 f 31.243 (Using)s 64.976 (\0506.10\051,)s 102.976 (a)s 112.976 (it)s 124.976 (is)s 137.043 (easy)s 163.443 (to)s 178.11 (sho)s 195.177 (w)s 207.843 (that)s 13 f 44.324 y 52.326 (\257)s 51.524 y 52.326 (\257)s 58.724 y 52.326 (\257)s 12 f 58.124 y 58.325 (h)s 10 f 62.992 (r)s 2 f 59.924 y 68.406 (0)s 11 f 73.189 (;e)s 16 f 61.124 y 80.592 (1)s 12 f 58.124 y 85.876 (i)s 11 f 62.158 y 90.542 (\275)s 10 f 58.124 y 98.121 (\261)s 11 f 59.924 y 103.455 (k)s 108.759 (;m)s 12 f 58.124 y 123.391 (\241)s 1 f 135.391 (2)s 10 f 141.391 (\302)s 1 f 148.899 (\050)s 10 f 153.566 (\275)s 1 f 159.77 (\051)s 10 f 164.436 (D)s 11 f 59.924 y 174.371 (k)s 179.676 (;m)s 1 f 58.124 y 191.641 (\050)s 10 f 196.308 (\275)s 1 f 202.512 (\051)s 12 f 209.845 (\241)s 1 f 221.845 (2)s 10 f 227.845 (\074)s 233.179 (\074)s 242.512 (W)s 2 f 59.924 y 253.845 (0)s 11 f 258.629 (;e)s 15 f 61.124 y 266.032 (m)s 10 f 58.124 y 274.6 (;)s 1 f 279.933 (I)s 282.106 (L)s 2 f 52.891 y 289.606 (0)s 10 f 58.124 y 294.99 (F)s 11 f 53.17 y 304.373 (k)s 309.677 (;n)s 10 f 58.124 y 319.059 (\076)s 324.393 (\076)s 11 f 59.924 y 333.726 (\275)s 13 f 44.324 y 339.305 (\257)s 51.524 y 339.305 (\257)s 58.724 y 339.305 (\257)s 1 f 96.358 y 79.659 (=)s 13 f 82.558 y 92.325 (\257)s 89.758 y 92.325 (\257)s 96.958 y 92.325 (\257)s 10 f 96.358 y 96.325 (\074)s 101.659 (\074)s 1 f 110.992 (2)s 10 f 116.992 (W)s 2 f 98.158 y 128.326 (0)s 11 f 133.109 (;m)s 10 f 96.358 y 145.074 (;)s 150.408 (W)s 2 f 98.158 y 161.741 (0)s 11 f 166.524 (;e)s 15 f 99.431 y 173.927 (k)s 1 f 96.358 y 182.44 (+)s 11 f 81.358 y 200.609 (d)s 13 f 84.958 y 194.44 (X)s 11 f 110.371 y 194.674 (r)s 2 f 199.388 (=1)s 10 f 96.358 y 213.773 (D)s 11 f 98.158 y 223.708 (k)s 229.012 (;r)s 1 f 96.358 y 237.176 (\050)s 10 f 241.843 (\275)s 1 f 248.047 (\051)s 254.714 ([)s 10 f 258.047 (\264)s 1 f 264.436 (\050)s 10 f 269.102 (e)s 11 f 98.158 y 274.69 (r)s 1 f 96.358 y 280.004 (\051)s 12 f 287.337 (\241)s 10 f 299.337 (\264)s 1 f 305.726 (\0500\051])s 12 f 327.059 (\241)s 1 f 339.059 (I)s 341.233 (L)s 2 f 91.124 y 348.733 (0)s 10 f 96.358 y 354.116 (F)s 11 f 91.403 y 363.499 (k)s 368.804 (;n)s 10 f 96.358 y 378.186 (\076)s 383.519 (\076)s 11 f 98.158 y 392.852 (\275)s 13 f 82.558 y 398.431 (\257)s 89.758 y 398.431 (\257)s 96.958 y 398.431 (\257)s 10 f 96.358 y 402.431 (:)s 1 f 137.999 y -5.69 (By)s 13.143 (Sc)s 24.81 (h)s 31.143 (w)s 39.477 (artz)s 64.177 (inequalit)s 109.51 (y)s 119.843 (the)s 140.51 (righ)s 160.877 (t)s 169.543 (hand)s 199.544 (side)s 223.61 (of)s 237.277 (the)s 257.944 (last)s 280.677 (expression)s 338.51 (is)s 350.577 (b)s 357.577 (ounded)s 399.577 (b)s 405.911 (y)s 13 f 170.231 y 38.921 (p)s 68.994 .48 50.921 170.231 r 10 f 180.46 y 50.921 (\074)s 56.254 (\074)s 1 f 65.588 (2)s 10 f 71.588 (W)s 2 f 182.26 y 82.921 (0)s 11 f 87.704 (;m)s 10 f 180.46 y 99.67 (\076)s 105.003 (\076)s 11 f 182.26 y 114.337 (\275)s 12 f 180.46 y 122.582 (\243)s 13 f 167.14 y 134.582 (\263)s 10 f 180.46 y 141.749 (\074)s 147.082 (\074)s 156.415 (W)s 2 f 182.26 y 167.749 (0)s 11 f 172.532 (;e)s 15 f 183.533 y 179.935 (k)s 1 f 180.46 y 188.448 (+)s 11 f 165.46 y 206.617 (d)s 13 f 169.06 y 200.448 (X)s 11 f 194.473 y 200.682 (r)s 2 f 205.396 (=1)s 10 f 180.46 y 219.781 (D)s 11 f 182.26 y 229.716 (k)s 235.02 (;r)s 1 f 180.46 y 243.184 (\050)s 10 f 247.851 (\275)s 1 f 254.055 (\051)s 260.721 ([)s 10 f 264.055 (\264)s 1 f 270.444 (\050)s 10 f 275.11 (e)s 11 f 182.26 y 280.698 (r)s 1 f 180.46 y 286.012 (\051)s 12 f 293.345 (\241)s 10 f 305.345 (\264)s 1 f 311.734 (\0500\051])s 12 f 333.067 (\241)s 1 f 345.067 (I)s 347.241 (L)s 2 f 175.227 y 354.741 (0)s 10 f 180.46 y 360.124 (F)s 11 f 175.505 y 369.507 (k)s 374.811 (;n)s 10 f 180.46 y 384.193 (\076)s 389.527 (\076)s 11 f 182.26 y 398.86 (\275)s 13 f 167.14 y 404.439 (\264)s 16 f 166.402 y 413.046 (1)s 4.083 .48 413.046 167.767 r 172.518 y 413.046 (2)s 1 f 223.371 y -5.69 (whic)s 17.976 (h)s 28.643 (is)s 40.71 (b)s 47.71 (ounded)s 89.71 (b)s 96.043 (y)s 10 f 106.377 (C)s 2 f 225.171 y 114.953 (0)s 10 f 223.371 y 120.337 (=)s 12 f 214.728 y 126.337 (p)s 7.203 .48 136.337 214.728 r 10 f 223.371 y 136.337 (n)s 1 f 147.54 (for)s 165.906 (some)s 195.973 (p)s 202.973 (ositiv)s 231.04 (e)s 240.373 (constan)s 280.106 (t)s 10 f 288.773 (C)s 2 f 225.171 y 297.35 (0)s 1 f 223.371 y 302.733 (.)s 8.16 .48 455.62 216.771 r .48 7.2 455.62 223.971 r .48 7.2 463.3 223.971 r 8.16 .48 455.62 224.451 r 240.291 y 8.71 (W)s 20.043 (e)s 29.06 (no)s 41.393 (w)s 53.743 (pro)s 70.776 (v)s 76.776 (e)s 85.793 (some)s 115.543 (estimates)s 168.026 (on)s 184.376 (the)s 204.726 (Diric)s 230.26 (hlet)s 253.943 (forms)s 286.726 (for)s 304.776 (the)s 325.126 (pro)s 342.826 (cess)s 366.643 (at)s 10 f 380.993 (\257)s 12 f 391.747 (6)s 1 f 391.747 (=)s 404.414 (0)s 414.097 (needed)s 453.78 (in)s 257.091 y -5.69 (the)s 14.976 (pro)s 32.677 (of)s 46.343 (of)s 60.01 (Theo)s 87.01 (em)s 106.343 (6.4)s 125.677 (and)s 149.01 (in)s 163.01 (the)s 183.677 (pro)s 201.377 (of)s 215.044 (of)s 228.71 (one)s 250.71 (and)s 274.044 (t)s 278.377 (w)s 286.71 (o)s 296.71 (blo)s 313.044 (cs)s 327.11 (estimates.)s 0 f 287.92 y -5.69 (Lemma)s 43.998 (6.8)s 17 f 71.643 (Ther)s 96.33 (e)s 106.747 (exists)s 140.211 (p)s 145.731 (ositive)s 184.055 (c)s 188.962 (onstant)s 10 f 232.499 (C)s 2 f 289.72 y 241.076 (1)s 17 f 287.92 y 251.356 (such)s 279.254 (that)s 304.391 (for)s 324.162 (every)s 356.506 (pr)s 367.086 (ob)s 378.126 (ability)s 414.916 (density)s 10 f 456.614 (f)s 17 f 304.72 y -5.69 (with)s 20.376 (r)s 24.823 (esp)s 40.769 (e)s 45.676 (ct)s 59.476 (to)s 10 f 73.889 (\272)s 11 f 300.365 y 80.581 (N)s 307.686 y 79.817 (\256)s 10 f 341.632 y 74.898 (N)s 2 f 336.677 y 85.848 (2)s 13 f 328.312 y 93.232 (D)s 330.786 y 100.565 (p)s 7.167 .48 112.565 330.786 r 10 f 341.632 y 112.565 (f)s 119.732 (;)s 1 f 125.065 (I)s 127.238 (L)s 11 f 335.865 y 134.738 (\257)s 345.159 y 134.738 (N)s 13 f 330.786 y 143.84 (p)s 7.167 .48 155.84 330.786 r 10 f 341.632 y 155.84 (f)s 13 f 328.312 y 163.007 (E)s 11 f 350.032 y 170.34 (\272)s 15 f 347.632 y 175.711 (N)s 352.432 y 175.151 (\256)s 12 f 341.632 y 190.686 (\267)s 1 f 333.514 y 208.126 (1)s 6 .48 208.126 338.872 r 349.863 y 208.126 (2)s 10 f 341.632 y 215.566 (N)s 2 f 336.677 y 226.516 (2)s 13 f 328.312 y 233.899 (D)s 330.786 y 241.232 (p)s 7.167 .48 253.232 330.786 r 10 f 341.632 y 253.232 (f)s 260.399 (;)s 1 f 265.732 (I)s 267.906 (L)s 2 f 336.399 y 275.406 (0)s 11 f 344.599 y 275.406 (N)s 13 f 330.786 y 284.507 (p)s 7.167 .48 296.507 330.786 r 10 f 341.632 y 296.507 (f)s 13 f 328.312 y 303.674 (E)s 11 f 350.032 y 311.007 (\272)s 15 f 347.632 y 316.378 (N)s 352.432 y 315.819 (\256)s 1 f 341.632 y 330.687 (+)s 10 f 346.02 (C)s 2 f 343.432 y 354.596 (1)s 10 f 341.632 y 359.98 (N)s 11 f 336.677 y 370.93 (d)s 10 f 341.632 y 379.858 (:)s 17 f 388.646 y -5.69 (Pr)s 6.896 (o)s 12.416 (of.)s 1 f 31.243 (Fix)s 52.743 (a)s 62.743 (probabilit)s 113.776 (y)s 124.11 (densit)s 155.177 (y)s 10 f 165.51 (f)s 1 f 172.677 (.)s 181.343 (A)s 194.343 (simple)s 231.743 (computation)s 301.744 (sho)s 318.81 (ws)s 336.21 (that)s 10 f 422.874 y 15.848 (N)s 2 f 417.92 y 26.798 (2)s 13 f 409.554 y 34.181 (D)s 412.028 y 41.515 (p)s 7.167 .48 53.515 412.028 r 10 f 422.874 y 53.515 (f)s 60.681 (;)s 1 f 66.015 (I)s 68.188 (L)s 11 f 417.108 y 75.688 (\257)s 426.401 y 75.688 (N)s 13 f 412.028 y 84.79 (p)s 7.167 .48 96.79 412.028 r 10 f 422.874 y 96.79 (f)s 13 f 409.554 y 103.956 (E)s 11 f 431.274 y 111.29 (\272)s 15 f 428.874 y 116.661 (N)s 433.674 y 116.101 (\256)s 1 f 422.874 y 128.302 (=)s 10 f 140.969 (N)s 2 f 417.92 y 151.919 (2)s 13 f 409.554 y 159.302 (D)s 412.028 y 166.636 (p)s 7.167 .48 178.636 412.028 r 10 f 422.874 y 178.636 (f)s 185.802 (;)s 1 f 191.136 (I)s 193.309 (L)s 2 f 417.641 y 200.809 (0)s 11 f 425.841 y 200.809 (N)s 13 f 412.028 y 209.911 (p)s 7.167 .48 221.911 412.028 r 10 f 422.874 y 221.911 (f)s 13 f 409.554 y 229.077 (E)s 11 f 431.274 y 236.411 (\272)s 15 f 428.874 y 241.781 (N)s 433.674 y 241.222 (\256)s 1 f 458.408 y 66.515 (+)s 450.29 y 79.955 (1)s 6 .48 79.955 455.648 r 466.639 y 79.955 (2)s 13 f 447.008 y 96.835 (X)s 15 f 473.596 y 93.454 (i;j)s 18 f 103.288 (2)s 16 f 108.955 (I)s 106.762 (T)s 15 f 471.175 y 112.512 (d)s 18 f 480.702 y 90.835 (j)s 15 f 93.585 (i)s 18 f 96.786 (\241)s 15 f 103.286 (j)s 18 f 107.169 (j)s 16 f 109.919 (=1)s 13 f 442.074 y 123.609 (Z)s 10 f 458.408 y 137.609 (r)s 11 f 460.208 y 143.023 (i;j)s 13 f 445.088 y 154.325 (h)s 1 f 458.408 y 159.991 (1)s 12 f 168.658 (\241)s 1 f 180.658 (\251)s 13 f 448.688 y 191.324 (\251)s 10 f 458.408 y 198.325 (\257)s 13 f 448.688 y 207.745 (\241)s 12 f 458.408 y 213.245 (r)s 11 f 453.453 y 223.245 (i;j)s 10 f 458.408 y 234.547 (H)s 11 f 460.208 y 244.522 (N)s 13 f 448.688 y 253.623 (\242)s 1 f 458.408 y 261.123 (\050)s 10 f 265.79 (\264)s 1 f 272.179 (\051)s 13 f 448.688 y 276.846 (\252)s 445.088 y 285.846 (i)s 447.562 y 291.512 (p)s 7.167 .48 303.512 447.562 r 10 f 458.408 y 303.512 (f)s 13 f 445.088 y 312.679 (h)s 12 f 458.408 y 318.346 (r)s 11 f 460.208 y 328.346 (i;j)s 13 f 447.562 y 339.647 (p)s 7.167 .48 351.647 447.562 r 10 f 458.408 y 351.647 (f)s 13 f 445.088 y 362.814 (i)s 1 f 458.408 y 370.481 (\050)s 10 f 375.147 (\264)s 1 f 381.536 (\051)s 10 f 386.203 (d\272)s 11 f 453.453 y 399.14 (N)s 461.374 y 398.376 (\256)s 10 f 458.408 y 408.242 (:)s 1 f 449.238 y 433.113 (\0506)s 10 f 443.78 (:)s 1 f 447.114 (14\051)s 509.83 y -5.69 (Recall)s 30.477 (that,)s 59.81 (b)s 66.143 (y)s 76.477 (Lemma)s 119.31 (6.9)s 138.643 (b)s 145.643 (elo)s 159.977 (w)s 13 f 529.725 y 136.221 (\257)s 536.925 y 136.221 (\257)s 1 f 539.925 y 140.221 (1)s 12 f 148.888 (\241)s 1 f 160.888 (\251)s 13 f 530.205 y 171.554 (\251)s 10 f 539.925 y 178.554 (\257)s 13 f 530.205 y 187.975 (\241)s 12 f 539.925 y 193.475 (r)s 11 f 534.97 y 203.475 (i;j)s 10 f 539.925 y 214.777 (H)s 11 f 541.725 y 224.752 (N)s 13 f 530.205 y 233.853 (\242)s 1 f 539.925 y 241.353 (\050)s 10 f 246.02 (\264)s 1 f 252.409 (\051)s 13 f 530.205 y 257.076 (\252)s 529.725 y 264.076 (\257)s 536.925 y 264.076 (\257)s 12 f 539.925 y 271.409 (\267)s 10 f 284.076 (C)s 2 f 541.725 y 292.652 (2)s 10 f 539.925 y 298.036 (N)s 14 f 534.97 y 308.985 (\241)s 2 f 316.486 (1)s 1 f 570.019 y -5.69 (for)s 13.214 (some)s 43.819 (p)s 50.819 (ositiv)s 78.886 (e)s 88.757 (constan)s 128.49 (t)s 10 f 137.695 (C)s 2 f 571.819 y 146.271 (2)s 1 f 570.019 y 151.655 (.)s 161.935 (T)s 169.601 (o)s 180.139 (conclude)s 230.011 (the)s 251.215 (pro)s 268.915 (of)s 283.12 (of)s 297.324 (the)s 318.529 (lemma)s 357.733 (it)s 370.271 (remains)s 415.576 (to)s 430.78 (b)s 437.78 (ound)s 586.819 y -5.69 (the)s 14.976 (second)s 53.71 (term)s 82.41 (of)s 96.077 (the)s 116.743 (righ)s 137.11 (t)s 145.777 (hand)s 175.777 (side)s 199.843 (of)s 213.51 (\0506.14\051)s 248.177 (b)s 254.51 (y)s 12 f 621.713 y 136.565 (\241)s 1 f 145.899 (\050)s 10 f 150.565 (N)s 2 f 616.759 y 161.515 (2)s 10 f 621.713 y 166.899 (=)s 1 f 172.899 (2\051)s 13 f 608.393 y 185.565 (D)s 610.868 y 192.899 (p)s 7.167 .48 204.899 610.868 r 10 f 621.713 y 204.899 (f)s 212.065 (;)s 1 f 217.399 (I)s 219.572 (L)s 2 f 616.48 y 227.072 (0)s 11 f 624.68 y 227.072 (N)s 13 f 610.868 y 236.174 (p)s 7.167 .48 248.174 610.868 r 10 f 621.713 y 248.174 (f)s 13 f 608.393 y 255.34 (E)s 11 f 630.114 y 262.674 (\272)s 15 f 627.714 y 268.045 (N)s 632.514 y 267.485 (\256)s 1 f 621.713 y 279.02 (+)s 10 f 291.019 (C)s 2 f 623.513 y 299.596 (2)s 10 f 621.713 y 304.979 (N)s 11 f 616.759 y 315.929 (d)s 1 f 660.376 y -5.69 (using)s 25.288 (the)s 45.532 (inequalities)s 108.177 (2)s 10 f 114.177 (xy)s 12 f 130.682 (\267)s 10 f 143.349 (ax)s 2 f 656.021 y 156.551 (2)s 1 f 660.376 y 163.756 (+)s 10 f 174.912 (a)s 14 f 656.021 y 181.255 (\241)s 2 f 188.755 (1)s 10 f 660.376 y 194.138 (y)s 2 f 656.021 y 200.452 (2)s 1 f 660.376 y 209.414 (for)s 227.358 (all)s 10 f 243.603 (a)s 253.279 (\076)s 1 f 265.946 (0)s 275.524 (and)s 298.435 (the)s 318.679 (fact)s 341.924 (that)s 10 f 367.502 (f)s 1 f 378.247 (is)s 389.891 (a)s 399.469 (densit)s 430.536 (y)s 440.447 (with)s 677.176 y -5.69 (resp)s 16.076 (ect)s 35.41 (to)s 10 f 50.077 (\272)s 11 f 672.821 y 56.768 (N)s 680.143 y 56.004 (\256)s 1 f 677.176 y 65.87 (.)s 8.16 .48 455.62 670.576 r .48 7.2 455.62 677.776 r .48 7.2 463.3 677.776 r 8.16 .48 455.62 678.256 r 705.976 y 223.045 (46)s do-end end endp %%Page: 47 47 %%BeginPageSetup initializepage (Raffaele Esposito; page: 47 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f0_12 sf ( )S -996 -1000 :M f1_12 sf ( )S -993 -1000 :M f2_12 sf ( )S -989 -1000 :M f10_12 sf ( )S -981 -1000 :M f11_12 sf ( )S -972 -1000 :M f12_12 sf ( )S -960 -1000 :M f13_12 sf ( )S -951 -1000 :M f14_12 sf ( )S -937 -1000 :M f15_12 sf ( )S -926 -1000 :M f17_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 1200 1000 div mul /CMBX10 findfont fdef 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 17 10 1200 1000 div mul /CMTI10 findfont fdef 58 60 translate 72 72.27 div dup scale 0 f 6.31 y -5.69 (Lemma)s 43.243 (6.9)s 17 f 69.476 (F)s 76.389 (or)s 91.876 (al)s 101.689 (l)s 10 f 109.049 (i)s 12 f 116.517 (2)s 1 f 127.85 (I)s 127.023 (T)s 11 f 1.076 y 135.69 (d)s 17 f 6.31 y 141.285 (,)s 149.259 (unit)s 174.405 (ve)s 184.832 (ctor)s 10 f 209.825 (e)s 12 f 218.745 (2)s 1 f 230.079 (I)s 229.252 (T)s 11 f 1.076 y 237.919 (d)s 17 f 6.31 y 247.807 (and)s 10 f 271.114 (\264)s 12 f 280.836 (2)s 1 f 292.169 (X)s 293.969 (X)s 11 f 8.11 y 302.969 (N)s 10 f 51.041 y 42.51 (C)s 11 f 45.274 y 51.945 (\257)s 54.568 y 51.087 (N)s 1 f 51.041 y 60.189 (\050)s 10 f 64.855 (i;)s 74.323 (i)s 1 f 81.124 (+)s 10 f 93.124 (e)s 1 f 98.711 (;)s 10 f 104.044 (\264)s 1 f 110.433 (\051)s 118.433 (=)s 131.1 (1)s 139.766 (+)s 13 f 37.721 y 151.766 (n)s 10 f 51.041 y 159.766 (\257)s 167.187 (N)s 14 f 46.086 y 178.137 (\241)s 11 f 185.637 (d)s 14 f 190.633 (\241)s 2 f 198.133 (1)s 13 f 39.641 y 207.408 (X)s 11 f 66.581 y 205.516 (j)s 14 f 209.972 (2)s 2 f 216.439 (I)s 214.746 (T)s 15 f 63.808 y 221.596 (d)s 1 f 51.041 y 228.634 (\050)s 10 f 233.301 (e)s 12 f 241.555 (\242)s 247.555 (r)s 10 f 257.555 (J)s 1 f 265.363 (\051)s 13 f 41.321 y 272.03 (\241)s 1 f 51.041 y 277.53 (\050)s 10 f 282.196 (i)s 12 f 288.997 (\241)s 10 f 300.997 (j)s 1 f 306.626 (\051)s 10 f 311.292 (=)s 316.626 (N)s 13 f 41.321 y 327.576 (\242)s 10 f 51.041 y 333.076 (\264)s 1 f 339.465 (\050)s 10 f 344.131 (j)s 1 f 349.76 (\051)s 13 f 37.721 y 354.426 (o)s 1 f 51.041 y 365.093 (+)s 10 f 377.093 (O)s 1 f 386.58 (\050)s 10 f 391.246 (N)s 2 f 46.086 y 402.196 (2)s 1 f 51.041 y 407.58 (\051)s 10 f 412.246 (:)s 17 f 167.962 y 8.71 (A)s 17.016 (cknow)s 49.523 (le)s 57.496 (dgments)s 1 f 100.123 (.)s 108.524 (W)s 119.857 (e)s 128.395 (w)s 136.729 (ould)s 162.6 (lik)s 175.267 (e)s 183.805 (to)s 197.676 (thank)s 231.214 (R.)s 246.585 (Esp)s 266.485 (osito)s 294.423 (and)s 316.961 (E.)s 331.666 (Presutti)s 377.137 (for)s 394.709 (useful)s 428.313 (discus-)s 184.762 y -5.69 (sions.)s 28.991 (R.)s 45.34 (M.)s 63.856 (is)s 76.105 (indebted)s 125.621 (to)s 140.47 (G.B.)s 169.236 (Giacomin)s 223.502 (for)s 242.051 (sending)s 285.634 (his)s 304.55 (preliminary)s 369.132 (notes)s 400.715 (on)s 417.564 (a)s 427.747 (related)s 201.562 y -5.69 (lattice)s 32.03 (gas)s 53.818 (mo)s 70.151 (del.)s 97.313 (R.)s 114.533 (M.)s 133.92 (w)s 142.254 (ould)s 169.974 (lik)s 182.641 (e)s 193.028 (to)s 208.749 (thank)s 244.136 (J.)s 258.69 (L.)s 274.577 (Leb)s 294.411 (o)s 300.077 (witz)s 327.131 (for)s 346.552 (bringing)s 394.972 (to)s 410.693 (her)s 432.447 (atten-)s 218.362 y -5.69 (tion)s 19.489 (the)s 40.669 (Blume-Cap)s 100.169 (el)s 113.348 (mo)s 129.681 (del.)s 155.22 (M.M.)s 188.399 (w)s 196.732 (ould)s 223.912 (lik)s 236.578 (e)s 246.424 (to)s 261.604 (thank)s 296.45 (the)s 317.629 (v)s 323.629 (ery)s 344.509 (kind)s 372.021 (hospitalit)s 421.088 (y)s 431.934 (at)s 447.114 (the)s 235.162 y -5.69 (Univ)s 19.31 (ersit)s 41.743 (y)s 52.077 (of)s 65.743 (Roma)s 100.577 (T)s 108.243 (or)s 122.943 (V)s 130.943 (ergata)s 167.643 (and)s 190.977 (R.)s 207.143 (M.)s 225.477 (the)s 246.144 (hospilatit)s 295.21 (y)s 305.544 (of)s 319.21 (the)s 339.877 (Univ)s 364.877 (ersit)s 387.31 (y)s 397.644 (of)s 411.311 (Rouen.)s 0 f 290.736 y -5.69 (App)s 20.46 (endix.)s 312.166 y -5.69 (Pro)s 16.71 (of)s 32.426 (of)s 48.143 (\0505.1\051)s 1 f 80.509 (F)s 87.343 (or)s 102.043 (1)s 12 f 111.376 (\267)s 10 f 124.043 (k)s 12 f 134.001 (\267)s 10 f 146.667 (d)s 1 f 152.913 (,)s 160.247 (w)s 168.58 (e)s 177.913 (ha)s 190.247 (v)s 196.247 (e)s 11 f 354.931 y 17.581 (d)s 13 f 358.531 y 11.412 (X)s 11 f 384.364 y 11.352 (k)s 2 f 16.656 (=1)s 13 f 359.731 y 30.806 (\257)s 366.931 y 30.806 (\257)s 10 f 369.931 y 34.806 (@)s 11 f 371.731 y 41.177 (k)s 10 f 369.931 y 47.081 (h)s 11 f 371.731 y 53.995 (t)s 2 f 57.62 (+)s 11 f 64.987 (\042)s 14 f 69.521 (\241)s 11 f 77.021 (s)s 1 f 369.931 y 82.15 (\050)s 10 f 86.817 (x)s 1 f 93.675 (\051)s 13 f 359.731 y 98.342 (\257)s 366.931 y 98.342 (\257)s 1 f 369.931 y 105.675 (=)s 13 f 360.211 y 118.341 (\241)s 1 f 369.931 y 123.841 (2)s 10 f 129.841 (\274)s 1 f 137.112 (\050)s 10 f 141.779 (t)s 1 f 148.779 (+)s 10 f 160.779 (\042)s 12 f 169.041 (\241)s 10 f 181.041 (s)s 1 f 186.666 (\051)s 13 f 360.211 y 191.333 (\242)s 14 f 362.697 y 196.833 (\241)s 11 f 204.333 (d=)s 2 f 214.245 (2)s 1 f 369.931 y 221.628 (exp)s 13 f 349.411 y 241.962 (\050)s 12 f 369.931 y 254.295 (\241)s 1 f 361.813 y 295.679 (1)s 61.887 .48 267.735 367.171 r 378.811 y 267.735 (8)s 13 f 369.091 y 273.735 (\241)s 10 f 378.811 y 279.235 (t)s 1 f 286.235 (+)s 10 f 298.235 (\042)s 12 f 306.497 (\241)s 10 f 318.497 (s)s 13 f 369.091 y 324.122 (\242)s 12 f 369.931 y 331.062 (k)s 10 f 337.062 (x)s 12 f 343.921 (k)s 2 f 364.976 y 349.921 (2)s 13 f 349.411 y 355.304 (\051)s 12 f 369.931 y 367.637 (\243)s 1 f 361.813 y 405.521 (1)s 54.887 .48 381.077 367.171 r 12 f 369.571 y 381.077 (p)s 44.887 .48 391.077 369.571 r 10 f 378.821 y 391.077 (t)s 1 f 398.077 (+)s 10 f 410.077 (\042)s 12 f 418.34 (\241)s 10 f 430.34 (s)s 12 f 369.931 y 437.405 (\243)s 414.964 y 177.008 (\243)s 13 f 397.684 y 192.771 (P)s 11 f 400.651 y 205.438 (d)s 410.284 y 205.438 (k)s 2 f 210.742 (=1)s 12 f 406.684 y 225.492 (j)s 10 f 228.826 (x)s 11 f 408.484 y 235.684 (i)s 12 f 406.684 y 239.679 (j)s 54.887 .48 190.448 412.204 r 414.604 y 190.448 (p)s 44.887 .48 200.448 414.604 r 10 f 423.855 y 200.448 (t)s 1 f 207.448 (+)s 10 f 219.448 (\042)s 12 f 227.711 (\241)s 10 f 239.711 (s)s 1 f 414.964 y 248.775 (exp)s 13 f 394.444 y 269.109 (\050)s 12 f 414.964 y 281.442 (\241)s 1 f 406.846 y 322.826 (1)s 61.887 .48 294.882 412.204 r 423.844 y 294.882 (8)s 13 f 414.124 y 300.882 (\241)s 10 f 423.844 y 306.382 (t)s 1 f 313.382 (+)s 10 f 325.382 (\042)s 12 f 333.644 (\241)s 10 f 345.644 (s)s 13 f 414.124 y 351.269 (\242)s 12 f 414.964 y 358.209 (k)s 10 f 364.209 (x)s 12 f 371.068 (k)s 2 f 410.01 y 377.068 (2)s 13 f 394.444 y 382.451 (\051)s 10 f 414.964 y 392.118 (;)s 1 f 478.649 y -5.69 (where)s 28.818 (for)s 10 f 46.993 (x)s 12 f 57.184 (2)s 1 f 68.518 (I)s 70.691 (R)s 11 f 473.416 y 79.524 (d)s 1 f 478.649 y 85.12 (,)s 12 f 92.3 (k)s 10 f 98.3 (x)s 12 f 105.158 (k)s 1 f 114.491 (=)s 13 f 463.656 y 127.158 (q)s 58.2 .48 139.158 463.656 r 469.649 y 139.158 (P)s 11 f 472.616 y 151.825 (d)s 482.249 y 151.825 (k)s 2 f 157.129 (=1)s 1 f 478.649 y 169.879 (\050)s 10 f 174.546 (x)s 11 f 480.449 y 181.404 (k)s 1 f 478.649 y 187.308 (\051)s 2 f 475.182 y 191.975 (2)s 1 f 478.649 y 197.358 (.)s 205.961 (Since)s 13 f 469.649 y 237.102 (P)s 11 f 472.616 y 249.769 (d)s 482.249 y 249.769 (k)s 2 f 255.073 (=1)s 12 f 478.649 y 269.823 (j)s 10 f 273.157 (x)s 11 f 480.449 y 280.015 (i)s 12 f 478.649 y 284.01 (j)s 290.677 (\267)s 10 f 303.343 (d)s 12 f 309.589 (k)s 10 f 315.589 (x)s 12 f 322.447 (k)s 1 f 332.256 (and)s 10 f 355.397 (\256)s 1 f 365.118 (exp)s 383.451 (\050)s 12 f 388.118 (\241)s 10 f 397.451 (\256)s 2 f 474.294 y 405.172 (2)s 1 f 478.649 y 410.556 (\051)s 12 f 418.555 (\267)s 10 f 431.222 (A)s 2 f 480.449 y 440.222 (1)s 1 f 478.649 y 449.414 (for)s 495.449 y -5.69 (all)s 10 f 10.977 (\256)s 12 f 22.031 (2)s 1 f 33.364 (I)s 35.537 (R)s 48.371 (and)s 71.704 (for)s 90.071 (some)s 120.137 (p)s 127.137 (ositiv)s 155.204 (e)s 164.537 (constan)s 204.271 (t)s 10 f 212.938 (A)s 2 f 497.249 y 221.938 (1)s 1 f 495.449 y 227.321 (.)s 235.988 (W)s 247.321 (e)s 256.654 (ha)s 268.988 (v)s 274.988 (e)s 284.321 (that)s 11 f 537.547 y 113.933 (d)s 13 f 541.147 y 107.764 (X)s 11 f 566.98 y 107.703 (k)s 2 f 113.007 (=1)s 13 f 542.347 y 127.157 (\257)s 549.547 y 127.157 (\257)s 10 f 552.547 y 131.157 (@)s 11 f 554.347 y 137.528 (k)s 10 f 552.547 y 143.432 (h)s 11 f 554.347 y 150.346 (t)s 2 f 153.971 (+)s 11 f 161.338 (\042)s 14 f 165.872 (\241)s 11 f 173.372 (s)s 1 f 552.547 y 178.501 (\050)s 10 f 183.168 (x)s 1 f 190.026 (\051)s 13 f 542.347 y 194.693 (\257)s 549.547 y 194.693 (\257)s 12 f 552.547 y 202.026 (\267)s 10 f 214.693 (A)s 2 f 554.347 y 223.693 (2)s 10 f 552.547 y 229.076 (h)s 2 f 554.714 y 235.99 (2\050)s 11 f 244.523 (t)s 2 f 248.148 (+)s 11 f 255.515 (\042)s 14 f 260.049 (\241)s 11 f 267.549 (s)s 2 f 272.078 (\051)s 1 f 552.547 y 276.428 (\050)s 10 f 281.095 (x)s 1 f 287.953 (\051)s 544.429 y 318.503 (1)s 54.887 .48 294.06 549.787 r 12 f 552.187 y 294.06 (p)s 44.887 .48 304.06 552.187 r 10 f 561.437 y 304.06 (t)s 1 f 311.06 (+)s 10 f 323.06 (\042)s 12 f 331.322 (\241)s 10 f 343.322 (s)s 1 f 609.245 y -5.69 (for)s 12.677 (some)s 42.743 (p)s 49.743 (ositiv)s 77.81 (e)s 87.143 (constan)s 126.877 (t)s 10 f 135.543 (A)s 2 f 611.045 y 144.543 (2)s 1 f 609.245 y 153.927 (that)s 179.927 (dep)s 198.927 (ends)s 226.327 (on)s 10 f 242.994 (d)s 1 f 249.239 (.)s 257.906 (On)s 277.906 (the)s 298.573 (other)s 329.94 (hand,)s 363.273 (w)s 371.606 (e)s 380.94 (ha)s 393.273 (v)s 399.273 (e)s 11 f 651.342 y 151.39 (d)s 13 f 654.942 y 145.221 (X)s 11 f 680.776 y 145.16 (k)s 2 f 150.464 (=1)s 10 f 666.343 y 164.614 (@)s 11 f 668.143 y 170.985 (k)s 12 f 666.343 y 176.889 (H)s 11 f 660.576 y 187.139 (f)s 669.296 y 187.024 (t;\042)s 1 f 666.343 y 201.966 (=)s 10 f 214.632 (f)s 12 f 224.466 (\244)s 13 f 656.622 y 233.132 (\241)s 11 f 651.342 y 246.862 (d)s 13 f 654.942 y 240.693 (X)s 11 f 680.776 y 240.632 (k)s 2 f 245.936 (=1)s 10 f 666.343 y 260.086 (@)s 11 f 668.143 y 266.457 (k)s 10 f 666.343 y 272.361 (h)s 11 f 668.143 y 279.275 (t)s 2 f 282.9 (+)s 11 f 290.267 (\042)s 14 f 294.801 (\241)s 11 f 302.301 (s)s 13 f 656.622 y 307.43 (\242)s 1 f 705.976 y 223.045 (47)s do-end end endp %%Page: 48 48 %%BeginPageSetup initializepage (Raffaele Esposito; page: 48 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f0_12 sf ( )S -996 -1000 :M f1_12 sf ( )S -993 -1000 :M f2_12 sf ( )S -989 -1000 :M f10_12 sf ( )S -981 -1000 :M f11_12 sf ( )S -972 -1000 :M f12_12 sf ( )S -960 -1000 :M f13_12 sf ( )S -951 -1000 :M f14_12 sf ( )S -937 -1000 :M f15_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 1200 1000 div mul /CMBX10 findfont fdef 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 14 7 1200 1000 div mul /CMSY7 findfont fdef 15 5 1200 1000 div mul /CMMI5 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 6.31 y -5.69 (and)s 17.643 (therefore)s 11 f 31.179 y 24.072 (d)s 13 f 34.779 y 17.903 (X)s 11 f 60.613 y 17.843 (k)s 2 f 23.147 (=1)s 13 f 29.846 y 37.297 (Z)s 11 f 32.812 y 49.297 (t)s 2 f 57.113 y 43.963 (0)s 13 f 32.379 y 55.522 (\257)s 39.579 y 55.522 (\257)s 46.779 y 55.522 (\257)s 36.459 y 59.522 (\255)s 10 f 46.179 y 65.188 (@)s 11 f 47.979 y 71.559 (k)s 12 f 46.179 y 77.463 (H)s 11 f 40.413 y 87.713 (f)s 49.132 y 87.598 (t;\042)s 1 f 46.179 y 99.206 (\050)s 10 f 103.873 (s;)s 114.831 (:)s 1 f 118.165 (\051)s 13 f 36.459 y 122.831 (\256)s 32.379 y 128.498 (\257)s 39.579 y 128.498 (\257)s 46.779 y 128.498 (\257)s 10 f 46.179 y 134.498 (ds)s 12 f 92.246 y 91.176 (\267)s 13 f 75.912 y 103.843 (Z)s 11 f 78.879 y 115.843 (t)s 2 f 103.179 y 110.509 (0)s 10 f 92.246 y 122.068 (ds)s 13 f 71.726 y 133.938 (\050)s 75.912 y 145.605 (Z)s 2 f 103.179 y 152.272 (I)s 153.578 (R)s 15 f 100.406 y 160.545 (d)s 10 f 92.246 y 168.183 (dx)s 13 f 78.926 y 181.287 (h)s 75.912 y 188.954 (Z)s 2 f 103.179 y 195.621 (I)s 196.927 (R)s 15 f 100.406 y 203.894 (d)s 12 f 92.246 y 211.532 (j)s 10 f 214.866 (f)s 1 f 222.032 (\050)s 10 f 226.699 (y)s 1 f 233.013 (\051)s 12 f 237.68 (j)s 11 f 77.246 y 249.242 (d)s 13 f 80.846 y 243.073 (X)s 11 f 106.679 y 243.013 (k)s 2 f 248.317 (=1)s 13 f 82.046 y 262.467 (\257)s 89.246 y 262.467 (\257)s 10 f 92.246 y 266.467 (@)s 11 f 94.046 y 272.838 (k)s 10 f 92.246 y 278.742 (h)s 11 f 94.046 y 285.656 (t)s 2 f 289.281 (+)s 11 f 296.648 (\042)s 14 f 301.182 (\241)s 11 f 308.682 (s)s 1 f 92.246 y 313.811 (\050)s 10 f 318.477 (y)s 12 f 327.458 (\241)s 10 f 339.458 (x)s 1 f 346.316 (\051)s 13 f 82.046 y 350.983 (\257)s 89.246 y 350.983 (\257)s 10 f 92.246 y 354.983 (dy)s 13 f 78.926 y 367.543 (i)s 71.726 y 373.209 (\051)s 12 f 137.279 y 91.176 (\267)s 10 f 103.843 (A)s 2 f 139.079 y 112.843 (2)s 13 f 120.946 y 120.226 (Z)s 11 f 123.913 y 132.226 (t)s 2 f 148.213 y 126.893 (0)s 10 f 137.279 y 138.451 (ds)s 13 f 116.759 y 150.322 (\050)s 120.946 y 161.988 (Z)s 2 f 148.213 y 168.655 (I)s 169.962 (R)s 15 f 145.44 y 176.928 (d)s 10 f 137.279 y 184.567 (dy)s 12 f 197.126 (j)s 10 f 200.46 (f)s 1 f 207.626 (\050)s 10 f 212.293 (y)s 1 f 218.607 (\051)s 12 f 223.274 (j)s 13 f 123.959 y 226.607 (h)s 120.946 y 234.274 (Z)s 2 f 148.213 y 240.94 (I)s 242.247 (R)s 15 f 145.44 y 249.214 (d)s 10 f 137.279 y 256.852 (h)s 2 f 139.446 y 263.766 (2\050)s 11 f 272.299 (t)s 2 f 275.924 (+)s 11 f 283.291 (\042)s 14 f 287.825 (\241)s 11 f 295.325 (s)s 2 f 299.854 (\051)s 1 f 137.279 y 304.204 (\050)s 10 f 308.871 (y)s 12 f 317.851 (\241)s 10 f 329.851 (x)s 1 f 336.709 (\051)s 10 f 341.376 (dx)s 13 f 123.959 y 354.48 (i)s 12 f 137.279 y 362.813 (\243)s 1 f 129.161 y 400.697 (1)s 54.887 .48 376.253 134.519 r 12 f 136.919 y 376.253 (p)s 44.887 .48 386.253 136.919 r 10 f 146.17 y 386.253 (t)s 1 f 393.253 (+)s 10 f 405.253 (\042)s 12 f 413.516 (\241)s 10 f 425.516 (s)s 13 f 116.759 y 432.581 (\051)s 12 f 179.213 y 91.176 (\267)s 10 f 103.843 (A)s 2 f 181.013 y 112.843 (2)s 12 f 179.213 y 118.226 (k)s 10 f 124.226 (f)s 12 f 131.393 (k)s 2 f 181.013 y 137.393 (1)s 13 f 162.88 y 144.776 (Z)s 11 f 165.846 y 156.776 (t)s 2 f 190.147 y 151.443 (0)s 1 f 171.095 y 188.885 (1)s 54.887 .48 164.441 176.453 r 12 f 178.853 y 164.441 (p)s 44.887 .48 174.441 178.853 r 10 f 188.104 y 174.441 (t)s 1 f 181.441 (+)s 10 f 193.441 (\042)s 12 f 201.703 (\241)s 10 f 213.703 (s)s 179.213 y 220.768 (ds)s 1 f 212.573 y 91.176 (=)s 10 f 103.843 (A)s 2 f 214.373 y 112.843 (2)s 12 f 212.573 y 118.226 (k)s 10 f 124.226 (f)s 12 f 131.393 (k)s 2 f 214.373 y 137.393 (1)s 13 f 199.253 y 142.776 (n)s 12 f 202.737 y 150.776 (p)s 24.596 .48 160.776 202.737 r 10 f 212.573 y 160.776 (t)s 1 f 167.776 (+)s 10 f 179.776 (\042)s 12 f 188.038 (\241)s 203.344 y 200.038 (p)s 5.596 .48 210.038 203.344 r 10 f 212.573 y 210.038 (\042)s 13 f 199.253 y 215.634 (o)s 10 f 212.573 y 223.634 (:)s 8.16 .48 455.62 238.689 r .48 7.2 455.62 245.889 r .48 7.2 463.3 245.889 r 8.16 .48 455.62 246.369 r 0 f 276.003 y -5.69 (Pro)s 16.71 (of)s 32.426 (of)s 48.143 (\0505.3\051)s 1 f 76.509 (:)s 85.176 (F)s 92.009 (or)s 106.709 (all)s 10 f 123.376 (\277)s 12 f 133.314 (2)s 1 f 144.647 ([0)s 10 f 153.98 (;)s 159.313 (t)s 1 f 163.647 (],)s 10 f 174.313 (W)s 1 f 187.314 (\050)s 10 f 191.98 (\277)s 197.918 (;)s 203.251 (:)s 1 f 206.584 (\051)s 12 f 214.584 (2)s 10 f 225.918 (L)s 14 f 271.648 y 234.084 (1)s 1 f 276.003 y 244.251 (\050I)s 251.091 (R)s 11 f 270.77 y 259.924 (d)s 1 f 276.003 y 265.52 (\051)s 274.186 (and)s 12 f 297.52 (k)s 10 f 303.52 (W)s 1 f 316.52 (\050)s 10 f 321.186 (\277)s 327.124 (;)s 332.457 (:)s 1 f 335.791 (\051)s 12 f 340.457 (k)s 14 f 277.803 y 346.457 (1)s 12 f 276.003 y 359.957 (\267)s 1 f 372.624 (2)s 10 f 378.624 (C)s 2 f 277.803 y 387.201 (3)s 12 f 266.253 y 392.584 (p)s 4.333 .48 402.584 266.253 r 10 f 276.003 y 402.584 (t)s 406.917 (R)s 1 f 416.121 (\050)s 10 f 420.788 (t)s 1 f 425.121 (\051.)s 296.372 y 8.71 (First,)s 41.765 (b)s 48.098 (y)s 58.796 (\0505.2\051,)s 91.251 (for)s 109.982 (an)s 122.315 (y)s 133.012 (op)s 146.012 (en)s 162.376 (set)s 10 f 181.474 (U)s 1 f 195.339 (of)s 209.37 (I)s 211.544 (R)s 11 f 291.138 y 220.377 (d)s 1 f 296.372 y 230.336 (with)s 258.034 (\257nite)s 289.065 (Leb)s 308.898 (esgue)s 341.329 (measure)s 10 f 388.46 (\270)s 1 f 395.46 (\050)s 10 f 400.126 (U)s 1 f 409.628 (\051,)s 422.083 (w)s 430.416 (e)s 440.114 (ha)s 452.447 (v)s 458.447 (e)s 313.172 y -5.69 (for)s 12.677 (all)s 29.343 (0)s 12 f 38.676 (\267)s 10 f 51.343 (\277)s 12 f 61.281 (\267)s 10 f 73.947 (t)s 1 f 78.28 (,)s 13 f 320.305 y 142.743 (Z)s 11 f 347.572 y 149.41 (U)s 10 f 336.638 y 159.448 (W)s 1 f 172.448 (\050)s 10 f 177.114 (\277)s 183.052 (;)s 188.385 (x)s 1 f 195.244 (\051)s 10 f 199.91 (dx)s 12 f 216.348 (\267)s 1 f 229.014 (2)s 10 f 235.014 (C)s 2 f 338.438 y 243.591 (3)s 12 f 326.302 y 248.974 (p)s 4.333 .48 258.974 326.302 r 10 f 336.638 y 258.974 (t)s 263.308 (R)s 1 f 272.512 (\050)s 10 f 277.178 (t)s 1 f 281.512 (\051)s 10 f 286.178 (\270)s 1 f 293.179 (\050)s 10 f 297.845 (U)s 1 f 307.347 (\051)s 10 f 312.014 (:)s 1 f 371.352 y 8.71 (Fix)s 29.38 (0)s 10 f 38.713 (\074)s 51.38 (\261)s 60.501 (\074)s 1 f 73.167 (1.)s 87.558 (F)s 94.391 (or)s 108.261 (an)s 120.595 (y)s 130.098 (op)s 143.098 (en)s 158.269 (set)s 10 f 176.172 (U)s 1 f 188.844 (of)s 201.682 (I)s 203.855 (R)s 11 f 366.119 y 212.688 (d)s 1 f 371.352 y 221.454 (with)s 247.958 (\257nite)s 277.795 (Leb)s 297.628 (esgue)s 328.865 (measure)s 374.802 (and)s 397.306 (for)s 414.843 (0)s 12 f 424.176 (\267)s 10 f 436.843 (\277)s 12 f 446.78 (\267)s 10 f 459.447 (t)s 1 f 388.152 y -5.69 (let)s 10 f 404.952 y 100.109 (B)s 11 f 399.998 y 109.813 (U)s 407.919 y 109.211 (\261)s 113.361 (;\277)s 1 f 404.952 y 125.541 (=)s 13 f 391.632 y 138.207 (n)s 10 f 404.952 y 146.207 (x)s 12 f 156.399 (2)s 10 f 167.732 (U)s 1 f 183.9 (:)s 10 f 197.233 (W)s 1 f 210.233 (\050)s 10 f 214.9 (\277)s 220.837 (;)s 226.171 (x)s 1 f 233.029 (\051)s 10 f 241.029 (\076)s 1 f 253.696 (2)s 10 f 259.696 (C)s 2 f 406.752 y 268.272 (3)s 12 f 394.616 y 273.656 (p)s 4.333 .48 283.656 394.616 r 10 f 404.952 y 283.656 (t)s 287.989 (R)s 1 f 297.193 (\050)s 10 f 301.86 (t)s 1 f 306.193 (\051\0501)s 324.193 (+)s 10 f 336.193 (\261)s 1 f 341.981 (\051)s 13 f 391.632 y 346.647 (o)s 10 f 404.952 y 354.647 (:)s 1 f 435.546 y -5.69 (Supp)s 21.31 (ose)s 40.044 (that)s 10 f 64.711 (\270)s 1 f 71.711 (\050)s 10 f 76.378 (B)s 11 f 431.192 y 86.082 (U)s 438.945 y 85.48 (\261)s 89.63 (;\277)s 1 f 435.546 y 98.476 (\051)s 10 f 106.476 (\076)s 1 f 119.142 (0,)s 131.41 (there)s 160.777 (exists)s 192.577 (an)s 207.911 (op)s 220.911 (en)s 235.579 (set)s 10 f 252.979 (V)s 1 f 262.646 (,)s 268.913 (suc)s 285.313 (h)s 294.647 (that,)s 10 f 322.914 (B)s 11 f 431.192 y 332.618 (U)s 438.945 y 332.016 (\261)s 336.166 (;\277)s 12 f 435.546 y 348.345 (\275)s 10 f 361.012 (V)s 1 f 373.346 (and)s 10 f 395.347 (\270)s 13 f 425.826 y 402.347 (\241)s 10 f 435.546 y 407.847 (V)s 12 f 417.514 (n)s 10 f 423.516 (B)s 11 f 431.192 y 433.22 (U)s 438.945 y 432.618 (\261)s 436.767 (;\277)s 13 f 425.826 y 445.614 (\242)s 12 f 435.546 y 454.447 (\267)s 10 f 452.346 y -5.69 (\270)s 1 f 1.31 (\050)s 10 f 5.977 (V)s 1 f 15.643 (\051)s 11 f 447.621 y 21.808 (\261)s 4.783 .48 21.75 449.586 r 2 f 456.484 y 21.75 (2)s 1 f 452.346 y 31.973 (and)s 55.307 (w)s 63.64 (e)s 72.973 (ha)s 85.307 (v)s 91.307 (e)s 10 f 485.617 y 65.605 (\270)s 1 f 72.605 (\050)s 10 f 77.271 (V)s 1 f 86.938 (\051)s 13 f 475.897 y 91.605 (\241)s 1 f 485.617 y 97.105 (2)s 10 f 103.105 (C)s 2 f 487.417 y 111.681 (3)s 12 f 475.28 y 117.065 (p)s 4.333 .48 127.065 475.28 r 10 f 485.617 y 127.065 (t)s 131.398 (R)s 1 f 140.602 (\050)s 10 f 145.269 (t)s 1 f 149.602 (\051)s 13 f 475.897 y 154.269 (\242)s 10 f 485.617 y 163.102 (\074)s 175.769 (\270)s 1 f 182.769 (\050)s 10 f 187.436 (V)s 1 f 197.102 (\051)s 13 f 475.897 y 201.769 (\241)s 1 f 485.617 y 207.269 (2)s 10 f 213.269 (C)s 2 f 487.417 y 221.846 (3)s 12 f 475.28 y 227.229 (p)s 4.333 .48 237.229 475.28 r 10 f 485.617 y 237.229 (t)s 241.562 (R)s 1 f 250.767 (\050)s 10 f 255.433 (t)s 1 f 259.767 (\051)s 13 f 475.897 y 264.433 (\242)s 1 f 485.617 y 269.933 (\0501)s 283.267 (+)s 10 f 295.267 (\261)s 1 f 301.054 (\051\0501)s 12 f 319.054 (\241)s 10 f 331.054 (\261)s 336.842 (=)s 1 f 342.842 (2\051)s 506.017 y 163.102 (=)s 13 f 496.296 y 175.769 (\241)s 1 f 506.017 y 181.269 (2)s 10 f 187.269 (C)s 2 f 507.817 y 195.846 (3)s 12 f 495.68 y 201.229 (p)s 4.333 .48 211.229 495.68 r 10 f 506.017 y 211.229 (t)s 215.562 (R)s 1 f 224.767 (\050)s 10 f 229.433 (t)s 1 f 233.767 (\051)s 13 f 496.296 y 238.433 (\242)s 1 f 506.017 y 243.933 (\0501)s 257.267 (+)s 10 f 269.267 (\261)s 1 f 275.054 (\051)s 13 f 496.296 y 279.721 (\241)s 10 f 506.017 y 285.221 (\270)s 1 f 292.221 (\050)s 10 f 296.887 (V)s 1 f 306.554 (\051)s 12 f 313.887 (\241)s 10 f 325.887 (\270)s 1 f 332.887 (\050)s 10 f 337.554 (V)s 1 f 347.221 (\051)s 10 f 351.887 (\261)s 357.675 (=)s 1 f 363.675 (2)s 13 f 496.296 y 369.675 (\242)s 12 f 526.417 y 163.102 (\267)s 13 f 516.697 y 175.769 (\241)s 1 f 526.417 y 181.269 (2)s 10 f 187.269 (C)s 2 f 528.217 y 195.846 (3)s 12 f 516.08 y 201.229 (p)s 4.333 .48 211.229 516.08 r 10 f 526.417 y 211.229 (t)s 215.562 (R)s 1 f 224.767 (\050)s 10 f 229.433 (t)s 1 f 233.767 (\051)s 13 f 516.697 y 238.433 (\242)s 1 f 526.417 y 243.933 (\0501)s 257.267 (+)s 10 f 269.267 (\261)s 1 f 275.054 (\051)s 13 f 516.697 y 279.721 (\241)s 10 f 526.417 y 285.221 (\270)s 1 f 292.221 (\050)s 10 f 296.887 (V)s 1 f 306.554 (\051)s 12 f 313.887 (\241)s 10 f 325.887 (\270)s 13 f 516.697 y 332.887 (\241)s 10 f 526.417 y 338.387 (V)s 12 f 350.721 (n)s 10 f 359.387 (B)s 11 f 521.462 y 369.092 (U)s 529.383 y 368.489 (\261)s 372.639 (;\277)s 13 f 516.697 y 381.485 (\242)s 386.985 (\242)s 1 f 546.817 y 163.102 (=)s 13 f 537.097 y 175.769 (\241)s 1 f 546.817 y 181.269 (2)s 10 f 187.269 (C)s 2 f 548.617 y 195.846 (3)s 12 f 536.48 y 201.229 (p)s 4.333 .48 211.229 536.48 r 10 f 546.817 y 211.229 (t)s 215.562 (R)s 1 f 224.767 (\050)s 10 f 229.433 (t)s 1 f 233.767 (\051)s 13 f 537.097 y 238.433 (\242)s 1 f 546.817 y 243.933 (\0501)s 257.267 (+)s 10 f 269.267 (\261)s 1 f 275.054 (\051)s 10 f 279.721 (\270)s 13 f 537.097 y 286.721 (\241)s 10 f 546.817 y 292.221 (B)s 11 f 541.862 y 301.925 (U)s 549.783 y 301.323 (\261)s 305.472 (;\277)s 13 f 537.097 y 314.319 (\242)s 10 f 576.15 y 163.102 (\074)s 13 f 559.817 y 175.769 (Z)s 11 f 587.083 y 182.436 (B)s 15 f 584.19 y 190.095 (U)s 590.277 y 189.686 (\261)s 193.388 (;\277)s 10 f 576.15 y 204.124 (W)s 1 f 217.124 (\050)s 10 f 221.791 (\277)s 227.728 (;)s 233.061 (x)s 1 f 239.92 (\051)s 10 f 244.586 (dx)s 12 f 616.177 y 163.102 (\267)s 13 f 599.843 y 175.769 (Z)s 11 f 627.11 y 182.436 (V)s 10 f 616.177 y 192.769 (W)s 1 f 205.769 (\050)s 10 f 210.436 (\277)s 216.373 (;)s 221.706 (x)s 1 f 228.565 (\051)s 10 f 233.231 (dx)s 12 f 646.807 y 163.102 (\267)s 13 f 637.086 y 175.769 (\241)s 1 f 646.807 y 181.269 (2)s 10 f 187.269 (C)s 2 f 648.606 y 195.846 (3)s 12 f 636.47 y 201.229 (p)s 4.333 .48 211.229 636.47 r 10 f 646.807 y 211.229 (t)s 215.562 (R)s 1 f 224.767 (\050)s 10 f 229.433 (t)s 1 f 233.767 (\051)s 13 f 637.086 y 238.433 (\242)s 10 f 646.807 y 243.933 (\270)s 1 f 250.933 (\050)s 10 f 255.6 (V)s 1 f 265.267 (\051)s 10 f 269.933 (:)s 1 f 677.176 y -5.69 (whic)s 17.976 (h)s 28.643 (leads)s 58.71 (to)s 73.377 (a)s 83.377 (con)s 101.043 (tradiction.)s 705.976 y 223.045 (48)s do-end end endp %%Page: 49 49 %%BeginPageSetup initializepage (Raffaele Esposito; page: 49 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f0_12 sf ( )S -996 -1000 :M f1_12 sf ( )S -993 -1000 :M f2_12 sf ( )S -989 -1000 :M f10_12 sf ( )S -981 -1000 :M f11_12 sf ( )S -972 -1000 :M f12_12 sf ( )S -960 -1000 :M f13_12 sf ( )S -951 -1000 :M f17_12 sf ( )S -948 -1000 :M f21_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 1200 1000 div mul /CMBX10 findfont fdef 1 10 1200 1000 div mul /CMR10 findfont fdef 2 7 1200 1000 div mul /CMR7 findfont fdef 10 10 1200 1000 div mul /CMMI10 findfont fdef 11 7 1200 1000 div mul /CMMI7 findfont fdef 12 10 1200 1000 div mul /CMSY10 findfont fdef 13 10 1200 1000 div mul /CMEX10 findfont fdef 17 10 1200 1000 div mul /CMTI10 findfont fdef 22 10 1200 1000 div mul /CMSL10 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 6.31 y 8.71 (By)s 28.998 (the)s 51.12 (arbitrariness)s 122.142 (of)s 137.263 (0)s 10 f 149.021 (\074)s 164.113 (\261)s 175.658 (\074)s 1 f 190.75 (1)s 202.205 (w)s 210.538 (e)s 221.327 (obtain)s 260.115 (that)s 287.57 (if)s 10 f 300.025 (U)s 1 f 314.982 (is)s 328.503 (an)s 340.836 (y)s 352.625 (op)s 365.625 (en)s 383.08 (set)s 403.268 (of)s 418.39 (I)s 420.563 (R)s 11 f 1.076 y 429.396 (d)s 1 f 6.31 y 440.447 (with)s 10 f 23.11 y -5.69 (\270)s 1 f 1.31 (\050)s 10 f 5.977 (U)s 1 f 15.478 (\051)s 10 f 23.478 (\074)s 12 f 36.145 (1)s 1 f 48.145 (,)s 10 f 47.117 y 115.385 (\270)s 13 f 33.797 y 122.385 (\263)s 129.552 (n)s 10 f 47.117 y 137.552 (x)s 12 f 147.744 (2)s 10 f 159.077 (U)s 1 f 175.245 (:)s 10 f 188.578 (W)s 1 f 201.578 (\050)s 10 f 206.245 (\277)s 212.182 (;)s 217.516 (x)s 1 f 224.374 (\051)s 10 f 232.374 (\076)s 1 f 245.041 (2)s 10 f 251.041 (C)s 2 f 48.917 y 259.617 (3)s 12 f 36.781 y 265.001 (p)s 4.333 .48 275.001 36.781 r 10 f 47.117 y 275.001 (t)s 279.334 (R)s 1 f 288.538 (\050)s 10 f 293.205 (t)s 1 f 297.538 (\051)s 13 f 33.797 y 302.205 (o)s 310.205 (\264)s 1 f 47.117 y 320.705 (=)s 333.371 (0)s 10 f 339.371 (:)s 1 f 74.724 y -5.69 (This)s 21.71 (implies)s 10 f 93.932 y 132.264 (W)s 1 f 145.264 (\050)s 10 f 149.931 (\277)s 155.868 (;)s 161.201 (x)s 1 f 168.06 (\051)s 12 f 176.06 (\267)s 1 f 188.726 (2)s 10 f 194.726 (C)s 2 f 95.732 y 203.303 (3)s 12 f 83.595 y 208.686 (p)s 4.333 .48 218.686 83.595 r 10 f 93.932 y 218.686 (t)s 223.02 (R)s 1 f 232.224 (\050)s 10 f 236.891 (t)s 1 f 241.224 (\051)s 269.891 (a)s 10 f 275.891 (:)s 1 f 279.224 (e)s 10 f 284.557 (:)s 1 f 291.891 (in)s 305.891 (I)s 308.064 (R)s 11 f 88.698 y 316.897 (d)s 10 f 93.932 y 322.493 (:)s 8.16 .48 455.62 114.939 r .48 7.2 455.62 122.139 r .48 7.2 463.3 122.139 r 8.16 .48 455.62 122.619 r 0 f 201.857 y -5.69 (References)s 1 f 228.384 y -12.457 ([B])s 8.71 (Blume,)s 49.608 (M,)s 67.606 (Theory)s 108.971 (of)s 122.303 (the)s 142.634 (First)s 171.565 (Order)s 205.963 (Magnetic)s 257.962 (Phase)s 292.526 (Change)s 335.524 (in)s 349.189 (UO)s 2 f 230.184 y 367.523 (2)s 1 f 228.384 y 376.571 (Ph)s 391.071 (ys.)s 410.692 (Rev.)s 0 f 439.747 (141)s 1 f 460.447 (,)s 245.184 y 8.71 (517,)s 34.043 (\0501996\051)s 262.907 y -12.624 ([C])s 8.71 (Cap)s 30.377 (el,)s 46.377 (H.W.,)s 81.71 (Ph)s 96.21 (ysica)s 0 f 125.943 (32)s 1 f 139.743 (,)s 147.077 (96)s 163.077 (\0501996\051.)s 280.629 y -30.04 ([BEG])s 8.71 (Blume,)s 49.405 (M.,)s 70.6 (Emery)s 104.133 (,)s 110.995 (V.)s 126.739 (J.)s 139.649 (and)s 162.393 (Gri\261ths)s 209.32 (R.)s 224.897 (B.)s 240.141 (Ising)s 268.618 (Mo)s 285.951 (del)s 304.695 (for)s 322.472 (the)s 10 f 342.549 (\270)s 1 f 352.959 (T)s 360.626 (ransition)s 410.136 (and)s 432.88 (Phase)s 297.429 y 8.71 (Separation)s 68.743 (in)s 82.743 (He)s 2 f 293.075 y 97.077 (3)s 1 f 297.429 y 102.46 (-He)s 2 f 293.075 y 120.793 (4)s 1 f 297.429 y 130.177 (Mixtures.)s 22 f 185.61 (Ph)s 200.11 (ys.)s 219.844 (Rev.)s 249.01 (A)s 1 f 258.01 (,)s 0 f 265.344 (4)s 1 f 272.244 (,)s 279.577 (1071-1077,)s 338.91 (\0501971\051.)s 315.152 y -19.124 ([BS])s 8.71 (Bricmon)s 52.91 (t,)s 64.902 (J.)s 78.392 (and)s 101.715 (Sla)s 117.382 (wn)s 132.382 (y)s 137.715 (.J,)s 154.538 (Phase)s 189.428 (transition)s 244.185 (in)s 258.174 (Systems)s 304.631 (with)s 331.954 (a)s 341.944 (Finite)s 377.101 (Num)s 402.434 (b)s 409.434 (er)s 423.457 (of)s 437.114 (dom-)s 331.952 y 8.71 (inan)s 31.043 (t)s 39.71 (Ground)s 83.827 (States,)s 123.227 (Journ.)s 162.093 (Stat.)s 192.76 (Ph)s 207.26 (ys.,)s 0 f 228.994 (54)s 1 f 242.794 (,)s 250.127 (89,)s 269.46 (\0501989\051.)s 349.674 y -30.624 ([CCO])s 8.71 (Carlen,)s 50.248 (E.)s 65.129 (A.,)s 84.3 (Carv)s 109.333 (alho,M.C.)s 164.381 (and)s 187.095 (Orlandi,)s 233.967 (E.)s 248.848 (Algebraic)s 301.929 (rate)s 326.009 (of)s 339.057 (deca)s 362.057 (y)s 371.771 (for)s 389.519 (the)s 409.566 (excess)s 444.747 (free)s 366.474 y 8.71 (energy)s 46.328 (and)s 68.913 (stabilit)s 105.313 (y)s 114.898 (of)s 127.816 (fron)s 148.516 (ts)s 161.168 (for)s 178.786 (a)s 188.037 (non-lo)s 221.037 (cal)s 238.956 (phase)s 271.607 (kinetics)s 314.592 (equation)s 362.844 (with)s 389.429 (a)s 398.68 (conserv)s 437.113 (ation)s 383.274 y 8.71 (la)s 17.71 (w,)s 33.71 (I.)s 45.376 (Preprin)s 84.61 (t)s 93.277 (\0501998\051)s 400.997 y 8.71 (Algebraic)s 62.381 (rate)s 87.053 (of)s 100.691 (deca)s 123.691 (y)s 133.995 (for)s 152.333 (the)s 172.971 (excess)s 208.743 (free)s 231.747 (energy)s 270.085 (and)s 293.39 (stabilit)s 329.79 (y)s 340.095 (of)s 353.733 (fron)s 374.433 (ts)s 387.804 (for)s 406.142 (a)s 416.113 (non-lo)s 449.113 (cal)s 417.797 y 8.71 (phase)s 42.11 (kinetics)s 85.843 (equation)s 134.843 (with)s 162.177 (a)s 172.177 (conserv)s 210.61 (ation)s 241.277 (la)s 250.277 (w,)s 266.277 (I)s 270.944 (I.)s 282.61 (Preprin)s 321.844 (t)s 330.51 (\0501998\051.)s 435.519 y -39.29 ([DOPT])s 8.71 (De)s 26.628 (Masi,)s 58.563 (A.,)s 77.764 (Orlandi,)s 124.665 (E.,)s 143.033 (T)s 150.7 (riolo,)s 180.934 (L.)s 195.186 (and)s 217.938 (Presutti,)s 267.072 (E.)s 281.99 (Glaub)s 314.407 (er)s 327.859 (ev)s 339.192 (olution)s 379.277 (with)s 406.029 (Kac)s 430.114 (p)s 437.114 (oten-)s 452.319 y 8.71 (tials)s 34.119 (I.)s 45.128 (Mesoscopic)s 106.937 (and)s 129.612 (macroscopic)s 196.388 (limits,)s 232.595 (in)s 242.262 (terface)s 280.637 (dynamics,)s 17 f 336.511 (Nonline)s 376.711 (arity)s 0 f 404.74 (7)s 1 f 411.64 (,)s 418.447 (287\173301,)s 469.119 y 8.71 (\0501996\051.)s 486.841 y 8.71 (Glaub)s 41.127 (er)s 55.16 (ev)s 66.493 (olution)s 107.16 (with)s 134.493 (Kac)s 159.16 (p)s 166.16 (oten)s 188.494 (tials)s 214.56 (I)s 219.227 (I.)s 230.894 (Fluctuation.)s 17 f 300.727 (Nonline)s 340.927 (arity)s 0 f 369.613 (9)s 1 f 376.513 (,)s 383.847 (27\17351,)s 421.18 (\0501996\051.)s 504.564 y 8.71 (Glaub)s 41.127 (er)s 56.009 (ev)s 67.342 (olution)s 108.857 (with)s 137.04 (Kac)s 162.555 (p)s 169.555 (oten)s 191.888 (tials.)s 225.168 (I)s 229.835 (I)s 234.501 (I.)s 247.017 (Spino)s 276.684 (dal)s 297.532 (decomp)s 337.866 (osition.)s 17 f 383.812 (Nonline)s 424.012 (arity)s 0 f 453.547 (9)s 1 f 460.447 (,)s 521.364 y 8.71 (53\173114,)s 52.043 (\0501996\051.)s 539.086 y -21.29 ([DP])s 8.71 (De)s 27.159 (Masi,)s 59.518 (A.)s 75.801 (and)s 99.083 (Presutti,)s 148.642 (E.)s 164.091 (Mathematical)s 240.374 (Metho)s 274.374 (ds)s 289.723 (for)s 308.039 (Hydro)s 341.072 (dynamic)s 389.355 (limits,)s 17 f 426.047 (L)s 432.961 (e)s 437.867 (ctur)s 458.26 (e)s 555.886 y 8.71 (Notes)s 42.47 (in)s 57.189 (Matematics)s 1 f 117.629 (,)s 0 f 124.962 (1501)s 1 f 152.562 (,)s 159.896 (Springer-V)s 215.962 (erlag,)s 248.662 (Berlin,)s 287.862 (\0501991\051.)s 573.609 y -11.79 ([F])s 8.71 (F)s 15.543 (ritz,)s 41.697 (J.)s 55.827 (On)s 76.457 (the)s 97.754 (di\256usiv)s 135.487 (e)s 145.451 (nature)s 184.114 (of)s 198.411 (the)s 219.707 (en)s 231.374 (trop)s 253.074 (y)s 264.037 (\260)s 270.704 (o)s 276.371 (w)s 289.667 (in)s 304.297 (in\257nite)s 345.594 (systems:)s 396.054 (remarks)s 442.484 (to)s 457.78 (a)s 590.409 y 8.71 (pap)s 28.377 (er)s 42.41 (b)s 48.743 (y)s 59.077 (Guo-P)s 92.993 (apanicolau-V)s 160.993 (aradhan.)s 22 f 212.36 (Comm)s 246.694 (un.)s 268.694 (Math.)s 305.694 (Ph)s 320.194 (ys)s 1 f 331.261 (.)s 0 f 339.927 (133)s 1 f 360.627 (,)s 367.96 (331-352.)s 416.627 (\0501990\051)s 608.131 y -20.874 ([GL])s 8.71 (Giacomin,)s 66.019 (G.)s 82.634 (and)s 105.833 (Leb)s 125.666 (o)s 131.333 (witz,)s 160.558 (J.)s 173.923 (L.)s 188.622 (Phase)s 223.387 (segregation)s 286.019 (dynamics)s 338.951 (in)s 352.816 (particle)s 396.048 (systems)s 440.447 (with)s 624.931 y 8.71 (long)s 34.71 (range)s 67.41 (in)s 77.077 (teraction)s 127.777 (I.)s 139.443 (Macroscopic)s 207.877 (limits.)s 22 f 245.944 (J.)s 259.444 (Stat.)s 290.11 (Ph)s 304.61 (ys.)s 0 f 324.344 (87)s 1 f 338.144 (,)s 345.477 (37-61.)s 382.144 (\0501997\051.)s 642.654 y 8.71 (Phase)s 43.065 (segregation)s 105.286 (dynamics)s 157.808 (in)s 171.263 (particle)s 214.084 (systems)s 258.072 (with)s 284.861 (long)s 310.316 (range)s 342.47 (in)s 352.137 (teraction)s 402.292 (I)s 406.959 (I.)s 418.08 (In)s 428.747 (terface)s 659.454 y 8.71 (motion,)s 22 f 52.71 (SIAM)s 87.71 (J.)s 101.21 (Appl.)s 135.543 (Math.)s 0 f 172.543 (58)s 1 f 186.343 (,)s 193.677 (1707\1731729)s 251.677 (\0501998\051.)s 677.176 y -31.874 ([GLM])s 8.71 (Giacomin,)s 66.127 (G.,)s 86.21 (Leb)s 106.043 (o)s 111.71 (witz,)s 141.043 (J.)s 154.543 (L.)s 169.377 (and)s 192.71 (Marra,)s 232.444 (R.)s 248.61 (in)s 262.61 (preparation.)s 705.976 y 223.045 (49)s do-end end endp %%Page: 50 50 %%BeginPageSetup initializepage (Raffaele Esposito; page: 50 of 50)setjob %%EndPageSetup gS 0 0 583 768 rC -1000 -1000 :M f0_12 sf ( )S -996 -1000 :M f1_12 sf ( )S -993 -1000 :M f17_12 sf ( )S -990 -1000 :M f21_12 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 1200 1000 div mul /CMBX10 findfont fdef 1 10 1200 1000 div mul /CMR10 findfont fdef 17 10 1200 1000 div mul /CMTI10 findfont fdef 22 10 1200 1000 div mul /CMSL10 findfont fdef 58 60 translate 72 72.27 div dup scale 1 f 6.31 y -29.04 ([GLP])s 8.71 (Giacomin,)s 66.189 (G.,)s 86.336 (Leb)s 106.169 (o)s 111.836 (witz,)s 141.232 (J.)s 154.782 (L.)s 169.666 (and)s 193.049 (Presutti,)s 242.712 (E.)s 258.262 (Deterministic)s 332.913 (and)s 356.296 (Sto)s 373.963 (c)s 378.963 (hastic)s 413.747 (Hydro)s 446.78 (dy-)s 23.11 y 8.71 (namic)s 44.043 (Equations)s 100.61 (Arising)s 142.377 (F)s 149.21 (rom)s 173.91 (Simple)s 213.244 (Microscopic)s 279.01 (Mo)s 296.344 (del)s 315.677 (Systems.)s 366.81 (Preprin)s 406.044 (t)s 414.711 (\0501998\051.)s 40.03 y -30.54 ([GPV])s 8.71 (Guo,)s 39.523 (M.Z.,)s 73.252 (P)s 81.085 (apanicolaou,)s 151.815 (G.C.)s 181.682 (and)s 206.132 (V)s 214.132 (aradhan,)s 265.562 (S.R.S.)s 302.846 (Nonlinear)s 358.996 (di\256usion)s 408.513 (limit)s 438.297 (for)s 457.78 (a)s 56.83 y 8.71 (system)s 48.51 (with)s 75.843 (nearest)s 117.277 (neigh)s 144.943 (b)s 151.943 (or)s 166.643 (in)s 176.31 (teractions,)s 22 f 235.077 (Comm.)s 278.41 (Math.)s 315.41 (Ph)s 329.91 (ys.)s 1 f 344.31 (,)s 0 f 351.644 (118)s 1 f 372.344 (,)s 379.677 (31-59.)s 416.344 (\0501988\051.)s 73.75 y -30.457 ([KUE])s 8.71 (Kac,)s 36.319 (M.,)s 57.595 (Uhlen)s 88.262 (b)s 95.262 (ec)s 105.595 (k,G.E.)s 143.023 (and)s 165.868 (Hemmer,)s 217.177 (P)s 224.344 (.C.)s 243.189 (On)s 262.7 (the)s 282.878 (v)s 288.545 (an)s 304.723 (der)s 324.934 (W)s 336.268 (aals)s 359.846 (theory)s 397.057 (of)s 410.235 (the)s 430.414 (v)s 436.08 (ap)s 449.08 (or-)s 90.55 y 8.71 (liquid)s 41.292 (equilibrium,)s 107.458 (I.)s 118.04 (Discussion)s 175.655 (of)s 188.237 (a)s 197.153 (one-dimensional)s 284.135 (mo)s 300.468 (del,)s 17 f 322.267 (J.)s 335.542 (Math.)s 371.423 (Phys.)s 0 f 405.081 (4)s 1 f 411.981 (,)s 418.447 (216\173228,)s 107.35 y 8.71 (\0501963\051.)s 124.27 y -20.79 ([KL])s 8.71 (Kipnis,)s 49.146 (C.)s 63.941 (and)s 86.07 (Landim,)s 132.606 (C.)s 22 f 147.401 (Hydro)s 180.435 (dynamic)s 227.563 (limit)s 255.025 (of)s 267.487 (in)s 277.154 (teracting)s 326.649 (particle)s 368.811 (systems)s 1 f 409.344 (,)s 415.714 (Springer-)s 141.07 y 8.71 (V)s 16.71 (erlag,)s 49.41 (1998.)s 157.99 y -36.124 ([KLO1])s 8.71 (C.)s 24.688 (Kipnis,)s 66.071 (C.)s 82.049 (Landim)s 126.194 (and)s 149.505 (S.)s 163.484 (Olla,)s 192.8 (Hydro)s 225.833 (dynamical)s 283.478 (limit)s 312.123 (for)s 330.468 (a)s 340.446 (nongradien)s 398.146 (t)s 406.791 (mo)s 423.124 (del:)s 447.114 (the)s 174.79 y 8.71 (generalized)s 70.743 (exclusion)s 122.477 (pro)s 140.177 (cesses,)s 22 f 177.71 (Comm.)s 221.043 (Pure)s 249.91 (Appl.)s 284.244 (Math)s 1 f 312.577 (,)s 0 f 319.91 (47)s 1 f 333.71 (,)s 341.044 (1994,)s 372.377 (pp.)s 394.377 (1475\1731545.)s 191.71 y -30.957 ([K)s -18.624 (O)s -9.624 (V])s 8.71 (Kipnis,)s 49.098 (C.,)s 67.42 (Olla,)s 95.742 (S.)s 108.477 (and)s 130.546 (V)s 138.546 (aradhan,)s 187.567 (S.R.S.)s 222.47 (Hydro)s 255.503 (dynamics)s 307.305 (and)s 329.374 (large)s 357.476 (deviations)s 413.278 (for)s 430.38 (simple)s 208.51 y 8.71 (exclusion)s 60.443 (pro)s 78.143 (cesses,)s 22 f 115.677 (Comm.)s 159.01 (Pure)s 187.877 (Appl.)s 222.21 (Math.)s 0 f 259.21 (42)s 1 f 273.01 (,)s 280.344 (115-137.)s 329.01 (\0501989\051.)s 225.43 y -14.79 ([Li])s 8.71 (Liggett,)s 53.349 (T.)s 69.106 (M.)s 22 f 87.197 (In)s 97.863 (teracting)s 148.32 (particle)s 191.444 (systems)s 0 f 235.735 (276)s 1 f 260.192 (Grundlehren)s 330.099 (der)s 350.556 (mathematisc)s 416.956 (hen)s 439.38 (Wis-)s 242.23 y 8.71 (sensc)s 35.176 (haften.)s 76.843 (Springer-V)s 132.91 (erlag.)s 166.943 (Berlin.)s 207.477 (\0501985\051.)s 259.15 y -22.457 ([LM])s 8.71 (Landim,)s 55.378 (C.)s 70.338 (and)s 92.631 (Mourragui,)s 154.2 (M.)s 171.493 (Hydro)s 204.526 (dynamic)s 251.82 (limit)s 279.447 (of)s 292.073 (mean)s 323.033 (zero)s 347.36 (asymmetric)s 410.754 (zero)s 435.08 (range)s 275.95 y 8.71 (pro)s 26.41 (cesses)s 60.61 (in)s 74.61 (in\257nite)s 115.277 (v)s 121.277 (olume.)s 22 f 161.277 (Ann.Inst.Henri.P)s 250.877 (oincar)s 282.577 (\266)s 282.91 (e)s 1 f 288.244 (.)s 296.91 (V)s 304.91 (ol)s 318.244 (33,)s 337.577 (N.)s 0 f 353.91 (1)s 1 f 360.81 (,)s 368.144 (p.361-385,)s 425.477 (\0501997\051.)s 292.87 y -29.124 ([LMS])s 8.71 (C.)s 26.571 (Landim,)s 76.397 (M.)s 96.592 (Mourragui)s 157.52 (and)s 182.714 (S.)s 198.576 (Sellami,)s 246.235 (Hydro)s 279.269 (dynamical)s 338.797 (limit)s 369.325 (for)s 389.552 (a)s 401.414 (nongradien)s 459.114 (t)s 309.67 y 8.71 (in)s 18.376 (teracting)s 69.077 (particle)s 112.443 (system)s 152.243 (with)s 179.577 (sto)s 195.31 (c)s 200.31 (hastic)s 235.044 (reserv)s 265.844 (oirs.)s 293.277 (Preprin)s 332.51 (t)s 341.177 (\0501998\051)s 326.59 y -19.624 ([LP])s 8.71 (Leb)s 28.543 (o)s 34.21 (witz,)s 63.313 (J.)s 76.525 (and)s 99.57 (P)s 107.403 (enrose,)s 147.273 (O.)s 163.651 (Rigorous)s 213.63 (treatmen)s 260.663 (t)s 269.042 (of)s 282.421 (the)s 302.799 (V)s 310.799 (an)s 327.178 (der)s 347.59 (W)s 358.923 (aals)s 382.702 (Maxw)s 414.368 (ell)s 430.08 (theory)s 343.39 y 8.71 (of)s 22.376 (the)s 43.043 (liquid)s 76.71 (v)s 82.377 (ap)s 95.377 (our)s 116.743 (transition,)s 174.844 (J.)s 188.344 (Math.)s 225.344 (Ph)s 239.844 (ys.)s 259.577 (7,98\173113)s 308.91 (\0501963\051)s 360.31 y -13.29 ([Q])s 8.71 (Quastel,)s 57.835 (J.)s 72.715 (Di\256usion)s 124.995 (of)s 140.042 (a)s 151.422 (color)s 182.169 (in)s 197.549 (the)s 219.596 (simple)s 258.376 (exclusion)s 311.49 (pro)s 329.19 (cess,)s 17 f 358.382 (Comm.)s 405.738 (Pur)s 424.764 (e)s 435.847 (Appl.)s 377.11 y 8.71 (Math.)s 0 f 44.736 (XL)s 61.936 (V)s 1 f 72.369 (,)s 79.703 (623\173679)s 125.703 (\0501992\051.)s 394.03 y -17.29 ([Sp])s 8.71 (Sp)s 22.377 (ohn,)s 49.043 (H.)s 22 f 65.377 (Large)s 98.91 (scale)s 127.643 (dynamics)s 180.71 (of)s 194.377 (in)s 204.044 (teracting)s 254.744 (particles)s 1 f 298.844 (,)s 306.177 (Springer,)s 357.577 (Berlin,)s 396.777 (\0501991\051.)s 410.95 y -12.957 ([V])s 8.71 (S.R.S.)s 45.123 (V)s 53.123 (aradhan,)s 103.464 (Nonlinear)s 158.744 (di\256usion)s 207.39 (limit)s 236.303 (for)s 254.916 (a)s 265.162 (system)s 305.208 (with)s 332.788 (nearest)s 374.467 (neigh)s 402.134 (b)s 409.134 (or)s 424.08 (in)s 433.747 (terac-)s 427.75 y 8.71 (tions)s 36.972 (I)s 41.638 (I,)s 52.167 (in)s 17 f 65.029 (Asymptotic)s 127.182 (Pr)s 139.768 (oblems)s 177.974 (in)s 191.647 (Pr)s 204.234 (ob)s 215.274 (ability)s 250.413 (The)s 270.04 (ory)s 290.306 (:)s 298.982 (Sto)s 315.236 (chastic)s 354.362 (Mo)s 370.641 (dels)s 393.514 (and)s 415.774 (Di\256usion)s 444.55 y 8.71 (on)s 25.4 (F)s 32.313 (r)s 36.76 (actals)s 1 f 66.506 (,)s 73.419 (edited)s 108.894 (b)s 115.227 (y)s 125.035 (K.)s 141.177 (Elw)s 161.01 (orth)s 182.71 (y)s 192.518 (and)s 215.326 (N.)s 231.135 (Ik)s 241.468 (eda,)s 266.381 (Pitman)s 308.689 (Researc)s 348.623 (h)s 358.764 (Notes)s 391.972 (in)s 405.447 (Mathemat-)s 461.35 y 8.71 (ics)s 26.11 (283,)s 51.443 (Wiley)s 81.11 (,)s 88.443 (\0501994\051.)s 478.27 y -21.957 ([VY])s 8.71 (S.)s 22.108 (R.)s 37.672 (S.)s 51.07 (V)s 59.07 (aradhan)s 105.169 (and)s 127.9 (H.T.)s 155.631 (Y)s 163.631 (au)s 17 f 179.696 (Di\256usive)s 229.602 (Limit)s 262.028 (of)s 275.58 (L)s 282.494 (attic)s 305.187 (e)s 314.446 (Gas)s 338.509 (with)s 364.021 (Mixing)s 403.714 (Conditions)s 1 f 460.447 (.)s 495.07 y 8.71 (Asian)s 42.443 (J.)s 55.943 (Math.)s 0 f 92.943 (1)s 1 f 99.843 (,)s 107.177 (623\173678)s 153.177 (\0501997\051.)s 511.99 y -12.957 ([Y])s 8.71 (Y)s 16.71 (au,)s 37.222 (H.)s 53.965 (T.)s 70.374 (Metastabilit)s 133.774 (y)s 144.517 (of)s 158.594 (Ginzburg-Landau)s 255.287 (mo)s 271.62 (del)s 291.363 (with)s 319.106 (a)s 329.516 (conserv)s 367.949 (ation)s 399.025 (la)s 408.025 (w,)s 22 f 424.537 (J.)s 438.447 (Stat.)s 528.79 y 8.71 (Ph)s 23.21 (ys)s 1 f 34.277 (.)s 0 f 42.943 (74)s 1 f 60.743 (705-742.)s 109.41 (\0501994\051.)s 705.976 y 223.045 (50)s do-end end endp %%Trailer end %%EOF ---------------9908230506225--