This is TeX, Version 3.14159 (Web2C 7.3) (format=latex 1999.4.27) 13 JUN 2000 23:09 **kakeya2.tex (kakeya2.tex LaTeX2e <1998/12/01> Babel and hyphenation patterns for american, french, german, ngerman, n ohyphenation, loaded. (/net/fern/m4/tex/teTeX-0.9/share/texmf/tex/latex/base/latex209.def File: latex209.def 1998/05/13 v0.52 Standard LaTeX file Entering LaTeX 2.09 COMPATIBILITY MODE ************************************************************* !!WARNING!! !!WARNING!! !!WARNING!! !!WARNING!! This mode attempts to provide an emulation of the LaTeX 2.09 author environment so that OLD documents can be successfully processed. It should NOT be used for NEW documents! New documents should use Standard LaTeX conventions and start with the \documentclass command. Compatibility mode is UNLIKELY TO WORK with LaTeX 2.09 style files that change any internal macros, especially not with those that change the FONT SELECTION or OUTPUT ROUTINES. Therefore such style files MUST BE UPDATED to use Current Standard LaTeX: LaTeX2e. If you suspect that you may be using such a style file, which is probably very, very old by now, then you should attempt to get it updated by sending a copy of this error message to the author of that file. ************************************************************* \footheight=\dimen102 \@maxsep=\dimen103 \@dblmaxsep=\dimen104 \@cla=\count79 \@clb=\count80 \mscount=\count81 (/net/fern/m4/tex/teTeX-0.9/share/texmf/tex/latex/base/tracefnt.sty Package: tracefnt 1997/05/29 v3.0j Standard LaTeX package (font tracing) \tracingfonts=\count82 LaTeX Info: Redefining \selectfont on input line 83. ) \symbold=\mathgroup4 \symsans=\mathgroup5 \symtypewriter=\mathgroup6 \symitalic=\mathgroup7 \symsmallcaps=\mathgroup8 \symslanted=\mathgroup9 LaTeX Font Info: Redeclaring math alphabet \mathbf on input line 275. LaTeX Font Info: Redeclaring math alphabet \mathsf on input line 276. 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(/net/fern/m4/tex/teTeX-0.9/share/texmf/tex/latex/base/ulasy.fd File: ulasy.fd 1998/08/17 v2.2eLaTeX symbol font definitions ))) (/net/fern/m4/tex/teTeX-0.9/share/texmf/tex/latex/base/article.cls Document Class: article 1999/01/07 v1.4a Standard LaTeX document class (/net/fern/m4/tex/teTeX-0.9/share/texmf/tex/latex/base/size12.clo File: size12.clo 1999/01/07 v1.4a Standard LaTeX file (size option) ) \c@part=\count83 \c@section=\count84 \c@subsection=\count85 \c@subsubsection=\count86 \c@paragraph=\count87 \c@subparagraph=\count88 \c@figure=\count89 \c@table=\count90 \abovecaptionskip=\skip41 \belowcaptionskip=\skip42 Compatibility mode: definition of \rm ignored. Compatibility mode: definition of \sf ignored. Compatibility mode: definition of \tt ignored. Compatibility mode: definition of \bf ignored. Compatibility mode: definition of \it ignored. Compatibility mode: definition of \sl ignored. Compatibility mode: definition of \sc ignored. LaTeX Info: Redefining \cal on input line 488. LaTeX Info: Redefining \mit on input line 489. \bibindent=\dimen105 ) (/net/fern/m4/tex/teTeX-0.9/share/texmf/tex/latex/amsfonts/amssymb.sty Package: amssymb 1996/11/03 v2.2b (/net/fern/m4/tex/teTeX-0.9/share/texmf/tex/latex/amsfonts/amsfonts.sty Package: amsfonts 1997/09/17 v2.2e \@emptytoks=\toks14 \symAMSa=\mathgroup11 \symAMSb=\mathgroup12 LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold' (Font) U/euf/m/n --> U/euf/b/n on input line 133. )) (/net/fern/m4/tex/teTeX-0.9/share/texmf/tex/generic/misc/psfig.sty \@unused=\write3 \ps@stream=\read1 \p@intvaluex=\dimen106 \p@intvaluey=\dimen107 psfig/tex 1.10-dvips ) (/u/sonia/h1/fa/tao/tex/MathMacro.tex) \c@theorem=\count91 \c@proposition=\count92 \c@lemma=\count93 \c@corollary=\count94 \c@remark=\count95 No file kakeya2.aux. \openout1 = `kakeya2.aux'. LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 42. LaTeX Font Info: ... okay on input line 42. LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 42. LaTeX Font Info: ... okay on input line 42. LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 42. LaTeX Font Info: ... okay on input line 42. LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 42. LaTeX Font Info: ... okay on input line 42. LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 42. LaTeX Font Info: ... okay on input line 42. LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 42. LaTeX Font Info: ... okay on input line 42. LaTeX Font Info: Try loading font information for U+msa on input line 67. (/net/fern/m4/tex/teTeX-0.9/share/texmf/tex/latex/amsfonts/umsa.fd File: umsa.fd 1995/01/05 v2.2e AMS font definitions ) LaTeX Font Info: Try loading font information for U+msb on input line 67. (/net/fern/m4/tex/teTeX-0.9/share/texmf/tex/latex/amsfonts/umsb.fd File: umsb.fd 1995/01/05 v2.2e AMS font definitions ) [1 ] LaTeX Font Info: Try loading font information for OMS+cmr on input line 77. (/net/fern/m4/tex/teTeX-0.9/share/texmf/tex/latex/base/omscmr.fd File: omscmr.fd 1998/03/27 v2.5g Standard LaTeX font definitions ) LaTeX Font Info: Font shape `OMS/cmr/m/n' in size <17.28> not available (Font) Font shape `OMS/cmsy/m/n' tried instead on input line 77. Overfull \hbox (16.629pt too wide) in paragraph at lines 77--78 []\OT1/cmr/m/n/17.28 The Kakeya con-jec-ture comes in three lev-els of strength . [] [2] [3] [4] psfig: searching kakeya-types.eps for bounding box psfig: including kakeya-types.eps [5] [6] Overfull \hbox (2.47427pt too wide) in paragraph at lines 150--151 \OT1/cmr/m/n/17.28 ing ar-gu-ments, we were able to im-prove Wolff's bound [] [7] [8] [9] [10] Overfull \hbox (75.91193pt too wide) detected at line 204 \OML/cmm/m/it/17.28 T[] \OT1/cmr/m/n/17.28 := \OMS/cmsy/m/n/17.28 f\OT1/cmr/m/n /17.28 ([]\OML/cmm/m/it/17.28 ; x[]\OT1/cmr/m/n/17.28 ) \OMS/cmsy/m/n/17.28 2 [ ][] ^^B [] \OT1/cmr/m/n/17.28 : 0 \OMS/cmsy/m/n/17.28 ^^T \OML/cmm/m/it/17.28 x [] \OMS/cmsy/m/n/17.28 ^^T \OT1/cmr/m/n/17.28 1; [] = \OML/cmm/m/it/17.28 x[] \ OT1/cmr/m/n/17.28 + \OML/cmm/m/it/17.28 v[]x[] \OT1/cmr/m/n/17.28 + \OML/cmm/m/ it/17.28 O\OT1/cmr/m/n/17.28 (\OML/cmm/m/it/17.28 ^^N\OT1/cmr/m/n/17.28 )\OMS/c msy/m/n/17.28 g [] [11] psfig: searching slices.eps for bounding box psfig: including slices.eps [12] [13] [14] [15] [16] psfig: searching trapezoid.eps for bounding box psfig: including trapezoid.eps Overfull \hbox (0.87639pt too wide) in paragraph at lines 259--260 \OT1/cmr/m/n/17.28 but there are four con-straints be-tween these el-e-ments. [] [17] psfig: searching move_slices.eps for bounding box psfig: including move_slices.eps [18] [19] psfig: searching quad.eps for bounding box psfig: including quad.eps [20] [21] [22] [23] [24] psfig: searching iterate.eps for bounding box psfig: including iterate.eps [25] Overfull \hbox (0.46654pt too wide) in paragraph at lines 333--334 \OML/cmm/m/it/17.28 N[]$\OT1/cmr/m/n/17.28 , which is a slight im-prove-ment ov er $\OML/cmm/m/it/17.28 N[] \OT1/cmr/m/n/17.28 = [] [26] [27] psfig: searching trapezopiped.eps for bounding box psfig: including trapezopiped.eps [28] [29] [30] (kakeya2.aux) ) Here is how much of TeX's memory you used: 1194 strings out of 10896 11828 string characters out of 71883 54934 words of memory out of 263001 4122 multiletter control sequences out of 10000+0 22736 words of font info for 87 fonts, out of 200000 for 1000 15 hyphenation exceptions out of 1000 25i,5n,24p,560b,240s stack positions out of 300i,100n,500p,30000b,4000s Output written on kakeya2.dvi (30 pages, 31148 bytes).