This is e-TeX, Version 3.14159-2.1 (Web2C 7.4.5) (format=latex 2005.5.21) 14 SEP 2005 00:05 entering extended mode **197.tex (./197.tex LaTeX2e <2001/06/01> Babel and hyphenation patterns for american, nohyphenation, catalan, ir ish, icelandic, swedish, loaded. (/usr/share/texmf/tex/latex/amscls/amsart.cls Document Class: amsart 2000/10/26 v2.08 \linespacing=\dimen102 \normalparindent=\dimen103 \normaltopskip=\skip41 (/usr/share/texmf/tex/latex/amsmath/amsmath.sty Package: amsmath 2000/07/18 v2.13 AMS math features \@mathmargin=\skip42 For additional information on amsmath, use the `?' option. 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LaTeX Font Info: Redeclaring font encoding OMS on input line 568. \macc@depth=\count84 \c@MaxMatrixCols=\count85 \dotsspace@=\muskip10 \c@parentequation=\count86 \dspbrk@lvl=\count87 \tag@help=\toks15 \row@=\count88 \column@=\count89 \maxfields@=\count90 \andhelp@=\toks16 \eqnshift@=\dimen107 \alignsep@=\dimen108 \tagshift@=\dimen109 \tagwidth@=\dimen110 \totwidth@=\dimen111 \lineht@=\dimen112 \@envbody=\toks17 \multlinegap=\skip43 \multlinetaggap=\skip44 \mathdisplay@stack=\toks18 LaTeX Info: Redefining \[ on input line 2666. LaTeX Info: Redefining \] on input line 2667. ) LaTeX Font Info: Try loading font information for U+msa on input line 395. (/usr/share/texmf/tex/latex/amsfonts/umsa.fd File: umsa.fd 2002/01/19 v2.2g AMS font definitions ) (/usr/share/texmf/tex/latex/amsfonts/amsfonts.sty Package: amsfonts 2001/10/25 v2.2f \symAMSa=\mathgroup4 \symAMSb=\mathgroup5 LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold' (Font) U/euf/m/n --> U/euf/b/n on input line 132. ) \copyins=\insert233 \abstractbox=\box28 \listisep=\skip45 \c@part=\count91 \c@section=\count92 \c@subsection=\count93 \c@subsubsection=\count94 \c@paragraph=\count95 \c@subparagraph=\count96 \c@figure=\count97 \c@table=\count98 \abovecaptionskip=\skip46 \belowcaptionskip=\skip47 \captionindent=\dimen113 \thm@style=\toks19 \thm@bodyfont=\toks20 \thm@headfont=\toks21 \thm@notefont=\toks22 \thm@headpunct=\toks23 \thm@preskip=\skip48 \thm@postskip=\skip49 \thm@headsep=\skip50 \dth@everypar=\toks24 ) (/usr/share/texmf/tex/latex/amsfonts/amssymb.sty Package: amssymb 2002/01/22 v2.2d ) (/usr/share/texmf/tex/generic/xypic/xypic.sty (/usr/share/texmf/tex/generic/xypic/xy.sty (/usr/share/texmf/tex/generic/xypic/xy.tex Bootstrap'ing: catcodes, docmode, (/usr/share/texmf/tex/generic/xypic/xyrecat.tex) (/usr/share/texmf/tex/generic/xypic/xyidioms.tex) Xy-pic version 3.7 <1999/02/16> Copyright (c) 1991-1998 by Kristoffer H. 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Loading kernel: messages; fonts; allocations: state, \X@c=\dimen114 \Y@c=\dimen115 \U@c=\dimen116 \D@c=\dimen117 \L@c=\dimen118 \R@c=\dimen119 \Edge@c=\toks25 \X@p=\dimen120 \Y@p=\dimen121 \U@p=\dimen122 \D@p=\dimen123 \L@p=\dimen124 \R@p=\dimen125 \Edge@p=\toks26 \X@origin=\dimen126 \Y@origin=\dimen127 \X@xbase=\dimen128 \Y@xbase=\dimen129 \X@ybase=\dimen130 \Y@ybase=\dimen131 \X@min=\dimen132 \Y@min=\dimen133 \X@max=\dimen134 \Y@max=\dimen135 \lastobjectbox@=\box29 \zerodotbox@=\box30 \almostz@=\dimen136 direction, \d@X=\dimen137 \d@Y=\dimen138 \K@=\count99 \KK@=\count100 \Direction=\count101 \K@dXdY=\dimen139 \K@dYdX=\dimen140 \xyread@=\read1 \xywrite@=\write3 \csp@=\count102 \quotPTK@=\dimen141 utility macros; pictures: \xy, positions, \swaptoks@@=\toks27 \connectobjectbox@@=\box31 objects, \styletoks@=\toks28 decorations; kernel objects: directionals, circles, text; options; algorithms: directions, edges, connections; Xy-pic loaded) LaTeX Warning: You have requested package `xypic', but the package provides `xy'. Package: xy 1999/02/16 Xy-pic version 3.7 ) (/usr/share/texmf/tex/generic/xypic/xyv2.tex Xy-pic option: Version 2 Compatibility v.3.4 Xy-pic Warning: `\stop' redefined. (/usr/share/texmf/tex/generic/xypic/xyframe.tex Xy-pic option: Frame and Bracket extension v.3.7 loaded) (/usr/share/texmf/tex/generic/xypic/xymatrix.tex Xy-pic option: Matrix feature v.3.4 \Row=\count103 \Col=\count104 \queue@=\toks29 \queue@@=\toks30 \qcount@=\count105 \qcount@@=\count106 \matrixsize@=\count107 loaded) (/usr/share/texmf/tex/generic/xypic/xyarrow.tex Xy-pic option: Arrow and Path feature v.3.5 path, \ar, loaded) loaded)) \c@lemma=\count108 (./197.aux) \openout1 = `197.aux'. LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 78. LaTeX Font Info: ... okay on input line 78. LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 78. LaTeX Font Info: ... okay on input line 78. LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 78. LaTeX Font Info: ... okay on input line 78. LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 78. LaTeX Font Info: ... okay on input line 78. LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 78. LaTeX Font Info: ... okay on input line 78. LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 78. LaTeX Font Info: ... okay on input line 78. LaTeX Font Info: Try loading font information for U+msa on input line 78. (/usr/share/texmf/tex/latex/amsfonts/umsa.fd File: umsa.fd 2002/01/19 v2.2g AMS font definitions ) LaTeX Font Info: Try loading font information for U+msb on input line 78. (/usr/share/texmf/tex/latex/amsfonts/umsb.fd File: umsb.fd 2002/01/19 v2.2g AMS font definitions ) (./197.toc) \tf@toc=\write4 \openout4 = `197.toc'. [1] LaTeX Font Info: Try loading font information for OMS+cmr on input line 206. (/usr/share/texmf/tex/latex/base/omscmr.fd File: omscmr.fd 1999/05/25 v2.5h Standard LaTeX font definitions ) LaTeX Font Info: Font shape `OMS/cmr/m/n' in size <10> not available (Font) Font shape `OMS/cmsy/m/n' tried instead on input line 206. Underfull \vbox (badness 10000) has occurred while \output is active [] [2] [3] Overfull \hbox (4.21397pt too wide) detected at line 326 \OML/cmm/m/it/10 G\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 V; h; q; \OT1/cmr/m/n/10 (\ OML/cmm/m/it/10 I; \OT1/cmr/m/n/10 ^^@)) = \OMS/cmsy/m/n/10 f\OML/cmm/m/it/10 ^ ^[ \OMS/cmsy/m/n/10 2 \OML/cmm/m/it/10 G\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 V; h; q\OT1/cmr/m/n/10 )\OMS/cmsy/m/n/10 j\OML/cmm/m/it/10 ^^[ \OMS/cmsy/m/n/10 ^^Q \OT1/cmr/m/n/10 1 \OML/cmm/m/it/10 modI; f\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 ^^[ v; ^^[v\OT1/cmr/m/n/10 ) \OMS/cmsy/m/n/10 ^^@ \OML/cmm/m/it/10 f\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 v; v\OT1/cmr/m/n/10 ) \OMS/cmsy/m/n/10 2 \OT1/cmr/m/n/10 ^^@ []\OML/cmm/m/it/10 v \OMS/cmsy/m/n/10 2 \OML/cmm/m/it/10 V\OMS/cmsy/m/n/10 g [] Overfull \hbox (19.57347pt too wide) in paragraph at lines 328--335 []\OT1/cmr/m/n/10 In his the-sis Bak proved that, if $(\OML/cmm/m/it/10 V; h; q \OT1/cmr/m/n/10 )$ is non-sin-gu-lar then the group $\OML/cmm/m/it/10 G\OT1/cmr /m/n/10 (\OML/cmm/m/it/10 V; h; q; \OT1/cmr/m/n/10 (\OML/cmm/m/it/10 I; \OT1/cm r/m/n/10 ^^@))$ [] Overfull \hbox (8.20137pt too wide) in paragraph at lines 392--398 \OT1/cmr/m/n/10 The nor-mal clo-sure $[][]\OML/cmm/m/it/10 F[]\OT1/cmr/m/n/10 ( \OML/cmm/m/it/10 I; \OT1/cmr/m/n/10 ^^@)$ of $\OML/cmm/m/it/10 F[]\OT1/cmr/m/n/ 10 (\OML/cmm/m/it/10 I; \OT1/cmr/m/n/10 ^^@)$ in $\OML/cmm/m/it/10 E[]\OT1/cmr/ m/n/10 (\OML/cmm/m/it/10 A; \OT1/cmr/m/n/10 ^^C)$ is de-noted by $\OML/cmm/m/it /10 E[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 I; \OT1/cmr/m/n/10 ^^@)$ [] [4] [5] LaTeX Font Info: Try loading font information for U+euf on input line 579. (/usr/share/texmf/tex/latex/amsfonts/ueuf.fd File: ueuf.fd 2002/01/19 v2.2g AMS font definitions ) [6] Package amsmath Warning: Foreign command \atop; (amsmath) \frac or \genfrac should be used instead (amsmath) on input line 592. [7] Overfull \hbox (68.87816pt too wide) detected at line 706 [] [] [8] Package amsfonts Warning: Obsolete command \Bbb; \mathbb should be used instead on input line 777. [9] Overfull \hbox (3.16798pt too wide) in paragraph at lines 817--819 \OT1/cmr/bx/n/10 Definition 3.2. \OT1/cmr/m/n/10 Let $(\OMS/cmsy/m/n/10 C\OML/c mm/m/it/10 ; \OMS/cmsy/m/n/10 S\OT1/cmr/m/n/10 (\OMS/cmsy/m/n/10 C\OT1/cmr/m/n/ 10 )\OML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 I\OT1/cmr/m/n/10 (\OMS/cmsy/m/n/10 C\OT 1/cmr/m/n/10 ))$ be a cat-e-gory with struc-ture. Let $\OML/cmm/m/it/10 d \OT1/ cmr/m/n/10 : \OMS/cmsy/m/n/10 O\OML/cmm/m/it/10 bj\OT1/cmr/m/n/10 (\OMS/cmsy/m/ n/10 C\OT1/cmr/m/n/10 ) [][]\OMS/cmsy/m/n/10 ! [] [10] [11] [12] [13] LaTeX Font Info: Font shape `OMS/cmr/m/n' in size <8> not available (Font) Font shape `OMS/cmsy/m/n' tried instead on input line 1112. [14] [15] Missing character: There is no ^^e8 in font cmr8! Missing character: There is no ^^e8 in font cmr8! Missing character: There is no ^^e9 in font cmr8! Missing character: There is no ^^e9 in font cmr8! [16] Overfull \hbox (5.7958pt too wide) in paragraph at lines 1352--1352 []\OT1/cmr/m/sc/8 Department of Math-e-mat-ics and Me-chan-ics, Saint-Petersbur g State Uni-ver-sity, Saint- [] [17] (./197.aux) ) Here is how much of TeX's memory you used: 3304 strings out of 95667 33950 string characters out of 1193946 116240 words of memory out of 1000001 6118 multiletter control sequences out of 10000+50000 12963 words of font info for 52 fonts, out of 500000 for 1000 247 hyphenation exceptions out of 1000 34i,15n,32p,240b,469s stack positions out of 1500i,500n,5000p,200000b,5000s Output written on 197.dvi (17 pages, 89904 bytes).