This is TeX, Version 3.14159 (Web2C 7.3.1) (format=latex 2003.4.12) 1 AUG 2003 02:16 **final.tex (final.tex LaTeX2e <2001/06/01> Babel and hyphenation patterns for american, french, german, ngerman, i talian, nohyphenation, loaded. (birkart.cls Document Class: birkart 2002/01/29 v1.1 \linespacing=\dimen102 \normalparindent=\dimen103 \normaltopskip=\skip41 (/usr/share/texmf/tex/latex/amsmath/amsgen.sty File: amsgen.sty 1999/11/30 v2.0 \@emptytoks=\toks14 \ex@=\dimen104 ) (/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. (/usr/share/texmf/tex/latex/amsmath/amstext.sty Package: amstext 2000/06/29 v2.01 ) (/usr/share/texmf/tex/latex/amsmath/amsbsy.sty Package: amsbsy 1999/11/29 v1.2d \pmbraise@=\dimen105 ) (/usr/share/texmf/tex/latex/amsmath/amsopn.sty Package: amsopn 1999/12/14 v2.01 operator names ) \inf@bad=\count79 LaTeX Info: Redefining \frac on input line 211. \uproot@=\count80 \leftroot@=\count81 LaTeX Info: Redefining \overline on input line 307. \classnum@=\count82 \DOTSCASE@=\count83 LaTeX Info: Redefining \ldots on input line 379. LaTeX Info: Redefining \dots on input line 382. LaTeX Info: Redefining \cdots on input line 467. \Mathstrutbox@=\box26 \strutbox@=\box27 \big@size=\dimen106 LaTeX Font Info: Redeclaring font encoding OML on input line 567. 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. ) (/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@figure=\count96 \c@table=\count97 \abovecaptionskip=\skip46 \belowcaptionskip=\skip47 \captionindent=\dimen113 (/usr/share/texmf/tex/latex/amscls/amsthm.sty Package: amsthm 2000/10/26 v2.08 \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 ) \c@theorem=\count98 (final.aux) \openout1 = `final.aux'. LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 91. LaTeX Font Info: ... okay on input line 91. LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 91. LaTeX Font Info: ... okay on input line 91. LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 91. LaTeX Font Info: ... okay on input line 91. LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 91. LaTeX Font Info: ... okay on input line 91. LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 91. LaTeX Font Info: ... okay on input line 91. LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 91. LaTeX Font Info: ... okay on input line 91. LaTeX Font Info: Checking defaults for OT2/cmr/m/n on input line 91. LaTeX Font Info: Try loading font information for OT2+cmr on input line 91. (/usr/share/texmf/tex/latex/cyrillic/ot2cmr.fd File: ot2cmr.fd 2001/08/11 v3.2c Computer Modern Cyrillic font definitions ) LaTeX Font Info: ... okay on input line 91. LaTeX Font Info: Try loading font information for U+msa on input line 91. (/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 91. (/usr/share/texmf/tex/latex/amsfonts/umsb.fd File: umsb.fd 2002/01/19 v2.2g AMS font definitions ) LaTeX Font Info: Try loading font information for OT2+wncyr on input line 10 1. (/usr/share/texmf/tex/latex/cyrillic/ot2wncyr.fd File: ot2wncyr.fd 1999/12/17 v3.2a Computer Modern Cyrillic font definitions ) [1] [2] Underfull \hbox (badness 10000) in paragraph at lines 281--282 [] [3] LaTeX Font Info: Try loading font information for U+euf on input line 327. (/usr/share/texmf/tex/latex/amsfonts/ueuf.fd File: ueuf.fd 2002/01/19 v2.2g AMS font definitions ) [4] [5] LaTeX Font Info: Try loading font information for OMS+cmr on input line 514. (/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 514. [6] [7] [8] 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 743. [9] Overfull \hbox (2.49785pt too wide) in paragraph at lines 815--826 []\OT1/cmr/m/n/10 Kato's the-o-rem ([[], \OMS/cmsy/m/n/10 x\OT1/cmr/m/n/10 8.1] and [[], Cor. 14.3]) im-plies that $[](\OML/cmm/m/it/10 E=K\OT1/cmr/m/n/10 )[\ OML/cmm/m/it/10 p[]\OT1/cmr/m/n/10 ]$ [] [10] [11] [12] [13] (final.aux) ) Here is how much of TeX's memory you used: 1716 strings out of 20880 18636 string characters out of 197306 65893 words of memory out of 350001 4508 multiletter control sequences out of 10000+15000 15620 words of font info for 60 fonts, out of 400000 for 1000 175 hyphenation exceptions out of 10000 33i,12n,32p,247b,415s stack positions out of 3000i,100n,1500p,50000b,4000s Output written on final.dvi (13 pages, 49952 bytes).