This is TeX, Version 3.14159 (Web2C 7.4.5) (format=latex 2003.9.11) 23 FEB 2004 12:44 **\nonstopmode\input 252-project.tex (./252-project.tex (./tran-l.cls Document Class: tran-l 1994/10/01 v1.2 TRAN Author Class (/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. (/usr/share/texmf/tex/latex/amsmath/amstext.sty Package: amstext 2000/06/29 v2.01 (/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/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. ) 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/amsmath/amscd.sty Package: amscd 1999/11/29 v2.0 \athelp@=\toks25 \minaw@=\dimen114 \bigaw@=\dimen115 \minCDarrowwidth=\dimen116 ) \c@thm=\count99 \c@example=\count100 (./252-project.aux) \openout1 = `252-project.aux'. LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 85. LaTeX Font Info: ... okay on input line 85. LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 85. LaTeX Font Info: ... okay on input line 85. LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 85. LaTeX Font Info: ... okay on input line 85. LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 85. LaTeX Font Info: ... okay on input line 85. LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 85. LaTeX Font Info: ... okay on input line 85. LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 85. LaTeX Font Info: ... okay on input line 85. LaTeX Font Info: Checking defaults for OT2/cmr/m/n on input line 85. LaTeX Font Info: Try loading font information for OT2+cmr on input line 85. (/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 85. LaTeX Font Info: Try loading font information for U+msa on input line 85. (/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 85. (/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 15 6. (/usr/share/texmf/tex/latex/cyrillic/ot2wncyr.fd File: ot2wncyr.fd 1999/12/17 v3.2a Computer Modern Cyrillic font definitions ) [1] Underfull \hbox (badness 10000) in paragraph at lines 226--228 [] Underfull \hbox (badness 10000) in paragraph at lines 266--267 [] [2] LaTeX Font Info: Try loading font information for OMS+cmr on input line 311. (/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 311. Underfull \hbox (badness 10000) in paragraph at lines 311--313 [] Underfull \hbox (badness 10000) in paragraph at lines 316--338 [] [3] Underfull \hbox (badness 10000) in paragraph at lines 385--386 [] Underfull \hbox (badness 10000) in paragraph at lines 401--416 [] Underfull \hbox (badness 10000) in paragraph at lines 447--455 [] [4] Underfull \hbox (badness 10000) in paragraph at lines 474--493 [] [5] [6] [7] Underfull \hbox (badness 10000) in paragraph at lines 741--746 [] Underfull \hbox (badness 10000) in paragraph at lines 762--763 [] Underfull \hbox (badness 10000) in paragraph at lines 784--798 [] [8] Underfull \hbox (badness 10000) in paragraph at lines 850--852 [] Underfull \hbox (badness 10000) in paragraph at lines 853--870 [] Overfull \hbox (7.66615pt too wide) in paragraph at lines 913--920 \OT1/cmr/m/n/10 By Hilbert Satz 90, $\OML/cmm/m/it/10 H[]\OT1/cmr/m/n/10 ([]([] \OML/cmm/m/it/10 =K\OT1/cmr/m/n/10 )\OML/cmm/m/it/10 ; ^^V[]\OT1/cmr/m/n/10 ) \ OMS/cmsy/m/n/10 ' \OML/cmm/m/it/10 K[]=\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 K[]\OT 1/cmr/m/n/10 )[]$. More-over, $\OML/cmm/m/it/10 H[]\OT1/cmr/m/n/10 ([]([]\OML/c mm/m/it/10 =K\OT1/cmr/m/n/10 )\OML/cmm/m/it/10 ; ^^V[]\OT1/cmr/m/n/10 ; \OML/cm m/m/it/10 S\OT1/cmr/m/n/10 ) [] \OML/cmm/m/it/10 K\OT1/cmr/m/n/10 (\OML/cmm/m/i t/10 S; m\OT1/cmr/m/n/10 )$. [] Underfull \hbox (badness 10000) in paragraph at lines 913--920 [] [9] Overfull \hbox (1.76222pt too wide) in paragraph at lines 928--933 \OT1/cmr/m/n/10 Since $\OML/cmm/m/it/10 E\OT1/cmr/m/n/10 [\OML/cmm/m/it/10 ^^^\ OT1/cmr/m/n/10 ] [] \OML/cmm/m/it/10 ^^V[]$ \OT1/cmr/m/n/10 as $[]([]\OML/cmm/m /it/10 =K\OT1/cmr/m/n/10 )$-modules, then Hilbert Satz 90 im-plies that $\OML/c mm/m/it/10 H[]\OT1/cmr/m/n/10 ([]([]\OML/cmm/m/it/10 =K\OT1/cmr/m/n/10 )\OML/cm m/m/it/10 ; E\OT1/cmr/m/n/10 [\OML/cmm/m/it/10 ^^^\OT1/cmr/m/n/10 ]; \OML/cmm/m /it/10 S\OT1/cmr/m/n/10 ) [] [] Underfull \hbox (badness 10000) in paragraph at lines 981--987 [] [10] Underfull \hbox (badness 10000) in paragraph at lines 1013--1019 [] [11] Underfull \hbox (badness 10000) in paragraph at lines 1109--1110 [] Underfull \hbox (badness 10000) in paragraph at lines 1123--1131 [] Underfull \hbox (badness 10000) in paragraph at lines 1189--1190 [] [12] [13] (./252-project.aux) ) Here is how much of TeX's memory you used: 1484 strings out of 95796 16715 string characters out of 1191756 69646 words of memory out of 1000001 4277 multiletter control sequences out of 10000+50000 12075 words of font info for 46 fonts, out of 500000 for 1000 187 hyphenation exceptions out of 1000 40i,17n,31p,286b,347s stack positions out of 3000i,1500n,5000p,200000b,15000s Output written on 252-project.dvi (13 pages, 77576 bytes).