This is TeX, Version 3.14159 (Web2C 7.3.1) (format=latex 1999.7.10) 8 SEP 2003 11:17 **1.tex (1.tex LaTeX2e <1998/12/01> patch level 1 Babel and hyphenation patterns for american, french, german, ngerman, n ohyphenation, loaded. (/mt/buddybolden.mathlab.sunysb.edu/share/teTeX-1.0/share/texmf/tex/latex/base/ article.cls Document Class: article 1999/01/07 v1.4a Standard LaTeX document class (/mt/buddybolden.mathlab.sunysb.edu/share/teTeX-1.0/share/texmf/tex/latex/base/ size10.clo File: size10.clo 1999/01/07 v1.4a Standard LaTeX file (size option) ) \c@part=\count79 \c@section=\count80 \c@subsection=\count81 \c@subsubsection=\count82 \c@paragraph=\count83 \c@subparagraph=\count84 \c@figure=\count85 \c@table=\count86 \abovecaptionskip=\skip41 \belowcaptionskip=\skip42 \bibindent=\dimen102 ) (/mt/buddybolden.mathlab.sunysb.edu/share/teTeX-1.0/share/texmf/tex/latex/amsla tex/amsmath.sty Package: amsmath 1997/03/20 v1.2d AMS math features \@mathmargin=\skip43 (/mt/buddybolden.mathlab.sunysb.edu/share/teTeX-1.0/share/texmf/tex/latex/amsla tex/amstext.sty Package: amstext 1996/10/28 v1.2b (/mt/buddybolden.mathlab.sunysb.edu/share/teTeX-1.0/share/texmf/tex/latex/amsla tex/amsgen.sty File: amsgen 1996/10/29 v1.2b \@emptytoks=\toks14 \ex@=\dimen103 )) (/mt/buddybolden.mathlab.sunysb.edu/share/teTeX-1.0/share/texmf/tex/latex/amsla tex/amsbsy.sty Package: amsbsy 1996/10/28 v1.2b \pmbraise@=\dimen104 ) (/mt/buddybolden.mathlab.sunysb.edu/share/teTeX-1.0/share/texmf/tex/latex/amsla tex/amsopn.sty Package: amsopn 1996/10/28 v1.2b operator names ) LaTeX Info: Redefining \frac on input line 188. \uproot@=\count87 \leftroot@=\count88 \classnum@=\count89 \DOTSCASE@=\count90 LaTeX Info: Redefining \dots on input line 335. LaTeX Info: Redefining \ldots on input line 418. LaTeX Info: Redefining \cdots on input line 422. \Mathstrutbox@=\box26 \strutbox@=\box27 \big@size=\dimen105 LaTeX Font Info: Redeclaring font encoding OML on input line 500. LaTeX Font Info: Redeclaring font encoding OMS on input line 501. \skewcharcount@=\count91 \familycount@=\count92 \pointcount@=\count93 \accentdimen@=\dimen106 \accentmu@=\count94 \minaw@=\dimen107 \c@MaxMatrixCols=\count95 \dotsspace@=\muskip10 \c@parentequation=\count96 \dspbrk@lvl=\count97 \tag@help=\toks15 \row@=\count98 \column@=\count99 \maxfields@=\count100 \andhelp@=\toks16 \eqnshift@=\dimen108 \alignsep@=\dimen109 \tagshift@=\dimen110 \tagwidth@=\dimen111 \totwidth@=\dimen112 \lineht@=\dimen113 \@envbody=\toks17 \multlinegap=\skip44 \multlinetaggap=\skip45 ) (/mt/buddybolden.mathlab.sunysb.edu/share/teTeX-1.0/share/texmf/tex/latex/amsfo nts/amssymb.sty Package: amssymb 1996/11/03 v2.2b (/mt/buddybolden.mathlab.sunysb.edu/share/teTeX-1.0/share/texmf/tex/latex/amsfo nts/amsfonts.sty Package: amsfonts 1997/09/17 v2.2e \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 133. )) (/mt/buddybolden.mathlab.sunysb.edu/share/teTeX-1.0/share/texmf/tex/latex/jknap pen/mathrsfs.sty Package: mathrsfs 1996/01/01 Math RSFS package v1.0 (jk) \symrsfs=\mathgroup6 ) (1.aux) \openout1 = `1.aux'. LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 12. LaTeX Font Info: ... okay on input line 12. LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 12. LaTeX Font Info: ... okay on input line 12. LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 12. LaTeX Font Info: ... okay on input line 12. LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 12. LaTeX Font Info: ... okay on input line 12. LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 12. LaTeX Font Info: ... okay on input line 12. LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 12. LaTeX Font Info: ... okay on input line 12. LaTeX Font Info: Try loading font information for U+msa on input line 13. (/mt/buddybolden.mathlab.sunysb.edu/share/teTeX-1.0/share/texmf/tex/latex/amsfo nts/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 13. (/mt/buddybolden.mathlab.sunysb.edu/share/teTeX-1.0/share/texmf/tex/latex/amsfo nts/umsb.fd File: umsb.fd 1995/01/05 v2.2e AMS font definitions ) LaTeX Font Info: Try loading font information for U+rsfs on input line 13. (/mt/buddybolden.mathlab.sunysb.edu/share/teTeX-1.0/share/texmf/tex/latex/jknap pen/ursfs.fd File: Ursfs.fd 1998/03/24 rsfs font definition file (jk) ) [1 ] Underfull \hbox (badness 10000) in paragraph at lines 53--63 [] LaTeX Font Info: Try loading font information for U+euf on input line 65. (/mt/buddybolden.mathlab.sunysb.edu/share/teTeX-1.0/share/texmf/tex/latex/amsfo nts/ueuf.fd File: ueuf.fd 1995/01/05 v2.2e AMS font definitions ) [2] Underfull \hbox (badness 10000) in paragraph at lines 106--137 [] Underfull \hbox (badness 10000) in paragraph at lines 106--137 [] [3] Overfull \hbox (17.57277pt too wide) in paragraph at lines 178--192 \OT1/cmr/m/n/10 Now we will show that the ba-sis of $\OML/cmm/m/it/10 R[]\OMS/c msy/m/n/10 f\OT1/cmr/m/n/10 ((\OML/cmm/m/it/10 r; i\OT1/cmr/m/n/10 )\OML/cmm/m/ it/10 ; \OT1/cmr/m/n/10 (\OML/cmm/m/it/10 s; j\OT1/cmr/m/n/10 ))\OMS/cmsy/m/n/1 0 j [] \OML/cmm/m/it/10 ; i; j; r; s \OMS/cmsy/m/n/10 2 [] Overfull \hbox (7.75906pt too wide) in paragraph at lines 178--192 \OT1/cmr/m/n/10 (\OML/cmm/m/it/10 r \OMS/cmsy/m/n/10 ^^B \OT1/cmr/m/n/10 (\OML/ cmm/m/it/10 i; \OT1/cmr/m/n/10 +\OMS/cmsy/m/n/10 1\OT1/cmr/m/n/10 )) \OMS/cmsy/ m/n/10 [ \OT1/cmr/m/n/10 ((\OML/cmm/m/it/10 r; s\OT1/cmr/m/n/10 ) \OMS/cmsy/m/n /10 ^^B \OT1/cmr/m/n/10 (\OMS/cmsy/m/n/10 ^^@1\OML/cmm/m/it/10 ; \OT1/cmr/m/n/1 0 +\OMS/cmsy/m/n/10 1\OT1/cmr/m/n/10 )) \OMS/cmsy/m/n/10 [ \OT1/cmr/m/n/10 (\OM L/cmm/m/it/10 s \OMS/cmsy/m/n/10 ^^B \OT1/cmr/m/n/10 (\OMS/cmsy/m/n/10 ^^@1\OML /cmm/m/it/10 ; j\OT1/cmr/m/n/10 )) = [][](\OML/cmm/m/it/10 r \OMS/cmsy/m/n/10 ^ ^B \OT1/cmr/m/n/10 (\OML/cmm/m/it/10 i; b\OT1/cmr/m/n/10 )) \OMS/cmsy/m/n/10 [ [][]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 t \OMS/cmsy/m/n/10 ^^B [] [4] [5] (1.aux) ) Here is how much of TeX's memory you used: 1067 strings out of 10901 12036 string characters out of 72185 61417 words of memory out of 263001 4016 multiletter control sequences out of 10000+0 11989 words of font info for 50 fonts, out of 400000 for 1000 14 hyphenation exceptions out of 1000 27i,8n,24p,217b,257s stack positions out of 300i,100n,500p,50000b,4000s Output written on 1.dvi (5 pages, 20676 bytes).