diff options
Diffstat (limited to '')
32 files changed, 498 insertions, 2364 deletions
diff --git a/buch/buch.aux b/buch/buch.aux deleted file mode 100644 index 6730af9..0000000 --- a/buch/buch.aux +++ /dev/null @@ -1,22 +0,0 @@ -\relax -\providecommand\hyper@newdestlabel[2]{} -\providecommand\babel@aux[2]{} -\@nameuse{bbl@beforestart} -\catcode `"\active -\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument} -\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined -\global\let\oldcontentsline\contentsline -\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}} -\global\let\oldnewlabel\newlabel -\gdef\newlabel#1#2{\newlabelxx{#1}#2} -\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}} -\AtEndDocument{\ifx\hyper@anchor\@undefined -\let\contentsline\oldcontentsline -\let\newlabel\oldnewlabel -\fi} -\fi} -\global\let\hyper@last\relax -\gdef\HyperFirstAtBeginDocument#1{#1} -\providecommand\HyField@AuxAddToFields[1]{} -\providecommand\HyField@AuxAddToCoFields[2]{} -\providecommand\BKM@entry[2]{} diff --git a/buch/buch.bbl b/buch/buch.bbl deleted file mode 100644 index e69de29..0000000 --- a/buch/buch.bbl +++ /dev/null diff --git a/buch/buch.blg b/buch/buch.blg deleted file mode 100644 index 706b1d8..0000000 --- a/buch/buch.blg +++ /dev/null @@ -1,48 +0,0 @@ -This is BibTeX, Version 0.99d -Capacity: max_strings=200000, hash_size=200000, hash_prime=170003 -The top-level auxiliary file: buch.aux -I found no \citation commands---while reading file buch.aux -I found no \bibdata command---while reading file buch.aux -I found no \bibstyle command---while reading file buch.aux -You've used 0 entries, - 0 wiz_defined-function locations, - 83 strings with 482 characters, -and the built_in function-call counts, 0 in all, are: -= -- 0 -> -- 0 -< -- 0 -+ -- 0 -- -- 0 -* -- 0 -:= -- 0 -add.period$ -- 0 -call.type$ -- 0 -change.case$ -- 0 -chr.to.int$ -- 0 -cite$ -- 0 -duplicate$ -- 0 -empty$ -- 0 -format.name$ -- 0 -if$ -- 0 -int.to.chr$ -- 0 -int.to.str$ -- 0 -missing$ -- 0 -newline$ -- 0 -num.names$ -- 0 -pop$ -- 0 -preamble$ -- 0 -purify$ -- 0 -quote$ -- 0 -skip$ -- 0 -stack$ -- 0 -substring$ -- 0 -swap$ -- 0 -text.length$ -- 0 -text.prefix$ -- 0 -top$ -- 0 -type$ -- 0 -warning$ -- 0 -while$ -- 0 -width$ -- 0 -write$ -- 0 -(There were 3 error messages) diff --git a/buch/buch.idx b/buch/buch.idx deleted file mode 100644 index e69de29..0000000 --- a/buch/buch.idx +++ /dev/null diff --git a/buch/buch.log b/buch/buch.log deleted file mode 100644 index 4175a27..0000000 --- a/buch/buch.log +++ /dev/null @@ -1,2106 +0,0 @@ -This is pdfTeX, Version 3.141592653-2.6-1.40.24 (MiKTeX 22.3) (preloaded format=pdflatex 2022.4.16) 17 MAY 2022 13:22 -entering extended mode - restricted \write18 enabled. - %&-line parsing enabled. -**./buch.tex -(buch.tex -LaTeX2e <2021-11-15> patch level 1 -L3 programming layer <2022-02-24> (common/content.tex -(D:\Programme\Miktex\tex/latex/base\book.cls -Document Class: book 2021/10/04 v1.4n Standard LaTeX document class -(D:\Programme\Miktex\tex/latex/base\bk10.clo -File: bk10.clo 2021/10/04 v1.4n Standard LaTeX file (size option) -) -\c@part=\count185 -\c@chapter=\count186 -\c@section=\count187 -\c@subsection=\count188 -\c@subsubsection=\count189 -\c@paragraph=\count190 -\c@subparagraph=\count191 -\c@figure=\count192 -\c@table=\count193 -\abovecaptionskip=\skip47 -\belowcaptionskip=\skip48 -\bibindent=\dimen138 -) (common/packages.tex -(D:\Programme\Miktex\tex/latex/etex-pkg\etex.sty -Package: etex 2016/08/01 v2.7 eTeX basic definition package (PEB,DPC) -\et@xins=\count194 -) -(D:\Programme\Miktex\tex/latex/geometry\geometry.sty -Package: geometry 2020/01/02 v5.9 Page Geometry - -(D:\Programme\Miktex\tex/latex/graphics\keyval.sty -Package: keyval 2014/10/28 v1.15 key=value parser (DPC) -\KV@toks@=\toks16 -) -(D:\Programme\Miktex\tex/generic/iftex\ifvtex.sty -Package: ifvtex 2019/10/25 v1.7 ifvtex legacy package. Use iftex instead. - -(D:\Programme\Miktex\tex/generic/iftex\iftex.sty -Package: iftex 2022/02/03 v1.0f TeX engine tests -)) -\Gm@cnth=\count195 -\Gm@cntv=\count196 -\c@Gm@tempcnt=\count197 -\Gm@bindingoffset=\dimen139 -\Gm@wd@mp=\dimen140 -\Gm@odd@mp=\dimen141 -\Gm@even@mp=\dimen142 -\Gm@layoutwidth=\dimen143 -\Gm@layoutheight=\dimen144 -\Gm@layouthoffset=\dimen145 -\Gm@layoutvoffset=\dimen146 -\Gm@dimlist=\toks17 - -(D:\Programme\Miktex\tex/latex/geometry\geometry.cfg)) -(D:\Programme\Miktex\tex/generic/babel\babel.sty -Package: babel 2022/02/26 3.73 The Babel package -\babel@savecnt=\count198 -\U@D=\dimen147 -\l@unhyphenated=\language79 - -(D:\Programme\Miktex\tex/generic/babel\txtbabel.def) -\bbl@readstream=\read2 -\bbl@dirlevel=\count199 - -************************************* -* Local config file bblopts.cfg used -* -(D:\Programme\Miktex\tex/latex/arabi\bblopts.cfg -File: bblopts.cfg 2005/09/08 v0.1 add Arabic and Farsi to "declared" options of - babel -) -(D:\Programme\Miktex\tex/latex/babel-english\english.ldf -Language: english 2017/06/06 v3.3r English support from the babel system -Package babel Info: Hyphen rules for 'canadian' set to \l@english -(babel) (\language0). Reported on input line 102. -Package babel Info: Hyphen rules for 'australian' set to \l@ukenglish -(babel) (\language73). Reported on input line 105. -Package babel Info: Hyphen rules for 'newzealand' set to \l@ukenglish -(babel) (\language73). Reported on input line 108. -) -(D:\Programme\Miktex\tex/latex/babel-german\ngerman.ldf -Language: ngerman 2021/02/27 v2.13 German support for babel (post-1996 orthogra -phy) - -(D:\Programme\Miktex\tex/latex/babel-german\ngermanb.ldf -Language: ngermanb 2021/02/27 v2.13 German support for babel (post-1996 orthogr -aphy) -Package babel Info: Making " an active character on input line 122. -))) -(D:\Programme\Miktex\tex/latex/base\inputenc.sty -Package: inputenc 2021/02/14 v1.3d Input encoding file -\inpenc@prehook=\toks18 -\inpenc@posthook=\toks19 -) -(D:\Programme\Miktex\tex/latex/base\fontenc.sty -Package: fontenc 2021/04/29 v2.0v Standard LaTeX package -) -(D:\Programme\Miktex\tex/latex/cancel\cancel.sty -Package: cancel 2013/04/12 v2.2 Cancel math terms -) -(D:\Programme\Miktex\tex/latex/psnfss\times.sty -Package: times 2020/03/25 PSNFSS-v9.3 (SPQR) -) -(D:\Programme\Miktex\tex/latex/amsmath\amsmath.sty -Package: amsmath 2021/10/15 v2.17l AMS math features -\@mathmargin=\skip49 - -For additional information on amsmath, use the `?' option. -(D:\Programme\Miktex\tex/latex/amsmath\amstext.sty -Package: amstext 2021/08/26 v2.01 AMS text - -(D:\Programme\Miktex\tex/latex/amsmath\amsgen.sty -File: amsgen.sty 1999/11/30 v2.0 generic functions -\@emptytoks=\toks20 -\ex@=\dimen148 -)) -(D:\Programme\Miktex\tex/latex/amsmath\amsbsy.sty -Package: amsbsy 1999/11/29 v1.2d Bold Symbols -\pmbraise@=\dimen149 -) -(D:\Programme\Miktex\tex/latex/amsmath\amsopn.sty -Package: amsopn 2021/08/26 v2.02 operator names -) -Normal \count register pool exhausted, switching to extended pool. -\inf@bad=\count277 -LaTeX Info: Redefining \frac on input line 234. -\uproot@=\count278 -\leftroot@=\count279 -LaTeX Info: Redefining \overline on input line 399. -\classnum@=\count280 -\DOTSCASE@=\count281 -LaTeX Info: Redefining \ldots on input line 496. -LaTeX Info: Redefining \dots on input line 499. -LaTeX Info: Redefining \cdots on input line 620. -\Mathstrutbox@=\box50 -\strutbox@=\box51 -\big@size=\dimen150 -LaTeX Font Info: Redeclaring font encoding OML on input line 743. -LaTeX Font Info: Redeclaring font encoding OMS on input line 744. -\macc@depth=\count282 -\c@MaxMatrixCols=\count283 -\dotsspace@=\muskip16 -\c@parentequation=\count284 -\dspbrk@lvl=\count285 -\tag@help=\toks21 -\row@=\count286 -\column@=\count287 -\maxfields@=\count288 -\andhelp@=\toks22 -\eqnshift@=\dimen151 -\alignsep@=\dimen152 -\tagshift@=\dimen153 -\tagwidth@=\dimen154 -\totwidth@=\dimen155 -\lineht@=\dimen156 -\@envbody=\toks23 -\multlinegap=\skip50 -\multlinetaggap=\skip51 -\mathdisplay@stack=\toks24 -LaTeX Info: Redefining \[ on input line 2938. -LaTeX Info: Redefining \] on input line 2939. -) -(D:\Programme\Miktex\tex/latex/amsmath\amscd.sty -Package: amscd 2017/04/14 v2.1 AMS Commutative Diagrams -\athelp@=\toks25 -\minaw@=\dimen157 -\bigaw@=\dimen158 -\minCDarrowwidth=\dimen159 -) -(D:\Programme\Miktex\tex/latex/amsfonts\amssymb.sty -Package: amssymb 2013/01/14 v3.01 AMS font symbols - -(D:\Programme\Miktex\tex/latex/amsfonts\amsfonts.sty -Package: amsfonts 2013/01/14 v3.01 Basic AMSFonts support -\symAMSa=\mathgroup4 -\symAMSb=\mathgroup5 -LaTeX Font Info: Redeclaring math symbol \hbar on input line 98. -LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold' -(Font) U/euf/m/n --> U/euf/b/n on input line 106. -)) -(D:\Programme\Miktex\tex/latex/amscls\amsthm.sty -Package: amsthm 2020/05/29 v2.20.6 -\thm@style=\toks26 -\thm@bodyfont=\toks27 -\thm@headfont=\toks28 -\thm@notefont=\toks29 -\thm@headpunct=\toks30 -\thm@preskip=\skip52 -\thm@postskip=\skip53 -\thm@headsep=\skip54 -\dth@everypar=\toks31 -) -(D:\Programme\Miktex\tex/latex/graphics\graphicx.sty -Package: graphicx 2021/09/16 v1.2d Enhanced LaTeX Graphics (DPC,SPQR) - -(D:\Programme\Miktex\tex/latex/graphics\graphics.sty -Package: graphics 2021/03/04 v1.4d Standard LaTeX Graphics (DPC,SPQR) - -(D:\Programme\Miktex\tex/latex/graphics\trig.sty -Package: trig 2021/08/11 v1.11 sin cos tan (DPC) -) -(D:\Programme\Miktex\tex/latex/graphics-cfg\graphics.cfg -File: graphics.cfg 2016/06/04 v1.11 sample graphics configuration -) -Package graphics Info: Driver file: pdftex.def on input line 107. - -(D:\Programme\Miktex\tex/latex/graphics-def\pdftex.def -File: pdftex.def 2020/10/05 v1.2a Graphics/color driver for pdftex -)) -\Gin@req@height=\dimen160 -\Gin@req@width=\dimen161 -) -(D:\Programme\Miktex\tex/latex/fancyhdr\fancyhdr.sty -Package: fancyhdr 2022/05/10 v4.0.2 Extensive control of page headers and foote -rs -\f@nch@headwidth=\skip55 -\f@nch@O@elh=\skip56 -\f@nch@O@erh=\skip57 -\f@nch@O@olh=\skip58 -\f@nch@O@orh=\skip59 -\f@nch@O@elf=\skip60 -\f@nch@O@erf=\skip61 -\f@nch@O@olf=\skip62 -\f@nch@O@orf=\skip63 -) -(D:\Programme\Miktex\tex/latex/base\textcomp.sty -Package: textcomp 2020/02/02 v2.0n Standard LaTeX package -) -(D:\Programme\Miktex\tex/latex/txfonts\txfonts.sty -Package: txfonts 2008/01/22 v3.2.1 -LaTeX Font Info: Redeclaring symbol font `operators' on input line 21. -LaTeX Font Info: Overwriting symbol font `operators' in version `normal' -(Font) OT1/cmr/m/n --> OT1/txr/m/n on input line 21. -LaTeX Font Info: Overwriting symbol font `operators' in version `bold' -(Font) OT1/cmr/bx/n --> OT1/txr/m/n on input line 21. -LaTeX Font Info: Overwriting symbol font `operators' in version `bold' -(Font) OT1/txr/m/n --> OT1/txr/bx/n on input line 22. -\symitalic=\mathgroup6 -LaTeX Font Info: Overwriting symbol font `italic' in version `bold' -(Font) OT1/txr/m/it --> OT1/txr/bx/it on input line 26. -LaTeX Font Info: Redeclaring math alphabet \mathbf on input line 29. -LaTeX Font Info: Overwriting math alphabet `\mathbf' in version `normal' -(Font) OT1/cmr/bx/n --> OT1/txr/bx/n on input line 29. -LaTeX Font Info: Overwriting math alphabet `\mathbf' in version `bold' -(Font) OT1/cmr/bx/n --> OT1/txr/bx/n on input line 29. -LaTeX Font Info: Redeclaring math alphabet \mathit on input line 30. -LaTeX Font Info: Overwriting math alphabet `\mathit' in version `normal' -(Font) OT1/cmr/m/it --> OT1/txr/m/it on input line 30. -LaTeX Font Info: Overwriting math alphabet `\mathit' in version `bold' -(Font) OT1/cmr/bx/it --> OT1/txr/m/it on input line 30. -LaTeX Font Info: Overwriting math alphabet `\mathit' in version `bold' -(Font) OT1/txr/m/it --> OT1/txr/bx/it on input line 31. -LaTeX Font Info: Redeclaring math alphabet \mathsf on input line 40. -LaTeX Font Info: Overwriting math alphabet `\mathsf' in version `normal' -(Font) OT1/cmss/m/n --> OT1/txss/m/n on input line 40. -LaTeX Font Info: Overwriting math alphabet `\mathsf' in version `bold' -(Font) OT1/cmss/bx/n --> OT1/txss/m/n on input line 40. -LaTeX Font Info: Overwriting math alphabet `\mathsf' in version `bold' -(Font) OT1/txss/m/n --> OT1/txss/b/n on input line 41. -LaTeX Font Info: Redeclaring math alphabet \mathtt on input line 50. -LaTeX Font Info: Overwriting math alphabet `\mathtt' in version `normal' -(Font) OT1/cmtt/m/n --> OT1/txtt/m/n on input line 50. -LaTeX Font Info: Overwriting math alphabet `\mathtt' in version `bold' -(Font) OT1/cmtt/m/n --> OT1/txtt/m/n on input line 50. -LaTeX Font Info: Overwriting math alphabet `\mathtt' in version `bold' -(Font) OT1/txtt/m/n --> OT1/txtt/b/n on input line 51. -LaTeX Font Info: Redeclaring symbol font `letters' on input line 58. -LaTeX Font Info: Overwriting symbol font `letters' in version `normal' -(Font) OML/cmm/m/it --> OML/txmi/m/it on input line 58. -LaTeX Font Info: Overwriting symbol font `letters' in version `bold' -(Font) OML/cmm/b/it --> OML/txmi/m/it on input line 58. -LaTeX Font Info: Overwriting symbol font `letters' in version `bold' -(Font) OML/txmi/m/it --> OML/txmi/bx/it on input line 59. -\symlettersA=\mathgroup7 -LaTeX Font Info: Overwriting symbol font `lettersA' in version `bold' -(Font) U/txmia/m/it --> U/txmia/bx/it on input line 67. -LaTeX Font Info: Redeclaring math alphabet \mathfrak on input line 70. -LaTeX Font Info: Redeclaring symbol font `symbols' on input line 77. -LaTeX Font Info: Overwriting symbol font `symbols' in version `normal' -(Font) OMS/cmsy/m/n --> OMS/txsy/m/n on input line 77. -LaTeX Font Info: Overwriting symbol font `symbols' in version `bold' -(Font) OMS/cmsy/b/n --> OMS/txsy/m/n on input line 77. -LaTeX Font Info: Overwriting symbol font `symbols' in version `bold' -(Font) OMS/txsy/m/n --> OMS/txsy/bx/n on input line 78. -LaTeX Font Info: Redeclaring symbol font `AMSa' on input line 93. -LaTeX Font Info: Overwriting symbol font `AMSa' in version `normal' -(Font) U/msa/m/n --> U/txsya/m/n on input line 93. -LaTeX Font Info: Overwriting symbol font `AMSa' in version `bold' -(Font) U/msa/m/n --> U/txsya/m/n on input line 93. -LaTeX Font Info: Overwriting symbol font `AMSa' in version `bold' -(Font) U/txsya/m/n --> U/txsya/bx/n on input line 94. -LaTeX Font Info: Redeclaring symbol font `AMSb' on input line 102. -LaTeX Font Info: Overwriting symbol font `AMSb' in version `normal' -(Font) U/msb/m/n --> U/txsyb/m/n on input line 102. -LaTeX Font Info: Overwriting symbol font `AMSb' in version `bold' -(Font) U/msb/m/n --> U/txsyb/m/n on input line 102. -LaTeX Font Info: Overwriting symbol font `AMSb' in version `bold' -(Font) U/txsyb/m/n --> U/txsyb/bx/n on input line 103. -\symsymbolsC=\mathgroup8 -LaTeX Font Info: Overwriting symbol font `symbolsC' in version `bold' -(Font) U/txsyc/m/n --> U/txsyc/bx/n on input line 113. -LaTeX Font Info: Redeclaring symbol font `largesymbols' on input line 120. -LaTeX Font Info: Overwriting symbol font `largesymbols' in version `normal' -(Font) OMX/cmex/m/n --> OMX/txex/m/n on input line 120. -LaTeX Font Info: Overwriting symbol font `largesymbols' in version `bold' -(Font) OMX/cmex/m/n --> OMX/txex/m/n on input line 120. -LaTeX Font Info: Overwriting symbol font `largesymbols' in version `bold' -(Font) OMX/txex/m/n --> OMX/txex/bx/n on input line 121. -\symlargesymbolsA=\mathgroup9 -LaTeX Font Info: Overwriting symbol font `largesymbolsA' in version `bold' -(Font) U/txexa/m/n --> U/txexa/bx/n on input line 129. -LaTeX Font Info: Redeclaring math symbol \mathsterling on input line 164. -LaTeX Info: Redefining \not on input line 1043. -LaTeX Info: Redefining \textsquare on input line 1063. -LaTeX Info: Redefining \openbox on input line 1064. -) -(D:\Programme\Miktex\tex/latex/jknappen\mathrsfs.sty -Package: mathrsfs 1996/01/01 Math RSFS package v1.0 (jk) -\symrsfs=\mathgroup10 -) -(D:\Programme\Miktex\tex/latex/units\nicefrac.sty -Package: nicefrac 1998/08/04 v0.9b Nice fractions -\L@UnitsRaiseDisplaystyle=\skip64 -\L@UnitsRaiseTextstyle=\skip65 -\L@UnitsRaiseScriptstyle=\skip66 - -(D:\Programme\Miktex\tex/latex/base\ifthen.sty -Package: ifthen 2020/11/24 v1.1c Standard LaTeX ifthen package (DPC) -)) -(D:\Programme\Miktex\tex/latex/tools\bm.sty -Package: bm 2021/04/25 v1.2e Bold Symbol Support (DPC/FMi) -Package bm Info: No bold for \U/rsfs/m/n, using \pmb. -) -(D:\Programme\Miktex\tex/latex/eepic\epic.sty -Enhancements to Picture Environment. Version 1.2 - Released June 1, 1986 -\@@multicnt=\count289 -\d@lta=\count290 -\@delta=\dimen162 -\@@delta=\dimen163 -\@gridcnt=\count291 -\@joinkind=\count292 -\@dotgap=\dimen164 -\@ddotgap=\dimen165 -\@x@diff=\count293 -\@y@diff=\count294 -\x@diff=\dimen166 -\y@diff=\dimen167 -\@dotbox=\box52 -\num@segments=\count295 -\num@segmentsi=\count296 -\@datafile=\read3 -) (D:\Programme\Miktex\tex/latex/tools\verbatim.sty -Package: verbatim 2020-07-07 v1.5u LaTeX2e package for verbatim enhancements -\every@verbatim=\toks32 -\verbatim@line=\toks33 -\verbatim@in@stream=\read4 -) -(D:\Programme\Miktex\tex/latex/paralist\paralist.sty -Package: paralist 2017/01/22 v2.7 Extended list environments -\pltopsep=\skip67 -\plpartopsep=\skip68 -\plitemsep=\skip69 -\plparsep=\skip70 -\pl@lab=\toks34 -) -(D:\Programme\Miktex\tex/latex/base\makeidx.sty -Package: makeidx 2021/10/04 v1.0m Standard LaTeX package -) -(D:\Programme\Miktex\tex/latex/tools\array.sty -Package: array 2021/10/04 v2.5f Tabular extension package (FMi) -\col@sep=\dimen168 -\ar@mcellbox=\box53 -\extrarowheight=\dimen169 -\NC@list=\toks35 -\extratabsurround=\skip71 -\backup@length=\skip72 -\ar@cellbox=\box54 -) -(D:\Programme\Miktex\tex/latex/multirow\multirow.sty -Package: multirow 2021/03/15 v2.8 Span multiple rows of a table -\multirow@colwidth=\skip73 -\multirow@cntb=\count297 -\multirow@dima=\skip74 -\bigstrutjot=\dimen170 -) -(D:\Programme\Miktex\tex/latex/hyperref\hyperref.sty -Package: hyperref 2022-02-21 v7.00n Hypertext links for LaTeX - -(D:\Programme\Miktex\tex/generic/ltxcmds\ltxcmds.sty -Package: ltxcmds 2020-05-10 v1.25 LaTeX kernel commands for general use (HO) -) -(D:\Programme\Miktex\tex/generic/pdftexcmds\pdftexcmds.sty -Package: pdftexcmds 2020-06-27 v0.33 Utility functions of pdfTeX for LuaTeX (HO -) - -(D:\Programme\Miktex\tex/generic/infwarerr\infwarerr.sty -Package: infwarerr 2019/12/03 v1.5 Providing info/warning/error messages (HO) -) -Package pdftexcmds Info: \pdf@primitive is available. -Package pdftexcmds Info: \pdf@ifprimitive is available. -Package pdftexcmds Info: \pdfdraftmode found. -) -(D:\Programme\Miktex\tex/generic/kvsetkeys\kvsetkeys.sty -Package: kvsetkeys 2019/12/15 v1.18 Key value parser (HO) -) -(D:\Programme\Miktex\tex/generic/kvdefinekeys\kvdefinekeys.sty -Package: kvdefinekeys 2019-12-19 v1.6 Define keys (HO) -) -(D:\Programme\Miktex\tex/generic/pdfescape\pdfescape.sty -Package: pdfescape 2019/12/09 v1.15 Implements pdfTeX's escape features (HO) -) -(D:\Programme\Miktex\tex/latex/hycolor\hycolor.sty -Package: hycolor 2020-01-27 v1.10 Color options for hyperref/bookmark (HO) -) -(D:\Programme\Miktex\tex/latex/letltxmacro\letltxmacro.sty -Package: letltxmacro 2019/12/03 v1.6 Let assignment for LaTeX macros (HO) -) -(D:\Programme\Miktex\tex/latex/auxhook\auxhook.sty -Package: auxhook 2019-12-17 v1.6 Hooks for auxiliary files (HO) -) -(D:\Programme\Miktex\tex/latex/kvoptions\kvoptions.sty -Package: kvoptions 2020-10-07 v3.14 Key value format for package options (HO) -) -\@linkdim=\dimen171 -\Hy@linkcounter=\count298 -\Hy@pagecounter=\count299 - -(D:\Programme\Miktex\tex/latex/hyperref\pd1enc.def -File: pd1enc.def 2022-02-21 v7.00n Hyperref: PDFDocEncoding definition (HO) -Now handling font encoding PD1 ... -... no UTF-8 mapping file for font encoding PD1 -) -(D:\Programme\Miktex\tex/generic/intcalc\intcalc.sty -Package: intcalc 2019/12/15 v1.3 Expandable calculations with integers (HO) -) -(D:\Programme\Miktex\tex/generic/etexcmds\etexcmds.sty -Package: etexcmds 2019/12/15 v1.7 Avoid name clashes with e-TeX commands (HO) -) -\Hy@SavedSpaceFactor=\count300 - -(D:\Programme\Miktex\tex/latex/hyperref\puenc.def -File: puenc.def 2022-02-21 v7.00n Hyperref: PDF Unicode definition (HO) -Now handling font encoding PU ... -... no UTF-8 mapping file for font encoding PU -) -Package hyperref Info: Hyper figures OFF on input line 4137. -Package hyperref Info: Link nesting OFF on input line 4142. -Package hyperref Info: Hyper index ON on input line 4145. -Package hyperref Info: Plain pages OFF on input line 4152. -Package hyperref Info: Backreferencing OFF on input line 4157. -Package hyperref Info: Implicit mode ON; LaTeX internals redefined. -Package hyperref Info: Bookmarks ON on input line 4390. -\c@Hy@tempcnt=\count301 - -(D:\Programme\Miktex\tex/latex/url\url.sty -\Urlmuskip=\muskip17 -Package: url 2013/09/16 ver 3.4 Verb mode for urls, etc. -) -LaTeX Info: Redefining \url on input line 4749. -\XeTeXLinkMargin=\dimen172 - -(D:\Programme\Miktex\tex/generic/bitset\bitset.sty -Package: bitset 2019/12/09 v1.3 Handle bit-vector datatype (HO) - -(D:\Programme\Miktex\tex/generic/bigintcalc\bigintcalc.sty -Package: bigintcalc 2019/12/15 v1.5 Expandable calculations on big integers (HO -) -)) -\Fld@menulength=\count302 -\Field@Width=\dimen173 -\Fld@charsize=\dimen174 -Package hyperref Info: Hyper figures OFF on input line 6027. -Package hyperref Info: Link nesting OFF on input line 6032. -Package hyperref Info: Hyper index ON on input line 6035. -Package hyperref Info: backreferencing OFF on input line 6042. -Package hyperref Info: Link coloring OFF on input line 6047. -Package hyperref Info: Link coloring with OCG OFF on input line 6052. -Package hyperref Info: PDF/A mode OFF on input line 6057. -LaTeX Info: Redefining \ref on input line 6097. -LaTeX Info: Redefining \pageref on input line 6101. - -(D:\Programme\Miktex\tex/latex/base\atbegshi-ltx.sty -Package: atbegshi-ltx 2021/01/10 v1.0c Emulation of the original atbegshi -package with kernel methods -) -\Hy@abspage=\count303 -\c@Item=\count304 -\c@Hfootnote=\count305 -) -Package hyperref Info: Driver (autodetected): hpdftex. - -(D:\Programme\Miktex\tex/latex/hyperref\hpdftex.def -File: hpdftex.def 2022-02-21 v7.00n Hyperref driver for pdfTeX - -(D:\Programme\Miktex\tex/latex/base\atveryend-ltx.sty -Package: atveryend-ltx 2020/08/19 v1.0a Emulation of the original atveryend pac -kage -with kernel methods -) -\Fld@listcount=\count306 -\c@bookmark@seq@number=\count307 - -(D:\Programme\Miktex\tex/latex/rerunfilecheck\rerunfilecheck.sty -Package: rerunfilecheck 2019/12/05 v1.9 Rerun checks for auxiliary files (HO) - -(D:\Programme\Miktex\tex/generic/uniquecounter\uniquecounter.sty -Package: uniquecounter 2019/12/15 v1.4 Provide unlimited unique counter (HO) -) -Package uniquecounter Info: New unique counter `rerunfilecheck' on input line 2 -86. -) -\Hy@SectionHShift=\skip75 -) -(D:\Programme\Miktex\tex/latex/subfigure\subfigure.sty -Package: subfigure 2002/07/30 v2.1.4 subfigure package -\subfigtopskip=\skip76 -\subfigcapskip=\skip77 -\subfigcaptopadj=\dimen175 -\subfigbottomskip=\skip78 -\subfigcapmargin=\dimen176 -\subfiglabelskip=\skip79 -\c@subfigure=\count308 -\c@lofdepth=\count309 -\c@subtable=\count310 -\c@lotdepth=\count311 - -**************************************** -* Local config file subfigure.cfg used * -**************************************** -(D:\Programme\Miktex\tex/latex/subfigure\subfigure.cfg) -\subfig@top=\skip80 -\subfig@bottom=\skip81 -) -(D:\Programme\Miktex\tex/latex/pgf/frontendlayer\tikz.sty -(D:\Programme\Miktex\tex/latex/pgf/basiclayer\pgf.sty -(D:\Programme\Miktex\tex/latex/pgf/utilities\pgfrcs.sty -(D:\Programme\Miktex\tex/generic/pgf/utilities\pgfutil-common.tex -\pgfutil@everybye=\toks36 -\pgfutil@tempdima=\dimen177 -\pgfutil@tempdimb=\dimen178 - -(D:\Programme\Miktex\tex/generic/pgf/utilities\pgfutil-common-lists.tex)) -(D:\Programme\Miktex\tex/generic/pgf/utilities\pgfutil-latex.def -\pgfutil@abb=\box55 -) -(D:\Programme\Miktex\tex/generic/pgf/utilities\pgfrcs.code.tex -(D:\Programme\Miktex\tex/generic/pgf\pgf.revision.tex) -Package: pgfrcs 2021/05/15 v3.1.9a (3.1.9a) -)) -Package: pgf 2021/05/15 v3.1.9a (3.1.9a) - -(D:\Programme\Miktex\tex/latex/pgf/basiclayer\pgfcore.sty -(D:\Programme\Miktex\tex/latex/pgf/systemlayer\pgfsys.sty -(D:\Programme\Miktex\tex/generic/pgf/systemlayer\pgfsys.code.tex -Package: pgfsys 2021/05/15 v3.1.9a (3.1.9a) - -(D:\Programme\Miktex\tex/generic/pgf/utilities\pgfkeys.code.tex -\pgfkeys@pathtoks=\toks37 -\pgfkeys@temptoks=\toks38 - -(D:\Programme\Miktex\tex/generic/pgf/utilities\pgfkeysfiltered.code.tex -\pgfkeys@tmptoks=\toks39 -)) -\pgf@x=\dimen179 -\pgf@y=\dimen180 -\pgf@xa=\dimen181 -\pgf@ya=\dimen182 -\pgf@xb=\dimen183 -\pgf@yb=\dimen184 -\pgf@xc=\dimen185 -\pgf@yc=\dimen186 -\pgf@xd=\dimen187 -\pgf@yd=\dimen188 -\w@pgf@writea=\write3 -\r@pgf@reada=\read5 -\c@pgf@counta=\count312 -\c@pgf@countb=\count313 -\c@pgf@countc=\count314 -\c@pgf@countd=\count315 -\t@pgf@toka=\toks40 -\t@pgf@tokb=\toks41 -\t@pgf@tokc=\toks42 -\pgf@sys@id@count=\count316 - -(D:\Programme\Miktex\tex/generic/pgf/systemlayer\pgf.cfg -File: pgf.cfg 2021/05/15 v3.1.9a (3.1.9a) -) -Driver file for pgf: pgfsys-pdftex.def - -(D:\Programme\Miktex\tex/generic/pgf/systemlayer\pgfsys-pdftex.def -File: pgfsys-pdftex.def 2021/05/15 v3.1.9a (3.1.9a) - -(D:\Programme\Miktex\tex/generic/pgf/systemlayer\pgfsys-common-pdf.def -File: pgfsys-common-pdf.def 2021/05/15 v3.1.9a (3.1.9a) -))) -(D:\Programme\Miktex\tex/generic/pgf/systemlayer\pgfsyssoftpath.code.tex -File: pgfsyssoftpath.code.tex 2021/05/15 v3.1.9a (3.1.9a) -\pgfsyssoftpath@smallbuffer@items=\count317 -\pgfsyssoftpath@bigbuffer@items=\count318 -) -(D:\Programme\Miktex\tex/generic/pgf/systemlayer\pgfsysprotocol.code.tex -File: pgfsysprotocol.code.tex 2021/05/15 v3.1.9a (3.1.9a) -)) -(D:\Programme\Miktex\tex/latex/xcolor\xcolor.sty -Package: xcolor 2021/10/31 v2.13 LaTeX color extensions (UK) - -(D:\Programme\Miktex\tex/latex/graphics-cfg\color.cfg -File: color.cfg 2016/01/02 v1.6 sample color configuration -) -Package xcolor Info: Driver file: pdftex.def on input line 227. -Package xcolor Info: Model `cmy' substituted by `cmy0' on input line 1352. -Package xcolor Info: Model `hsb' substituted by `rgb' on input line 1356. -Package xcolor Info: Model `RGB' extended on input line 1368. -Package xcolor Info: Model `HTML' substituted by `rgb' on input line 1370. -Package xcolor Info: Model `Hsb' substituted by `hsb' on input line 1371. -Package xcolor Info: Model `tHsb' substituted by `hsb' on input line 1372. -Package xcolor Info: Model `HSB' substituted by `hsb' on input line 1373. -Package xcolor Info: Model `Gray' substituted by `gray' on input line 1374. -Package xcolor Info: Model `wave' substituted by `hsb' on input line 1375. -) -(D:\Programme\Miktex\tex/generic/pgf/basiclayer\pgfcore.code.tex -Package: pgfcore 2021/05/15 v3.1.9a (3.1.9a) - -(D:\Programme\Miktex\tex/generic/pgf/math\pgfmath.code.tex -(D:\Programme\Miktex\tex/generic/pgf/math\pgfmathcalc.code.tex -(D:\Programme\Miktex\tex/generic/pgf/math\pgfmathutil.code.tex) -(D:\Programme\Miktex\tex/generic/pgf/math\pgfmathparser.code.tex -\pgfmath@dimen=\dimen189 -\pgfmath@count=\count319 -\pgfmath@box=\box56 -\pgfmath@toks=\toks43 -\pgfmath@stack@operand=\toks44 -\pgfmath@stack@operation=\toks45 -) -(D:\Programme\Miktex\tex/generic/pgf/math\pgfmathfunctions.code.tex -(D:\Programme\Miktex\tex/generic/pgf/math\pgfmathfunctions.basic.code.tex) -(D:\Programme\Miktex\tex/generic/pgf/math\pgfmathfunctions.trigonometric.code.t -ex) (D:\Programme\Miktex\tex/generic/pgf/math\pgfmathfunctions.random.code.tex) -(D:\Programme\Miktex\tex/generic/pgf/math\pgfmathfunctions.comparison.code.tex) -(D:\Programme\Miktex\tex/generic/pgf/math\pgfmathfunctions.base.code.tex) -(D:\Programme\Miktex\tex/generic/pgf/math\pgfmathfunctions.round.code.tex) -(D:\Programme\Miktex\tex/generic/pgf/math\pgfmathfunctions.misc.code.tex) -(D:\Programme\Miktex\tex/generic/pgf/math\pgfmathfunctions.integerarithmetics.c -ode.tex))) (D:\Programme\Miktex\tex/generic/pgf/math\pgfmathfloat.code.tex -\c@pgfmathroundto@lastzeros=\count320 -)) -(D:\Programme\Miktex\tex/generic/pgf/math\pgfint.code.tex) -(D:\Programme\Miktex\tex/generic/pgf/basiclayer\pgfcorepoints.code.tex -File: pgfcorepoints.code.tex 2021/05/15 v3.1.9a (3.1.9a) -\pgf@picminx=\dimen190 -\pgf@picmaxx=\dimen191 -\pgf@picminy=\dimen192 -\pgf@picmaxy=\dimen193 -\pgf@pathminx=\dimen194 -\pgf@pathmaxx=\dimen195 -\pgf@pathminy=\dimen196 -\pgf@pathmaxy=\dimen197 -\pgf@xx=\dimen198 -\pgf@xy=\dimen199 -Normal \dimen register pool exhausted, switching to extended pool. -\pgf@yx=\dimen256 -\pgf@yy=\dimen257 -\pgf@zx=\dimen258 -\pgf@zy=\dimen259 -) -(D:\Programme\Miktex\tex/generic/pgf/basiclayer\pgfcorepathconstruct.code.tex -File: pgfcorepathconstruct.code.tex 2021/05/15 v3.1.9a (3.1.9a) -\pgf@path@lastx=\dimen260 -\pgf@path@lasty=\dimen261 -) -(D:\Programme\Miktex\tex/generic/pgf/basiclayer\pgfcorepathusage.code.tex -File: pgfcorepathusage.code.tex 2021/05/15 v3.1.9a (3.1.9a) -\pgf@shorten@end@additional=\dimen262 -\pgf@shorten@start@additional=\dimen263 -) -(D:\Programme\Miktex\tex/generic/pgf/basiclayer\pgfcorescopes.code.tex -File: pgfcorescopes.code.tex 2021/05/15 v3.1.9a (3.1.9a) -\pgfpic=\box57 -\pgf@hbox=\box58 -\pgf@layerbox@main=\box59 -\pgf@picture@serial@count=\count321 -) -(D:\Programme\Miktex\tex/generic/pgf/basiclayer\pgfcoregraphicstate.code.tex -File: pgfcoregraphicstate.code.tex 2021/05/15 v3.1.9a (3.1.9a) -\pgflinewidth=\dimen264 -) -(D:\Programme\Miktex\tex/generic/pgf/basiclayer\pgfcoretransformations.code.tex -File: pgfcoretransformations.code.tex 2021/05/15 v3.1.9a (3.1.9a) -\pgf@pt@x=\dimen265 -\pgf@pt@y=\dimen266 -\pgf@pt@temp=\dimen267 -) (D:\Programme\Miktex\tex/generic/pgf/basiclayer\pgfcorequick.code.tex -File: pgfcorequick.code.tex 2021/05/15 v3.1.9a (3.1.9a) -) -(D:\Programme\Miktex\tex/generic/pgf/basiclayer\pgfcoreobjects.code.tex -File: pgfcoreobjects.code.tex 2021/05/15 v3.1.9a (3.1.9a) -) -(D:\Programme\Miktex\tex/generic/pgf/basiclayer\pgfcorepathprocessing.code.tex -File: pgfcorepathprocessing.code.tex 2021/05/15 v3.1.9a (3.1.9a) -) (D:\Programme\Miktex\tex/generic/pgf/basiclayer\pgfcorearrows.code.tex -File: pgfcorearrows.code.tex 2021/05/15 v3.1.9a (3.1.9a) -\pgfarrowsep=\dimen268 -) -(D:\Programme\Miktex\tex/generic/pgf/basiclayer\pgfcoreshade.code.tex -File: pgfcoreshade.code.tex 2021/05/15 v3.1.9a (3.1.9a) -\pgf@max=\dimen269 -\pgf@sys@shading@range@num=\count322 -\pgf@shadingcount=\count323 -) -(D:\Programme\Miktex\tex/generic/pgf/basiclayer\pgfcoreimage.code.tex -File: pgfcoreimage.code.tex 2021/05/15 v3.1.9a (3.1.9a) - -(D:\Programme\Miktex\tex/generic/pgf/basiclayer\pgfcoreexternal.code.tex -File: pgfcoreexternal.code.tex 2021/05/15 v3.1.9a (3.1.9a) -\pgfexternal@startupbox=\box60 -)) -(D:\Programme\Miktex\tex/generic/pgf/basiclayer\pgfcorelayers.code.tex -File: pgfcorelayers.code.tex 2021/05/15 v3.1.9a (3.1.9a) -) -(D:\Programme\Miktex\tex/generic/pgf/basiclayer\pgfcoretransparency.code.tex -File: pgfcoretransparency.code.tex 2021/05/15 v3.1.9a (3.1.9a) -) -(D:\Programme\Miktex\tex/generic/pgf/basiclayer\pgfcorepatterns.code.tex -File: pgfcorepatterns.code.tex 2021/05/15 v3.1.9a (3.1.9a) -) -(D:\Programme\Miktex\tex/generic/pgf/basiclayer\pgfcorerdf.code.tex -File: pgfcorerdf.code.tex 2021/05/15 v3.1.9a (3.1.9a) -))) -(D:\Programme\Miktex\tex/generic/pgf/modules\pgfmoduleshapes.code.tex -File: pgfmoduleshapes.code.tex 2021/05/15 v3.1.9a (3.1.9a) -\pgfnodeparttextbox=\box61 -) -(D:\Programme\Miktex\tex/generic/pgf/modules\pgfmoduleplot.code.tex -File: pgfmoduleplot.code.tex 2021/05/15 v3.1.9a (3.1.9a) -) -(D:\Programme\Miktex\tex/latex/pgf/compatibility\pgfcomp-version-0-65.sty -Package: pgfcomp-version-0-65 2021/05/15 v3.1.9a (3.1.9a) -\pgf@nodesepstart=\dimen270 -\pgf@nodesepend=\dimen271 -) -(D:\Programme\Miktex\tex/latex/pgf/compatibility\pgfcomp-version-1-18.sty -Package: pgfcomp-version-1-18 2021/05/15 v3.1.9a (3.1.9a) -)) -(D:\Programme\Miktex\tex/latex/pgf/utilities\pgffor.sty -(D:\Programme\Miktex\tex/latex/pgf/utilities\pgfkeys.sty -(D:\Programme\Miktex\tex/generic/pgf/utilities\pgfkeys.code.tex)) -(D:\Programme\Miktex\tex/latex/pgf/math\pgfmath.sty -(D:\Programme\Miktex\tex/generic/pgf/math\pgfmath.code.tex)) -(D:\Programme\Miktex\tex/generic/pgf/utilities\pgffor.code.tex -Package: pgffor 2021/05/15 v3.1.9a (3.1.9a) - -(D:\Programme\Miktex\tex/generic/pgf/math\pgfmath.code.tex) -\pgffor@iter=\dimen272 -\pgffor@skip=\dimen273 -\pgffor@stack=\toks46 -\pgffor@toks=\toks47 -)) -(D:\Programme\Miktex\tex/generic/pgf/frontendlayer/tikz\tikz.code.tex -Package: tikz 2021/05/15 v3.1.9a (3.1.9a) - -(D:\Programme\Miktex\tex/generic/pgf/libraries\pgflibraryplothandlers.code.tex -File: pgflibraryplothandlers.code.tex 2021/05/15 v3.1.9a (3.1.9a) -\pgf@plot@mark@count=\count324 -\pgfplotmarksize=\dimen274 -) -\tikz@lastx=\dimen275 -\tikz@lasty=\dimen276 -\tikz@lastxsaved=\dimen277 -\tikz@lastysaved=\dimen278 -\tikz@lastmovetox=\dimen279 -\tikz@lastmovetoy=\dimen280 -\tikzleveldistance=\dimen281 -\tikzsiblingdistance=\dimen282 -\tikz@figbox=\box62 -\tikz@figbox@bg=\box63 -\tikz@tempbox=\box64 -\tikz@tempbox@bg=\box65 -\tikztreelevel=\count325 -\tikznumberofchildren=\count326 -\tikznumberofcurrentchild=\count327 -\tikz@fig@count=\count328 -(D:\Programme\Miktex\tex/generic/pgf/modules\pgfmodulematrix.code.tex -File: pgfmodulematrix.code.tex 2021/05/15 v3.1.9a (3.1.9a) -\pgfmatrixcurrentrow=\count329 -\pgfmatrixcurrentcolumn=\count330 -\pgf@matrix@numberofcolumns=\count331 -) -\tikz@expandcount=\count332 - -(D:\Programme\Miktex\tex/generic/pgf/frontendlayer/tikz/libraries\tikzlibraryto -paths.code.tex -File: tikzlibrarytopaths.code.tex 2021/05/15 v3.1.9a (3.1.9a) -))) (D:\Programme\Miktex\tex/latex/tikz-cd\tikz-cd.sty -Package: tikz-cd 2021/05/04 v1.0 Commutative diagrams with TikZ - -(D:\Programme\Miktex\tex/latex/tikz-cd\tikzlibrarycd.code.tex -(D:\Programme\Miktex\tex/generic/pgf/frontendlayer/tikz/libraries\tikzlibraryma -trix.code.tex -File: tikzlibrarymatrix.code.tex 2021/05/15 v3.1.9a (3.1.9a) -) -(D:\Programme\Miktex\tex/generic/pgf/frontendlayer/tikz/libraries\tikzlibraryqu -otes.code.tex -File: tikzlibraryquotes.code.tex 2021/05/15 v3.1.9a (3.1.9a) -) -(D:\Programme\Miktex\tex/generic/pgf/libraries\pgflibraryarrows.meta.code.tex -File: pgflibraryarrows.meta.code.tex 2021/05/15 v3.1.9a (3.1.9a) -\pgfarrowinset=\dimen283 -\pgfarrowlength=\dimen284 -\pgfarrowwidth=\dimen285 -\pgfarrowlinewidth=\dimen286 -))) (D:\Programme\Miktex\tex/latex/pgfplots\pgfplots.sty -(D:\Programme\Miktex\tex/generic/pgfplots\pgfplots.revision.tex) -Package: pgfplots 2021/05/15 v1.18.1 Data Visualization (1.18.1) - -(D:\Programme\Miktex\tex/generic/pgfplots\pgfplots.code.tex -(D:\Programme\Miktex\tex/generic/pgfplots\pgfplotscore.code.tex -\t@pgfplots@toka=\toks48 -\t@pgfplots@tokb=\toks49 -\t@pgfplots@tokc=\toks50 -\pgfplots@tmpa=\dimen287 -\c@pgfplots@coordindex=\count333 -\c@pgfplots@scanlineindex=\count334 - -(D:\Programme\Miktex\tex/generic/pgfplots/sys\pgfplotssysgeneric.code.tex)) -(D:\Programme\Miktex\tex/generic/pgfplots/libs\pgfplotslibrary.code.tex) -(D:\Programme\Miktex\tex/generic/pgfplots/oldpgfcompatib\pgfplotsoldpgfsupp_loa -der.code.tex -(D:\Programme\Miktex\tex/generic/pgf/libraries\pgflibraryfpu.code.tex)) -(D:\Programme\Miktex\tex/generic/pgfplots/util\pgfplotsutil.code.tex -(D:\Programme\Miktex\tex/generic/pgfplots/liststructure\pgfplotsliststructure.c -ode.tex) -(D:\Programme\Miktex\tex/generic/pgfplots/liststructure\pgfplotsliststructureex -t.code.tex) -(D:\Programme\Miktex\tex/generic/pgfplots/liststructure\pgfplotsarray.code.tex -\c@pgfplotsarray@tmp=\count335 -) -(D:\Programme\Miktex\tex/generic/pgfplots/liststructure\pgfplotsmatrix.code.tex -) -(D:\Programme\Miktex\tex/generic/pgfplots/numtable\pgfplotstableshared.code.tex -\c@pgfplotstable@counta=\count336 -\t@pgfplotstable@a=\toks51 -) -(D:\Programme\Miktex\tex/generic/pgfplots/liststructure\pgfplotsdeque.code.tex) -(D:\Programme\Miktex\tex/generic/pgfplots/util\pgfplotsbinary.code.tex -(D:\Programme\Miktex\tex/generic/pgfplots/util\pgfplotsbinary.data.code.tex)) -(D:\Programme\Miktex\tex/generic/pgfplots/util\pgfplotsutil.verb.code.tex) -(D:\Programme\Miktex\tex/generic/pgfplots/libs\pgflibrarypgfplots.surfshading.c -ode.tex -\c@pgfplotslibrarysurf@no=\count337 - -(D:\Programme\Miktex\tex/generic/pgfplots/sys\pgflibrarypgfplots.surfshading.pg -fsys-pdftex.def))) -(D:\Programme\Miktex\tex/generic/pgfplots/util\pgfplotscolormap.code.tex -(D:\Programme\Miktex\tex/generic/pgfplots/util\pgfplotscolor.code.tex)) -(D:\Programme\Miktex\tex/generic/pgfplots\pgfplotsstackedplots.code.tex) -(D:\Programme\Miktex\tex/generic/pgfplots\pgfplotsplothandlers.code.tex -(D:\Programme\Miktex\tex/generic/pgfplots\pgfplotsmeshplothandler.code.tex -(D:\Programme\Miktex\tex/generic/pgfplots\pgfplotsmeshplotimage.code.tex))) -(D:\Programme\Miktex\tex/generic/pgfplots\pgfplots.scaling.code.tex) -(D:\Programme\Miktex\tex/generic/pgfplots\pgfplotscoordprocessing.code.tex) -(D:\Programme\Miktex\tex/generic/pgfplots\pgfplots.errorbars.code.tex) -(D:\Programme\Miktex\tex/generic/pgfplots\pgfplots.markers.code.tex) -(D:\Programme\Miktex\tex/generic/pgfplots\pgfplotsticks.code.tex) -(D:\Programme\Miktex\tex/generic/pgfplots\pgfplots.paths.code.tex) -(D:\Programme\Miktex\tex/generic/pgf/frontendlayer/tikz/libraries\tikzlibraryde -corations.code.tex -(D:\Programme\Miktex\tex/generic/pgf/modules\pgfmoduledecorations.code.tex -\pgfdecoratedcompleteddistance=\dimen288 -\pgfdecoratedremainingdistance=\dimen289 -\pgfdecoratedinputsegmentcompleteddistance=\dimen290 -\pgfdecoratedinputsegmentremainingdistance=\dimen291 -\pgf@decorate@distancetomove=\dimen292 -\pgf@decorate@repeatstate=\count338 -\pgfdecorationsegmentamplitude=\dimen293 -\pgfdecorationsegmentlength=\dimen294 -) -\tikz@lib@dec@box=\box66 -) -(D:\Programme\Miktex\tex/generic/pgf/frontendlayer/tikz/libraries\tikzlibraryde -corations.pathmorphing.code.tex -(D:\Programme\Miktex\tex/generic/pgf/libraries/decorations\pgflibrarydecoration -s.pathmorphing.code.tex)) -(D:\Programme\Miktex\tex/generic/pgf/frontendlayer/tikz/libraries\tikzlibraryde -corations.pathreplacing.code.tex -(D:\Programme\Miktex\tex/generic/pgf/libraries/decorations\pgflibrarydecoration -s.pathreplacing.code.tex)) -(D:\Programme\Miktex\tex/generic/pgfplots/libs\tikzlibrarypgfplots.contourlua.c -ode.tex) -\pgfplots@numplots=\count339 -\pgfplots@xmin@reg=\dimen295 -\pgfplots@xmax@reg=\dimen296 -\pgfplots@ymin@reg=\dimen297 -\pgfplots@ymax@reg=\dimen298 -\pgfplots@zmin@reg=\dimen299 -\pgfplots@zmax@reg=\dimen300 -) -(D:\Programme\Miktex\tex/generic/pgf/frontendlayer/tikz/libraries\tikzlibrarypl -otmarks.code.tex -File: tikzlibraryplotmarks.code.tex 2021/05/15 v3.1.9a (3.1.9a) - -(D:\Programme\Miktex\tex/generic/pgf/libraries\pgflibraryplotmarks.code.tex -File: pgflibraryplotmarks.code.tex 2021/05/15 v3.1.9a (3.1.9a) -))) -(D:\Programme\Miktex\tex/latex/pgfplots\pgfplotstable.sty -(D:\Programme\Miktex\tex/generic/pgfplots\pgfplots.revision.tex) -Package: pgfplotstable 2021/05/15 v1.18.1 Table typesetting and Pretty-printing - (1.18.1) - -(D:\Programme\Miktex\tex/generic/pgfplots/numtable\pgfplotstable.code.tex -(D:\Programme\Miktex\tex/generic/pgfplots/numtable\pgfplotstable.coltype.code.t -ex))) (D:\Programme\Miktex\tex/latex/csquotes\csquotes.sty -Package: csquotes 2021-02-22 v5.2l context-sensitive quotations (JAW) - -(D:\Programme\Miktex\tex/latex/etoolbox\etoolbox.sty -Package: etoolbox 2020/10/05 v2.5k e-TeX tools for LaTeX (JAW) -\etb@tempcnta=\count340 -) -\csq@reset=\count341 -\csq@gtype=\count342 -\csq@glevel=\count343 -\csq@qlevel=\count344 -\csq@maxlvl=\count345 -\csq@tshold=\count346 -\csq@ltx@everypar=\toks52 - -(D:\Programme\Miktex\tex/latex/csquotes\csquotes.def -File: csquotes.def 2021-02-22 v5.2l csquotes generic definitions (JAW) -) -Package csquotes Info: Trying to load configuration file 'csquotes.cfg'... -Package csquotes Info: ... configuration file loaded successfully. - -(D:\Programme\Miktex\tex/latex/csquotes\csquotes.cfg -File: csquotes.cfg -) -Package csquotes Info: Disabling multilingual quotes. -Package csquotes Info: Redefining alias 'english' -> 'english/american'. -) -(D:\Programme\Miktex\tex/latex/wasysym\wasysym.sty -Package: wasysym 2020/01/19 v2.4 Wasy-2 symbol support package -\symwasy=\mathgroup11 -LaTeX Font Info: Overwriting symbol font `wasy' in version `bold' -(Font) U/wasy/m/n --> U/wasy/b/n on input line 93. -) -(D:\Programme\Miktex\tex/latex/environ\environ.sty -Package: environ 2014/05/04 v0.3 A new way to define environments - -(D:\Programme\Miktex\tex/latex/trimspaces\trimspaces.sty -Package: trimspaces 2009/09/17 v1.1 Trim spaces around a token list -)) -(D:\Programme\Miktex\tex/latex/appendix\appendix.sty -Package: appendix 2020/02/08 v1.2c extra appendix facilities -\c@@pps=\count347 -\c@@ppsavesec=\count348 -\c@@ppsaveapp=\count349 -) -(D:\Programme\Miktex\tex/latex/placeins\placeins.sty -Package: placeins 2005/04/18 v 2.2 -) -(D:\Programme\Miktex\tex/generic/xypic\xy.sty -(D:\Programme\Miktex\tex/generic/xypic\xy.tex Bootstrap'ing: catcodes, -docmode, (D:\Programme\Miktex\tex/generic/xypic\xyrecat.tex) -(D:\Programme\Miktex\tex/generic/xypic\xyidioms.tex) - - Xy-pic version 3.8.9 <2013/10/06> - Copyright (c) 1991-2013 by Kristoffer H. Rose <krisrose@tug.org> and others - Xy-pic is free software: see the User's Guide for details. - -Loading kernel: messages; fonts; allocations: state, -\X@c=\dimen301 -\Y@c=\dimen302 -\U@c=\dimen303 -\D@c=\dimen304 -\L@c=\dimen305 -\R@c=\dimen306 -\Edge@c=\toks53 -\X@p=\dimen307 -\Y@p=\dimen308 -\U@p=\dimen309 -\D@p=\dimen310 -\L@p=\dimen311 -\R@p=\dimen312 -\Edge@p=\toks54 -\X@origin=\dimen313 -\Y@origin=\dimen314 -\X@xbase=\dimen315 -\Y@xbase=\dimen316 -\X@ybase=\dimen317 -\Y@ybase=\dimen318 -\X@min=\dimen319 -\Y@min=\dimen320 -\X@max=\dimen321 -\Y@max=\dimen322 -\lastobjectbox@=\box67 -\zerodotbox@=\box68 -\almostz@=\dimen323 - direction, -\d@X=\dimen324 -\d@Y=\dimen325 -\K@=\count350 -\KK@=\count351 -\Direction=\count352 -\K@dXdY=\dimen326 -\K@dYdX=\dimen327 -\xyread@=\read6 -\xywrite@=\write4 -\csp@=\count353 -\quotPTK@=\dimen328 - -utility macros; pictures: \xy, positions, -\swaptoks@@=\toks55 -\connectobjectbox@@=\box69 - objects, -\styletoks@=\toks56 - decorations; -kernel objects: directionals, circles, text; options; algorithms: directions, -edges, connections; Xy-pic loaded) -(D:\Programme\Miktex\tex/generic/iftex\ifpdf.sty -Package: ifpdf 2019/10/25 v3.4 ifpdf legacy package. Use iftex instead. -) -Package: xy 2013/10/06 Xy-pic version 3.8.9 - -(D:\Programme\Miktex\tex/generic/xypic\xyall.tex - Xy-pic option: All features v.3.8 -(D:\Programme\Miktex\tex/generic/xypic\xycurve.tex - Xy-pic option: Curve and Spline extension v.3.12 curve, -\crv@cnt@=\count354 -\crvpts@=\toks57 -\splinebox@=\box70 -\splineval@=\dimen329 -\splinedepth@=\dimen330 -\splinetol@=\dimen331 -\splinelength@=\dimen332 - circles, -\L@=\dimen333 - loaded) -(D:\Programme\Miktex\tex/generic/xypic\xyframe.tex - Xy-pic option: Frame and Bracket extension v.3.14 loaded) -(D:\Programme\Miktex\tex/generic/xypic\xycmtip.tex - Xy-pic option: Computer Modern tip extension v.3.7 -(D:\Programme\Miktex\tex/generic/xypic\xytips.tex - Xy-pic option: More Tips extension v.3.11 loaded) loaded) -(D:\Programme\Miktex\tex/generic/xypic\xyline.tex - Xy-pic option: Line styles extension v.3.10 -\xylinethick@=\dimen334 - loaded) -(D:\Programme\Miktex\tex/generic/xypic\xyrotate.tex - Xy-pic option: Rotate and Scale extension v.3.8 loaded) -(D:\Programme\Miktex\tex/generic/xypic\xycolor.tex - Xy-pic option: Colour extension v.3.11 loaded) -(D:\Programme\Miktex\tex/generic/xypic\xymatrix.tex - Xy-pic option: Matrix feature v.3.14 -\Row=\count355 -\Col=\count356 -\queue@=\toks58 -\queue@@=\toks59 -\qcount@=\count357 -\qcount@@=\count358 -\matrixsize@=\count359 - loaded) -(D:\Programme\Miktex\tex/generic/xypic\xyarrow.tex - Xy-pic option: Arrow and Path feature v.3.9 path, \ar, loaded) -(D:\Programme\Miktex\tex/generic/xypic\xygraph.tex - Xy-pic option: Graph feature v.3.11 loaded) loaded) -(D:\Programme\Miktex\tex/generic/xypic\xypdf.tex - Xy-pic option: PDF driver v.1.7 Xy-pic pdf driver: `color' extension support -(D:\Programme\Miktex\tex/generic/xypic\xypdf-co.tex loaded) -Xy-pic pdf driver: `curve' extension support -(D:\Programme\Miktex\tex/generic/xypic\xypdf-cu.tex loaded) -Xy-pic pdf driver: `frame' extension support -(D:\Programme\Miktex\tex/generic/xypic\xypdf-fr.tex loaded) -Xy-pic pdf driver: `line' extension support -(D:\Programme\Miktex\tex/generic/xypic\xypdf-li.tex loaded) -Xy-pic pdf driver: `rotate' extension support -(D:\Programme\Miktex\tex/generic/xypic\xypdf-ro.tex loaded) loaded)) -(D:\Programme\Miktex\tex/generic/pgf/frontendlayer/tikz/libraries\tikzlibraryca -lc.code.tex -File: tikzlibrarycalc.code.tex 2021/05/15 v3.1.9a (3.1.9a) -) -(D:\Programme\Miktex\tex/generic/pgf/frontendlayer/tikz/libraries\tikzlibraryin -tersections.code.tex -(D:\Programme\Miktex\tex/generic/pgf/libraries\pgflibraryintersections.code.tex -\pgf@intersect@solutions=\count360 -)) -(D:\Programme\Miktex\tex/generic/pgf/frontendlayer/tikz/libraries\tikzlibraryth -rough.code.tex -File: tikzlibrarythrough.code.tex 2021/05/15 v3.1.9a (3.1.9a) -) -(D:\Programme\Miktex\tex/generic/pgf/frontendlayer/tikz/libraries\tikzlibraryba -ckgrounds.code.tex -File: tikzlibrarybackgrounds.code.tex 2021/05/15 v3.1.9a (3.1.9a) -\pgf@layerbox@background=\box71 -\pgf@layerboxsaved@background=\box72 -) -(D:\Programme\Miktex\tex/generic/pgf/frontendlayer/tikz/libraries/graphs\tikzli -brarygraphs.code.tex -File: tikzlibrarygraphs.code.tex 2021/05/15 v3.1.9a (3.1.9a) -\tikz@lib@auto@number=\count361 -\tikz@qnode@count=\count362 -) -(D:\Programme\Miktex\tex/generic/pgf/frontendlayer/tikz/libraries\tikzlibrarypo -sitioning.code.tex -File: tikzlibrarypositioning.code.tex 2021/05/15 v3.1.9a (3.1.9a) -) -(D:\Programme\Miktex\tex/generic/pgf/frontendlayer/tikz/libraries\tikzlibrarysh -apes.code.tex -File: tikzlibraryshapes.code.tex 2021/05/15 v3.1.9a (3.1.9a) - -(D:\Programme\Miktex\tex/generic/pgf/frontendlayer/tikz/libraries\tikzlibrarysh -apes.geometric.code.tex -File: tikzlibraryshapes.geometric.code.tex 2021/05/15 v3.1.9a (3.1.9a) - -(D:\Programme\Miktex\tex/generic/pgf/libraries/shapes\pgflibraryshapes.geometri -c.code.tex -File: pgflibraryshapes.geometric.code.tex 2021/05/15 v3.1.9a (3.1.9a) -)) -(D:\Programme\Miktex\tex/generic/pgf/frontendlayer/tikz/libraries\tikzlibrarysh -apes.misc.code.tex -File: tikzlibraryshapes.misc.code.tex 2021/05/15 v3.1.9a (3.1.9a) - -(D:\Programme\Miktex\tex/generic/pgf/libraries/shapes\pgflibraryshapes.misc.cod -e.tex -File: pgflibraryshapes.misc.code.tex 2021/05/15 v3.1.9a (3.1.9a) -)) -(D:\Programme\Miktex\tex/generic/pgf/frontendlayer/tikz/libraries\tikzlibrarysh -apes.symbols.code.tex -File: tikzlibraryshapes.symbols.code.tex 2021/05/15 v3.1.9a (3.1.9a) - -(D:\Programme\Miktex\tex/generic/pgf/libraries/shapes\pgflibraryshapes.symbols. -code.tex -File: pgflibraryshapes.symbols.code.tex 2021/05/15 v3.1.9a (3.1.9a) -)) -(D:\Programme\Miktex\tex/generic/pgf/frontendlayer/tikz/libraries\tikzlibrarysh -apes.arrows.code.tex -File: tikzlibraryshapes.arrows.code.tex 2021/05/15 v3.1.9a (3.1.9a) - -(D:\Programme\Miktex\tex/generic/pgf/libraries/shapes\pgflibraryshapes.arrows.c -ode.tex -File: pgflibraryshapes.arrows.code.tex 2021/05/15 v3.1.9a (3.1.9a) -)) -(D:\Programme\Miktex\tex/generic/pgf/frontendlayer/tikz/libraries\tikzlibrarysh -apes.callouts.code.tex -(D:\Programme\Miktex\tex/generic/pgf/libraries/shapes\pgflibraryshapes.callouts -.code.tex)) -(D:\Programme\Miktex\tex/generic/pgf/frontendlayer/tikz/libraries\tikzlibrarysh -apes.multipart.code.tex -File: tikzlibraryshapes.multipart.code.tex 2021/05/15 v3.1.9a (3.1.9a) - -(D:\Programme\Miktex\tex/generic/pgf/libraries/shapes\pgflibraryshapes.multipar -t.code.tex -File: pgflibraryshapes.multipart.code.tex 2021/05/15 v3.1.9a (3.1.9a) -\pgfnodepartlowerbox=\box73 -\pgfnodeparttwobox=\box74 -\pgfnodepartthreebox=\box75 -\pgfnodepartfourbox=\box76 -\pgfnodeparttwentybox=\box77 -\pgfnodepartnineteenbox=\box78 -\pgfnodeparteighteenbox=\box79 -\pgfnodepartseventeenbox=\box80 -\pgfnodepartsixteenbox=\box81 -\pgfnodepartfifteenbox=\box82 -\pgfnodepartfourteenbox=\box83 -\pgfnodepartthirteenbox=\box84 -\pgfnodeparttwelvebox=\box85 -\pgfnodepartelevenbox=\box86 -\pgfnodeparttenbox=\box87 -\pgfnodepartninebox=\box88 -\pgfnodeparteightbox=\box89 -\pgfnodepartsevenbox=\box90 -\pgfnodepartsixbox=\box91 -\pgfnodepartfivebox=\box92 -))) -(D:\Programme\Miktex\tex/generic/pgf/frontendlayer/tikz/libraries\tikzlibraryar -rows.code.tex -File: tikzlibraryarrows.code.tex 2021/05/15 v3.1.9a (3.1.9a) - -(D:\Programme\Miktex\tex/generic/pgf/libraries\pgflibraryarrows.code.tex -File: pgflibraryarrows.code.tex 2021/05/15 v3.1.9a (3.1.9a) -\arrowsize=\dimen335 -)) -(D:\Programme\Miktex\tex/generic/pgf/frontendlayer/tikz/libraries\tikzlibraryfi -t.code.tex -File: tikzlibraryfit.code.tex 2021/05/15 v3.1.9a (3.1.9a) -) -(D:\Programme\Miktex\tex/generic/pgf/frontendlayer/tikz/libraries\tikzlibraryma -th.code.tex -(D:\Programme\Miktex\tex/generic/pgf/frontendlayer/tikz/libraries\tikzlibraryfp -u.code.tex) -\tikz@math@for@depth=\count363 -\tikz@math@dimen=\dimen336 -\tikz@math@toks=\toks60 -) -(D:\Programme\Miktex\tex/generic/pgf/frontendlayer/tikz/libraries\tikzlibrarypa -tterns.code.tex -File: tikzlibrarypatterns.code.tex 2021/05/15 v3.1.9a (3.1.9a) - -(D:\Programme\Miktex\tex/generic/pgf/libraries\pgflibrarypatterns.code.tex -File: pgflibrarypatterns.code.tex 2021/05/15 v3.1.9a (3.1.9a) -)) -(D:\Programme\Miktex\tex/latex/pgf/frontendlayer/libraries\tikzlibraryexternal. -code.tex -(D:\Programme\Miktex\tex/generic/pgf/frontendlayer/tikz/libraries\tikzexternals -hared.code.tex)) -(D:\Programme\Miktex\tex/generic/pgf/frontendlayer/tikz/libraries/datavisualiza -tion\tikzlibrarydatavisualization.code.tex -File: tikzlibrarydatavisualization.code.tex 2021/05/15 v3.1.9a (3.1.9a) - -(D:\Programme\Miktex\tex/generic/pgf/modules\pgfmoduledatavisualization.code.te -x -File: pgfmoduledatavisualization.code.tex 2021/05/15 v3.1.9a (3.1.9a) - (D:\Programme\Miktex\tex/generic/pgf/modules\pgfmoduleoo.code.tex -\pgfoo@objectcount=\count364 -\pgfoothis@count=\count365 -\pgfoo@toks=\toks61 -) -\pgf@lib@dv@cache@count=\count366 -\pgf@lib@dv@cache@count=\count367 -) -\tikzdvvisualizercounter=\count368 -) -(D:\Programme\Miktex\tex/latex/circuitikz\circuitikz.sty -Package: circuitikz 2022/05/08{} The CircuiTikz circuit drawing package version - 1.5.2 - -(D:\Programme\Miktex\tex/generic/pgf/frontendlayer/tikz/libraries\tikzlibrarybe -nding.code.tex -File: tikzlibrarybending.code.tex 2021/05/15 v3.1.9a (3.1.9a) - -(D:\Programme\Miktex\tex/generic/pgf/modules\pgfmodulebending.code.tex -File: pgfmodulebending.code.tex 2021/05/15 v3.1.9a (3.1.9a) - -(D:\Programme\Miktex\tex/generic/pgf/modules\pgfmodulenonlineartransformations. -code.tex -File: pgfmodulenonlineartransformations.code.tex 2021/05/15 v3.1.9a (3.1.9a) -\pgftransformnonlinearflatness=\dimen337 -) -(D:\Programme\Miktex\tex/generic/pgf/libraries\pgflibrarycurvilinear.code.tex -File: pgflibrarycurvilinear.code.tex 2021/05/15 v3.1.9a (3.1.9a) -\pgf@curvilinear@time@a=\dimen338 -\pgf@curvilinear@length@a=\dimen339 -\pgf@curvilinear@length@b=\dimen340 -\pgf@curvilinear@length@c=\dimen341 -\pgf@curvilinear@length@d=\dimen342 -) -\pgf@arrows@the@rigidity=\dimen343 -)) (D:\Programme\Miktex\tex/generic/circuitikz\pgfcirc.defines.tex -\pgf@circ@count@a=\count369 -\pgf@circ@count@b=\count370 -\pgf@circ@count@c=\count371 -\pgf@circ@res@up=\dimen344 -\pgf@circ@res@down=\dimen345 -\pgf@circ@res@zero=\dimen346 -\pgf@circ@res@left=\dimen347 -\pgf@circ@res@right=\dimen348 -\pgf@circ@res@other=\dimen349 -\pgf@circ@res@step=\dimen350 -\pgf@circ@res@temp=\dimen351 -\pgf@circ@Rlen=\dimen352 -\pgf@circ@scaled@Rlen=\dimen353 -\pgfstartlinewidth=\dimen354 -) -(D:\Programme\Miktex\tex/generic/circuitikz\pgfcircutils.tex -\ctikz@scratchbox=\box93 -) -(D:\Programme\Miktex\tex/generic/circuitikz\pgfcircpath.tex) -(D:\Programme\Miktex\tex/generic/circuitikz\pgfcircshapes.tex) -(D:\Programme\Miktex\tex/generic/circuitikz\pgfcircmonopoles.tex) -(D:\Programme\Miktex\tex/generic/circuitikz\pgfcircbipoles.tex) -(D:\Programme\Miktex\tex/generic/circuitikz\pgfcirctripoles.tex -\pgf@circ@res@count=\count372 -) -(D:\Programme\Miktex\tex/generic/circuitikz\pgfcircquadpoles.tex) -(D:\Programme\Miktex\tex/generic/circuitikz\pgfcircmultipoles.tex) -(D:\Programme\Miktex\tex/generic/circuitikz\pgfcirclabel.tex) -(D:\Programme\Miktex\tex/generic/circuitikz\pgfcircvoltage.tex -\pgfcirc@labelshift=\dimen355 -) -(D:\Programme\Miktex\tex/generic/circuitikz\pgfcirccurrent.tex) -(D:\Programme\Miktex\tex/generic/circuitikz\pgfcircflow.tex) -(D:\Programme\Miktex\tex/latex/xstring\xstring.sty -(D:\Programme\Miktex\tex/generic/xstring\xstring.tex -\integerpart=\count373 -\decimalpart=\count374 -) -Package: xstring 2021/07/21 v1.84 String manipulations (CT) -) -(D:\Programme\Miktex\tex/latex/siunitx\siunitx.sty -Package: siunitx 2022-05-03 v3.1.1 A comprehensive (SI) units package -\l__siunitx_angle_tmp_dim=\dimen356 -\l__siunitx_angle_marker_box=\box94 -\l__siunitx_angle_unit_box=\box95 -\l__siunitx_compound_count_int=\count375 - -(D:\Programme\Miktex\tex/latex/translations\translations.sty -Package: translations 2022/02/05 v1.12 internationalization of LaTeX2e packages - (CN) -) -\l__siunitx_number_exponent_fixed_int=\count376 -\l__siunitx_number_min_decimal_int=\count377 -\l__siunitx_number_min_integer_int=\count378 -\l__siunitx_number_round_precision_int=\count379 -\l__siunitx_number_group_first_int=\count380 -\l__siunitx_number_group_size_int=\count381 -\l__siunitx_number_group_minimum_int=\count382 -\l__siunitx_table_tmp_box=\box96 -\l__siunitx_table_tmp_dim=\dimen357 -\l__siunitx_table_column_width_dim=\dimen358 -\l__siunitx_table_integer_box=\box97 -\l__siunitx_table_decimal_box=\box98 -\l__siunitx_table_before_box=\box99 -\l__siunitx_table_after_box=\box100 -\l__siunitx_table_before_dim=\dimen359 -\l__siunitx_table_carry_dim=\dimen360 -\l__siunitx_unit_tmp_int=\count383 -\l__siunitx_unit_position_int=\count384 -\l__siunitx_unit_total_int=\count385 - -(D:\Programme\Miktex\tex/latex/l3packages/l3keys2e\l3keys2e.sty -(D:\Programme\Miktex\tex/latex/l3kernel\expl3.sty -Package: expl3 2022-02-24 L3 programming layer (loader) - -(D:\Programme\Miktex\tex/latex/l3backend\l3backend-pdftex.def -File: l3backend-pdftex.def 2022-02-07 L3 backend support: PDF output (pdfTeX) -\l__color_backend_stack_int=\count386 -\l__pdf_internal_box=\box101 -)) -Package: l3keys2e 2022-01-12 LaTeX2e option processing using LaTeX3 keys -))) -(D:\Programme\Miktex\tex/latex/tools\tabularx.sty -Package: tabularx 2020/01/15 v2.11c `tabularx' package (DPC) -\TX@col@width=\dimen361 -\TX@old@table=\dimen362 -\TX@old@col=\dimen363 -\TX@target=\dimen364 -\TX@delta=\dimen365 -\TX@cols=\count387 -\TX@ftn=\toks62 -) -(D:\Programme\Miktex\tex/latex/algorithmicx\algpseudocode.sty -Package: algpseudocode - -(D:\Programme\Miktex\tex/latex/algorithmicx\algorithmicx.sty -Package: algorithmicx 2005/04/27 v1.2 Algorithmicx - -Document Style algorithmicx 1.2 - a greatly improved `algorithmic' style -\c@ALG@line=\count388 -\c@ALG@rem=\count389 -\c@ALG@nested=\count390 -\ALG@tlm=\skip82 -\ALG@thistlm=\skip83 -\c@ALG@Lnr=\count391 -\c@ALG@blocknr=\count392 -\c@ALG@storecount=\count393 -\c@ALG@tmpcounter=\count394 -\ALG@tmplength=\skip84 -) -Document Style - pseudocode environments for use with the `algorithmicx' style -) (D:\Programme\Miktex\tex/latex/algorithms\algorithm.sty -Package: algorithm 2009/08/24 v0.1 Document Style `algorithm' - floating enviro -nment - -(D:\Programme\Miktex\tex/latex/float\float.sty -Package: float 2001/11/08 v1.3d Float enhancements (AL) -\c@float@type=\count395 -\float@exts=\toks63 -\float@box=\box102 -\@float@everytoks=\toks64 -\@floatcapt=\box103 -) -\@float@every@algorithm=\toks65 -\c@algorithm=\count396 -) -(D:\Programme\Miktex\tex/latex/was\gensymb.sty -Package: gensymb 2003/07/02 v1.0 (WaS) -) -(D:\Programme\Miktex\tex/latex/mathtools\mathtools.sty -Package: mathtools 2022/02/07 v1.28a mathematical typesetting tools - -(D:\Programme\Miktex\tex/latex/tools\calc.sty -Package: calc 2017/05/25 v4.3 Infix arithmetic (KKT,FJ) -\calc@Acount=\count397 -\calc@Bcount=\count398 -\calc@Adimen=\dimen366 -\calc@Bdimen=\dimen367 -\calc@Askip=\skip85 -\calc@Bskip=\skip86 -LaTeX Info: Redefining \setlength on input line 80. -LaTeX Info: Redefining \addtolength on input line 81. -\calc@Ccount=\count399 -\calc@Cskip=\skip87 -) -(D:\Programme\Miktex\tex/latex/mathtools\mhsetup.sty -Package: mhsetup 2021/03/18 v1.4 programming setup (MH) -) -\g_MT_multlinerow_int=\count400 -\l_MT_multwidth_dim=\dimen368 -\origjot=\skip88 -\l_MT_shortvdotswithinadjustabove_dim=\dimen369 -\l_MT_shortvdotswithinadjustbelow_dim=\dimen370 -\l_MT_above_intertext_sep=\dimen371 -\l_MT_below_intertext_sep=\dimen372 -\l_MT_above_shortintertext_sep=\dimen373 -\l_MT_below_shortintertext_sep=\dimen374 -\xmathstrut@box=\box104 -\xmathstrut@dim=\dimen375 -) -(D:\Programme\Miktex\tex/latex/tcolorbox\tcolorbox.sty -Package: tcolorbox 2022/01/07 version 5.0.2 text color boxes -\tcb@titlebox=\box105 -\tcb@upperbox=\box106 -\tcb@lowerbox=\box107 -\tcb@phantombox=\box108 -\c@tcbbreakpart=\count401 -\c@tcblayer=\count402 -\c@tcolorbox@number=\count403 -\tcb@temp=\box109 -\tcb@temp=\box110 -\tcb@temp=\box111 -\tcb@temp=\box112 - -(D:\Programme\Miktex\tex/latex/tcolorbox\tcbraster.code.tex -Library (tcolorbox): 'tcbraster.code.tex' version '5.0.2' -\c@tcbrastercolumn=\count404 -\c@tcbrasterrow=\count405 -\c@tcbrasternum=\count406 -\c@tcbraster=\count407 -) (D:\Programme\Miktex\tex/latex/tcolorbox\tcbskins.code.tex -Library (tcolorbox): 'tcbskins.code.tex' version '5.0.2' -\tcb@waterbox=\box113 -(D:\Programme\Miktex\tex/latex/tcolorbox\tcbskinsjigsaw.code.tex -Library (tcolorbox): 'tcbskinsjigsaw.code.tex' version '5.0.2' -)) (D:\Programme\Miktex\tex/latex/tcolorbox\tcbbreakable.code.tex -Library (tcolorbox): 'tcbbreakable.code.tex' version '5.0.2' -(D:\Programme\Miktex\tex/generic/oberdiek\pdfcol.sty -Package: pdfcol 2019/12/29 v1.6 Handle new color stacks for pdfTeX (HO) -) -Package pdfcol Info: New color stack `tcb@breakable' = 1 on input line 23. -\tcb@testbox=\box114 -\tcb@totalupperbox=\box115 -\tcb@totallowerbox=\box116 -) -(D:\Programme\Miktex\tex/latex/tcolorbox\tcbhooks.code.tex -Library (tcolorbox): 'tcbhooks.code.tex' version '5.0.2' -) (D:\Programme\Miktex\tex/latex/tcolorbox\tcbtheorems.code.tex -Library (tcolorbox): 'tcbtheorems.code.tex' version '5.0.2' -) (D:\Programme\Miktex\tex/latex/tcolorbox\tcbfitting.code.tex -Library (tcolorbox): 'tcbfitting.code.tex' version '5.0.2' -\tcbfitdim=\dimen376 -\tcb@lowerfitdim=\dimen377 -\tcb@upperfitdim=\dimen378 -\tcb@cur@hbadness=\count408 -) (D:\Programme\Miktex\tex/latex/tcolorbox\tcbxparse.code.tex -Library (tcolorbox): 'tcbxparse.code.tex' version '5.0.2' -(D:\Programme\Miktex\tex/latex/l3packages/xparse\xparse.sty -Package: xparse 2022-01-12 L3 Experimental document command parser -))) -(D:\Programme\Miktex\tex/latex/incgraph\incgraph.sty -Package: incgraph 2021/10/20 version 1.2.0 LaTeX special graphics inclusion - -(D:\Programme\Miktex\tex/latex/bookmark\bookmark.sty -Package: bookmark 2020-11-06 v1.29 PDF bookmarks (HO) - -(D:\Programme\Miktex\tex/latex/bookmark\bkm-pdftex.def -File: bkm-pdftex.def 2020-11-06 v1.29 bookmark driver for pdfTeX (HO) -\BKM@id=\count409 -)) -\igrbox=\box117 -\igr@length=\dimen379 -\c@igrtarget=\count410 -) (common/lststyles.tex (D:\Programme\Miktex\tex/latex/listings\listings.sty -\lst@mode=\count411 -\lst@gtempboxa=\box118 -\lst@token=\toks66 -\lst@length=\count412 -\lst@currlwidth=\dimen380 -\lst@column=\count413 -\lst@pos=\count414 -\lst@lostspace=\dimen381 -\lst@width=\dimen382 -\lst@newlines=\count415 -\lst@lineno=\count416 -\lst@maxwidth=\dimen383 - -(D:\Programme\Miktex\tex/latex/listings\lstmisc.sty -File: lstmisc.sty 2020/03/24 1.8d (Carsten Heinz) -\c@lstnumber=\count417 -\lst@skipnumbers=\count418 -\lst@framebox=\box119 -) -(D:\Programme\Miktex\tex/latex/listings\listings.cfg -File: listings.cfg 2020/03/24 1.8d listings configuration -)) -Package: listings 2020/03/24 1.8d (Carsten Heinz) -) -(D:\Programme\Miktex\tex/latex/caption\caption.sty -Package: caption 2022/03/01 v3.6b Customizing captions (AR) - -(D:\Programme\Miktex\tex/latex/caption\caption3.sty -Package: caption3 2022/03/17 v2.3b caption3 kernel (AR) -\caption@tempdima=\dimen384 -\captionmargin=\dimen385 -\caption@leftmargin=\dimen386 -\caption@rightmargin=\dimen387 -\caption@width=\dimen388 -\caption@indent=\dimen389 -\caption@parindent=\dimen390 -\caption@hangindent=\dimen391 -Package caption Info: Standard document class detected. -) -\c@caption@flags=\count419 -\c@continuedfloat=\count420 -Package caption Info: float package is loaded. -Package caption Info: hyperref package is loaded. -Package caption Info: listings package is loaded. -Package caption Info: subfigure package is loaded. -) -(D:\Programme\Miktex\tex/latex/standalone\standalone.sty -Package: standalone 2018/03/26 v1.3a Package to include TeX sub-files with prea -mbles - -(D:\Programme\Miktex\tex/latex/tools\shellesc.sty -Package: shellesc 2019/11/08 v1.0c unified shell escape interface for LaTeX -Package shellesc Info: Restricted shell escape enabled on input line 77. -) -(D:\Programme\Miktex\tex/latex/xkeyval\xkeyval.sty -Package: xkeyval 2020/11/20 v2.8 package option processing (HA) - -(D:\Programme\Miktex\tex/generic/xkeyval\xkeyval.tex -(D:\Programme\Miktex\tex/generic/xkeyval\xkvutils.tex -\XKV@toks=\toks67 -\XKV@tempa@toks=\toks68 -) -\XKV@depth=\count421 -File: xkeyval.tex 2014/12/03 v2.7a key=value parser (HA) -)) -(D:\Programme\Miktex\tex/latex/currfile\currfile.sty -Package: currfile 2020/09/29 v0.7d Provides the file path elements of the curre -nt input file - -(D:\Programme\Miktex\tex/latex/filehook\filehook.sty -Package: filehook 2020/09/29 v0.8a Hooks for input files - -(D:\Programme\Miktex\tex/latex/filehook\filehook-2020.sty -Package: filehook-2020 2020/09/29 v0.8a Hooks for input files -)) -\c@currfiledepth=\count422 -) -(D:\Programme\Miktex\tex/latex/gincltex\gincltex.sty -(D:\Programme\Miktex\tex/latex/svn-prov\svn-prov.sty -Package: svn-prov 2010/04/24 v3.1862 Package Date/Version from SVN Keywords -) -Package: gincltex 2011/09/04 v0.3 Include external LaTeX files like graphics - -(D:\Programme\Miktex\tex/latex/adjustbox\adjustbox.sty -Package: adjustbox 2020/08/19 v1.3 Adjusting TeX boxes (trim, clip, ...) - -(D:\Programme\Miktex\tex/latex/adjustbox\adjcalc.sty -Package: adjcalc 2012/05/16 v1.1 Provides advanced setlength with multiple back --ends (calc, etex, pgfmath) -) -(D:\Programme\Miktex\tex/latex/adjustbox\trimclip.sty -Package: trimclip 2020/08/19 v1.2 Trim and clip general TeX material - -(D:\Programme\Miktex\tex/latex/collectbox\collectbox.sty -Package: collectbox 2012/05/17 v0.4b Collect macro arguments as boxes -\collectedbox=\box120 -) -\tc@llx=\dimen392 -\tc@lly=\dimen393 -\tc@urx=\dimen394 -\tc@ury=\dimen395 -Package trimclip Info: Using driver 'tc-pdftex.def'. - -(D:\Programme\Miktex\tex/latex/adjustbox\tc-pdftex.def -File: tc-pdftex.def 2019/01/04 v2.2 Clipping driver for pdftex -)) -\adjbox@Width=\dimen396 -\adjbox@Height=\dimen397 -\adjbox@Depth=\dimen398 -\adjbox@Totalheight=\dimen399 -\adjbox@pwidth=\dimen400 -\adjbox@pheight=\dimen401 -\adjbox@pdepth=\dimen402 -\adjbox@ptotalheight=\dimen403 - -(D:\Programme\Miktex\tex/latex/ifoddpage\ifoddpage.sty -Package: ifoddpage 2016/04/23 v1.1 Conditionals for odd/even page detection -\c@checkoddpage=\count423 -) -(D:\Programme\Miktex\tex/latex/varwidth\varwidth.sty -Package: varwidth 2009/03/30 ver 0.92; Variable-width minipages -\@vwid@box=\box121 -\sift@deathcycles=\count424 -\@vwid@loff=\dimen404 -\@vwid@roff=\dimen405 -)) -\gincltex@box=\box122 -) -(D:\Programme\Miktex\tex/latex/filemod\filemod-expmin.sty -Package: filemod-expmin 2011/09/19 v1.2 Get and compare file modification times - (expandable; minimal) -)) -(D:\Programme\Miktex\tex/latex/biblatex\biblatex.sty -Package: biblatex 2022/02/02 v3.17 programmable bibliographies (PK/MW) - -(D:\Programme\Miktex\tex/latex/logreq\logreq.sty -Package: logreq 2010/08/04 v1.0 xml request logger -\lrq@indent=\count425 - -(D:\Programme\Miktex\tex/latex/logreq\logreq.def -File: logreq.def 2010/08/04 v1.0 logreq spec v1.0 -)) -\c@tabx@nest=\count426 -\c@listtotal=\count427 -\c@listcount=\count428 -\c@liststart=\count429 -\c@liststop=\count430 -\c@citecount=\count431 -\c@citetotal=\count432 -\c@multicitecount=\count433 -\c@multicitetotal=\count434 -\c@instcount=\count435 -\c@maxnames=\count436 -\c@minnames=\count437 -\c@maxitems=\count438 -\c@minitems=\count439 -\c@citecounter=\count440 -\c@maxcitecounter=\count441 -\c@savedcitecounter=\count442 -\c@uniquelist=\count443 -\c@uniquename=\count444 -\c@refsection=\count445 -\c@refsegment=\count446 -\c@maxextratitle=\count447 -\c@maxextratitleyear=\count448 -\c@maxextraname=\count449 -\c@maxextradate=\count450 -\c@maxextraalpha=\count451 -\c@abbrvpenalty=\count452 -\c@highnamepenalty=\count453 -\c@lownamepenalty=\count454 -\c@maxparens=\count455 -\c@parenlevel=\count456 -\blx@tempcnta=\count457 -\blx@tempcntb=\count458 -\blx@tempcntc=\count459 -\c@blx@maxsection=\count460 -\c@blx@maxsegment@0=\count461 -\blx@notetype=\count462 -\blx@parenlevel@text=\count463 -\blx@parenlevel@foot=\count464 -\c@blx@sectionciteorder@0=\count465 -\blx@entrysetcounter=\count466 -\blx@biblioinstance=\count467 -\labelnumberwidth=\skip89 -\labelalphawidth=\skip90 -\biblabelsep=\skip91 -\bibitemsep=\skip92 -\bibnamesep=\skip93 -\bibinitsep=\skip94 -\bibparsep=\skip95 -\bibhang=\skip96 -\blx@bcfin=\read7 -\blx@bcfout=\write5 -\blx@langwohyphens=\language80 -\c@mincomprange=\count468 -\c@maxcomprange=\count469 -\c@mincompwidth=\count470 -Package biblatex Info: Trying to load biblatex default data model... -Package biblatex Info: ... file 'blx-dm.def' found. - -(D:\Programme\Miktex\tex/latex/biblatex\blx-dm.def -File: blx-dm.def 2022/02/02 v3.17 biblatex localization (PK/MW) -) -Package biblatex Info: Trying to load biblatex custom data model... -Package biblatex Info: ... file 'biblatex-dm.cfg' not found. -\c@afterword=\count471 -\c@savedafterword=\count472 -\c@annotator=\count473 -\c@savedannotator=\count474 -\c@author=\count475 -\c@savedauthor=\count476 -\c@bookauthor=\count477 -\c@savedbookauthor=\count478 -\c@commentator=\count479 -\c@savedcommentator=\count480 -\c@editor=\count481 -\c@savededitor=\count482 -\c@editora=\count483 -\c@savededitora=\count484 -\c@editorb=\count485 -\c@savededitorb=\count486 -\c@editorc=\count487 -\c@savededitorc=\count488 -\c@foreword=\count489 -\c@savedforeword=\count490 -\c@holder=\count491 -\c@savedholder=\count492 -\c@introduction=\count493 -\c@savedintroduction=\count494 -\c@namea=\count495 -\c@savednamea=\count496 -\c@nameb=\count497 -\c@savednameb=\count498 -\c@namec=\count499 -\c@savednamec=\count500 -\c@translator=\count501 -\c@savedtranslator=\count502 -\c@shortauthor=\count503 -\c@savedshortauthor=\count504 -\c@shorteditor=\count505 -\c@savedshorteditor=\count506 -\c@labelname=\count507 -\c@savedlabelname=\count508 -\c@institution=\count509 -\c@savedinstitution=\count510 -\c@lista=\count511 -\c@savedlista=\count512 -\c@listb=\count513 -\c@savedlistb=\count514 -\c@listc=\count515 -\c@savedlistc=\count516 -\c@listd=\count517 -\c@savedlistd=\count518 -\c@liste=\count519 -\c@savedliste=\count520 -\c@listf=\count521 -\c@savedlistf=\count522 -\c@location=\count523 -\c@savedlocation=\count524 -\c@organization=\count525 -\c@savedorganization=\count526 -\c@origlocation=\count527 -\c@savedoriglocation=\count528 -\c@origpublisher=\count529 -\c@savedorigpublisher=\count530 -\c@publisher=\count531 -\c@savedpublisher=\count532 -\c@language=\count533 -\c@savedlanguage=\count534 -\c@origlanguage=\count535 -\c@savedoriglanguage=\count536 -\c@pageref=\count537 -\c@savedpageref=\count538 -\shorthandwidth=\skip97 -\shortjournalwidth=\skip98 -\shortserieswidth=\skip99 -\shorttitlewidth=\skip100 -\shortauthorwidth=\skip101 -\shorteditorwidth=\skip102 -\locallabelnumberwidth=\skip103 -\locallabelalphawidth=\skip104 -\localshorthandwidth=\skip105 -\localshortjournalwidth=\skip106 -\localshortserieswidth=\skip107 -\localshorttitlewidth=\skip108 -\localshortauthorwidth=\skip109 -\localshorteditorwidth=\skip110 -Package biblatex Info: Trying to load compatibility code... -Package biblatex Info: ... file 'blx-compat.def' found. - -(D:\Programme\Miktex\tex/latex/biblatex\blx-compat.def -File: blx-compat.def 2022/02/02 v3.17 biblatex compatibility (PK/MW) -) -Package biblatex Info: Trying to load BibTeX backend compatibility... -Package biblatex Info: ... file 'blx-bibtex.def' found. - -(D:\Programme\Miktex\tex/latex/biblatex\blx-bibtex.def -File: blx-bibtex.def 2022/02/02 v3.17 biblatex compatibility (PK/MW) - - -Package biblatex Warning: Using fall-back BibTeX(8) backend: -(biblatex) functionality may be reduced/unavailable. - -) -Package biblatex Info: Trying to load generic definitions... -Package biblatex Info: ... file 'biblatex.def' found. - (D:\Programme\Miktex\tex/latex/biblatex\biblatex.def -File: biblatex.def 2022/02/02 v3.17 biblatex compatibility (PK/MW) -\c@textcitecount=\count539 -\c@textcitetotal=\count540 -\c@textcitemaxnames=\count541 -\c@biburlbigbreakpenalty=\count542 -\c@biburlbreakpenalty=\count543 -\c@biburlnumpenalty=\count544 -\c@biburlucpenalty=\count545 -\c@biburllcpenalty=\count546 -\biburlbigskip=\muskip18 -\biburlnumskip=\muskip19 -\biburlucskip=\muskip20 -\biburllcskip=\muskip21 -\c@smartand=\count547 -) -Package biblatex Info: Trying to load bibliography style 'numeric'... -Package biblatex Info: ... file 'numeric.bbx' found. - -(D:\Programme\Miktex\tex/latex/biblatex/bbx\numeric.bbx -File: numeric.bbx 2022/02/02 v3.17 biblatex bibliography style (PK/MW) -Package biblatex Info: Trying to load bibliography style 'standard'... -Package biblatex Info: ... file 'standard.bbx' found. - -(D:\Programme\Miktex\tex/latex/biblatex/bbx\standard.bbx -File: standard.bbx 2022/02/02 v3.17 biblatex bibliography style (PK/MW) -\c@bbx:relatedcount=\count548 -\c@bbx:relatedtotal=\count549 -)) -Package biblatex Info: Trying to load citation style 'numeric'... -Package biblatex Info: ... file 'numeric.cbx' found. - -(D:\Programme\Miktex\tex/latex/biblatex/cbx\numeric.cbx -File: numeric.cbx 2022/02/02 v3.17 biblatex citation style (PK/MW) -Package biblatex Info: Redefining '\cite'. -Package biblatex Info: Redefining '\parencite'. -Package biblatex Info: Redefining '\footcite'. -Package biblatex Info: Redefining '\footcitetext'. -Package biblatex Info: Redefining '\smartcite'. -Package biblatex Info: Redefining '\supercite'. -Package biblatex Info: Redefining '\textcite'. -Package biblatex Info: Redefining '\textcites'. -Package biblatex Info: Redefining '\cites'. -Package biblatex Info: Redefining '\parencites'. -Package biblatex Info: Redefining '\smartcites'. -) -Package biblatex Info: Trying to load configuration file... -Package biblatex Info: ... file 'biblatex.cfg' found. - -(D:\Programme\Miktex\tex/latex/biblatex\biblatex.cfg -File: biblatex.cfg -) -Package biblatex Info: Input encoding 'utf8' detected. -Package biblatex Info: Document encoding is UTF8 .... -Package biblatex Info: ... and expl3 -(biblatex) 2022-02-24 L3 programming layer (loader) -(biblatex) is new enough (at least 2020/04/06), -(biblatex) setting 'casechanger=expl3'. - -(D:\Programme\Miktex\tex/latex/biblatex\blx-case-expl3.sty -Package: blx-case-expl3 2022/02/02 v3.17 expl3 case changing code for biblatex -))) -(papers/common/addpackages.tex (papers/000template/packages.tex) -(papers/lambertw/packages.tex) (papers/fm/packages.tex) -(papers/parzyl/packages.tex) (papers/fresnel/packages.tex) -(papers/kreismembran/packages.tex) (papers/sturmliouville/packages.tex) -(papers/laguerre/packages.tex) -(D:\Programme\Miktex\tex/latex/derivative\derivative.sty -Package: derivative 2021/06/03 v1.1 Nice and easy derivatives and differentials - for LaTeX -\l__deriv_vmo_int=\count550 -\l__deriv_tmpa_int=\count551 -\l__deriv_tmpb_int=\count552 -\l__deriv_numerical_int=\count553 -\l__deriv_sort_counter_int=\count554 -\l__deriv_sort_max_int=\count555 -\l__deriv_position_int=\count556 -\l__deriv_rebuild_int=\count557 -) -(papers/zeta/packages.tex) (papers/0f1/packages.tex) (papers/nav/packages.tex) -(papers/transfer/packages.tex) (papers/kra/packages.tex) -(papers/kugel/packages.tex) (papers/hermite/packages.tex) -(papers/ellfilter/packages.tex) (papers/dreieck/packages.tex)) -(papers/common/addbibresources.tex) -\@indexfile=\write6 -\openout6 = `buch.idx'. - - -Writing index file buch.idx -LaTeX Font Info: Trying to load font information for T1+txr on input line 35 -. -(D:\Programme\Miktex\tex/latex/txfonts\t1txr.fd -File: t1txr.fd 2000/12/15 v3.1 -) (buch.aux) -\openout1 = `buch.aux'. - -LaTeX Font Info: Checking defaults for OML/txmi/m/it on input line 35. -LaTeX Font Info: Trying to load font information for OML+txmi on input line -35. - -(D:\Programme\Miktex\tex/latex/txfonts\omltxmi.fd -File: omltxmi.fd 2000/12/15 v3.1 -) -LaTeX Font Info: ... okay on input line 35. -LaTeX Font Info: Checking defaults for OMS/txsy/m/n on input line 35. -LaTeX Font Info: Trying to load font information for OMS+txsy on input line -35. - -(D:\Programme\Miktex\tex/latex/txfonts\omstxsy.fd -File: omstxsy.fd 2000/12/15 v3.1 -) -LaTeX Font Info: ... okay on input line 35. -LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 35. -LaTeX Font Info: ... okay on input line 35. -LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 35. -LaTeX Font Info: ... okay on input line 35. -LaTeX Font Info: Checking defaults for TS1/cmr/m/n on input line 35. -LaTeX Font Info: ... okay on input line 35. -LaTeX Font Info: Checking defaults for OMX/txex/m/n on input line 35. -LaTeX Font Info: Trying to load font information for OMX+txex on input line -35. - -(D:\Programme\Miktex\tex/latex/txfonts\omxtxex.fd -File: omxtxex.fd 2000/12/15 v3.1 -) -LaTeX Font Info: ... okay on input line 35. -LaTeX Font Info: Checking defaults for U/txexa/m/n on input line 35. -LaTeX Font Info: Trying to load font information for U+txexa on input line 3 -5. - -(D:\Programme\Miktex\tex/latex/txfonts\utxexa.fd -File: utxexa.fd 2000/12/15 v3.1 -) -LaTeX Font Info: ... okay on input line 35. -LaTeX Font Info: Checking defaults for PD1/pdf/m/n on input line 35. -LaTeX Font Info: ... okay on input line 35. -LaTeX Font Info: Checking defaults for PU/pdf/m/n on input line 35. -LaTeX Font Info: ... okay on input line 35. - -*geometry* driver: auto-detecting -*geometry* detected driver: pdftex -*geometry* verbose mode - [ preamble ] result: -* driver: pdftex -* paper: custom -* layout: <same size as paper> -* layoutoffset:(h,v)=(0.0pt,0.0pt) -* bindingoffset: 28.45274pt -* modes: twoside -* h-part:(L,W,R)=(22.7622pt, 398.33858pt, 34.14331pt) -* v-part:(T,H,B)=(59.75078pt, 569.05511pt, 54.06024pt) -* \paperwidth=483.69684pt -* \paperheight=682.86613pt -* \textwidth=398.33858pt -* \textheight=569.05511pt -* \oddsidemargin=-21.05504pt -* \evensidemargin=-38.12668pt -* \topmargin=-42.5867pt -* \headheight=15.0pt -* \headsep=18.06749pt -* \topskip=10.0pt -* \footskip=25.29494pt -* \marginparwidth=125.0pt -* \marginparsep=7.0pt -* \columnsep=10.0pt -* \skip\footins=9.0pt plus 4.0pt minus 2.0pt -* \hoffset=0.0pt -* \voffset=0.0pt -* \mag=1000 -* \@twocolumnfalse -* \@twosidetrue -* \@mparswitchtrue -* \@reversemarginfalse -* (1in=72.27pt=25.4mm, 1cm=28.453pt) - -(D:\Programme\Miktex\tex/context/base/mkii\supp-pdf.mkii -[Loading MPS to PDF converter (version 2006.09.02).] -\scratchcounter=\count558 -\scratchdimen=\dimen406 -\scratchbox=\box123 -\nofMPsegments=\count559 -\nofMParguments=\count560 -\everyMPshowfont=\toks69 -\MPscratchCnt=\count561 -\MPscratchDim=\dimen407 -\MPnumerator=\count562 -\makeMPintoPDFobject=\count563 -\everyMPtoPDFconversion=\toks70 -) (D:\Programme\Miktex\tex/latex/epstopdf-pkg\epstopdf-base.sty -Package: epstopdf-base 2020-01-24 v2.11 Base part for package epstopdf -Package epstopdf-base Info: Redefining graphics rule for `.eps' on input line 4 -85. - -(D:\Programme\Miktex\tex/latex/00miktex\epstopdf-sys.cfg -File: epstopdf-sys.cfg 2021/03/18 v2.0 Configuration of epstopdf for MiKTeX -)) -Package hyperref Info: Link coloring OFF on input line 35. - -(D:\Programme\Miktex\tex/latex/hyperref\nameref.sty -Package: nameref 2021-04-02 v2.47 Cross-referencing by name of section - -(D:\Programme\Miktex\tex/latex/refcount\refcount.sty -Package: refcount 2019/12/15 v3.6 Data extraction from label references (HO) -) -(D:\Programme\Miktex\tex/generic/gettitlestring\gettitlestring.sty -Package: gettitlestring 2019/12/15 v1.6 Cleanup title references (HO) -) -\c@section@level=\count564 -) -LaTeX Info: Redefining \ref on input line 35. -LaTeX Info: Redefining \pageref on input line 35. -LaTeX Info: Redefining \nameref on input line 35. - - -Package pgfplots Warning: running in backwards compatibility mode (unsuitable t -ick labels; missing features). Consider writing \pgfplotsset{compat=1.18} into -your preamble. - on input line 35. - -LaTeX Font Info: Trying to load font information for OT1+txr on input line 3 -5. -(D:\Programme\Miktex\tex/latex/txfonts\ot1txr.fd -File: ot1txr.fd 2000/12/15 v3.1 -) -LaTeX Font Info: Trying to load font information for U+txsya on input line 3 -5. - -(D:\Programme\Miktex\tex/latex/txfonts\utxsya.fd -File: utxsya.fd 2000/12/15 v3.1 -) -LaTeX Font Info: Trying to load font information for U+txsyb on input line 3 -5. - -(D:\Programme\Miktex\tex/latex/txfonts\utxsyb.fd -File: utxsyb.fd 2000/12/15 v3.1 -) -LaTeX Font Info: Trying to load font information for U+txmia on input line 3 -5. - -(D:\Programme\Miktex\tex/latex/txfonts\utxmia.fd -File: utxmia.fd 2000/12/15 v3.1 -) -LaTeX Font Info: Trying to load font information for U+txsyc on input line 3 -5. - -(D:\Programme\Miktex\tex/latex/txfonts\utxsyc.fd -File: utxsyc.fd 2000/12/15 v3.1 -) -LaTeX Font Info: Trying to load font information for U+rsfs on input line 35 -. - -(D:\Programme\Miktex\tex/latex/jknappen\ursfs.fd -File: ursfs.fd 1998/03/24 rsfs font definition file (jk) -) -LaTeX Font Info: Trying to load font information for U+wasy on input line 35 -. - -(D:\Programme\Miktex\tex/latex/wasysym\uwasy.fd -File: uwasy.fd 2020/01/19 v2.4 Wasy-2 symbol font definitions -) -Package xypdf Info: Line width: 0.56pt on input line 35. - -(D:\Programme\Miktex\tex/latex/translations/dicts\translations-basic-dictionary --german.trsl -File: translations-basic-dictionary-german.trsl (german translation file `trans -lations-basic-dictionary') -) -Package translations Info: loading dictionary `translations-basic-dictionary' f -or `german'. on input line 35. - -(D:\Programme\Miktex\tex/latex/translations/dicts\translations-basic-dictionary --english.trsl -File: translations-basic-dictionary-english.trsl (english translation file `tra -nslations-basic-dictionary') -) -Package translations Info: loading dictionary `translations-basic-dictionary' f -or `english'. on input line 35. -\symgns@font=\mathgroup12 -LaTeX Font Info: Overwriting symbol font `gns@font' in version `bold' -(Font) TS1/txr/m/n --> TS1/txr/b/n on input line 35. -Package gensymb Info: Math companion symbols declared on input line 35. -LaTeX Info: Redefining \degree on input line 35. -LaTeX Info: Redefining \celsius on input line 35. -Package gensymb Info: Using text companion symbols for \degree, \celsius and \p -erthousand on input line 35. -LaTeX Info: Redefining \ohm on input line 35. -Package gensymb Info: Using \textohm for \ohm on input line 35. -LaTeX Info: Redefining \micro on input line 35. -Package gensymb Info: Using \textmu for \micro on input line 35. -\c@lstlisting=\count565 -Package caption Info: Begin \AtBeginDocument code. -Package caption Info: End \AtBeginDocument code. -Package biblatex Info: Trying to load language 'ngerman'... -Package biblatex Info: ... file 'ngerman.lbx' found. - (D:\Programme\Miktex\tex/latex/biblatex/lbx\ngerman.lbx -File: ngerman.lbx 2022/02/02 v3.17 biblatex localization (PK/MW) -Package biblatex Info: Trying to load language 'german'... -Package biblatex Info: ... file 'german.lbx' found. - -(D:\Programme\Miktex\tex/latex/biblatex/lbx\german.lbx -File: german.lbx 2022/02/02 v3.17 biblatex localization (PK/MW) -) -Package biblatex Info: Trying to load language 'german'... -Package biblatex Info: ... file 'german.lbx' found. - -(D:\Programme\Miktex\tex/latex/biblatex/lbx\german.lbx -File: german.lbx 2022/02/02 v3.17 biblatex localization (PK/MW) - -Runaway definition? --> -! TeX capacity exceeded, sorry [main memory size=3000000]. -<argument> \XKV@resb - -l.575 } - -If you really absolutely need more capacity, -you can ask a wizard to enlarge me. - - -Here is how much of TeX's memory you used: - 81845 strings out of 478582 - 2061696 string characters out of 2856069 - 3000001 words of memory out of 3000000 - 98832 multiletter control sequences out of 15000+600000 - 484206 words of font info for 75 fonts, out of 8000000 for 9000 - 1143 hyphenation exceptions out of 8191 - 105i,3n,99p,3369b,2422s stack positions out of 10000i,1000n,20000p,200000b,80000s -! ==> Fatal error occurred, no output PDF file produced! diff --git a/buch/chapters/050-differential/uebungsaufgaben/airy.cpp b/buch/chapters/050-differential/uebungsaufgaben/airy.cpp index e4df8e1..eb5c6be 100644 --- a/buch/chapters/050-differential/uebungsaufgaben/airy.cpp +++ b/buch/chapters/050-differential/uebungsaufgaben/airy.cpp @@ -44,8 +44,8 @@ double h0f1(double c, double x) { double f1(double x) { // unfortunately, gsl_sf_hyperg_0F1 does not work if c<1, because // it uses a relation to the bessel functions - //return gsl_sf_hyperg_0F1(2/3, x*x*x/9.); - return h0f1(2./3., x*x*x/9.); + return gsl_sf_hyperg_0F1(2/3, x*x*x/9.); + //return h0f1(2./3., x*x*x/9.); } double f2(double x) { diff --git a/buch/chapters/110-elliptisch/ellintegral.tex b/buch/chapters/110-elliptisch/ellintegral.tex index 4cb2ba3..3acce2f 100644 --- a/buch/chapters/110-elliptisch/ellintegral.tex +++ b/buch/chapters/110-elliptisch/ellintegral.tex @@ -651,7 +651,7 @@ werden, dass $1-k'^2=k^2$ ist. \begin{definition} Ist $0\le k\le 1$ der Modul eines elliptischen Integrals, dann heisst -$k' = \sqrt{1-k^2}$ er {\em Komplementärmodul} oder {\em Komplement +$k' = \sqrt{1-k^2}$ der {\em Komplementärmodul} oder {\em Komplement des Moduls}. Es ist $k^2+k'^2=1$. \end{definition} diff --git a/buch/papers/kreismembran/main.tex b/buch/papers/kreismembran/main.tex index 67b436c..e63a118 100644 --- a/buch/papers/kreismembran/main.tex +++ b/buch/papers/kreismembran/main.tex @@ -3,29 +3,10 @@ % % (c) 2020 Hochschule Rapperswil % -\chapter{Thema\label{chapter:kreismembran}} -\lhead{Thema} +\chapter{Schwingungen einer kreisförmligen Membran\label{chapter:kreismembran}} +\lhead{Schwingungen einer kreisförmligen Membran} \begin{refsection} -\chapterauthor{Hans Muster} - -Ein paar Hinweise für die korrekte Formatierung des Textes -\begin{itemize} -\item -Absätze werden gebildet, indem man eine Leerzeile einfügt. -Die Verwendung von \verb+\\+ ist nur in Tabellen und Arrays gestattet. -\item -Die explizite Platzierung von Bildern ist nicht erlaubt, entsprechende -Optionen werden gelöscht. -Verwenden Sie Labels und Verweise, um auf Bilder hinzuweisen. -\item -Beginnen Sie jeden Satz auf einer neuen Zeile. -Damit ermöglichen Sie dem Versionsverwaltungssysteme, Änderungen -in verschiedenen Sätzen von verschiedenen Autoren ohne Konflikt -anzuwenden. -\item -Bilden Sie auch für Formeln kurze Zeilen, einerseits der besseren -Übersicht wegen, aber auch um GIT die Arbeit zu erleichtern. -\end{itemize} +\chapterauthor{Andrea Mozzini Vellen und Tim Tönz} \input{papers/kreismembran/teil0.tex} \input{papers/kreismembran/teil1.tex} diff --git a/buch/papers/kreismembran/teil0.tex b/buch/papers/kreismembran/teil0.tex index e4b1711..1552259 100644 --- a/buch/papers/kreismembran/teil0.tex +++ b/buch/papers/kreismembran/teil0.tex @@ -3,20 +3,8 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Teil 0\label{kreismembran:section:teil0}} -\rhead{Teil 0} -Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam -nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -erat, sed diam voluptua \cite{kreismembran:bibtex}. -At vero eos et accusam et justo duo dolores et ea rebum. -Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum -dolor sit amet. +\section{Einleitung\label{kreismembran:section:teil0}} +\rhead{Einleitung} -Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam -nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -erat, sed diam voluptua. -At vero eos et accusam et justo duo dolores et ea rebum. Stet clita -kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit -amet. diff --git a/buch/papers/kreismembran/teil1.tex b/buch/papers/kreismembran/teil1.tex index b715075..aef5b79 100644 --- a/buch/papers/kreismembran/teil1.tex +++ b/buch/papers/kreismembran/teil1.tex @@ -2,54 +2,99 @@ % teil1.tex -- Beispiel-File für das Paper % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{Teil 1 -\label{kreismembran:section:teil1}} -\rhead{Problemstellung} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. -Nemo enim ipsam voluptatem quia voluptas sit aspernatur aut odit -aut fugit, sed quia consequuntur magni dolores eos qui ratione -voluptatem sequi nesciunt -\begin{equation} -\int_a^b x^2\, dx -= -\left[ \frac13 x^3 \right]_a^b -= -\frac{b^3-a^3}3. -\label{kreismembran:equation1} -\end{equation} -Neque porro quisquam est, qui dolorem ipsum quia dolor sit amet, -consectetur, adipisci velit, sed quia non numquam eius modi tempora -incidunt ut labore et dolore magnam aliquam quaerat voluptatem. -Ut enim ad minima veniam, quis nostrum exercitationem ullam corporis -suscipit laboriosam, nisi ut aliquid ex ea commodi consequatur? -Quis autem vel eum iure reprehenderit qui in ea voluptate velit -esse quam nihil molestiae consequatur, vel illum qui dolorem eum -fugiat quo voluptas nulla pariatur? -\subsection{De finibus bonorum et malorum -\label{kreismembran:subsection:finibus}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga \eqref{000tempmlate:equation1}. +\section{Lösungsmethode 1: Separationsmethode + \label{kreismembran:section:teil1}} +\rhead{Lösungsmethode 1: Separationsmethode} +An diesem Punkt bleibt also nur noch die Lösung der partiellen Differentialgleichung. In diesem Kapitel wird sie mit Hilfe der Separationsmetode gelöst. -Et harum quidem rerum facilis est et expedita distinctio -\ref{kreismembran:section:loesung}. -Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil -impedit quo minus id quod maxime placeat facere possimus, omnis -voluptas assumenda est, omnis dolor repellendus -\ref{kreismembran:section:folgerung}. -Temporibus autem quibusdam et aut officiis debitis aut rerum -necessitatibus saepe eveniet ut et voluptates repudiandae sint et -molestiae non recusandae. -Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis -voluptatibus maiores alias consequatur aut perferendis doloribus -asperiores repellat. +Wie im vorherigen Kapitel gezeigt, lautet die partielle Differentialgleichung, die die Schwingungen einer Membran beschreibt: +\begin{equation*} + \frac{1}{c^2}\frac{\partial^2u}{\partial t^2} = \Delta u +\end{equation*} +Da es sich um eine Kreisscheibe handelt, werden Polarkoordinaten verwendet, so dass sich der Laplaceoperator ergibt: +\begin{equation*} + \Delta + = + \frac{\partial^2}{\partial r^2} + + + \frac1r + \frac{\partial}{\partial r} + + + \frac{1}{r 2} + \frac{\partial^2}{\partial\varphi^2}. + \label{buch:pde:kreis:laplace} +\end{equation*} +Es wird eine runde elastische Membran berücksichtigt, die den Gebietbereich $\Omega$ abdeckt und am Rand $\Gamma$ befestigt ist. +Es wird daher davon ausgegangen, dass die Membran aus einem homogenen Material von vernachlässigbarer Dicke gefertigt ist. +Die Membran kann verformt werden, aber innere elastische Kräfte wirken den Verformungen entgegen. Es wirken keine äusseren Kräfte. Es handelt sich somit von einer kreisförmligen eigespannten homogenen schwingenden Membran. + +Daher ist die Membranabweichung im Punkt $(r,\varphi)$ $\in$ $\overline{\rm \Omega}$ zum Zeitpunkt $t$: +\begin{align*} + u: \overline{\rm \Omega} \times \mathbb{R}_{\geq 0} &\longrightarrow \mathbb{R}\\ + (r,\varphi,t) &\longmapsto u(r,\varphi,t) +\end{align*} +Da die Membran am Rand befestigt ist, kann es keine Schwingungen geben, so dass die \textit{Dirichlet-Randbedingung} gilt: +\begin{equation*} + u\big|_{\Gamma} = 0 +\end{equation*} +Um eine eindeutige Lösung bestimmen zu können, werden die folgenden Anfangsbedingungen festgelegt: +\begin{align*} + u(r,\varphi, 0) &= f(r,\varphi)\\ + \frac{\partial}{\partial t} u(r,\varphi, 0) &= g(r,\varphi) +\end{align*} +Daher muss an dieser Stelle von einer Separation der Variablen ausgegangen werden: +\begin{equation*} + u(r,\varphi, t) = F(r)G(\varphi)T(t) +\end{equation*} +Dank der Randbedingungen kann also gefordert werden, dass $F(R)=0$ ist, und natürlich, dass $G(\varphi)$ $2\pi$ periodisch ist. Eingesetz in der Differenzialgleichung ergibt: +\begin{equation*} + \frac{1}{c^2}\frac{T''(t)}{T(t)}=\frac{F''(r)}{F(r)}+\frac{1}{r}\frac{F'(r)}{F(r)}+\frac{1}{r^2}\frac{G''(\varphi)}{G(\varphi)} +\end{equation*} +Da die linke Seite nur von $t$ und die rechte Seite nur von $r$ und $\varphi$ abhängt, müssen sie gleich einer reellen Zahl sein. Aus physikalischen Grunden suchen wir nach Lösungen, die weder exponentiell in der Zeit wachsen noch exponentiell abklingen. Dies bedeutet, dass die Konstante negativ sein muss, also schreibt man $k=-k^2$. Daraus ergeben sich die folgenden zwei Gleichungen: +\begin{gather*} + T''(t) + c^2\kappa^2T(t) = 0\\ + r^2\frac{F''(r)}{F(r)} + r \frac{F'(r)}{F(r)} +\kappa^2 r^2 = - \frac{G''(\varphi)}{G(\varphi)} +\end{gather*} +In der zweiten Gleichung hängt die linke Seite nur von $r$ ab, während die rechte Seite nur von $\varphi$ abhängt. Sie müssen also wiederum gleich einer reellen Zahl $\nu$ sein. Also das: +\begin{gather*} + r^2F''(r) + rF'(r) + (\kappa^2 r^2 - \nu)F(r) = 0 \\ + G''(\varphi) = \nu G(\varphi) +\end{gather*} +$G$ kann in einer Fourierreihe entwickelt werden, so dass man sieht, dass $\nu$ die Form $n^2$ mit einer positiven ganzen Zahl sein muss, also: +\begin{equation*} + G(\varphi) = C_n \cos(\varphi) + D_n \sin(\varphi) +\end{equation*} +Die Gleichung $F$ hat die Gestalt +\begin{equation*} + r^2F''(r) + rF'(r) + (\kappa^2 r^2 - n^2)F(r) = 0 \quad (*) +\end{equation*} +Wir bereits in der Vorlesung von Prof. Müller gezeigt, sind die Besselfunktionen +\begin{equation*} + J_{\nu}(x) = r^\nu \displaystyle\sum_{m=0}^{\infty} \frac{(-1)^m x^{2m}}{2^{2m+\nu}m! \Gamma (\nu + m+1)} +\end{equation*} +Lösungen der "Besselschen Differenzialgleichung" +\begin{equation*} + x^2 y'' + xy' + (x^2 - \nu^2)y = 0 +\end{equation*} +Die Funktionen $F(r) = J_n(\kappa r)$ lösen also die Differentialgleichung $(*)$. Die +Randbedingung $F(R)=0$ impliziert, dass $\kappa R$ eine Nullstelle der Besselfunktion +$J_n$ sein muss. Man kann zeigen, dass die Besselfunktionen $J_n, n \geq 0$, alle unendlich +viele Nullstellen +\begin{equation*} + \alpha_{1n} < \alpha_{2n} < ... +\end{equation*} +haben, und dass $\underset{\substack{m\to\infty}}{\text{lim}} \alpha_{mn}=\infty$. Somit ergit sich, dass $\kappa = \frac{\alpha_{mn}}{R}$ für ein $m\geq 1$, und dass +\begin{equation*} + F(r) = J_n (\kappa_{mn}r) \quad mit \quad \kappa_{mn}=\frac{\alpha_{mn}}{R} +\end{equation*} +Die Differenzialgleichung $T''(t) + c^2\kappa^2T(t) = 0$, wird auf ähnliche Weise gelöst wie $G(\varphi)$. Durch Überlagerung aller Ergebnisse erhält man die Lösung +\begin{equation} + u(r, \varphi, t) = \displaystyle\sum_{m=1}^{\infty}\displaystyle\sum_{n=0}^{\infty} J_n (k_{mn}r)\cos(n\varphi)[a_{mn}\cos(c \kappa_{mn} t)+b_{mn}\sin(c \kappa_{mn} t)] +\end{equation} +Dabei sind m und n ganze Zahlen, wobei m für die Anzahl der Knotenkreise und n +für die Anzahl der Knotenlinien steht. Es gibt bestimmte Bereiche auf der Membran, in denen es keine Bewegung oder Vibration gibt. Wenn der nicht schwingende Bereich ein Kreis ist, nennt man ihn einen Knotenkreis, und wenn er eine Linie ist, nennt man ihn ebenfalls eine Knotenlinie. $Jn(\kappa_{mn}r)$ ist die Besselfunktion $n$-ter Ordnung, wobei kmn die Wellenzahl und $r$ der Radius ist. $a_{mn}$ und $b_{mn}$ sind die zu bestimmenden Konstanten. +An diesem Punkt stellte sich die Frage, ob es möglich wäre, die partielle Differentialgleichung mit einer anderen Methode als der der Trennung der Variablen zu lösen. Nach einer kurzen Recherche und Diskussion mit Prof. Müller wurde festgestellt, dass die beste Methode die Transformationsmethode ist, genauer gesagt die Anwendung der Hankel-Transformation. Im nächsten Kapitel wird daher diese Integraltransformation vorgestellt und entwickelt, und es wird erläutert, warum sie für diese Art von Problem geeignet ist. diff --git a/buch/papers/kreismembran/teil2.tex b/buch/papers/kreismembran/teil2.tex index 7ed217f..8afe817 100644 --- a/buch/papers/kreismembran/teil2.tex +++ b/buch/papers/kreismembran/teil2.tex @@ -1,40 +1,113 @@ % -% teil2.tex -- Beispiel-File für teil2 -% % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Teil 2 -\label{kreismembran:section:teil2}} -\rhead{Teil 2} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit -aspernatur aut odit aut fugit, sed quia consequuntur magni dolores -eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam -est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci -velit, sed quia non numquam eius modi tempora incidunt ut labore -et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima -veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, -nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure -reprehenderit qui in ea voluptate velit esse quam nihil molestiae -consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla -pariatur? - -\subsection{De finibus bonorum et malorum -\label{kreismembran:subsection:bonorum}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis -est et expedita distinctio. Nam libero tempore, cum soluta nobis -est eligendi optio cumque nihil impedit quo minus id quod maxime -placeat facere possimus, omnis voluptas assumenda est, omnis dolor -repellendus. Temporibus autem quibusdam et aut officiis debitis aut -rerum necessitatibus saepe eveniet ut et voluptates repudiandae -sint et molestiae non recusandae. Itaque earum rerum hic tenetur a -sapiente delectus, ut aut reiciendis voluptatibus maiores alias -consequatur aut perferendis doloribus asperiores repellat. + +\section{Die Hankel Transformation \label{kreismembran:section:teil2}} +\rhead{Die Hankel Transformation} + +Hermann Hankel (1839-1873) war ein deutscher Mathematiker, der für seinen Beitrag zur mathematischen Analyse und insbesondere für seine namensgebende Transformation bekannt ist. +Diese Transformation tritt bei der Untersuchung von funktionen auf, die nur von der Enternung des Ursprungs abhängen. +Er studierte auch funktionen, jetzt Hankel- oder Bessel- Funktionen genannt, der dritten Art. +Die Hankel Transformation mit Bessel Funktionen al Kern taucht natürlich bei achsensymmetrischen Problemen auf, die in Zylindrischen Polarkoordinaten formuliert sind. +In diesem Kapitel werden die Theorie der Transformation und einige Eigenschaften der Grundoperationen erläutert. + + +Wir führen die Definition der Hankel Transformation aus der zweidimensionalen Fourier Transformation und ihrer Umkehrung ein, die durch: +\begin{align} + \mathscr{F}\{f(x,y)\} & = F(k,l)=\frac{1}{2\pi}\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}e^{-i( \bm{\kappa}\cdot \mathbf{r})}f(x,y) dx dy,\label{equation:fourier_transform}\\ + \mathscr{F}^{-1}\{F(x,y)\} & = f(x,y)=\frac{1}{2\pi}\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}e^{i(\bm{\kappa}\cdot \mathbf{r}))}F(k,l) dx dy \label{equation:inv_fourier_transform} +\end{align} +wo $\mathbf{r}=(x,y)$ und $\bm{\kappa}=(k,l)$. Wie bereits erwähnt, sind Polarkoordinaten für diese Art von Problemen am besten geeignet, also mit, $(x,y)=r(\cos\theta,\sin\theta)$ und $(k,l)=\kappa(\cos\phi,\sin\phi)$, findet man $\bm{\kappa}\cdot\mathbf{r}=\kappa r(\cos(\theta-\phi))$ und danach: +\begin{align} + F(k,\phi)=\frac{1}{2\pi}\int_{0}^{\infty}r dr \int_{0}^{2\pi}e^{-ikr\cos(\theta-\phi)}f(r,\theta) d\phi. + \label{equation:F_ohne_variable_wechsel} +\end{align} +Dann wird angenommen dass, $f(r,\theta)=e^{in\theta}f(r)$, was keine strenge Einschränkung ist, und es wird eine Änderung der Variabeln vorgenommen $\theta-\phi=\alpha-\frac{\pi}{2}$, um \eqref{equation:F_ohne_variable_wechsel} zu reduzieren: +\begin{align} + F(k,\phi)=\frac{1}{2\pi}\int_{0}^{\infty}rf(r) dr \int_{\phi_{0}}^{2\pi+\phi_{0}}e^{in(\phi-\frac{\pi}{2})+i(n\alpha-kr\sin\alpha)} d\alpha, + \label{equation:F_ohne_bessel} +\end{align} +wo $\phi_{0}=(\frac{\pi}{2}-\phi)$. + +Unter Verwendung der Integral Darstellung der Besselfunktion vom Ordnung n +\begin{align} + J_n(\kappa r)=\frac{1}{2\pi}\int_{\phi_{0}}^{2\pi + \phi_{0}}e^{i(n\alpha-\kappa r \sin \alpha)} d\alpha + \label{equation:bessel_n_ordnung} +\end{align} +\eqref{equation:F_ohne_bessel} wird sie zu: +\begin{align} + F(k,\phi)&=e^{in(\phi-\frac{\pi}{2})}\int_{0}^{\infty}rJ_n(\kappa r) f(r) dr \label{equation:F_mit_bessel_step_1} \\ + &=e^{in(\phi-\frac{\pi}{2})}\tilde{f}_n(\kappa), + \label{equation:F_mit_bessel_step_2} +\end{align} +wo $\tilde{f}_n(\kappa)$ ist die \textit{Hankel Transformation} von $f(r)$ und ist formell definiert durch: +\begin{align} + \mathscr{H}_n\{f(r)\}=\tilde{f}_n(\kappa)=\int_{0}^{\infty}rJ_n(\kappa r) f(r) dr. + \label{equation:hankel} +\end{align} + +Ähnlich verhält es sich mit der inversen Fourier Transformation in Form von polaren Koordinaten unter der Annahme $f(r,\theta)=e^{in\theta}f(r)$ mit \eqref{equation:F_mit_bessel_step_2}, wird die inverse Fourier Transformation \eqref{equation:inv_fourier_transform}: + +\begin{align} + e^{in\theta}f(r)&=\frac{1}{2\pi}\int_{0}^{\infty}\kappa d\kappa \int_{0}^{2\pi}e^{i\kappa r \cos (\theta - \phi)}F(\kappa,\phi) d\phi\\ + &= \frac{1}{2\pi}\int_{0}^{\infty}\kappa \tilde{f}_n(\kappa) d\kappa \int_{0}^{2\pi}e^{in(\phi - \frac{\pi}{2})- i\kappa r \cos (\theta - \phi)} d\phi, +\end{align} +was durch den Wechsel der Variablen $\theta-\phi=-(\alpha+\frac{\pi}{2})$ und $\theta_0=-(\theta+\frac{\pi}{2})$, + +\begin{align} + &= \frac{1}{2\pi}\int_{0}^{\infty}\kappa \tilde{f}_n(\kappa) d\kappa \int_{\theta_0}^{2\pi+\theta_0}e^{in(\theta + \alpha - i\kappa r \sin\alpha)} d\alpha \nonumber \\ + &= e^{in\theta}\int_{0}^{\infty}\kappa J_n(\kappa r) \tilde{f}_n(\kappa) d\kappa,\quad \text{von \eqref{equation:bessel_n_ordnung}} +\end{align} + +Also, die inverse \textit{Hankel Transformation} ist so definiert: +\begin{align} + \mathscr{H}^{-1}_n\{\tilde{f}_n(\kappa)\}=f(r)=\int_{0}^{\infty}\kappa J_n(\kappa r) \tilde{f}_n(\kappa) d\kappa. + \label{equation:inv_hankel} +\end{align} + +Anstelle von $\tilde{f}_n(\kappa)$, wird häufig für die Hankel Transformation verwendet, indem die Ordnung angegeben wird. +\eqref{equation:hankel} und \eqref{equation:inv_hankel} Integralen existieren für eine grosse Klasse von Funktionen, die normalerweise in physikalischen Anwendungen benötigt werden. +Alternativ kann auch die berühmte Hankel Transformationsformel verwendet werden, + +\begin{align} + f(r) = \int_{0}^{\infty}\kappa J_n(\kappa r) d\kappa \int_{0}^{\infty} p J_n(\kappa p)f(p) dp, + \label{equation:hankel_integral_formula} +\end{align} +um die Hankel Transformation \eqref{equation:hankel} und ihre Inverse \eqref{equation:inv_hankel} zu definieren. +Insbesondere die Hankel Transformation der nullten Ordnung ($n=0$) und der ersten Ordnung ($n=1$) sind häufig nützlich, um Lösungen für Probleme mit der Laplace Gleichung in einer achsensymmetrischen zylindrischen Geometrie zu finden. + +\subsection{Operative Eigenschaften der Hankel Transformation\label{sub:op_properties_hankel}} +In diesem Kapitel werden die operativen Eigenschaften der Hankel Transformation aufgeführt. Der Beweis für ihre Gültigkeit wird jedoch nicht analysiert. + +\subsubsection{Theorem 1: Skalierung \label{subsub:skalierung}} +Wenn $\mathscr{H}_n\{f(r)\}=\tilde{f}_n(\kappa)$, dann: + +\begin{equation*} + \mathscr{H}_n\{f(ar)\}=\frac{1}{a^{2}}\tilde{f}_n \left(\frac{\kappa}{a}\right), \quad a>0. +\end{equation*} + +\subsubsection{Theorem 2: Persevalsche Relation \label{subsub:perseval}} +Wenn $\tilde{f}(\kappa)=\mathscr{H}_n\{f(r)\}$ und $\tilde{g}(\kappa)=\mathscr{H}_n\{g(r)\}$, dann: + +\begin{equation*} + \int_{0}^{\infty}rf(r) dr = \int_{0}^{\infty}\kappa\tilde{f}(\kappa)\tilde{g}(\kappa) d\kappa. +\end{equation*} + +\subsubsection{Theorem 3: Hankel Transformationen von Ableitungen \label{subsub:ableitungen}} +Wenn $\tilde{f}_n(\kappa)=\mathscr{H}_n\{f(r)\}$, dann: + +\begin{align*} + &\mathscr{H}_n\{f'(r)\}=\frac{\kappa}{2n}\left[(n-1)\tilde{f}_{n+1}(\kappa)-(n+1)\tilde{f}_{n-1}(\kappa)\right], \quad n\geq1, \\ + &\mathscr{H}_1\{f'(r)\}=-\kappa \tilde{f}_0(\kappa), +\end{align*} +bereitgestellt dass $[rf(r)]$ verschwindet als $r\to0$ und $r\to\infty$. + +\subsubsection{Theorem 4 \label{subsub:thorem4}} +Wenn $\mathscr{H}_n\{f(r)\}=\tilde{f}_n(\kappa)$, dann: + +\begin{equation*} + \mathscr{H}_n \left\{ \left( \nabla^2 - \frac{n^2}{r^2} f(r)\right)\right\}= \mathscr{H}_n\left\{\frac{1}{r}\frac{d}{dr}\left(r\frac{df}{dr}\right) - \frac{n^2}{r^2}f(r)\right\}=-\kappa^2\tilde{f}_{n}(\kappa), +\end{equation*} +bereitgestellt dass $rf'(r)$ und $rf(r)$ verschwinden als $r\to0$ und $r\to\infty$. diff --git a/buch/papers/kreismembran/teil3.tex b/buch/papers/kreismembran/teil3.tex index 73dee0f..bef8b5f 100644 --- a/buch/papers/kreismembran/teil3.tex +++ b/buch/papers/kreismembran/teil3.tex @@ -3,38 +3,76 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Teil 3 +\section{Lösungsmethode 2: Transformationsmethode \label{kreismembran:section:teil3}} -\rhead{Teil 3} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit -aspernatur aut odit aut fugit, sed quia consequuntur magni dolores -eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam -est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci -velit, sed quia non numquam eius modi tempora incidunt ut labore -et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima -veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, -nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure -reprehenderit qui in ea voluptate velit esse quam nihil molestiae -consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla -pariatur? - -\subsection{De finibus bonorum et malorum -\label{kreismembran:subsection:malorum}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis -est et expedita distinctio. Nam libero tempore, cum soluta nobis -est eligendi optio cumque nihil impedit quo minus id quod maxime -placeat facere possimus, omnis voluptas assumenda est, omnis dolor -repellendus. Temporibus autem quibusdam et aut officiis debitis aut -rerum necessitatibus saepe eveniet ut et voluptates repudiandae -sint et molestiae non recusandae. Itaque earum rerum hic tenetur a -sapiente delectus, ut aut reiciendis voluptatibus maiores alias -consequatur aut perferendis doloribus asperiores repellat. +\rhead{Lösungsmethode 2: Transformationsmethode} +Die Hankel-Transformation wird dann zur Lösung der Differentialgleichung verwendet. Es müssen jedoch einige Änderungen an dem Problem vorgenommen werden, damit es mit den Annahmen übereinstimmt, die für die Verwendung der Hankel-Transformation erforderlich sind. Das heisst, dass die Funktion u nur von der Entfernung zum Ausgangspunkt abhängt. Wir führen also das Konzept einer unendlichen und achsensymmetrischen Membran ein: +\begin{equation*} + \frac{\partial^2u}{\partial t^2} + = + c^2 \left(\frac{\partial^2 u}{\partial r^2} + + + \frac{1}{r} + \frac{\partial u}{\partial r} \right), \quad 0<r<\infty, \quad t>0 + \label{eq:PDE_inf_membane} +\end{equation*} + +\begin{align} + u(r,0)=f(r), \quad \frac{\partial}{\partial t} u(r,0) = g(r), \quad \text{für} \quad 0<r<\infty + \label{eq:PDE_inf_membane_RB} +\end{align} + +Mit Anwendung der Hankel-Transformation nullter Ordnung in Abhängigkeit von $r$ auf die Gleichungen \eqref{eq:PDE_inf_membane} und \eqref{eq:PDE_inf_membane_RB}: + +\begin{align} + \tilde{u}(\kappa,t)=\int_{0}^{\infty}r J_0(\kappa r)u(r,t) dr, +\end{align} + +bekommt man: + +\begin{equation*} + \frac{d^2 \tilde{u}}{dt^2} + c^2\kappa^2\tilde{u}=0, +\end{equation*} + +\begin{equation*} + \tilde{u}(\kappa,0)=\tilde{f}(\kappa), \quad + \frac{\partial}{\partial t}\tilde{u}(\kappa,0)=\tilde{g}(\kappa). +\end{equation*} + +Die allgemeine Lösung für diese Transformation lautet, wie schon gesehen, wie folgt + +\begin{equation*} + \tilde{u}(\kappa,t)=\tilde{f}(\kappa)\cos(c\kappa t) + \frac{1}{c\kappa}\tilde{g}(\kappa)\sin(c\kappa t). +\end{equation*} + +Wendet man an nun die inverse Hankel-Transformation an, so erhält man die formale Lösung + +\begin{align} + u(r,t)=\int_{0}^{\infty}\kappa\tilde{f}(\kappa)\cos(c\kappa t) J_0(\kappa r) d\kappa +\frac{1}{c}\int_{0}^{\infty}\tilde{g}(\kappa)\sin(c\kappa t)J_0(\kappa r) d\kappa. + \label{eq:formale_lösung} +\end{align} + +Es wird daher davon ausgegangen, dass sich die Membran verformt und zum Zeitpunkt $t=0$ freigegeben wird + +\begin{equation*} + u(r,0)=f(r)=Aa(r^2 + a^2)^{-\frac{1}{2}}, \quad \frac{d}{dt}(r,0)=g(r)=0 +\end{equation*} + +so dass $\tilde{g}(\kappa)\equiv 0$ und + +\begin{equation*} + \tilde{f}(\kappa)=Aa\int_{0}^{\infty}r(a^2 + r^2)^{-\frac{1}{2}} J_0 (\kappa r) dr=\frac{Aa}{\kappa}e^{-a\kappa} +\end{equation*} + +Die formale Lösung \eqref{eq:formale_lösung} lautet also +\begin{align*} + u(r,t)&=Aa\int_{0}^{\infty}e^{-a\kappa} J_0(\kappa r)\cos(c\kappa t)dk=AaRe\int_{0}^{\infty}e^{-\kappa(a+ict)} J_0(\kappa r)dk\\ + &=AaRe\left\{r^2+\left(a+ict\right)^2\right\}^{-\frac{1}{2}} +\end{align*} + + +\subsection{Vergleich der Lösungen +\label{kreismembran:vergleich}} +Hier kommt noch der Vergleich der Lösungen ;) diff --git a/buch/papers/nav/Makefile.inc b/buch/papers/nav/Makefile.inc index b30377e..24ab4ee 100644 --- a/buch/papers/nav/Makefile.inc +++ b/buch/papers/nav/Makefile.inc @@ -6,9 +6,11 @@ dependencies-nav = \ papers/nav/packages.tex \ papers/nav/main.tex \ - papers/nav/references.bib \ - papers/nav/teil0.tex \ - papers/nav/teil1.tex \ - papers/nav/teil2.tex \ - papers/nav/teil3.tex + papers/nav/einleitung.tex \ + papers/nav/flatearth.tex \ + papers/nav/geschichte.tex \ + papers/nav/nautischesdreieck.tex \ + papers/nav/sincos.tex \ + papers/nav/trigo.tex \ + papers/nav/references.bib diff --git a/buch/papers/nav/images/Makefile b/buch/papers/nav/images/Makefile index c9dcacc..bbdea2f 100644 --- a/buch/papers/nav/images/Makefile +++ b/buch/papers/nav/images/Makefile @@ -50,7 +50,8 @@ DREIECKE3D = \ dreieck3d4.pdf \ dreieck3d5.pdf \ dreieck3d6.pdf \ - dreieck3d7.pdf + dreieck3d7.pdf \ + dreieck3d8.pdf dreiecke3d: $(DREIECKE3D) @@ -106,3 +107,10 @@ dreieck3d7.jpg: dreieck3d7.png dreieck3d7.pdf: dreieck3d7.tex dreieck3d7.jpg pdflatex dreieck3d7.tex +dreieck3d8.png: dreieck3d8.pov common.inc + povray +A0.1 $(POVRAYOPTIONS) -Odreieck3d8.png dreieck3d8.pov +dreieck3d8.jpg: dreieck3d8.png + convert dreieck3d8.png -density 300 -units PixelsPerInch dreieck3d8.jpg +dreieck3d8.pdf: dreieck3d8.tex dreieck3d8.jpg + pdflatex dreieck3d8.tex + diff --git a/buch/papers/nav/images/common.inc b/buch/papers/nav/images/common.inc index 33d9384..e2a1ed0 100644 --- a/buch/papers/nav/images/common.inc +++ b/buch/papers/nav/images/common.inc @@ -97,13 +97,13 @@ union { } #end -#macro winkel(w, p, q, staerke) +#macro winkel(w, p, q, staerke, r) #declare n = vnormalize(w); #declare pp = vnormalize(p - vdot(n, p) * n); #declare qq = vnormalize(q - vdot(n, q) * n); intersection { sphere { <0, 0, 0>, 1 + staerke } - cone { <0, 0, 0>, 0, 1.2 * vnormalize(w), 0.4 } + cone { <0, 0, 0>, 0, 1.2 * vnormalize(w), r } plane { -vcross(n, qq) * vdot(vcross(n, qq), pp), 0 } plane { -vcross(n, pp) * vdot(vcross(n, pp), qq), 0 } } @@ -113,8 +113,30 @@ union { sphere { p, 1.5 * staerke } #end +#macro dreieck(p, q, r, farbe) + #declare n1 = vnormalize(vcross(p, q)); + #declare n2 = vnormalize(vcross(q, r)); + #declare n3 = vnormalize(vcross(r, p)); + intersection { + plane { n1, 0 } + plane { n2, 0 } + plane { n3, 0 } + sphere { <0, 0, 0>, 1 + 0.001 } + pigment { + color farbe + } + finish { + metallic + specular 0.4 + } + } +#end + #declare fett = 0.015; -#declare fine = 0.010; +#declare fein = 0.010; + +#declare klein = 0.3; +#declare gross = 0.4; #declare dreieckfarbe = rgb<0.6,0.6,0.6>; #declare rot = rgb<0.8,0.2,0.2>; diff --git a/buch/papers/nav/images/dreieck3d1.pdf b/buch/papers/nav/images/dreieck3d1.pdf Binary files differnew file mode 100644 index 0000000..015bce7 --- /dev/null +++ b/buch/papers/nav/images/dreieck3d1.pdf diff --git a/buch/papers/nav/images/dreieck3d1.pov b/buch/papers/nav/images/dreieck3d1.pov index 8afe60e..e491075 100644 --- a/buch/papers/nav/images/dreieck3d1.pov +++ b/buch/papers/nav/images/dreieck3d1.pov @@ -12,9 +12,9 @@ union { punkt(A, fett) punkt(B, fett) punkt(C, fett) - punkt(P, fine) - seite(B, P, fine) - seite(C, P, fine) + punkt(P, fein) + seite(B, P, fein) + seite(C, P, fein) pigment { color dreieckfarbe } @@ -25,7 +25,7 @@ union { } object { - winkel(A, B, C, fine) + winkel(A, B, C, fein, gross) pigment { color rot } @@ -36,7 +36,7 @@ object { } object { - winkel(B, C, A, fine) + winkel(B, C, A, fein, gross) pigment { color gruen } @@ -47,7 +47,7 @@ object { } object { - winkel(C, A, B, fine) + winkel(C, A, B, fein, gross) pigment { color blau } diff --git a/buch/papers/nav/images/dreieck3d2.pdf b/buch/papers/nav/images/dreieck3d2.pdf Binary files differnew file mode 100644 index 0000000..6b3f09d --- /dev/null +++ b/buch/papers/nav/images/dreieck3d2.pdf diff --git a/buch/papers/nav/images/dreieck3d2.pov b/buch/papers/nav/images/dreieck3d2.pov index c23a54c..c0625ce 100644 --- a/buch/papers/nav/images/dreieck3d2.pov +++ b/buch/papers/nav/images/dreieck3d2.pov @@ -12,9 +12,9 @@ union { punkt(A, fett) punkt(B, fett) punkt(C, fett) - punkt(P, fine) - seite(B, P, fine) - seite(C, P, fine) + punkt(P, fein) + seite(B, P, fein) + seite(C, P, fein) pigment { color dreieckfarbe } diff --git a/buch/papers/nav/images/dreieck3d3.pdf b/buch/papers/nav/images/dreieck3d3.pdf Binary files differnew file mode 100644 index 0000000..7d79455 --- /dev/null +++ b/buch/papers/nav/images/dreieck3d3.pdf diff --git a/buch/papers/nav/images/dreieck3d3.pov b/buch/papers/nav/images/dreieck3d3.pov index f2496b5..b6f64d5 100644 --- a/buch/papers/nav/images/dreieck3d3.pov +++ b/buch/papers/nav/images/dreieck3d3.pov @@ -12,9 +12,9 @@ union { punkt(A, fett) punkt(B, fett) punkt(C, fett) - punkt(P, fine) - seite(B, P, fine) - seite(C, P, fine) + punkt(P, fein) + seite(B, P, fein) + seite(C, P, fein) pigment { color dreieckfarbe } @@ -25,7 +25,7 @@ union { } object { - winkel(A, B, C, fine) + winkel(A, B, C, fein, gross) pigment { color rot } diff --git a/buch/papers/nav/images/dreieck3d4.pdf b/buch/papers/nav/images/dreieck3d4.pdf Binary files differnew file mode 100644 index 0000000..e1ea757 --- /dev/null +++ b/buch/papers/nav/images/dreieck3d4.pdf diff --git a/buch/papers/nav/images/dreieck3d4.pov b/buch/papers/nav/images/dreieck3d4.pov index bddcf7c..b6f17e3 100644 --- a/buch/papers/nav/images/dreieck3d4.pov +++ b/buch/papers/nav/images/dreieck3d4.pov @@ -6,9 +6,9 @@ #include "common.inc" union { - seite(A, B, fine) - seite(A, C, fine) - punkt(A, fine) + seite(A, B, fein) + seite(A, C, fein) + punkt(A, fein) punkt(B, fett) punkt(C, fett) punkt(P, fett) @@ -25,7 +25,7 @@ union { } object { - winkel(B, C, P, fine) + winkel(B, C, P, fein, gross) pigment { color rgb<0.6,0.4,0.2> } diff --git a/buch/papers/nav/images/dreieck3d5.pdf b/buch/papers/nav/images/dreieck3d5.pdf Binary files differnew file mode 100644 index 0000000..0c86d36 --- /dev/null +++ b/buch/papers/nav/images/dreieck3d5.pdf diff --git a/buch/papers/nav/images/dreieck3d5.pov b/buch/papers/nav/images/dreieck3d5.pov index 32fc9e6..188f181 100644 --- a/buch/papers/nav/images/dreieck3d5.pov +++ b/buch/papers/nav/images/dreieck3d5.pov @@ -6,9 +6,9 @@ #include "common.inc" union { - seite(A, B, fine) - seite(A, C, fine) - punkt(A, fine) + seite(A, B, fein) + seite(A, C, fein) + punkt(A, fein) punkt(B, fett) punkt(C, fett) punkt(P, fett) diff --git a/buch/papers/nav/images/dreieck3d6.pov b/buch/papers/nav/images/dreieck3d6.pov index 7611950..191a1e7 100644 --- a/buch/papers/nav/images/dreieck3d6.pov +++ b/buch/papers/nav/images/dreieck3d6.pov @@ -25,7 +25,7 @@ union { } object { - winkel(B, A, P, fine) + winkel(B, A, P, fein, gross) pigment { color rgb<0.6,0.2,0.6> } diff --git a/buch/papers/nav/images/dreieck3d7.pov b/buch/papers/nav/images/dreieck3d7.pov index fa48f5b..aae5c6c 100644 --- a/buch/papers/nav/images/dreieck3d7.pov +++ b/buch/papers/nav/images/dreieck3d7.pov @@ -10,13 +10,13 @@ union { seite(A, P, fett) seite(C, P, fett) - seite(A, B, fine) - seite(B, C, fine) - seite(B, P, fine) + seite(A, B, fein) + seite(B, C, fein) + seite(B, P, fein) punkt(A, fett) punkt(C, fett) punkt(P, fett) - punkt(B, fine) + punkt(B, fein) pigment { color dreieckfarbe } @@ -27,7 +27,7 @@ union { } object { - winkel(A, P, C, fine) + winkel(A, P, C, fein, gross) pigment { color rgb<0.4,0.4,1> } diff --git a/buch/papers/nav/images/dreieck3d8.jpg b/buch/papers/nav/images/dreieck3d8.jpg Binary files differnew file mode 100644 index 0000000..52bd25e --- /dev/null +++ b/buch/papers/nav/images/dreieck3d8.jpg diff --git a/buch/papers/nav/images/dreieck3d8.pdf b/buch/papers/nav/images/dreieck3d8.pdf Binary files differnew file mode 100644 index 0000000..9d630aa --- /dev/null +++ b/buch/papers/nav/images/dreieck3d8.pdf diff --git a/buch/papers/nav/images/dreieck3d8.pov b/buch/papers/nav/images/dreieck3d8.pov new file mode 100644 index 0000000..9e9921a --- /dev/null +++ b/buch/papers/nav/images/dreieck3d8.pov @@ -0,0 +1,96 @@ +// +// dreiecke3d8.pov +// +// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// +#include "common.inc" + +union { + seite(A, B, fett) + seite(B, C, fett) + seite(A, C, fett) + seite(A, P, fein) + seite(B, P, fett) + seite(C, P, fett) + punkt(A, fett) + punkt(B, fett) + punkt(C, fett) + punkt(P, fett) + pigment { + color dreieckfarbe + } + finish { + specular 0.95 + metallic + } +} + +object { + winkel(A, B, C, fein, klein) + pigment { + color rot + } + finish { + specular 0.95 + metallic + } +} + +object { + winkel(B, C, A, fein, klein) + pigment { + color gruen + } + finish { + specular 0.95 + metallic + } +} + +object { + winkel(C, A, B, fein, gross) + pigment { + color blau + } + finish { + specular 0.95 + metallic + } +} + +object { + winkel(A, P, C, fein/2, gross) + pigment { + color rgb<0.8,0,0.8> + } + finish { + specular 0.95 + metallic + } +} + +object { + winkel(B, P, C, fein, klein) + pigment { + color rgb<1,0.8,0> + } + finish { + specular 0.95 + metallic + } +} + +object { + winkel(B, P, A, fein/2, gross) + pigment { + color rgb<0.4,0.6,0.8> + } + finish { + specular 0.95 + metallic + } +} + +dreieck(A, B, C, White) + + diff --git a/buch/papers/nav/images/dreieck3d8.tex b/buch/papers/nav/images/dreieck3d8.tex new file mode 100644 index 0000000..c59c7b0 --- /dev/null +++ b/buch/papers/nav/images/dreieck3d8.tex @@ -0,0 +1,57 @@ +% +% dreieck3d8.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{times} +\usepackage{amsmath} +\usepackage{txfonts} +\usepackage[utf8]{inputenc} +\usepackage{graphics} +\usetikzlibrary{arrows,intersections,math} +\usepackage{ifthen} +\begin{document} + +\newboolean{showgrid} +\setboolean{showgrid}{false} +\def\breite{4} +\def\hoehe{4} + +\begin{tikzpicture}[>=latex,thick] + +% Povray Bild +\node at (0,0) {\includegraphics[width=8cm]{dreieck3d8.jpg}}; + +% Gitter +\ifthenelse{\boolean{showgrid}}{ +\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw (-\breite,-\hoehe) grid (\breite, \hoehe); +\fill (0,0) circle[radius=0.05]; +}{} + +\node at (0.7,3.8) {$A$}; +\node at (-3.4,-0.8) {$B$}; +\node at (3.3,-2.1) {$C$}; +\node at (-1.4,-3.5) {$P$}; + +\node at (-1.9,2.1) {$c$}; +\node at (-0.2,-1.2) {$a$}; +\node at (2.6,1.5) {$b$}; +\node at (-0.8,0) {$l$}; + +\node at (-2.6,-2.2) {$p_b$}; +\node at (1,-2.9) {$p_c$}; + +\node at (0.7,3.3) {$\alpha$}; +\node at (0.8,2.85) {$\omega$}; +\node at (-2.6,-0.6) {$\beta$}; +\node at (2.3,-1.2) {$\gamma$}; +\node at (-2.6,-1.3) {$\beta_1$}; +\node at (-2.1,-0.8) {$\kappa$}; + +\end{tikzpicture} + +\end{document} + diff --git a/buch/splitpapers b/buch/splitpapers index 9ae5aae..e1b6834 100755 --- a/buch/splitpapers +++ b/buch/splitpapers @@ -16,7 +16,7 @@ then fi awk 'BEGIN { - offsetpage = 10 + offsetpage = 12 startpage = 0 identifier = "" chapterno = 0 |
