This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) (format=pdflatex 2009.1.7) 4 FEB 2013 14:17 entering extended mode %&-line parsing enabled. **til3 (./til3.tex LaTeX2e <2005/12/01> Babel and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, arabic, basque, bulgarian, coptic, welsh, czech, slovak, german, ng erman, danish, esperanto, spanish, catalan, galician, estonian, farsi, finnish, french, greek, monogreek, ancientgreek, croatian, hungarian, interlingua, ibyc us, indonesian, icelandic, italian, latin, mongolian, dutch, norsk, polish, por tuguese, pinyin, romanian, russian, slovenian, uppersorbian, serbian, swedish, turkish, ukenglish, ukrainian, loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size12.clo File: size12.clo 2005/09/16 v1.4f Standard LaTeX file (size option) ) \c@part=\count79 \c@section=\count80 \c@subsection=\count81 \c@subsubsection=\count82 \c@paragraph=\count83 \c@subparagraph=\count84 \c@figure=\count85 \c@table=\count86 \abovecaptionskip=\skip41 \belowcaptionskip=\skip42 \bibindent=\dimen102 ) (./bok.sty) (./makro.sty (/usr/share/texmf/tex/latex/base/latexsym.sty Package: latexsym 1998/08/17 v2.2e Standard LaTeX package (lasy symbols) \symlasy=\mathgroup4 LaTeX Font Info: Overwriting symbol font `lasy' in version `bold' (Font) U/lasy/m/n --> U/lasy/b/n on input line 47. ) (/usr/share/texmf/tex/latex/base/inputenc.sty Package: inputenc 2006/05/05 v1.1b Input encoding file \inpenc@prehook=\toks14 \inpenc@posthook=\toks15 (/usr/share/texmf/tex/latex/base/latin1.def File: latin1.def 2006/05/05 v1.1b Input encoding file ))) (/usr/share/texmf/tex/latex/graphics/graphicx.sty Package: graphicx 1999/02/16 v1.0f Enhanced LaTeX Graphics (DPC,SPQR) (/usr/share/texmf/tex/latex/graphics/keyval.sty Package: keyval 1999/03/16 v1.13 key=value parser (DPC) \KV@toks@=\toks16 ) (/usr/share/texmf/tex/latex/graphics/graphics.sty Package: graphics 2006/02/20 v1.0o Standard LaTeX Graphics (DPC,SPQR) (/usr/share/texmf/tex/latex/graphics/trig.sty Package: trig 1999/03/16 v1.09 sin cos tan (DPC) ) (/usr/share/texmf/tex/latex/config/graphics.cfg File: graphics.cfg 2007/01/18 v1.5 graphics configuration of teTeX/TeXLive ) Package graphics Info: Driver file: pdftex.def on input line 90. (/usr/share/texmf/tex/latex/pdftex-def/pdftex.def File: pdftex.def 2007/01/08 v0.04d Graphics/color for pdfTeX \Gread@gobject=\count87 )) \Gin@req@height=\dimen103 \Gin@req@width=\dimen104 ) (./til3.aux) \openout1 = `til3.aux'. LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 34. LaTeX Font Info: ... okay on input line 34. LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 34. LaTeX Font Info: ... okay on input line 34. LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 34. LaTeX Font Info: ... okay on input line 34. LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 34. LaTeX Font Info: ... okay on input line 34. LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 34. LaTeX Font Info: ... okay on input line 34. LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 34. LaTeX Font Info: ... okay on input line 34. LaTeX Font Info: External font `cmex10' loaded for size (Font) <12> on input line 68. LaTeX Font Info: External font `cmex10' loaded for size (Font) <8> on input line 68. LaTeX Font Info: External font `cmex10' loaded for size (Font) <6> on input line 68. LaTeX Font Info: Try loading font information for U+lasy on input line 68. (/usr/share/texmf/tex/latex/base/ulasy.fd File: ulasy.fd 1998/08/17 v2.2e LaTeX symbol font definitions ) Overfull \hbox (8.6741pt too wide) in paragraph at lines 84--85 \OT1/cmr/m/n/12 (i) For et $[]$, $ \OMS/cmsy/m/n/12 j\OML/cmm/m/it/12 V\OT1/cmr /m/n/12 (\OML/cmm/m/it/12 x\OT1/cmr/m/n/12 )\OMS/cmsy/m/n/12 j \OML/cmm/m/it/12 < \OMS/cmsy/m/n/12 1$\OT1/cmr/m/n/12 , ser vi av [] at den 2.-deriverte av b^^ \lgefunksjonen [] [1{/usr/share/texmf/fonts/map/pdftex/updmap/pdftex.map} ] File: fig4250til6-1.png Graphic file (type png) File: fig4250til6-2.png Graphic file (type png) LaTeX Font Info: External font `cmex10' loaded for size (Font) <14.4> on input line 103. LaTeX Font Info: External font `cmex10' loaded for size (Font) <7> on input line 103. File: fig4250til6-3.png Graphic file (type png) [2 <./fig4250til6-1.png (PNG copy)> <./fig4250til6-2.png (PNG copy)> <./fig4250 til6-3.png (PNG copy)>] Overfull \hbox (20.91399pt too wide) in paragraph at lines 133--138 \OT1/cmr/m/n/12 ser vi at denne difer-en-sial-lignin-gen bestem-mer den lokale \OT1/cmr/m/it/12 rel-a-tive krumnin-gen \OT1/cmr/m/n/12 av b^^\lgefunksjonen, [] Underfull \hbox (badness 10000) in paragraph at lines 133--138 [] File: fig4048-2-4.png Graphic file (type png) Underfull \hbox (badness 10000) in paragraph at lines 144--150 [] File: fig4048-2-5.png Graphic file (type png) [3 <./fig4048-2-4.png (PNG copy)>] Overfull \hbox (4.17322pt too wide) in paragraph at lines 159--160 []\OT1/cmr/m/n/12 I de klas-sisk tillatte omr^^Wadene (mel-lom vendepunk-tene) ser vi at $\OML/cmm/m/it/12 []\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 x\OT1/cmr/m/n/ 12 )$ krum-mer $[]$ [] File: fig4250b5-3.png Graphic file (type png) LaTeX Font Info: External font `cmex10' loaded for size (Font) <5> on input line 169. Underfull \hbox (badness 10000) in paragraph at lines 168--174 [] [4 <./fig4048-2-5.png (PNG copy)> <./fig4250b5-3.png (PNG copy)>] File: fig4250til6-4.png Graphic file (type png) Overfull \hbox (26.64482pt too wide) in paragraph at lines 186--187 \OT1/cmr/m/n/12 Den endi-men-sjonale bok-sen og den endi-men-sjonale har-monisk e os-cil-la-toren har \OT1/cmr/bx/n/12 ikke-degenererte [] Overfull \hbox (16.67867pt too wide) in paragraph at lines 188--189 []\OT1/cmr/m/n/12 Det kan vises at det samme gjelder for $[]$, for $[]$: [] [5 <./fig4250til6-4.png (PNG copy)>] File: fig4250til6-5.png Graphic file (type png) File: fig42155til3-1.png Graphic file (type png) [6 <./fig4250til6-5.png (PNG copy)>] File: fig4215til-5-1.png Graphic file (type png) [7 <./fig42155til3-1.png (PNG copy)>] Underfull \hbox (badness 10000) in paragraph at lines 261--267 [] Underfull \hbox (badness 10000) in paragraph at lines 261--267 [] [8 <./fig4215til-5-1.png (PNG copy)>] Underfull \hbox (badness 10000) in paragraph at lines 280--283 [] [9] File: fig4215til-5-2.png Graphic file (type png) [10 <./fig4215til-5-2.png (PNG copy)>] File: fig4215til-5-3.png Graphic file (type png) [11 <./fig4215til-5-3.png (PNG copy)>] File: fig4215til-5-4.png Graphic file (type png) [12] [13 <./fig4215til-5-4.png (PNG copy)>] File: fig42155til3-2.png Graphic file (type png) File: fig42155til3-3.png Graphic file (type png) File: fig42155til3-4.png Graphic file (type png) [14 <./fig42155til3-2.png (PNG copy)> <./fig42155til3-3.png (PNG copy)>] Overfull \hbox (10.78584pt too wide) in paragraph at lines 415--419 \OT1/cmr/bx/n/12 2.4 \OT1/cmr/m/n/12 Hvor-for har poten-sialet i fig-uren in-ge n bundne til-stander (en-ergiegen-funksjoner) [] Underfull \hbox (badness 10000) in paragraph at lines 415--419 [] File: fig42155til3-5.png Graphic file (type png) Underfull \hbox (badness 10000) in paragraph at lines 424--426 [] Overfull \hbox (19.87074pt too wide) in paragraph at lines 428--428 []\OT1/cmr/bx/n/14.4 3.2.e Diskusjon av en-ergik-van-tis-er-ing ut fra krumn-in gsegen-skaper***[] [] [15 <./fig42155til3-4.png (PNG copy)> <./fig42155til3-5.png (PNG copy)>] Overfull \hbox (1.0569pt too wide) in paragraph at lines 442--443 []\OT1/cmr/m/n/12 (i) Mask-i-nen vil finne \OT1/cmr/bx/n/12 sym-metriske l^^\sn inger \OT1/cmr/m/n/12 der-som vi gir den startver-di-ene $[]$ [] Overfull \hbox (7.50294pt too wide) in paragraph at lines 443--447 \OT1/cmr/m/n/12 ger vi f.eks grun-ntil-stand-sen-ergien $\OML/cmm/m/it/12 E[]$\ OT1/cmr/m/n/12 , vil mask-i-nen gi oss en cosinus-l^^\sning $[]$ [] File: fig4250til7-1.png Graphic file (type png) File: fig4250til7-2.png Graphic file (type png) [16 <./fig4250til7-1.png (PNG copy)>] File: fig4250til7-3.png Graphic file (type png) File: fig4250til7-5.png Graphic file (type png) [17 <./fig4250til7-2.png (PNG copy)> <./fig4250til7-3.png (PNG copy)>] File: fig4250til7-6.png Graphic file (type png) [18 <./fig4250til7-5.png (PNG copy)> <./fig4250til7-6.png (PNG copy)>] File: fig4250til7-4.png Graphic file (type png) LaTeX Font Info: Try loading font information for OMS+cmr on input line 515. (/usr/share/texmf/tex/latex/base/omscmr.fd File: omscmr.fd 1999/05/25 v2.5h Standard LaTeX font definitions ) LaTeX Font Info: Font shape `OMS/cmr/m/n' in size <12> not available (Font) Font shape `OMS/cmsy/m/n' tried instead on input line 515. [19 <./fig4250til7-4.png (PNG copy)>] File: fig4250til7-7.png Graphic file (type png) File: fig4250til7-8.png Graphic file (type png) [20 <./fig4250til7-7.png (PNG copy)> <./fig4250til7-8.p ng (PNG copy)>] File: fig4250til7-9.png Graphic file (type png) Overfull \hbox (14.22638pt too wide) in paragraph at lines 569--570 [] [] [21 <./fig4250til7-9.png (PNG copy)>] File: fig4250b5-2.png Graphic file (type png) [22 <./fig4250b5-2.png (PNG copy)>] [23] [24] Overfull \hbox (4.05704pt too wide) in paragraph at lines 669--672 \OT1/cmr/m/n/12 rekkeutviklin-gen for $\OML/cmm/m/it/12 x[]e[]$ \OT1/cmr/m/n/12 der $\OML/cmm/m/it/12 x[]$ \OT1/cmr/m/n/12 er en vilk^^Warlig potens av $\OML/ cmm/m/it/12 x$\OT1/cmr/m/n/12 . Dette be-tyr at $[]$ [] [25] File: fig4250b5-3.png Graphic file (type png) [26] [27] [28] File: fig4250til9-1.png Graphic file (type png) Overfull \hbox (5.24373pt too wide) in paragraph at lines 769--771 []\OT1/cmr/m/n/12 For de laveste $\OML/cmm/m/it/12 n$\OT1/cmr/m/n/12 -verdiene, hvor $\OML/cmm/m/it/12 V\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 q\OT1/cmr/m/n/12 )$ og $\OML/cmm/m/it/12 V[]\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 q\OT1/cmr/m/n/12 )$ e r nesten sam-men-fal-l-ende mel-lom vendepunk- [] [29 <./fig4250til9-1.png (PNG copy)>] File: fig4250til9-2.png Graphic file (type png) [30 <./fig4250til9-2.png (PNG copy)>] File: fig42155til3-6.png Graphic file (type png) [31 <./fig42155til3-6.png (PNG copy)>] [32] [33] Overfull \hbox (15.06898pt too wide) in paragraph at lines 872--875 \OT1/cmr/m/n/12 Denne s^^Wakalte \OT1/cmr/bx/n/12 fase-hastigheten \OT1/cmr/m/n /12 er uavhengig av b^^\lgetallet $\OML/cmm/m/it/12 k$\OT1/cmr/m/n/12 ; b^^\lge r med forskjel-lig b^^\lgelengde [] File: fig4250a5a6-1.png Graphic file (type png) File: fig4250a5a6-2.png Graphic file (type png) [34 <./fig4250a5a6-1.png (PNG copy)> <./fig4250a5a6-2.png (PNG copy)>] File: fig4250a5a6-3.png Graphic file (type png) [35 <./fig4250a5a6-3.png (PNG copy)>] Overfull \hbox (9.25581pt too wide) in paragraph at lines 939--942 \OT1/cmr/m/n/12 dette med det siste in-te-gralet i [] ser vi da at det sist-nev nte er $[]$ [] [36] Overfull \hbox (8.08237pt too wide) in paragraph at lines 947--949 \OT1/cmr/m/n/12 I det ak-tuelle til-fel-let, med dis-per-sjon-sre-lasjo-nen $[ ]$ finner vi at grup-pe-hastigheten [] [37] File: fig4250til8-1.png Graphic file (type png) [38 <./fig4250til8-1.png (PNG copy)>] [39] LaTeX Font Info: Font shape `U/lasy/b/n' in size <8> not available (Font) Font shape `U/lasy/m/n' tried instead on input line 1037. LaTeX Font Info: Font shape `U/lasy/b/n' in size <6> not available (Font) Font shape `U/lasy/m/n' tried instead on input line 1037. Overfull \hbox (6.40608pt too wide) in paragraph at lines 1037--1038 \OT1/cmr/m/n/12 lighet. Dette kan vi bekrefte ved ^^Wa merke oss at for en stas jon^^Zr til-stand $[]$ [] File: fig4250til8-2.png Graphic file (type png) [40 <./fig4250til8-2.png (PNG copy)>] File: fig4250til8-3.png Graphic file (type png) File: fig4250til8-4.png Graphic file (type png) [41 <./fig4250til8-3.png (PNG copy)>] File: fig4250til8-5.png Graphic file (type png) File: fig4250til8-6.png Graphic file (type png) [42 <./fig4250til8-4.png (PNG copy)> <./fig4250til8-5.png (PNG copy)>] File: fig4250til8-7.png Graphic file (type png) Overfull \hbox (3.39685pt too wide) in paragraph at lines 1124--1125 []\OT1/cmr/m/n/12 Transmisjons- og refleksjons-koeffisientene er n^^Wa ^^Wapenb art gitt ved sannsyn-lighetsinnholdet [] Underfull \hbox (badness 10000) in paragraph at lines 1127--1131 [] [43 <./fig4250til8-6.png (PNG copy)> <./fig4250til8-7.png (PNG copy)>] File: fig4250til8-8.png Graphic file (type png) Underfull \hbox (badness 10000) in paragraph at lines 1151--1154 [] Underfull \hbox (badness 10000) in paragraph at lines 1151--1154 [] File: fig4250til8-9.png Graphic file (type png) [44 <./fig4250til8-8.png (PNG copy)> <./fig4250til8-9.png (PNG copy)>] File: fig4250til8-10.png Graphic file (type png) [45 <./fig4250til8-10.png (PNG copy)>] File: fig4250til8-11.png Graphic file (type png) [46 <./fig4250til8-11.png (PNG copy)>] File: fig4250til8-12.png Graphic file (type png) Underfull \hbox (badness 10000) in paragraph at lines 1231--1236 [] Underfull \hbox (badness 10000) in paragraph at lines 1231--1236 [] File: fig4250til8-13.png Graphic file (type png) [47 <./fig4250til8-12.png (PNG copy)> <./fig4250til8-13.png (PNG copy)>] Overfull \hbox (17.95512pt too wide) in paragraph at lines 1253--1254 \OT1/cmr/m/n/12 Det nye her er at den generelle l^^\sningen i omr^^Wade II (for $\OML/cmm/m/it/12 x > \OT1/cmr/m/n/12 0$) tar for-men $[]$ [] [48] File: fig4250til8-14.png Graphic file (type png) File: fig4250til8-15.png Graphic file (type png) [49 <./fig4250til8-14.png (PNG copy)>] File: fig4250til8-16.png Graphic file (type png) File: fig4250til8-17.png Graphic file (type png) [50 <./fig4250til8-15.png (PNG copy)> <./fig4250til8-16.png (PNG copy)>] Underfull \hbox (badness 10000) in paragraph at lines 1321--1325 [] File: fig4250til8-18.png Graphic file (type png) [51 <./fig4250til8-17.png (PNG copy)> <./fig4250til8-18.png (PNG copy)>] Underfull \hbox (badness 10000) in paragraph at lines 1349--1353 [] Underfull \hbox (badness 10000) in paragraph at lines 1354--1356 [] [52] File: fig4250til8-19.png Graphic file (type png) Overfull \hbox (1.59402pt too wide) in alignment at lines 1392--1393 [][][] [] [] [53 <./fig4250til8-19.png (PNG copy)>] File: fig4250til8-20.png Graphic file (type png) File: fig4250til8-19a.png Graphic file (type png) File: fig4250til8-21.png Graphic file (type png) [54 <./fig4250til8-20.png (PNG copy)> <./fig4250til8-1 9a.png (PNG copy)>] LaTeX Warning: Command \o invalid in math mode on input line 1434. 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[59 <./fig4250til8-27.png (PNG copy)>] File: fig4250til8-28.png Graphic file (type png) File: fig4250til8-29.png Graphic file (type png) [60 <./fig4250til8-28.png (PNG copy)> <./fig4250til8-2 9.png (PNG copy)>] File: fig4250til8-30.png Graphic file (type png) [61 <./fig4250til8-30.png (PNG copy)>] File: fig4250til8-31.png Graphic file (type png) [62 <./fig4250til8-31.png (PNG copy)>] File: fig4250til8-32.png Graphic file (type png) [63 <./fig4250til8-32.png (PNG copy)>] File: fig4250til8-33.png Graphic file (type png) [64 <./fig4250til8-33.png (PNG copy)>] (./til3.aux) ) Here is how much of TeX's memory you used: 1375 strings out of 256216 17137 string characters out of 1917073 63040 words of memory out of 1500000 4605 multiletter control sequences out of 10000+200000 14713 words of font info for 55 fonts, out of 1200000 for 2000 645 hyphenation exceptions out of 8191 28i,13n,21p,1033b,242s stack positions out of 5000i,500n,6000p,200000b,15000s < /usr/share/texmf/fonts/type1/bluesky/cm/cmbsy10.pfb> Output written on til3.pdf (64 pages, 1254722 bytes). 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