From 3cea2164f5db9082c027c7f93096c42f0d054867 Mon Sep 17 00:00:00 2001 From: abegehr Date: Tue, 21 Aug 2018 15:27:10 +0200 Subject: [PATCH] fix switching off and g in 5.5.3 also fix switch of f and g in 5.5.1 (three cases -> choose f/g) --- thesis/.texpadtmp/thesis.blg | 28 ++++++++++++++-------------- thesis/.texpadtmp/thesis.log | 4 ++-- thesis/.texpadtmp/thesis.synctex.gz | Bin 246918 -> 246930 bytes thesis/3_main.tex | 10 +++++----- thesis/thesis.pdf | Bin 2658682 -> 2658667 bytes thesis/title.pdf | Bin 0 -> 21422 bytes 6 files changed, 21 insertions(+), 21 deletions(-) create mode 100644 thesis/title.pdf diff --git a/thesis/.texpadtmp/thesis.blg b/thesis/.texpadtmp/thesis.blg index cf92ab4..72081f1 100644 --- a/thesis/.texpadtmp/thesis.blg +++ b/thesis/.texpadtmp/thesis.blg @@ -1,15 +1,15 @@ -[1] Config.pm:302> INFO - This is Biber 2.11 -[1] Config.pm:305> INFO - Logfile is '/Users/anton/Documents/Studium/BA/frechet/thesis/.texpadtmp/thesis.blg' -[62] biber-darwin:313> INFO - === Tue Aug 21, 2018, 11:00:43 -[95] Biber.pm:371> INFO - Reading '/Users/anton/Documents/Studium/BA/frechet/thesis/.texpadtmp/thesis.bcf' -[198] Biber.pm:857> INFO - Found 2 citekeys in bib section 0 +[0] Config.pm:302> INFO - This is Biber 2.11 +[0] Config.pm:305> INFO - Logfile is '/Users/anton/Documents/Studium/BA/frechet/thesis/.texpadtmp/thesis.blg' +[56] biber-darwin:313> INFO - === Tue Aug 21, 2018, 15:22:50 +[86] Biber.pm:371> INFO - Reading '/Users/anton/Documents/Studium/BA/frechet/thesis/.texpadtmp/thesis.bcf' +[193] Biber.pm:857> INFO - Found 2 citekeys in bib section 0 [214] Biber.pm:3976> INFO - Processing section 0 -[229] Biber.pm:4136> INFO - Looking for bibtex format file '/Users/anton/Documents/Studium/BA/frechet/thesis/bibliography.bib' for section 0 -[230] bibtex.pm:1500> INFO - LaTeX decoding ... -[235] bibtex.pm:1316> INFO - Found BibTeX data source '/Users/anton/Documents/Studium/BA/frechet/thesis/bibliography.bib' -[259] UCollate.pm:68> INFO - Overriding locale 'en-US' defaults 'variable = shifted' with 'variable = non-ignorable' -[260] UCollate.pm:68> INFO - Overriding locale 'en-US' defaults 'normalization = NFD' with 'normalization = prenormalized' -[260] Biber.pm:3804> INFO - Sorting list 'nty/global//global/global' of type 'entry' with template 'nty' and locale 'en-US' -[260] Biber.pm:3810> INFO - No sort tailoring available for locale 'en-US' -[263] bbl.pm:617> INFO - Writing '/Users/anton/Documents/Studium/BA/frechet/thesis/.texpadtmp/thesis.bbl' with encoding 'UTF-8' -[265] bbl.pm:720> INFO - Output to /Users/anton/Documents/Studium/BA/frechet/thesis/.texpadtmp/thesis.bbl +[230] Biber.pm:4136> INFO - Looking for bibtex format file '/Users/anton/Documents/Studium/BA/frechet/thesis/bibliography.bib' for section 0 +[231] bibtex.pm:1500> INFO - LaTeX decoding ... +[236] bibtex.pm:1316> INFO - Found BibTeX data source '/Users/anton/Documents/Studium/BA/frechet/thesis/bibliography.bib' +[267] UCollate.pm:68> INFO - Overriding locale 'en-US' defaults 'variable = shifted' with 'variable = non-ignorable' +[267] UCollate.pm:68> INFO - Overriding locale 'en-US' defaults 'normalization = NFD' with 'normalization = prenormalized' +[267] Biber.pm:3804> INFO - Sorting list 'nty/global//global/global' of type 'entry' with template 'nty' and locale 'en-US' +[267] Biber.pm:3810> INFO - No sort tailoring available for locale 'en-US' +[271] bbl.pm:617> INFO - Writing '/Users/anton/Documents/Studium/BA/frechet/thesis/.texpadtmp/thesis.bbl' with encoding 'UTF-8' +[272] bbl.pm:720> INFO - Output to /Users/anton/Documents/Studium/BA/frechet/thesis/.texpadtmp/thesis.bbl diff --git a/thesis/.texpadtmp/thesis.log b/thesis/.texpadtmp/thesis.log index 13ba38b..0afe7a4 100644 --- a/thesis/.texpadtmp/thesis.log +++ b/thesis/.texpadtmp/thesis.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.14159265-2.6-1.40.19 (TeX Live 2018) (preloaded format=pdflatex 2018.5.8) 21 AUG 2018 11:14 +This is pdfTeX, Version 3.14159265-2.6-1.40.19 (TeX Live 2018) (preloaded format=pdflatex 2018.5.8) 21 AUG 2018 15:24 entering extended mode restricted \write18 enabled. file:line:error style messages enabled. @@ -1012,7 +1012,7 @@ pdfTeX warning (dest): name{Hfootnote.3} has been referenced but does not exist, pdfTeX warning (dest): name{Hfootnote.2} has been referenced but does not exist, replaced by a fixed one -Output written on /Users/anton/Documents/Studium/BA/frechet/thesis/.texpadtmp/thesis.pdf (42 pages, 2658682 bytes). +Output written on /Users/anton/Documents/Studium/BA/frechet/thesis/.texpadtmp/thesis.pdf (42 pages, 2658667 bytes). 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\hat{g}'_{\epsilon_0}(\epsilon_0)$: Choose traversal for $f$. + \item $\hat{f}'_{\epsilon_0}(\epsilon_0) > \hat{g}'_{\epsilon_0}(\epsilon_0)$: Choose traversal for $g$. \item $\hat{f}'_{\epsilon_0}(\epsilon_0) = \hat{g}'_{\epsilon_0}(\epsilon_0)$: Cannot decide. \end{enumerate} @@ -453,7 +453,7 @@ \subsubsection{Second Derivative} [h^{-1}]''(\epsilon) &= - \frac{u^2}{a^2\left(\frac{\epsilon^2 - u^2}{a}\right)^{\frac{3}{2}}}\label{eq:hinvd2} \end{align} -We can write a simple equation for $[h^{-1}]'(\epsilon_0)$ by using the equations \ref{eq:hinvd2} and \ref{eq:veps0}: +We can write a simple equation for $[h^{-1}]''(\epsilon_0)$ by using the equations \ref{eq:hinvd2} and \ref{eq:veps0}: \begin{align} [h^{-1}]''(\epsilon_0) &= - \frac{u^2}{a^2 \left| v \right|^3}\label{eq:hinvd2eps0} @@ -476,7 +476,7 @@ \subsubsection{Example: First Derivative} \end{figure} \footnotetext{View the example here: \url{https://abegehr.github.io/frechet/?p=(0_1)(4_1)(2_2)&q=(1_0)(1_4)(3_3)}} -In the example depicted in figure \ref{fig:ces_ad_1}, there are two classical critical events of type b at critical height $\epsilon_0 = 3$ to consider: $C_1(1, 4)$ and $C_2(4, 1)$. +In the example depicted in figure \ref{fig:ces_ad_1}, there are two classical critical events of type b at critical height $\epsilon_0 = 3$ to consider: $C_1(4, 1)$ and $C_2(1, 4)$. The algorithm \ref{alg:gengraph} that generates a traversability graph for multiple critical events at the same height as defined in section \ref{sec:gengraph} returns that there are two possible paths through the critical events $C_1$ and $C_2$. Either the graph is traversed from the startpoint to the endpoint over $C_1$ (traversal path $f$) or over $C_2$ (traversal path $g$). @@ -509,7 +509,7 @@ \subsubsection{Example: First Derivative} $$\hat{f}'_{\epsilon_0}(\epsilon_0) \approx 2.118 < \hat{g}'_{\epsilon_0}(\epsilon_0) \approx 3.236$$ -The descent from height $\epsilon_0$ is steeper when taking path $g$ over $C_2(4, 1)$. This can also be seen in figure \ref{fig:ces_ad_1}. The contour lines (lines of equal $\epsilon$) are closer together on the right of $C_2(4, 1)$ than they are above $C_1(1, 4)$. +The descent from height $\epsilon_0$ is steeper when taking path $f$ over $C_1(4, 1)$. This can also be seen in figure \ref{fig:ces_ad_1}. The contour lines (lines of equal $\epsilon$) are closer together on the right of $C_2(4, 1)$ than they are above $C_2(1, 4)$. \subsubsection{Example: Second Derivative} diff --git a/thesis/thesis.pdf b/thesis/thesis.pdf index da48824e7af8addd681945ee35333e81f0555cd3..a6f5bf19bd7146fad2ebc760e90a3926fbdfdded 100644 GIT binary patch delta 8088 zcmajkMNk|HurA8H`2T{nHG2h|Pe%$Mcl4_PN`MOA9E>s0=*+1ua&3IZ6{n_2MT7OUY zM*6tW=6`d5A8>3UuzDQbbX0-C0Edtgoi~}T?v9Mx#8idxh6=}(4*5#U1U>nz=uFmv z-Fc*Y%|?S@KFCZ!0SBawp^aP(!A}f52{j+FM-2R3ZM3t#UmiH>KH;+H=wYbG=6-29 zT1p>d5@4eJt&*aO zye^{*`gfQLe0tkd;ITBmLXAYji1le z?e0PougR%M`&sAxdFvDZ)crm`Q52Bnq)PcQeW>%__t41 z*2LL=-Ms5oHgyhqO^2Sb|Lmw4V|k_^xA0dQ<2V`ginGD3RC#f{+WsTT5jd$P;Jar! zB8_YQp(ty57zo}b-H(fTp%x)1qW}BL)6UXixUuEicNb1xaz`F{u#N^UR_c!(?}Wh~ zP5%B#xW4TsOU9jVGYONSr4~%O1?n`-m;B9vY(kiWb;SvSo`2xL>1wSQWKe5LPWBB| z(CL(FoFcu?X=phfx-O@lgee_tQRAR#z9 zx8_$HoZ7@U#NAoBewe;VD3$qq(+F`NI3b6BQDF%kPn#Mpfe!vcfb|I%$8^YI#|Gu$ 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