nonlinear_exact_chart.tex

Paper III: Typed Transfer, Nonlinear Packets, and Obstruction Theory

nonlinear_exact_chart.tex

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1 \begin{tikzpicture}[x=1cm,y=1cm,>=Latex,font=\sffamily\small,line cap=round,line join=round]
2 \node[font=\sffamily\bfseries] at (2.10000,4.45000) {$(x,y)$ chart};
3 \node[font=\sffamily\bfseries] at (9.00000,4.45000) {$(u,v)=(x,y+x^2)$ chart};
4 \draw[->] (0.50000,0.30000) -- (4.00000,0.30000);
5 \draw[->] (0.50000,0.30000) -- (0.50000,3.80000);
6 \draw[fill=black!12,draw=black!40,line width=.35pt,] (0.50000,0.30000) rectangle ++(2.80000,2.80000);
7 \draw[black!40] (0.50000,0.30000) -- (3.30000,0.30000);
8 \draw[black!40] (0.50000,1.00000) -- (3.30000,1.00000);
9 \draw[black!40] (0.50000,1.70000) -- (3.30000,1.70000);
10 \draw[black!40] (0.50000,2.40000) -- (3.30000,2.40000);
11 \draw[black!40] (0.50000,3.10000) -- (3.30000,3.10000);
12 \node[] at (2.10000,-0.40000) {$0\le x,y\le1$};
13 \draw[->] (7.00000,0.30000) -- (11.10000,0.30000);
14 \draw[->] (7.00000,0.30000) -- (7.00000,3.90000);
15 \draw[line width=1pt] (7.00000,0.30000) -- (7.12500,0.30260) -- (7.25000,0.31042) -- (7.37500,0.32344) -- (7.50000,0.34167) -- (7.62500,0.36510) -- (7.75000,0.39375) -- (7.87500,0.42760) -- (8.00000,0.46667) -- (8.12500,0.51094) -- (8.25000,0.56042) -- (8.37500,0.61510) -- (8.50000,0.67500) -- (8.62500,0.74010) -- (8.75000,0.81042) -- (8.87500,0.88594) -- (9.00000,0.96667) -- (9.12500,1.05260) -- (9.25000,1.14375) -- (9.37500,1.24010) -- (9.50000,1.34167) -- (9.62500,1.44844) -- (9.75000,1.56042) -- (9.87500,1.67760) -- (10.00000,1.80000);
16 \draw[black!50] (7.00000,0.67500) -- (7.12500,0.67760) -- (7.25000,0.68542) -- (7.37500,0.69844) -- (7.50000,0.71667) -- (7.62500,0.74010) -- (7.75000,0.76875) -- (7.87500,0.80260) -- (8.00000,0.84167) -- (8.12500,0.88594) -- (8.25000,0.93542) -- (8.37500,0.99010) -- (8.50000,1.05000) -- (8.62500,1.11510) -- (8.75000,1.18542) -- (8.87500,1.26094) -- (9.00000,1.34167) -- (9.12500,1.42760) -- (9.25000,1.51875) -- (9.37500,1.61510) -- (9.50000,1.71667) -- (9.62500,1.82344) -- (9.75000,1.93542) -- (9.87500,2.05260) -- (10.00000,2.17500);
17 \draw[black!50] (7.00000,1.05000) -- (7.12500,1.05260) -- (7.25000,1.06042) -- (7.37500,1.07344) -- (7.50000,1.09167) -- (7.62500,1.11510) -- (7.75000,1.14375) -- (7.87500,1.17760) -- (8.00000,1.21667) -- (8.12500,1.26094) -- (8.25000,1.31042) -- (8.37500,1.36510) -- (8.50000,1.42500) -- (8.62500,1.49010) -- (8.75000,1.56042) -- (8.87500,1.63594) -- (9.00000,1.71667) -- (9.12500,1.80260) -- (9.25000,1.89375) -- (9.37500,1.99010) -- (9.50000,2.09167) -- (9.62500,2.19844) -- (9.75000,2.31042) -- (9.87500,2.42760) -- (10.00000,2.55000);
18 \draw[black!50] (7.00000,1.42500) -- (7.12500,1.42760) -- (7.25000,1.43542) -- (7.37500,1.44844) -- (7.50000,1.46667) -- (7.62500,1.49010) -- (7.75000,1.51875) -- (7.87500,1.55260) -- (8.00000,1.59167) -- (8.12500,1.63594) -- (8.25000,1.68542) -- (8.37500,1.74010) -- (8.50000,1.80000) -- (8.62500,1.86510) -- (8.75000,1.93542) -- (8.87500,2.01094) -- (9.00000,2.09167) -- (9.12500,2.17760) -- (9.25000,2.26875) -- (9.37500,2.36510) -- (9.50000,2.46667) -- (9.62500,2.57344) -- (9.75000,2.68542) -- (9.87500,2.80260) -- (10.00000,2.92500);
19 \draw[line width=1pt] (7.00000,1.80000) -- (7.12500,1.80260) -- (7.25000,1.81042) -- (7.37500,1.82344) -- (7.50000,1.84167) -- (7.62500,1.86510) -- (7.75000,1.89375) -- (7.87500,1.92760) -- (8.00000,1.96667) -- (8.12500,2.01094) -- (8.25000,2.06042) -- (8.37500,2.11510) -- (8.50000,2.17500) -- (8.62500,2.24010) -- (8.75000,2.31042) -- (8.87500,2.38594) -- (9.00000,2.46667) -- (9.12500,2.55260) -- (9.25000,2.64375) -- (9.37500,2.74010) -- (9.50000,2.84167) -- (9.62500,2.94844) -- (9.75000,3.06042) -- (9.87500,3.17760) -- (10.00000,3.30000);
20 \draw[line width=1pt] (7.00000,0.30000) -- (7.00000,1.80000);
21 \draw[line width=1pt] (10.00000,1.80000) -- (10.00000,3.30000);
22 \node[] at (9.00000,-0.40000) {$u^2\le v\le1+u^2$};
23 \node[] at (5.30000,2.05000) {$\mathcal A$};
24 \end{tikzpicture}

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