Paper X: Universal Residual Seeds and Conditional Occupied-System Completion

Download original file

This is the original TeX manuscript source. Use the paper’s PDF for typeset equations.

Read the typeset paper

1 \begin{tikzpicture}[x=1cm,y=1cm,>=Stealth,line cap=round,line join=round]
2 \path[use as bounding box] (0,-.6) rectangle (14,4.8);
3 \draw[black!13,line width=.25pt] (1.4125,0.8) -- (1.4125,3.8);
4 \draw[] (1.4125,0.74) -- (1.4125,0.86);
5 \node[font=\small,align=center,font=\scriptsize] at (1.4125,0.54) {0.75};
6 \draw[black!13,line width=.25pt] (2.975,0.8) -- (2.975,3.8);
7 \draw[] (2.975,0.74) -- (2.975,0.86);
8 \node[font=\small,align=center,font=\scriptsize] at (2.975,0.54) {1};
9 \draw[black!13,line width=.25pt] (4.5375,0.8) -- (4.5375,3.8);
10 \draw[] (4.5375,0.74) -- (4.5375,0.86);
11 \node[font=\small,align=center,font=\scriptsize] at (4.5375,0.54) {1.25};
12 \draw[black!13,line width=.25pt] (6.1,0.8) -- (6.1,3.8);
13 \draw[] (6.1,0.74) -- (6.1,0.86);
14 \node[font=\small,align=center,font=\scriptsize] at (6.1,0.54) {1.5};
15 \draw[black!13,line width=.25pt] (1.1,1.55) -- (6.1,1.55);
16 \node[font=\small,align=center,anchor=east,font=\scriptsize] at (0.94,1.55) {1};
17 \draw[black!13,line width=.25pt] (1.1,2.3) -- (6.1,2.3);
18 \node[font=\small,align=center,anchor=east,font=\scriptsize] at (0.94,2.3) {2};
19 \draw[black!13,line width=.25pt] (1.1,3.05) -- (6.1,3.05);
20 \node[font=\small,align=center,anchor=east,font=\scriptsize] at (0.94,3.05) {3};
21 \draw[black!13,line width=.25pt] (1.1,3.8) -- (6.1,3.8);
22 \node[font=\small,align=center,anchor=east,font=\scriptsize] at (0.94,3.8) {4};
23 \draw[->,line width=.6pt] (1.1,0.8) -- (6.22,0.8);
24 \draw[->,line width=.6pt] (1.1,0.8) -- (1.1,3.92);
25 \node[font=\small,align=center,font=\scriptsize] at (3.6,0.25) {$s$};
26 \node[font=\small,align=center,anchor=west,font=\scriptsize] at (1.1,4.2) {$I(s)=s/(s-1/2)$};
27 \draw[line width=1.1pt] plot coordinates {(1.1,3.425) (1.15,3.352885) (1.2,3.286111) (1.25,3.224107) (1.3,3.166379) (1.35,3.1125) (1.4,3.062097) (1.45,3.014844) (1.5,2.970455) (1.55,2.928676) (1.6,2.889286) (1.65,2.852083) (1.7,2.816892) (1.75,2.783553) (1.8,2.751923) (1.85,2.721875) (1.9,2.693293) (1.95,2.666071) (2,2.640116) (2.05,2.615341) (2.1,2.591667) (2.15,2.569022) (2.2,2.54734) (2.25,2.526562) (2.3,2.506633) (2.35,2.4875) (2.4,2.469118) (2.45,2.451442) (2.5,2.434434) (2.55,2.418056) (2.6,2.402273) (2.65,2.387054) (2.7,2.372368) (2.75,2.35819) (2.8,2.344492) (2.85,2.33125) (2.9,2.318443) (2.95,2.306048) (3,2.294048) (3.05,2.282422) (3.1,2.271154) (3.15,2.260227) (3.2,2.249627) (3.25,2.239338) (3.3,2.229348) (3.35,2.219643) (3.4,2.210211) (3.45,2.201042) (3.5,2.192123) (3.55,2.183446) (3.6,2.175) (3.65,2.166776) (3.7,2.158766) (3.75,2.150962) (3.8,2.143354) (3.85,2.135938) (3.9,2.128704) (3.95,2.121646) (4,2.114759) (4.05,2.108036) (4.1,2.101471) (4.15,2.095058) (4.2,2.088793) (4.25,2.08267) (4.3,2.076685) (4.35,2.070833) (4.4,2.06511) (4.45,2.059511) (4.5,2.054032) (4.55,2.04867) (4.6,2.043421) (4.65,2.038281) (4.7,2.033247) (4.75,2.028316) (4.8,2.023485) (4.85,2.01875) (4.9,2.014109) (4.95,2.009559) (5,2.005097) (5.05,2.000721) (5.1,1.996429) (5.15,1.992217) (5.2,1.988084) (5.25,1.984028) (5.3,1.980046) (5.35,1.976136) (5.4,1.972297) (5.45,1.968527) (5.5,1.964823) (5.55,1.961184) (5.6,1.957609) (5.65,1.954095) (5.7,1.950641) (5.75,1.947246) (5.8,1.943908) (5.85,1.940625) (5.9,1.937397) (5.95,1.934221) (6,1.931098) (6.05,1.928024) (6.1,1.925)};
28 \path[fill=black] (2.975,2.3) circle (0.06);
29 \draw[black!13,line width=.25pt] (8.2,0.8) -- (8.2,3.8);
30 \draw[] (8.2,0.74) -- (8.2,0.86);
31 \node[font=\small,align=center,font=\scriptsize] at (8.2,0.54) {-0.25};
32 \draw[black!13,line width=.25pt] (10.5,0.8) -- (10.5,3.8);
33 \draw[] (10.5,0.74) -- (10.5,0.86);
34 \node[font=\small,align=center,font=\scriptsize] at (10.5,0.54) {0};
35 \draw[black!13,line width=.25pt] (12.8,0.8) -- (12.8,3.8);
36 \draw[] (12.8,0.74) -- (12.8,0.86);
37 \node[font=\small,align=center,font=\scriptsize] at (12.8,0.54) {0.25};
38 \draw[black!13,line width=.25pt] (8.2,0.8) -- (12.8,0.8);
39 \node[font=\small,align=center,anchor=east,font=\scriptsize] at (8.04,0.8) {0};
40 \draw[black!13,line width=.25pt] (8.2,2.228571) -- (12.8,2.228571);
41 \node[font=\small,align=center,anchor=east,font=\scriptsize] at (8.04,2.228571) {0.5};
42 \draw[black!13,line width=.25pt] (8.2,3.657143) -- (12.8,3.657143);
43 \node[font=\small,align=center,anchor=east,font=\scriptsize] at (8.04,3.657143) {1};
44 \draw[->,line width=.6pt] (8.2,0.8) -- (12.92,0.8);
45 \draw[->,line width=.6pt] (8.2,0.8) -- (8.2,3.92);
46 \node[font=\small,align=center,font=\scriptsize] at (10.5,0.25) {$h$};
47 \node[font=\small,align=center,anchor=west,font=\scriptsize] at (8.2,4.2) {endpoint difference};
48 \draw[line width=1.1pt] plot coordinates {(8.2,3.657143) (8.246,3.545098) (8.292,3.437363) (8.338,3.333693) (8.384,3.233862) (8.43,3.137662) (8.476,3.044898) (8.522,2.955388) (8.568,2.868966) (8.614,2.785472) (8.66,2.704762) (8.706,2.626698) (8.752,2.551152) (8.798,2.478005) (8.844,2.407143) (8.89,2.338462) (8.936,2.271861) (8.982,2.207249) (9.028,2.144538) (9.074,2.083644) (9.12,2.02449) (9.166,1.967002) (9.212,1.911111) (9.258,1.856751) (9.304,1.803861) (9.35,1.752381) (9.396,1.702256) (9.442,1.653432) (9.488,1.605861) (9.534,1.559494) (9.58,1.514286) (9.626,1.470194) (9.672,1.427178) (9.718,1.385198) (9.764,1.344218) (9.81,1.304202) (9.856,1.265116) (9.902,1.226929) (9.948,1.18961) (9.994,1.15313) (10.04,1.11746) (10.086,1.082575) (10.132,1.048447) (10.178,1.015054) (10.224,0.982371) (10.27,0.950376) (10.316,0.919048) (10.362,0.888365) (10.408,0.858309) (10.454,0.82886) (10.5,0.8) (10.546,0.828289) (10.592,0.856022) (10.638,0.883218) (10.684,0.90989) (10.73,0.936054) (10.776,0.961725) (10.822,0.986916) (10.868,1.01164) (10.914,1.035911) (10.96,1.05974) (11.006,1.08314) (11.052,1.106122) (11.098,1.128698) (11.144,1.150877) (11.19,1.172671) (11.236,1.194089) (11.282,1.21514) (11.328,1.235835) (11.374,1.256182) (11.42,1.27619) (11.466,1.295868) (11.512,1.315222) (11.558,1.334262) (11.604,1.352995) (11.65,1.371429) (11.696,1.389569) (11.742,1.407424) (11.788,1.425) (11.834,1.442303) (11.88,1.459341) (11.926,1.476118) (11.972,1.492641) (12.018,1.508915) (12.064,1.524947) (12.11,1.540741) (12.156,1.556303) (12.202,1.571637) (12.248,1.586749) (12.294,1.601644) (12.34,1.616327) (12.386,1.6308) (12.432,1.64507) (12.478,1.659141) (12.524,1.673016) (12.57,1.6867) (12.616,1.700196) (12.662,1.713508) (12.708,1.726641) (12.754,1.739597) (12.8,1.752381)};
49 \draw[dashed,line width=.8pt] plot coordinates {(8.2,3.657143) (8.246,3.6) (8.292,3.542857) (8.338,3.485714) (8.384,3.428571) (8.43,3.371429) (8.476,3.314286) (8.522,3.257143) (8.568,3.2) (8.614,3.142857) (8.66,3.085714) (8.706,3.028571) (8.752,2.971429) (8.798,2.914286) (8.844,2.857143) (8.89,2.8) (8.936,2.742857) (8.982,2.685714) (9.028,2.628571) (9.074,2.571429) (9.12,2.514286) (9.166,2.457143) (9.212,2.4) (9.258,2.342857) (9.304,2.285714) (9.35,2.228571) (9.396,2.171429) (9.442,2.114286) (9.488,2.057143) (9.534,2) (9.58,1.942857) (9.626,1.885714) (9.672,1.828571) (9.718,1.771429) (9.764,1.714286) (9.81,1.657143) (9.856,1.6) (9.902,1.542857) (9.948,1.485714) (9.994,1.428571) (10.04,1.371429) (10.086,1.314286) (10.132,1.257143) (10.178,1.2) (10.224,1.142857) (10.27,1.085714) (10.316,1.028571) (10.362,0.971429) (10.408,0.914286) (10.454,0.857143) (10.5,0.8) (10.546,0.857143) (10.592,0.914286) (10.638,0.971429) (10.684,1.028571) (10.73,1.085714) (10.776,1.142857) (10.822,1.2) (10.868,1.257143) (10.914,1.314286) (10.96,1.371429) (11.006,1.428571) (11.052,1.485714) (11.098,1.542857) (11.144,1.6) (11.19,1.657143) (11.236,1.714286) (11.282,1.771429) (11.328,1.828571) (11.374,1.885714) (11.42,1.942857) (11.466,2) (11.512,2.057143) (11.558,2.114286) (11.604,2.171429) (11.65,2.228571) (11.696,2.285714) (11.742,2.342857) (11.788,2.4) (11.834,2.457143) (11.88,2.514286) (11.926,2.571429) (11.972,2.628571) (12.018,2.685714) (12.064,2.742857) (12.11,2.8) (12.156,2.857143) (12.202,2.914286) (12.248,2.971429) (12.294,3.028571) (12.34,3.085714) (12.386,3.142857) (12.432,3.2) (12.478,3.257143) (12.524,3.314286) (12.57,3.371429) (12.616,3.428571) (12.662,3.485714) (12.708,3.542857) (12.754,3.6) (12.8,3.657143)};
50 \node[font=\small,align=center,font=\scriptsize] at (10.5,-0.28) {solid: exact\quad dashed: $4|h|$};
51 \end{tikzpicture}

Back to source controls

Back to Paper X: Universal Residual Seeds and Conditional Occupied-System Completion