.sp 0.25i \fBTitle\fP .ce DcNine .sp 0.25i \fBDescription\fP .P This circuit is a combination of two multi-stable circuits, something like the Schmitt trigger cascade. However, in this case, parameters have been chosen to generate separate solutions. There are a total of \fInine\fP distinct solutions. Default NPN models are adequate for all the transistors, which are all the same size. This circuit is due to Ushida and Chua, and appeared in \fIIEEE TCAD\fP, Vol. 9, No. 5, May 1990 in an article by Yamamura and Horiuchi. .P Some of the solutions for this circuit will exhibit very small domains of convergence for Newton's method. .sp 0.25i \fBDescription of successful operating point computation, if available\fP .P A homotopy method has been used to identify the nine DC solutions. .bp .sp 0.25i \fBSpice File\fP .DS I \f(CW * DcNine * * This circuit is adapted from Ushida and Chua in the * reference cited above. There are *nine* distinct * operating points. * Default models are adequate for the transistors, * which are all the same size. * VCC 99 0 12.0 * V1 1 2 10.0 V2 11 3 2.0 * R1 2 3 10k R2 4 99 4k R3 5 99 4k R4 2 0 5k R5 4 6 30k R6 8 0 0.5k R7 9 0 0.5k R8 5 7 30k R9 6 0 10.10k R10 7 0 10.10k R11 99 10 4k R12 99 12 4k R13 10 3 30k R14 12 11 30k * Q1 4 1 8 npn Q2 5 1 9 npn Q3 12 7 9 npn Q4 10 6 8 npn * * Good luck! * * \&.end \fP .DE .bp .sp 0.25i .PS Q1:[B:box ht 1.4 wid 1.4; "\f(CWQ1\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW +8.928" ljust at B.ne+(-0.5,-0.03); " +1.395" ljust at B.se+(-0.5,0.05); " +2.128" ljust at B.w; "+542.50u" ljust at B.ne+(-1.1,-0.1); "-545.23u" ljust at B.se+(-1.1,0.05); " +2.73u\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 199.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); line -> from (4/14) to (3/14); line from (1/14) to (3/14); box invis ht 1.5 wid 1.5 with .c at B.c;]; Q4:[B:box ht 1.4 wid 1.4; "\f(CWQ4\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW +2.404" ljust at B.ne+(-0.5,-0.03); " +1.395" ljust at B.se+(-0.5,0.05); " +2.164" ljust at B.w; " +2.23m" ljust at B.ne+(-1.1,-0.1); " -2.25m" ljust at B.se+(-1.1,0.05); "+11.23u\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 199.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); line -> from (4/14) to (3/14); line from (1/14) to (3/14); box invis ht 1.5 wid 1.5 with .c at B.c;] with .w at Q1.e; Q2:[B:box ht 1.4 wid 1.4; "\f(CWQ2\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW +1.440" ljust at B.ne+(-0.5,-0.03); " +1.355" ljust at B.se+(-0.5,0.05); " +2.128" ljust at B.w; " +2.60m" ljust at B.ne+(-1.1,-0.1); " -2.71m" ljust at B.se+(-1.1,0.05); "+105.01u\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 24.799)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (5/14); line from (1/14) to (5/14); line -> from (4/14) to (3/14); line from (1/14) to (3/14); box invis ht 1.5 wid 1.5 with .c at B.c;] with .n at Q1.s; Q3:[B:box ht 1.4 wid 1.4; "\f(CWQ3\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW+10.525" ljust at B.ne+(-0.5,-0.03); " +1.355" ljust at B.se+(-0.5,0.05); " +0.363" ljust at B.w; "+100.00a" ljust at B.ne+(-1.1,-0.1); "~0.0~" ljust at B.se+(-1.1,0.05); "-100.50a\s+4\fP" ljust at B.w+(0.05,-0.3); line from (4/14) to (3/14); line from (1/14) to (3/14); line -> from (4/14) to (5/14); line from (1/14) to (5/14); box invis ht 1.5 wid 1.5 with .c at B.c;] with .w at Q2.e; .PE .nf \f(CW[1]: 2.12849 [3]: -2.53719 [4]: 8.92811 [5]: 1.44007 [6]: 2.16388 [7]: 0.36271 [8]: 1.39544 [9]: 1.35454 [10]: 2.40351 [12]: 10.52504 .ce \fBDcNine: Solution 1; signature: 126.63544; ||rho(x*,1)|| 2.829e-17\fP .bp .sp 0.25i .PS Q1:[B:box ht 1.4 wid 1.4; "\f(CWQ1\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW +1.447" ljust at B.ne+(-0.5,-0.03); " +1.368" ljust at B.se+(-0.5,0.05); " +2.143" ljust at B.w; " +2.60m" ljust at B.ne+(-1.1,-0.1); " -2.74m" ljust at B.se+(-1.1,0.05); "+134.91u\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 19.287)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (5/14); line from (1/14) to (5/14); line -> from (4/14) to (3/14); line from (1/14) to (3/14); box invis ht 1.5 wid 1.5 with .c at B.c;]; Q4:[B:box ht 1.4 wid 1.4; "\f(CWQ4\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW+10.486" ljust at B.ne+(-0.5,-0.03); " +1.368" ljust at B.se+(-0.5,0.05); " +0.365" ljust at B.w; "+100.00a" ljust at B.ne+(-1.1,-0.1); "~0.0~" ljust at B.se+(-1.1,0.05); "-100.50a\s+4\fP" ljust at B.w+(0.05,-0.3); line from (4/14) to (3/14); line from (1/14) to (3/14); line -> from (4/14) to (5/14); line from (1/14) to (5/14); box invis ht 1.5 wid 1.5 with .c at B.c;] with .w at Q1.e; Q2:[B:box ht 1.4 wid 1.4; "\f(CWQ2\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW +1.447" ljust at B.ne+(-0.5,-0.03); " +1.368" ljust at B.se+(-0.5,0.05); " +2.143" ljust at B.w; " +2.60m" ljust at B.ne+(-1.1,-0.1); " -2.74m" ljust at B.se+(-1.1,0.05); "+134.91u\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 19.287)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (5/14); line from (1/14) to (5/14); line -> from (4/14) to (3/14); line from (1/14) to (3/14); box invis ht 1.5 wid 1.5 with .c at B.c;] with .n at Q1.s; Q3:[B:box ht 1.4 wid 1.4; "\f(CWQ3\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW+10.721" ljust at B.ne+(-0.5,-0.03); " +1.368" ljust at B.se+(-0.5,0.05); " +0.365" ljust at B.w; "+100.00a" ljust at B.ne+(-1.1,-0.1); "~0.0~" ljust at B.se+(-1.1,0.05); "-100.50a\s+4\fP" ljust at B.w+(0.05,-0.3); line from (4/14) to (3/14); line from (1/14) to (3/14); line -> from (4/14) to (5/14); line from (1/14) to (5/14); box invis ht 1.5 wid 1.5 with .c at B.c;] with .w at Q2.e; .PE .nf \f(CW[1]: 2.14294 [3]: -0.87297 [4]: 1.44747 [5]: 1.44747 [6]: 0.36458 [7]: 0.36458 [8]: 1.36847 [9]: 1.36847 [10]: 10.48553 [12]: 10.72083 .ce \fBDcNine: Solution 2; signature: 162.26392; ||rho(x*,1)|| 1.286e-17\fP .bp .sp 0.25i .PS Q1:[B:box ht 1.4 wid 1.4; "\f(CWQ1\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW +9.830" ljust at B.ne+(-0.5,-0.03); " +1.404" ljust at B.se+(-0.5,0.05); " +2.121" ljust at B.w; "+287.36u" ljust at B.ne+(-1.1,-0.1); "-288.80u" ljust at B.se+(-1.1,0.05); " +1.44u\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 199.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); line -> from (4/14) to (3/14); line from (1/14) to (3/14); box invis ht 1.5 wid 1.5 with .c at B.c;]; Q4:[B:box ht 1.4 wid 1.4; "\f(CWQ4\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW +1.517" ljust at B.ne+(-0.5,-0.03); " +1.404" ljust at B.se+(-0.5,0.05); " +2.175" ljust at B.w; " +2.48m" ljust at B.ne+(-1.1,-0.1); " -2.52m" ljust at B.se+(-1.1,0.05); "+39.75u\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 62.366)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (5/14); line from (1/14) to (5/14); line -> from (4/14) to (3/14); line from (1/14) to (3/14); box invis ht 1.5 wid 1.5 with .c at B.c;] with .w at Q1.e; Q2:[B:box ht 1.4 wid 1.4; "\f(CWQ2\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW +1.437" ljust at B.ne+(-0.5,-0.03); " +1.347" ljust at B.se+(-0.5,0.05); " +2.121" ljust at B.w; " +2.60m" ljust at B.ne+(-1.1,-0.1); " -2.69m" ljust at B.se+(-1.1,0.05); "+89.91u\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 28.973)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (5/14); line from (1/14) to (5/14); line -> from (4/14) to (3/14); line from (1/14) to (3/14); box invis ht 1.5 wid 1.5 with .c at B.c;] with .n at Q1.s; Q3:[B:box ht 1.4 wid 1.4; "\f(CWQ3\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW+10.503" ljust at B.ne+(-0.5,-0.03); " +1.347" ljust at B.se+(-0.5,0.05); " +0.362" ljust at B.w; "+100.00a" ljust at B.ne+(-1.1,-0.1); "~0.0~" ljust at B.se+(-1.1,0.05); "-100.50a\s+4\fP" ljust at B.w+(0.05,-0.3); line from (4/14) to (3/14); line from (1/14) to (3/14); line -> from (4/14) to (5/14); line from (1/14) to (5/14); box invis ht 1.5 wid 1.5 with .c at B.c;] with .w at Q2.e; .PE .nf \f(CW[1]: 2.12108 [3]: -2.72323 [4]: 9.82998 [5]: 1.43715 [6]: 2.17550 [7]: 0.36198 [8]: 1.40392 [9]: 1.34739 [10]: 1.51743 [12]: 10.50315 .ce \fBDcNine: Solution 3; signature: 122.37882; ||rho(x*,1)|| 2.718e-17\fP .bp .sp 0.25i .PS Q1:[B:box ht 1.4 wid 1.4; "\f(CWQ1\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW+10.683" ljust at B.ne+(-0.5,-0.03); " +1.298" ljust at B.se+(-0.5,0.05); " +1.967" ljust at B.w; "+42.20u" ljust at B.ne+(-1.1,-0.1); "-42.41u" ljust at B.se+(-1.1,0.05); "+212.04n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 199.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); line -> from (4/14) to (3/14); line from (1/14) to (3/14); box invis ht 1.5 wid 1.5 with .c at B.c;]; Q4:[B:box ht 1.4 wid 1.4; "\f(CWQ4\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW +1.389" ljust at B.ne+(-0.5,-0.03); " +1.298" ljust at B.se+(-0.5,0.05); " +2.070" ljust at B.w; " +2.47m" ljust at B.ne+(-1.1,-0.1); " -2.55m" ljust at B.se+(-1.1,0.05); "+82.12u\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 30.094)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (5/14); line from (1/14) to (5/14); line -> from (4/14) to (3/14); line from (1/14) to (3/14); box invis ht 1.5 wid 1.5 with .c at B.c;] with .w at Q1.e; Q2:[B:box ht 1.4 wid 1.4; "\f(CWQ2\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW +8.142" ljust at B.ne+(-0.5,-0.03); " +1.226" ljust at B.se+(-0.5,0.05); " +1.967" ljust at B.w; "+759.34u" ljust at B.ne+(-1.1,-0.1); "-763.16u" ljust at B.se+(-1.1,0.05); " +3.82u\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 199.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); line -> from (4/14) to (3/14); line from (1/14) to (3/14); box invis ht 1.5 wid 1.5 with .c at B.c;] with .n at Q1.s; Q3:[B:box ht 1.4 wid 1.4; "\f(CWQ3\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW +4.418" ljust at B.ne+(-0.5,-0.03); " +1.226" ljust at B.se+(-0.5,0.05); " +1.987" ljust at B.w; " +1.68m" ljust at B.ne+(-1.1,-0.1); " -1.69m" ljust at B.se+(-1.1,0.05); " +8.44u\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 199.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); line -> from (4/14) to (3/14); line from (1/14) to (3/14); box invis ht 1.5 wid 1.5 with .c at B.c;] with .w at Q2.e; .PE .nf \f(CW[1]: 1.96709 [3]: -4.05844 [4]: 10.68286 [5]: 8.14196 [6]: 2.07021 [7]: 1.98694 [8]: 1.29789 [9]: 1.22564 [10]: 1.38870 [12]: 4.41781 .ce \fBDcNine: Solution 4; signature: 92.59405; ||rho(x*,1)|| 2.427e-17\fP .bp .sp 0.25i .PS Q1:[B:box ht 1.4 wid 1.4; "\f(CWQ1\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW +8.508" ljust at B.ne+(-0.5,-0.03); " +1.304" ljust at B.se+(-0.5,0.05); " +2.042" ljust at B.w; "+658.37u" ljust at B.ne+(-1.1,-0.1); "-661.67u" ljust at B.se+(-1.1,0.05); " +3.31u\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 199.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); line -> from (4/14) to (3/14); line from (1/14) to (3/14); box invis ht 1.5 wid 1.5 with .c at B.c;]; Q4:[B:box ht 1.4 wid 1.4; "\f(CWQ4\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW +3.302" ljust at B.ne+(-0.5,-0.03); " +1.304" ljust at B.se+(-0.5,0.05); " +2.069" ljust at B.w; " +1.94m" ljust at B.ne+(-1.1,-0.1); " -1.95m" ljust at B.se+(-1.1,0.05); " +9.74u\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 199.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); line -> from (4/14) to (3/14); line from (1/14) to (3/14); box invis ht 1.5 wid 1.5 with .c at B.c;] with .w at Q1.e; Q2:[B:box ht 1.4 wid 1.4; "\f(CWQ2\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW +8.508" ljust at B.ne+(-0.5,-0.03); " +1.304" ljust at B.se+(-0.5,0.05); " +2.042" ljust at B.w; "+658.37u" ljust at B.ne+(-1.1,-0.1); "-661.67u" ljust at B.se+(-1.1,0.05); " +3.31u\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 199.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); line -> from (4/14) to (3/14); line from (1/14) to (3/14); box invis ht 1.5 wid 1.5 with .c at B.c;] with .n at Q1.s; Q3:[B:box ht 1.4 wid 1.4; "\f(CWQ3\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW +3.537" ljust at B.ne+(-0.5,-0.03); " +1.304" ljust at B.se+(-0.5,0.05); " +2.069" ljust at B.w; " +1.94m" ljust at B.ne+(-1.1,-0.1); " -1.95m" ljust at B.se+(-1.1,0.05); " +9.74u\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 199.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); line -> from (4/14) to (3/14); line from (1/14) to (3/14); box invis ht 1.5 wid 1.5 with .c at B.c;] with .w at Q2.e; .PE .nf \f(CW[1]: 2.04237 [3]: -3.80673 [4]: 8.50804 [5]: 8.50804 [6]: 2.06935 [7]: 2.06935 [8]: 1.30448 [9]: 1.30448 [10]: 3.30199 [12]: 3.53728 .ce \fBDcNine: Solution 5; signature: 95.79494; ||rho(x*,1)|| 7.646e-18\fP .bp .sp 0.25i .PS Q1:[B:box ht 1.4 wid 1.4; "\f(CWQ1\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW +1.440" ljust at B.ne+(-0.5,-0.03); " +1.355" ljust at B.se+(-0.5,0.05); " +2.128" ljust at B.w; " +2.60m" ljust at B.ne+(-1.1,-0.1); " -2.71m" ljust at B.se+(-1.1,0.05); "+105.01u\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 24.799)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (5/14); line from (1/14) to (5/14); line -> from (4/14) to (3/14); line from (1/14) to (3/14); box invis ht 1.5 wid 1.5 with .c at B.c;]; Q4:[B:box ht 1.4 wid 1.4; "\f(CWQ4\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW+10.290" ljust at B.ne+(-0.5,-0.03); " +1.355" ljust at B.se+(-0.5,0.05); " +0.363" ljust at B.w; "+100.00a" ljust at B.ne+(-1.1,-0.1); "~0.0~" ljust at B.se+(-1.1,0.05); "-100.50a\s+4\fP" ljust at B.w+(0.05,-0.3); line from (4/14) to (3/14); line from (1/14) to (3/14); line -> from (4/14) to (5/14); line from (1/14) to (5/14); box invis ht 1.5 wid 1.5 with .c at B.c;] with .w at Q1.e; Q2:[B:box ht 1.4 wid 1.4; "\f(CWQ2\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW +8.928" ljust at B.ne+(-0.5,-0.03); " +1.395" ljust at B.se+(-0.5,0.05); " +2.128" ljust at B.w; "+542.50u" ljust at B.ne+(-1.1,-0.1); "-545.23u" ljust at B.se+(-1.1,0.05); " +2.73u\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 199.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); line -> from (4/14) to (3/14); line from (1/14) to (3/14); box invis ht 1.5 wid 1.5 with .c at B.c;] with .n at Q1.s; Q3:[B:box ht 1.4 wid 1.4; "\f(CWQ3\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW +2.639" ljust at B.ne+(-0.5,-0.03); " +1.395" ljust at B.se+(-0.5,0.05); " +2.164" ljust at B.w; " +2.23m" ljust at B.ne+(-1.1,-0.1); " -2.25m" ljust at B.se+(-1.1,0.05); "+11.23u\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 199.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); line -> from (4/14) to (3/14); line from (1/14) to (3/14); box invis ht 1.5 wid 1.5 with .c at B.c;] with .w at Q2.e; .PE .nf \f(CW[1]: 2.12849 [3]: -2.53719 [4]: 1.44007 [5]: 8.92811 [6]: 0.36271 [7]: 2.16388 [8]: 1.35454 [9]: 1.39544 [10]: 10.28974 [12]: 2.63881 .ce \fBDcNine: Solution 6; signature: 118.94741; ||rho(x*,1)|| 5.467e-17\fP .bp .sp 0.25i .PS Q1:[B:box ht 1.4 wid 1.4; "\f(CWQ1\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW +1.437" ljust at B.ne+(-0.5,-0.03); " +1.345" ljust at B.se+(-0.5,0.05); " +2.119" ljust at B.w; " +2.61m" ljust at B.ne+(-1.1,-0.1); " -2.69m" ljust at B.se+(-1.1,0.05); "+85.88u\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 30.335)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (5/14); line from (1/14) to (5/14); line -> from (4/14) to (3/14); line from (1/14) to (3/14); box invis ht 1.5 wid 1.5 with .c at B.c;]; Q4:[B:box ht 1.4 wid 1.4; "\f(CWQ4\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW+10.262" ljust at B.ne+(-0.5,-0.03); " +1.345" ljust at B.se+(-0.5,0.05); " +0.362" ljust at B.w; "+100.00a" ljust at B.ne+(-1.1,-0.1); "~0.0~" ljust at B.se+(-1.1,0.05); "-100.50a\s+4\fP" ljust at B.w+(0.05,-0.3); line from (4/14) to (3/14); line from (1/14) to (3/14); line -> from (4/14) to (5/14); line from (1/14) to (5/14); box invis ht 1.5 wid 1.5 with .c at B.c;] with .w at Q1.e; Q2:[B:box ht 1.4 wid 1.4; "\f(CWQ2\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW+10.054" ljust at B.ne+(-0.5,-0.03); " +1.408" ljust at B.se+(-0.5,0.05); " +2.119" ljust at B.w; "+224.18u" ljust at B.ne+(-1.1,-0.1); "-225.31u" ljust at B.se+(-1.1,0.05); " +1.13u\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 199.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); line -> from (4/14) to (3/14); line from (1/14) to (3/14); box invis ht 1.5 wid 1.5 with .c at B.c;] with .n at Q1.s; Q3:[B:box ht 1.4 wid 1.4; "\f(CWQ3\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW +1.517" ljust at B.ne+(-0.5,-0.03); " +1.408" ljust at B.se+(-0.5,0.05); " +2.180" ljust at B.w; " +2.54m" ljust at B.ne+(-1.1,-0.1); " -2.59m" ljust at B.se+(-1.1,0.05); "+46.55u\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 54.662)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (5/14); line from (1/14) to (5/14); line -> from (4/14) to (3/14); line from (1/14) to (3/14); box invis ht 1.5 wid 1.5 with .c at B.c;] with .w at Q2.e; .PE .nf \f(CW[1]: 2.11909 [3]: -2.77273 [4]: 1.43650 [5]: 10.05354 [6]: 0.36181 [7]: 2.18046 [8]: 1.34546 [9]: 1.40813 [10]: 10.26203 [12]: 1.51708 .ce \fBDcNine: Solution 7; signature: 112.38776; ||rho(x*,1)|| 1.109e-17\fP .bp .sp 0.25i .PS Q1:[B:box ht 1.4 wid 1.4; "\f(CWQ1\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW +8.098" ljust at B.ne+(-0.5,-0.03); " +1.216" ljust at B.se+(-0.5,0.05); " +1.958" ljust at B.w; "+771.45u" ljust at B.ne+(-1.1,-0.1); "-775.33u" ljust at B.se+(-1.1,0.05); " +3.88u\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 199.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); line -> from (4/14) to (3/14); line from (1/14) to (3/14); box invis ht 1.5 wid 1.5 with .c at B.c;]; Q4:[B:box ht 1.4 wid 1.4; "\f(CWQ4\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW +4.288" ljust at B.ne+(-0.5,-0.03); " +1.216" ljust at B.se+(-0.5,0.05); " +1.977" ljust at B.w; " +1.65m" ljust at B.ne+(-1.1,-0.1); " -1.66m" ljust at B.se+(-1.1,0.05); " +8.29u\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 199.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); line -> from (4/14) to (3/14); line from (1/14) to (3/14); box invis ht 1.5 wid 1.5 with .c at B.c;] with .w at Q1.e; Q2:[B:box ht 1.4 wid 1.4; "\f(CWQ2\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW+10.782" ljust at B.ne+(-0.5,-0.03); " +1.315" ljust at B.se+(-0.5,0.05); " +1.958" ljust at B.w; "+14.83u" ljust at B.ne+(-1.1,-0.1); "-14.90u" ljust at B.se+(-1.1,0.05); "+74.52n\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 199.000)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (3/14); line from (1/14) to (3/14); line -> from (4/14) to (3/14); line from (1/14) to (3/14); box invis ht 1.5 wid 1.5 with .c at B.c;] with .n at Q1.s; Q3:[B:box ht 1.4 wid 1.4; "\f(CWQ3\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW +1.406" ljust at B.ne+(-0.5,-0.03); " +1.315" ljust at B.se+(-0.5,0.05); " +2.088" ljust at B.w; " +2.53m" ljust at B.ne+(-1.1,-0.1); " -2.62m" ljust at B.se+(-1.1,0.05); "+83.06u\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 30.483)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (5/14); line from (1/14) to (5/14); line -> from (4/14) to (3/14); line from (1/14) to (3/14); box invis ht 1.5 wid 1.5 with .c at B.c;] with .w at Q2.e; .PE .nf \f(CW[1]: 1.95807 [3]: -4.08629 [4]: 8.09806 [5]: 10.78153 [6]: 1.97705 [7]: 2.08791 [8]: 1.21621 [9]: 1.31500 [10]: 4.28817 [12]: 1.40618 .ce \fBDcNine: Solution 8; signature: 88.70589; ||rho(x*,1)|| 2.588e-17\fP .bp .sp 0.25i .PS Q1:[B:box ht 1.4 wid 1.4; "\f(CWQ1\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW+10.829" ljust at B.ne+(-0.5,-0.03); " +1.272" ljust at B.se+(-0.5,0.05); " +1.729" ljust at B.w; " +8.64n" ljust at B.ne+(-1.1,-0.1); " -8.68n" ljust at B.se+(-1.1,0.05); "+43.42p\s+4\fP" ljust at B.w+(0.05,-0.3); line from (4/14) to (3/14); line from (1/14) to (3/14); line -> from (4/14) to (5/14); line from (1/14) to (5/14); box invis ht 1.5 wid 1.5 with .c at B.c;]; Q4:[B:box ht 1.4 wid 1.4; "\f(CWQ4\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW +1.360" ljust at B.ne+(-0.5,-0.03); " +1.272" ljust at B.se+(-0.5,0.05); " +2.045" ljust at B.w; " +2.45m" ljust at B.ne+(-1.1,-0.1); " -2.54m" ljust at B.se+(-1.1,0.05); "+90.37u\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 27.157)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (5/14); line from (1/14) to (5/14); line -> from (4/14) to (3/14); line from (1/14) to (3/14); box invis ht 1.5 wid 1.5 with .c at B.c;] with .w at Q1.e; Q2:[B:box ht 1.4 wid 1.4; "\f(CWQ2\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW+10.832" ljust at B.ne+(-0.5,-0.03); " +1.300" ljust at B.se+(-0.5,0.05); " +1.729" ljust at B.w; " +2.89n" ljust at B.ne+(-1.1,-0.1); " -2.90n" ljust at B.se+(-1.1,0.05); "+14.51p\s+4\fP" ljust at B.w+(0.05,-0.3); line from (4/14) to (3/14); line from (1/14) to (3/14); line -> from (4/14) to (5/14); line from (1/14) to (5/14); box invis ht 1.5 wid 1.5 with .c at B.c;] with .n at Q1.s; Q3:[B:box ht 1.4 wid 1.4; "\f(CWQ3\fP" at B.nw+(0.05,-0.3) ljust; C:(12/14); E:(12/14); line from (3/14) to (11/14); line from (5/14) to B.c; "\s-4\f(CW +1.389" ljust at B.ne+(-0.5,-0.03); " +1.300" ljust at B.se+(-0.5,0.05); " +2.072" ljust at B.w; " +2.51m" ljust at B.ne+(-1.1,-0.1); " -2.60m" ljust at B.se+(-1.1,0.05); "+86.79u\s+4\fP" ljust at B.w+(0.05,-0.3); "\s-4( 28.950)\s+4" ljust at B.c+(0.1,0); line from (4/14) to (5/14); line from (1/14) to (5/14); line -> from (4/14) to (3/14); line from (1/14) to (3/14); box invis ht 1.5 wid 1.5 with .c at B.c;] with .w at Q2.e; .PE .nf \f(CW[1]: 1.72914 [3]: -4.81258 [4]: 10.82874 [5]: 10.83205 [6]: 2.04459 [7]: 2.07248 [8]: 1.27228 [9]: 1.29968 [10]: 1.36026 [12]: 1.38942 .ce \fBDcNine: Solution 9; signature: 74.61658; ||rho(x*,1)|| 2.530e-17\fP