(************** Content-type: application/mathematica ************** Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 190833, 5364]*) (*NotebookOutlinePosition[ 191766, 5393]*) (* CellTagsIndexPosition[ 191722, 5389]*) (*WindowFrame->Normal*) Notebook[{ Cell["\<\ In this part we defined the relevant constants. alpha is where the \ pulse begins and bet where it ends in the theta coordinates. Period is the period of the cycle in the new coordinates, \ i.e. the periodicity of phi.\ \>", "Text"], Cell[BoxData[ \(alph\ = \ 0.18*Pi; \ bet\ = \ 0.28*Pi; \ l\ = \ 1.736; DD\ = 1.05;\)], "Input"], Cell["\<\ Next we define the period of the cycle and the value of the phi \ coordinate when it ends. Note that in phi coordinates the perturbation lasts from alph to bdry which makes phi T periodic rather \ than 2*Pi periodic.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(period = 2*Pi\ + \ l/\((1 + l)\)\ *\ \((alph\ - bet)\)\)], "Input"], Cell[BoxData[ \(6.08385033471497`\)], "Output"] }, Open ]], Cell[BoxData[ \(\(bdry\ = \ \((bet\ + \ l*alph)\)/\((1 + l)\);\)\)], "Input"], Cell["\<\ The following definitions then give phi as a function of theta. \ The first is valid between alph and bet, while the second is valid after bet. This just follows from the condition phi' = te\ \>", "Text"], Cell[BoxData[ \(def1[s_]\ := \ \((1 + l)\)*s\ - \ alph*l; \ def2[s_]\ := \ s\ + \ \((bet - alph)\)\ *\ l/\((1 + l)\);\)], "Input"], Cell["\<\ Next we define the function corresponding to sin 2*theta in the \ paper. This is a function of phi, so that it is different in the interval [alph,bdry] and outside of it. We also take into account the different \ definitions in each of the separate regions.\ \>", "Text"], Cell[BoxData[ \(p[t_\ ]\ := \ \((s\ = \ Mod[t, \ period]; Which[s > alph\ && \ s < \ bdry, \ \(-Sin[2*def1[s]]\)/\((l + 1)\), \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ s\ > \ bdry, \ \(-Sin[ 2*def2[s]]\), \ \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ True, \ \ \(-Sin[ 2*s]\)])\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Plot[p[t], \ {t, \ 0, \ period}]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.156542 0.309018 0.294303 [ [.18035 .29652 -3 -9 ] [.18035 .29652 3 0 ] [.33689 .29652 -3 -9 ] [.33689 .29652 3 0 ] [.49344 .29652 -3 -9 ] [.49344 .29652 3 0 ] [.64998 .29652 -3 -9 ] [.64998 .29652 3 0 ] [.80652 .29652 -3 -9 ] [.80652 .29652 3 0 ] [.96306 .29652 -3 -9 ] [.96306 .29652 3 0 ] [.01131 .01471 -12 -4.5 ] [.01131 .01471 0 4.5 ] [.01131 .16187 -24 -4.5 ] [.01131 .16187 0 4.5 ] [.01131 .45617 -18 -4.5 ] [.01131 .45617 0 4.5 ] [.01131 .60332 -6 -4.5 ] [.01131 .60332 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .18035 .30902 m .18035 .31527 L s [(1)] .18035 .29652 0 1 Mshowa .33689 .30902 m .33689 .31527 L s [(2)] .33689 .29652 0 1 Mshowa .49344 .30902 m .49344 .31527 L s [(3)] .49344 .29652 0 1 Mshowa .64998 .30902 m .64998 .31527 L s [(4)] .64998 .29652 0 1 Mshowa .80652 .30902 m .80652 .31527 L s [(5)] .80652 .29652 0 1 Mshowa .96306 .30902 m .96306 .31527 L s [(6)] .96306 .29652 0 1 Mshowa .125 Mabswid .05512 .30902 m .05512 .31277 L s .08643 .30902 m .08643 .31277 L s .11774 .30902 m .11774 .31277 L s .14904 .30902 m .14904 .31277 L s .21166 .30902 m .21166 .31277 L s .24297 .30902 m .24297 .31277 L s .27428 .30902 m .27428 .31277 L s .30559 .30902 m .30559 .31277 L s .3682 .30902 m .3682 .31277 L s .39951 .30902 m .39951 .31277 L s .43082 .30902 m .43082 .31277 L s .46213 .30902 m .46213 .31277 L s .52475 .30902 m .52475 .31277 L s .55605 .30902 m .55605 .31277 L s .58736 .30902 m .58736 .31277 L s .61867 .30902 m .61867 .31277 L s .68129 .30902 m .68129 .31277 L s .7126 .30902 m .7126 .31277 L s .7439 .30902 m .7439 .31277 L s .77521 .30902 m .77521 .31277 L s .83783 .30902 m .83783 .31277 L s .86914 .30902 m .86914 .31277 L s .90045 .30902 m .90045 .31277 L s .93176 .30902 m .93176 .31277 L s .99437 .30902 m .99437 .31277 L s .25 Mabswid 0 .30902 m 1 .30902 L s .02381 .01471 m .03006 .01471 L s [(-1)] .01131 .01471 1 0 Mshowa .02381 .16187 m .03006 .16187 L s [(-0.5)] .01131 .16187 1 0 Mshowa .02381 .45617 m .03006 .45617 L s [(0.5)] .01131 .45617 1 0 Mshowa .02381 .60332 m .03006 .60332 L s [(1)] .01131 .60332 1 0 Mshowa .125 Mabswid .02381 .04415 m .02756 .04415 L s .02381 .07358 m .02756 .07358 L s .02381 .10301 m .02756 .10301 L s .02381 .13244 m .02756 .13244 L s .02381 .1913 m .02756 .1913 L s .02381 .22073 m .02756 .22073 L s .02381 .25016 m .02756 .25016 L s .02381 .27959 m .02756 .27959 L s .02381 .33845 m .02756 .33845 L s .02381 .36788 m .02756 .36788 L s .02381 .39731 m .02756 .39731 L s .02381 .42674 m .02756 .42674 L s .02381 .4856 m .02756 .4856 L s .02381 .51503 m .02756 .51503 L s .02381 .54446 m .02756 .54446 L s .02381 .57389 m .02756 .57389 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .30902 m .06244 .16958 L .08255 .1083 L .0932 .08098 L .09905 .06772 L .10458 .05642 L .10708 .05173 L .10972 .04705 L .1111 .04472 L .11189 .04344 L .11263 .21122 L .11392 .2093 L .11531 .20746 L .11656 .20601 L .11792 .20465 L .11912 .20365 L .1204 .20279 L .12167 .20214 L .12282 .20174 L .12398 .20151 L .12507 .20145 L .12617 .20155 L .12739 .20185 L .12866 .20237 L .12984 .20304 L .13095 .02039 L .13196 .02116 L .13423 .02306 L .14415 .03414 L .15407 .04963 L .16324 .06766 L .184 .12024 L .22326 .25208 L .26101 .3925 L .28199 .46424 L .30122 .5204 L .32006 .56313 L .32954 .5792 L .33487 .58652 L .3399 .59224 L .34483 .59671 L .34743 .59861 L .35018 .60027 L .35249 .6014 L .35372 .60189 L .35504 .60233 L .35625 .60267 L .35735 .60292 L .35846 .60311 L .35952 .60323 L Mistroke .36084 .60331 L .36203 .60331 L .3627 .60328 L .36342 .60323 L .36472 .60306 L .36594 .60284 L .36723 .60252 L .36954 .60175 L .37224 .60053 L .37475 .59908 L .38047 .59468 L .38549 .58955 L .39094 .58267 L .40086 .5668 L .41943 .52621 L .43924 .46955 L .46026 .39834 L .49806 .2579 L .51908 .18285 L .53832 .12193 L .5572 .07307 L .56681 .05331 L .57706 .03648 L .5824 .02954 L .58743 .02419 L .59195 .02039 L .59428 .01881 L .59684 .01736 L .59924 .01629 L .60149 .01554 L .60273 .01523 L .60386 .01501 L .60517 .01483 L .60641 .01474 L .60747 .01472 L .6086 .01475 L .60956 .01483 L .61063 .01497 L .61177 .01518 L .61299 .01548 L .61522 .0162 L .61761 .01724 L .62017 .01865 L .62477 .02198 L .63025 .02723 L .63524 .0332 L .64608 .05002 L .65633 .07048 L .67632 .12177 L .69476 .17995 L Mistroke .73413 .32344 L .77199 .45847 L .79304 .52048 L .81229 .56396 L .82181 .5799 L .82683 .58673 L .83219 .59274 L .83733 .59726 L .84199 .60028 L .84424 .60138 L .84542 .60185 L .84667 .60228 L .84777 .6026 L .84897 .60288 L .85007 .60308 L .85109 .60321 L .85235 .6033 L .85299 .60332 L .85369 .60332 L .85493 .60325 L .8561 .60312 L .85676 .60302 L .85747 .60289 L .85872 .6026 L .86155 .60167 L .864 .60055 L .86628 .59925 L .87145 .59539 L .87616 .5908 L .88043 .58574 L .89001 .57144 L .90921 .53123 L .93002 .47274 L .97095 .32869 L .97619 .30902 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgool00`00ooooo`03ool00`00ooooo`02ool00`00oooo o`08ool00`00ooooo`1Rool00`00ooooo`0Kool00`00ooooo`1Hool001_oo`03003ooooo00koo`03 003ooooo00?oo`03003ooooo00;oo`03003ooooo00Soo`03003ooooo06;oo`03003ooooo01_oo`03 003ooooo05Soo`006ooo00<00?ooool03_oo00<00?ooool00ooo00<00?ooool00_oo00<00?ooool0 2?oo00<00?ooool0H_oo00<00?ooool06ooo00<00?ooool0F?oo000Kool00`00ooooo`0=ool00`00 ooooo`04ool00`00ooooo`02ool00`00ooooo`09ool00`00ooooo`1Pool00`00ooooo`0Mool00`00 ooooo`1Gool001_oo`8000koo`03003ooooo00Coo`03003ooooo00;oo`03003ooooo00Woo`03003o oooo063oo`03003ooooo01goo`03003ooooo05Ooo`006ooo00<00?ooool03?oo00<00?ooool01Ooo 00<00?ooool00_oo00<00?ooool02_oo00<00?ooool0Gooo00<00?ooool07Ooo00<00?ooool0Eooo 000Kool00`00ooooo`0ool0 0`00ooooo`1Fool00`00ooooo`0Wool00`00ooooo`1Bool000Ooo`04003ooooo000;ool00`00oooo o`02ool00`00ooooo`08ool00`00ooooo`09ool00`00ooooo`02ool00`00ooooo`0>ool00`00oooo o`1Fool00`00ooooo`0Wool00`00ooooo`1Bool000Ooo`04003ooooo000;ool00`00ooooo`02ool2 0009ool00`00ooooo`09ool00`00ooooo`02ool00`00ooooo`0>ool00`00ooooo`1Fool00`00oooo o`0Wool00`00ooooo`1Bool00003ool00000008000;oo`04003ooooo0008ool30005ool00`00oooo o`07ool00`00ooooo`0:ool00`00ooooo`02ool00`00ooooo`0?ool00`00ooooo`1Dool00`00oooo o`0Yool00`00ooooo`1Aool000Ooo`04003ooooo0008ool00`00ooooo`05ool00`00ooooo`07ool0 0`00ooooo`0:ool00`00ooooo`02ool00`00ooooo`0?ool00`00ooooo`1Dool00`00ooooo`0Yool0 0`00ooooo`1Aool000Ooo`04003ooooo0008ool00`00ooooo`05ool00`00ooooo`07ool00`00oooo o`0:ool00`00ooooo`02ool00`00ooooo`0?ool00`00ooooo`1Dool00`00ooooo`0Yool00`00oooo o`1Aool000Soo`8000Woo`@000Coo`03003ooooo00Koo`03003ooooo00_oo`03003ooooo00;oo`03 003ooooo013oo`03003ooooo05;oo`03003ooooo02_oo`03003ooooo053oo`006ooo00<00?ooool0 1_oo00<00?ooool02ooo00<00?ooool00_oo00<00?ooool04?oo00<00?ooool0D_oo00<00?ooool0 :ooo00<00?ooool0D?oo000Kool00`00ooooo`06ool00`00ooooo`0;ool00`00ooooo`02ool00`00 ooooo`0@ool00`00ooooo`1Bool00`00ooooo`0[ool00`00ooooo`1@ool001_oo`03003ooooo00Ko o`03003ooooo00_oo`03003ooooo00;oo`03003ooooo017oo`03003ooooo053oo`03003ooooo02go o`03003ooooo04ooo`006ooo0P001_oo00<00?ooool03?oo00<00?ooool00_oo00<00?ooool04Ooo 00<00?ooool0D?oo00<00?ooool0;Ooo00<00?ooool0Cooo000Kool00`00ooooo`05ool00`00oooo o`0ool00`00ooooo`0_ool00`00ooooo`1>ool001_o o`03003ooooo00Coo`03003ooooo00goo`8001Woo`03003ooooo04goo`03003ooooo02ooo`03003o oooo04koo`006ooo00<00?ooool01?oo00<00?ooool0:?oo00<00?ooool0C?oo00<00?ooool0?oo00<00?ooool0B_oo000Kool01000ooooo`00<_oo00<00?ooool0A?oo 00<00?ooool0>Ooo00<00?ooool0BOoo000Kool01000ooooo`008ooo10002ooo00<00?ooool06?oo 10009ooo0P00:?oo00<00?ooool04?oo00<00?ooool04_oo0`00:?oo0P002_oo000Kool00`00ool0 000Vool00`00ooooo`0;ool00`00ooooo`0Gool00`00ooooo`0Wool01000ool000009ooo00<00?oo ool04?oo00<00?ooool05Ooo00<00?ooool09?oo00@00?ooool000Woo`006ooo0`009_oo00<00?oo ool02ooo00<00?ooool06?oo00<00?ooool09ooo00<00?oo00009?oo1@004_oo00<00?ooool05?oo 00<00?ooool09?oo00@00?ooool000Woo`006ooo00<00?oo00009_oo00<00?ooool02ooo00<00?oo ool06Ooo00<00?ooool09_oo0P009Ooo00@00?ooool001?oo`03003ooooo017oo`<002Ooo`<000[o o`006ooo00<00?oo00009_oo00<00?ooool02ooo00<00?ooool06_oo00<00?ooool09Ooo00<00?oo 00009Ooo00<00?oo00004ooo00<00?ooool04Ooo00<00?ooool09ooo00<00?ooool02_oo000Kool2 000Uool3000>ool00`00ooooo`0Fool01000ooooo`009_oo0P0000?oo`00ool09Ooo0P004ooo00<0 0?ooool04Ooo00<00?ooool09ooo00<00?ooool02_oo000Kool2000Wool00`00ooooo`0ool00`00ooooo`0Fool00`00ooooo`0Tool01000ooooo`00 :?oo00<00?ooool04ooo00<00?ooool04Ooo00<00?ooool09ooo00@00?ooool000Ooo`006ooo00<0 0?ooool0=ooo00<00?ooool0?Ooo00<00?ooool0@?oo00<00?ooool0??oo00<00?ooool01_oo000K ool00`00ooooo`0gool00`00ooooo`0lool00`00ooooo`11ool00`00ooooo`0lool00`00ooooo`06 ool001_oo`03003ooooo03Ooo`03003ooooo03coo`03003ooooo047oo`03003ooooo03coo`03003o oooo00Koo`006ooo00<00?ooool0>?oo00<00?ooool0>ooo00<00?ooool0@_oo00<00?ooool0>ooo 00<00?ooool01_oo000Kool00`00ooooo`0hool00`00ooooo`0jool00`00ooooo`13ool00`00oooo o`0jool00`00ooooo`07ool001_oo`8003Woo`03003ooooo03[oo`03003ooooo04?oo`03003ooooo 03[oo`03003ooooo00Ooo`006ooo00<00?ooool0>?oo00<00?ooool0>_oo00<00?ooool0@ooo00<0 0?ooool0>_oo00<00?ooool01ooo000Kool00`00ooooo`0iool00`00ooooo`0iool00`00ooooo`14 ool00`00ooooo`0iool00`00ooooo`07ool001_oo`03003ooooo03Woo`03003ooooo03Soo`03003o oooo04Goo`03003ooooo03Soo`03003ooooo00Soo`006ooo00<00?ooool0>Ooo00<00?ooool0>?oo 00<00?ooool0AOoo00<00?ooool0>?oo00<00?ooool02?oo000Kool00`00ooooo`0jool00`00oooo o`0gool00`00ooooo`15ool00`00ooooo`0hool00`00ooooo`08ool001_oo`03003ooooo03[oo`03 003ooooo03Ooo`03003ooooo04Koo`03003ooooo03Koo`03003ooooo00Woo`006ooo00<00?ooool0 >_oo00<00?ooool0=_oo00<00?ooool0Aooo00<00?ooool0=_oo00<00?ooool02Ooo000Kool2000k ool00`00ooooo`0fool00`00ooooo`17ool00`00ooooo`0fool00`00ooooo`09ool001_oo`03003o oooo03_oo`03003ooooo03Goo`03003ooooo04Soo`03003ooooo03Goo`03003ooooo00Woo`006ooo 00<00?ooool0>ooo00<00?ooool0=Ooo00<00?ooool0B?oo00<00?ooool0=?oo00<00?ooool02_oo 000Kool00`00ooooo`0kool00`00ooooo`0dool00`00ooooo`19ool00`00ooooo`0dool00`00oooo o`0:ool001_oo`03003ooooo03_oo`03003ooooo03Coo`03003ooooo04Woo`03003ooooo03Coo`03 003ooooo00[oo`006ooo00<00?ooool0??oo00<00?ooool0ool00`00ooooo`0_ool00`00ooooo`0ool001_oo`03003ooooo043oo`03003ooooo02_oo`03003ooooo05;oo`03003ooooo02_o o`03003ooooo00koo`006ooo00<00?ooool0@?oo00<00?ooool0:_oo00<00?ooool0Dooo00<00?oo ool0:_oo00<00?ooool03ooo0008ool20004ool00`00ooooo`02ool30005ool00`00ooooo`11ool0 0`00ooooo`0Yool00`00ooooo`1Cool00`00ooooo`0Zool00`00ooooo`0?ool000Ooo`04003ooooo 000;ool00`00ooooo`02ool00`00ooooo`11ool00`00ooooo`0Yool00`00ooooo`1Cool00`00oooo o`0Zool00`00ooooo`0?ool000Ooo`04003ooooo000;ool00`00ooooo`02ool20012ool00`00oooo o`0Xool00`00ooooo`1Eool00`00ooooo`0Xool00`00ooooo`0@ool000Ooo`04003ooooo0008ool3 0005ool00`00ooooo`12ool00`00ooooo`0Wool00`00ooooo`1Eool00`00ooooo`0Xool00`00oooo o`0@ool000Ooo`04003ooooo0008ool00`00ooooo`05ool00`00ooooo`12ool00`00ooooo`0Wool0 0`00ooooo`1Eool00`00ooooo`0Xool00`00ooooo`0@ool000Ooo`04003ooooo0008ool00`00oooo o`05ool00`00ooooo`12ool00`00ooooo`0Vool00`00ooooo`1Gool00`00ooooo`0Wool00`00oooo o`0@ool000Soo`8000Woo`@000Coo`03003ooooo04?oo`03003ooooo02Goo`03003ooooo05Ooo`03 003ooooo02Koo`03003ooooo017oo`006ooo00<00?ooool0@ooo00<00?ooool09Ooo00<00?ooool0 Eooo00<00?ooool09_oo00<00?ooool04Ooo000Kool00`00ooooo`13ool00`00ooooo`0Tool00`00 ooooo`1Iool00`00ooooo`0Uool00`00ooooo`0Aool001_oo`03003ooooo04Coo`03003ooooo02?o o`03003ooooo05Woo`03003ooooo02Coo`03003ooooo01;oo`006ooo0P00AOoo00<00?ooool08ooo 00<00?ooool0FOoo00<00?ooool09?oo00<00?ooool04_oo000Kool00`00ooooo`14ool00`00oooo o`0Rool00`00ooooo`1Jool00`00ooooo`0Sool00`00ooooo`0Cool001_oo`03003ooooo04Goo`03 003ooooo027oo`03003ooooo05_oo`03003ooooo02;oo`03003ooooo01?oo`006ooo00<00?ooool0 AOoo00<00?ooool08Ooo00<00?ooool0Fooo00<00?ooool08_oo00<00?ooool04ooo000Kool00`00 ooooo`15ool00`00ooooo`0Pool00`00ooooo`1Lool00`00ooooo`0Qool00`00ooooo`0Dool001_o o`03003ooooo04Koo`03003ooooo01ooo`03003ooooo05goo`03003ooooo023oo`03003ooooo01Co o`006ooo00<00?ooool0A_oo00<00?ooool07ooo00<00?ooool0GOoo00<00?ooool07ooo00<00?oo ool05Ooo000Kool00`00ooooo`16ool00`00ooooo`0Nool00`00ooooo`1Nool00`00ooooo`0Oool0 0`00ooooo`0Eool001_oo`8004Soo`03003ooooo01goo`03003ooooo05ooo`03003ooooo01koo`03 003ooooo01Goo`006ooo00<00?ooool0Aooo00<00?ooool07Ooo00<00?ooool0Gooo00<00?ooool0 7Ooo00<00?ooool05_oo000Kool00`00ooooo`17ool00`00ooooo`0Lool00`00ooooo`1Pool00`00 ooooo`0Mool00`00ooooo`0Fool001_oo`03003ooooo04Soo`03003ooooo01_oo`03003ooooo067o o`03003ooooo01_oo`03003ooooo01Ooo`006ooo00<00?ooool0B?oo00<00?ooool06ooo00<00?oo ool0HOoo00<00?ooool06ooo00<00?ooool05ooo000Kool00`00ooooo`19ool00`00ooooo`0Iool0 0`00ooooo`1Sool00`00ooooo`0Jool00`00ooooo`0Gool001_oo`03003ooooo04Woo`03003ooooo 01Woo`03003ooooo06?oo`03003ooooo01Woo`03003ooooo01Soo`006ooo00<00?ooool0BOoo00<0 0?ooool06?oo00<00?ooool0IOoo00<00?ooool06?oo00<00?ooool06?oo000Kool2001;ool00`00 ooooo`0Gool00`00ooooo`1Uool00`00ooooo`0Gool00`00ooooo`0Iool001_oo`03003ooooo04[o o`03003ooooo01Koo`03003ooooo06Ooo`03003ooooo01Koo`03003ooooo01Woo`006ooo00<00?oo ool0Booo00<00?ooool05Ooo00<00?ooool0Iooo00<00?ooool05Ooo00<00?ooool06_oo000Kool0 0`00ooooo`1;ool00`00ooooo`0Dool00`00ooooo`1Yool00`00ooooo`0Dool00`00ooooo`0Jool0 01_oo`03003ooooo04coo`03003ooooo01?oo`03003ooooo06Woo`03003ooooo01?oo`03003ooooo 01_oo`006ooo00<00?ooool0C?oo00<00?ooool04_oo00<00?ooool0Jooo00<00?ooool04_oo00<0 0?ooool06ooo000Kool00`00ooooo`1ool00`00ooooo`0>ool00`00ooooo`1_ool0 0`00ooooo`0>ool00`00ooooo`0Mool001_oo`03003ooooo04ooo`03003ooooo00coo`03003ooooo 073oo`03003ooooo00koo`03003ooooo01goo`006ooo00<00?ooool0D?oo00<00?ooool02ooo00<0 0?ooool0LOoo00<00?ooool03?oo00<00?ooool07_oo000Kool00`00ooooo`1Aool00`00ooooo`09 ool00`00ooooo`1cool00`00ooooo`09ool2000Qool001?oo`@000Coo`03003ooooo057oo`03003o oooo00Ooo`8007Ooo`03003ooooo00Ooo`03003ooooo027oo`005Ooo00<00?ooool00ooo00<00?oo ool0D_oo0P001_oo00<00?ooool0N?oo00<00?ooool01Ooo00<00?ooool08_oo000Eool00`00oooo o`03ool2001Eool7001kool7000Uool001Goo`03003ooooo00?oo`03003ooooo0?ooo`?oo`005Ooo 00<00?ooool00ooo00<00?ooool0oooo0ooo000Cool30005ool00`00ooooo`3oool3ool001Goo`03 003ooooo00?oo`03003ooooo0?ooo`?oo`00oooo8Ooo003ooolQool00?ooob7oo`00oooo8Ooo003o oolQool00?ooob7oo`00\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-0.656233, -1.13008, \ 0.0240147, 0.0127736}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell["\<\ Next we define the places where the singularities in the \ integration occur. This is necessary because otherwise the integrator will complain.\ \>", "Text"], Cell[BoxData[{ \(n = 0; \ sing = \ {t, 0};\), "\[IndentingNewLine]", \(\(alphmod\ = \ \((alph\ - \ Psi)\)/DD;\)\), "\[IndentingNewLine]", \(\ \(bdrymod\ = \ \((bdry\ - Psi)\)/DD;\)\), "\[IndentingNewLine]", \(\ \ \ \ \ \ \ \ \ While[\((n*period/DD + alphmod)\) < period/DD, \ \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ If[\((n*period/DD + alphmod)\) > \ 0\ , \ \ sing = Append[sing, n*period/DD + alphmod]]; \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ If\ [\((n*period/DD + bdrymod)\) > \ 0\ && \ \((n*period/DD + bdrymod)\)\ < \ period/DD, \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ sing = Append[sing, n*period/DD + bdrymod]\[IndentingNewLine]\ \ \ \ ]; \ \[IndentingNewLine]\ \ \ n\ = \ n + 1\[IndentingNewLine]]\), "\[IndentingNewLine]", \(\(sing = Append[sing, \ period/DD];\)\)}], "Input"], Cell["\<\ Lastly we define the integral. This procedure just computes the \ points of discontinuity first, puts them in a list, and then integrates over \ them. The list sing contains the values where the singularities appear.\ \>", "Text"], Cell[BoxData[ \(V[Psi_]\ := \ \((n = 0; \ sing = \ {t, 0}; \[IndentingNewLine]alphmod\ = \ \((alph\ - \ Psi)\)/ DD; \[IndentingNewLine]\ \(bdrymod\ = \ \((bdry\ - Psi)\)/ DD;\)\[IndentingNewLine]\ \ \ \ \ \ \ \ \ While[\((n* period/DD + alphmod)\) < period/DD, \ \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ If[\((n*period/DD + alphmod)\) > \ 0\ , \ \ sing = Append[sing, n*period/DD + alphmod]]; \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ If\ [\((n*period/DD + bdrymod)\) > \ 0\ && \ \((n*period/DD + bdrymod)\)\ < \ period/DD, \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ sing = Append[sing, n*period/DD + bdrymod]\[IndentingNewLine]\ \ \ \ ]; \ \ \[IndentingNewLine]\ \ n\ = \ n + 1\[IndentingNewLine]]\[IndentingNewLine]\(sing = Append[sing, \ period/DD]\); \ \[IndentingNewLine]\ 1/period*\ \ NIntegrate[p[DD*t + Psi], Evaluate[sing]]\ )\)\)], "Input"], Cell["\<\ Now we can compute the contribution from the term sin 2*theta on \ the dynamics of the phase. The fluctuations are due to numerical \ integration. This could have been done in a much more straigthforward fashion, but it \ allowed us to set up the functions necessary in the next section.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Plot[0.075*V[Psi]/\((2*Pi)\), \ {Psi, \ 0, \ 2*Pi}]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.151576 -2.30027e+13 4.63444e+16 [ [.17539 .07422 -3 -9 ] [.17539 .07422 3 0 ] [.32696 .07422 -3 -9 ] [.32696 .07422 3 0 ] [.47854 .07422 -3 -9 ] [.47854 .07422 3 0 ] [.63011 .07422 -3 -9 ] [.63011 .07422 3 0 ] [.78169 .07422 -3 -9 ] [.78169 .07422 3 0 ] [.93327 .07422 -3 -9 ] [.93327 .07422 3 0 ] [.01131 .17578 -66 -4.5 ] [.01131 .17578 0 4.5 ] [.01131 .27344 -66 -4.5 ] [.01131 .27344 0 4.5 ] [.01131 .36328 -66 -4.5 ] [.01131 .36328 0 4.5 ] [.01131 .45703 -66 -4.5 ] [.01131 .45703 0 4.5 ] [.01131 .54688 -66 -4.5 ] [.01131 .54688 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .17539 .08594 m .17539 .08984 L s [(1)] .17539 .07422 0 1 Mshowa .32696 .08594 m .32696 .08984 L s [(2)] .32696 .07422 0 1 Mshowa .47854 .08594 m .47854 .08984 L s [(3)] .47854 .07422 0 1 Mshowa .63011 .08594 m .63011 .08984 L s [(4)] .63011 .07422 0 1 Mshowa .78169 .08594 m .78169 .08984 L s [(5)] .78169 .07422 0 1 Mshowa .93327 .08594 m .93327 .08984 L s [(6)] .93327 .07422 0 1 Mshowa .125 Mabswid .05412 .08594 m .05412 .08984 L s .08444 .08594 m .08444 .08984 L s .11476 .08594 m .11476 .08984 L s .14507 .08594 m .14507 .08984 L s .2057 .08594 m .2057 .08984 L s .23602 .08594 m .23602 .08984 L s .26633 .08594 m .26633 .08984 L s .29665 .08594 m .29665 .08984 L s .35728 .08594 m .35728 .08984 L s .38759 .08594 m .38759 .08984 L s .41791 .08594 m .41791 .08984 L s .44822 .08594 m .44822 .08984 L s .50885 .08594 m .50885 .08984 L s .53917 .08594 m .53917 .08984 L s .56948 .08594 m .56948 .08984 L s .5998 .08594 m .5998 .08984 L s .66043 .08594 m .66043 .08984 L s .69074 .08594 m .69074 .08984 L s .72106 .08594 m .72106 .08984 L s .75138 .08594 m .75138 .08984 L s .81201 .08594 m .81201 .08984 L s .84232 .08594 m .84232 .08984 L s .87264 .08594 m .87264 .08984 L s .90295 .08594 m .90295 .08984 L s .96358 .08594 m .96358 .08984 L s .9939 .08594 m .9939 .08984 L s .25 Mabswid 0 .08594 m 1 .08594 L s .02381 .17578 m .03006 .17578 L s [(0.000496343)] .01131 .17578 1 0 Mshowa .02381 .27344 m .03006 .27344 L s [(0.000496343)] .01131 .27344 1 0 Mshowa .02381 .36328 m .03006 .36328 L s [(0.000496343)] .01131 .36328 1 0 Mshowa .02381 .45703 m .03006 .45703 L s [(0.000496343)] .01131 .45703 1 0 Mshowa .02381 .54688 m .03006 .54688 L s [(0.000496343)] .01131 .54688 1 0 Mshowa .125 Mabswid .02381 .10547 m .02756 .10547 L s .02381 .12109 m .02756 .12109 L s .02381 .14063 m .02756 .14063 L s .02381 .15625 m .02756 .15625 L s .02381 .19531 m .02756 .19531 L s .02381 .21094 m .02756 .21094 L s .02381 .23047 m .02756 .23047 L s .02381 .24609 m .02756 .24609 L s .02381 .29297 m .02756 .29297 L s .02381 .30859 m .02756 .30859 L s .02381 .32813 m .02756 .32813 L s .02381 .34375 m .02756 .34375 L s .02381 .38281 m .02756 .38281 L s .02381 .39844 m .02756 .39844 L s .02381 .41797 m .02756 .41797 L s .02381 .43359 m .02756 .43359 L s .02381 .47656 m .02756 .47656 L s .02381 .49219 m .02756 .49219 L s .02381 .51172 m .02756 .51172 L s .02381 .52734 m .02756 .52734 L s .02381 .06641 m .02756 .06641 L s .02381 .04688 m .02756 .04688 L s .02381 .02734 m .02756 .02734 L s .02381 .00391 m .02756 .00391 L s .02381 .56641 m .02756 .56641 L s .02381 .58984 m .02756 .58984 L s .02381 .60938 m .02756 .60938 L s .25 Mabswid .02381 0 m .02381 .61719 L s 0 0 m 1 0 L 1 .61719 L 0 .61719 L closepath clip newpath .5 Mabswid .02381 .27344 m .02499 .39063 L .02605 .29297 L .02729 .27344 L .02846 .29297 L .02946 .36328 L .03053 .33203 L .0317 .38672 L .03279 .32813 L .03395 .48828 L .0352 .27734 L .03638 .33594 L .03746 .47266 L .03873 .39844 L .03944 .38672 L .04011 .26172 L .04132 .38281 L .04262 .33203 L .04327 .35547 L .04396 .31641 L .04519 .36719 L .04588 .37109 L .04652 .32031 L .04722 .27734 L .04797 .39063 L .04862 .42188 L .04933 .38281 L .05061 .41406 L .05186 .52734 L .05302 .52734 L .05414 .29297 L .05519 .34766 L .05634 .40234 L .05759 .36328 L .05882 .31641 L .06012 .42188 L .06123 .34375 L .06244 .43359 L .06315 .45313 L .06381 .31641 L .06453 .35156 L .06529 .34375 L .06797 .30859 L .0704 .27344 L .07103 .35156 L .07173 .47656 L .073 .23047 L .07375 .32031 L .07445 .39844 L .07509 .33203 L Mistroke .07577 .33203 L .07647 .34375 L .07713 .4375 L .07837 .36328 L .07909 .24219 L .07985 .43359 L .08049 .30859 L .08121 .30859 L .08197 .41406 L .08279 .34766 L .08351 .4375 L .08427 .19531 L .08492 .48438 L .08563 .51953 L .08689 .38281 L .0876 .47266 L .08836 .35547 L .08908 .35547 L .08973 .38672 L .09104 .29297 L .09225 .48438 L .09352 .37891 L .09418 .26172 L .0949 .29297 L .09616 .36328 L .09736 .24219 L .09852 .37109 L .09958 .29297 L .10074 .41406 L .10201 .24219 L .10265 .36328 L .10334 .24609 L .10458 .21094 L .10579 .39844 L .10649 .17969 L .10714 .42188 L .10844 .46094 L .10918 .37109 L .10985 .38672 L .11099 .45703 L .11223 .27734 L .11353 .37109 L .11474 .39844 L .11543 .46094 L .11618 .41406 L .11684 .30859 L .11754 .33594 L .11817 .40625 L .11886 .29297 L .12008 .46875 L Mistroke .12082 .27734 L .1215 .27734 L .12229 .38672 L .12303 .46875 L .12435 .28516 L .1251 .45703 L .12579 .39063 L .12706 .23828 L .12777 .38281 L .12843 .43359 L .12963 .44141 L .1309 .46094 L .13205 .29297 L .13311 .51953 L .13428 .15625 L .13553 .37891 L .13623 .32031 L .13687 .36719 L .13757 .29297 L .13832 .28516 L .13958 .36328 L .1403 .25781 L .14096 .45703 L .14219 .49609 L .14283 .48828 L .14351 .39844 L .14466 .24609 L .14591 .32031 L .14714 .30078 L .14845 .44922 L .14913 .30078 L .14988 .43359 L .1512 .35547 L .15244 .41797 L .15314 .39063 L .15378 .31641 L .15502 .38281 L .15619 .40625 L .15732 .36328 L .15851 .19141 L .15964 .28516 L .16066 .35547 L .16187 .37109 L .16317 .22266 L .1644 .33203 L .16553 .32031 L .16675 .37891 L .16805 .30859 L .16918 .27734 L .1704 .21484 L Mistroke .17115 .20313 L .17184 .33203 L .17249 .48828 L .17319 .25781 L .1744 .30859 L .17509 .51172 L .17573 .44141 L .17712 .33594 L .17844 .23047 L .17962 .37109 L .18091 .28516 L .18165 .36328 L .18231 .37891 L .18308 .29297 L .18381 .28516 L .18509 .30078 L .18582 .31641 L .18649 .21094 L .18775 .30859 L .18894 .29297 L .19002 .31641 L .19118 .37891 L .19245 .41406 L .19309 .49609 L .1938 .50391 L .19505 .23047 L .19622 .23828 L .19733 .30859 L .1985 .27734 L .1995 .40234 L .20059 .37891 L .20177 .42578 L .20303 .35547 L .20422 .29297 L .20531 .16016 L .20659 .20313 L .20724 .28516 L .20796 .39844 L .20922 .47266 L .2104 .13672 L .21112 .44141 L .21179 .38281 L .21307 .27344 L .21378 .33203 L .21444 .26172 L .21516 .30859 L .21593 .30078 L .21723 .31641 L .21797 .38281 L .21864 .51172 L Mistroke .21988 .47656 L .2212 .33203 L .22237 .37891 L .22347 .34766 L .22467 .30859 L .22596 .31641 L .22719 .17969 L .22788 .35547 L .22853 .28516 L .22985 .41406 L .23059 .25 L .23126 .39063 L .2324 .39844 L .23365 .26172 L .23495 .33203 L .23616 .35156 L .23685 .35156 L .2376 .30859 L .23831 .27734 L .23897 .41406 L .24021 .32813 L .24152 .35547 L .2422 .36328 L .24293 .24609 L .24424 .54297 L .24504 .26563 L .24581 .35156 L .24649 .33594 L .24724 .27734 L .24848 .23828 L .24964 .30859 L .25092 .25781 L .25164 .45313 L .2523 .35156 L .25355 .45703 L .25426 .29297 L .25492 .35156 L .25562 .36719 L .25626 .35156 L .25699 .21484 L .25769 .33594 L .25886 .15625 L .2601 .23047 L .26117 .34375 L .26233 .39844 L .26357 .33203 L .26473 .36328 L .26543 .38281 L .2661 .28516 L .26737 .30078 L Mistroke .26861 .29297 L .26931 .4375 L .26996 .26172 L .27114 .26172 L .2724 .51953 L .27352 .42188 L .27457 .29297 L .27572 .32813 L .27696 .27344 L .27827 .30859 L .27901 .55469 L .2797 .26172 L .28096 .37109 L .2816 .21484 L .2823 .54297 L .28351 .24219 L .28482 .36328 L .28605 .41406 L .28718 .27734 L .28825 .33594 L .28939 .35156 L .29047 .37891 L .29146 .21484 L .29261 .39063 L .29386 .43359 L .29505 .13281 L .29614 .37891 L .29726 .40234 L .29832 .39063 L .29947 .36719 L .30072 .28516 L .30202 .25 L .30325 .49609 L .30436 .43359 L .30557 .27344 L .30622 .30078 L .3069 .36328 L .30813 .44141 L .30945 .44141 L .3102 .29297 L .3109 .30078 L .31217 .33594 L .31332 .38281 L .31396 .27344 L .31465 .19141 L .31591 .43359 L .31704 .25781 L .31828 .17188 L .31957 .42188 L .32078 .47266 L Mistroke .32192 .53125 L .32295 .32031 L .32415 .38281 L .32528 .39063 L .3266 .41406 L .3278 .38672 L .32909 .41406 L .32982 .26172 L .33048 .32031 L .33169 .36328 L .33297 .45313 L .33409 .30859 L .33531 .29297 L .33599 .27344 L .33672 .20313 L .33741 .27344 L .33805 .27344 L .33879 .29297 L .33958 .28516 L .34025 .27734 L .34098 .22656 L .34229 .37109 L .34303 .47266 L .34371 .34766 L .34496 .24609 L .34627 .27734 L .3475 .30078 L .3482 .36328 L .34884 .24219 L .35002 .33203 L .35126 .20703 L .35238 .39063 L .35343 .25781 L .35457 .45313 L .3558 .41797 L .35711 .27734 L .35785 .34766 L .35853 .42188 L .35979 .25781 L .36049 .33203 L .36113 .17969 L .36233 .27734 L .36363 .22656 L .36486 .23828 L .36599 .34766 L .36706 .31641 L .3682 .27734 L .36927 .37891 L .37025 .41406 L .3714 .45313 L Mistroke .37265 .24609 L .37383 .20313 L .37493 .37109 L .37605 .30078 L .3771 .39063 L .37826 .38281 L .3795 .25 L .38073 .49609 L .38203 .26172 L .38314 .38672 L .38436 .36719 L .38559 .25 L .3869 .25 L .38758 .33594 L .38833 .34375 L .38965 .30078 L .39089 .20313 L .39159 .27344 L .39223 .44922 L .39347 .34375 L .39464 .30859 L .39577 .36328 L .39696 .37109 L .39809 .40234 L .39912 .26172 L .40032 .23047 L .40163 .30078 L .40286 .35156 L .40399 .28516 L .4052 .31641 L .40651 .36328 L .40774 .25781 L .40885 .16797 L .41017 .36328 L .41091 .26563 L .4116 .27344 L .41285 .35156 L .41349 .38281 L .41419 .49609 L .4149 .36719 L .41558 .29297 L .41686 .25 L .41758 .35156 L .41824 .30078 L .41897 .34766 L .41974 .32031 L .42042 .30078 L .42115 .40625 L .42184 .36719 L .42247 .25781 L Mistroke .42367 .24219 L .42494 .38281 L .42616 .41797 L .42685 .27734 L .42749 .25781 L .42866 .40625 L .4299 .27344 L .43101 .26172 L .43205 .29297 L .43318 .38672 L .43442 .37109 L .43566 .36719 L .43697 .34766 L .43818 .42188 L .43931 .36328 L .43999 .28516 L .44064 .27734 L .44186 .30078 L .44316 .35547 L .4439 .29297 L .44458 .31641 L .44563 .27344 L .44677 .34375 L .44784 .30859 L .44882 .21094 L .44996 .16016 L .45121 .30859 L .45239 .26563 L .45348 .34766 L .45472 .27734 L .45588 .33203 L .45692 .35156 L .45805 .22656 L .45928 .22266 L .46058 .44141 L .46169 .43359 L .46291 .44922 L .46422 .37109 L .46543 .27344 L .46606 .51172 L .46676 .36719 L .46748 .34766 L .46817 .27734 L .46942 .41797 L .47056 .41406 L .47182 .30078 L .47314 .39063 L .47426 .27344 L .47545 .33594 L .47657 .42578 L Mistroke .47759 .33594 L .47879 .39063 L .4801 .38281 L .48132 .47266 L .48246 .22266 L .48366 .34375 L .48496 .37891 L .48608 .27734 L .4873 .46094 L .48804 .30078 L .48873 .34375 L .48939 .31641 L .49009 .38281 L .49129 .27734 L .49198 .38281 L .49263 .27344 L .49394 .36328 L .4946 .20313 L .49532 .30859 L .49661 .40234 L .4978 .36719 L .49853 .40625 L .49921 .48438 L .5005 .48438 L .50122 .25 L .50188 .28516 L .50261 .32031 L .50338 .30078 L .50459 .30859 L .5059 .34375 L .50715 .27734 L .5083 .48828 L .50944 .54297 L .51048 .25 L .51168 .33203 L .5128 .51172 L .51403 .41406 L .51534 .30078 L .51645 .48828 L .51767 .30078 L .51898 .26172 L .51972 .30078 L .52039 .30859 L .52169 .38281 L .52293 .41406 L .52398 .44141 L .52514 .30859 L .52635 .29297 L .52748 .21484 L .52854 .33203 L Mistroke .52951 .23828 L .53058 .42578 L .5317 .31641 L .53284 .30859 L .53406 .17969 L .53521 .33203 L .53625 .41406 L .53748 .23047 L .53818 .22656 L .53881 .39063 L .53999 .46094 L .54123 .27344 L .54244 .54688 L .54377 .21484 L .54501 .35156 L .54617 .32813 L .54731 .30859 L .54835 .33203 L .54955 .33594 L .55068 .36328 L .55191 .32813 L .55322 .44141 L .55433 .27734 L .55555 .30078 L .55687 .24219 L .55761 .40234 L .55828 .37109 L .55951 .44141 L .56082 .29297 L .56193 .4375 L .56316 .42188 L .56428 .29297 L .56533 .29297 L .56656 .40625 L .56769 .30859 L .56899 .32031 L .57023 .36328 L .5713 .24609 L .57244 .40234 L .57351 .26172 L .57449 .38672 L .57564 .19141 L .57688 .43359 L .57805 .33203 L .57914 .30859 L .5804 .27344 L .58159 .44922 L .58266 .32031 L .58383 .30078 L .5851 .30859 L Mistroke .58574 .29297 L .58644 .46094 L .58769 .46875 L .58886 .51172 L .58997 .22266 L .59114 .34375 L .59215 .25 L .59323 .60156 L .5944 .41406 L .59548 .33203 L .59677 .42578 L .59795 .25 L .59924 .31641 L .59994 .27344 L .6006 .39844 L .60176 .10938 L .60304 .46875 L .60376 .22266 L .60444 .30859 L .60571 .32813 L .60642 .32813 L .60708 .4375 L .6078 .34766 L .60857 .40625 L .60988 .25781 L .61061 .38281 L .61128 .46094 L .61253 .21484 L .61384 .33594 L .61501 .41797 L .61611 .24219 L .61732 .23047 L .61861 .37891 L .61983 .38281 L .62052 .24219 L .62117 .33203 L .62249 .26172 L .62323 .37891 L .6239 .48438 L .62504 .23047 L .62629 .26172 L .62759 .21094 L .6288 .26172 L .62949 .23047 L .63024 .42188 L .63095 .36719 L .63161 .29297 L .63284 .24219 L .63415 .29297 L .63483 .33203 L Mistroke .63556 .47656 L .63688 .30859 L .63768 .26172 L .63844 .39063 L .63913 .35156 L .63987 .40234 L .64111 .30859 L .64228 .42578 L .64356 .38281 L .64428 .5625 L .64494 .41797 L .64619 .35156 L .6469 .30859 L .64756 .32031 L .64826 .30859 L .64889 .42188 L .64963 .53125 L .65032 .41797 L .65149 .43359 L .65274 .23047 L .6538 .41406 L .65496 .41797 L .65622 .32813 L .65691 .37109 L .65757 .23828 L .65884 .41406 L .66 .28516 L .66125 .17188 L .66195 .37891 L .66259 .20313 L .66378 .27344 L .66503 .33203 L .66608 .45703 L .6672 .41406 L .66844 .37891 L .66959 .45313 L .6709 .23828 L .67165 .32031 L .67234 .42578 L .6736 .28516 L .67423 .27734 L .67494 .26563 L .67615 .39844 L .67745 .27734 L .67868 .30859 L .67981 .34375 L .68088 .27734 L .68203 .33203 L .68311 .30078 L .68409 .39063 L Mistroke .68524 .35547 L .6865 .32031 L .68768 .40234 L .68877 .35156 L .68989 .31641 L .69095 .32813 L .69211 .27734 L .69335 .32813 L .69465 .32031 L .69588 .27734 L .69699 .25 L .6982 .29297 L .69885 .20313 L .69953 .30859 L .70076 .24219 L .70208 .45703 L .70283 .20313 L .70353 .41406 L .7048 .26172 L .70595 .37109 L .70659 .33203 L .70728 .22266 L .70854 .33203 L .70967 .45313 L .71091 .32031 L .7122 .19531 L .71341 .40234 L .71454 .26563 L .71558 .25 L .71672 .36719 L .71791 .27734 L .71923 .20703 L .72043 .32813 L .72109 .39844 L .72181 .30078 L .72311 .31641 L .72433 .38672 L .72563 .27734 L .72673 .125 L .72794 .41797 L .72868 .08203 L .72937 .28516 L .73067 .32813 L .73141 .19531 L .7322 .34375 L .73287 .33203 L .73361 .39063 L .73491 .23047 L .73614 .36719 L .73683 .33203 L Mistroke .73747 .25781 L .73816 .22266 L .7389 .36328 L .74013 .26563 L .74082 .45313 L .74147 .39063 L .74262 .30078 L .74389 .15234 L .74503 .08203 L .74609 .32031 L .74722 .19531 L .74843 .17188 L .74973 .27344 L .75042 .19141 L .75116 .41406 L .75186 .23047 L .7525 .17969 L .75375 .30078 L .75496 .21484 L .75626 .36719 L .75749 .32813 L .75862 .27734 L .75968 .27344 L .76082 .51953 L .7619 .41797 L .76288 .43359 L .76403 .27734 L .76528 .20703 L .76646 .14453 L .76755 .31641 L .76867 .27734 L .76972 .27734 L .77088 .41797 L .77212 .28516 L .77336 .27344 L .77466 .27734 L .77576 .26563 L .77698 .42578 L .7783 .27734 L .77952 .26563 L .78015 .23047 L .78086 .28516 L .78159 .30859 L .78227 .08984 L .78353 .26563 L .78468 .25 L .78531 .26172 L .78601 .19141 L .78726 .30859 L .7885 .24609 L Mistroke .78961 .37109 L .7909 .23047 L .79211 .30078 L .79324 .29297 L .79427 .37109 L .79541 .37109 L .7966 .17969 L .79791 .17188 L .79911 .25 L .79977 .32813 L .80048 .23047 L .80178 .32813 L .803 .30078 L .80429 .25781 L .80539 .27734 L .80661 .32031 L .80733 .35547 L .80803 .08984 L .80933 .27734 L .81006 .27344 L .81073 .34375 L .81147 .33203 L .81226 .40234 L .81295 .24219 L .81369 .34375 L .81439 .27734 L .81504 .17188 L .81627 .29297 L .81756 .27734 L .81878 .43359 L .81947 .29297 L .82011 .15625 L .82127 .13672 L .82252 .27344 L .82362 .14063 L .82466 .23047 L .8258 .21094 L .82703 .24219 L .82837 .27344 L .82962 .30859 L .83091 .41797 L .8316 .33203 L .83233 .33594 L .83364 .26172 L .83488 .40234 L .83599 .20313 L .83719 .26172 L .83833 .22266 L .8394 .27344 L .84057 .35156 L Mistroke .84182 .28516 L .84314 .34375 L .84439 .34375 L .84551 .13281 L .84673 .27734 L .84789 .21484 L .84894 .34375 L .85015 .32031 L .85129 .36328 L .85235 .21094 L .85333 .26172 L .8544 .27734 L .85552 .31641 L .85675 .19141 L .85744 .30859 L .85808 .17969 L .85925 .17578 L .86049 .26563 L .86161 .29297 L .86265 .37109 L .86379 .27734 L .86502 .32031 L .86567 .21484 L .86636 .20313 L .86761 .42188 L .86891 .35547 L .86966 .35547 L .87033 .37891 L .87153 .30078 L .87283 .29297 L .87406 .25781 L .87519 .17969 L .87625 .34375 L .87739 .09766 L .87846 .27734 L .87944 .24219 L .88059 .34375 L .88184 .27734 L .88301 .24219 L .88411 .16797 L .88524 .38672 L .88648 .09766 L .8877 .24219 L .889 .08203 L .89016 .37109 L .89137 .24609 L .8924 .26563 L .89354 .37109 L .89485 .27344 L .89607 .30078 L Mistroke .8967 .22266 L .8974 .29297 L .89813 .33203 L .89881 .27344 L .90006 .16016 L .90121 .17188 L .90184 .37109 L .90253 .19141 L .90379 .43359 L .90502 .22656 L .90613 .38281 L .90742 .26172 L .90863 .27734 L .90975 .33594 L .91079 .40625 L .91192 .30859 L .91312 .24219 L .91442 .24609 L .91561 .42188 L .91627 .30859 L .91698 .21094 L .91828 .23047 L .9231 .32813 L .92379 .30078 L .92453 .11719 L .92522 .26563 L .92586 .36719 L .92654 .29297 L .92726 .32031 L .92799 .32031 L .92879 .23047 L .93011 .30859 L .93085 .23828 L .93152 .21094 L .93283 .45313 L .93406 .33203 L .93521 .30859 L .93645 .37109 L .93762 .43359 L .93869 .36719 L .93994 .25 L .94065 .15234 L .9413 .30078 L .94251 .17188 L .94378 .26563 L .94448 .39063 L .94512 .17578 L .94583 .22656 L .94657 .26172 L .94722 .17578 L Mistroke .94792 .27734 L .94919 .38672 L .95041 .32031 L .95152 .27734 L .95284 .17578 L .95408 .32031 L .95514 .21484 L .95631 .26563 L .95745 .42188 L .95868 .40625 L .95982 .21094 L .96087 .01563 L .96192 .35547 L .96293 .28516 L .96408 .11719 L .96531 .38672 L .96647 .26563 L .96752 .39063 L .96876 .36328 L .96946 .41797 L .9701 .35156 L .97128 .33203 L .97253 .26172 L .97345 .36328 L .97442 .36328 L .97535 .36719 L .97619 .34375 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg_oo00<00?oo ool0@Ooo00<00?ooool06Ooo0P000_oo0P001ooo00<00?ooool00ooo00<00?ooool01Ooo00<00?oo ool01?oo00@00?oo000000Ooo`03003ooooo00Goo`03003ooooo00Ooo`00A?oo0P00:?oo00<00?oo ool04?oo00<00?ooool0@Ooo00<00?ooool06Ooo0P000_oo0P001ooo00<00?ooool00ooo00@00?oo ool000Coo`03003ooooo00Coo`04003oo`000007ool00`00ooooo`05ool00`00ooooo`07ool004Co o`03003ooooo02Ooo`03003ooooo013oo`03003ooooo047oo`03003ooooo01Woo`8000;oo`8000?o o`05003oooooool00005ool01000ooooo`001?oo00<00?ooool01?oo00@00?oo000000Ooo`03003o oooo00Goo`03003ooooo00Ooo`00A?oo00<00?ooool09ooo00<00?ooool04?oo00<00?ooool0@Ooo 00<00?ooool06Ooo0P000_oo0P000ooo00D00?ooooooo`0000Goo`04003ooooo0004ool00`00oooo o`04ool01000ool000001ooo00<00?ooool01Ooo00<00?ooool01ooo0014ool00`00ooooo`0Wool0 0`00ooooo`0@ool00`00ooooo`11ool00`00ooooo`0Iool20002ool20003ool01@00oooooooo0000 1Ooo00@00?oo000000Coo`03003ooooo00Coo`04003oo`000007ool01000ooooo`001?oo00<00?oo ool01ooo0014ool2000Gool00`00ooooo`0>ool00`00ooooo`08ool00`00ooooo`05ool00`00oooo o`11ool00`00ooooo`0Iool20002ool20003ool01@00oooooooo00001Ooo00@00?oo000000Coo`03 003ooooo00Coo`04003oo`000007ool01000ooooo`001?oo00<00?ooool01ooo0014ool00`00oooo o`0Fool00`00ooooo`0=ool2000:ool00`00ooooo`05ool00`00ooooo`0Pool00`00ooooo`0Nool0 0`00ooooo`0Iool20002ool20003ool01@00oooooooo00001Ooo00@00?oo000000Coo`03003ooooo 00Coo`06003oo`00003oo`001Ooo00@00?ooool000Coo`03003ooooo00Ooo`000_oo0P001?oo00<0 0?ooool00ooo0P001?oo0P001?oo0P001Ooo00@00?ooooooo`<000Coo`8000Coo`8000Goo`03003o oooo00;oo`8000Coo`03003ooooo01Koo`03003ooooo00goo`8000[oo`03003ooooo00Goo`03003o oooo023oo`03003ooooo01koo`03003ooooo01Woo`8000;oo`8000?oo`05003oooooool00005ool0 1000ool000001?oo00<00?ooool01?oo00H00?oo00000?oo0005ool01000ooooo`001?oo00<00?oo ool01ooo00001Ooo003ooooo00002?oo00@00?ooool000;oo`04003ooooo0002ool01000ooooo`00 1?oo00<00?ooool01?oo00@00?ooool000;oo`04003ooooo0002ool00`00ooooo`02ool01@00oooo oooo00000_oo00D00?ooooooo`0001Soo`03003ooooo00goo`8000[oo`03003ooooo00Goo`03003o oooo00;oo`03003ooooo017oo`03003ooooo00Ooo`03003ooooo01koo`03003ooooo00_oo`03003o oooo00_oo`8000;oo`8000?oo`05003oooooool00002ool00`00ooooo`040004ool00`00ooooo`04 ool01P00ool00000ool000Goo`03003ooooo008000?oo`03003ooooo00Ooo`0000Goo`00ooooo`00 00Soo`04003ooooo0002ool01000ooooo`000_oo00D00?ooool00?oo00D000Goo`04003ooooo0002 ool00`00ooooo`03ool00`00ool000040005ool01000oooooooo0`005_oo00<00?ooool03Ooo0P00 2_oo00<00?ooool01Ooo00<00?ooool00_oo00<00?ooool04Ooo00<00?ooool01ooo00<00?ooool0 7_oo00<00?ooool02ooo00<00?ooool02ooo0P000_oo0P000ooo00D00?ooooooo`0000;oo`03003o oooo00@000Coo`04003ooooo0003ool01P00ool00000ool000Goo`03003ooooo00@00003ool00?oo 00Soo`0000Goo`00ooooo`0000Soo`04003ooooo0002ool01000ooooo`000_oo00H00?ooool00?oo 0002ool00`00ooooo`02ool30002ool30004ool20002ool01000ooooo`001?oo0P001?oo00<00?oo ool04?oo00<00?ooool00ooo00<00?ooool03Ooo0P000ooo00<00?ooool01?oo00<00?ooool01Ooo 00<00?ooool00_oo00<00?ooool01ooo00<00?ooool01ooo00<00?ooool01ooo00<00?ooool03ooo 00<00?ooool03?oo00<00?ooool02ooo00<00?ooool02ooo0P000_oo0`000_oo00D00?ooooooo`00 00;oo`03003ooooo00@000Coo`04003ooooo0003ool01P00ool00000ool000Goo`03003ooooo00@0 0003ool00?oo00Soo`0000Goo`00ooooo`0000Soo`04003ooooo0002ool01000ooooo`000_oo00@0 0?ooool000;oo`03003oo`0000?oo`04003ooooo0002ool00`00ooooo`06ool01P00ooooo`00ool0 00Koo`05003oooooool0000Bool00`00ooooo`03ool00`00ooooo`0=ool20003ool00`00ooooo`04 ool00`00ooooo`05ool00`00ooooo`02ool00`00ooooo`07ool00`00ooooo`07ool00`00ooooo`07 ool00`00ooooo`0?ool00`00ooooo`00002ool40000 0ooo0000000200000ooo003oo`08ool004Coo`03003ooooo00Soo`04003ooooo0003ool20003ool0 0`00ool00004ool200002Ooo003oo`00ool00?oo003oo`020003ool00`00ooooo`02ool30004ool0 1000ool000000ooo0P000ooo0P0000Coo`00ooooo`@000;oo`05003oo`00ool00008ool40004ool0 1000ooooo`001_oo0`0000?oo`00ool01Ooo00D00?ooool00?oo00800004ool00000ool20004ool3 00000ooo003oo`04ool400000ooo0000000700001?oo00000?oo300000?oo`00ool03P000_oo1000 00?oo`0000000P0000?oo`00ool02?oo0014ool00`00ooooo`08ool01000ool000000_oo0`000ooo 00<00?oo00001?oo0P0000Woo`00ool00?oo003oo`00ool00P000ooo00<00?ooool00_oo0`001?oo 00@00?oo000000?oo`8000?oo`800004ool00?ooool40002ool300000ooo003oo`02ool00`00oooo o`02ool40004ool01000ooooo`001_oo0`0000Coo`00ool000Coo`05003ooooo003oo`0200000ooo 000000030004ool300000ooo003oo`04ool400000ooo0000000700001?oo00000?oo300000?oo`00 ool03P0000?oo`0000000`0000?oo`00000010002Ooo0014ool20009ool01000ool000000_oo0`00 0ooo00D00?oo003oo`0000;oo`800009ool00?oo003oo`00ool00?oo008000?oo`05003ooooo003o o`030004ool01000ool000000ooo0P000ooo10000_oo10000_oo0`0000?oo`00ool00_oo00<00?oo ool00_oo10001?oo00@00?ooool000Koo`<00004ool00?oo0003ool20002ool01@00ool00000ool0 1@001?oo0`0000?oo`00ool01?oo3P0000Coo`00003oo``00003ool00?oo00h00003ool0000000<0 0003ool0000000@000Woo`00A?oo00<00?ooool02?oo00@00?oo000000;oo`<000?oo`05003oo`00 ool00002ool200002Ooo003oo`00ool00?oo003oo`020002ool300000ooo003oo`030004ool00`00 ool000020002ool20003ool40002ool900001_oo003oo`00ool000Coo`@000Coo`03003ooooo0080 0003ool00?oo00;oo`<00004ool00?oo0003ool20002ool01@00ool00000ool01@001?oo0`0000?o o`00ool01?oo3P0000Coo`00003oo``00003ool0000000h00003ool0000000<00003ool0000000@0 00Woo`00A?oo00<00?ooool02?oo00@00?oo000000;oo`<000?oo`05003oo`00ool00002ool20000 2Ooo003oo`00ool00?oo003oo`020002ool300000ooo003oo`030004ool00`00ool000020002ool2 0003ool40002ool900000ooo003oo`030004ool40004ool00`00ooooo`0200000ooo003oo`02ool3 00001?oo003oo`000ooo0P000_oo00D00?oo00000?oo00D000Coo`<00003ool00?oo00Coo`h00004 ool00000ool<00000ooo0000000>00000ooo0000000300000ooo000000050008ool004Coo`05003o ooooool00006ool01@00ool00000ool010000ooo00<00?oo00000P000_oo0P0000Woo`0000000?oo 003oo`00ool00`0000Goo`0000000?oo00D00003ool0000000800004ool000000002ool20002ool@ 00000ooo003oo`040003ool40004ool00`00ooooo`0200001Ooo003oo`00ool00`0000Coo`00ool0 00?oo`8000;oo`03003oo`0000L00004ool00?ooool300000ooo003oo`04ool>00001?oo00000?oo 8`0000?oo`0000001P001ooo0002ool20004ool00`00ooooo`03ool20004ool20004ool20005ool0 1000oooooooo0`001?oo0P001?oo0P001Ooo00<00?ooool00_oo0P001?oo00D00?ooooooo`0000Ko o`05003oo`00003oo`040003ool00`00ool000020002ool200002Ooo00000000ool00?oo003oo`03 00001Ooo00000000ool01@0000?oo`0000000P0000Coo`00000000;oo`8000;ooa000003ool00000 00@000?oo`@000Coo`03003ooooo00800005ool00?oo003oo`0300001?oo003oo`000ooo0P000_oo 00<00?oo00001`0000Coo`00ooooo`<00003ool0000000Coo`h00003ool0000002@00003ool00000 00H000Ooo`0000Goo`00ooooo`0000Soo`04003ooooo0002ool01000ooooo`000_oo00@00?ooool0 00Coo`03003ooooo00Coo`04003ooooo0002ool01000ooooo`000_oo00<00?ooool00_oo00D00?oo ooooo`0000;oo`05003oooooool00003ool00`00ooooo`04ool01@00ool00000ool010000ooo00<0 0?oo00000P000_oo0P0000Woo`0000000?oo003oo`00ool00`0000Goo`0000000?oo00D00003ool0 000000800004ool000000002ool20002oolG0003ool40004ool00`00ooooo`0200001Ooo003oo`00 ool00`0000Coo`00ool000?oo`8000;oo`03003oo`0000T000;oo`<00003ool0000000Coo`h00003 ool0000002@00003ool0000000H000Ooo`0000Goo`00ooooo`0000Soo`04003ooooo0002ool01000 ooooo`000_oo00D00?ooool00?oo00D000Goo`04003ooooo0002ool00`00ooooo`03ool00`00ool0 00040005ool01000oooooooo0`0000?oo`00ool01Ooo00D00?oo00000?oo00@000?oo`03003oo`00 008000;oo`800009ool00000003oo`00ool00?oo00<00005ool00000003oo`0500000ooo00000002 00000ooo0000000200000ooo00000002oolG0003ool500001Ooo003oo`00ool00`0000Goo`00ool0 0?oo00D00003ool00?oo00;oo`<00003ool00?oo00X000;oo`<00003ool0000000CoocD00003ool0 000000H000Ooo`0000Goo`00ooooo`0000Soo`04003ooooo0002ool01000ooooo`000_oo00H00?oo ool00?oo0002ool00`00ooooo`02ool30002ool30004ool20002ool01000ooooo`001?oo0P001?oo 0P0000Goo`00003oo`0000Coo`05003oo`00003oo`0500001?oo00000?oo0`000_oo0P0000Woo`00 00000?oo003oo`00ool00`0000?oo`0000001`0000?oo`0000001`0000?oo`0000000_oo6@0000?o o`0000001@0000?oo`0000001@0000?oo`00ool01@0000?oo`00ool00_oo0`0000?oo`00ool02P00 0_oo0`0000Coo`00000000;ooad00003ool0000001H00003ool0000000H000Ooo`0000Goo`00oooo o`0000Soo`04003ooooo0002ool01000ooooo`000_oo00@00?ooool000;oo`03003oo`0000?oo`04 003ooooo0002ool00`00ooooo`06ool01P00ooooo`00ool000Koo`04003oooooool200001Ooo0000 0?oo00001?oo00D00?oo00000?oo00D00004ool00000ool30002ool600001Ooo003oo`00ool00`00 00?oo`0000001`0000?oo`0000001`0000?oo`0000000_oo6@0000?oo`0000001@0000?oo`000000 1@0000?oo`00ool01@0000?oo`00ool00_oo0`0000?oo`00ool02P000_oo0`0000Coo`00000000;o oad00003ool0000001H00003ool0000000H000Ooo`0000Goo`00ooooo`0000Soo`04003ooooo0002 ool01000ooooo`000_oo00@00?ooool000?oo`8000?oo`04003ooooo0002ool00`00ooooo`03ool0 1000ooooo`000ooo0P000ooo00@00?ooool000?oo`800005ool00000ool00004ool01@00ool00000 ool01@0000Coo`00003oo`@00003ool0000000H00003ool00?oo00<00003ool0000001400003ool0 000000;ooaT00003ool0000000D00003ool0000000D00003ool00?oo00D00003ool00?oo00;oo`<0 0003ool00?oo00X000;oo`<00004ool000000002oolM00000ooo0000000F00000ooo000000060007 ool000;oo`8000[oo`8000Coo`8000Coo`8000Goo`03003ooooo00;oo`8000Coo`<000?oo`8000Go o`03003ooooo00;oo`8000Coo`800004ool00000ool20003ool00`00ool0000700000ooo00000005 00000ooo0000000600000ooo003oo`0300000ooo0000000D0002oolQ00000ooo0000000500000ooo 003oo`0500001Ooo00000000ool01@0000?oo`00000020000_oo0`0000Coo`00000000;ooad00003 ool0000001H00003ool0000000H000Ooo`00A?oo0P0000Coo`00003oo`8000;oo`800003ool00000 00H00003ool0000000D00003ool0000000H00003ool00?oo00<00003ool0000001@000;oob400003 ool0000000D00003ool00?oo00D00005ool00000003oo`0500000ooo000000080002ool300001?oo 000000000_oo7@0000?oo`0000005P0000?oo`0000001P001ooo0014ool200001?oo00000?oo0P00 0_oo0P0000?oo`0000001P0000?oo`0000001@0000?oo`0000001P0000?oo`00ool00`0000?oo`00 000050000_oo8@0000?oo`0000001`0000?oo`0000000`0000Goo`0000000?oo00D00003ool00000 00P000;oo`<00003ool0000000800003ool0000001/00003ool0000001H00003ool0000000H000Oo o`00A?oo0P0000?oo`0000000`000_oo2`0000?oo`0000001@0000?oo`0000001P0000?oo`00ool0 0`0000?oo`00000050000_oo8@0000?oo`0000003@0000Goo`0000000?oo00D00003ool0000000P0 00;oobH00003ool0000001H00003ool0000000H000Ooo`00A?oo0P0000?oo`0000000`000_oo4`00 00?oo`0000001P0000?oo`00ool00`0000?oo`00000050000_oo8@0000?oo`0000003@0000?oo`00 00001`0000?oo`000000200000?oo`0000009@0000?oo`0000007`001ooo0014ool200000ooo0000 00030002oolC00000ooo0000000600000ooo003oo`0J0002oolQ00000ooo0000000=00000ooo0000 000700000ooo0000000800000ooo0000000900000ooo0000000@00000ooo0000000600000ooo0000 000500000ooo0000000H0006ool004Coo`800003ool0000002400003ool00?oo01X000;oob400003 ool0000000d00003ool0000000L00003ool0000000P00003ool0000000T00003ool0000001000003 ool0000000H00003ool0000000D00003ool0000001P000Koo`00A?oo0P0000?oo`0000008@0000?o o`00ool06`0000?oo`0000007`0000?oo`0000005`0000?oo`000000200000?oo`0000002@0000?o o`000000400000?oo`0000001P0000?oo`00000010000_oo6P001_oo0014oolV00000ooo0000000K 00000ooo0000000O00000ooo0000000G00000ooo0000000800000ooo0000000900000ooo00000008 00000ooo0000000500000ooo0000000600000ooo000000040002oolD00000ooo000000030006ool0 04CoobH00003ool0000001/00003ool0000001l00003ool0000002800003ool0000000P000;oo`X0 0003ool0000000D00005ool00000003oo`0400000ooo000000040002ool=00000ooo000000040000 0ooo000000030006ool004CoobH00003ool0000000800003ool0000001H00003ool0000000D00003 ool0000002800003ool00000028000;oo`X00003ool0000000D00005ool00?oo003oo`0400000ooo 000000040002ool800000ooo0000000200000ooo0000000400000ooo000000030006ool004CoobH0 0003ool0000000800003ool0000001H00003ool0000000D00003ool0000002800003ool000000280 00;oo`X00003ool0000000D00005ool00?oo003oo`0400000ooo000000040002ool800000ooo0000 000200000ooo0000000400000ooo000000030006ool004CoobH00003ool0000000800003ool00000 01H00003ool0000000D00003ool0000002800003ool00000028000;oo`X00003ool0000000D00005 ool00?oo003oo`0400000ooo000000040002ool800000ooo0000000200000ooo0000000400000ooo 000000030006ool004CoobH00003ool0000000800003ool0000001H00003ool0000000D00003ool0 000000<00003ool0000000X00003ool0000000l00003ool0000001l00003ool0000000;oo`X00003 ool0000000D00005ool00?oo003oo`0400000ooo0000000200001?oo003ooooo0`000_oo0`0000?o o`0000000P0000?oo`000000100000?oo`0000000`001_oo0002ool20004ool00`00ooooo`03ool2 0004ool20004ool20005ool01000oooooooo0`001?oo0P001?oo0P001Ooo00<00?ooool00_oo0P00 1?oo2P0000?oo`000000600000?oo`0000000`0000?oo`0000005P0000?oo`0000001@000_oo1000 00?oo`0000002P000_oo400000?oo`0000007`0000?oo`0000000_oo2P0000?oo`0000000`0000Oo o`00ool00?oo003oo`0400000ooo0000000200001?oo003ooooo0`000_oo0`0000?oo`0000000P00 00?oo`000000100000?oo`0000000`001_oo00001Ooo003ooooo00002?oo00@00?ooool000;oo`04 003ooooo0002ool01000ooooo`001?oo00<00?ooool01?oo00@00?ooool000;oo`04003ooooo0002 ool00`00ooooo`02ool01@00oooooooo00000_oo00@00?ooooooo`X00003ool0000001P00003ool0 000000<00003ool0000001H00003ool0000000D000;oo`@00004ool00000ool80004ool?00000ooo 0000000C00000ooo0000000900000ooo00000002ool:00003?oo00000000ool00?oo003oo`00ool0 00;oo`<00004ool000000002ool00`00ooooo`030002ool300000ooo0000000200000ooo00000004 00000ooo003oo`030006ool00005ool00?ooool00008ool01000ooooo`000_oo00@00?ooool000;o o`05003ooooo003oo`050005ool01000ooooo`000_oo00<00?ooool00ooo00<00?oo000010001Ooo 00@00?ooooooo`X00003ool0000001P00003ool0000000<00003ool0000001H00003ool0000000D0 00;oo`@00004ool00000ool80004ool?00000ooo0000000C00000ooo0000000900000ooo00000002 ool:00003?oo00000000ool00?oo003oo`00ool000;oo`<00004ool000000002ool00`00ooooo`03 0002ool300000ooo0000000200000ooo0000000400000ooo003oo`030006ool00005ool00?ooool0 0008ool01000ooooo`000_oo00@00?ooool000;oo`06003ooooo003oo`000_oo00<00?ooool00_oo 0`000_oo0`001?oo0P000_oo00@00?ooool000Coo`8000Coo`X00003ool0000000D00003ool00000 01000003ool0000000<00003ool0000001H00003ool0000000800003ool0000000;oo`@00003ool0 000000;oo`L000Coo`l00003ool0000001<00003ool0000000T00003ool0000000;oo`X0000ool0 0?oo003oo`00ool00?oo003oo`00ool000?oo`8000;oo`8000Goo`<000;oo`<00003ool000000080 00;oo`D00003ool00?oo008000Ooo`0000Goo`00ooooo`0000Soo`04003ooooo0002ool01000oooo o`000_oo00@00?ooool000?oo`8000?oo`04003ooooo0002ool00`00ooooo`03ool01000ooooo`00 0ooo0P000ooo00@00?ooool000?oo`D00003ool0000000800003ool0000000D00003ool0000000X0 0003ool0000000<00003ool00?oo00<00003ool0000000L00003ool0000000`00003ool000000080 0003ool0000000;oo`@00003ool0000000;oo`L000Coo`l00003ool0000001<00003ool0000000T0 0003ool0000000;oo`<00003ool000000080000:ool00?oo003oo`00ool00?oo0007ool20002ool2 0006ool20002ool01000oooooooo10000_oo1@0000?oo`00ool00P001ooo0002ool2000:ool20004 ool20004ool20005ool00`00ooooo`02ool20004ool30003ool20005ool00`00ooooo`02ool20004 ool500000ooo0000000200000ooo0000000500000ooo0000000:00000ooo0000000300000ooo003o o`0300000ooo0000000700000ooo0000000<00000ooo0000000200000ooo00000002ool400000ooo 00000002ool70004ool?00000ooo0000000C00000ooo0000000900000ooo00000002ool300000ooo 0000000200002_oo003oo`00ool00?oo003oo`001ooo0P000_oo0P001_oo0P000_oo00@00?oooooo o`@000;oo`D00003ool00?oo008000Ooo`00A?oo1@0000?oo`0000000P0000?oo`0000001@0000?o o`0000002P000_oo0`000_oo00<00?oo00000P0000?oo`00ool01`0000?oo`0000003P0000Coo`00 003oo`8000;oo`@00003ool0000000;oo`L000Coo`X00003ool0000000800005ool00000003oo`0? 00000ooo003oo`0700001Ooo00000000ool00P000_oo0`0000?oo`0000000P0000[oo`00ool00?oo 003oo`00ool000Ooo`8000;oo`8000Koo`05003oooooool00003ool40002ool500000ooo003oo`02 0007ool004Coo`D00003ool0000000800003ool0000000D00003ool0000000X000;oo`<000;oo`03 003oo`0000800003ool00?oo00L00003ool0000000T00003ool0000000800004ool00000ool20002 ool30002ool20002ool500000ooo003oo`03ool700001?oo00000?oo100000Coo`00000000;oo`h0 0003ool00?oo00L00005ool00000003oo`020002ool300000ooo003oo`0200002_oo003oo`00ool0 0?oo003oo`001ooo0P000_oo0P001_oo00<00?ooool01Ooo00@00?oo000000;oo`@000;oo`04003o o`000007ool004Coo`03003oo`0000800003ool0000000800003ool0000000D00003ool0000000X0 00;oo`8000?oo`03003oo`0000800003ool00?oo00L00003ool0000000T00003ool0000000800004 ool00000ool20002ool00`00ool00002ool20002ool500000ooo003oo`03ool300001Ooo00000000 ool00P0000?oo`0000000P0000Coo`00000000;oo`h00003ool00?oo00L00004ool000000002ool0 2P00ooooo`00ool00?oo003oo`000_oo00T00?oo003oo`00ool00?oo00001ooo0P000_oo0P001_oo 00<00?ooool01Ooo00@00?oo000000;oo`<000?oo`04003ooooo0007ool004Coo`D00003ool00000 00800003ool0000000D00003ool0000000X000;oo`8000?oo`03003oo`0000800003ool00?oo00<0 0005ool00000003oo`0800001?oo00000?oo100000Coo`00003oo`8000;oo`03003oo`0000;oo`80 00;oo`D00003ool00?oo00?oo`<00005ool00000003oo`0200001_oo00000?oo003oo`<000;oo`h0 0003ool00?oo00L00004ool000000002ool02P00ooooo`00ool00?oo003oo`000_oo00T00?oo003o o`00ool00?oo00001ooo0P000_oo0P001_oo00<00?ooool01Ooo00@00?oo000000;oo`<000?oo`04 003ooooo0007ool004Coo`03003oo`0000800003ool0000000800003ool0000000D00003ool00000 00X000;oo`8000?oo`03003oo`0000800007ool00?oo003oo`00ool00`000_oo1`0000Coo`00003o o`@00004ool00000ool20002ool00`00ool00002ool20002ool500000ooo003oo`03ool300001Ooo 00000000ool00P0000Koo`00003oo`00ool30002ool:00001ooo00000000ool00?oo00L00003ool0 000000?oo`06003ooooo003oo`000ooo00`00?ooool00?oo003oo`00ool00?oo0007ool20002ool2 0006ool00`00ooooo`05ool01000ool000000_oo0`000ooo00@00?ooool000Ooo`00A?oo00<00?oo 00000P0000?oo`0000000P0000?oo`0000001@0000?oo`0000002P000_oo0P000ooo00<00?oo0000 0P0000Ooo`00ool00?oo003oo`030002ool700001?oo00000?oo100000Coo`00003oo`8000;oo`03 003oo`0000;oo`04003oooooool500000ooo003oo`03ool300001Ooo00000000ool00P0000Koo`00 003oo`00ool30002ool400000ooo0000000300001ooo00000000ool00?oo00800003ool000000080 0003ool0000000Koo`03003oo`0000?oo`0<003ooooo003oo`00ool00?oo003oo`002?oo00@00?oo ool000Ooo`03003ooooo00Goo`04003oo`000002ool00`00ool00003ool01000ooooo`001ooo0014 ool00`00ooooo`0200000ooo0000000200000ooo0000000500000ooo000000090004ool01P00oooo oooo003oo`<00007ool00?oo003oo`00ool00`000_oo1`0000Coo`00003oo`@00004ool00000ool2 0002ool00`00ool00002ool01000oooooooo0P0000Goo`00ooooo`0000Coo`<00005ool00000003o o`0200001_oo00000?oo003oo`<000;oo`<000;oo`D00007ool00000003oo`00ool00P0000?oo`00 00000P0000?oo`0000001_oo00<00?oo00000ooo00`00?ooool00?oo003oo`00ool00?oo0008ool0 1000ooooo`001ooo00<00?ooool01Ooo00@00?ooool000;oo`03003oo`0000?oo`04003ooooo0007 ool004Coo`800004ool00000ool400000ooo0000000500000ooo000000090004ool01P00oooooooo 003oo`<00007ool00?oo003oo`00ool00`000_oo1@0000?oo`00ool00P0000?oo`0000000P0000Co o`00003oo`8000;oo`03003oo`0000;oo`04003oooooool200001Ooo003ooooo00001?oo0`0000Go o`0000000?oo00800006ool00000ool00?oo0`000_oo0`000_oo1@0000Ooo`0000000?oo003oo`02 00000ooo0000000200000ooo00000006ool00`00ool00003ool03000ooooo`00ool00?oo003oo`00 ool000Soo`04003ooooo0007ool00`00ooooo`05ool01000ooooo`000_oo00<00?oo00000ooo00@0 0?ooool000Ooo`00A?oo00<00?ooool00P0000?oo`0000000P0000?oo`00000010000_oo2P001Ooo 00H00?ooooooo`00ool300000ooo003oo`04ool30002ool40002ool01@00ool00000ool00P0000?o o`00ool00P0000?oo`0000000_oo00<00?oo00000_oo00@00?ooooooo`8000Coo`03003ooooo00;o o`8000;oo`<00004ool00000ool200000ooo003oo`030002ool30002ool500001ooo00000000ool0 0?oo00800004ool000000002ool20006ool00`00ool00006ool01@00oooooooo00000ooo00<00?oo ool01_oo00<00?ooool02?oo00<00?ooool01Ooo00@00?ooool000;oo`03003oo`0000?oo`03003o oooo00Soo`00A?oo00<00?ooool00P0000Koo`00003oo`00ool60002ool:0005ool01P00oooooooo 003oo`<00003ool00?oo00Coo`<000;oo`@000;oo`05003oo`00003oo`0200001_oo003ooooo003o o`8000;oo`03003oo`0000;oo`04003oooooool20009ool20002ool300001?oo00000?oo0P0000?o o`00ool00`000_oo0`000_oo1@0000Koo`0000000?oo0002ool00`00ool000020002ool20006ool0 0`00ool00006ool01@00oooooooo00000ooo00<00?ooool01_oo00<00?ooool04?oo00<00?ooool0 0ooo00<00?oo00003_oo0014ool00`00ooooo`0200001_oo00000?oo003oo`H000;oo`X000Goo`05 003oooooool00002ool200000ooo003oo`04ool30002ool40002ool01@00ool00000ool00P0000Ko o`00ooooo`00ool20002ool00`00ool00002ool01000oooooooo0P002Ooo0P000_oo0`0000Coo`00 003oo`800003ool00?oo00;oo`03003ooooo00<000;oo`D00006ool00000003oo`000_oo00<00?oo 00000P000_oo0P001_oo00<00?oo00001_oo00D00?ooooooo`0000coo`03003ooooo013oo`03003o oooo00?oo`03003oo`0000koo`00A?oo0P0000Coo`00003oo`800003ool00?oo00H000;oo`X000Go o`05003oooooool00002ool200000ooo003oo`04ool30002ool40002ool01@00ool00000ool00P00 00Koo`00ooooo`00ool20002ool00`00ool00002ool01000oooooooo0P002Ooo0P000ooo0P0000Co o`00003oo`800003ool00?oo00;oo`03003ooooo00<000;oo`D00006ool00000003oo`000_oo00<0 0?oo00000P000_oo0P001_oo00<00?oo00001_oo00D00?ooooooo`0000coo`03003ooooo013oo`03 003ooooo00?oo`03003oo`0000koo`00A?oo00@00?ooool000;oo`800003ool00?oo00800004ool0 00000002ool:0005ool01@00oooooooo00000ooo00<00?oo00001Ooo0`000_oo10001?oo0P0000Go o`00003oo`0000;oo`03003oo`0000?oo`03003oo`0000;oo`04003oooooool20009ool20003ool2 00001?oo00000?oo0P0000?oo`00ool00_oo00<00?ooool00`000ooo100000Koo`0000000?oo0002 ool01000ool000000ooo0P001_oo00<00?oo00001_oo00D00?ooooooo`0002Goo`03003ooooo00ko o`00A?oo00@00?ooool000;oo`800004ool00?oo0002ool30002ool:0005ool01@00oooooooo0000 0ooo00<00?oo00001Ooo0`000ooo0`001?oo0P0000Goo`00003oo`0000;oo`03003oo`0000?oo`03 003oo`0000;oo`03003ooooo00;oo`03003ooooo00Ooo`8000?oo`800004ool00000ool200000ooo 003oo`02ool00`00ooooo`020004ool400001_oo003oo`00ool000;oo`04003oo`000003ool20006 ool00`00ool00006ool01@00oooooooo00009Ooo00<00?ooool03_oo0002ool20004ool00`00oooo o`03ool20004ool20004ool20005ool01000oooooooo0`001?oo0P001?oo0P001Ooo00<00?ooool0 0_oo0P001?oo00@00?ooool000;oo`800004ool00?oo0002ool30002ool:0005ool01@00oooooooo 00000ooo00<00?oo00001Ooo0`000ooo0`001?oo00<00?ooool00P0000Ooo`00ooooo`00ool00003 ool00`00ool00002ool00`00ooooo`02ool00`00ooooo`07ool20003ool20002ool01000ool00000 1Ooo00<00?ooool01_oo100000Koo`00ool00?oo0002ool01000ool000000ooo0P001_oo00<00?oo 00001_oo00D00?ooooooo`0002Goo`03003ooooo00koo`0000Goo`00ooooo`0000Soo`04003ooooo 0002ool01000ooooo`000_oo00@00?ooool000Coo`03003ooooo00Coo`04003ooooo0002ool01000 ooooo`000_oo00<00?ooool00_oo00D00?ooooooo`0000;oo`05003oooooool00002ool00`00oooo o`0200001?oo003oo`000_oo0`000_oo2@001_oo00D00?ooooooo`0000?oo`03003oo`0000Goo`<0 00?oo`<000Coo`07003oooooool00?oo00000_oo00<00?oo00000ooo00<00?oo00001ooo00<00?oo ool02?oo00@00?ooooooo`8000;oo`04003oo`000005ool00`00ooooo`07ool300001_oo003oo`00 ool000;oo`04003oo`000003ool20006ool00`00ool00006ool01@00oooooooo00009Ooo00<00?oo ool03_oo00001Ooo003ooooo00002?oo00@00?ooool000;oo`04003ooooo0002ool01@00ooooo`00 ool01@001Ooo00@00?ooool000;oo`03003ooooo00?oo`03003oo`0000@000Goo`04003oooooool4 0002ool20003ool00`00ooooo`030002ool90006ool01@00oooooooo00000ooo00<00?oo00001Ooo 00<00?oo00000ooo0`001?oo00D00?ooooooo`0000Coo`03003ooooo00Goo`03003ooooo00Goo`03 003ooooo00Soo`04003oooooool20002ool01000ool000001Ooo00<00?ooool01ooo0`0000Koo`00 ool00?oo0002ool01000ool000000ooo00<00?ooool01Ooo00<00?ooool02_oo00<00?ooool0=?oo 00001Ooo003ooooo00002?oo00@00?ooool000;oo`04003ooooo0002ool01P00ooooo`00ool000;o o`03003ooooo00;oo`<000;oo`<000Coo`8000;oo`04003ooooo0004ool20004ool01000ooooo`00 0_oo0P000ooo00<00?ooool00`000_oo00D00?oo00000?oo00@000Koo`05003oooooool00003ool0 0`00ool00005ool00`00ooooo`03ool30004ool01@00oooooooo00001?oo00<00?ooool01Ooo00<0 0?ooool01Ooo00<00?ooool02?oo00@00?ooooooo`8000;oo`04003oo`000005ool00`00ooooo`07 ool300001_oo003oo`00ool000;oo`04003oo`00000Hool00`00ooooo`0dool00005ool00?ooool0 0008ool01000ooooo`000_oo00@00?ooool000;oo`04003ooooo0002ool00`00ool00003ool01000 ooooo`000_oo00<00?ooool01_oo00H00?ooool00?oo0006ool01@00oooooooo00000_oo00<00?oo ool00P000ooo00<00?ooool00`001Ooo00<00?ooool00`001_oo00D00?ooooooo`0000?oo`03003o o`0000Goo`03003ooooo00?oo`<000Coo`05003oooooool00004ool00`00ooooo`05ool00`00oooo o`05ool00`00ooooo`08ool01@00oooooooo00000ooo00@00?oo000000Goo`03003ooooo00Ooo`<0 0003ool00?oo00;oo`05003ooooo003oo`02000Hool00`00ooooo`0dool00005ool00?ooool00008 ool01000ooooo`000_oo00@00?ooool000;oo`04003ooooo0003ool20003ool01000ooooo`000_oo 00<00?ooool00ooo00@00?ooool000?oo`8000?oo`04003ooooo0003ool01000ooooo`000_oo0P00 0ooo00<00?ooool00`001Ooo00<00?ooool00`001_oo00D00?ooooooo`0000?oo`03003oo`0000Go o`03003ooooo00?oo`<000Coo`05003oooooool00004ool00`00ooooo`05ool00`00ooooo`05ool0 0`00ooooo`08ool01@00oooooooo00000ooo00@00?oo000000Goo`03003ooooo00Ooo`<00003ool0 0?oo00;oo`05003ooooo003oo`02000Hool00`00ooooo`0dool000;oo`8000[oo`8000Coo`8000Co o`8000Goo`03003ooooo00;oo`8000Coo`<000?oo`8000Goo`03003ooooo00;oo`8000Coo`800003 ool00?oo00;oo`05003oooooool00002ool30008ool30006ool01@00oooooooo00000ooo00<00?oo 00001Ooo00<00?ooool00ooo0`001?oo00D00?ooooooo`0000Coo`03003ooooo00Goo`03003ooooo 00Goo`03003ooooo00Soo`05003oooooool00003ool01000ool000001Ooo00<00?ooool01ooo0`00 1Ooo00D00?ooool00?oo008001Soo`03003ooooo03Coo`00A?oo00@00?ooool000?oo`03003ooooo 00Coo`03003oo`0000Soo`03003oo`0000Koo`05003oooooool00005ool00`00ooooo`03ool00`00 ooooo`03ool30004ool01@00oooooooo00003?oo00<00?ooool01Ooo00<00?ooool02?oo00<00?oo ool01Ooo00@00?oo000000Goo`03003ooooo00Ooo`<000Goo`03003ooooo00;oo`8001Soo`03003o oooo03Coo`00A?oo00@00?ooool000?oo`03003ooooo00Coo`03003oo`0000Soo`03003oo`0000Ko o`05003oooooool00005ool00`00ooooo`03ool00`00ooooo`03ool30004ool01@00oooooooo0000 3?oo00<00?ooool01Ooo00<00?ooool02?oo00<00?ooool01Ooo00@00?oo000000Goo`03003ooooo 00Ooo`<000Goo`03003ooooo00;oo`8001Soo`03003ooooo03Coo`00A?oo00@00?ooool000?oo`03 003ooooo00Coo`03003ooooo00Soo`03003oo`0000Koo`05003oooooool00005ool00`00ooooo`03 ool00`00ooooo`03ool30004ool01@00oooooooo00003?oo00<00?ooool01Ooo00<00?ooool02?oo 00<00?ooool01ooo0P001Ooo00<00?ooool01ooo0`002_oo0P006?oo00<00?ooool0=?oo0014ool2 0005ool00`00ooooo`04ool00`00ooooo`08ool00`00ool00006ool01@00oooooooo00001Ooo00<0 0?ooool00ooo00<00?ooool00ooo0`001?oo00D00?ooooooo`0000coo`03003ooooo00Goo`03003o oooo00Soo`03003ooooo00Ooo`8000Goo`03003ooooo00Soo`8000[oo`8001Soo`03003ooooo03Co o`00A?oo00<00?ooool01?oo00<00?ooool01?oo00<00?ooool02?oo00<00?oo00001_oo00D00?oo ooooo`0000Goo`03003ooooo00?oo`03003ooooo00?oo`<000Coo`05003oooooool0000ool00005ool00?ooool00008ool01000ooooo`000_oo00@00?oo ool000;oo`04003ooooo0004ool00`00ooooo`04ool01000ooooo`000_oo00@00?ooool000;oo`03 003ooooo00;oo`05003oooooool00002ool01@00oooooooo0000ool00005ool00?ooool00008ool01000oooo o`000_oo00@00?ooool000;oo`06003ooooo003oo`000_oo00<00?ooool00_oo0`000_oo0`001?oo 0P000_oo00@00?ooool000Coo`8000Coo`03003ooooo03Koo`03003ooooo04Coo`03003ooooo00So o`03003ooooo04koo`0000Goo`00ooooo`0000Soo`04003ooooo0002ool01000ooooo`000_oo00@0 0?ooool000;oo`03003oo`0000?oo`04003ooooo0002ool00`00ooooo`06ool01P00ooooo`00ool0 00Koo`05003oooooool0000hool00`00ooooo`14ool00`00ooooo`08ool00`00ooooo`1>ool00005 ool00?ooool00008ool01000ooooo`000_oo00@00?ooool000;oo`04003ooooo0003ool20003ool0 1000ooooo`000_oo00<00?ooool00ooo00@00?ooool000?oo`8000?oo`04003ooooo0003ool00`00 ooooo`1mool00`00ooooo`08ool00`00ooooo`1>ool000;oo`8000[oo`8000Coo`8000Coo`8000Go o`03003ooooo00;oo`8000Coo`<000?oo`8000Goo`03003ooooo00;oo`8000Coo`03003ooooo07go o`03003ooooo00Soo`03003ooooo04koo`00A?oo0P00O_oo00<00?ooool0FOoo0014ool00`00oooo o`1mool00`00ooooo`1Iool004Coo`03003ooooo07goo`03003ooooo05Woo`00A?oo00<00?ooool0 OOoo00<00?ooool0FOoo0014ool00`00ooooo`1mool00`00ooooo`1Iool004Coo`8007koo`03003o oooo05Woo`00A?oo00<00?ooool0OOoo00<00?ooool0FOoo0014ool00`00ooooo`1mool00`00oooo o`1Iool004Coo`03003ooooo0=Woo`00A?oo0P00f_oo0014ool00`00ooooo`3Iool004Coo`03003o oooo0=Woo`00oooo8Ooo003ooolQool00?ooob7oo`00oooo8Ooo003ooolQool00?ooob7oo`00oooo 8Ooo003ooolQool00?ooob7oo`00oooo8Ooo003ooolQool00?ooob7oo`00oooo8Ooo003ooolQool0 0?ooob7oo`00oooo8Ooo003ooolQool00?ooob7oo`00oooo8Ooo0000\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-2.03048, 0.000496343, \ 0.0295149, 9.65328*^-20}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell["\<\ Since this term is small and constant for all values of Psi, it \ will only shift the Arnold tongue slightly.\ \>", "Text"], Cell[CellGroupData[{ Cell["Calculating the Gamma function", "Subtitle"], Cell["\<\ Next we define the omega function and integrate as above. R \ denotes the radius, while o is the driving frequency.\ \>", "Text"], Cell[BoxData[ \(R = \ 11; \ o\ = \ \((2*Pi)\)\ /\ \((DD*period)\);\)], "Input"], Cell["\<\ Here we compute the approximation to the function Gamma, by \ ignoring the jumps.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(od/\((2*Pi)\)\)\(*\)\(Integrate[\(-Sin[od\ t + Psi]\)\ *\ Sin[od*t]/R, \ {t, \ 0, \ 2*Pi/od}]\)\(\ \)\)\)], "Input"], Cell[BoxData[ \(\(-\(Cos[Psi]\/22\)\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(s2\ = \ Plot[\(-\ Cos[t]\)/\((11*2)\), \ {t, \ 0, \ 2*Pi}]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.151576 0.309018 6.47466 [ [.17539 .29652 -3 -9 ] [.17539 .29652 3 0 ] [.32696 .29652 -3 -9 ] [.32696 .29652 3 0 ] [.47854 .29652 -3 -9 ] [.47854 .29652 3 0 ] [.63011 .29652 -3 -9 ] [.63011 .29652 3 0 ] [.78169 .29652 -3 -9 ] [.78169 .29652 3 0 ] [.93327 .29652 -3 -9 ] [.93327 .29652 3 0 ] [.01131 .05003 -30 -4.5 ] [.01131 .05003 0 4.5 ] [.01131 .17952 -30 -4.5 ] [.01131 .17952 0 4.5 ] [.01131 .43851 -24 -4.5 ] [.01131 .43851 0 4.5 ] [.01131 .568 -24 -4.5 ] [.01131 .568 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .17539 .30902 m .17539 .31527 L s [(1)] .17539 .29652 0 1 Mshowa .32696 .30902 m .32696 .31527 L s [(2)] .32696 .29652 0 1 Mshowa .47854 .30902 m .47854 .31527 L s [(3)] .47854 .29652 0 1 Mshowa .63011 .30902 m .63011 .31527 L s [(4)] .63011 .29652 0 1 Mshowa .78169 .30902 m .78169 .31527 L s [(5)] .78169 .29652 0 1 Mshowa .93327 .30902 m .93327 .31527 L s [(6)] .93327 .29652 0 1 Mshowa .125 Mabswid .05412 .30902 m .05412 .31277 L s .08444 .30902 m .08444 .31277 L s .11476 .30902 m .11476 .31277 L s .14507 .30902 m .14507 .31277 L s .2057 .30902 m .2057 .31277 L s .23602 .30902 m .23602 .31277 L s .26633 .30902 m .26633 .31277 L s .29665 .30902 m .29665 .31277 L s .35728 .30902 m .35728 .31277 L s .38759 .30902 m .38759 .31277 L s .41791 .30902 m .41791 .31277 L s .44822 .30902 m .44822 .31277 L s .50885 .30902 m .50885 .31277 L s .53917 .30902 m .53917 .31277 L s .56948 .30902 m .56948 .31277 L s .5998 .30902 m .5998 .31277 L s .66043 .30902 m .66043 .31277 L s .69074 .30902 m .69074 .31277 L s .72106 .30902 m .72106 .31277 L s .75138 .30902 m .75138 .31277 L s .81201 .30902 m .81201 .31277 L s .84232 .30902 m .84232 .31277 L s .87264 .30902 m .87264 .31277 L s .90295 .30902 m .90295 .31277 L s .96358 .30902 m .96358 .31277 L s .9939 .30902 m .9939 .31277 L s .25 Mabswid 0 .30902 m 1 .30902 L s .02381 .05003 m .03006 .05003 L s [(-0.04)] .01131 .05003 1 0 Mshowa .02381 .17952 m .03006 .17952 L s [(-0.02)] .01131 .17952 1 0 Mshowa .02381 .43851 m .03006 .43851 L s [(0.02)] .01131 .43851 1 0 Mshowa .02381 .568 m .03006 .568 L s [(0.04)] .01131 .568 1 0 Mshowa .125 Mabswid .02381 .0824 m .02756 .0824 L s .02381 .11478 m .02756 .11478 L s .02381 .14715 m .02756 .14715 L s .02381 .2119 m .02756 .2119 L s .02381 .24427 m .02756 .24427 L s .02381 .27664 m .02756 .27664 L s .02381 .34139 m .02756 .34139 L s .02381 .37376 m .02756 .37376 L s .02381 .40614 m .02756 .40614 L s .02381 .47088 m .02756 .47088 L s .02381 .50326 m .02756 .50326 L s .02381 .53563 m .02756 .53563 L s .02381 .01766 m .02756 .01766 L s .02381 .60038 m .02756 .60038 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .01472 m .02499 .01472 L .02605 .01475 L .02729 .01479 L .02846 .01485 L .03053 .015 L .03279 .01523 L .03527 .01556 L .0379 .01599 L .04262 .01698 L .04749 .0183 L .05205 .01981 L .06244 .02422 L .07305 .03011 L .08274 .03668 L .10458 .05552 L .14429 .10289 L .18248 .16177 L .22313 .23454 L .26226 .3097 L .30384 .3894 L .34391 .46058 L .38246 .51918 L .402 .54393 L .42346 .56659 L .44388 .58338 L .45301 .58929 L .46295 .59457 L .46838 .59694 L .4734 .5988 L .4781 .60026 L .4833 .60154 L .48553 .60198 L .48794 .60239 L .49002 .60268 L .4923 .60294 L .49473 .60314 L .49605 .60322 L .49728 .60327 L .49844 .6033 L .49949 .60332 L .50071 .60332 L .50186 .6033 L .50301 .60326 L .50425 .60321 L .50542 .60313 L .50648 .60305 L .5091 .60279 L .51158 .60246 L .5165 .60158 L Mistroke .52187 .60026 L .53144 .59701 L .54032 .59297 L .56088 .5799 L .5795 .56376 L .61962 .51633 L .65822 .45702 L .69928 .38356 L .73882 .30761 L .77684 .2346 L .81732 .1621 L .85628 .1021 L .87613 .07654 L .89769 .0533 L .91843 .03582 L .92832 .02927 L .93759 .02421 L .94643 .02037 L .95595 .01733 L .9611 .01617 L .96369 .01572 L .96652 .01531 L .96894 .01505 L .9703 .01494 L .97153 .01485 L .97268 .01479 L .97393 .01475 L .97511 .01472 L .97619 .01472 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgool0027oo`03003ooooo00Ko o`800>7oo`<0013oo`008Ooo00<00?ooool02?oo0P00g_oo00<00?ooool04Ooo000Qool00`00oooo o`0:ool00`00ooooo`3Iool2000Dool0027oo`03003ooooo00_oo`800=Soo`03003ooooo01Coo`00 8Ooo00<00?ooool03Ooo00<00?ooool0e?oo00<00?ooool05Ooo0008ool20004ool00`00ooooo`03 ool20005ool00`00ooooo`03ool00`00ooooo`0>ool00`00ooooo`3Bool00`00ooooo`0Fool000Oo o`04003ooooo0008ool01000ooooo`001?oo00<00?ooool00ooo00<00?ooool03ooo0P00dOoo00<0 0?ooool05ooo0007ool01000ooooo`002?oo00D00?ooool00?oo00D000Coo`8001;oo`03003ooooo 0?oo000Qool00`00 ooooo`0`ool00`00ooooo`2>ool00`00ooooo`0hool0027oo`03003ooooo037oo`03003ooooo08co o`03003ooooo03Woo`008Ooo00<00?ooool0<_oo00<00?ooool0Rooo00<00?ooool0>Ooo000Qool2 000cool00`00ooooo`2:ool00`00ooooo`0jool0027oo`03003ooooo03?oo`03003ooooo08Woo`03 003ooooo03[oo`008Ooo00<00?ooool0ooo000Qool00`00 ooooo`0dool00`00ooooo`27ool00`00ooooo`0kool0027oo`03003ooooo03Coo`03003ooooo08Ko o`03003ooooo03coo`008Ooo00<00?ooool0=Ooo00<00?ooool0QOoo00<00?ooool0??oo000Qool0 0`00ooooo`0eool00`00ooooo`24ool00`00ooooo`0mool0027oo`03003ooooo02;oo`@0013oo`03 003ooooo017oo`@002Coo`8002Koo`03003ooooo01ooo`04003oooooool3000Uool2000Bool0027o o`03003ooooo02Coo`03003ooooo00ooo`03003ooooo017oo`03003ooooo02Coo`04003ooooo000U ool00`00ooooo`0Nool00`00ooooo`05ool00`00ooooo`0Qool01000ooooo`004Ooo000Qool2000U ool00`00ooooo`0@ool00`00ooooo`0Aool00`00ooooo`0Vool00`00ooooo`0Pool5000Oool00`00 ooooo`05ool00`00ooooo`0Qool01000ooooo`004Ooo000Qool00`00ooooo`0Tool00`00ooooo`0@ ool00`00ooooo`0Bool00`00ooooo`0Sool2000Sool01000ooooo`007ooo00<00?ooool00ooo0`00 9?oo0`004_oo000Qool00`00ooooo`0Tool00`00ooooo`0Aool00`00ooooo`0Bool00`00ooooo`0T ool00`00ooooo`0Qool00`00ool0000Oool00`00ooooo`03ool00`00ooooo`0Tool00`00ooooo`0B ool0027oo`03003ooooo02;oo`<001?oo`03003ooooo00ooo`04003ooooo000Sool01000ooooo`00 9?oo0P007_oo00<00?ooool01?oo00<00?ooool09?oo00<00?ooool04_oo000Qool00`00ooooo`0T ool00`00ooooo`0Bool00`00ooooo`0?ool2000Uool2000Vool00`00ooooo`0Lool00`00ooooo`04 ool4000Tool3000Aool0027oo`03003ooooo03Woo`03003ooooo07coo`03003ooooo047oo`008Ooo 00<00?ooool0>_oo00<00?ooool0Nooo00<00?ooool0@Ooo000Qool00`00ooooo`0jool00`00oooo o`1jool00`00ooooo`12ool001_oool000H000008Ooo00<00?ooool01Ooo00<00?ooool01Ooo00<0 0?ooool01?oo00<00?ooool01Ooo00<00?ooool01Ooo00<00?ooool01Ooo00<00?ooool01Ooo00<0 0?ooool01Ooo00<00?ooool01Ooo00<00?ooool01Ooo00<00?ooool01?oo00<00?ooool01Ooo00<0 0?ooool01Ooo00<00?ooool01Ooo00<00?ooool01Ooo00<00?ooool01Ooo00<00?ooool01Ooo00<0 0?ooool01Ooo00<00?ooool01?oo00<00?ooool01Ooo00<00?ooool01Ooo00<00?ooool01Ooo00<0 0?ooool01Ooo00D00?ooooooo`0000?oo`03003ooooo00Goo`03003ooooo00Goo`03003ooooo00Go o`03003ooooo00Coo`03003ooooo00Goo`03003ooooo00Goo`03003ooooo00Goo`03003ooooo00Go o`40007oo`7oo`008Ooo00<00?ooool09?oo00<00?ooool05Ooo00<00?ooool03Ooo00<00?ooool0 9?oo00<00?ooool09?oo00<00?ooool06Ooo00<00?ooool02Ooo00<00?ooool09?oo00<00?ooool0 4?oo000Qool00`00ooooo`0mool00`00ooooo`1eool00`00ooooo`14ool0027oo`03003ooooo03go o`03003ooooo07Goo`03003ooooo04Coo`008Ooo00<00?ooool0?_oo00<00?ooool0Looo00<00?oo ool0AOoo000Qool00`00ooooo`0nool00`00ooooo`1cool00`00ooooo`15ool0027oo`03003ooooo 03ooo`03003ooooo077oo`03003ooooo04Koo`008Ooo0P00@?oo00<00?ooool0L?oo00<00?ooool0 Aooo000Qool00`00ooooo`10ool00`00ooooo`1_ool00`00ooooo`17ool0027oo`03003ooooo043o o`03003ooooo06koo`03003ooooo04Soo`008Ooo00<00?ooool0@Ooo00<00?ooool0KOoo00<00?oo ool0B?oo000Qool00`00ooooo`11ool00`00ooooo`1/ool00`00ooooo`19ool0027oo`03003ooooo 04;oo`03003ooooo06[oo`03003ooooo04[oo`008Ooo00<00?ooool0@_oo00<00?ooool0J_oo00<0 0?ooool0B_oo000Qool00`00ooooo`13ool00`00ooooo`1Xool00`00ooooo`1;ool0027oo`03003o oooo04?oo`03003ooooo06Soo`03003ooooo04_oo`008Ooo0P00AOoo00<00?ooool0I_oo00<00?oo ool0C?oo000Qool00`00ooooo`14ool00`00ooooo`1Vool00`00ooooo`1ool0027oo`03003o oooo04Ooo`03003ooooo067oo`03003ooooo04koo`008Ooo00<00?ooool0Aooo00<00?ooool0H?oo 00<00?ooool0Cooo000Qool00`00ooooo`18ool00`00ooooo`1Oool00`00ooooo`1?ool0027oo`80 04Woo`03003ooooo05koo`03003ooooo053oo`008Ooo00<00?ooool0BOoo00<00?ooool0GOoo00<0 0?ooool0D?oo000Qool00`00ooooo`19ool00`00ooooo`1Lool00`00ooooo`1Aool0027oo`03003o oooo04[oo`03003ooooo05_oo`03003ooooo057oo`008Ooo00<00?ooool0B_oo00<00?ooool0F_oo 00<00?ooool0D_oo000Qool00`00ooooo`1;ool00`00ooooo`1Iool00`00ooooo`1Bool0027oo`03 003ooooo04coo`03003ooooo05Ooo`03003ooooo05?oo`002?oo0P001?oo00<00?ooool00ooo0P00 0ooo10001?oo00<00?ooool0C?oo00<00?ooool0Eooo00<00?ooool0Dooo0007ool01000ooooo`00 2?oo00@00?ooool000;oo`03003ooooo00Goo`03003ooooo04goo`03003ooooo05Goo`03003ooooo 05Coo`001ooo00@00?ooool000Soo`04003ooooo0003ool00`00ooooo`04ool2001>ool00`00oooo o`1Eool00`00ooooo`1Dool000Ooo`04003ooooo0008ool01000ooooo`001?oo00<00?ooool00ooo 00<00?ooool0C_oo00<00?ooool0Dooo00<00?ooool0EOoo0007ool01000ooooo`002?oo00@00?oo ool000Goo`03003ooooo00;oo`03003ooooo04koo`03003ooooo05?oo`03003ooooo05Goo`001ooo 00@00?ooool000Soo`04003ooooo0002ool01000ooooo`001?oo00<00?ooool0Cooo00<00?ooool0 DOoo00<00?ooool0E_oo0008ool2000:ool20004ool20005ool00`00ooooo`1?ool00`00ooooo`1A ool00`00ooooo`1Fool0027oo`03003ooooo053oo`03003ooooo04ooo`03003ooooo05Ooo`008Ooo 00<00?ooool0DOoo00<00?ooool0COoo00<00?ooool0F?oo000Qool00`00ooooo`1Aool00`00oooo o`1=ool00`00ooooo`1Hool0027oo`8005?oo`03003ooooo04_oo`03003ooooo05Woo`008Ooo00<0 0?ooool0D_oo00<00?ooool0B_oo00<00?ooool0F_oo000Qool00`00ooooo`1Cool00`00ooooo`19 ool00`00ooooo`1Jool0027oo`03003ooooo05Coo`03003ooooo04Ooo`03003ooooo05_oo`008Ooo 00<00?ooool0E?oo00<00?ooool0A_oo00<00?ooool0G?oo000Qool00`00ooooo`1Eool00`00oooo o`15ool00`00ooooo`1Lool0027oo`03003ooooo05Koo`03003ooooo04?oo`03003ooooo05goo`00 8Ooo00<00?ooool0E_oo00<00?ooool0@_oo00<00?ooool0G_oo000Qool00`00ooooo`1Gool00`00 ooooo`11ool00`00ooooo`1Nool0027oo`8005Soo`03003ooooo043oo`03003ooooo05ooo`008Ooo 00<00?ooool0F?oo00<00?ooool0?_oo00<00?ooool0H?oo000Qool00`00ooooo`1Iool00`00oooo o`0mool00`00ooooo`1Pool0027oo`03003ooooo05Woo`03003ooooo03coo`03003ooooo067oo`00 8Ooo00<00?ooool0F_oo00<00?ooool0>_oo00<00?ooool0H_oo000Qool00`00ooooo`1Kool00`00 ooooo`0hool00`00ooooo`1Sool0027oo`03003ooooo05coo`03003ooooo03Koo`03003ooooo06Co o`008Ooo00<00?ooool0G?oo00<00?ooool0=Ooo00<00?ooool0IOoo000Qool2001Nool00`00oooo o`0cool00`00ooooo`1Vool0027oo`03003ooooo05koo`03003ooooo03;oo`03003ooooo06Koo`00 8Ooo00<00?ooool0Gooo00<00?ooool0"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-0.843912, -0.0525664, \ 0.0253805, 0.000594175}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell["\<\ Next we compute the actual value of the function by taking into \ account the jumps. Again, we compute the set of singularities. The function Omega is defined differently on three \ intervals. \ \>", "Text"], Cell[BoxData[ \(Omega[phi_]\ := \ \((s\ = \ Mod[phi, \ period]; Which[s > alph\ && \ s < \ bdry, \ \(-Sin[def1[s]]\)* Sin[o*t]\ /\((R*\((l + 1)\))\), \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ s\ > \ bdry, \ \(-Sin[def2[s]]\)\ * Sin[o*t]/ R, \ \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ True, \ \ \(-Sin[s]\)* Sin[o*t]/R])\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(gamma[Psi_, \ DD_]\ := \ \((n = 0; \ sing = \ {t, 0}; \[IndentingNewLine]period = 2*Pi\ + \ l/\((1 + l)\)\ *\ \((alph\ - bet)\); \[IndentingNewLine]bdry\ = \ \((bet\ + \ l*alph)\)/\((1 + l)\); \[IndentingNewLine]alphmod\ = \ \((alph\ - \ Psi)\)/ DD; \[IndentingNewLine]\ \(bdrymod\ = \ \((bdry\ - Psi)\)/ DD;\)\[IndentingNewLine]\ \ \ \ \ \ \ \ \ While[\((n* period/DD + alphmod)\) < period/DD, \ \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ If[\((n*period/DD + alphmod)\) > \ 0\ , \ \ sing = Append[sing, n*period/DD + alphmod]]; \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ If\ [\((n*period/DD + bdrymod)\) > \ 0\ && \ \((n*period/DD + bdrymod)\)\ < \ period/DD, \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ sing = Append[sing, n*period/DD + bdrymod]\[IndentingNewLine]\ \ \ \ ]; \ \ \[IndentingNewLine]\ \ n\ = \ n + 1\[IndentingNewLine]]\[IndentingNewLine]\(sing = Append[sing, \ period/DD]\); \ \[IndentingNewLine]\ \ \ \((1/ period)\)* NIntegrate[Omega[DD*t + Psi], Evaluate[sing]]\ )\)\)], "Input"], Cell[BoxData[ \(General::"spell1" \(\(:\)\(\ \)\) "Possible spelling error: new symbol name \"\!\(gamma\)\" is similar to \ existing symbol \"\!\(Gamma\)\"."\)], "Message"] }, Open ]], Cell["\<\ Now we plot the exact solution in red, and the approximate solution \ from above in black and compare the two.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(s1 = \ Plot[gamma[t, \ 1], \ {t, \ 0, \ period}, PlotStyle \[Rule] {RGBColor[1, 0, 0]}]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.156542 0.308808 6.41602 [ [.18035 .29631 -3 -9 ] [.18035 .29631 3 0 ] [.33689 .29631 -3 -9 ] [.33689 .29631 3 0 ] [.49344 .29631 -3 -9 ] [.49344 .29631 3 0 ] [.64998 .29631 -3 -9 ] [.64998 .29631 3 0 ] [.80652 .29631 -3 -9 ] [.80652 .29631 3 0 ] [.96306 .29631 -3 -9 ] [.96306 .29631 3 0 ] [.01131 .05217 -30 -4.5 ] [.01131 .05217 0 4.5 ] [.01131 .18049 -30 -4.5 ] [.01131 .18049 0 4.5 ] [.01131 .43713 -24 -4.5 ] [.01131 .43713 0 4.5 ] [.01131 .56545 -24 -4.5 ] [.01131 .56545 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .18035 .30881 m .18035 .31506 L s [(1)] .18035 .29631 0 1 Mshowa .33689 .30881 m .33689 .31506 L s [(2)] .33689 .29631 0 1 Mshowa .49344 .30881 m .49344 .31506 L s [(3)] .49344 .29631 0 1 Mshowa .64998 .30881 m .64998 .31506 L s [(4)] .64998 .29631 0 1 Mshowa .80652 .30881 m .80652 .31506 L s [(5)] .80652 .29631 0 1 Mshowa .96306 .30881 m .96306 .31506 L s [(6)] .96306 .29631 0 1 Mshowa .125 Mabswid .05512 .30881 m .05512 .31256 L s .08643 .30881 m .08643 .31256 L s .11774 .30881 m .11774 .31256 L s .14904 .30881 m .14904 .31256 L s .21166 .30881 m .21166 .31256 L s .24297 .30881 m .24297 .31256 L s .27428 .30881 m .27428 .31256 L s .30559 .30881 m .30559 .31256 L s .3682 .30881 m .3682 .31256 L s .39951 .30881 m .39951 .31256 L s .43082 .30881 m .43082 .31256 L s .46213 .30881 m .46213 .31256 L s .52475 .30881 m .52475 .31256 L s .55605 .30881 m .55605 .31256 L s .58736 .30881 m .58736 .31256 L s .61867 .30881 m .61867 .31256 L s .68129 .30881 m .68129 .31256 L s .7126 .30881 m .7126 .31256 L s .7439 .30881 m .7439 .31256 L s .77521 .30881 m .77521 .31256 L s .83783 .30881 m .83783 .31256 L s .86914 .30881 m .86914 .31256 L s .90045 .30881 m .90045 .31256 L s .93176 .30881 m .93176 .31256 L s .99437 .30881 m .99437 .31256 L s .25 Mabswid 0 .30881 m 1 .30881 L s .02381 .05217 m .03006 .05217 L s [(-0.04)] .01131 .05217 1 0 Mshowa .02381 .18049 m .03006 .18049 L s [(-0.02)] .01131 .18049 1 0 Mshowa .02381 .43713 m .03006 .43713 L s [(0.02)] .01131 .43713 1 0 Mshowa .02381 .56545 m .03006 .56545 L s [(0.04)] .01131 .56545 1 0 Mshowa .125 Mabswid .02381 .08425 m .02756 .08425 L s .02381 .11633 m .02756 .11633 L s .02381 .14841 m .02756 .14841 L s .02381 .21257 m .02756 .21257 L s .02381 .24465 m .02756 .24465 L s .02381 .27673 m .02756 .27673 L s .02381 .34089 m .02756 .34089 L s .02381 .37297 m .02756 .37297 L s .02381 .40505 m .02756 .40505 L s .02381 .46921 m .02756 .46921 L s .02381 .50129 m .02756 .50129 L s .02381 .53337 m .02756 .53337 L s .02381 .02009 m .02756 .02009 L s .02381 .59753 m .02756 .59753 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath 1 0 0 r .5 Mabswid .02381 .02008 m .03279 .02389 L .04262 .02921 L .06244 .04349 L .08426 .06443 L .10458 .08849 L .14357 .1446 L .18502 .21768 L .22495 .29433 L .26336 .36889 L .30423 .44371 L .34358 .50648 L .38141 .55431 L .40082 .57307 L .4217 .58842 L .43181 .59395 L .43715 .59637 L .44284 .59855 L .4483 .60027 L .45325 .60149 L .45565 .60197 L .45823 .60241 L .46069 .60274 L .46293 .60298 L .46406 .60308 L .4653 .60317 L .46661 .60324 L .46784 .60328 L .469 .60331 L .47023 .60332 L .47127 .60331 L .47243 .60329 L .47309 .60326 L .47378 .60324 L .47502 .60317 L .47635 .60307 L .47781 .60295 L .48043 .60265 L .48287 .60229 L .4882 .60124 L .49305 .59998 L .50393 .59606 L .51391 .59117 L .52311 .58558 L .54391 .56924 L .58331 .52524 L .6212 .46924 L .66154 .39881 L .70037 .32503 L .74164 .24555 L Mistroke .7814 .17334 L .81965 .11255 L .84101 .08377 L .86035 .06154 L .88077 .04242 L .89953 .02909 L .90891 .02401 L .91881 .01983 L .92361 .01825 L .92875 .01688 L .9317 .01624 L .93439 .01576 L .93689 .01539 L .93965 .01507 L .94074 .01498 L .94193 .01489 L .94295 .01483 L .94406 .01477 L .94526 .01474 L .94651 .01472 L .94767 .01472 L .94875 .01473 L .94985 .01476 L .95088 .0148 L .95181 .01485 L .95282 .01492 L .95508 .01511 L .95716 .01535 L .96157 .01604 L .96641 .01708 L .97147 .01848 L .97619 .02008 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgool00oP0ooooo`33ool00oP0 ooooo`0Uool0027oo`03003ooooo00ooo`03n03ooooo0<7oo`03n03ooooo02Koo`008Ooo00<00?oo ool03ooo00?h0?ooool0`?oo00?h0?ooool09ooo000Qool00`00ooooo`0@ool00oP0ooooo`2nool0 0oP0ooooo`0Xool0027oo`8001;oo`03n03ooooo0;coo`03n03ooooo02Woo`008Ooo00<00?ooool0 4_oo00?h0?ooool0^ooo00?h0?ooool0:Ooo000Qool00`00ooooo`0Cool00oP0ooooo`2iool00oP0 ooooo`0Zool0027oo`03003ooooo01?oo`03n03ooooo0;Woo`03n03ooooo02[oo`008Ooo00<00?oo ool05?oo00?h0?ooool0]ooo00?h0?ooool0:ooo000Qool00`00ooooo`0Eool00oP0ooooo`2eool0 0oP0ooooo`0/ool0027oo`03003ooooo01Koo`03n03ooooo0;Coo`03n03ooooo02coo`008Ooo00<0 0?ooool05_oo00?h0?ooool0/ooo00?h0?ooool0;Ooo000Qool2000Hool00oP0ooooo`2aool00oP0 ooooo`0^ool0027oo`03003ooooo01Soo`03n03ooooo0;3oo`03n03ooooo02koo`008Ooo00<00?oo ool06?oo00?h0?ooool0[ooo00?h0?ooool0;ooo000Qool00`00ooooo`0Iool00oP0ooooo`2^ool0 0oP0ooooo`0_ool0027oo`03003ooooo01[oo`03n03ooooo0:coo`03n03ooooo033oo`008Ooo00<0 0?ooool06ooo00?h0?ooool0Z_oo00?h0?ooool0?oo0007ool01000ooooo`002?oo00@00?ooool000?oo`03003ooooo00Coo`8002?oo`03n03o oooo09coo`03n03ooooo03Soo`0000?oo`0000000P000_oo00@00?ooool000Soo`04003ooooo0004 ool00`00ooooo`03ool00`00ooooo`0Rool00oP0ooooo`2Kool00oP0ooooo`0iool000Ooo`04003o oooo0008ool01000ooooo`001Ooo00<00?ooool00_oo00<00?ooool08ooo00?h0?ooool0V_oo00?h 0?ooool0>Ooo0007ool01000ooooo`002?oo00@00?ooool000;oo`04003ooooo0004ool00`00oooo o`0Tool00oP0ooooo`2Hool00oP0ooooo`0jool000Soo`8000[oo`8000Coo`8000Goo`03003ooooo 02Coo`03n03ooooo09Soo`03n03ooooo03[oo`008Ooo00<00?ooool09Ooo00?h0?ooool0U_oo00?h 0?ooool0>ooo000Qool00`00ooooo`0Uool00oP0ooooo`2Eool00oP0ooooo`0lool0027oo`03003o oooo02Koo`03n03ooooo09Coo`03n03ooooo03coo`008Ooo0P009ooo00?h0?ooool0Tooo00?h0?oo ool0?Ooo000Qool00`00ooooo`0Wool00oP0ooooo`2Bool00oP0ooooo`0mool0027oo`03003ooooo 02Ooo`03n03ooooo097oo`03n03ooooo03koo`008Ooo00<00?ooool0:?oo00?h0?ooool0Sooo00?h 0?ooool0?ooo000Qool00`00ooooo`0Xool00oP0ooooo`2?ool00oP0ooooo`0oool0027oo`03003o oooo02Woo`03n03ooooo08goo`03n03ooooo043oo`008Ooo00<00?ooool0:Ooo00?h0?ooool0SOoo 00?h0?ooool0@?oo000Qool00`00ooooo`0Zool00oP0ooooo`2;ool00oP0ooooo`11ool0027oo`80 02_oo`03n03ooooo08_oo`03n03ooooo047oo`008Ooo00<00?ooool0:ooo00?h0?ooool0ROoo00?h 0?ooool0@_oo000Qool00`00ooooo`0[ool00oP0ooooo`29ool00oP0ooooo`12ool0027oo`03003o oooo02coo`03n03ooooo08Ooo`03n03ooooo04?oo`008Ooo00<00?ooool0;?oo00?h0?ooool0Qooo 00?h0?ooool0@ooo000Qool00`00ooooo`0]ool00oP0ooooo`25ool00oP0ooooo`14ool0027oo`03 003ooooo02goo`03n03ooooo08Goo`03n03ooooo04Coo`008Ooo00<00?ooool08ooo10001ooo00?h 0?ooool06ooo10009_oo0P00:?oo00<00?ooool04Ooo00?h0?ooool03ooo0`009ooo0P002_oo000Q ool00`00ooooo`0Uool00`00ooooo`06ool00oP0ooooo`0Kool00`00ooooo`0Vool01000ooooo`00 9ooo00<00?ooool04Ooo00?h0?ooool04_oo00<00?ooool08ooo00@00?ooool000Woo`008Ooo0P00 9_oo00<00?ooool01ooo00?h0?ooool06ooo00<00?ooool0:?oo00<00?ooool08_oo1@004Ooo00?h 0?ooool04ooo00<00?ooool08ooo00@00?ooool000Woo`008Ooo00<00?ooool09Ooo00<00?ooool0 1ooo00?h0?ooool07?oo00<00?ooool09Ooo0P009Ooo00@00?ooool001;oo`03n03ooooo013oo`<0 02Koo`<000[oo`008Ooo00<00?ooool09Ooo00<00?ooool02?oo00?h0?ooool07?oo00<00?ooool0 9_oo00<00?ooool08ooo00<00?oo00004Ooo00?h0?ooool04Ooo00<00?ooool09_oo00<00?ooool0 2_oo000Qool00`00ooooo`0Sool3000:ool00oP0ooooo`0Iool01000ooooo`009Ooo00@00?ooool0 02Koo`80017oo`03n03ooooo017oo`03003ooooo02Koo`03003ooooo00[oo`008Ooo00<00?ooool0 9Ooo00<00?ooool02Ooo00?h0?ooool06Ooo0P009ooo0P00:?oo00<00?ooool03_oo00?h0?ooool0 4_oo10009_oo0`002Ooo000Qool00`00ooooo`0aool00oP0ooooo`1mool00oP0ooooo`18ool0027o o`03003ooooo03;oo`03n03ooooo07_oo`03n03ooooo04Woo`008Ooo00<00?ooool0<_oo00?h0?oo ool0Nooo00?h0?ooool0BOoo000Kooll00000oP00000001i00000oP00000001:0000027oo`03003o oooo00Goo`03003ooooo00Goo`03003ooooo00Goo`03003ooooo00Goo`03003ooooo00Goo`03003o oooo00Koo`03003ooooo00;oo`04n03ooooo0007ool00`00ooooo`05ool00`00ooooo`05ool00`00 ooooo`05ool00`00ooooo`05ool00`00ooooo`06ool00`00ooooo`05ool00`00ooooo`05ool00`00 ooooo`05ool00`00ooooo`05ool00`00ooooo`05ool00`00ooooo`05ool00`00ooooo`06ool00`00 ooooo`05ool00`00ooooo`04ool00oP0003oo`06ool00`00ooooo`05ool00`00ooooo`05ool00`00 ooooo`05ool00`00ooooo`05ool00`00ooooo`06ool00`00ooooo`05ool00`00ooooo`05ool00`00 ooooo`05ool10001ool1ool0027oo`03003ooooo02Goo`03003ooooo00coo`03n03ooooo01Ooo`03 003ooooo02Koo`03003ooooo02Koo`03003ooooo00_oo`03n03ooooo01Ooo`03003ooooo02Koo`03 003ooooo00Soo`008Ooo00<00?ooool0=?oo00?h0?ooool0Mooo00?h0?ooool0Booo000Qool00`00 ooooo`0eool00oP0ooooo`1eool00oP0ooooo`1ool0027oo`8003Soo`03n03ooooo077oo`03 n03ooooo04koo`008Ooo00<00?ooool0=ooo00?h0?ooool0L?oo00?h0?ooool0Cooo000Qool00`00 ooooo`0hool00oP0ooooo`1_ool00oP0ooooo`1?ool0027oo`03003ooooo03Soo`03n03ooooo06ko o`03n03ooooo053oo`008Ooo00<00?ooool0>Ooo00?h0?ooool0KOoo00?h0?ooool0D?oo000Qool0 0`00ooooo`0iool00oP0ooooo`1/ool00oP0ooooo`1Aool0027oo`03003ooooo03[oo`03n03ooooo 06_oo`03n03ooooo057oo`008Ooo00<00?ooool0>_oo00?h0?ooool0J_oo00?h0?ooool0D_oo000Q ool00`00ooooo`0kool00oP0ooooo`1Yool00oP0ooooo`1Bool0027oo`8003goo`03n03ooooo06Oo o`03n03ooooo05?oo`008Ooo00<00?ooool0??oo00?h0?ooool0Iooo00?h0?ooool0Dooo000Qool0 0`00ooooo`0mool00oP0ooooo`1Uool00oP0ooooo`1Dool0027oo`03003ooooo03goo`03n03ooooo 06Goo`03n03ooooo05Coo`008Ooo00<00?ooool0?_oo00?h0?ooool0Hooo00?h0?ooool0EOoo000Q ool00`00ooooo`0nool00oP0ooooo`1Sool00oP0ooooo`1Eool0027oo`03003ooooo03ooo`03n03o oooo067oo`03n03ooooo05Koo`008Ooo00<00?ooool0@?oo00?h0?ooool0Gooo00?h0?ooool0Eooo 000Qool20011ool00oP0ooooo`1Oool00oP0ooooo`1Gool0027oo`03003ooooo047oo`03n03ooooo 05goo`03n03ooooo05Soo`008Ooo00<00?ooool0@Ooo00?h0?ooool0GOoo00?h0?ooool0F?oo000Q ool00`00ooooo`12ool00oP0ooooo`1Kool00oP0ooooo`1Iool0027oo`03003ooooo04?oo`03n03o oooo05[oo`03n03ooooo05Woo`008Ooo00<00?ooool0@ooo00?h0?ooool0FOoo00?h0?ooool0F_oo 0008ool20004ool00`00ooooo`03ool20003ool40004ool00`00ooooo`14ool00oP0ooooo`1Gool0 0oP0ooooo`1Kool000Ooo`04003ooooo0008ool01000ooooo`000_oo00<00?ooool01Ooo00<00?oo ool0A?oo00?h0?ooool0Eooo00?h0?ooool0Fooo0007ool01000ooooo`002?oo00@00?ooool000?o o`03003ooooo00Coo`8004Koo`03n03ooooo05Goo`03n03ooooo05coo`001ooo00@00?ooool000So o`04003ooooo0004ool00`00ooooo`03ool00`00ooooo`15ool00oP0ooooo`1Eool00oP0ooooo`1L ool000Ooo`04003ooooo0008ool01000ooooo`001Ooo00<00?ooool00_oo00<00?ooool0A_oo00?h 0?ooool0Dooo00?h0?ooool0GOoo0007ool01000ooooo`002?oo00@00?ooool000;oo`04003ooooo 0004ool00`00ooooo`17ool00oP0ooooo`1Aool00oP0ooooo`1Nool000Soo`8000[oo`8000Coo`80 00Goo`03003ooooo04Ooo`03n03ooooo057oo`03n03ooooo05koo`008Ooo00<00?ooool0B?oo00?h 0?ooool0Cooo00?h0?ooool0Gooo000Qool00`00ooooo`18ool00oP0ooooo`1?ool00oP0ooooo`1O ool0027oo`03003ooooo04Woo`03n03ooooo04goo`03n03ooooo063oo`008Ooo00<00?ooool0B_oo 00?h0?ooool0C?oo00?h0?ooool0H?oo000Qool2001;ool00oP0ooooo`1;ool00oP0ooooo`1Qool0 027oo`03003ooooo04_oo`03n03ooooo04Woo`03n03ooooo06;oo`008Ooo00<00?ooool0C?oo00?h 0?ooool0B?oo00?h0?ooool0H_oo000Qool00`00ooooo`1ool00oP0ooooo`13ool00oP0oooo o`1Uool0027oo`03003ooooo04ooo`03n03ooooo047oo`03n03ooooo06Koo`008Ooo0P00D?oo00?h 0?ooool0@?oo00?h0?ooool0Iooo000Qool00`00ooooo`1@ool00oP0ooooo`0oool00oP0ooooo`1W ool0027oo`03003ooooo057oo`03n03ooooo03goo`03n03ooooo06Soo`008Ooo00<00?ooool0D_oo 00?h0?ooool0>ooo00?h0?ooool0JOoo000Qool00`00ooooo`1Bool00oP0ooooo`0jool00oP0oooo o`1Zool0027oo`03003ooooo05?oo`03n03ooooo03Woo`03n03ooooo06[oo`008Ooo00<00?ooool0 E?oo00?h0?ooool0=ooo00?h0?ooool0Jooo000Qool00`00ooooo`1Eool00oP0ooooo`0eool00oP0 ooooo`1/ool0027oo`8005Koo`03n03ooooo03Coo`03n03ooooo06goo`008Ooo00<00?ooool0E_oo 00?h0?ooool0"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-0.817141, -0.0530141, \ 0.0245754, 0.000599606}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Show[s1, s2]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.151576 0.308808 6.41602 [ [.17539 .29631 -3 -9 ] [.17539 .29631 3 0 ] [.32696 .29631 -3 -9 ] [.32696 .29631 3 0 ] [.47854 .29631 -3 -9 ] [.47854 .29631 3 0 ] [.63011 .29631 -3 -9 ] [.63011 .29631 3 0 ] [.78169 .29631 -3 -9 ] [.78169 .29631 3 0 ] [.93327 .29631 -3 -9 ] [.93327 .29631 3 0 ] [.01131 .05217 -30 -4.5 ] [.01131 .05217 0 4.5 ] [.01131 .18049 -30 -4.5 ] [.01131 .18049 0 4.5 ] [.01131 .43713 -24 -4.5 ] [.01131 .43713 0 4.5 ] [.01131 .56545 -24 -4.5 ] [.01131 .56545 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .17539 .30881 m .17539 .31506 L s [(1)] .17539 .29631 0 1 Mshowa .32696 .30881 m .32696 .31506 L s [(2)] .32696 .29631 0 1 Mshowa .47854 .30881 m .47854 .31506 L s [(3)] .47854 .29631 0 1 Mshowa .63011 .30881 m .63011 .31506 L s [(4)] .63011 .29631 0 1 Mshowa .78169 .30881 m .78169 .31506 L s [(5)] .78169 .29631 0 1 Mshowa .93327 .30881 m .93327 .31506 L s [(6)] .93327 .29631 0 1 Mshowa .125 Mabswid .05412 .30881 m .05412 .31256 L s .08444 .30881 m .08444 .31256 L s .11476 .30881 m .11476 .31256 L s .14507 .30881 m .14507 .31256 L s .2057 .30881 m .2057 .31256 L s .23602 .30881 m .23602 .31256 L s .26633 .30881 m .26633 .31256 L s .29665 .30881 m .29665 .31256 L s .35728 .30881 m .35728 .31256 L s .38759 .30881 m .38759 .31256 L s .41791 .30881 m .41791 .31256 L s .44822 .30881 m .44822 .31256 L s .50885 .30881 m .50885 .31256 L s .53917 .30881 m .53917 .31256 L s .56948 .30881 m .56948 .31256 L s .5998 .30881 m .5998 .31256 L s .66043 .30881 m .66043 .31256 L s .69074 .30881 m .69074 .31256 L s .72106 .30881 m .72106 .31256 L s .75138 .30881 m .75138 .31256 L s .81201 .30881 m .81201 .31256 L s .84232 .30881 m .84232 .31256 L s .87264 .30881 m .87264 .31256 L s .90295 .30881 m .90295 .31256 L s .96358 .30881 m .96358 .31256 L s .9939 .30881 m .9939 .31256 L s .25 Mabswid 0 .30881 m 1 .30881 L s .02381 .05217 m .03006 .05217 L s [(-0.04)] .01131 .05217 1 0 Mshowa .02381 .18049 m .03006 .18049 L s [(-0.02)] .01131 .18049 1 0 Mshowa .02381 .43713 m .03006 .43713 L s [(0.02)] .01131 .43713 1 0 Mshowa .02381 .56545 m .03006 .56545 L s [(0.04)] .01131 .56545 1 0 Mshowa .125 Mabswid .02381 .08425 m .02756 .08425 L s .02381 .11633 m .02756 .11633 L s .02381 .14841 m .02756 .14841 L s .02381 .21257 m .02756 .21257 L s .02381 .24465 m .02756 .24465 L s .02381 .27673 m .02756 .27673 L s .02381 .34089 m .02756 .34089 L s .02381 .37297 m .02756 .37297 L s .02381 .40505 m .02756 .40505 L s .02381 .46921 m .02756 .46921 L s .02381 .50129 m .02756 .50129 L s .02381 .53337 m .02756 .53337 L s .02381 .02009 m .02756 .02009 L s .02381 .59753 m .02756 .59753 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath 1 0 0 r .5 Mabswid .02381 .02008 m .0325 .02389 L .04202 .02921 L .06122 .04349 L .08234 .06443 L .10202 .08849 L .13977 .1446 L .1799 .21768 L .21857 .29433 L .25576 .36889 L .29533 .44371 L .33343 .50648 L .37007 .55431 L .38886 .57307 L .40908 .58842 L .41886 .59395 L .42403 .59637 L .42954 .59855 L .43483 .60027 L .43963 .60149 L .44195 .60197 L .44445 .60241 L .44683 .60274 L .449 .60298 L .4501 .60308 L .45129 .60317 L .45256 .60324 L .45376 .60328 L .45487 .60331 L .45606 .60332 L .45708 .60331 L .4582 .60329 L .45884 .60326 L .45951 .60324 L .46071 .60317 L .462 .60307 L .46341 .60295 L .46594 .60265 L .4683 .60229 L .47347 .60124 L .47816 .59998 L .4887 .59606 L .49836 .59117 L .50727 .58558 L .52741 .56924 L .56556 .52524 L .60225 .46924 L .64131 .39881 L .6789 .32503 L .71887 .24555 L Mistroke .75737 .17334 L .7944 .11255 L .81508 .08377 L .83381 .06154 L .85358 .04242 L .87175 .02909 L .88083 .02401 L .89042 .01983 L .89507 .01825 L .90004 .01688 L .9029 .01624 L .9055 .01576 L .90792 .01539 L .91059 .01507 L .91165 .01498 L .9128 .01489 L .91379 .01483 L .91487 .01477 L .91602 .01474 L .91724 .01472 L .91836 .01472 L .91941 .01473 L .92047 .01476 L .92147 .0148 L .92237 .01485 L .92335 .01492 L .92554 .01511 L .92755 .01535 L .93182 .01604 L .93651 .01708 L .9414 .01848 L .94598 .02008 L Mfstroke 0 g .02381 .01717 m .02499 .01718 L .02605 .0172 L .02729 .01725 L .02846 .01731 L .03053 .01746 L .03279 .01768 L .03527 .018 L .0379 .01843 L .04262 .01941 L .04749 .02072 L .05205 .02222 L .06244 .02659 L .07305 .03242 L .08274 .03894 L .10458 .05761 L .14429 .10455 L .18248 .16289 L .22313 .23501 L .26226 .30949 L .30384 .38847 L .34391 .459 L .38246 .51706 L .402 .54159 L .42346 .56405 L .44388 .58068 L .45301 .58655 L .46295 .59178 L .46838 .59412 L .4734 .59597 L .4781 .59741 L .4833 .59868 L .48553 .59912 L .48794 .59952 L .49002 .59981 L .4923 .60007 L .49473 .60027 L .49605 .60035 L .49728 .6004 L .49844 .60043 L .49949 .60044 L .50071 .60044 L .50186 .60042 L .50301 .60039 L .50425 .60033 L .50542 .60026 L .50648 .60018 L .5091 .59992 L .51158 .5996 L .5165 .59872 L Mistroke .52187 .59742 L .53144 .59419 L .54032 .59019 L .56088 .57723 L .5795 .56124 L .61962 .51424 L .65822 .45547 L .69928 .38268 L .73882 .30741 L .77684 .23506 L .81732 .16322 L .85628 .10377 L .87613 .07844 L .89769 .05541 L .91843 .03809 L .92832 .03159 L .93759 .02658 L .94643 .02277 L .95595 .01977 L .9611 .01861 L .96369 .01816 L .96652 .01776 L .96894 .0175 L .9703 .01739 L .97153 .01731 L .97268 .01725 L .97393 .0172 L .97511 .01718 L .97619 .01717 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgool3000@ool0027oo`03003ooooo00;oo`03n03ooooo00Coo`800Ooo000Qool0 0`00ooooo`0Xool00oP0ooooo`07ool00`00ooooo`1mool00oP0ooooo`0;ool00`00ooooo`0iool0 027oo`8002Woo`03n03ooooo00Ooo`03003ooooo07goo`03n03ooooo00[oo`03003ooooo03[oo`00 8Ooo00<00?ooool0:Ooo00?h0?ooool01ooo00<00?ooool0Nooo00?h0?ooool02ooo00<00?ooool0 >_oo000Qool00`00ooooo`0Yool00oP0ooooo`07ool00`00ooooo`1kool00oP0ooooo`0:ool00`00 ooooo`0kool0027oo`03003ooooo02[oo`03n03ooooo00Ooo`03003ooooo07Woo`03n03ooooo00_o o`03003ooooo03_oo`008Ooo00<00?ooool0:_oo00?h0?ooool01ooo00<00?ooool0NOoo00?h0?oo ool02_oo00<00?ooool0??oo000Qool00`00ooooo`0[ool00oP0ooooo`07ool00`00ooooo`1gool0 0oP0ooooo`0;ool00`00ooooo`0lool0027oo`03003ooooo02_oo`03n03ooooo00Ooo`03003ooooo 07Ooo`03n03ooooo00[oo`03003ooooo03goo`008Ooo00<00?ooool08_oo10001_oo00?h0?ooool0 1ooo00<00?ooool04Ooo10009?oo0P009_oo00<00?ooool04Ooo00?h0?ooool02ooo00@00?oooooo o`<002Goo`8001;oo`008Ooo00<00?ooool09?oo00<00?ooool01Ooo00?h0?ooool01ooo00<00?oo ool04Ooo00<00?ooool09?oo00@00?ooool002Goo`03003ooooo017oo`03n03ooooo00[oo`03003o oooo00Goo`03003ooooo027oo`04003ooooo000Aool0027oo`8002Goo`03003ooooo00Koo`03n03o oooo00Ooo`03003ooooo017oo`03003ooooo02Koo`03003ooooo023oo`D0017oo`03n03ooooo00_o o`03003ooooo00Goo`03003ooooo027oo`04003ooooo000Aool0027oo`03003ooooo02Coo`03003o oooo00Koo`03n03ooooo00Ooo`03003ooooo01;oo`03003ooooo02?oo`8002?oo`04003ooooo000B ool00oP0ooooo`0:ool00`00ooooo`03ool3000Tool3000Bool0027oo`03003ooooo02Coo`03003o oooo00Ooo`03n03ooooo00Ooo`03003ooooo01;oo`03003ooooo02Coo`03003ooooo027oo`03003o o`00017oo`03n03ooooo00_oo`03003ooooo00?oo`03003ooooo02Coo`03003ooooo01;oo`008Ooo 00<00?ooool08_oo0`002Ooo00?h0?ooool01ooo00<00?ooool03ooo00@00?ooool002?oo`04003o oooo000Tool2000Aool00oP0ooooo`0:ool00`00ooooo`04ool00`00ooooo`0Tool00`00ooooo`0B ool0027oo`03003ooooo02Coo`03003ooooo00Soo`03n03ooooo00Ooo`03003ooooo00ooo`8002Go o`8002Koo`03003ooooo00koo`03n03ooooo00_oo`03003ooooo00Coo`@002Coo`<0017oo`008Ooo 00<00?ooool0;ooo00?h0?ooool01ooo00<00?ooool0Kooo00?h0?ooool02_oo00<00?ooool0@Ooo 000Qool00`00ooooo`0`ool00oP0ooooo`07ool00`00ooooo`1]ool00oP0ooooo`0;ool00`00oooo o`11ool0027oo`03003ooooo033oo`03n03ooooo00Ooo`03003ooooo06goo`03n03ooooo00[oo`03 003ooooo04;oo`006ooo>P0000?h00000000M@0000?h00000000D000000Qool00`00ooooo`05ool0 0`00ooooo`05ool00`00ooooo`04ool00`00ooooo`05ool00`00ooooo`05ool00`00ooooo`05ool0 0`00ooooo`02ool01?P0ooooo`001ooo00<00?ooool01Ooo00<00?ooool01Ooo00<00?ooool01?oo 00<00?ooool01Ooo00<00?ooool01Ooo00<00?ooool01Ooo00<00?ooool01Ooo00<00?ooool01Ooo 00<00?ooool01Ooo00<00?ooool01Ooo00<00?ooool01?oo00<00?ooool01Ooo00<00?ooool01Ooo 00<00?ooool01?oo00?h0000ool01_oo00D00?ooooooo`0000?oo`03003ooooo00Goo`03003ooooo 00Goo`03003ooooo00Goo`03003ooooo00Coo`03003ooooo00Goo`03003ooooo00Goo`03003ooooo 00Goo`03003ooooo00Goo`40007oo`7oo`008Ooo00<00?ooool09?oo00<00?ooool02ooo00?h0?oo ool01ooo00<00?ooool03Ooo00<00?ooool09?oo00<00?ooool09?oo00<00?ooool02ooo00?h0?oo ool02ooo00<00?ooool02Ooo00<00?ooool09?oo00<00?ooool04?oo000Qool00`00ooooo`0bool0 0oP0ooooo`08ool00`00ooooo`1Xool00oP0ooooo`0:ool00`00ooooo`14ool0027oo`03003ooooo 03?oo`03n03ooooo00Ooo`03003ooooo06Ooo`03n03ooooo00_oo`03003ooooo04Coo`008Ooo00<0 0?ooool0?oo00?h0?ooool01ooo 00<00?ooool0GOoo00?h0?ooool02_oo00<00?ooool0B_oo000Qool00`00ooooo`0hool00oP0oooo o`08ool00`00ooooo`1Kool00oP0ooooo`0:ool00`00ooooo`1;ool0027oo`03003ooooo03Woo`03 n03ooooo00Ooo`03003ooooo05_oo`03n03ooooo00[oo`03003ooooo04_oo`008Ooo0P00>ooo00?h 0?ooool01ooo00<00?ooool0FOoo00?h0?ooool02_oo00<00?ooool0C?oo000Qool00`00ooooo`0j ool00oP0ooooo`07ool00`00ooooo`1Iool00oP0ooooo`0:ool00`00ooooo`1ooo00?h0?ooool01ooo00<00?ooool0Eooo00?h0?ooool02Ooo00<00?ooool0C_oo 000Qool00`00ooooo`0lool00oP0ooooo`07ool00`00ooooo`1Eool00oP0ooooo`0:ool00`00oooo o`1>ool0027oo`03003ooooo03coo`03n03ooooo00Soo`03003ooooo05Coo`03n03ooooo00Woo`03 003ooooo04ooo`008Ooo00<00?ooool0?Ooo00?h0?ooool01ooo00<00?ooool0Dooo00?h0?ooool0 2_oo00<00?ooool0Cooo000Qool00`00ooooo`0mool00oP0ooooo`08ool00`00ooooo`1Aool00oP0 ooooo`0:ool00`00ooooo`1@ool0027oo`8003ooo`03n03ooooo00Ooo`03003ooooo057oo`03n03o oooo00[oo`03003ooooo053oo`008Ooo00<00?ooool0?_oo00?h0?ooool02?oo00<00?ooool0Cooo 00?h0?ooool02_oo00<00?ooool0DOoo000Qool00`00ooooo`0oool00oP0ooooo`07ool00`00oooo o`1?ool00oP0ooooo`0:ool00`00ooooo`1Aool0027oo`03003ooooo03ooo`03n03ooooo00Soo`03 003ooooo04goo`03n03ooooo00[oo`03003ooooo05;oo`008Ooo00<00?ooool0@?oo00?h0?ooool0 1ooo00<00?ooool0COoo00?h0?ooool02_oo00<00?ooool0D_oo000Qool00`00ooooo`10ool00oP0 ooooo`08ool00`00ooooo`1;ool00oP0ooooo`0:ool00`00ooooo`1Cool000Soo`8000Coo`03003o oooo00?oo`8000?oo`@000Coo`03003ooooo047oo`03n03ooooo00Soo`03003ooooo04[oo`03n03o oooo00[oo`03003ooooo05?oo`001ooo00@00?ooool000Soo`04003ooooo0002ool00`00ooooo`05 ool00`00ooooo`11ool00oP0ooooo`08ool00`00ooooo`19ool00oP0ooooo`0:ool00`00ooooo`1D ool000Ooo`04003ooooo0008ool01000ooooo`000ooo00<00?ooool01?oo0P00@ooo00?h0?ooool0 2?oo00<00?ooool0B?oo00?h0?ooool02_oo00<00?ooool0E?oo0007ool01000ooooo`002?oo00@0 0?ooool000Coo`03003ooooo00?oo`03003ooooo04;oo`03n03ooooo00Soo`03003ooooo04Ooo`03 n03ooooo00[oo`03003ooooo05Goo`001ooo00@00?ooool000Soo`04003ooooo0005ool00`00oooo o`02ool00`00ooooo`13ool00oP0ooooo`08ool00`00ooooo`16ool00oP0ooooo`0:ool00`00oooo o`1Eool000Ooo`04003ooooo0008ool01000ooooo`000_oo00@00?ooool000Coo`03003ooooo04Co o`03n03ooooo00Ooo`03003ooooo04Goo`03n03ooooo00[oo`03003ooooo05Koo`002?oo0P002_oo 0P001?oo0P001Ooo00<00?ooool0A?oo00?h0?ooool02?oo00<00?ooool0A?oo00?h0?ooool02_oo 00<00?ooool0E_oo000Qool00`00ooooo`15ool00oP0ooooo`07ool00`00ooooo`13ool00oP0oooo o`0:ool00`00ooooo`1Gool0027oo`03003ooooo04Goo`03n03ooooo00Soo`03003ooooo04;oo`03 n03ooooo00Woo`03003ooooo05Soo`008Ooo00<00?ooool0A_oo00?h0?ooool02?oo00<00?ooool0 @?oo00?h0?ooool02_oo00<00?ooool0F?oo000Qool00`00ooooo`17ool00oP0ooooo`07ool00`00 ooooo`10ool00oP0ooooo`09ool00`00ooooo`1Iool0027oo`8004Soo`03n03ooooo00Soo`03003o oooo03koo`03n03ooooo00Woo`03003ooooo05[oo`008Ooo00<00?ooool0B?oo00?h0?ooool02?oo 00<00?ooool0??oo00?h0?ooool02_oo00<00?ooool0F_oo000Qool00`00ooooo`19ool00oP0oooo o`07ool00`00ooooo`0lool00oP0ooooo`09ool00`00ooooo`1Kool0027oo`03003ooooo04Woo`03 n03ooooo00Soo`03003ooooo03[oo`03n03ooooo00Woo`03003ooooo05coo`008Ooo00<00?ooool0 B_oo00?h0?ooool02?oo00<00?ooool0>?oo00?h0?ooool02_oo00<00?ooool0G?oo000Qool00`00 ooooo`1:ool00oP0ooooo`08ool00`00ooooo`0hool00oP0ooooo`09ool00`00ooooo`1Mool0027o o`03003ooooo04_oo`03n03ooooo00Soo`03003ooooo03Koo`03n03ooooo00Woo`03003ooooo05ko o`008Ooo00<00?ooool0C?oo00?h0?ooool02?oo00<00?ooool0=Ooo00?h0?ooool02Ooo00<00?oo ool0G_oo000Qool2001=ool00oP0ooooo`08ool00`00ooooo`0dool00oP0ooooo`09ool00`00oooo o`1Oool0027oo`03003ooooo04goo`03n03ooooo00Soo`03003ooooo03;oo`03n03ooooo00Woo`03 003ooooo063oo`008Ooo00<00?ooool0C_oo00?h0?ooool02?oo00<00?ooool0"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-0.843912, -0.0530141, \ 0.0253805, 0.000599606}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell["\<\ Next we compute the Arnold tongue. First we find the points at \ which the Gamma reaches its minimum or maximum depending on the sign of \ epsilon Delta.\ \>", "Text"], Cell[BoxData[ \(r =. \)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(min[DD_] := \ Mod[If\ [DD < 1, \ r\ /. \(FindMinimum[ gamma[r, \ DD], \ {r, \ 1.5, \ 5}]\)[\([2]\)], \ \[IndentingNewLine]r\ /. \ \(FindMinimum[\(-gamma[r, \ DD]\), \ {r, \ 1.5, \ 5}]\)[\([2]\)]], \ period]\)], "Input"], Cell[BoxData[ \(General::"spell1" \(\(:\)\(\ \)\) "Possible spelling error: new symbol name \"\!\(min\)\" is similar to \ existing symbol \"\!\(Min\)\"."\)], "Message"] }, Open ]], Cell["\<\ The function epsilon now gives the boundary of the Arnold tongue.\ \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(epsilon[DD_]\ := \ \((DD - 1)\)/gamma[min[DD], \ DD]\)], "Input"], Cell[BoxData[ \(General::"spell1" \(\(:\)\(\ \)\) "Possible spelling error: new symbol name \"\!\(min\)\" is similar to \ existing symbol \"\!\(Min\)\"."\)], "Message"] }, Open ]], Cell["Finally we compare the results with the data.", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(p2\ = Plot[epsilon[DD + 1], \ {DD\ , \ \(-0.004\), \ 0.005}]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.44709 105.82 0.0147151 5.38694 [ [.02381 .00222 -18 -9 ] [.02381 .00222 18 0 ] [.23545 .00222 -18 -9 ] [.23545 .00222 18 0 ] [.65873 .00222 -15 -9 ] [.65873 .00222 15 0 ] [.87037 .00222 -15 -9 ] [.87037 .00222 15 0 ] [.43459 .12245 -24 -4.5 ] [.43459 .12245 0 4.5 ] [.43459 .23019 -24 -4.5 ] [.43459 .23019 0 4.5 ] [.43459 .33793 -24 -4.5 ] [.43459 .33793 0 4.5 ] [.43459 .44567 -24 -4.5 ] [.43459 .44567 0 4.5 ] [.43459 .55341 -18 -4.5 ] [.43459 .55341 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .02381 .01472 m .02381 .02097 L s [(-0.004)] .02381 .00222 0 1 Mshowa .23545 .01472 m .23545 .02097 L s [(-0.002)] .23545 .00222 0 1 Mshowa .65873 .01472 m .65873 .02097 L s [(0.002)] .65873 .00222 0 1 Mshowa .87037 .01472 m .87037 .02097 L s [(0.004)] .87037 .00222 0 1 Mshowa .125 Mabswid .07672 .01472 m .07672 .01847 L s .12963 .01472 m .12963 .01847 L s .18254 .01472 m .18254 .01847 L s .28836 .01472 m .28836 .01847 L s .34127 .01472 m .34127 .01847 L s .39418 .01472 m .39418 .01847 L s .5 .01472 m .5 .01847 L s .55291 .01472 m .55291 .01847 L s .60582 .01472 m .60582 .01847 L s .71164 .01472 m .71164 .01847 L s .76455 .01472 m .76455 .01847 L s .81746 .01472 m .81746 .01847 L s .92328 .01472 m .92328 .01847 L s .97619 .01472 m .97619 .01847 L s .25 Mabswid 0 .01472 m 1 .01472 L s .44709 .12245 m .45334 .12245 L s [(0.02)] .43459 .12245 1 0 Mshowa .44709 .23019 m .45334 .23019 L s [(0.04)] .43459 .23019 1 0 Mshowa .44709 .33793 m .45334 .33793 L s [(0.06)] .43459 .33793 1 0 Mshowa .44709 .44567 m .45334 .44567 L s [(0.08)] .43459 .44567 1 0 Mshowa .44709 .55341 m .45334 .55341 L s [(0.1)] .43459 .55341 1 0 Mshowa .125 Mabswid .44709 .04165 m .45084 .04165 L s .44709 .06858 m .45084 .06858 L s .44709 .09552 m .45084 .09552 L s .44709 .14939 m .45084 .14939 L s .44709 .17632 m .45084 .17632 L s .44709 .20326 m .45084 .20326 L s .44709 .25713 m .45084 .25713 L s .44709 .28406 m .45084 .28406 L s .44709 .311 m .45084 .311 L s .44709 .36487 m .45084 .36487 L s .44709 .3918 m .45084 .3918 L s .44709 .41874 m .45084 .41874 L s .44709 .4726 m .45084 .4726 L s .44709 .49954 m .45084 .49954 L s .44709 .52647 m .45084 .52647 L s .44709 .58034 m .45084 .58034 L s .44709 .60728 m .45084 .60728 L s .25 Mabswid .44709 0 m .44709 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .48318 m .06244 .44054 L .10458 .39401 L .14415 .35028 L .18221 .3082 L .22272 .26339 L .26171 .22023 L .30316 .17433 L .34309 .13009 L .3815 .08749 L .40095 .06592 L .42237 .04216 L .43215 .03129 L .43755 .0253 L .44268 .01961 L .44498 .01705 L .44625 .01565 L .44744 .0151 L .44811 .01585 L .44885 .01666 L .45013 .01808 L .45262 .02085 L .46172 .03093 L .50272 .0764 L .54221 .12022 L .58018 .16237 L .6206 .20727 L .65951 .25051 L .70087 .2965 L .74072 .34084 L .77905 .3835 L .81983 .42893 L .8591 .47269 L .89685 .51478 L .93705 .55963 L .97574 .60281 L .97619 .60332 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgool007goo`03003ooooo00Koo`03003ooooo00Ooo`03003ooooo08goo`00O?oo00<00?oo ool01ooo00<00?ooool02?oo00<00?ooool0S?oo001kool00`00ooooo`08ool00`00ooooo`09ool0 0`00ooooo`2;ool007[oo`03003ooooo00Woo`03003ooooo00Woo`03003ooooo08_oo`00NOoo00<0 0?ooool02_oo0P002ooo00<00?ooool0R_oo001hool00`00ooooo`0;ool00`00ooooo`0;ool00`00 ooooo`29ool007Ooo`03003ooooo00coo`03003ooooo00coo`03003ooooo08Soo`00M_oo00<00?oo ool03Ooo00<00?ooool03Ooo00<00?ooool0Qooo001eool00`00ooooo`0>ool00`00ooooo`0>ool0 0`00ooooo`26ool007Coo`03003ooooo00ooo`03003ooooo00ooo`03003ooooo08Goo`00Looo00<0 0?ooool04?oo00<00?ooool04?oo00<00?ooool0Q?oo001bool00`00ooooo`0Aool2000Bool00`00 ooooo`23ool0077oo`03003ooooo01;oo`03003ooooo017oo`03003ooooo08?oo`00L?oo00<00?oo ool04ooo00<00?ooool04_oo00<00?ooool0P_oo001_ool00`00ooooo`0Dool00`00ooooo`0Cool0 0`00ooooo`21ool006ooo`03003ooooo01Coo`03003ooooo01Coo`03003ooooo083oo`00KOoo0P00 1?oo00<00?ooool00ooo0P000ooo10001?oo00<00?ooool05Ooo00<00?ooool0Oooo001/ool20000 0ooo003oo`07ool01000ooooo`000_oo00<00?ooool01Ooo00<00?ooool05_oo00<00?ooool0O_oo 001/ool01000ooooo`002?oo00@00?ooool000?oo`03003ooooo00Coo`<001Ooo`03003ooooo07go o`00Jooo0P000_oo00<00?ooool01_oo00@00?ooool000Coo`03003ooooo00?oo`03003ooooo01So o`03003ooooo07coo`00J_oo00<00?oo00000_oo00<00?ooool01_oo00@00?ooool000Goo`03003o oooo00;oo`03003ooooo01Woo`03003ooooo07_oo`00JOoo00@00?ooool000;oo`03003ooooo00Ko o`04003ooooo0002ool01000ooooo`001?oo00<00?ooool06_oo00<00?ooool0N_oo001Xool00`00 ooooo`02ool2000:ool20004ool20005ool00`00ooooo`0Kool00`00ooooo`1iool006Ooo`03003o oooo01coo`03003ooooo01coo`03003ooooo07Soo`00I_oo00<00?ooool07Ooo00<00?ooool07Ooo 00<00?ooool0Mooo001Uool00`00ooooo`0Nool00`00ooooo`0Nool00`00ooooo`1fool006Goo`03 003ooooo01koo`80023oo`03003ooooo07Goo`00I?oo00<00?ooool07ooo00<00?ooool08?oo00<0 0?ooool0M?oo001Sool00`00ooooo`0Pool00`00ooooo`0Qool00`00ooooo`1cool006;oo`03003o oooo027oo`03003ooooo02;oo`03003ooooo07;oo`00HOoo00<00?ooool08_oo00<00?ooool08ooo 00<00?ooool0LOoo001Pool00`00ooooo`0Sool00`00ooooo`0Tool00`00ooooo`1`ool005ooo`03 003ooooo02Coo`03003ooooo02Goo`03003ooooo06ooo`00G_oo00<00?ooool09Ooo0P009ooo00<0 0?ooool0K_oo001Mool00`00ooooo`0Vool00`00ooooo`0Wool00`00ooooo`1]ool005coo`03003o oooo02Ooo`03003ooooo02Ooo`03003ooooo06goo`00G?oo00<00?ooool09ooo00<00?ooool0:?oo 00<00?ooool0K?oo001Kool00`00ooooo`0Xool00`00ooooo`0Yool00`00ooooo`1[ool005[oo`03 003ooooo02Woo`03003ooooo02[oo`03003ooooo06[oo`00FOoo00<00?ooool0:_oo00<00?ooool0 :ooo00<00?ooool0JOoo001Hool00`00ooooo`0[ool2000]ool00`00ooooo`1Xool005Ooo`03003o oooo02coo`03003ooooo02goo`03003ooooo06Ooo`00Eooo00<00?ooool0;?oo00<00?ooool0;_oo 00<00?ooool0I_oo001Fool00`00ooooo`0]ool00`00ooooo`0_ool00`00ooooo`1Uool005Goo`03 003ooooo02koo`03003ooooo02ooo`03003ooooo06Goo`00E?oo00<00?ooool0;ooo00<00?ooool0 Ooo00<00?ooool0>_oo00<00?ooool0F_oo0019ool00`00ooooo`0jool00`00oooo o`0kool00`00ooooo`1Iool004Soo`03003ooooo03_oo`03003ooooo03coo`03003ooooo05Soo`00 Aooo00<00?ooool0??oo00<00?ooool0?Ooo00<00?ooool0Eooo0016ool00`00ooooo`0mool00`00 ooooo`0mool00`00ooooo`1Gool004Goo`03003ooooo03koo`03003ooooo03koo`03003ooooo05Ko o`00A?oo00<00?ooool0?ooo0P00@?oo00<00?ooool0EOoo0014ool00`00ooooo`0oool00`00oooo o`10ool00`00ooooo`1Dool004?oo`03003ooooo043oo`03003ooooo047oo`03003ooooo05?oo`00 @_oo00<00?ooool0@Ooo00<00?ooool0@_oo00<00?ooool0D_oo0011ool00`00ooooo`12ool00`00 ooooo`13ool00`00ooooo`1Aool0043oo`03003ooooo04?oo`03003ooooo04Coo`03003ooooo053o o`00?ooo00<00?ooool0A?oo00<00?ooool0AOoo00<00?ooool0Cooo000nool00`00ooooo`15ool0 0`00ooooo`15ool00`00ooooo`1?ool003goo`03003ooooo04Koo`8004Ooo`03003ooooo04koo`00 ??oo00<00?ooool0Aooo00<00?ooool0Aooo00<00?ooool0COoo000kool00`00ooooo`18ool00`00 ooooo`18ool00`00ooooo`1Ooo00<00?ooool0B_oo00<00?ooool0B_oo00<00?ooool0B_oo000iool00`00ooooo`0aool2 0004ool00`00ooooo`03ool20004ool20005ool00`00ooooo`1:ool00`00ooooo`1:ool003Soo`03 003ooooo037oo`04003ooooo0008ool01000ooooo`000_oo00@00?ooool000Coo`03003ooooo04_o o`03003ooooo04Woo`00=ooo00<00?ooool0<_oo00@00?ooool000Soo`04003ooooo0002ool01000 ooooo`001?oo0`00C?oo00<00?ooool0B?oo000fool00`00ooooo`0cool01000ooooo`002?oo00@0 0?ooool000;oo`<000Goo`03003ooooo04goo`03003ooooo04Ooo`00=Ooo00<00?ooool0=?oo00@0 0?ooool000Soo`04003ooooo0002ool00`00ooooo`05ool00`00ooooo`1>ool00`00ooooo`16ool0 03Coo`03003ooooo03Goo`04003ooooo0008ool01000ooooo`000_oo00<00?ooool01Ooo00<00?oo ool0Cooo00<00?ooool0AOoo000cool00`00ooooo`0gool2000:ool20004ool30004ool00`00oooo o`1@ool00`00ooooo`14ool003;oo`03003ooooo057oo`03003ooooo057oo`03003ooooo04?oo`00 _oo000Xool00`00ooooo`1Kool00`00oooo o`1Kool00`00ooooo`0iool002Ooo`03003ooooo05coo`03003ooooo05coo`03003ooooo03Soo`00 9_oo00<00?ooool0GOoo00<00?ooool0GOoo00<00?ooool0=ooo000Uool00`00ooooo`1Nool00`00 ooooo`1Mool00`00ooooo`0gool002Coo`03003ooooo05ooo`03003ooooo05koo`03003ooooo03Ko o`008ooo00<00?ooool0H?oo00<00?ooool0Gooo00<00?ooool0=Ooo000Sool00`00ooooo`1Pool2 001Qool00`00ooooo`0dool002;oo`03003ooooo067oo`03003ooooo067oo`03003ooooo03?oo`00 8Ooo00<00?ooool0H_oo00<00?ooool0H_oo00<00?ooool0<_oo000Pool00`00ooooo`1Sool00`00 ooooo`1Sool00`00ooooo`0aool001ooo`03003ooooo06Coo`03003ooooo06Coo`03003ooooo033o o`007_oo00<00?ooool0C?oo0P001?oo00<00?ooool00ooo0P001?oo0P001Ooo00<00?ooool0IOoo 00<00?ooool0;ooo000Mool00`00ooooo`1"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-0.00467202, -0.00844647, \ 3.46526*^-5, 0.000680709}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell["\<\ Next we define the data that was calculated from numerical \ experiments:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(data\ = \ ReadList["\", \ {Number, \ Number}]\)], "Input"], Cell[BoxData[ \({{1.029`, 0.077`}, {1.0295`, 0.067`}, {1.03`, 0.057`}, {1.0305`, 0.046`}, {1.031`, 0.036`}, {1.0315`, 0.0265`}, {1.032`, 0.0177`}, {1.0325`, 0.006`}, {1.033`, 0.0025`}, {1.0335`, 0.0132`}, {1.034`, 0.022`}, {1.0345`, 0.0325`}, {1.035`, 0.0415`}, {1.0355`, 0.0515`}, {1.036`, 0.0615`}, {1.0365`, 0.071`}, {1.037`, 0.081`}, {1.0375`, 0.091`}, {1.038`, 0.1`}}\)], "Output"] }, Open ]], Cell[BoxData[ \(\(data1 = Table[{data[\([n, 1]\)]\ /1.0329\ - \ 1, data[\([n, 2]\)]}, {n, 1, Length[data]}];\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(p1\ = \ ListPlot[data1, \ Prolog \[Rule] AbsolutePointSize[6]]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.436508 109.302 0.0147151 5.88604 [ [.2179 .00222 -18 -9 ] [.2179 .00222 18 0 ] [.65511 .00222 -15 -9 ] [.65511 .00222 15 0 ] [.87371 .00222 -15 -9 ] [.87371 .00222 15 0 ] [.42401 .13244 -24 -4.5 ] [.42401 .13244 0 4.5 ] [.42401 .25016 -24 -4.5 ] [.42401 .25016 0 4.5 ] [.42401 .36788 -24 -4.5 ] [.42401 .36788 0 4.5 ] [.42401 .4856 -24 -4.5 ] [.42401 .4856 0 4.5 ] [.42401 .60332 -18 -4.5 ] [.42401 .60332 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .2179 .01472 m .2179 .02097 L s [(-0.002)] .2179 .00222 0 1 Mshowa .65511 .01472 m .65511 .02097 L s [(0.002)] .65511 .00222 0 1 Mshowa .87371 .01472 m .87371 .02097 L s [(0.004)] .87371 .00222 0 1 Mshowa .125 Mabswid .05395 .01472 m .05395 .01847 L s .1086 .01472 m .1086 .01847 L s .16325 .01472 m .16325 .01847 L s .27256 .01472 m .27256 .01847 L s .32721 .01472 m .32721 .01847 L s .38186 .01472 m .38186 .01847 L s .49116 .01472 m .49116 .01847 L s .54581 .01472 m .54581 .01847 L s .60046 .01472 m .60046 .01847 L s .70976 .01472 m .70976 .01847 L s .76441 .01472 m .76441 .01847 L s .81906 .01472 m .81906 .01847 L s .92837 .01472 m .92837 .01847 L s .98302 .01472 m .98302 .01847 L s .25 Mabswid 0 .01472 m 1 .01472 L s .43651 .13244 m .44276 .13244 L s [(0.02)] .42401 .13244 1 0 Mshowa .43651 .25016 m .44276 .25016 L s [(0.04)] .42401 .25016 1 0 Mshowa .43651 .36788 m .44276 .36788 L s [(0.06)] .42401 .36788 1 0 Mshowa .43651 .4856 m .44276 .4856 L s [(0.08)] .42401 .4856 1 0 Mshowa .43651 .60332 m .44276 .60332 L s [(0.1)] .42401 .60332 1 0 Mshowa .125 Mabswid .43651 .04415 m .44026 .04415 L s .43651 .07358 m .44026 .07358 L s .43651 .10301 m .44026 .10301 L s .43651 .16187 m .44026 .16187 L s .43651 .1913 m .44026 .1913 L s .43651 .22073 m .44026 .22073 L s .43651 .27959 m .44026 .27959 L s .43651 .30902 m .44026 .30902 L s .43651 .33845 m .44026 .33845 L s .43651 .39731 m .44026 .39731 L s .43651 .42674 m .44026 .42674 L s .43651 .45617 m .44026 .45617 L s .43651 .51503 m .44026 .51503 L s .43651 .54446 m .44026 .54446 L s .43651 .57389 m .44026 .57389 L s .25 Mabswid .43651 0 m .43651 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath 6 Mabswid .02381 .46794 Mdot .07672 .40908 Mdot .12963 .35022 Mdot .18254 .28547 Mdot .23545 .22661 Mdot .28836 .1707 Mdot .34127 .1189 Mdot .39418 .05003 Mdot .44709 .02943 Mdot .5 .09241 Mdot .55291 .14421 Mdot .60582 .20601 Mdot .65873 .25899 Mdot .71164 .31785 Mdot .76455 .37671 Mdot .81746 .43262 Mdot .87037 .49148 Mdot .92328 .55034 Mdot .97619 .60332 Mdot % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg?oo1@00H_oo001Tool2000:ool20005ool00`00ooooo`04ool00`00ooooo`0hool5001Rool0 07koo`03003ooooo03[oo`03003ooooo06;oo`00O_oo00<00?ooool0Wooo000gool50012ool00`00 ooooo`2Oool003Ooo`D004;oo`800:3oo`00=_oo1P00@_oo00<00?ooool0Wooo000gool50012ool0 0`00ooooo`2Oool003Ooo`D004;oo`03003ooooo09ooo`00>Ooo00<00?ooool0@_oo00<00?ooool0 Wooo001nool00`00ooooo`2Oool007koo`03003ooooo09ooo`00O_oo00<00?ooool0Wooo001nool2 0017ool5001Dool007koo`03003ooooo04Koo`D005Coo`00O_oo00<00?ooool0AOoo1P00E?oo001n ool00`00ooooo`16ool5001Dool007koo`03003ooooo04Koo`D005Coo`00O_oo00<00?ooool0B?oo 00<00?ooool0E?oo001nool00`00ooooo`2Oool007koo`03003ooooo09ooo`00O_oo0P00X?oo000Y ool5001@ool00`00ooooo`2Oool002Woo`D0053oo`03003ooooo09ooo`00:?oo1P00D?oo00<00?oo ool0Wooo000Yool5001@ool00`00ooooo`2Oool002Woo`D0053oo`03003ooooo09ooo`00:ooo00<0 0?ooool0=_oo0P001?oo00<00?ooool00ooo0P001?oo0P001_oo00<00?ooool0Wooo001Sool01000 ooooo`002?oo00@00?ooool000;oo`04003ooooo0005ool00`00ooooo`2Oool006?oo`04003ooooo 0008ool01000ooooo`000_oo00@00?ooool000Goo`8005Goo`D004Koo`00Hooo00@00?ooool000So o`04003ooooo0002ool30006ool00`00ooooo`1Dool50016ool006?oo`04003ooooo0008ool01000 ooooo`000_oo00<00?ooool01_oo00<00?ooool0Dooo1P00A_oo001Sool01000ooooo`002?oo00@0 0?ooool000;oo`03003ooooo00Koo`03003ooooo05Coo`D004Koo`00I?oo0P002_oo0P001?oo0`00 1Ooo00<00?ooool0E?oo1@00A_oo001nool00`00ooooo`1Fool00`00ooooo`16ool007koo`03003o oooo09ooo`00O_oo00<00?ooool0Wooo001nool2002Pool001[oo`D005ooo`03003ooooo09ooo`00 6_oo1@00Gooo00<00?ooool0Wooo000Iool6001Oool00`00ooooo`2Oool001[oo`D005ooo`03003o oooo09ooo`006_oo1@00Gooo00<00?ooool0Wooo000Lool00`00ooooo`1Oool00`00ooooo`2Oool0 07koo`03003ooooo06?oo`D003Ooo`00O_oo0P00I?oo1@00=ooo001nool00`00ooooo`1Rool6000g ool007koo`03003ooooo06?oo`D003Ooo`00O_oo00<00?ooool0Hooo1@00=ooo001nool00`00oooo o`1Uool00`00ooooo`0gool007koo`03003ooooo09ooo`00O_oo00<00?ooool0Wooo001nool00`00 ooooo`2Oool007koo`800:3oo`003?oo1@00KOoo00<00?ooool0Wooo000ool5000"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-0.00424774, -0.007747, \ 3.36489*^-5, 0.000624851}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(fig\)\(\ \)\(=\)\(\ \)\(Show[p1, \ p2, \ Ticks\ \[Rule] \ {Automatic, \ {0.025, \ 0.05, \ 0.075, \ 0.1}}, AxesLabel\ \[Rule] "\", \ Epilog\ \[Rule] \ \ Text["\", \ {1.003, \ 0.01}]]\)\(\ \ \)\)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.44709 105.82 0.0147151 5.38694 [ [.02381 .00222 -18 -9 ] [.02381 .00222 18 0 ] [.23545 .00222 -18 -9 ] [.23545 .00222 18 0 ] [.65873 .00222 -15 -9 ] [.65873 .00222 15 0 ] [.87037 .00222 -15 -9 ] [.87037 .00222 15 0 ] [.43459 .14939 -30 -4.5 ] [.43459 .14939 0 4.5 ] [.43459 .28406 -24 -4.5 ] [.43459 .28406 0 4.5 ] [.43459 .41874 -30 -4.5 ] [.43459 .41874 0 4.5 ] [.43459 .55341 -18 -4.5 ] [.43459 .55341 0 4.5 ] [.44709 .64303 -53 0 ] [.44709 .64303 53 10.125 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .02381 .01472 m .02381 .02097 L s [(-0.004)] .02381 .00222 0 1 Mshowa .23545 .01472 m .23545 .02097 L s [(-0.002)] .23545 .00222 0 1 Mshowa .65873 .01472 m .65873 .02097 L s [(0.002)] .65873 .00222 0 1 Mshowa .87037 .01472 m .87037 .02097 L s [(0.004)] .87037 .00222 0 1 Mshowa .125 Mabswid .07672 .01472 m .07672 .01847 L s .12963 .01472 m .12963 .01847 L s .18254 .01472 m .18254 .01847 L s .28836 .01472 m .28836 .01847 L s .34127 .01472 m .34127 .01847 L s .39418 .01472 m .39418 .01847 L s .5 .01472 m .5 .01847 L s .55291 .01472 m .55291 .01847 L s .60582 .01472 m .60582 .01847 L s .71164 .01472 m .71164 .01847 L s .76455 .01472 m .76455 .01847 L s .81746 .01472 m .81746 .01847 L s .92328 .01472 m .92328 .01847 L s .97619 .01472 m .97619 .01847 L s .25 Mabswid 0 .01472 m 1 .01472 L s .44709 .14939 m .45334 .14939 L s [(0.025)] .43459 .14939 1 0 Mshowa .44709 .28406 m .45334 .28406 L s [(0.05)] .43459 .28406 1 0 Mshowa .44709 .41874 m .45334 .41874 L s [(0.075)] .43459 .41874 1 0 Mshowa .44709 .55341 m .45334 .55341 L s [(0.1)] .43459 .55341 1 0 Mshowa .44709 0 m .44709 .61803 L s gsave .44709 .64303 -114 -4 Mabsadd m 1 1 Mabs scale currentpoint translate 0 18.125 translate 1 -1 scale 63.000 11.562 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 11.562 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (coupling) show 117.000 11.562 moveto (strength) show 165.000 11.562 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath 6 Mabswid .04754 .42951 Mdot .09876 .37564 Mdot .14999 .32177 Mdot .20121 .26251 Mdot .25244 .20864 Mdot .30366 .15747 Mdot .35489 .11006 Mdot .40611 .04704 Mdot .45733 .02818 Mdot .50856 .08582 Mdot .55978 .13323 Mdot .61101 .18979 Mdot .66223 .23827 Mdot .71346 .29214 Mdot .76468 .34601 Mdot .81591 .39719 Mdot .86713 .45106 Mdot .91836 .50493 Mdot .96958 .55341 Mdot .5 Mabswid .02381 .48318 m .06244 .44054 L .10458 .39401 L .14415 .35028 L .18221 .3082 L .22272 .26339 L .26171 .22023 L .30316 .17433 L .34309 .13009 L .3815 .08749 L .40095 .06592 L .42237 .04216 L .43215 .03129 L .43755 .0253 L .44268 .01961 L .44498 .01705 L .44625 .01565 L .44744 .0151 L .44811 .01585 L .44885 .01666 L .45013 .01808 L .45262 .02085 L .46172 .03093 L .50272 .0764 L .54221 .12022 L .58018 .16237 L .6206 .20727 L .65951 .25051 L .70087 .2965 L .74072 .34084 L .77905 .3835 L .81983 .42893 L .8591 .47269 L .89685 .51478 L .93705 .55963 L .97574 .60281 L .97619 .60332 L s gsave 106.585 .06858 -108 -9.0625 Mabsadd m 1 1 Mabs scale currentpoint translate 0 18.125 translate 1 -1 scale 63.000 11.562 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 11.562 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (frequency) show 123.000 11.562 moveto (ratio) show 153.000 11.562 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgOoo00@00?ooooooo`D005?oo`00C?oo 00<00?ooool07ooo00@00?ooool000Soo`04003ooooo0002ool30005ool00`00ooooo`0jool00`00 ool00005001Cool004_oo`03003ooooo023oo`04003ooooo0008ool01000ooooo`000_oo00<00?oo ool01Ooo00<00?ooool0>ooo00<00?oo00001000Dooo001:ool00`00ooooo`0Qool01000ooooo`00 2?oo00@00?ooool000;oo`03003ooooo00Goo`03003ooooo03coo`H005?oo`00BOoo00<00?ooool0 8ooo0P002_oo0P000ooo10001?oo00<00?ooool0?Ooo00<00?oo0000EOoo0018ool00`00ooooo`0m ool00`00ooooo`0nool00`00ooooo`1Dool004Ooo`03003ooooo03koo`03003ooooo03koo`03003o oooo05Coo`00?Ooo1@001?oo00<00?ooool0?ooo00<00?ooool0?ooo00<00?ooool0Dooo000mool5 0003ool00`00ooooo`10ool00`00ooooo`10ool00`00ooooo`1Bool003coo`H000;oo`03003ooooo 047oo`03003ooooo047oo`03003ooooo057oo`00?Ooo1@0000?oo`00ool0@ooo00<00?ooool0@_oo 00<00?ooool0D?oo000mool60015ool00`00ooooo`13ool00`00ooooo`1?ool003ooo`03003oo`00 04Koo`03003ooooo04?oo`03003ooooo04ooo`00@?oo00<00?ooool0AOoo00<00?ooool0A?oo00<0 0?ooool00ooo1@00A_oo000oool00`00ooooo`16ool00`00ooooo`15ool00`00ooooo`02ool50016 ool003koo`03003ooooo04Ooo`03003ooooo04Koo`03003ooooo00H004Koo`00?Ooo00<00?ooool0 B?oo00<00?ooool0Aooo00<00?ooool01@00A_oo000lool00`00ooooo`19ool00`00ooooo`18ool0 0`00ool000040016ool003_oo`03003ooooo04[oo`03003ooooo04Woo`04003ooooo0018ool003_o o`03003ooooo04[oo`03003ooooo04[oo`03003ooooo04Soo`00_oo000aool00`00ooooo`1Dool00`00ooooo`1Dool01@00oooooooo0000??oo000`ool00`00 ooooo`0fool20004ool00`00ooooo`03ool20004ool00`00ooooo`02ool30005ool00`00ooooo`1E ool00`00ooooo`0mool002ooo`03003ooooo03Koo`04003ooooo0008ool01000ooooo`000ooo00<0 0?ooool01Ooo00<00?ooool00_oo00<00?ooool0E_oo00<00?ooool0??oo000Tool50006ool00`00 ooooo`0fool01000ooooo`002?oo00@00?ooool000Coo`03003ooooo00Coo`03003ooooo00;oo`<0 05Koo`03003ooooo03coo`009?oo1@001Ooo00<00?ooool0=ooo00@00?ooool000Soo`04003ooooo 0004ool01000oooooooo0`001Ooo00<00?ooool0Eooo00<00?ooool0>ooo000Sool60004ool00`00 ooooo`0hool01000ooooo`002?oo00@00?ooool000Goo`04003ooooo0007ool00`00ooooo`1Hool0 0`00ooooo`0jool002Coo`D000?oo`03003ooooo03Woo`04003ooooo0008ool01000ooooo`000_oo 00@00?ooool000;oo`03003ooooo00Goo`03003ooooo05Woo`03003ooooo03Woo`009?oo1@000_oo 00<00?ooool0>ooo0P002_oo0P000ooo10000_oo10001?oo00<00?ooool0F_oo00<00?ooool0>?oo 000Vool01@00oooooooo0000GOoo00<00?ooool0Fooo00<00?ooool0=ooo000Yool00`00ooooo`1L ool00`00ooooo`1Lool00`00ooooo`04ool5000]ool002Soo`03003ooooo05goo`03003ooooo05go o`03003ooooo00?oo`D002goo`009ooo00<00?ooool0G_oo00<00?ooool0G_oo00@00?ooooooo`H0 02goo`009_oo00<00?ooool0Gooo00<00?ooool0Gooo00@00?ooooooo`D002goo`009Ooo00<00?oo ool0H?oo00<00?ooool0H?oo00<00?ooool01@00;Ooo000Uool00`00ooooo`1Pool00`00ooooo`1Q ool01@00oooooooo0000;ooo000Tool00`00ooooo`1Qool00`00ooooo`1Rool00`00ooooo`0`ool0 02?oo`03003ooooo06;oo`03003ooooo06?oo`03003ooooo02ooo`008_oo00<00?ooool0Hooo00<0 0?ooool0I?oo00<00?ooool0;_oo000Qool00`00ooooo`1Tool00`00ooooo`1Uool00`00ooooo`0] ool0023oo`03003ooooo06Goo`03003ooooo06Goo`03003ooooo02goo`00R?oo00<00?ooool0I_oo 00<00?ooool0;?oo0028ool00`00ooooo`1Wool00`00ooooo`0[ool008Soo`03003ooooo06Soo`03 003ooooo00Goo`D0023oo`00R?oo00<00?ooool0JOoo00<00?ooool01?oo1@008?oo0028ool00`00 ooooo`1Zool00`00ooooo`02ool6000Pool008Soo`03003ooooo06[oo`03003ooooo00?oo`D0023o o`00R?oo00<00?ooool0Jooo00<00?ooool00_oo1@008?oo0028ool00`00ooooo`1/ool00`00oooo o`03ool00`00ooooo`0Pool008Soo`03003ooooo06goo`03003ooooo02Goo`00R?oo00<00?ooool0 K_oo00<00?ooool09?oo0028ool00`00ooooo`1_ool00`00ooooo`0Sool008Soo`03003ooooo073o o`03003ooooo02;oo`00R?oo00<00?ooool0LOoo00<00?ooool08Ooo0028ool00`00ooooo`1aool0 0`00ooooo`0Qool007Goo`8000Coo`03003ooooo00;oo`@000Coo`03003ooooo07;oo`03003ooooo 00Ooo`D001Coo`00M?oo00@00?ooool000[oo`03003ooooo00?oo`03003ooooo07?oo`03003ooooo 00Koo`D001Coo`00M?oo00@00?ooool000[oo`03003ooooo00?oo`<007Coo`03003ooooo00Coo`H0 01Coo`00M?oo00@00?ooool000[oo`03003ooooo00?oo`03003ooooo07Goo`03003ooooo00Coo`D0 01Coo`00M?oo00@00?ooool000[oo`03003ooooo00?oo`03003ooooo07Koo`03003ooooo00?oo`D0 01Coo`00M?oo00@00?ooool000Soo`<000Goo`03003ooooo07Ooo`03003ooooo00Coo`03003ooooo 01Coo`00MOoo0P002ooo00<00?ooool00ooo00<00?ooool0N?oo00<00?ooool06_oo0028ool00`00 ooooo`1iool00`00ooooo`0Iool008Soo`03003ooooo07[oo`03003ooooo01Soo`00R?oo00<00?oo ool0N_oo00<00?ooool06?oo0028ool00`00ooooo`1kool00`00ooooo`0Gool008Soo`03003ooooo 07coo`03003ooooo01Koo`00R?oo00<00?ooool0OOoo00<00?ooool05Ooo0028ool00`00ooooo`1n ool00`00ooooo`0Dool008Soo`03003ooooo07ooo`03003ooooo01?oo`00R?oo00<00?ooool0Oooo 00<00?ooool04ooo0028ool00`00ooooo`2Eool008Soo`03003ooooo09Goo`00R?oo00<00?ooool0 UOoo003ooolQool00?ooob7oo`00oooo8Ooo003ooolQool00?ooob7oo`00oooo8Ooo003ooolQool0 06Ooo`<001Koo`<002Ooo`<007?oo`00J?oo00<00?ooool06?oo00<00?ooool09ooo00<00?ooool0 L?oo001Gool20004ool20004ool200000ooo003oo`030003ool500000ooo0000000600000ooo0000 0002ool30008ool30005ool20002ool40003ool300001Ooo00000000ool00P000_oo0`001?oo0P00 00Goo`0000000?oo008006Goo`00E_oo00@00?ooool000;oo`04003ooooo0002ool01000ooooo`00 0_oo00@00?ooool000Coo`03003ooooo00?oo`05003oooooool00002ool01000ooooo`000_oo00<0 0?ooool02Ooo00D00?ooooooo`0000;oo`04003ooooo0004ool00`00ooooo`03ool01000ooooo`00 0_oo00@00?ooool000?oo`06003ooooo003oo`000_oo00<00?ooool0I?oo001Fool00`00ooooo`03 ool01000ooooo`000_oo00@00?ooool000;oo`04003ooooo0004ool00`00ooooo`03ool01@00oooo oooo00000_oo00@00?ooool000;oo`03003ooooo00Ooo`8000Coo`03003ooooo00?oo`03003ooooo 00;oo`<000?oo`04003ooooo0002ool01000ooooo`000ooo00<00?ooool00_oo00@00?ooool006Ko o`00E_oo00@00?ooool000;oo`04003ooooo0002ool01000ooooo`000_oo00@00?ooool000Coo`03 003ooooo00?oo`05003oooooool00002ool01000ooooo`000_oo00<00?ooool01_oo00<00?ooool0 1?oo00<00?ooool00ooo00<00?ooool00_oo00@00?ooool000;oo`04003ooooo0002ool01000oooo o`000ooo00<00?ooool00_oo00@00?ooool006Koo`00Eooo0P001?oo0P000_oo0P0000Koo`00003o o`00ool20005ool00`00ooooo`02ool20002ool01000ool000001?oo0P0000?oo`00ool01ooo0`00 0_oo10000_oo00<00?oo00000P000_oo0P000_oo00@00?oo000000Coo`800003ool00?oo00@000;o o`<006Ooo`00L?oo00<00?ooool08?oo00<00?ooool06ooo00<00?ooool00_oo00<00?ooool0Iooo 001_ool20005ool00`00ooooo`0Jool00`00ooooo`0Kool01000oooooooo0P00JOoo0000\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-0.00523936, -0.00910422, \ 3.83729*^-5, 0.000753789}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(Export["\", \ fig, \ "\"]\)\(\ \)\)\)], "Input"], Cell[BoxData[ \("arnoldtongue.eps"\)], "Output"] }, Open ]] }, Open ]] }, FrontEndVersion->"4.1 for X", ScreenRectangle->{{0, 1280}, {0, 1024}}, WindowSize->{941, 832}, WindowMargins->{{74, Automatic}, {Automatic, 50}}, PrintingPageRange->{Automatic, Automatic}, PrintingOptions->{"PaperSize"->{612, 792}, "PaperOrientation"->"Portrait", "PostScriptOutputFile":>FrontEnd`FileName[{$RootDirectory, "net", "math", \ "export", "home2", "josic"}, "calculations.nb.ps", CharacterEncoding -> \ "ISO8859-1"], "Magnification"->1} ] (******************************************************************* Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. The cache data will then be recreated when you save this file from within Mathematica. *******************************************************************) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[1705, 50, 245, 5, 50, "Text"], Cell[1953, 57, 108, 2, 27, "Input"], Cell[2064, 61, 241, 5, 50, "Text"], Cell[CellGroupData[{ Cell[2330, 70, 89, 1, 27, "Input"], Cell[2422, 73, 51, 1, 27, "Output"] }, Open ]], Cell[2488, 77, 83, 1, 27, "Input"], Cell[2574, 80, 216, 4, 50, "Text"], Cell[2793, 86, 143, 2, 27, "Input"], Cell[2939, 90, 282, 5, 50, "Text"], Cell[3224, 97, 648, 11, 59, "Input"], Cell[CellGroupData[{ Cell[3897, 112, 65, 1, 27, "Input"], Cell[3965, 115, 21943, 580, 186, 5399, 371, "GraphicsData", "PostScript", \ "Graphics"], Cell[25911, 697, 130, 3, 27, "Output"] }, Open ]], Cell[26056, 703, 168, 4, 50, "Text"], Cell[26227, 709, 953, 17, 187, "Input"], Cell[27183, 728, 241, 5, 50, "Text"], Cell[27427, 735, 1167, 22, 203, "Input"], Cell[28597, 759, 313, 7, 68, "Text"], Cell[CellGroupData[{ Cell[28935, 770, 84, 1, 27, "Input"], Cell[29022, 773, 56475, 1692, 186, 18668, 1221, "GraphicsData", "PostScript", \ "Graphics"], Cell[85500, 2467, 130, 3, 27, "Output"] }, Open ]], Cell[85645, 2473, 133, 3, 32, "Text"], Cell[CellGroupData[{ Cell[85803, 2480, 50, 0, 64, "Subtitle"], Cell[85856, 2482, 140, 3, 32, "Text"], Cell[85999, 2487, 84, 1, 27, "Input"], Cell[86086, 2490, 105, 3, 32, "Text"], Cell[CellGroupData[{ Cell[86216, 2497, 151, 2, 27, "Input"], Cell[86370, 2501, 55, 1, 44, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[86462, 2507, 92, 1, 27, "Input"], Cell[86557, 2510, 15732, 455, 186, 4461, 311, "GraphicsData", "PostScript", \ "Graphics"], Cell[102292, 2967, 130, 3, 27, "Output"] }, Open ]], Cell[102437, 2973, 221, 5, 50, "Text"], Cell[102661, 2980, 708, 12, 75, "Input"], Cell[CellGroupData[{ Cell[103394, 2996, 1399, 26, 235, "Input"], Cell[104796, 3024, 183, 3, 23, "Message"] }, Open ]], Cell[104994, 3030, 134, 3, 32, "Text"], Cell[CellGroupData[{ Cell[105153, 3037, 136, 3, 27, "Input"], Cell[105292, 3042, 15798, 456, 186, 4511, 312, "GraphicsData", "PostScript", \ "Graphics"], Cell[121093, 3500, 130, 3, 27, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[121260, 3508, 45, 1, 27, "Input"], Cell[121308, 3511, 21784, 599, 186, 5803, 397, "GraphicsData", "PostScript", \ "Graphics"], Cell[143095, 4112, 130, 3, 27, "Output"] }, Open ]], Cell[143240, 4118, 178, 4, 32, "Text"], Cell[143421, 4124, 38, 1, 27, "Input"], Cell[CellGroupData[{ Cell[143484, 4129, 303, 7, 43, "Input"], Cell[143790, 4138, 179, 3, 23, "Message"] }, Open ]], Cell[143984, 4144, 91, 3, 32, "Text"], Cell[CellGroupData[{ Cell[144100, 4151, 86, 1, 27, "Input"], Cell[144189, 4154, 179, 3, 23, "Message"] }, Open ]], Cell[144383, 4160, 61, 0, 32, "Text"], Cell[CellGroupData[{ Cell[144469, 4164, 101, 2, 27, "Input"], Cell[144573, 4168, 15569, 390, 186, 3406, 235, "GraphicsData", "PostScript", \ "Graphics"], Cell[160145, 4560, 130, 3, 27, "Output"] }, Open ]], Cell[160290, 4566, 97, 3, 32, "Text"], Cell[CellGroupData[{ Cell[160412, 4573, 90, 1, 27, "Input"], Cell[160505, 4576, 444, 7, 59, "Output"] }, Open ]], Cell[160964, 4586, 150, 3, 27, "Input"], Cell[CellGroupData[{ Cell[161139, 4593, 103, 2, 27, "Input"], Cell[161245, 4597, 11162, 309, 186, 2995, 204, "GraphicsData", "PostScript", \ "Graphics"], Cell[172410, 4908, 130, 3, 27, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[172577, 4916, 313, 5, 43, "Input"], Cell[172893, 4923, 17583, 422, 186, 4623, 258, "GraphicsData", "PostScript", \ "Graphics"], Cell[190479, 5347, 130, 3, 27, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[190646, 5355, 104, 2, 27, "Input"], Cell[190753, 5359, 52, 1, 27, "Output"] }, Open ]] }, Open ]] } ] *) (******************************************************************* End of Mathematica Notebook file. *******************************************************************)