(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 4.2' 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[ 441853, 13253]*) (*NotebookOutlinePosition[ 442546, 13277]*) (* CellTagsIndexPosition[ 442502, 13273]*) (*WindowFrame->Normal*) Notebook[{ Cell[TextData[StyleBox["Biophysics 101, Fall 2002\nProblem Set 1, part 3", \ "DisplayFormula"]], "Text", TextAlignment->Right, TextJustification->0], Cell["Warm-up Notebook", "Subtitle", TextAlignment->Center, TextJustification->0], Cell[TextData[StyleBox["warmup_answers", "Title", FontFamily->"Garamond", FontWeight->"Bold", FontColor->RGBColor[1, 0.501961, 0.752941]]], "Subtitle", Evaluatable->False, TextAlignment->Center, TextJustification->0, FormatType->TextForm], Cell[TextData[{ "This notebook is for beginners that have done the ", StyleBox["Mathematica", FontSlant->"Italic"], " tutorial. Most of it is no harder than a coloring book It starts with \ cell manipulation and formatting, and it works its way up to discrete \ recursive functions that operate on ", StyleBox["Mathematica", FontSlant->"Italic"], " tables and arrays. Many of us are new to ", StyleBox["Mathematica", FontSlant->"Italic"], ", so ", StyleBox["if you discover anything useful, please include them in your \ finished notebook.", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]] }], "Text"], Cell[CellGroupData[{ Cell[TextData[StyleBox["1: Saving notebooks", "Subsection"]], "Text", TextAlignment->Center, TextJustification->0], Cell["\<\ Your first challenge is to save a copy of this notebook, and you get to name \ it after you. On the menu bar at the top of the screen its \"File-> Save \ As.... \". If your name is Jack Flapjack then name it Jack_Flapjack.nb. If \ your name is not Jack Flapjack then name it after your own name instead. Put \ your answers in your self-named copy and turn it in to your TF. \ \>", "Text"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["2: Inserting and deleting ", "Subsection"], StyleBox["Mathematica", "Subsection", FontSlant->"Italic"], StyleBox[" cells", "Subsection"] }], "Text", TextAlignment->Center, TextJustification->0], Cell["\<\ If you click in the thin horizontal space between cells, a thin black line \ appears. Hit the enter key, and voila, a new cell. Insert a cell between the \ second and third cells in this notebook, and type your name in it. If you are \ feeling stylish, format your name text with the many options available under \ the format menu. On the menu, check out \"Format->Show Toolbar\" Though short \ on features, the formatting toolbar may be worth it's screen real estate. To \ delete a cell, click to highlight it's blue bracket on the right, and press \ the delete key. To copy/paste a cell - highlight the blue bracket of the cell \ you want to copy, ->copy,then make the thin horizontal black \ line appear where you want it to go, and ->paste.\ \>", "Text", TextAlignment->Left, TextJustification->0] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["3: ", "Subsection"], StyleBox["Mathematica", "Subsection", FontSlant->"Italic"], StyleBox[" cell types", "Subsection"] }], "Text", TextAlignment->Center, TextJustification->0], Cell[TextData[{ "Notice the subtle differences in the cell bracket shapes. They tell you \ what type of cell it is. This type, with the double line at the top, means \ its a non-evaluatable text cell. If you press while the cursor \ is in this type of cell, ", StyleBox["Mathematica", FontSlant->"Italic"], " will beep at you.", StyleBox[" \n", FontColor->RGBColor[1, 0, 0]], StyleBox["(2 pts)", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], StyleBox["Try it on the cell below. Now to make it evaluatable, highlight \ the cell bracket, and then its \"Cell->Cell Properties->Cell Evaluatable\"", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]] }], "Text", TextAlignment->Left, TextJustification->0], Cell[CellGroupData[{ Cell[TextData[StyleBox["2+2", "Subsubsection"]], "Text", Evaluatable->True, TextAlignment->Center, TextJustification->0], Cell[BoxData[ \(4\)], "Output"] }, Open ]], Cell["\<\ The default cell type, for example the one you just typed your name in, is \ called \"Input Form\", and its cell bracket has a small triangle at the top. \ Change the property of the cell containing your name to non-evaluatable, and \ convert its display type to Text thru the menu via \"Cell->Display \ As->Text\".\ \>", "Text", TextAlignment->Left, TextJustification->0], Cell[CellGroupData[{ Cell["\<\ This is an input type cell in text display mode. If you press \ in this cell, you will see what this sentence means to the Mathematica kernel \ (not much). \ \>", "Input", TextAlignment->Left, TextJustification->0], Cell[BoxData[ \(General::"spell1" \(\(:\)\(\ \)\) "Possible spelling error: new symbol name \"\!\(input\)\" is similar to \ existing symbol \"\!\(Input\)\"."\)], "Message"], Cell[BoxData[ \(General::"spell1" \(\(:\)\(\ \)\) "Possible spelling error: new symbol name \"\!\(cell\)\" is similar to \ existing symbol \"\!\(Cell\)\"."\)], "Message"], Cell[BoxData[ \(General::"spell1" \(\(:\)\(\ \)\) "Possible spelling error: new symbol name \"\!\(text\)\" is similar to \ existing symbol \"\!\(Text\)\"."\)], "Message"], Cell[BoxData[ \(General::"stop" \(\(:\)\(\ \)\) "Further output of \!\(General :: \"spell1\"\) will be suppressed \ during this calculation."\)], "Message"], Cell[BoxData[ \(General::"spell" \(\(:\)\(\ \)\) "Possible spelling error: new symbol name \"\!\(enter\)\" is similar to \ existing symbols \!\({Center, Enter}\)."\)], "Message"], Cell["\<\ Syntax::sntxf: \"cell in text display mode. If you press in \ this cell\" cannot be followed by \", you will see what this sentence means to \ <<11>>tica kernel (not much).\".\ \>", "Message"] }, Open ]], Cell[BoxData[ FormBox[ StyleBox[\(This\ is\ a\ traditional\ form\ cell . \ \ It\ has\ the\ \ coolest\ bracket\ shape, \ but\ it' s\ a\ relic\ of\ old\ Mathematica\ versions\ that' s\ \ still\ \ compatable\ with\ version\ \ \(\(4.2\)\(.\)\)\), "Text"], TraditionalForm]], "Input"] }, Open ]], Cell[TextData[StyleBox["4: Cell grouping", "Subsection"]], "Text", TextAlignment->Center, TextJustification->0], Cell["\<\ Notice how most of these cells are nested, but the two cells in this section \ are not. To group them, first go on the menu to \"Cell->Cell Grouping\" and \ make sure \"Manual Grouping\" is checked. Then select both brackets by \ dragging the mouse along the right margin, and its \"Cell->Cell \ Grouping->Group Cells\". Double click on the outermost bracket to make the \ nest expand and collapse.\ \>", "Text"], Cell[CellGroupData[{ Cell[TextData[StyleBox["5: Named lists", "Subsection"]], "Text", TextAlignment->Center, TextJustification->0], Cell[TextData[{ "In the next cell there are some named lists and a name based list \ operation. ", StyleBox["(2 pts)", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], " ", StyleBox["Evaluate the expressions by placing the cursor to the right of \ the last line, and . To get the total oil consumption for all \ five years, replace the \"*\" with a \".\" and evaluate again.", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(census\ = \ {7, \ 12, \ 11, \ 17, \ 28}\), "\[IndentingNewLine]", \(perCapitaOil\ = \ {300, \ 445, \ 425, \ 625, \ 850}\), "\[IndentingNewLine]", \(census\ . \ perCapitaOil\)}], "Input"], Cell[BoxData[ \({7, 12, 11, 17, 28}\)], "Output"], Cell[BoxData[ \({300, 445, 425, 625, 850}\)], "Output"], Cell[BoxData[ \(46540\)], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox["6: Calculated lists using the Table method", \ "Subsection"]], "Text", TextAlignment->Center, TextJustification->0], Cell[TextData[{ "The first example creates a length b array of a. ", StyleBox["Evaluate the expression", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], "." }], "Text", TextAlignment->Left, TextJustification->0], Cell[CellGroupData[{ Cell[BoxData[{ \(a = 3\), "\[IndentingNewLine]", \(b = 4\), "\[IndentingNewLine]", \(Table[a, \ {b}]\)}], "Input"], Cell[BoxData[ \(3\)], "Output"], Cell[BoxData[ \(4\)], "Output"], Cell[BoxData[ \({3, 3, 3, 3}\)], "Output"] }, Open ]], Cell["Evaluate these expressions.", "Text", TextAlignment->Left, TextJustification->0], Cell[CellGroupData[{ Cell[BoxData[{ \(Prime[5]\), "\[IndentingNewLine]", \(Table[Prime[n], \ {n, \ 1, \ 10}]\), "\[IndentingNewLine]", \(Random[Real, \ {0, 1}]\)}], "Input"], Cell[BoxData[ \(11\)], "Output"], Cell[BoxData[ \({2, 3, 5, 7, 11, 13, 17, 19, 23, 29}\)], "Output"], Cell[BoxData[ \(0.94127986139163`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\[IndentingNewLine]\)\(Table[ Random[Real, \ {1, \ 50}], \ {20}]\)\)\)], "Input"], Cell[BoxData[ \({14.556840234489927`, 33.078928353359785`, 10.156443695978671`, 39.59380185009969`, 46.6495343533104`, 38.52922586331066`, 13.07540143960344`, 17.229586972539`, 43.04399743824508`, 37.02509447266429`, 17.845463372599585`, 19.076441212256032`, 4.1217915629010635`, 44.92846297637551`, 25.88415998048764`, 8.492839502008037`, 4.723503541876793`, 30.606596936008366`, 11.198791359134926`, 22.87579907055333`}\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["(2 pts) ", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], StyleBox["Now insert a cell below this one that creates a list of 20 random \ numbers. Choose your own range (in the above case the range is between 0 and \ 1), and your number type choices are (Integer, Real, or Complex).", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]] }], "Text", TextAlignment->Left, TextJustification->0], Cell["\<\ Evaluate these different ways to count to ten.\ \>", "Text", TextAlignment->Left, TextJustification->0], Cell[BoxData[{ \(Table[x, \ {x, \ 10}]\), "\[IndentingNewLine]", \(Table[x, \ {x, \ 1, \ 10}]\), "\[IndentingNewLine]", \(Table[x/2, \ {x, 2, 20, 2}]\), "\[IndentingNewLine]", \(Range[10]\)}], "Input"], Cell[TextData[StyleBox["Inset a formula in a cell at the bottom of this group \ that counts backwards from ten.", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]]], "Text", TextAlignment->Left, TextJustification->0] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Table[x, \ {x, \ 10, \ 1, \ \(-1\)}]\)], "Input"], Cell[BoxData[ \({10, 9, 8, 7, 6, 5, 4, 3, 2, 1}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox[" 7: List generation using functions with the Array \ method", "Subsection"]], "Text", TextAlignment->Center, TextJustification->0], Cell[TextData[{ "This example introduces functions and arrays. Notice the underscore (x_) \ after the variable definition in the function. Arg 1 in the Array \ specification is the creation method that takes an integer, arg 2 is the \ array length, arg 3 is the starting point. ", StyleBox["(2 pts)", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], " ", StyleBox["Evaluate these expressions. ", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]] }], "Text", TextAlignment->Left, TextJustification->0], Cell[CellGroupData[{ Cell[BoxData[{\(f[x_]\ := \ x^2;\), "\[IndentingNewLine]", \(qT = \ Array[f, \ 20, \ \(-12\)]\), "\[IndentingNewLine]", "qT", "\[IndentingNewLine]", \(ListPlot[qT];\), "\[IndentingNewLine]", RowBox[{"ListPlot", "[", RowBox[{"qT", ",", " ", RowBox[{ StyleBox["PlotJoined", "MR"], " ", "\[Rule]", " ", StyleBox["True", "MR"]}]}], "]"}]}], "Input"], Cell[BoxData[ \({144, 121, 100, 81, 64, 49, 36, 25, 16, 9, 4, 1, 0, 1, 4, 9, 16, 25, 36, 49}\)], "Output"], Cell[BoxData[ \({144, 121, 100, 81, 64, 49, 36, 25, 16, 9, 4, 1, 0, 1, 4, 9, 16, 25, 36, 49}\)], "Output"], 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 0.047619 0.0147151 0.00408753 [ [.2619 .00222 -3 -9 ] [.2619 .00222 3 0 ] [.5 .00222 -6 -9 ] [.5 .00222 6 0 ] [.7381 .00222 -6 -9 ] [.7381 .00222 6 0 ] [.97619 .00222 -6 -9 ] [.97619 .00222 6 0 ] [.01131 .09647 -12 -4.5 ] [.01131 .09647 0 4.5 ] [.01131 .17822 -12 -4.5 ] [.01131 .17822 0 4.5 ] [.01131 .25997 -12 -4.5 ] [.01131 .25997 0 4.5 ] [.01131 .34172 -12 -4.5 ] [.01131 .34172 0 4.5 ] [.01131 .42347 -18 -4.5 ] [.01131 .42347 0 4.5 ] [.01131 .50522 -18 -4.5 ] [.01131 .50522 0 4.5 ] [.01131 .58697 -18 -4.5 ] [.01131 .58697 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 .2619 .01472 m .2619 .02097 L s [(5)] .2619 .00222 0 1 Mshowa .5 .01472 m .5 .02097 L s [(10)] .5 .00222 0 1 Mshowa .7381 .01472 m .7381 .02097 L s [(15)] .7381 .00222 0 1 Mshowa .97619 .01472 m .97619 .02097 L s [(20)] .97619 .00222 0 1 Mshowa .125 Mabswid .07143 .01472 m .07143 .01847 L s .11905 .01472 m .11905 .01847 L s .16667 .01472 m .16667 .01847 L s .21429 .01472 m .21429 .01847 L s .30952 .01472 m .30952 .01847 L s .35714 .01472 m .35714 .01847 L s .40476 .01472 m .40476 .01847 L s .45238 .01472 m .45238 .01847 L s .54762 .01472 m .54762 .01847 L s .59524 .01472 m .59524 .01847 L s .64286 .01472 m .64286 .01847 L s .69048 .01472 m .69048 .01847 L s .78571 .01472 m .78571 .01847 L s .83333 .01472 m .83333 .01847 L s .88095 .01472 m .88095 .01847 L s .92857 .01472 m .92857 .01847 L s .25 Mabswid 0 .01472 m 1 .01472 L s .02381 .09647 m .03006 .09647 L s [(20)] .01131 .09647 1 0 Mshowa .02381 .17822 m .03006 .17822 L s [(40)] .01131 .17822 1 0 Mshowa .02381 .25997 m .03006 .25997 L s [(60)] .01131 .25997 1 0 Mshowa .02381 .34172 m .03006 .34172 L s [(80)] .01131 .34172 1 0 Mshowa .02381 .42347 m .03006 .42347 L s [(100)] .01131 .42347 1 0 Mshowa .02381 .50522 m .03006 .50522 L s [(120)] .01131 .50522 1 0 Mshowa .02381 .58697 m .03006 .58697 L s [(140)] .01131 .58697 1 0 Mshowa .125 Mabswid .02381 .03515 m .02756 .03515 L s .02381 .05559 m .02756 .05559 L s .02381 .07603 m .02756 .07603 L s .02381 .1169 m .02756 .1169 L s .02381 .13734 m .02756 .13734 L s .02381 .15778 m .02756 .15778 L s .02381 .19865 m .02756 .19865 L s .02381 .21909 m .02756 .21909 L s .02381 .23953 m .02756 .23953 L s .02381 .2804 m .02756 .2804 L s .02381 .30084 m .02756 .30084 L s .02381 .32128 m .02756 .32128 L s .02381 .36215 m .02756 .36215 L s .02381 .38259 m .02756 .38259 L s .02381 .40303 m .02756 .40303 L s .02381 .44391 m .02756 .44391 L s .02381 .46434 m .02756 .46434 L s .02381 .48478 m .02756 .48478 L s .02381 .52566 m .02756 .52566 L s .02381 .54609 m .02756 .54609 L s .02381 .56653 m .02756 .56653 L s .02381 .60741 m .02756 .60741 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 .008 w .07143 .60332 Mdot .11905 .50931 Mdot .16667 .42347 Mdot .21429 .3458 Mdot .2619 .27632 Mdot .30952 .215 Mdot .35714 .16187 Mdot .40476 .1169 Mdot .45238 .08012 Mdot .5 .0515 Mdot .54762 .03107 Mdot .59524 .0188 Mdot .64286 .01472 Mdot .69048 .0188 Mdot .7381 .03107 Mdot .78571 .0515 Mdot .83333 .08012 Mdot .88095 .1169 Mdot .92857 .16187 Mdot .97619 .215 Mdot % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg03oool500000080oooo0P00000h0?oo o`@000000`3oool2000000@0oooo001D0?ooo`040000003oool0oooo000003/0oooo00D000000?oo o`3oool0oooo000000020?ooo`030000003oool0oooo03L0oooo00D000000?ooo`3oool0oooo0000 00020?ooo`030000003oool0oooo03D0oooo00<000000?ooo`3oool00`3oool010000000oooo0?oo o`0000030?ooo`00E`3oool00`000000oooo0?ooo`0i0?ooo`050000003oool0oooo0?ooo`000000 0P3oool00`000000oooo0?ooo`0g0?ooo`030000003oool0oooo00@0oooo00<000000?ooo`3oool0 =P3oool00`000000oooo0?ooo`020?ooo`040000003oool0oooo000000<0oooo001E0?ooo`800000 ?03oool01@000000oooo0?ooo`3oool000000080oooo00<000000?ooo`3oool0=`3oool00`000000 oooo0?ooo`020?ooo`800000>P3oool01@000000oooo0?ooo`3oool000000080oooo00<000000?oo o`3oool00@3oool005D0oooo00<000000?ooo`3oool0>`3oool01@000000oooo0?ooo`3oool00000 0080oooo00<000000?ooo`3oool0=`3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo 03L0oooo00@000000?ooo`3oool000000P3oool010000000oooo0?ooo`0000030?ooo`00E@3oool3 000003X0oooo0P0000040?ooo`800000>@3oool2000000@0oooo0`00000h0?ooo`800000103oool2 000000@0oooo003o0?ooob40oooo000E0?ooo`030000003oool0oooo0?l0oooo2@3oool001D0oooo 00<000000?ooo`3oool0o`3oool90?ooo`005@3oool00`000000oooo0?ooo`3o0?ooo`T0oooo000E 0?ooo`030000003oool0oooo0?l0oooo2@3oool000h0ooooo`00000C000000005@3oool00`000000 oooo0?ooo`0:0?ooo`030000003oool0oooo00X0oooo00<000000?ooo`3oool02P3oool00`000000 oooo0?ooo`0:0?ooo`030000003oool0oooo00X0oooo00<000000?ooo`3oool02P3oool00`000000 oooo0?ooo`0:0?ooo`030000003oool0oooo00X0oooo00<000000?ooo`3oool02P3oool00`000000 oooo0?ooo`090?ooo`030000003oool0oooo00X0oooo00<000000?ooo`3oool02P3oool00`000000 oooo0?ooo`0:0?ooo`030000003oool0oooo00X0oooo00<000000?ooo`3oool02P3oool00`000000 oooo0?ooo`0:0?ooo`030000003oool0oooo00X0oooo00<000000?ooo`3oool02P3oool00`000000 oooo0?ooo`0:0?ooo`030000003oool0oooo00X0oooo00<000000?ooo`3oool01@3oool001D0oooo 00<000000?ooo`3oool0?P3oool00`000000oooo0?ooo`0m0?ooo`030000003oool0oooo01L0oooo 00<000000?ooo`3oool05`3oool00`000000oooo0?ooo`0:0?ooo`030000003oool0oooo03h0oooo 00<000000?ooo`3oool01@3oool001D0oooo00<000000?ooo`3oool0o`3oool90?ooo`005@3oool0 0`000000oooo0?ooo`2;0?ooo`030000003oool0oooo0340oooo00<000000?ooo`3oool0AP3oool0 01D0oooo00<000000?ooo`3oool0R`3oool00`000000oooo0?ooo`0a0?ooo`030000003oool0oooo 04H0oooo000E0?ooo`800000o`3oool:0?ooo`005@3oool00`000000oooo0?ooo`3o0?ooo`T0oooo 000E0?ooo`030000003oool0oooo0?l0oooo2@3oool001D0oooo00<000000?ooo`3oool0o`3oool9 0?ooo`005@3oool00`000000oooo0?ooo`1n0?ooo`030000003oool0oooo04/0oooo00<000000?oo o`3oool0>@3oool001D0oooo0P00001o0?ooo`030000003oool0oooo04/0oooo00<000000?ooo`3o ool0>@3oool001D0oooo00<000000?ooo`3oool0o`3oool90?ooo`005@3oool00`000000oooo0?oo o`3o0?ooo`T0oooo000E0?ooo`030000003oool0oooo0?l0oooo2@3oool001D0oooo00<000000?oo o`3oool0o`3oool90?ooo`005@3oool00`000000oooo0?ooo`3o0?ooo`T0oooo000E0?ooo`800000 o`3oool:0?ooo`005@3oool00`000000oooo0?ooo`1a0?ooo`030000003oool0oooo06D0oooo00<0 00000?ooo`3oool0;03oool001D0oooo00<000000?ooo`3oool0L@3oool00`000000oooo0?ooo`1U 0?ooo`030000003oool0oooo02`0oooo00070?ooo`@000000`3oool2000000D0oooo00<000000?oo o`3oool0o`3oool90?ooo`001`3oool00`000000oooo0?ooo`030?ooo`040000003oool0oooo0000 00@0oooo00<000000?ooo`3oool0o`3oool90?ooo`00203oool00`000000oooo0?ooo`020?ooo`04 0000003oool0oooo000000@0oooo0`00003o0?ooo`T0oooo00090?ooo`050000003oool0oooo0?oo o`0000000P3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo0?l0oooo2@3oool000L0 oooo00@000000?ooo`3oool000000P3oool010000000oooo0?ooo`0000040?ooo`030000003oool0 oooo0?l0oooo2@3oool000P0oooo0P0000040?ooo`8000001@3oool00`000000oooo0?ooo`3o0?oo o`T0oooo000E0?ooo`030000003oool0oooo0?l0oooo2@3oool001D0oooo00<000000?ooo`3oool0 o`3oool90?ooo`005@3oool2000006D0oooo00<000000?ooo`3oool0O`3oool00`000000oooo0?oo o`0O0?ooo`005@3oool00`000000oooo0?ooo`1T0?ooo`030000003oool0oooo07l0oooo00<00000 0?ooo`3oool07`3oool001D0oooo00<000000?ooo`3oool0o`3oool90?ooo`005@3oool00`000000 oooo0?ooo`3o0?ooo`T0oooo000E0?ooo`030000003oool0oooo0?l0oooo2@3oool001D0oooo00<0 00000?ooo`3oool0o`3oool90?ooo`005@3oool200000?l0oooo2P3oool001D0oooo00<000000?oo o`3oool0o`3oool90?ooo`005@3oool00`000000oooo0?ooo`3o0?ooo`T0oooo000E0?ooo`030000 003oool0oooo0?l0oooo2@3oool001D0oooo00<000000?ooo`3oool0o`3oool90?ooo`005@3oool2 00000?l0oooo2P3oool001D0oooo00<000000?ooo`3oool0E`3oool00`000000oooo0?ooo`2I0?oo o`030000003oool0oooo0180oooo000E0?ooo`030000003oool0oooo05L0oooo00<000000?ooo`3o ool0V@3oool00`000000oooo0?ooo`0B0?ooo`005@3oool00`000000oooo0?ooo`3o0?ooo`T0oooo 00090?ooo`<000000P3oool2000000D0oooo00<000000?ooo`3oool0o`3oool90?ooo`002P3oool0 10000000oooo0?ooo`0000020?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool0o`3o ool90?ooo`001`3oool5000000050?ooo`000000oooo0?ooo`000000103oool300000?l0oooo2@3o ool000L0oooo00@000000?ooo`3oool000000P3oool010000000oooo0?ooo`0000040?ooo`030000 003oool0oooo0?l0oooo2@3oool000P0oooo00<000000?ooo`0000000P3oool010000000oooo0?oo o`0000040?ooo`030000003oool0oooo0?l0oooo2@3oool000T0oooo0P0000030?ooo`8000001@3o ool00`000000oooo0?ooo`3o0?ooo`T0oooo000E0?ooo`030000003oool0oooo0?l0oooo2@3oool0 01D0oooo0P00003o0?ooo`X0oooo000E0?ooo`030000003oool0oooo0?l0oooo2@3oool001D0oooo 00<000000?ooo`3oool0o`3oool90?ooo`005@3oool00`000000oooo0?ooo`3o0?ooo`T0oooo000E 0?ooo`030000003oool0oooo04X0oooo00<000000?ooo`3oool0/P3oool00`000000oooo0?ooo`06 0?ooo`005@3oool00`000000oooo0?ooo`1:0?ooo`030000003oool0oooo0;80oooo00<000000?oo o`3oool01P3oool001D0oooo0P00003o0?ooo`X0oooo000E0?ooo`030000003oool0oooo0?l0oooo 2@3oool001D0oooo00<000000?ooo`3oool0o`3oool90?ooo`005@3oool00`000000oooo0?ooo`3o 0?ooo`T0oooo000E0?ooo`030000003oool0oooo0?l0oooo2@3oool001D0oooo0P00003o0?ooo`X0 oooo000E0?ooo`030000003oool0oooo0?l0oooo2@3oool001D0oooo00<000000?ooo`3oool0o`3o ool90?ooo`005@3oool00`000000oooo0?ooo`3o0?ooo`T0oooo00070?ooo`<00000103oool20000 00D0oooo00<000000?ooo`3oool0o`3oool90?ooo`001`3oool010000000oooo0?ooo`0000020?oo o`040000003oool0oooo000000@0oooo00<000000?ooo`3oool0o`3oool90?ooo`001`3oool01000 0000oooo0?ooo`0000020?ooo`040000003oool0oooo000000@0oooo0`00003o0?ooo`T0oooo0007 0?ooo`<000000`3oool010000000oooo0?ooo`0000040?ooo`030000003oool0oooo0?l0oooo2@3o ool000P0oooo00<000000?ooo`3oool00P3oool010000000oooo0?ooo`0000040?ooo`030000003o ool0oooo0?l0oooo2@3oool000P0oooo0`0000030?ooo`8000001@3oool00`000000oooo0?ooo`3o 0?ooo`T0oooo000E0?ooo`030000003oool0oooo03d0oooo00<000000?ooo`3oool0b03oool001D0 oooo0P00000n0?ooo`030000003oool0oooo080oooo00030?ooo`050000003oool0oooo0?ooo`0000000P3o ool010000000oooo0?ooo`0000020?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool0 o`3oool90?ooo`000P3oool2000000@0oooo0P0000040?ooo`8000001@3oool00`000000oooo0?oo o`3o0?ooo`T0oooo000E0?ooo`030000003oool0oooo0?l0oooo2@3oool001D0oooo00<000000?oo o`3oool0o`3oool90?ooo`005@3oool200000?l0oooo2P3oool001D0oooo00<000000?ooo`3oool0 o`3oool90?ooo`005@3oool00`000000oooo0?ooo`3o0?ooo`T0oooo000E0?ooo`030000003oool0 oooo0?l0oooo2@3oool001D0oooo00<000000?ooo`3oool0o`3oool90?ooo`005@3oool200000?l0 oooo2P3oool001D0oooo00<000000?ooo`3oool0o`3oool90?ooo`005@3oool00`000000oooo0?oo o`3o0?ooo`T0oooo000E0?ooo`030000003oool0oooo0?l0oooo2@3oool001D0oooo00<000000?oo o`3oool0o`3oool90?ooo`005@3oool00`000000oooo0?ooo`3o0?ooo`T0oooo000E0?ooo`800000 o`3oool:0?ooo`005@3oool00`000000oooo0?ooo`3o0?ooo`T0oooo000E0?ooo`030000003oool0 oooo0?l0oooo2@3oool001D0oooo00<000000?ooo`3oool0o`3oool90?ooo`0000<0oooo00000000 00000`0000000`3oool0000000000002000000<0oooo0P0000050?ooo`030000003oool0oooo0?l0 oooo2@3oool000<0oooo00D000000?ooo`3oool0oooo000000050?ooo`040000003oool0oooo0000 00@0oooo00<000000?ooo`3oool0o`3oool90?ooo`000`3oool00`000000oooo0?ooo`020?ooo`03 0000003oool0oooo0080oooo00@000000?ooo`3oool00000103oool3000001H0oooo00<000000?oo o`3oool0k`3oool000<0oooo00<000000?ooo`3oool00`3oool01@000000oooo0?ooo`3oool00000 0080oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`0F0?ooo`030000003oool0oooo 0>l0oooo00030?ooo`050000003oool0oooo0?ooo`0000000P3oool010000000oooo0?ooo`000002 0?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool0o`3oool90?ooo`000P3oool20000 00@0oooo0P0000040?ooo`8000001@3oool00`000000oooo0?ooo`3o0?ooo`T0oooo000E0?ooo`03 0000003oool0oooo0?l0oooo2@3oool001D0oooo0P00003o0?ooo`X0oooo000E0?ooo`030000003o ool0oooo0?l0oooo2@3oool001D0oooo00<000000?ooo`3oool0o`3oool90?ooo`005@3oool00`00 0000oooo0?ooo`3o0?ooo`T0oooo000E0?ooo`030000003oool0oooo0?l0oooo2@3oool001D0oooo 00<000000?ooo`3oool0o`3oool90?ooo`005@3oool200000?l0oooo2P3oool001D0oooo00<00000 0?ooo`3oool0o`3oool90?ooo`005@3oool00`000000oooo0?ooo`3o0?ooo`T0oooo000E0?ooo`03 0000003oool0oooo0?l0oooo2@3oool001D0oooo00<000000?ooo`3oool0o`3oool90?ooo`005@3o ool200000?l0oooo2P3oool001D0oooo00<000000?ooo`3oool0o`3oool90?ooo`005@3oool00`00 0000oooo0?ooo`3o0?ooo`T0oooo000E0?ooo`030000003oool0oooo0?l0oooo2@3oool000030?oo o`000000000000<000000`3oool300000080oooo0P0000050?ooo`030000003oool0oooo0?l0oooo 2@3oool000<0oooo00<000000?ooo`3oool0103oool010000000oooo0?ooo`0000020?ooo`030000 003oool0oooo0080oooo00<000000?ooo`3oool0o`3oool90?ooo`000`3oool010000000oooo0?oo o`3oool5000000050?ooo`000000oooo0?ooo`000000103oool300000?l0oooo2@3oool000<0oooo 00D000000?ooo`3oool0oooo000000020?ooo`040000003oool0oooo00000080oooo00<000000?oo o`3oool00P3oool00`000000oooo0?ooo`3o0?ooo`T0oooo00030?ooo`030000003oool0oooo0080 oooo00<000000?ooo`0000000P3oool010000000oooo0?ooo`0000040?ooo`030000003oool0oooo 0?l0oooo2@3oool00080oooo0P0000050?ooo`8000000`3oool2000000D0oooo00<000000?ooo`3o ool0o`3oool90?ooo`005@3oool00`000000oooo0?ooo`090?ooo`030000003oool0oooo0?`0oooo 000E0?ooo`8000002P3oool00`000000oooo0?ooo`3l0?ooo`005@3oool00`000000oooo0?ooo`3o 0?ooo`T0oooo000E0?ooo`030000003oool0oooo0?l0oooo2@3oool001D0oooo00<000000?ooo`3o ool0o`3oool90?ooo`00\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-1.65192, -11.3255, \ 0.0771848, 0.89919}}], 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 0.047619 0.0147151 0.00408753 [ [.2619 .00222 -3 -9 ] [.2619 .00222 3 0 ] [.5 .00222 -6 -9 ] [.5 .00222 6 0 ] [.7381 .00222 -6 -9 ] [.7381 .00222 6 0 ] [.97619 .00222 -6 -9 ] [.97619 .00222 6 0 ] [.01131 .09647 -12 -4.5 ] [.01131 .09647 0 4.5 ] [.01131 .17822 -12 -4.5 ] [.01131 .17822 0 4.5 ] [.01131 .25997 -12 -4.5 ] [.01131 .25997 0 4.5 ] [.01131 .34172 -12 -4.5 ] [.01131 .34172 0 4.5 ] [.01131 .42347 -18 -4.5 ] [.01131 .42347 0 4.5 ] [.01131 .50522 -18 -4.5 ] [.01131 .50522 0 4.5 ] [.01131 .58697 -18 -4.5 ] [.01131 .58697 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 .2619 .01472 m .2619 .02097 L s [(5)] .2619 .00222 0 1 Mshowa .5 .01472 m .5 .02097 L s [(10)] .5 .00222 0 1 Mshowa .7381 .01472 m .7381 .02097 L s [(15)] .7381 .00222 0 1 Mshowa .97619 .01472 m .97619 .02097 L s [(20)] .97619 .00222 0 1 Mshowa .125 Mabswid .07143 .01472 m .07143 .01847 L s .11905 .01472 m .11905 .01847 L s .16667 .01472 m .16667 .01847 L s .21429 .01472 m .21429 .01847 L s .30952 .01472 m .30952 .01847 L s .35714 .01472 m .35714 .01847 L s .40476 .01472 m .40476 .01847 L s .45238 .01472 m .45238 .01847 L s .54762 .01472 m .54762 .01847 L s .59524 .01472 m .59524 .01847 L s .64286 .01472 m .64286 .01847 L s .69048 .01472 m .69048 .01847 L s .78571 .01472 m .78571 .01847 L s .83333 .01472 m .83333 .01847 L s .88095 .01472 m .88095 .01847 L s .92857 .01472 m .92857 .01847 L s .25 Mabswid 0 .01472 m 1 .01472 L s .02381 .09647 m .03006 .09647 L s [(20)] .01131 .09647 1 0 Mshowa .02381 .17822 m .03006 .17822 L s [(40)] .01131 .17822 1 0 Mshowa .02381 .25997 m .03006 .25997 L s [(60)] .01131 .25997 1 0 Mshowa .02381 .34172 m .03006 .34172 L s [(80)] .01131 .34172 1 0 Mshowa .02381 .42347 m .03006 .42347 L s [(100)] .01131 .42347 1 0 Mshowa .02381 .50522 m .03006 .50522 L s [(120)] .01131 .50522 1 0 Mshowa .02381 .58697 m .03006 .58697 L s [(140)] .01131 .58697 1 0 Mshowa .125 Mabswid .02381 .03515 m .02756 .03515 L s .02381 .05559 m .02756 .05559 L s .02381 .07603 m .02756 .07603 L s .02381 .1169 m .02756 .1169 L s .02381 .13734 m .02756 .13734 L s .02381 .15778 m .02756 .15778 L s .02381 .19865 m .02756 .19865 L s .02381 .21909 m .02756 .21909 L s .02381 .23953 m .02756 .23953 L s .02381 .2804 m .02756 .2804 L s .02381 .30084 m .02756 .30084 L s .02381 .32128 m .02756 .32128 L s .02381 .36215 m .02756 .36215 L s .02381 .38259 m .02756 .38259 L s .02381 .40303 m .02756 .40303 L s .02381 .44391 m .02756 .44391 L s .02381 .46434 m .02756 .46434 L s .02381 .48478 m .02756 .48478 L s .02381 .52566 m .02756 .52566 L s .02381 .54609 m .02756 .54609 L s .02381 .56653 m .02756 .56653 L s .02381 .60741 m .02756 .60741 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 .07143 .60332 m .11905 .50931 L .16667 .42347 L .21429 .3458 L .2619 .27632 L .30952 .215 L .35714 .16187 L .40476 .1169 L .45238 .08012 L .5 .0515 L .54762 .03107 L .59524 .0188 L .64286 .01472 L .69048 .0188 L .7381 .03107 L .78571 .0515 L .83333 .08012 L .88095 .1169 L .92857 .16187 L .97619 .215 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]HGAYHf4PAg9QL6QYHg03oool500000080oooo0P00000h0?oo o`@000000`3oool2000000@0oooo001D0?ooo`040000003oool0oooo000003/0oooo00D000000?oo o`3oool0oooo000000020?ooo`030000003oool0oooo03L0oooo00D000000?ooo`3oool0oooo0000 00020?ooo`030000003oool0oooo03D0oooo00<000000?ooo`3oool00`3oool010000000oooo0?oo o`0000030?ooo`00E`3oool00`000000oooo0?ooo`0i0?ooo`050000003oool0oooo0?ooo`000000 0P3oool00`000000oooo0?ooo`0g0?ooo`030000003oool0oooo00@0oooo00<000000?ooo`3oool0 =P3oool00`000000oooo0?ooo`020?ooo`040000003oool0oooo000000<0oooo001E0?ooo`800000 ?03oool01@000000oooo0?ooo`3oool000000080oooo00<000000?ooo`3oool0=`3oool00`000000 oooo0?ooo`020?ooo`800000>P3oool01@000000oooo0?ooo`3oool000000080oooo00<000000?oo o`3oool00@3oool005D0oooo00<000000?ooo`3oool0>`3oool01@000000oooo0?ooo`3oool00000 0080oooo00<000000?ooo`3oool0=`3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo 03L0oooo00@000000?ooo`3oool000000P3oool010000000oooo0?ooo`0000030?ooo`00E@3oool3 000003X0oooo0P0000040?ooo`800000>@3oool2000000@0oooo0`00000h0?ooo`800000103oool2 000000@0oooo003o0?ooob40oooo000E0?ooo`030000003oool0oooo0?l0oooo2@3oool001D0oooo 00<000000?ooo`3oool0o`3oool90?ooo`005@3oool00`000000oooo0?ooo`3o0?ooo`T0oooo000E 0?ooo`030000003oool0oooo0?l0oooo2@3oool000h0ooooo`00000C000000005@3oool00`000000 oooo0?ooo`0:0?ooo`030000003oool0oooo00X0oooo00<000000?ooo`3oool02P3oool00`000000 oooo0?ooo`0:0?ooo`030000003oool0oooo00X0oooo00<000000?ooo`3oool02P3oool00`000000 oooo0?ooo`0:0?ooo`030000003oool0oooo00X0oooo00<000000?ooo`3oool02P3oool00`000000 oooo0?ooo`090?ooo`030000003oool0oooo00X0oooo00<000000?ooo`3oool02@3oool8000000H0 oooo00<000000?ooo`3oool0103oool8000000/0oooo00<000000?ooo`3oool02P3oool00`000000 oooo0?ooo`0:0?ooo`030000003oool0oooo00X0oooo00<000000?ooo`3oool02P3oool00`000000 oooo0?ooo`0:0?ooo`030000003oool0oooo00D0oooo000E0?ooo`030000003oool0oooo03h0oooo 00<000000?ooo`3oool0?@3oool00`000000oooo0?ooo`0C0?ooo`<000007@3oool3000000P0oooo 00<000000?ooo`3oool0?P3oool00`000000oooo0?ooo`050?ooo`005@3oool00`000000oooo0?oo o`2@0?ooo`@000008`3oool4000004d0oooo000E0?ooo`030000003oool0oooo08d0oooo0`00000[ 0?ooo`<00000BP3oool001D0oooo00<000000?ooo`3oool0RP3oool300000340oooo0`0000170?oo o`005@3oool2000008T0oooo0P00000g0?ooo`800000A@3oool001D0oooo00<000000?ooo`3oool0 Q@3oool3000003/0oooo0`0000120?ooo`005@3oool00`000000oooo0?ooo`220?ooo`<00000@@3o ool3000003l0oooo000E0?ooo`030000003oool0oooo0800oooo0P0000170?ooo`800000?@3oool0 01D0oooo00<000000?ooo`3oool0OP3oool2000004/0oooo0P00000k0?ooo`005@3oool2000007d0 oooo0P00001?0?ooo`800000>@3oool001D0oooo00<000000?ooo`3oool0N`3oool00`000000oooo 0?ooo`1A0?ooo`800000=`3oool001D0oooo00<000000?ooo`3oool0N@3oool2000005H0oooo00<0 00000?ooo`3oool0=03oool001D0oooo00<000000?ooo`3oool0N03oool00`000000oooo0?ooo`1G 0?ooo`800000=03oool001D0oooo00<000000?ooo`3oool0MP3oool2000005`0oooo00<000000?oo o`3oool0<@3oool001D0oooo00<000000?ooo`3oool0M@3oool00`000000oooo0?ooo`1M0?ooo`80 0000<@3oool001D0oooo0P00001d0?ooo`800000HP3oool2000002l0oooo000E0?ooo`030000003o ool0oooo0780oooo00<000000?ooo`3oool0I03oool00`000000oooo0?ooo`0/0?ooo`005@3oool0 0`000000oooo0?ooo`1a0?ooo`030000003oool0oooo06H0oooo00<000000?ooo`3oool0:`3oool0 00L0oooo100000030?ooo`8000001@3oool00`000000oooo0?ooo`1_0?ooo`800000JP3oool20000 02/0oooo00070?ooo`030000003oool0oooo00<0oooo00@000000?ooo`3oool00000103oool00`00 0000oooo0?ooo`1^0?ooo`030000003oool0oooo06`0oooo00<000000?ooo`3oool0:03oool000P0 oooo00<000000?ooo`3oool00P3oool010000000oooo0?ooo`0000040?ooo`<00000K@3oool00`00 0000oooo0?ooo`1^0?ooo`030000003oool0oooo02L0oooo00090?ooo`050000003oool0oooo0?oo o`0000000P3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo06/0oooo0P00001b0?oo o`8000009`3oool000L0oooo00@000000?ooo`3oool000000P3oool010000000oooo0?ooo`000004 0?ooo`030000003oool0oooo06X0oooo00<000000?ooo`3oool0M03oool00`000000oooo0?ooo`0T 0?ooo`00203oool2000000@0oooo0P0000050?ooo`030000003oool0oooo06T0oooo00<000000?oo o`3oool0MP3oool00`000000oooo0?ooo`0S0?ooo`005@3oool00`000000oooo0?ooo`1W0?ooo`80 0000NP3oool2000002<0oooo000E0?ooo`030000003oool0oooo06H0oooo00<000000?ooo`3oool0 O03oool00`000000oooo0?ooo`0P0?ooo`005@3oool2000006H0oooo00<000000?ooo`3oool0OP3o ool00`000000oooo0?ooo`0O0?ooo`005@3oool00`000000oooo0?ooo`1T0?ooo`030000003oool0 oooo0800oooo00<000000?ooo`3oool07P3oool001D0oooo00<000000?ooo`3oool0H`3oool00`00 0000oooo0?ooo`220?ooo`030000003oool0oooo01d0oooo000E0?ooo`030000003oool0oooo0680 oooo00<000000?ooo`3oool0Q03oool00`000000oooo0?ooo`0L0?ooo`005@3oool00`000000oooo 0?ooo`1Q0?ooo`030000003oool0oooo08H0oooo00<000000?ooo`3oool06`3oool001D0oooo00<0 00000?ooo`3oool0H03oool00`000000oooo0?ooo`280?ooo`030000003oool0oooo01X0oooo000E 0?ooo`800000G`3oool2000008`0oooo0P00000J0?ooo`005@3oool00`000000oooo0?ooo`1M0?oo o`030000003oool0oooo08h0oooo00<000000?ooo`3oool05`3oool001D0oooo00<000000?ooo`3o ool0G03oool00`000000oooo0?ooo`2@0?ooo`030000003oool0oooo01H0oooo000E0?ooo`030000 003oool0oooo05/0oooo00<000000?ooo`3oool0TP3oool00`000000oooo0?ooo`0E0?ooo`005@3o ool00`000000oooo0?ooo`1J0?ooo`030000003oool0oooo09@0oooo00<000000?ooo`3oool0503o ool001D0oooo0P00001J0?ooo`030000003oool0oooo09H0oooo00<000000?ooo`3oool04`3oool0 01D0oooo00<000000?ooo`3oool0F03oool00`000000oooo0?ooo`2H0?ooo`030000003oool0oooo 0180oooo000E0?ooo`030000003oool0oooo05L0oooo00<000000?ooo`3oool0VP3oool00`000000 oooo0?ooo`0A0?ooo`005@3oool00`000000oooo0?ooo`1F0?ooo`030000003oool0oooo09`0oooo 00<000000?ooo`3oool0403oool000T0oooo0`0000020?ooo`8000001@3oool00`000000oooo0?oo o`1E0?ooo`030000003oool0oooo09h0oooo00<000000?ooo`3oool03`3oool000X0oooo00@00000 0?ooo`3oool000000P3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo05D0oooo00<0 00000?ooo`3oool0WP3oool00`000000oooo0?ooo`0?0?ooo`001`3oool5000000050?ooo`000000 oooo0?ooo`000000103oool3000005@0oooo00<000000?ooo`3oool0X03oool00`000000oooo0?oo o`0>0?ooo`001`3oool010000000oooo0?ooo`0000020?ooo`040000003oool0oooo000000@0oooo 00<000000?ooo`3oool0D`3oool00`000000oooo0?ooo`2R0?ooo`030000003oool0oooo00d0oooo 00080?ooo`030000003oool000000080oooo00@000000?ooo`3oool00000103oool00`000000oooo 0?ooo`1B0?ooo`030000003oool0oooo0:@0oooo00<000000?ooo`3oool0303oool000T0oooo0P00 00030?ooo`8000001@3oool00`000000oooo0?ooo`1A0?ooo`030000003oool0oooo0:H0oooo00<0 00000?ooo`3oool02`3oool001D0oooo00<000000?ooo`3oool0D03oool00`000000oooo0?ooo`2X 0?ooo`030000003oool0oooo00X0oooo000E0?ooo`800000D03oool00`000000oooo0?ooo`2Z0?oo o`030000003oool0oooo00T0oooo000E0?ooo`030000003oool0oooo04h0oooo00<000000?ooo`3o ool0[03oool00`000000oooo0?ooo`080?ooo`005@3oool00`000000oooo0?ooo`1>0?ooo`030000 003oool0oooo0:`0oooo00<000000?ooo`3oool0203oool001D0oooo00<000000?ooo`3oool0C@3o ool00`000000oooo0?ooo`2^0?ooo`030000003oool0oooo00L0oooo000E0?ooo`030000003oool0 oooo04`0oooo00<000000?ooo`3oool0/03oool00`000000oooo0?ooo`060?ooo`005@3oool00`00 0000oooo0?ooo`1;0?ooo`030000003oool0oooo0;80oooo00<000000?ooo`3oool01@3oool001D0 oooo0P00001;0?ooo`030000003oool0oooo0;/0oooo000E0?ooo`030000003oool0oooo04T0oooo 00<000000?ooo`3oool0_03oool001D0oooo00<000000?ooo`3oool0B@3oool00`000000oooo0?oo o`2l0?ooo`005@3oool00`000000oooo0?ooo`180?ooo`030000003oool0oooo0;d0oooo000E0?oo o`030000003oool0oooo04L0oooo00<000000?ooo`3oool0_P3oool001D0oooo0P0000170?ooo`03 0000003oool0oooo0;l0oooo000E0?ooo`030000003oool0oooo04D0oooo00<000000?ooo`3oool0 `03oool001D0oooo00<000000?ooo`3oool0A03oool00`000000oooo0?ooo`310?ooo`005@3oool0 0`000000oooo0?ooo`140?ooo`030000003oool0oooo0<40oooo00070?ooo`<00000103oool20000 00D0oooo00<000000?ooo`3oool0@`3oool00`000000oooo0?ooo`320?ooo`001`3oool010000000 oooo0?ooo`0000020?ooo`040000003oool0oooo000000@0oooo00<000000?ooo`3oool0@P3oool0 0`000000oooo0?ooo`330?ooo`001`3oool010000000oooo0?ooo`0000020?ooo`040000003oool0 oooo000000@0oooo0`0000110?ooo`030000003oool0oooo0<@0oooo00070?ooo`<000000`3oool0 10000000oooo0?ooo`0000040?ooo`030000003oool0oooo0400oooo00<000000?ooo`3oool0a@3o ool000P0oooo00<000000?ooo`3oool00P3oool010000000oooo0?ooo`0000040?ooo`030000003o ool0oooo0400oooo00<000000?ooo`3oool0a@3oool000P0oooo0`0000030?ooo`8000001@3oool0 0`000000oooo0?ooo`0o0?ooo`030000003oool0oooo0P3oool00`000000oooo0?ooo`3;0?ooo`00 5@3oool2000003X0oooo00<000000?ooo`3oool0c03oool001D0oooo00<000000?ooo`3oool0>@3o ool00`000000oooo0?ooo`3<0?ooo`005@3oool00`000000oooo0?ooo`0h0?ooo`030000003oool0 oooo080oooo0003 0?ooo`050000003oool0oooo0?ooo`0000000P3oool010000000oooo0?ooo`0000020?ooo`030000 003oool0oooo0080oooo00<000000?ooo`3oool08`3oool00`000000oooo0?ooo`3R0?ooo`000P3o ool2000000@0oooo0P0000040?ooo`8000001@3oool00`000000oooo0?ooo`0R0?ooo`030000003o ool0oooo0><0oooo000E0?ooo`030000003oool0oooo0280oooo00<000000?ooo`3oool0h`3oool0 01D0oooo00<000000?ooo`3oool08@3oool00`000000oooo0?ooo`3T0?ooo`005@3oool200000280 oooo00<000000?ooo`3oool0i03oool001D0oooo00<000000?ooo`3oool0803oool00`000000oooo 0?ooo`3U0?ooo`005@3oool00`000000oooo0?ooo`0P0?ooo`030000003oool0oooo0>D0oooo000E 0?ooo`030000003oool0oooo01l0oooo00<000000?ooo`3oool0iP3oool001D0oooo00<000000?oo o`3oool07`3oool00`000000oooo0?ooo`3V0?ooo`005@3oool2000001l0oooo00<000000?ooo`3o ool0i`3oool001D0oooo00<000000?ooo`3oool07@3oool00`000000oooo0?ooo`3X0?ooo`005@3o ool00`000000oooo0?ooo`0M0?ooo`030000003oool0oooo0>P0oooo000E0?ooo`030000003oool0 oooo01`0oooo00<000000?ooo`3oool0j@3oool001D0oooo00<000000?ooo`3oool0703oool00`00 0000oooo0?ooo`3Y0?ooo`005@3oool00`000000oooo0?ooo`0K0?ooo`030000003oool0oooo0>X0 oooo000E0?ooo`800000703oool00`000000oooo0?ooo`3Z0?ooo`005@3oool00`000000oooo0?oo o`0J0?ooo`030000003oool0oooo0>/0oooo000E0?ooo`030000003oool0oooo01X0oooo00<00000 0?ooo`3oool0j`3oool001D0oooo00<000000?ooo`3oool06@3oool00`000000oooo0?ooo`3/0?oo o`0000<0oooo0000000000000`0000000`3oool0000000000002000000<0oooo0P0000050?ooo`03 0000003oool0oooo01T0oooo00<000000?ooo`3oool0k03oool000<0oooo00D000000?ooo`3oool0 oooo000000050?ooo`040000003oool0oooo000000@0oooo00<000000?ooo`3oool0603oool00`00 0000oooo0?ooo`3]0?ooo`000`3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo0080 oooo00@000000?ooo`3oool00000103oool3000001P0oooo00<000000?ooo`3oool0k@3oool000<0 oooo00<000000?ooo`3oool00`3oool01@000000oooo0?ooo`3oool000000080oooo00<000000?oo o`3oool00P3oool00`000000oooo0?ooo`0G0?ooo`030000003oool0oooo0>h0oooo00030?ooo`05 0000003oool0oooo0?ooo`0000000P3oool010000000oooo0?ooo`0000020?ooo`030000003oool0 oooo0080oooo00<000000?ooo`3oool05P3oool00`000000oooo0?ooo`3_0?ooo`000P3oool20000 00@0oooo0P0000040?ooo`8000001@3oool00`000000oooo0?ooo`0F0?ooo`030000003oool0oooo 0>l0oooo000E0?ooo`030000003oool0oooo01D0oooo00<000000?ooo`3oool0l03oool001D0oooo 0P00000F0?ooo`030000003oool0oooo0?00oooo000E0?ooo`030000003oool0oooo01@0oooo00<0 00000?ooo`3oool0l@3oool001D0oooo00<000000?ooo`3oool0503oool00`000000oooo0?ooo`3a 0?ooo`005@3oool00`000000oooo0?ooo`0C0?ooo`030000003oool0oooo0?80oooo000E0?ooo`03 0000003oool0oooo01<0oooo00<000000?ooo`3oool0lP3oool001D0oooo00<000000?ooo`3oool0 4P3oool00`000000oooo0?ooo`3c0?ooo`005@3oool2000001<0oooo00<000000?ooo`3oool0l`3o ool001D0oooo00<000000?ooo`3oool04@3oool00`000000oooo0?ooo`3d0?ooo`005@3oool00`00 0000oooo0?ooo`0A0?ooo`030000003oool0oooo0?@0oooo000E0?ooo`030000003oool0oooo0100 oooo00<000000?ooo`3oool0m@3oool001D0oooo00<000000?ooo`3oool0403oool00`000000oooo 0?ooo`3e0?ooo`005@3oool200000100oooo00<000000?ooo`3oool0mP3oool001D0oooo00<00000 0?ooo`3oool03`3oool00`000000oooo0?ooo`3f0?ooo`005@3oool00`000000oooo0?ooo`0>0?oo o`030000003oool0oooo0?L0oooo000E0?ooo`030000003oool0oooo00h0oooo00<000000?ooo`3o ool0m`3oool000030?ooo`000000000000<000000`3oool300000080oooo0P0000050?ooo`030000 003oool0oooo00d0oooo00<000000?ooo`3oool0n03oool000<0oooo00<000000?ooo`3oool0103o ool010000000oooo0?ooo`0000020?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool0 3@3oool00`000000oooo0?ooo`3h0?ooo`000`3oool010000000oooo0?ooo`3oool5000000050?oo o`000000oooo0?ooo`000000103oool3000000`0oooo00<000000?ooo`3oool0n@3oool000<0oooo 00D000000?ooo`3oool0oooo000000020?ooo`040000003oool0oooo00000080oooo00<000000?oo o`3oool00P3oool00`000000oooo0?ooo`0<0?ooo`030000003oool0oooo0?T0oooo00030?ooo`03 0000003oool0oooo0080oooo00<000000?ooo`0000000P3oool010000000oooo0?ooo`0000040?oo o`030000003oool0oooo00/0oooo00<000000?ooo`3oool0nP3oool00080oooo0P0000050?ooo`80 00000`3oool2000000D0oooo00<000000?ooo`3oool02`3oool00`000000oooo0?ooo`3j0?ooo`00 5@3oool00`000000oooo0?ooo`0:0?ooo`030000003oool0oooo0?/0oooo000E0?ooo`800000o`3o ool:0?ooo`005@3oool00`000000oooo0?ooo`3o0?ooo`T0oooo000E0?ooo`030000003oool0oooo 0?l0oooo2@3oool001D0oooo00<000000?ooo`3oool0o`3oool90?ooo`00\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-1.65192, -11.3255, \ 0.0771848, 0.89919}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[TextData[{ StyleBox["Note 1) ", FontWeight->"Bold", FontColor->RGBColor[0.682353, 0.32549, 0.317647]], StyleBox["Notice how the arrays are printed out when you evaluate the cell. \ This can be annoying when you want to look at a complicated graph but don't \ want to see all of it's underlying points printed out. Put a \";\" at the end \ of the expressions that you don't want to display the results of.\n\nNote 2) \ It's considered good ", FontWeight->"Bold", FontColor->RGBColor[0.682353, 0.32549, 0.317647], FontVariations->{"CompatibilityType"->0}], StyleBox["Mathematica", FontWeight->"Bold", FontSlant->"Italic", FontColor->RGBColor[0.682353, 0.32549, 0.317647], FontVariations->{"CompatibilityType"->0}], StyleBox[" practice to begin your custom variable names with a lower case \ letter, which will prevent name collisions with the ", FontWeight->"Bold", FontColor->RGBColor[0.682353, 0.32549, 0.317647], FontVariations->{"CompatibilityType"->0}], StyleBox["Mathematicas ", FontWeight->"Bold", FontSlant->"Italic", FontColor->RGBColor[0.682353, 0.32549, 0.317647], FontVariations->{"CompatibilityType"->0}], StyleBox["names, all of which begin with uppercase letters.\n\nNote 3) \ Don't forget to put the colon in front of the equals sign \":=\" when you \ define a function. This can be very frustrating, because leaving it off won't \ cause an error. So if your function is giving you unexpected results, don't \ forget to re-read this note!", FontWeight->"Bold", FontColor->RGBColor[0.682353, 0.32549, 0.317647], FontVariations->{"CompatibilityType"->0}] }], "Text", TextAlignment->Left, TextJustification->0] }, Open ]], Cell[TextData[StyleBox["8: Using lists to graph a built in function", \ "Subsection"]], "Text", TextAlignment->Center, TextJustification->0], Cell[CellGroupData[{ Cell[TextData[{ "You can compose your own custom functions with ", StyleBox["Mathematica", FontSlant->"Italic"], " built in functions. Remember N from the tutorial? -", StyleBox[" evaluate these expressions.", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]] }], "Text", TextAlignment->Left, TextJustification->0], Cell[CellGroupData[{ Cell[BoxData[{ \(\(k\ = \ 3;\)\), "\[IndentingNewLine]", \(\(f[x_]\ = k*Tanh[x];\)\), "\[IndentingNewLine]", \(\(f[3];\)\), "\[IndentingNewLine]", \(N[f[3]]\)}], "Input"], Cell[BoxData[ \(2.9851642610601914`\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["(2 pts) ", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], StyleBox["Make a plot of Tanh[x], with the y values between -0.9 and 0.9. \ Bonus: Make it exactly between -0.9 and 0.9 (hint: look in Help->Master \ Index->Built-in Functions->Mathematical Functions).", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]] }], "Text", TextAlignment->Left, TextJustification->0] }, Open ]], Cell[TextData[{ StyleBox["Its possible to do this using functions with plot or using a \ lists with listplot. In order to get the y range exactly between -0.9 and \ 0.9, use the ArcTanh function.", FontColor->RGBColor[1, 0.501961, 1]], "\n" }], "Input", Evaluatable->False, FormatType->TextForm], Cell[CellGroupData[{ Cell[BoxData[{ \(Plot[\ Tanh[x], \ {x, \ ArcTanh[\(-0.9\)], \ ArcTanh[0.9]}\ ]\), "\[IndentingNewLine]", \(\(numPoints\ = \ 50;\)\), "\[IndentingNewLine]", \(stepSize\ = \ \((ArcTanh[0.9]\ - ArcTanh[\(-0.9\)])\)/ numPoints\), "\[IndentingNewLine]", \(\(dataPoints\ = \ Table[Tanh[ArcTanh[\(-0.9\)] + \ x*stepSize], \ {x, \ 1\ , \ numPoints\ - \ 1}];\)\), "\[IndentingNewLine]", \(ListPlot[dataPoints, \ PlotJoined \[Rule] True]\)}], "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 0.5 0.323451 0.309017 0.327002 [ [.01482 .29652 -12 -9 ] [.01482 .29652 12 0 ] [.17655 .29652 -6 -9 ] [.17655 .29652 6 0 ] [.33827 .29652 -12 -9 ] [.33827 .29652 12 0 ] [.66173 .29652 -9 -9 ] [.66173 .29652 9 0 ] [.82345 .29652 -3 -9 ] [.82345 .29652 3 0 ] [.98518 .29652 -9 -9 ] [.98518 .29652 9 0 ] [.4875 .06377 -30 -4.5 ] [.4875 .06377 0 4.5 ] [.4875 .14552 -24 -4.5 ] [.4875 .14552 0 4.5 ] [.4875 .22727 -30 -4.5 ] [.4875 .22727 0 4.5 ] [.4875 .39077 -24 -4.5 ] [.4875 .39077 0 4.5 ] [.4875 .47252 -18 -4.5 ] [.4875 .47252 0 4.5 ] [.4875 .55427 -24 -4.5 ] [.4875 .55427 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 .01482 .30902 m .01482 .31527 L s [(-1.5)] .01482 .29652 0 1 Mshowa .17655 .30902 m .17655 .31527 L s [(-1)] .17655 .29652 0 1 Mshowa .33827 .30902 m .33827 .31527 L s [(-0.5)] .33827 .29652 0 1 Mshowa .66173 .30902 m .66173 .31527 L s [(0.5)] .66173 .29652 0 1 Mshowa .82345 .30902 m .82345 .31527 L s [(1)] .82345 .29652 0 1 Mshowa .98518 .30902 m .98518 .31527 L s [(1.5)] .98518 .29652 0 1 Mshowa .125 Mabswid .04717 .30902 m .04717 .31277 L s .07951 .30902 m .07951 .31277 L s .11186 .30902 m .11186 .31277 L s .1442 .30902 m .1442 .31277 L s .20889 .30902 m .20889 .31277 L s .24124 .30902 m .24124 .31277 L s .27358 .30902 m .27358 .31277 L s .30593 .30902 m .30593 .31277 L s .37062 .30902 m .37062 .31277 L s .40296 .30902 m .40296 .31277 L s .43531 .30902 m .43531 .31277 L s .46765 .30902 m .46765 .31277 L s .53235 .30902 m .53235 .31277 L s .56469 .30902 m .56469 .31277 L s .59704 .30902 m .59704 .31277 L s .62938 .30902 m .62938 .31277 L s .69407 .30902 m .69407 .31277 L s .72642 .30902 m .72642 .31277 L s .75876 .30902 m .75876 .31277 L s .79111 .30902 m .79111 .31277 L s .8558 .30902 m .8558 .31277 L s .88814 .30902 m .88814 .31277 L s .92049 .30902 m .92049 .31277 L s .95283 .30902 m .95283 .31277 L s .25 Mabswid 0 .30902 m 1 .30902 L s .5 .06377 m .50625 .06377 L s [(-0.75)] .4875 .06377 1 0 Mshowa .5 .14552 m .50625 .14552 L s [(-0.5)] .4875 .14552 1 0 Mshowa .5 .22727 m .50625 .22727 L s [(-0.25)] .4875 .22727 1 0 Mshowa .5 .39077 m .50625 .39077 L s [(0.25)] .4875 .39077 1 0 Mshowa .5 .47252 m .50625 .47252 L s [(0.5)] .4875 .47252 1 0 Mshowa .5 .55427 m .50625 .55427 L s [(0.75)] .4875 .55427 1 0 Mshowa .125 Mabswid .5 .08012 m .50375 .08012 L s .5 .09647 m .50375 .09647 L s .5 .11282 m .50375 .11282 L s .5 .12917 m .50375 .12917 L s .5 .16187 m .50375 .16187 L s .5 .17822 m .50375 .17822 L s .5 .19457 m .50375 .19457 L s .5 .21092 m .50375 .21092 L s .5 .24362 m .50375 .24362 L s .5 .25997 m .50375 .25997 L s .5 .27632 m .50375 .27632 L s .5 .29267 m .50375 .29267 L s .5 .32537 m .50375 .32537 L s .5 .34172 m .50375 .34172 L s .5 .35807 m .50375 .35807 L s .5 .37442 m .50375 .37442 L s .5 .40712 m .50375 .40712 L s .5 .42347 m .50375 .42347 L s .5 .43982 m .50375 .43982 L s .5 .45617 m .50375 .45617 L s .5 .48887 m .50375 .48887 L s .5 .50522 m .50375 .50522 L s .5 .52157 m .50375 .52157 L s .5 .53792 m .50375 .53792 L s .5 .04742 m .50375 .04742 L s .5 .03107 m .50375 .03107 L s .5 .01472 m .50375 .01472 L s .5 .57062 m .50375 .57062 L s .5 .58697 m .50375 .58697 L s .5 .60332 m .50375 .60332 L s .25 Mabswid .5 0 m .5 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .01472 m .06244 .02299 L .10458 .03421 L .14415 .04723 L .18221 .06241 L .22272 .0818 L .26171 .10394 L .30316 .13141 L .34309 .16175 L .3815 .1943 L .42237 .232 L .46172 .27049 L .49955 .30856 L .53984 .34909 L .57861 .38696 L .61984 .42491 L .65954 .45839 L .69774 .48725 L .73838 .51415 L .77751 .53635 L .81909 .55619 L .85916 .57199 L .89771 .5845 L .93871 .59532 L .97619 .60332 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{42, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg03oool2000003`0oooo00@00000 0?ooo`3oool000002P3oool01@000000oooo0?ooo`3oool000000080oooo00<000000?ooo`3oool0 0`3oool00`000000oooo0?ooo`2<0?ooo`00>P3oool2000003X0oooo00@000000?ooo`3oool00000 2P3oool00`000000oooo0?ooo`040?ooo`030000003oool0oooo00<0oooo0P00002=0?ooo`00?03o ool200000380oooo100000020?ooo`040000003oool0oooo000000/0oooo00@000000?ooo`3oool0 oooo0P0000060?ooo`030000003oool0oooo08`0oooo000n0?ooo`800000=P3oool010000000oooo 0?ooo`0000080?ooo`040000003oool0oooo000000<0oooo00<000000?ooo`3oool01@3oool00`00 0000oooo0?ooo`2<0?ooo`00@03oool2000003D0oooo0P0000090?ooo`@000000`3oool3000000D0 oooo00<000000?ooo`3oool0S03oool00480oooo0P00001=0?ooo`800000S@3oool004@0oooo00<0 00000?ooo`3oool0BP3oool00`000000oooo0?ooo`2<0?ooo`00A@3oool2000004X0oooo00<00000 0?ooo`3oool0S03oool004L0oooo0P0000180?ooo`030000003oool0oooo08`0oooo00190?ooo`80 0000AP3oool00`000000oooo0?ooo`2<0?ooo`00B`3oool2000004@0oooo0P00002=0?ooo`00C@3o ool200000480oooo00<000000?ooo`3oool0S03oool004l0oooo00<000000?ooo`3oool0?`3oool0 0`000000oooo0?ooo`2<0?ooo`00D03oool2000003l0oooo00<000000?ooo`3oool0S03oool00580 oooo0P00000m0?ooo`800000S@3oool005@0oooo00<000000?ooo`3oool0>P3oool00`000000oooo 0?ooo`2<0?ooo`00E@3oool2000003X0oooo00<000000?ooo`3oool0S03oool005L0oooo0P00000h 0?ooo`030000003oool0oooo08`0oooo001I0?ooo`800000=P3oool00`000000oooo0?ooo`2<0?oo o`00F`3oool00`000000oooo0?ooo`0c0?ooo`800000S@3oool005`0oooo00<000000?ooo`3oool0 0?ooo`00SP3oool0 10000000oooo0?ooo`00002>0?ooo`00S`3oool00`000000oooo0000002>0?ooo`001`3ooooo0000 01D000001@3oool000`0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`060?ooo`03 0000003oool0oooo00H0oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`060?ooo`03 0000003oool0oooo00H0oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`050?ooo`03 0000003oool0oooo00H0oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`060?ooo`03 0000003oool0oooo00H0oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`060?ooo`03 0000003oool0oooo00H0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`060?ooo`03 0000003oool0oooo00H0oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`060?ooo`03 0000003oool0oooo00H0oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`050?ooo`03 0000003oool0oooo00H0oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`060?ooo`03 0000003oool0oooo00H0oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`060?ooo`03 0000003oool0oooo00H0oooo00<000000?ooo`3oool01`3oool000`0oooo00<000000?ooo`3oool0 :@3oool00`000000oooo0?ooo`0Y0?ooo`030000003oool0oooo02X0oooo0P00000Z0?ooo`030000 003oool0oooo02T0oooo00<000000?ooo`3oool0:P3oool00`000000oooo0?ooo`070?ooo`00T@3o ool00`000000oooo0000002<0?ooo`00T@3oool010000000oooo0?ooo`00002;0?ooo`00T@3oool2 00000080oooo00<000000?ooo`3oool0R03oool00940oooo00<000000?ooo`3oool00P3oool00`00 0000oooo0?ooo`270?ooo`00T@3oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo08H0 oooo002A0?ooo`030000003oool0oooo00@0oooo00<000000?ooo`3oool0Q@3oool00940oooo0P00 00060?ooo`030000003oool0oooo08@0oooo002A0?ooo`030000003oool0oooo00H0oooo00<00000 0?ooo`3oool0P`3oool00940oooo00<000000?ooo`3oool01`3oool00`000000oooo0?ooo`220?oo o`00T@3oool00`000000oooo0?ooo`080?ooo`030000003oool0oooo0840oooo002A0?ooo`800000 2P3oool00`000000oooo0?ooo`200?ooo`00T@3oool00`000000oooo0?ooo`0:0?ooo`030000003o ool0oooo07l0oooo002A0?ooo`030000003oool0oooo00/0oooo00<000000?ooo`3oool0OP3oool0 0940oooo00<000000?ooo`3oool0303oool2000007h0oooo002A0?ooo`030000003oool0oooo00h0 oooo00<000000?ooo`3oool0N`3oool00940oooo0P00000@0?ooo`030000003oool0oooo07X0oooo 002A0?ooo`030000003oool0oooo0100oooo00<000000?ooo`3oool0N@3oool007L0oooo0P000004 0?ooo`8000000`3oool4000000<0oooo0P0000060?ooo`030000003oool0oooo0140oooo00<00000 0?ooo`3oool0N03oool007H0oooo00@000000?ooo`3oool00000203oool00`000000oooo0?ooo`03 0?ooo`040000003oool0oooo000000D0oooo00<000000?ooo`3oool04P3oool00`000000oooo0?oo o`1g0?ooo`00MP3oool010000000oooo0?ooo`0000090?ooo`030000003oool0oooo00D0oooo00<0 00000?ooo`3oool00`3oool2000001@0oooo00<000000?ooo`3oool0MP3oool007H0oooo00@00000 0?ooo`3oool000002P3oool00`000000oooo0?ooo`020?ooo`8000001P3oool00`000000oooo0?oo o`0D0?ooo`030000003oool0oooo07D0oooo001f0?ooo`040000003oool0oooo000000P0oooo00@0 00000?ooo`3oool000000`3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo01D0oooo 00<000000?ooo`3oool0M03oool007L0oooo0P00000:0?ooo`800000103oool3000000D0oooo00<0 00000?ooo`3oool05P3oool00`000000oooo0?ooo`1c0?ooo`00T@3oool00`000000oooo0?ooo`0G 0?ooo`030000003oool0oooo0780oooo002A0?ooo`8000006@3oool00`000000oooo0?ooo`1a0?oo o`00T@3oool00`000000oooo0?ooo`0I0?ooo`030000003oool0oooo0700oooo002A0?ooo`030000 003oool0oooo01X0oooo00<000000?ooo`3oool0K`3oool00940oooo00<000000?ooo`3oool06`3o ool00`000000oooo0?ooo`1^0?ooo`00T@3oool2000001d0oooo00<000000?ooo`3oool0K@3oool0 0940oooo00<000000?ooo`3oool07@3oool00`000000oooo0?ooo`1/0?ooo`00T@3oool00`000000 oooo0?ooo`0N0?ooo`030000003oool0oooo06/0oooo002A0?ooo`030000003oool0oooo01l0oooo 0P00001[0?ooo`00T@3oool00`000000oooo0?ooo`0Q0?ooo`030000003oool0oooo06P0oooo002A 0?ooo`8000008`3oool00`000000oooo0?ooo`1W0?ooo`00T@3oool00`000000oooo0?ooo`0S0?oo o`030000003oool0oooo06H0oooo002A0?ooo`030000003oool0oooo02@0oooo00<000000?ooo`3o ool0I@3oool00940oooo00<000000?ooo`3oool09@3oool2000006D0oooo002A0?ooo`800000:03o ool00`000000oooo0?ooo`1R0?ooo`00T@3oool00`000000oooo0?ooo`0X0?ooo`030000003oool0 oooo0640oooo002A0?ooo`030000003oool0oooo02T0oooo0P00001Q0?ooo`00O@3oool2000000@0 oooo0P0000040?ooo`8000001P3oool00`000000oooo0?ooo`0[0?ooo`030000003oool0oooo05h0 oooo001l0?ooo`040000003oool0oooo000000P0oooo00@000000?ooo`3oool000001@3oool00`00 0000oooo0?ooo`0/0?ooo`030000003oool0oooo05d0oooo001l0?ooo`040000003oool0oooo0000 00/0oooo00<000000?ooo`3oool00`3oool2000002h0oooo0P00001M0?ooo`00O03oool010000000 oooo0?ooo`0000090?ooo`8000001P3oool00`000000oooo0?ooo`0_0?ooo`030000003oool0oooo 05X0oooo001l0?ooo`040000003oool0oooo000000T0oooo00<000000?ooo`3oool01@3oool00`00 0000oooo0?ooo`0`0?ooo`030000003oool0oooo05T0oooo001m0?ooo`8000002P3oool3000000D0 oooo00<000000?ooo`3oool0<@3oool2000005T0oooo002A0?ooo`800000=03oool00`000000oooo 0?ooo`1F0?ooo`00T@3oool00`000000oooo0?ooo`0d0?ooo`800000EP3oool00940oooo00<00000 0?ooo`3oool0=P3oool00`000000oooo0?ooo`1C0?ooo`00T@3oool00`000000oooo0?ooo`0g0?oo o`800000D`3oool00940oooo00<000000?ooo`3oool0>@3oool200000540oooo002A0?ooo`800000 ?03oool00`000000oooo0?ooo`1>0?ooo`00T@3oool00`000000oooo0?ooo`0l0?ooo`800000CP3o ool00940oooo00<000000?ooo`3oool0?P3oool00`000000oooo0?ooo`1;0?ooo`00T@3oool00`00 0000oooo0?ooo`0o0?ooo`800000B`3oool00940oooo0P0000120?ooo`800000B@3oool00940oooo 00<000000?ooo`3oool0@`3oool2000004L0oooo002A0?ooo`030000003oool0oooo04D0oooo0P00 00150?ooo`00T@3oool00`000000oooo0?ooo`170?ooo`800000@`3oool00940oooo00<000000?oo o`3oool0B@3oool00`000000oooo0?ooo`100?ooo`00T@3oool2000004/0oooo0P0000100?ooo`00 T@3oool00`000000oooo0?ooo`1<0?ooo`800000?P3oool007L0oooo0P0000040?ooo`8000001@3o ool00`000000oooo0?ooo`020?ooo`8000001P3oool00`000000oooo0?ooo`1>0?ooo`800000?03o ool007H0oooo00@000000?ooo`3oool000002P3oool01@000000oooo0?ooo`3oool000000080oooo 00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`1@0?ooo`800000>P3oool007H0oooo00@0 00000?ooo`3oool000002P3oool00`000000oooo0?ooo`040?ooo`030000003oool0oooo00<0oooo 0P00001C0?ooo`800000>03oool007H0oooo00@000000?ooo`3oool000002`3oool010000000oooo 0?ooo`3oool2000000H0oooo00<000000?ooo`3oool0E03oool2000003H0oooo001f0?ooo`040000 003oool0oooo000000P0oooo00@000000?ooo`3oool000000`3oool00`000000oooo0?ooo`050?oo o`030000003oool0oooo05H0oooo0`00000c0?ooo`00M`3oool2000000T0oooo100000030?ooo`<0 00001@3oool00`000000oooo0?ooo`1I0?ooo`800000<@3oool00940oooo00<000000?ooo`3oool0 F`3oool3000002h0oooo002A0?ooo`800000G`3oool3000002/0oooo002A0?ooo`030000003oool0 oooo0640oooo0`00000X0?ooo`00T@3oool00`000000oooo0?ooo`1T0?ooo`8000009P3oool00940 oooo00<000000?ooo`3oool0IP3oool3000002<0oooo002A0?ooo`800000JP3oool300000200oooo 002A0?ooo`030000003oool0oooo06`0oooo1000000L0?ooo`00T@3oool00`000000oooo0?ooo`1` 0?ooo`@00000603oool00940oooo00<000000?ooo`3oool0M03oool4000001@0oooo002A0?ooo`03 0000003oool0oooo07P0oooo1@00000?0?ooo`00T@3oool2000007h0oooo0`00000<0?ooo`00T@3o ool00`000000oooo0?ooo`2<0?ooo`00T@3oool00`000000oooo0?ooo`2<0?ooo`00T@3oool00`00 0000oooo0?ooo`2<0?ooo`00T@3oool00`000000oooo0?ooo`2<0?ooo`00o`3ooolQ0?ooo`00o`3o oolQ0?ooo`00o`3ooolQ0?ooo`00\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-1.63537, -0.986956, \ 0.0112784, 0.0111559}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"], Cell[BoxData[ \(0.05888877958332881`\)], "Output"], 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 0.0194363 0.309017 0.331347 [ [.21817 .29652 -6 -9 ] [.21817 .29652 6 0 ] [.41254 .29652 -6 -9 ] [.41254 .29652 6 0 ] [.6069 .29652 -6 -9 ] [.6069 .29652 6 0 ] [.80126 .29652 -6 -9 ] [.80126 .29652 6 0 ] [.99563 .29652 -6 -9 ] [.99563 .29652 6 0 ] [.01131 .06051 -30 -4.5 ] [.01131 .06051 0 4.5 ] [.01131 .14334 -24 -4.5 ] [.01131 .14334 0 4.5 ] [.01131 .22618 -30 -4.5 ] [.01131 .22618 0 4.5 ] [.01131 .39185 -24 -4.5 ] [.01131 .39185 0 4.5 ] [.01131 .47469 -18 -4.5 ] [.01131 .47469 0 4.5 ] [.01131 .55753 -24 -4.5 ] [.01131 .55753 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 .21817 .30902 m .21817 .31527 L s [(10)] .21817 .29652 0 1 Mshowa .41254 .30902 m .41254 .31527 L s [(20)] .41254 .29652 0 1 Mshowa .6069 .30902 m .6069 .31527 L s [(30)] .6069 .29652 0 1 Mshowa .80126 .30902 m .80126 .31527 L s [(40)] .80126 .29652 0 1 Mshowa .99563 .30902 m .99563 .31527 L s [(50)] .99563 .29652 0 1 Mshowa .125 Mabswid .06268 .30902 m .06268 .31277 L s .10155 .30902 m .10155 .31277 L s .14043 .30902 m .14043 .31277 L s .1793 .30902 m .1793 .31277 L s .25705 .30902 m .25705 .31277 L s .29592 .30902 m .29592 .31277 L s .33479 .30902 m .33479 .31277 L s .37366 .30902 m .37366 .31277 L s .45141 .30902 m .45141 .31277 L s .49028 .30902 m .49028 .31277 L s .52915 .30902 m .52915 .31277 L s .56803 .30902 m .56803 .31277 L s .64577 .30902 m .64577 .31277 L s .68465 .30902 m .68465 .31277 L s .72352 .30902 m .72352 .31277 L s .76239 .30902 m .76239 .31277 L s .84014 .30902 m .84014 .31277 L s .87901 .30902 m .87901 .31277 L s .91788 .30902 m .91788 .31277 L s .95675 .30902 m .95675 .31277 L s .25 Mabswid 0 .30902 m 1 .30902 L s .02381 .06051 m .03006 .06051 L s [(-0.75)] .01131 .06051 1 0 Mshowa .02381 .14334 m .03006 .14334 L s [(-0.5)] .01131 .14334 1 0 Mshowa .02381 .22618 m .03006 .22618 L s [(-0.25)] .01131 .22618 1 0 Mshowa .02381 .39185 m .03006 .39185 L s [(0.25)] .01131 .39185 1 0 Mshowa .02381 .47469 m .03006 .47469 L s [(0.5)] .01131 .47469 1 0 Mshowa .02381 .55753 m .03006 .55753 L s [(0.75)] .01131 .55753 1 0 Mshowa .125 Mabswid .02381 .07707 m .02756 .07707 L s .02381 .09364 m .02756 .09364 L s .02381 .11021 m .02756 .11021 L s .02381 .12678 m .02756 .12678 L s .02381 .15991 m .02756 .15991 L s .02381 .17648 m .02756 .17648 L s .02381 .19305 m .02756 .19305 L s .02381 .20961 m .02756 .20961 L s .02381 .24275 m .02756 .24275 L s .02381 .25931 m .02756 .25931 L s .02381 .27588 m .02756 .27588 L s .02381 .29245 m .02756 .29245 L s .02381 .32558 m .02756 .32558 L s .02381 .34215 m .02756 .34215 L s .02381 .35872 m .02756 .35872 L s .02381 .37529 m .02756 .37529 L s .02381 .40842 m .02756 .40842 L s .02381 .42499 m .02756 .42499 L s .02381 .44156 m .02756 .44156 L s .02381 .45812 m .02756 .45812 L s .02381 .49126 m .02756 .49126 L s .02381 .50783 m .02756 .50783 L s .02381 .52439 m .02756 .52439 L s .02381 .54096 m .02756 .54096 L s .02381 .04394 m .02756 .04394 L s .02381 .02737 m .02756 .02737 L s .02381 .0108 m .02756 .0108 L s .02381 .57409 m .02756 .57409 L s .02381 .59066 m .02756 .59066 L s .02381 .60723 m .02756 .60723 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 .04325 .01472 m .06268 .01906 L .08212 .02387 L .10155 .02919 L .12099 .03508 L .14043 .04156 L .15986 .04869 L .1793 .05651 L .19874 .06507 L .21817 .0744 L .23761 .08454 L .25705 .09552 L .27648 .10737 L .29592 .12009 L .31535 .1337 L .33479 .14819 L .35423 .16352 L .37366 .17967 L .3931 .19658 L .41254 .21418 L .43197 .23238 L .45141 .25108 L .47085 .27017 L .49028 .28953 L .50972 .30902 L .52915 .32851 L .54859 .34786 L .56803 .36695 L .58746 .38566 L .6069 .40385 L .62634 .42145 L .64577 .43836 L .66521 .45451 L .68465 .46985 L .70408 .48433 L .72352 .49794 L .74295 .51067 L .76239 .52252 L .78183 .5335 L .80126 .54364 L .8207 .55297 L .84014 .56152 L .85957 .56934 L .87901 .57647 L .89845 .58296 L .91788 .58884 L .93732 .59417 L .95675 .59898 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]HGAYHf4PAg9QL6QYHgh0oooo000Q0?ooo`8000003`3oool200000>`0oooo000Q0?ooo`030000003oool0oooo0100 oooo0`00003Y0?ooo`008@3oool00`000000oooo0?ooo`0C0?ooo`@00000i@3oool00240oooo00<0 00000?ooo`3oool05`3oool200000><0oooo000Q0?ooo`8000006P3oool300000>00oooo000Q0?oo o`030000003oool0oooo01`0oooo0P00003N0?ooo`008@3oool00`000000oooo0?ooo`0N0?ooo`<0 0000f`3oool000P0oooo0P0000040?ooo`8000001@3oool00`000000oooo0?ooo`020?ooo`800000 1@3oool00`000000oooo0?ooo`0Q0?ooo`800000f@3oool000L0oooo00@000000?ooo`3oool00000 2P3oool01@000000oooo0?ooo`3oool000000080oooo00<000000?ooo`3oool00P3oool00`000000 oooo0?ooo`0S0?ooo`<00000eP3oool000L0oooo00@000000?ooo`3oool000002P3oool00`000000 oooo0?ooo`040?ooo`030000003oool0oooo0080oooo0P00000W0?ooo`800000e03oool000030?oo o`0000000000008000000P3oool010000000oooo0?ooo`00000;0?ooo`040000003oool0oooo0?oo o`8000001@3oool00`000000oooo0?ooo`0X0?ooo`<00000d@3oool000L0oooo00@000000?ooo`3o ool00000203oool010000000oooo0?ooo`0000030?ooo`030000003oool0oooo00@0oooo00<00000 0?ooo`3oool0:`3oool20000003oool00`000000 oooo0?ooo`310?ooo`008@3oool00`000000oooo0?ooo`0i0?ooo`800000`@3oool00240oooo00<0 00000?ooo`3oool0>`3oool200000;l0oooo000Q0?ooo`800000?P3oool00`000000oooo0?ooo`2l 0?ooo`008@3oool00`000000oooo0?ooo`0n0?ooo`800000_03oool00240oooo00<000000?ooo`3o ool0@03oool200000;X0oooo000Q0?ooo`030000003oool0oooo0480oooo00<000000?ooo`3oool0 ]`3oool00240oooo00<000000?ooo`3oool0@`3oool200000;L0oooo000Q0?ooo`800000AP3oool2 00000;D0oooo000Q0?ooo`030000003oool0oooo04L0oooo00<000000?ooo`3oool0/P3oool000h0 oooo0P0000040?ooo`800000103oool2000000D0oooo00<000000?ooo`3oool0B03oool00`000000 oooo0?ooo`2a0?ooo`003@3oool010000000oooo0?ooo`0000080?ooo`040000003oool0oooo0000 00@0oooo00<000000?ooo`3oool0B@3oool200000;40oooo000=0?ooo`040000003oool0oooo0000 00/0oooo00<000000?ooo`3oool00P3oool2000004`0oooo00<000000?ooo`3oool0[P3oool000L0 oooo100000020?ooo`040000003oool0oooo000000T0oooo0P0000050?ooo`030000003oool0oooo 04`0oooo00<000000?ooo`3oool0[@3oool000d0oooo00@000000?ooo`3oool000002@3oool00`00 0000oooo0?ooo`040?ooo`030000003oool0oooo04d0oooo00<000000?ooo`3oool0[03oool000h0 oooo0P00000:0?ooo`<00000103oool00`000000oooo0?ooo`1>0?ooo`800000[03oool00240oooo 0P00001A0?ooo`030000003oool0oooo0:T0oooo000Q0?ooo`030000003oool0oooo0540oooo00<0 00000?ooo`3oool0Z03oool00240oooo00<000000?ooo`3oool0DP3oool00`000000oooo0?ooo`2W 0?ooo`008@3oool00`000000oooo0?ooo`1C0?ooo`800000Y`3oool00240oooo0P00001F0?ooo`03 0000003oool0oooo0:@0oooo000Q0?ooo`030000003oool0oooo05H0oooo00<000000?ooo`3oool0 X`3oool00240oooo00<000000?ooo`3oool0E`3oool00`000000oooo0?ooo`2R0?ooo`008@3oool0 0`000000oooo0?ooo`1H0?ooo`800000XP3oool00240oooo0P00001K0?ooo`030000003oool0oooo 09l0oooo000Q0?ooo`030000003oool0oooo05/0oooo00<000000?ooo`3oool0WP3oool00240oooo 00<000000?ooo`3oool0G03oool00`000000oooo0?ooo`2M0?ooo`008@3oool00`000000oooo0?oo o`1M0?ooo`030000003oool0oooo09`0oooo000Q0?ooo`030000003oool0oooo05h0oooo00<00000 0?ooo`3oool0V`3oool00240oooo0P00001P0?ooo`030000003oool0oooo09X0oooo000Q0?ooo`03 0000003oool0oooo0600oooo00<000000?ooo`3oool0V@3oool000P0oooo0P0000040?ooo`800000 0`3oool4000000<0oooo0P0000050?ooo`030000003oool0oooo0640oooo00<000000?ooo`3oool0 V03oool000L0oooo00@000000?ooo`3oool00000203oool00`000000oooo0?ooo`030?ooo`040000 003oool0oooo000000@0oooo00<000000?ooo`3oool0HP3oool2000009P0oooo00070?ooo`040000 003oool0oooo000000T0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`020?ooo`80 0000I@3oool00`000000oooo0?ooo`2E0?ooo`0000<0oooo0000000000000P0000020?ooo`040000 003oool0oooo000000X0oooo00<000000?ooo`3oool00P3oool2000000D0oooo00<000000?ooo`3o ool0I@3oool00`000000oooo0?ooo`2D0?ooo`001`3oool010000000oooo0?ooo`0000080?ooo`04 0000003oool0oooo000000<0oooo00<000000?ooo`3oool0103oool00`000000oooo0?ooo`1V0?oo o`030000003oool0oooo09<0oooo00080?ooo`8000002P3oool2000000@0oooo0`0000040?ooo`03 0000003oool0oooo06L0oooo00<000000?ooo`3oool0TP3oool00240oooo0P00001Y0?ooo`030000 003oool0oooo0940oooo000Q0?ooo`030000003oool0oooo06T0oooo00<000000?ooo`3oool0T03o ool00240oooo00<000000?ooo`3oool0JP3oool00`000000oooo0?ooo`2?0?ooo`008@3oool00`00 0000oooo0?ooo`1[0?ooo`030000003oool0oooo08h0oooo000Q0?ooo`800000K@3oool00`000000 oooo0?ooo`2=0?ooo`008@3oool00`000000oooo0?ooo`1]0?ooo`030000003oool0oooo08`0oooo 000Q0?ooo`030000003oool0oooo02T0oooo1@0000020?ooo`800000:@3oool4000000<0oooo0P00 000:0?ooo`030000003oool0oooo01`0oooo0P0000040?ooo`800000:`3oool300000080oooo0P00 000Z0?ooo`800000103oool2000000<0oooo000Q0?ooo`030000003oool0oooo02/0oooo00D00000 0?ooo`3oool0oooo000000020?ooo`030000003oool0oooo02H0oooo00<000000?ooo`3oool00`3o ool010000000oooo0?ooo`00000:0?ooo`030000003oool0oooo01X0oooo00@000000?ooo`3oool0 00000P3oool010000000oooo0?ooo`00000[0?ooo`040000003oool0oooo00000080oooo00<00000 0?ooo`3oool09P3oool010000000oooo0?ooo`0000020?ooo`040000003oool0oooo00000080oooo 000Q0?ooo`030000003oool0oooo02/0oooo00D000000?ooo`3oool0oooo000000020?ooo`030000 003oool0oooo02L0oooo00<000000?ooo`3oool00P3oool010000000oooo0?ooo`00000;0?ooo`03 0000003oool0oooo01/0oooo00D000000?ooo`3oool0oooo000000020?ooo`030000003oool0oooo 02H0oooo1@0000001@3oool000000?ooo`3oool0000002/0oooo00@000000?ooo`3oool000000P3o ool100000040oooo0@3oool00240oooo0P00000/0?ooo`050000003oool0oooo0?ooo`0000000P3o ool00`000000oooo0?ooo`0X0?ooo`050000003oool0oooo0?ooo`0000000P3oool00`000000oooo 0?ooo`0:0?ooo`030000003oool0oooo01/0oooo00@000000?ooo`3oool000000P3oool00`000000 oooo0?ooo`0V0?ooo`040000003oool0oooo00000080oooo00@000000?ooo`3oool00000:@3oool2 000000<0oooo00@000000?ooo`3oool000000P3oool00240oooo00<000000?ooo`3oool0:`3oool0 1@000000oooo0?ooo`3oool000000080oooo00<000000?ooo`3oool09P3oool010000000oooo0?oo o`0000020?ooo`040000003oool0oooo000000d0oooo00<000000?ooo`3oool05`3oool010000000 oooo0?ooo`0000020?ooo`040000003oool0oooo000002T0oooo00<000000?ooo`0000000P3oool0 10000000oooo0?ooo`00000Y0?ooo`030000003oool0oooo0080oooo00@000000?ooo`3oool00000 0P3oool00240oooo00<000000?ooo`3oool0:P3oool2000000@0oooo0P00000Z0?ooo`800000103o ool2000000l0oooo00<000000?ooo`3oool05`3oool2000000@0oooo0P00000[0?ooo`8000000`3o ool2000002X0oooo0`0000030?ooo`8000000`3oool00240oooo00<000000?ooo`3oool0M03oool0 0`000000oooo0?ooo`250?ooo`008@3oool2000007H0oooo00<000000?ooo`3oool0Q03oool00240 oooo00<000000?ooo`3oool0MP3oool00`000000oooo0?ooo`230?ooo`008@3oool00`000000oooo 0?ooo`1g0?ooo`030000003oool0oooo0880oooo000Q0?ooo`030000003oool0oooo07P0oooo00<0 00000?ooo`3oool0P@3oool001/0ooooo`000001000000D0oooo000Q0?ooo`030000003oool0oooo 00L0oooo00<000000?ooo`3oool01`3oool00`000000oooo0?ooo`060?ooo`030000003oool0oooo 00L0oooo00<000000?ooo`3oool01`3oool00`000000oooo0?ooo`070?ooo`030000003oool0oooo 00L0oooo00<000000?ooo`3oool01`3oool00`000000oooo0?ooo`070?ooo`030000003oool0oooo 00L0oooo00<000000?ooo`3oool01`3oool00`000000oooo0?ooo`070?ooo`030000003oool0oooo 00<0oooo00D000000?ooo`3oool0oooo000000080?ooo`030000003oool0oooo00L0oooo00<00000 0?ooo`3oool01`3oool00`000000oooo0?ooo`070?ooo`030000003oool0oooo00L0oooo00<00000 0?ooo`3oool01`3oool00`000000oooo0?ooo`070?ooo`030000003oool0oooo00L0oooo00<00000 0?ooo`3oool01`3oool00`000000oooo0?ooo`070?ooo`030000003oool0oooo00L0oooo00<00000 0?ooo`3oool01`3oool00`000000oooo0?ooo`040?ooo`008@3oool00`000000oooo0?ooo`0^0?oo o`030000003oool0oooo02l0oooo00<000000?ooo`3oool0603oool00`000000oooo0?ooo`0C0?oo o`030000003oool0oooo02l0oooo00<000000?ooo`3oool0;`3oool00`000000oooo0?ooo`040?oo o`008@3oool00`000000oooo0?ooo`1l0?ooo`030000003oool0oooo07d0oooo000Q0?ooo`800000 OP3oool00`000000oooo0?ooo`1l0?ooo`008@3oool00`000000oooo0?ooo`1n0?ooo`030000003o ool0oooo07/0oooo000Q0?ooo`030000003oool0oooo07l0oooo00<000000?ooo`3oool0NP3oool0 0240oooo00<000000?ooo`3oool0P03oool00`000000oooo0?ooo`1i0?ooo`008@3oool200000880 oooo00<000000?ooo`3oool0N03oool00240oooo00<000000?ooo`3oool0PP3oool00`000000oooo 0?ooo`1g0?ooo`008@3oool00`000000oooo0?ooo`230?ooo`030000003oool0oooo07H0oooo000Q 0?ooo`030000003oool0oooo08@0oooo00<000000?ooo`3oool0M@3oool00240oooo00<000000?oo o`3oool0Q@3oool00`000000oooo0?ooo`1d0?ooo`008@3oool2000008H0oooo00<000000?ooo`3o ool0M03oool00240oooo00<000000?ooo`3oool0QP3oool00`000000oooo0?ooo`1c0?ooo`008@3o ool00`000000oooo0?ooo`270?ooo`030000003oool0oooo0780oooo000Q0?ooo`030000003oool0 oooo08P0oooo00<000000?ooo`3oool0L@3oool00240oooo0P00002:0?ooo`030000003oool0oooo 0700oooo000Q0?ooo`030000003oool0oooo08X0oooo00<000000?ooo`3oool0K`3oool000P0oooo 0P0000040?ooo`8000000`3oool4000000<0oooo0P0000050?ooo`030000003oool0oooo08/0oooo 00<000000?ooo`3oool0KP3oool000L0oooo00@000000?ooo`3oool00000203oool00`000000oooo 0?ooo`030?ooo`040000003oool0oooo000000@0oooo00<000000?ooo`3oool0S03oool00`000000 oooo0?ooo`1]0?ooo`001`3oool010000000oooo0?ooo`0000090?ooo`030000003oool0oooo00D0 oooo00<000000?ooo`3oool00P3oool2000008h0oooo00<000000?ooo`3oool0K03oool000L0oooo 00@000000?ooo`3oool000002P3oool00`000000oooo0?ooo`020?ooo`8000001@3oool00`000000 oooo0?ooo`2>0?ooo`800000K03oool000L0oooo00@000000?ooo`3oool00000203oool010000000 oooo0?ooo`0000030?ooo`030000003oool0oooo00@0oooo00<000000?ooo`3oool0T03oool00`00 0000oooo0?ooo`1Y0?ooo`00203oool2000000X0oooo0P0000040?ooo`<00000103oool00`000000 oooo0?ooo`2A0?ooo`030000003oool0oooo06P0oooo000Q0?ooo`800000T`3oool00`000000oooo 0?ooo`1W0?ooo`008@3oool00`000000oooo0?ooo`2C0?ooo`030000003oool0oooo06H0oooo000Q 0?ooo`030000003oool0oooo09@0oooo00<000000?ooo`3oool0I@3oool00240oooo00<000000?oo o`3oool0U@3oool00`000000oooo0?ooo`1T0?ooo`008@3oool00`000000oooo0?ooo`2F0?ooo`03 0000003oool0oooo06<0oooo000Q0?ooo`800000V03oool00`000000oooo0?ooo`1R0?ooo`008@3o ool00`000000oooo0?ooo`2H0?ooo`800000HP3oool00240oooo00<000000?ooo`3oool0VP3oool0 0`000000oooo0?ooo`1O0?ooo`008@3oool00`000000oooo0?ooo`2K0?ooo`030000003oool0oooo 05h0oooo000Q0?ooo`800000W@3oool00`000000oooo0?ooo`1M0?ooo`008@3oool00`000000oooo 0?ooo`2M0?ooo`800000G@3oool00240oooo00<000000?ooo`3oool0W`3oool00`000000oooo0?oo o`1J0?ooo`008@3oool00`000000oooo0?ooo`2P0?ooo`030000003oool0oooo05T0oooo000Q0?oo o`800000XP3oool00`000000oooo0?ooo`1H0?ooo`008@3oool00`000000oooo0?ooo`2R0?ooo`80 0000F03oool000h0oooo0P0000040?ooo`800000103oool2000000D0oooo00<000000?ooo`3oool0 Y03oool00`000000oooo0?ooo`1E0?ooo`003@3oool010000000oooo0?ooo`0000080?ooo`040000 003oool0oooo000000@0oooo00<000000?ooo`3oool0Y@3oool00`000000oooo0?ooo`1D0?ooo`00 3@3oool010000000oooo0?ooo`00000;0?ooo`030000003oool0oooo0080oooo0P00002W0?ooo`03 0000003oool0oooo05<0oooo000=0?ooo`040000003oool0oooo000000T0oooo0P0000050?ooo`03 0000003oool0oooo0:L0oooo0P00001C0?ooo`003@3oool010000000oooo0?ooo`0000090?ooo`03 0000003oool0oooo00@0oooo00<000000?ooo`3oool0Z@3oool00`000000oooo0?ooo`1@0?ooo`00 3P3oool2000000X0oooo0`0000040?ooo`030000003oool0oooo0:X0oooo00<000000?ooo`3oool0 C`3oool00240oooo00<000000?ooo`3oool0Z`3oool2000004l0oooo000Q0?ooo`800000[P3oool2 000004d0oooo000Q0?ooo`030000003oool0oooo0:l0oooo00<000000?ooo`3oool0BP3oool00240 oooo00<000000?ooo`3oool0/03oool2000004X0oooo000Q0?ooo`030000003oool0oooo0;80oooo 0P0000180?ooo`008@3oool200000;D0oooo00<000000?ooo`3oool0A@3oool00240oooo00<00000 0?ooo`3oool0]@3oool2000004D0oooo000Q0?ooo`030000003oool0oooo0;L0oooo0P0000130?oo o`008@3oool00`000000oooo0?ooo`2i0?ooo`030000003oool0oooo0400oooo000Q0?ooo`800000 ^`3oool200000400oooo000Q0?ooo`030000003oool0oooo0;`0oooo0P00000n0?ooo`008@3oool0 0`000000oooo0?ooo`2n0?ooo`030000003oool0oooo03/0oooo000Q0?ooo`030000003oool0oooo 0;l0oooo0P00000k0?ooo`008@3oool200000<80oooo0P00000i0?ooo`008@3oool00`000000oooo 0?ooo`330?ooo`800000=`3oool000P0oooo0P0000040?ooo`8000001@3oool00`000000oooo0?oo o`020?ooo`8000001@3oool00`000000oooo0?ooo`350?ooo`800000=@3oool000L0oooo00@00000 0?ooo`3oool000002P3oool01@000000oooo0?ooo`3oool000000080oooo00<000000?ooo`3oool0 0P3oool00`000000oooo0?ooo`370?ooo`<00000D0oooo1000000C0?ooo`008@3oool00`000000oooo0?ooo`3Y0?ooo`D000003P3oool0 0240oooo00<000000?ooo`3oool0kP3oool3000000/0oooo000Q0?ooo`800000o@3oool00240oooo 00<000000?ooo`3oool0o03oool00240oooo00<000000?ooo`3oool0o03oool00240oooo00<00000 0?ooo`3oool0o03oool00?l0oooo8@3oool00?l0oooo8@3oool00?l0oooo8@3oool00?l0oooo8@3o ool00?l0oooo8@3oool00?l0oooo8@3oool00?l0oooo8@3oool00?l0oooo8@3oool00?l0oooo8@3o ool00001\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-6.69641, -1.04707, \ 0.201768, 0.0118354}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox["9: The Table method", "Subsection"]], "Text", TextAlignment->Center, TextJustification->0], Cell[TextData[{ "Similar to the Array method, these two have a lot of overlapping \ functionality. ", StyleBox["Evaluate ", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], "and notice we didn't have to redefine f, because this variable has \ notebook level scope. ", StyleBox["(2 pts)", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], " ", StyleBox["Create a second list populated with decimal approximations of f.", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]] }], "Text", TextAlignment->Left, TextJustification->0], Cell[CellGroupData[{ Cell[BoxData[{ \(\(myTableGeneratedList\ = Table[f[x], \ {x, 2, 20, 2}];\)\), "\[IndentingNewLine]", \(myTableGeneratedList\)}], "Input"], Cell[BoxData[ \({3\ Tanh[2], 3\ Tanh[4], 3\ Tanh[6], 3\ Tanh[8], 3\ Tanh[10], 3\ Tanh[12], 3\ Tanh[14], 3\ Tanh[16], 3\ Tanh[18], 3\ Tanh[20]}\)], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ \(\(myList\ = \ Table[N[f[x]], \ {x, \ 2, \ 20, \ 2}];\)\), "\[IndentingNewLine]", \(myList\), "\[IndentingNewLine]", \(\)}], "Input"], Cell[BoxData[ \({2.8920827402274507`, 2.9979878992172013`, 2.9999631349523868`, 2.9999993247890275`, 2.9999999876330783`, 2.999999999773492`, 2.9999999999958513`, 2.999999999999924`, 2.9999999999999987`, 3.`}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox["10: Recursive functions", "Subsection"]], "Text", TextAlignment->Center, TextJustification->0], Cell[TextData[{ "Recursive functions take whole numbers as inputs, while their output \ variables can be as simple as true/false, whole numbers, or as complicated as \ you can imagine. A recursive function, rF, is made out of a regular function, \ f, and a seed value, s. s is usually the same type of thing as the output of \ f. \nrF(0) = s\nrF(1) = f(s)\nrF(2) = f(f(s)), or generally speaking, rF(n) = \ f(rF(n-1)).\n", StyleBox["(2 pts)", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], " ", StyleBox["In the cell below is the definition of a ", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], StyleBox["Mathematica", FontWeight->"Bold", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[" function that doubles at every step. Insert some expressions \ that evaluate it at a few more steps. What is the function \"f\" in this \ case?", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]] }], "Text", TextAlignment->Left, TextJustification->0], Cell[CellGroupData[{ Cell[BoxData[{ \(\(rF[t_] := \ \(rF[t]\ = \ rF[t - 1]*2\);\)\), "\[IndentingNewLine]", \(\(rF[0]\ = \ 7;\)\), "\[IndentingNewLine]", \(rF[3]\)}], "Input"], Cell[BoxData[ \(56\)], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\[IndentingNewLine]\)\(rF[4]\[IndentingNewLine] rF[5]\[IndentingNewLine] rF[6]\)\)\)], "Input"], Cell[BoxData[ \(112\)], "Output"], Cell[BoxData[ \(224\)], "Output"], Cell[BoxData[ \(448\)], "Output"] }, Open ]], Cell[TextData[{ "\n", StyleBox["In this case, f(x) = 2x.", Evaluatable->False, FontColor->RGBColor[1, 0.501961, 1]] }], "Input", FormatType->TextForm], Cell[CellGroupData[{ Cell[TextData[StyleBox["11: Modeling population growth", "Subsection"]], \ "Text", TextAlignment->Center, TextJustification->0], Cell[TextData[{ "Recursive functions are perfect for modeling systems that change in a step \ by step way at regular time points. Dynamic systems such as populations of \ organisms don't change their numbers on a fixed schedule, but recursive \ functions can be a good rough model, since the population at year n has a big \ influence on the population at year n+1. ", StyleBox["(2 pts)", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], " ", StyleBox["Use the methods in steps 6-9 to create a graph of F defined \ above. Can you think of a real biological system that F is a good model for?", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]] }], "Text", TextAlignment->Left, TextJustification->0] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"ListPlot", "[", RowBox[{\(Table[rF[t], \ {t, \ 0, 10}]\), ",", StyleBox[" ", FontWeight->"Plain"], RowBox[{ StyleBox["PlotJoined", "MR", FontWeight->"Plain"], StyleBox[" ", FontWeight->"Plain"], StyleBox["\[Rule]", FontWeight->"Plain"], StyleBox[" ", FontWeight->"Plain"], StyleBox["True", "MR", FontWeight->"Plain"]}]}], StyleBox["]", FontWeight->"Plain"]}], "\[IndentingNewLine]"}]], "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 -0.0714286 0.0952381 0.0141397 8.21958e-005 [ [.30952 .00164 -3 -9 ] [.30952 .00164 3 0 ] [.5 .00164 -3 -9 ] [.5 .00164 3 0 ] [.69048 .00164 -3 -9 ] [.69048 .00164 3 0 ] [.88095 .00164 -6 -9 ] [.88095 .00164 6 0 ] [.10655 .09634 -24 -4.5 ] [.10655 .09634 0 4.5 ] [.10655 .17853 -24 -4.5 ] [.10655 .17853 0 4.5 ] [.10655 .26073 -24 -4.5 ] [.10655 .26073 0 4.5 ] [.10655 .34292 -24 -4.5 ] [.10655 .34292 0 4.5 ] [.10655 .42512 -24 -4.5 ] [.10655 .42512 0 4.5 ] [.10655 .50731 -24 -4.5 ] [.10655 .50731 0 4.5 ] [.10655 .58951 -24 -4.5 ] [.10655 .58951 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 .30952 .01414 m .30952 .02039 L s [(4)] .30952 .00164 0 1 Mshowa .5 .01414 m .5 .02039 L s [(6)] .5 .00164 0 1 Mshowa .69048 .01414 m .69048 .02039 L s [(8)] .69048 .00164 0 1 Mshowa .88095 .01414 m .88095 .02039 L s [(10)] .88095 .00164 0 1 Mshowa .125 Mabswid .16667 .01414 m .16667 .01789 L s .21429 .01414 m .21429 .01789 L s .2619 .01414 m .2619 .01789 L s .35714 .01414 m .35714 .01789 L s .40476 .01414 m .40476 .01789 L s .45238 .01414 m .45238 .01789 L s .54762 .01414 m .54762 .01789 L s .59524 .01414 m .59524 .01789 L s .64286 .01414 m .64286 .01789 L s .7381 .01414 m .7381 .01789 L s .78571 .01414 m .78571 .01789 L s .83333 .01414 m .83333 .01789 L s .07143 .01414 m .07143 .01789 L s .02381 .01414 m .02381 .01789 L s .92857 .01414 m .92857 .01789 L s .97619 .01414 m .97619 .01789 L s .25 Mabswid 0 .01414 m 1 .01414 L s .11905 .09634 m .1253 .09634 L s [(1000)] .10655 .09634 1 0 Mshowa .11905 .17853 m .1253 .17853 L s [(2000)] .10655 .17853 1 0 Mshowa .11905 .26073 m .1253 .26073 L s [(3000)] .10655 .26073 1 0 Mshowa .11905 .34292 m .1253 .34292 L s [(4000)] .10655 .34292 1 0 Mshowa .11905 .42512 m .1253 .42512 L s [(5000)] .10655 .42512 1 0 Mshowa .11905 .50731 m .1253 .50731 L s [(6000)] .10655 .50731 1 0 Mshowa .11905 .58951 m .1253 .58951 L s [(7000)] .10655 .58951 1 0 Mshowa .125 Mabswid .11905 .03058 m .1228 .03058 L s .11905 .04702 m .1228 .04702 L s .11905 .06346 m .1228 .06346 L s .11905 .0799 m .1228 .0799 L s .11905 .11277 m .1228 .11277 L s .11905 .12921 m .1228 .12921 L s .11905 .14565 m .1228 .14565 L s .11905 .16209 m .1228 .16209 L s .11905 .19497 m .1228 .19497 L s .11905 .21141 m .1228 .21141 L s .11905 .22785 m .1228 .22785 L s .11905 .24429 m .1228 .24429 L s .11905 .27717 m .1228 .27717 L s .11905 .29361 m .1228 .29361 L s .11905 .31004 m .1228 .31004 L s .11905 .32648 m .1228 .32648 L s .11905 .35936 m .1228 .35936 L s .11905 .3758 m .1228 .3758 L s .11905 .39224 m .1228 .39224 L s .11905 .40868 m .1228 .40868 L s .11905 .44156 m .1228 .44156 L s .11905 .458 m .1228 .458 L s .11905 .47444 m .1228 .47444 L s .11905 .49088 m .1228 .49088 L s .11905 .52375 m .1228 .52375 L s .11905 .54019 m .1228 .54019 L s .11905 .55663 m .1228 .55663 L s .11905 .57307 m .1228 .57307 L s .11905 .60595 m .1228 .60595 L s .25 Mabswid .11905 0 m .11905 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .01472 m .11905 .01529 L .21429 .01644 L .30952 .01874 L .40476 .02335 L .5 .03255 L .59524 .05096 L .69048 .08779 L .78571 .16143 L .88095 .30873 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]HGAYHf4PAg9QL6QYHg0?ooo`009`3oool00`000000oooo0?ooo`2V 0?ooo`030000003oool0oooo04d0oooo000W0?ooo`800000Z03oool00`000000oooo0?ooo`1<0?oo o`009`3oool00`000000oooo0?ooo`2X0?ooo`800000C03oool002L0oooo00<000000?ooo`3oool0 ZP3oool00`000000oooo0?ooo`190?ooo`009`3oool00`000000oooo0?ooo`2[0?ooo`030000003o ool0oooo04P0oooo000W0?ooo`030000003oool0oooo0:`0oooo0P0000180?ooo`009`3oool20000 0:l0oooo00<000000?ooo`3oool0A@3oool002L0oooo00<000000?ooo`3oool0[`3oool00`000000 oooo0?ooo`140?ooo`009`3oool00`000000oooo0?ooo`2`0?ooo`800000A03oool002L0oooo00<0 00000?ooo`3oool0/P3oool00`000000oooo0?ooo`110?ooo`009`3oool200000;@0oooo00<00000 0?ooo`3oool0@03oool002L0oooo00<000000?ooo`3oool0]03oool00`000000oooo0?ooo`0o0?oo o`009`3oool00`000000oooo0?ooo`2d0?ooo`030000003oool0oooo03l0oooo000=0?ooo`@00000 0`3oool2000000@0oooo0P0000040?ooo`8000001@3oool00`000000oooo0?ooo`2e0?ooo`030000 003oool0oooo03h0oooo000=0?ooo`030000003oool0oooo00<0oooo00@000000?ooo`3oool00000 0P3oool010000000oooo0?ooo`0000020?ooo`040000003oool0oooo000000@0oooo00<000000?oo o`3oool0]P3oool00`000000oooo0?ooo`0m0?ooo`003P3oool00`000000oooo0?ooo`020?ooo`04 0000003oool0oooo00000080oooo00@000000?ooo`3oool000000P3oool010000000oooo0?ooo`00 00040?ooo`<00000]P3oool00`000000oooo0?ooo`0m0?ooo`003`3oool01@000000oooo0?ooo`3o ool000000080oooo00@000000?ooo`3oool000000P3oool010000000oooo0?ooo`0000020?ooo`03 0000003oool0oooo0080oooo00<000000?ooo`3oool0]`3oool00`000000oooo0?ooo`0l0?ooo`00 3@3oool010000000oooo0?ooo`0000020?ooo`040000003oool0oooo00000080oooo00@000000?oo o`3oool000000P3oool010000000oooo0?ooo`0000040?ooo`030000003oool0oooo0;P0oooo00<0 00000?ooo`3oool0>`3oool000h0oooo0P0000040?ooo`800000103oool2000000@0oooo0P000005 0?ooo`030000003oool0oooo0;P0oooo00<000000?ooo`3oool0>`3oool002L0oooo0P00002j0?oo o`030000003oool0oooo03X0oooo000W0?ooo`030000003oool0oooo0;T0oooo00<000000?ooo`3o ool0>P3oool002L0oooo00<000000?ooo`3oool0^P3oool00`000000oooo0?ooo`0i0?ooo`009`3o ool00`000000oooo0?ooo`2k0?ooo`030000003oool0oooo03P0oooo000W0?ooo`030000003oool0 oooo0;/0oooo00<000000?ooo`3oool0>03oool002L0oooo0P00002m0?ooo`030000003oool0oooo 03L0oooo000W0?ooo`030000003oool0oooo0;d0oooo00<000000?ooo`3oool0=P3oool002L0oooo 00<000000?ooo`3oool0_@3oool00`000000oooo0?ooo`0f0?ooo`009`3oool00`000000oooo0?oo o`2n0?ooo`030000003oool0oooo03D0oooo000W0?ooo`800000`03oool00`000000oooo0?ooo`0d 0?ooo`009`3oool00`000000oooo0?ooo`2o0?ooo`030000003oool0oooo03@0oooo000W0?ooo`03 0000003oool0oooo0<00oooo00<000000?ooo`3oool0<`3oool002L0oooo00<000000?ooo`3oool0 `@3oool00`000000oooo0?ooo`0b0?ooo`009`3oool00`000000oooo0?ooo`310?ooo`030000003o ool0oooo0380oooo000W0?ooo`800000``3oool00`000000oooo0?ooo`0a0?ooo`009`3oool00`00 0000oooo0?ooo`330?ooo`030000003oool0oooo0300oooo000>0?ooo`800000103oool2000000@0 oooo0P0000040?ooo`8000001@3oool00`000000oooo0?ooo`330?ooo`030000003oool0oooo0300 oooo000=0?ooo`040000003oool0oooo00000080oooo00@000000?ooo`3oool000000P3oool01000 0000oooo0?ooo`0000020?ooo`040000003oool0oooo000000@0oooo00<000000?ooo`3oool0a03o ool00`000000oooo0?ooo`0_0?ooo`003`3oool01@000000oooo0?ooo`3oool000000080oooo00@0 00000?ooo`3oool000000P3oool010000000oooo0?ooo`0000020?ooo`030000003oool0oooo0080 oooo0`0000350?ooo`030000003oool0oooo02h0oooo000@0?ooo`040000003oool0oooo00000080 oooo00@000000?ooo`3oool000000P3oool010000000oooo0?ooo`0000020?ooo`030000003oool0 oooo0080oooo00<000000?ooo`3oool0a@3oool00`000000oooo0?ooo`0^0?ooo`003@3oool01000 0000oooo0?ooo`0000020?ooo`040000003oool0oooo00000080oooo00@000000?ooo`3oool00000 0P3oool010000000oooo0?ooo`0000040?ooo`030000003oool0oooo00?ooo`030000003oool0oooo02H0oooo000W0?ooo`030000003oool0 oooo00?ooo`030000003oool0oooo02D0 oooo000W0?ooo`800000d03oool00`000000oooo0?ooo`0T0?ooo`009`3oool00`000000oooo0?oo o`3?0?ooo`030000003oool0oooo02@0oooo000W0?ooo`030000003oool0oooo00?ooo`030000003oool000000080oooo00@000000?ooo`3oool000000P3o ool010000000oooo0?ooo`0000020?ooo`040000003oool0oooo000000@0oooo00<000000?ooo`3o ool0d@3oool00`000000oooo0?ooo`0R0?ooo`003`3oool2000000<0oooo0P0000040?ooo`800000 103oool2000000D0oooo00<000000?ooo`3oool0d@3oool00`000000oooo0?ooo`0R0?ooo`009`3o ool200000=<0oooo00<000000?ooo`3oool08@3oool002L0oooo00<000000?ooo`3oool0dP3oool0 0`000000oooo0?ooo`0Q0?ooo`009`3oool00`000000oooo0?ooo`3B0?ooo`030000003oool0oooo 0240oooo000W0?ooo`030000003oool0oooo0=<0oooo00<000000?ooo`3oool0803oool002L0oooo 00<000000?ooo`3oool0d`3oool00`000000oooo0?ooo`0P0?ooo`009`3oool200000=@0oooo00<0 00000?ooo`3oool0803oool002L0oooo00<000000?ooo`3oool0d`3oool00`000000oooo0?ooo`0P 0?ooo`009`3oool00`000000oooo0?ooo`3D0?ooo`030000003oool0oooo01l0oooo000W0?ooo`03 0000003oool0oooo0=@0oooo00<000000?ooo`3oool07`3oool002L0oooo0P00003E0?ooo`030000 003oool0oooo01l0oooo000W0?ooo`030000003oool0oooo0=D0oooo00<000000?ooo`3oool07P3o ool002L0oooo00<000000?ooo`3oool0e@3oool00`000000oooo0?ooo`0N0?ooo`009`3oool00`00 0000oooo0?ooo`3E0?ooo`030000003oool0oooo01h0oooo000W0?ooo`800000e`3oool00`000000 oooo0?ooo`0M0?ooo`009`3oool00`000000oooo0?ooo`3F0?ooo`030000003oool0oooo01d0oooo 000W0?ooo`030000003oool0oooo0=H0oooo00<000000?ooo`3oool07@3oool000h0oooo0P000004 0?ooo`800000103oool2000000@0oooo0P0000050?ooo`030000003oool0oooo0=L0oooo00<00000 0?ooo`3oool0703oool000d0oooo00@000000?ooo`3oool000000P3oool010000000oooo0?ooo`00 00020?ooo`040000003oool0oooo00000080oooo00@000000?ooo`3oool00000103oool00`000000 oooo0?ooo`3G0?ooo`030000003oool0oooo01`0oooo000@0?ooo`040000003oool0oooo00000080 oooo00@000000?ooo`3oool000000P3oool010000000oooo0?ooo`0000020?ooo`030000003oool0 oooo0080oooo0`00003G0?ooo`030000003oool0oooo01`0oooo000>0?ooo`8000000`3oool01000 0000oooo0?ooo`0000020?ooo`040000003oool0oooo00000080oooo00@000000?ooo`3oool00000 103oool00`000000oooo0?ooo`3H0?ooo`030000003oool0oooo01/0oooo000>0?ooo`030000003o ool0oooo0080oooo00@000000?ooo`3oool000000P3oool010000000oooo0?ooo`0000020?ooo`04 0000003oool0oooo000000@0oooo00<000000?ooo`3oool0f03oool00`000000oooo0?ooo`0K0?oo o`003P3oool3000000<0oooo0P0000040?ooo`800000103oool2000000D0oooo00<000000?ooo`3o ool0f03oool00`000000oooo0?ooo`0K0?ooo`009`3oool200000=X0oooo00<000000?ooo`3oool0 6P3oool002L0oooo00<000000?ooo`3oool0f@3oool00`000000oooo0?ooo`0J0?ooo`009`3oool0 0`000000oooo0?ooo`3I0?ooo`030000003oool0oooo01X0oooo000W0?ooo`030000003oool0oooo 0=X0oooo00<000000?ooo`3oool06@3oool002L0oooo00<000000?ooo`3oool0fP3oool00`000000 oooo0?ooo`0I0?ooo`009`3oool200000=/0oooo00<000000?ooo`3oool06@3oool002L0oooo00<0 00000?ooo`3oool0f`3oool00`000000oooo0?ooo`0H0?ooo`009`3oool00`000000oooo0?ooo`3K 0?ooo`030000003oool0oooo01P0oooo000W0?ooo`030000003oool0oooo0=/0oooo00<000000?oo o`3oool0603oool002L0oooo0P00003M0?ooo`030000003oool0oooo01L0oooo000W0?ooo`030000 003oool0oooo0=`0oooo00<000000?ooo`3oool05`3oool002L0oooo00<000000?ooo`3oool0g03o ool00`000000oooo0?ooo`0G0?ooo`009`3oool00`000000oooo0?ooo`3M0?ooo`030000003oool0 oooo01H0oooo000W0?ooo`030000003oool0oooo0=d0oooo00<000000?ooo`3oool05P3oool002L0 oooo0P00003N0?ooo`030000003oool0oooo01H0oooo000W0?ooo`030000003oool0oooo0=h0oooo 00<000000?ooo`3oool05@3oool000d0oooo0`0000040?ooo`800000103oool2000000@0oooo0P00 00050?ooo`030000003oool0oooo0=h0oooo00<000000?ooo`3oool05@3oool000d0oooo00@00000 0?ooo`3oool000000P3oool010000000oooo0?ooo`0000020?ooo`040000003oool0oooo00000080 oooo00@000000?ooo`3oool00000103oool00`000000oooo0?ooo`3N0?ooo`030000003oool0oooo 01D0oooo000=0?ooo`040000003oool0oooo00000080oooo00@000000?ooo`3oool000000P3oool0 10000000oooo0?ooo`0000020?ooo`040000003oool0oooo000000@0oooo0`00003O0?ooo`030000 003oool0oooo01@0oooo000=0?ooo`<000000`3oool010000000oooo0?ooo`0000020?ooo`040000 003oool0oooo00000080oooo00@000000?ooo`3oool00000103oool00`000000oooo0?ooo`3O0?oo o`030000003oool0oooo01@0oooo000>0?ooo`030000003oool0oooo0080oooo00@000000?ooo`3o ool000000P3oool010000000oooo0?ooo`0000020?ooo`040000003oool0oooo000000@0oooo00<0 00000?ooo`3oool0g`3oool00`000000oooo0?ooo`0D0?ooo`003P3oool3000000<0oooo0P000004 0?ooo`800000103oool2000000D0oooo00<000000?ooo`3oool0h03oool00`000000oooo0?ooo`0C 0?ooo`009`3oool00`000000oooo0?ooo`3P0?ooo`030000003oool0oooo01<0oooo000W0?ooo`80 0000h@3oool00`000000oooo0?ooo`0C0?ooo`009`3oool00`000000oooo0?ooo`3P0?ooo`030000 003oool0oooo01<0oooo000W0?ooo`030000003oool0oooo0>40oooo00<000000?ooo`3oool04P3o ool002L0oooo00<000000?ooo`3oool0h@3oool00`000000oooo0?ooo`0B0?ooo`009`3oool20000 0>80oooo00<000000?ooo`3oool04P3oool002L0oooo00<000000?ooo`3oool0hP3oool00`000000 oooo0?ooo`0A0?ooo`009`3oool00`000000oooo0?ooo`3R0?ooo`030000003oool0oooo0140oooo 000W0?ooo`030000003oool0oooo0>80oooo00<000000?ooo`3oool04@3oool002L0oooo00<00000 0?ooo`3oool0h`3oool00`000000oooo0?ooo`0@0?ooo`009`3oool200000>@0oooo00<000000?oo o`3oool0403oool002L0oooo00<000000?ooo`3oool0h`3oool00`000000oooo0?ooo`0@0?ooo`00 9`3oool00`000000oooo0?ooo`3T0?ooo`030000003oool0oooo00l0oooo000W0?ooo`030000003o ool0oooo0>@0oooo00<000000?ooo`3oool03`3oool002L0oooo0P00003U0?ooo`030000003oool0 oooo00l0oooo000W0?ooo`030000003oool0oooo0>D0oooo00<000000?ooo`3oool03P3oool002L0 oooo00<000000?ooo`3oool0i@3oool00`000000oooo0?ooo`0>0?ooo`003`3oool00`000000oooo 0?ooo`020?ooo`800000103oool2000000@0oooo0P0000050?ooo`030000003oool0oooo0>D0oooo 00<000000?ooo`3oool03P3oool000l0oooo00D000000?ooo`3oool0oooo000000020?ooo`040000 003oool0oooo00000080oooo00@000000?ooo`3oool000000P3oool00`000000oooo0?ooo`020?oo o`030000003oool0oooo0>H0oooo00<000000?ooo`3oool03@3oool000l0oooo00D000000?ooo`3o ool0oooo000000020?ooo`040000003oool0oooo00000080oooo00@000000?ooo`3oool000000P3o ool00`000000oooo0?ooo`020?ooo`<00000iP3oool00`000000oooo0?ooo`0=0?ooo`00403oool0 10000000oooo0?ooo`0000020?ooo`040000003oool0oooo00000080oooo00@000000?ooo`3oool0 00000P3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo0>H0oooo00<000000?ooo`3o ool03@3oool000d0oooo00@000000?ooo`3oool000000P3oool010000000oooo0?ooo`0000020?oo o`040000003oool0oooo00000080oooo00@000000?ooo`3oool00000103oool00`000000oooo0?oo o`3W0?ooo`030000003oool0oooo00`0oooo000=0?ooo`@000000`3oool2000000@0oooo0P000004 0?ooo`8000001@3oool00`000000oooo0?ooo`3W0?ooo`030000003oool0oooo00`0oooo000W0?oo o`800000m`3oool002L0oooo00<000000?ooo`3oool0mP3oool002L0oooo00<000000?ooo`3oool0 mP3oool002L0oooo00<000000?ooo`3oool0mP3oool00001\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {0.46964, -553.998, \ 0.0385391, 44.6542}}], Cell[TextData[{ "\n", StyleBox["This population chart models pools of organisims with no \ predators and insignificant resource constraints, like bacterial cultures in \ \"mid log phase\", and people until recently. ", Evaluatable->False, FontColor->RGBColor[1, 0.501961, 1]] }], "Input", FormatType->TextForm], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[TextData[StyleBox["12: A more complex model", "Subsection"]], "Text", TextAlignment->Center, TextJustification->0], Cell[TextData[{ "The logistic model is presented below. It is considered to be the simplest \ dynamical system that exhibits chaotic behavior. It is implemented here with \ three parameters: r, k, and g. Set these three numbers to different values, \ evaluate, and observe how the graph changes. In ", StyleBox["Mathematica", FontSlant->"Italic"], " it is necessary to clear a function before you change the parameters that \ are part of it's definition, which explains the first command: Clear[pop]. \ Note: use values for r, 0 < r < 4, or you will get overflow errors. Also, \ when setting r to a whole number, such as 2, put a decimal point after the \ number: write \"r = 2.\" instead of \"r=2\" . The latter will cause ", StyleBox["Mathematica", FontSlant->"Italic"], " to hang. ", StyleBox["\n(12 pts) Match the four parameters to the following \ definitions:\n1) The population at time zero.\n2) The number of generations.\n\ 3) The capacity of the enviroment to sustain the population.\n4) The \ fertility of the organisims.\nCreate three copies of this cell. In one cell \ choose parameters that produce a graph that shows unchecked exponential \ growth, similar to the graph you created in (11). \nIn the second cell, set \ parameters that produce a graph that shows periodic behavior (i.e. the \ population changes from generation to generation in a regular way.\nIn the \ thrid cell, set parameters that result in chaotic behavior. Which parameter \ controls the chaotic/non-chaotic behavior of the system? ", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]] }], "Text"], Cell[TextData[{ StyleBox["r - A measure of the fecundity of the population.\nk - The \ carrying capacity of the enviroment: (1-pop[t]/k) becomes negative when the \ population exceeds k.\ng - The number of generations plotted.\ns - The \ population at time 0.\n\n", FontColor->RGBColor[1, 0.501961, 1]], StyleBox["The parameters below show unrestrained population growth. A \ large carrying capacity was chosen, and saturation was avoided by choosing \ small enough k, g, and s.", Evaluatable->False, FontColor->RGBColor[1, 0.501961, 1]], "\n" }], "Input", Evaluatable->False, FormatType->TextForm], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\[IndentingNewLine]\)\(Clear\ [pop]\n \(r\ = \ 1.2;\)\n \(k\ = \ 10000;\)\n \(g\ = \ 30;\)\n \(s\ = \ 2;\)\n \(pop[t_]\ := \ \(pop[t]\ = \ r\ pop[t - 1] \((1 - \ pop[t - 1]/k)\)\);\)\n \(pop[0]\ = \ 5;\)\n \(dt\ = Table[pop[x], \ {x, 0, g, 1}];\)\n ListPlot[dt, \ PlotJoined\ \[Rule] True, \ PlotRange \[Rule] {0, \ k/16}]\)\)\)], "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 0.030722 -1.6263e-018 0.000988854 [ [.17742 -0.0125 -3 -9 ] [.17742 -0.0125 3 0 ] [.33103 -0.0125 -6 -9 ] [.33103 -0.0125 6 0 ] [.48464 -0.0125 -6 -9 ] [.48464 -0.0125 6 0 ] [.63825 -0.0125 -6 -9 ] [.63825 -0.0125 6 0 ] [.79186 -0.0125 -6 -9 ] [.79186 -0.0125 6 0 ] [.94547 -0.0125 -6 -9 ] [.94547 -0.0125 6 0 ] [.01131 .09889 -18 -4.5 ] [.01131 .09889 0 4.5 ] [.01131 .19777 -18 -4.5 ] [.01131 .19777 0 4.5 ] [.01131 .29666 -18 -4.5 ] [.01131 .29666 0 4.5 ] [.01131 .39554 -18 -4.5 ] [.01131 .39554 0 4.5 ] [.01131 .49443 -18 -4.5 ] [.01131 .49443 0 4.5 ] [.01131 .59331 -18 -4.5 ] [.01131 .59331 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 .17742 0 m .17742 .00625 L s [(5)] .17742 -0.0125 0 1 Mshowa .33103 0 m .33103 .00625 L s [(10)] .33103 -0.0125 0 1 Mshowa .48464 0 m .48464 .00625 L s [(15)] .48464 -0.0125 0 1 Mshowa .63825 0 m .63825 .00625 L s [(20)] .63825 -0.0125 0 1 Mshowa .79186 0 m .79186 .00625 L s [(25)] .79186 -0.0125 0 1 Mshowa .94547 0 m .94547 .00625 L s [(30)] .94547 -0.0125 0 1 Mshowa .125 Mabswid .05453 0 m .05453 .00375 L s .08525 0 m .08525 .00375 L s .11598 0 m .11598 .00375 L s .1467 0 m .1467 .00375 L s .20814 0 m .20814 .00375 L s .23886 0 m .23886 .00375 L s .26959 0 m .26959 .00375 L s .30031 0 m .30031 .00375 L s .36175 0 m .36175 .00375 L s .39247 0 m .39247 .00375 L s .4232 0 m .4232 .00375 L s .45392 0 m .45392 .00375 L s .51536 0 m .51536 .00375 L s .54608 0 m .54608 .00375 L s .5768 0 m .5768 .00375 L s .60753 0 m .60753 .00375 L s .66897 0 m .66897 .00375 L s .69969 0 m .69969 .00375 L s .73041 0 m .73041 .00375 L s .76114 0 m .76114 .00375 L s .82258 0 m .82258 .00375 L s .8533 0 m .8533 .00375 L s .88402 0 m .88402 .00375 L s .91475 0 m .91475 .00375 L s .97619 0 m .97619 .00375 L s .25 Mabswid 0 0 m 1 0 L s .02381 .09889 m .03006 .09889 L s [(100)] .01131 .09889 1 0 Mshowa .02381 .19777 m .03006 .19777 L s [(200)] .01131 .19777 1 0 Mshowa .02381 .29666 m .03006 .29666 L s [(300)] .01131 .29666 1 0 Mshowa .02381 .39554 m .03006 .39554 L s [(400)] .01131 .39554 1 0 Mshowa .02381 .49443 m .03006 .49443 L s [(500)] .01131 .49443 1 0 Mshowa .02381 .59331 m .03006 .59331 L s [(600)] .01131 .59331 1 0 Mshowa .125 Mabswid .02381 .01978 m .02756 .01978 L s .02381 .03955 m .02756 .03955 L s .02381 .05933 m .02756 .05933 L s .02381 .07911 m .02756 .07911 L s .02381 .11866 m .02756 .11866 L s .02381 .13844 m .02756 .13844 L s .02381 .15822 m .02756 .15822 L s .02381 .17799 m .02756 .17799 L s .02381 .21755 m .02756 .21755 L s .02381 .23733 m .02756 .23733 L s .02381 .2571 m .02756 .2571 L s .02381 .27688 m .02756 .27688 L s .02381 .31643 m .02756 .31643 L s .02381 .33621 m .02756 .33621 L s .02381 .35599 m .02756 .35599 L s .02381 .37576 m .02756 .37576 L s .02381 .41532 m .02756 .41532 L s .02381 .4351 m .02756 .4351 L s .02381 .45487 m .02756 .45487 L s .02381 .47465 m .02756 .47465 L s .02381 .5142 m .02756 .5142 L s .02381 .53398 m .02756 .53398 L s .02381 .55376 m .02756 .55376 L s .02381 .57354 m .02756 .57354 L s .02381 .61309 m .02756 .61309 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 .05453 .00494 m .08525 .00593 L .11598 .00711 L .1467 .00853 L .17742 .01022 L .20814 .01226 L .23886 .01469 L .26959 .0176 L .30031 .02109 L .33103 .02525 L .36175 .03022 L .39247 .03615 L .4232 .04323 L .45392 .05164 L .48464 .06165 L .51536 .07352 L .54608 .08757 L .5768 .10415 L .60753 .12366 L .63825 .14654 L .66897 .17324 L .69969 .20425 L .73041 .24004 L .76114 .28105 L .79186 .32767 L .82258 .38018 L .8533 .43868 L .88402 .50306 L .91475 .57296 L s .91475 .57296 m .93327 .61803 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]HGAYHf4PAg9QL6QYHg0?ooo`00@P3oool00`000000oooo0?ooo`0Q0?ooo`050000003oool0oooo 0?ooo`0000000P3oool00`000000oooo0?ooo`0O0?ooo`030000003oool0oooo00@0oooo00<00000 0?ooo`3oool07P3oool00`000000oooo0?ooo`020?ooo`040000003oool0oooo00000200oooo00<0 00000?ooo`3oool01@3oool00`000000oooo0?ooo`0O0?ooo`050000003oool0oooo0?ooo`000000 0P3oool00`000000oooo0?ooo`0<0?ooo`00@03oool2000002@0oooo00D000000?ooo`3oool0oooo 000000020?ooo`030000003oool0oooo01l0oooo00<000000?ooo`3oool00P3oool200000280oooo 00D000000?ooo`3oool0oooo000000020?ooo`030000003oool0oooo01l0oooo00<000000?ooo`3o ool00P3oool2000002<0oooo00@000000?ooo`3oool000000P3oool00`000000oooo0?ooo`0<0?oo o`00@03oool00`000000oooo0?ooo`0S0?ooo`050000003oool0oooo0?ooo`0000000P3oool00`00 0000oooo0?ooo`0O0?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool07`3oool01000 0000oooo0?ooo`0000020?ooo`040000003oool0oooo000001l0oooo00@000000?ooo`3oool00000 0`3oool00`000000oooo0?ooo`0O0?ooo`040000003oool0oooo00000080oooo00@000000?ooo`3o ool000003P3oool00400oooo0`00000R0?ooo`800000103oool200000240oooo0P0000040?ooo`<0 0000803oool2000000@0oooo0P00000Q0?ooo`800000103oool300000200oooo0P0000040?ooo`80 00003`3oool00?l0oooo8@3oool00?l0oooo8@3oool00?l0oooo8@3oool00?l0oooo8@3oool00?l0 oooo8@3oool00140ooooo`00000=000000<0oooo000H0?ooo`030000003oool0oooo00D0oooo3000 00040?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool01P3oool00`000000oooo0?oo o`050?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?oo o`050?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool01P3oool00`000000oooo0?oo o`050?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?oo o`050?ooo`030000003oool0oooo00H0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?oo o`050?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?oo o`050?ooo`030000003oool0oooo00H0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?oo o`050?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?oo o`060?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?oo o`050?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool0203oool001P0oooo00<00000 0?ooo`3oool04@3ooolA000000@0oooo00<000000?ooo`3oool09@3oool00`000000oooo0?ooo`0V 0?ooo`030000003oool0oooo02H0oooo00<000000?ooo`3oool09P3oool00`000000oooo0?ooo`0V 0?ooo`030000003oool0oooo0100oooo000H0?ooo`030000003oool0oooo0280oooo4000003C0?oo o`00603oool00`000000oooo0?ooo`0b0?ooo`P00000b`3oool001P0oooo0P00000k0?ooo`P00000 ``3oool001P0oooo00<000000?ooo`3oool0@P3oool800000;/0oooo000H0?ooo`030000003oool0 oooo04X0oooo2@00002b0?ooo`00603oool00`000000oooo0?ooo`1C0?ooo`H00000[03oool001P0 oooo00<000000?ooo`3oool0F@3oool400000:P0oooo000H0?ooo`800000GP3oool600000:80oooo 000H0?ooo`030000003oool0oooo06<0oooo1P00002L0?ooo`00603oool00`000000oooo0?ooo`1Y 0?ooo`800000VP3oool001P0oooo00<000000?ooo`3oool0J`3oool3000009L0oooo000H0?ooo`03 0000003oool0oooo06h0oooo0`00002D0?ooo`00603oool00`000000oooo0?ooo`1a0?ooo`@00000 T03oool001P0oooo0P00001f0?ooo`@00000S03oool001P0oooo00<000000?ooo`3oool0N@3oool3 000008T0oooo000H0?ooo`030000003oool0oooo07`0oooo0`0000260?ooo`00603oool00`000000 oooo0?ooo`1o0?ooo`800000Q03oool001P0oooo00<000000?ooo`3oool0P@3oool200000880oooo 000H0?ooo`800000Q03oool200000800oooo000H0?ooo`030000003oool0oooo08D0oooo0P00001n 0?ooo`00603oool00`000000oooo0?ooo`270?ooo`800000O03oool000<0oooo1@0000020?ooo`80 0000103oool2000000H0oooo00<000000?ooo`3oool0R@3oool2000007X0oooo00050?ooo`050000 003oool0oooo0?ooo`0000000P3oool010000000oooo0?ooo`0000020?ooo`030000003oool0oooo 00<0oooo00<000000?ooo`3oool0R`3oool00`000000oooo0?ooo`1g0?ooo`001@3oool01@000000 oooo0?ooo`3oool000000080oooo00@000000?ooo`3oool000000P3oool00`000000oooo0?ooo`03 0?ooo`800000S@3oool2000007L0oooo00050?ooo`050000003oool0oooo0?ooo`0000000P3oool0 10000000oooo0?ooo`0000020?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool0SP3o ool2000007D0oooo00050?ooo`050000003oool0oooo0?ooo`0000000P3oool010000000oooo0?oo o`0000020?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool0T03oool00`000000oooo 0?ooo`1b0?ooo`00103oool2000000@0oooo0P0000040?ooo`8000001P3oool00`000000oooo0?oo o`2A0?ooo`800000LP3oool001P0oooo00<000000?ooo`3oool0T`3oool00`000000oooo0?ooo`1_ 0?ooo`00603oool2000009D0oooo0P00001_0?ooo`00603oool00`000000oooo0?ooo`2F0?ooo`80 0000K@3oool001P0oooo00<000000?ooo`3oool0V03oool00`000000oooo0?ooo`1Z0?ooo`00603o ool00`000000oooo0?ooo`2I0?ooo`030000003oool0oooo06T0oooo000H0?ooo`030000003oool0 oooo09X0oooo0P00001Y0?ooo`00603oool00`000000oooo0?ooo`2L0?ooo`030000003oool0oooo 06H0oooo000H0?ooo`800000WP3oool00`000000oooo0?ooo`1U0?ooo`00603oool00`000000oooo 0?ooo`2N0?ooo`800000I@3oool001P0oooo00<000000?ooo`3oool0X03oool00`000000oooo0?oo o`1R0?ooo`00603oool00`000000oooo0?ooo`2Q0?ooo`030000003oool0oooo0640oooo000H0?oo o`030000003oool0oooo0:80oooo00<000000?ooo`3oool0H03oool001P0oooo0P00002T0?ooo`03 0000003oool0oooo05l0oooo000H0?ooo`030000003oool0oooo0:@0oooo0P00001O0?ooo`00603o ool00`000000oooo0?ooo`2V0?ooo`030000003oool0oooo05`0oooo000H0?ooo`030000003oool0 oooo0:L0oooo00<000000?ooo`3oool0F`3oool001P0oooo00<000000?ooo`3oool0Z03oool00`00 0000oooo0?ooo`1J0?ooo`00603oool200000:X0oooo00<000000?ooo`3oool0F@3oool001P0oooo 00<000000?ooo`3oool0ZP3oool00`000000oooo0?ooo`1H0?ooo`00603oool00`000000oooo0?oo o`2[0?ooo`030000003oool0oooo05L0oooo000H0?ooo`030000003oool0oo