Browse Source

BИ.⚪✤Ⓞᙁߦ⚪ᗱᗴᴥᑎ✤ᗩᗯᴥᑎᑐᑕ⚪ИNⓄꖴ✤ᑐᑕИNᑎꗳ⚪ᔓᔕᑎꖴ⚭ᗩꗳ⚪◌⚪◌⚪◌⚪◌⚪◌⚪◌⚪ꗳᗩ⚭ꖴᑎᔓᔕ⚪ꗳᑎИNᑐᑕ✤ꖴⓄИN⚪ᑐᑕᑎᴥᗯᗩ✤ᑎᴥᗱᗴ⚪ߦᙁⓄ✤⚪.NB

BИ.⚪✤⚪Ⓞ⚪ᙁ⚪ߦ⚪◯⚪ᗱᗴ⚪ᴥ⚪ᑎ⚪✤⚪ᗩ⚪ᗯ⚪ᴥ⚪ᑎ⚪ᑐᑕ⚪◯⚪ИN⚪Ⓞ⚪ꖴ⚪✤⚪ᑐᑕ⚪ИN⚪ᑎ⚪ꗳ⚪◯⚪ᔓᔕ⚪ᑎ⚪ꖴ⚪⚭⚪ᗩ⚪ꗳ⚪◌⚪◌⚪◌⚪◌⚪◌⚪◌⚪ꗳ⚪ᗩ⚪⚭⚪ꖴ⚪ᑎ⚪ᔓᔕ⚪◯⚪ꗳ⚪ᑎ⚪ИN⚪ᑐᑕ⚪✤⚪ꖴ⚪Ⓞ⚪ИN⚪◯⚪ᑐᑕ⚪ᑎ⚪ᴥ⚪ᗯ⚪ᗩ⚪✤⚪ᑎ⚪ᴥ⚪ᗱᗴ⚪◯⚪ߦ⚪ᙁ⚪Ⓞ⚪✤⚪.NB

Signed-off-by: OOOO <oooooooooooooooo@skiff.com>
OOOO 2 years ago
parent
commit
2591852e9a

+ 688
- 0
ⵙ∣❁∣ⵙ✤ⵙ✻ⵙЭЄⵙᗩⵙߦⵙറⵙ◯ⵙ◯ⵙറⵙߦⵙᗩⵙЭЄⵙ✻ⵙ✤ⵙ∣❁∣ⵙ/⚪ИN⚪Ⓞ⚪ꖴ⚪✤⚪ᑐᑕ⚪ИN⚪ᑎ⚪ꗳ⚪◯⚪ᔓᔕ⚪ᑎ⚪ꖴ⚪⚭⚪ᗩ⚪ꗳ⚪◌⚪◌⚪◌⚪◌⚪◌⚪◌⚪ꗳ⚪ᗩ⚪⚭⚪ꖴ⚪ᑎ⚪ᔓᔕ⚪◯⚪ꗳ⚪ᑎ⚪ИN⚪ᑐᑕ⚪✤⚪ꖴ⚪Ⓞ⚪ИN⚪/⚪ᗱᗴ⚪ᴥ⚪ᑎ⚪✤⚪ᗩ⚪ᗯ⚪ᴥ⚪ᑎ⚪ᑐᑕ⚪◌⚪◌⚪◌⚪◌⚪◌⚪◌⚪ᑐᑕ⚪ᑎ⚪ᴥ⚪ᗯ⚪ᗩ⚪✤⚪ᑎ⚪ᴥ⚪ᗱᗴ⚪/BИ.⚪✤⚪Ⓞ⚪ᙁ⚪ߦ⚪◯⚪ᗱᗴ⚪ᴥ⚪ᑎ⚪✤⚪ᗩ⚪ᗯ⚪ᴥ⚪ᑎ⚪ᑐᑕ⚪◯⚪ИN⚪Ⓞ⚪ꖴ⚪✤⚪ᑐᑕ⚪ИN⚪ᑎ⚪ꗳ⚪◯⚪ᔓᔕ⚪ᑎ⚪ꖴ⚪⚭⚪ᗩ⚪ꗳ⚪◌⚪◌⚪◌⚪◌⚪◌⚪◌⚪ꗳ⚪ᗩ⚪⚭⚪ꖴ⚪ᑎ⚪ᔓᔕ⚪◯⚪ꗳ⚪ᑎ⚪ИN⚪ᑐᑕ⚪✤⚪ꖴ⚪Ⓞ⚪ИN⚪◯⚪ᑐᑕ⚪ᑎ⚪ᴥ⚪ᗯ⚪ᗩ⚪✤⚪ᑎ⚪ᴥ⚪ᗱᗴ⚪◯⚪ߦ⚪ᙁ⚪Ⓞ⚪✤⚪.NB View File

@@ -0,0 +1,688 @@
1
+(* Content-type: application/vnd.wolfram.mathematica *)
2
+
3
+(*** Wolfram Notebook File ***)
4
+(* http://www.wolfram.com/nb *)
5
+
6
+(* CreatedBy='Mathematica 12.1' *)
7
+
8
+(*CacheID: 234*)
9
+(* Internal cache information:
10
+NotebookFileLineBreakTest
11
+NotebookFileLineBreakTest
12
+NotebookDataPosition[       158,          7]
13
+NotebookDataLength[     28766,        678]
14
+NotebookOptionsPosition[     28088,        659]
15
+NotebookOutlinePosition[     28488,        675]
16
+CellTagsIndexPosition[     28445,        672]
17
+WindowFrame->Normal*)
18
+
19
+(* Beginning of Notebook Content *)
20
+Notebook[{
21
+Cell[BoxData[{
22
+ RowBox[{
23
+  RowBox[{
24
+   RowBox[{"FabiusF", "::", "usage"}], " ", "=", " ", 
25
+   "\"\<FabiusF[x] gives the value of the Fabius function F(x) for a \
26
+non-negative real argument x.\>\""}], ";"}], "\n", 
27
+ RowBox[{
28
+  RowBox[{"Macros`SetArgumentCount", "[", 
29
+   RowBox[{"FabiusF", ",", " ", "1"}], "]"}], ";"}], "\n", 
30
+ RowBox[{
31
+  RowBox[{
32
+   RowBox[{"SyntaxInformation", "[", "FabiusF", "]"}], " ", "=", " ", 
33
+   RowBox[{"{", 
34
+    RowBox[{"\"\<ArgumentsPattern\>\"", " ", "->", " ", 
35
+     RowBox[{"{", "_", "}"}]}], "}"}]}], ";"}], "\n", 
36
+ RowBox[{
37
+  RowBox[{
38
+   RowBox[{"SetAttributes", "[", 
39
+    RowBox[{"FabiusF", ",", " ", 
40
+     RowBox[{"{", 
41
+      RowBox[{"NumericFunction", ",", " ", "Listable"}], "}"}]}], "]"}], 
42
+   ";"}], "\n"}], "\n", 
43
+ RowBox[{
44
+  RowBox[{
45
+   RowBox[{
46
+    RowBox[{"Derivative", "[", "n_Integer", "]"}], "[", "FabiusF", "]"}], " ",
47
+    ":=", " ", 
48
+   RowBox[{
49
+    RowBox[{
50
+     RowBox[{"2", "^", 
51
+      RowBox[{"(", 
52
+       RowBox[{"n", " ", 
53
+        RowBox[{
54
+         RowBox[{"(", 
55
+          RowBox[{"n", " ", "+", " ", "1"}], ")"}], "/", "2"}]}], ")"}]}], 
56
+     " ", 
57
+     RowBox[{"FabiusF", "[", 
58
+      RowBox[{
59
+       RowBox[{"2", "^", "n"}], " ", "#"}], "]"}]}], " ", "&"}]}], "\n", "\n", 
60
+  RowBox[{"(*", 
61
+   RowBox[{
62
+    RowBox[{"https", ":"}], "//", 
63
+    RowBox[{
64
+     RowBox[{
65
+      RowBox[{"mathematica", ".", "stackexchange", ".", "com"}], "/", "a"}], 
66
+     "/", "13245"}]}], "*)"}]}], "\n", 
67
+ RowBox[{
68
+  RowBox[{
69
+   RowBox[{"powerOfTwoQ", "[", "n_", "]"}], " ", ":=", " ", 
70
+   RowBox[{
71
+    RowBox[{"IntegerQ", "[", "n", "]"}], " ", "&&", " ", 
72
+    RowBox[{
73
+     RowBox[{"BitAnd", "[", 
74
+      RowBox[{"n", ",", " ", 
75
+       RowBox[{"n", " ", "-", " ", "1"}]}], "]"}], " ", "==", " ", "0"}]}]}], 
76
+  "\n"}], "\n", 
77
+ RowBox[{
78
+  RowBox[{
79
+   RowBox[{"FabiusF", "[", "Infinity", "]"}], " ", "=", " ", 
80
+   RowBox[{"Interval", "[", 
81
+    RowBox[{"{", 
82
+     RowBox[{
83
+      RowBox[{"-", "1"}], ",", " ", "1"}], "}"}], "]"}]}], ";"}], "\n", 
84
+ RowBox[{
85
+  RowBox[{
86
+   RowBox[{
87
+    RowBox[{"FabiusF", "[", 
88
+     RowBox[{"x_", "?", "NumberQ"}], "]"}], " ", "/;", " ", 
89
+    RowBox[{"If", "[", 
90
+     RowBox[{
91
+      RowBox[{
92
+       RowBox[{"0", " ", "<=", " ", 
93
+        RowBox[{"Re", "[", "x", "]"}]}], " ", "&&", " ", 
94
+       RowBox[{
95
+        RowBox[{"Im", "[", "x", "]"}], " ", "==", " ", "0"}]}], ",", " ", 
96
+      RowBox[{"powerOfTwoQ", "[", 
97
+       RowBox[{"Denominator", "[", "x", "]"}], "]"}], ",", " ", 
98
+      RowBox[{
99
+       RowBox[{"Message", "[", 
100
+        RowBox[{
101
+         RowBox[{"FabiusF", "::", "realnn"}], ",", " ", "x"}], "]"}], ";", 
102
+       " ", "False"}]}], "]"}]}], " ", ":=", " ", 
103
+   RowBox[{"iFabiusF", "[", "x", "]"}]}], "\n"}], "\n", 
104
+ RowBox[{
105
+  RowBox[{
106
+   RowBox[{"ariasD", "[", "0", "]"}], " ", "=", " ", "1"}], ";"}], "\n", 
107
+ RowBox[{
108
+  RowBox[{
109
+   RowBox[{
110
+    RowBox[{"ariasD", "[", 
111
+     RowBox[{"n_Integer", "?", "Positive"}], "]"}], " ", ":=", " ", 
112
+    RowBox[{
113
+     RowBox[{"ariasD", "[", "n", "]"}], " ", "=", " ", 
114
+     RowBox[{
115
+      RowBox[{"Sum", "[", 
116
+       RowBox[{
117
+        RowBox[{
118
+         RowBox[{"2", "^", 
119
+          RowBox[{"(", 
120
+           RowBox[{
121
+            RowBox[{"(", 
122
+             RowBox[{
123
+              RowBox[{"k", " ", 
124
+               RowBox[{"(", 
125
+                RowBox[{"k", " ", "-", " ", "1"}], ")"}]}], " ", "-", " ", 
126
+              RowBox[{"n", " ", 
127
+               RowBox[{"(", 
128
+                RowBox[{"n", " ", "-", " ", "1"}], ")"}]}]}], ")"}], "/", 
129
+            "2"}], ")"}]}], " ", 
130
+         RowBox[{
131
+          RowBox[{"ariasD", "[", "k", "]"}], "/", 
132
+          RowBox[{
133
+           RowBox[{"(", 
134
+            RowBox[{"n", " ", "-", " ", "k", " ", "+", " ", "1"}], ")"}], 
135
+           "!"}]}]}], ",", " ", 
136
+        RowBox[{"{", 
137
+         RowBox[{"k", ",", " ", "0", ",", " ", 
138
+          RowBox[{"n", " ", "-", " ", "1"}]}], "}"}]}], "]"}], "/", 
139
+      RowBox[{"(", 
140
+       RowBox[{
141
+        RowBox[{"2", "^", "n"}], " ", "-", " ", "1"}], ")"}]}]}]}], ";"}], 
142
+  "\n"}], "\n", 
143
+ RowBox[{
144
+  RowBox[{
145
+   RowBox[{"tri", "[", "x_", "]"}], " ", ":=", " ", 
146
+   RowBox[{"Piecewise", "[", 
147
+    RowBox[{
148
+     RowBox[{"{", 
149
+      RowBox[{"{", 
150
+       RowBox[{
151
+        RowBox[{"2", " ", "-", " ", "x"}], ",", " ", 
152
+        RowBox[{"x", " ", ">", " ", "1"}]}], "}"}], "}"}], ",", " ", "x"}], 
153
+    "]"}]}], "\n"}], "\n", 
154
+ RowBox[{
155
+  RowBox[{"iFabiusF", "[", "x_", "]"}], " ", ":=", " ", 
156
+  RowBox[{"Module", "[", 
157
+   RowBox[{
158
+    RowBox[{"{", 
159
+     RowBox[{
160
+      RowBox[{"prec", " ", "=", " ", 
161
+       RowBox[{"Precision", "[", "x", "]"}]}], ",", " ", 
162
+      RowBox[{"s", " ", "=", " ", "1"}], ",", " ", 
163
+      RowBox[{"y", " ", "=", " ", "0"}], ",", " ", 
164
+      RowBox[{"z", " ", "=", " ", 
165
+       RowBox[{"SetPrecision", "[", 
166
+        RowBox[{"x", ",", " ", "Infinity"}], "]"}]}], ",", " ", "n", ",", " ",
167
+       "p", ",", " ", "q", ",", " ", "tol", ",", " ", "w"}], "}"}], ",", " ", 
168
+    RowBox[{
169
+     RowBox[{"z", " ", "=", " ", 
170
+      RowBox[{"If", "[", 
171
+       RowBox[{
172
+        RowBox[{"0", " ", "<=", " ", "z", " ", "<=", " ", "2"}], ",", " ", 
173
+        RowBox[{"tri", "[", "z", "]"}], ",", " ", 
174
+        RowBox[{
175
+         RowBox[{"q", " ", "=", " ", 
176
+          RowBox[{"Quotient", "[", 
177
+           RowBox[{"z", ",", " ", "2"}], "]"}]}], ";", "\n", "        ", 
178
+         RowBox[{"(*", 
179
+          RowBox[{
180
+           RowBox[{"can", " ", "replace", " ", 
181
+            RowBox[{"ThueMorse", "[", "]"}], " ", "with", " ", "the", " ", 
182
+            "implementation", " ", "in", " ", 
183
+            RowBox[{"https", ":"}]}], "//", 
184
+           RowBox[{
185
+            RowBox[{
186
+             RowBox[{"mathematica", ".", "stackexchange", ".", "com"}], "/", 
187
+             "a"}], "/", "89351"}]}], "*)"}], 
188
+         RowBox[{"If", "[", 
189
+          RowBox[{
190
+           RowBox[{
191
+            RowBox[{"ThueMorse", "[", "q", "]"}], " ", "==", " ", "1"}], ",", 
192
+           " ", 
193
+           RowBox[{"s", " ", "=", " ", 
194
+            RowBox[{"-", "1"}]}]}], "]"}], ";", " ", 
195
+         RowBox[{"tri", "[", 
196
+          RowBox[{"z", " ", "-", " ", 
197
+           RowBox[{"2", " ", "q"}]}], "]"}]}]}], "]"}]}], ";", "\n", "    ", 
198
+     RowBox[{"tol", " ", "=", " ", 
199
+      RowBox[{"10", "^", 
200
+       RowBox[{"(", 
201
+        RowBox[{"-", "prec"}], ")"}]}]}], ";", "\n", "    ", 
202
+     RowBox[{"While", "[", 
203
+      RowBox[{
204
+       RowBox[{"z", " ", ">", " ", "0"}], ",", " ", 
205
+       RowBox[{
206
+        RowBox[{"n", " ", "=", " ", 
207
+         RowBox[{"-", 
208
+          RowBox[{"Floor", "[", 
209
+           RowBox[{"RealExponent", "[", 
210
+            RowBox[{"z", ",", " ", "2"}], "]"}], "]"}]}]}], ";", " ", 
211
+        RowBox[{"p", " ", "=", " ", 
212
+         RowBox[{"2", "^", "n"}]}], ";", " ", 
213
+        RowBox[{"z", " ", "-=", " ", 
214
+         RowBox[{"1", "/", "p"}]}], ";", " ", 
215
+        RowBox[{"w", " ", "=", " ", "1"}], ";", "\n", "      ", 
216
+        RowBox[{"Do", "[", 
217
+         RowBox[{
218
+          RowBox[{
219
+           RowBox[{"w", " ", "=", " ", 
220
+            RowBox[{
221
+             RowBox[{"ariasD", "[", "m", "]"}], " ", "+", " ", 
222
+             RowBox[{"p", " ", "z", " ", 
223
+              RowBox[{"w", "/", 
224
+               RowBox[{"(", 
225
+                RowBox[{"n", " ", "-", " ", "m", " ", "+", " ", "1"}], 
226
+                ")"}]}]}]}]}], ";", " ", 
227
+           RowBox[{"p", " ", "/=", " ", "2"}]}], ",", " ", 
228
+          RowBox[{"{", 
229
+           RowBox[{"m", ",", " ", "n"}], "}"}]}], "]"}], ";", "\n", "      ", 
230
+        RowBox[{"y", " ", "=", " ", 
231
+         RowBox[{"w", " ", "-", " ", "y"}]}], ";", "\n", "      ", 
232
+        RowBox[{"If", "[", 
233
+         RowBox[{
234
+          RowBox[{
235
+           RowBox[{"Abs", "[", "w", "]"}], " ", "<", " ", 
236
+           RowBox[{
237
+            RowBox[{"Abs", "[", "y", "]"}], " ", "tol"}]}], ",", " ", 
238
+          RowBox[{"Break", "[", "]"}]}], "]"}]}]}], "]"}], ";", "\n", "    ", 
239
+     RowBox[{"SetPrecision", "[", 
240
+      RowBox[{
241
+       RowBox[{"s", " ", 
242
+        RowBox[{"Abs", "[", "y", "]"}]}], ",", " ", "prec"}], "]"}]}]}], 
243
+   "]"}]}]}], "Input",
244
+ CellLabel->
245
+  "In[183]:=",ExpressionUUID->"b6d7bb97-f801-4b79-84e9-03757a7fafc8"],
246
+
247
+Cell[BoxData[{
248
+ RowBox[{"ClearAll", "[", 
249
+  RowBox[{"iCurvaturePlotHelper", ",", "CurvaturePlot"}], 
250
+  "]"}], "\[IndentingNewLine]", 
251
+ RowBox[{
252
+  RowBox[{"iCurvaturePlotHelper", "[", 
253
+   RowBox[{
254
+    RowBox[{"f_", "?", 
255
+     RowBox[{"(", 
256
+      RowBox[{
257
+       RowBox[{
258
+        RowBox[{"Head", "[", "#", "]"}], "=!=", "List"}], "&"}], ")"}]}], ",", 
259
+    RowBox[{"{", 
260
+     RowBox[{"t_", ",", "tmin_", ",", "tmax_"}], "}"}], ",", 
261
+    RowBox[{"{", 
262
+     RowBox[{
263
+      RowBox[{"{", 
264
+       RowBox[{"x0_", ",", "y0_"}], "}"}], ",", "\[Theta]0_"}], "}"}], ",", 
265
+    RowBox[{"opts", ":", 
266
+     RowBox[{"OptionsPattern", "[", "]"}]}]}], "]"}], ":=", 
267
+  RowBox[{"Module", "[", 
268
+   RowBox[{
269
+    RowBox[{"{", 
270
+     RowBox[{"sol", ",", "\[Theta]", ",", "x", ",", "y", ",", "if"}], "}"}], 
271
+    ",", "\[IndentingNewLine]", 
272
+    RowBox[{
273
+     RowBox[{"sol", "=", 
274
+      RowBox[{"NDSolve", "[", 
275
+       RowBox[{
276
+        RowBox[{"{", "\[IndentingNewLine]", 
277
+         RowBox[{
278
+          RowBox[{
279
+           RowBox[{
280
+            RowBox[{"\[Theta]", "'"}], "[", "t", "]"}], "\[Equal]", "f"}], 
281
+          ",", "\[IndentingNewLine]", 
282
+          RowBox[{
283
+           RowBox[{
284
+            RowBox[{"x", "'"}], "[", "t", "]"}], "\[Equal]", 
285
+           RowBox[{"Cos", "[", 
286
+            RowBox[{"\[Theta]", "[", "t", "]"}], "]"}]}], ",", 
287
+          "\[IndentingNewLine]", 
288
+          RowBox[{
289
+           RowBox[{
290
+            RowBox[{"y", "'"}], "[", "t", "]"}], "\[Equal]", 
291
+           RowBox[{"Sin", "[", 
292
+            RowBox[{"\[Theta]", "[", "t", "]"}], "]"}]}], ",", 
293
+          "\[IndentingNewLine]", 
294
+          RowBox[{
295
+           RowBox[{"\[Theta]", "[", "tmin", "]"}], "\[Equal]", "\[Theta]0"}], 
296
+          ",", "\[IndentingNewLine]", 
297
+          RowBox[{
298
+           RowBox[{"x", "[", "tmin", "]"}], "\[Equal]", "x0"}], ",", 
299
+          "\[IndentingNewLine]", 
300
+          RowBox[{
301
+           RowBox[{"y", "[", "tmin", "]"}], "\[Equal]", "y0"}]}], 
302
+         "\[IndentingNewLine]", "}"}], ",", 
303
+        RowBox[{"{", 
304
+         RowBox[{"x", ",", "y"}], "}"}], ",", 
305
+        RowBox[{"{", 
306
+         RowBox[{"t", ",", "tmin", ",", "tmax"}], "}"}], ",", "opts"}], 
307
+       "]"}]}], ";", "\[IndentingNewLine]", 
308
+     RowBox[{"if", "=", 
309
+      RowBox[{
310
+       RowBox[{
311
+        RowBox[{"{", 
312
+         RowBox[{
313
+          RowBox[{"x", "[", "#", "]"}], ",", 
314
+          RowBox[{"y", "[", "#", "]"}]}], "}"}], "&"}], "/.", 
315
+       RowBox[{"First", "[", "sol", "]"}]}]}], ";", "\[IndentingNewLine]", 
316
+     "if"}]}], "\[IndentingNewLine]", "]"}]}], "\[IndentingNewLine]", 
317
+ RowBox[{
318
+  RowBox[{"CurvaturePlot", "[", 
319
+   RowBox[{"f_", ",", 
320
+    RowBox[{"{", 
321
+     RowBox[{"t_", ",", "tmin_", ",", "tmax_"}], "}"}], ",", 
322
+    RowBox[{"opts", ":", 
323
+     RowBox[{"OptionsPattern", "[", "]"}]}]}], "]"}], ":=", 
324
+  RowBox[{"CurvaturePlot", "[", 
325
+   RowBox[{"f", ",", 
326
+    RowBox[{"{", 
327
+     RowBox[{"t", ",", "tmin", ",", "tmax"}], "}"}], ",", 
328
+    RowBox[{"{", 
329
+     RowBox[{
330
+      RowBox[{"{", 
331
+       RowBox[{"0", ",", "0"}], "}"}], ",", "0"}], "}"}], ",", "opts"}], 
332
+   "]"}]}], "\[IndentingNewLine]", 
333
+ RowBox[{
334
+  RowBox[{"CurvaturePlot", "[", 
335
+   RowBox[{"f_", ",", 
336
+    RowBox[{"{", 
337
+     RowBox[{"t_", ",", "tmin_", ",", "tmax_"}], "}"}], ",", 
338
+    RowBox[{"p", ":", 
339
+     RowBox[{"{", 
340
+      RowBox[{
341
+       RowBox[{"{", 
342
+        RowBox[{"x0_", ",", "y0_"}], "}"}], ",", "\[Theta]0_"}], "}"}]}], ",", 
343
+    RowBox[{"opts", ":", 
344
+     RowBox[{"OptionsPattern", "[", "]"}]}]}], "]"}], ":=", 
345
+  RowBox[{"Module", "[", 
346
+   RowBox[{
347
+    RowBox[{"{", 
348
+     RowBox[{
349
+     "\[Theta]", ",", "x", ",", "y", ",", "sol", ",", "rlsplot", ",", 
350
+      "rlsndsolve", ",", "if", ",", "ifs"}], "}"}], ",", 
351
+    "\[IndentingNewLine]", 
352
+    RowBox[{
353
+     RowBox[{"rlsplot", "=", 
354
+      RowBox[{"FilterRules", "[", 
355
+       RowBox[{
356
+        RowBox[{"{", "opts", "}"}], ",", 
357
+        RowBox[{"Options", "[", "ParametricPlot", "]"}]}], "]"}]}], ";", 
358
+     "\[IndentingNewLine]", 
359
+     RowBox[{"rlsndsolve", "=", 
360
+      RowBox[{"FilterRules", "[", 
361
+       RowBox[{
362
+        RowBox[{"{", "opts", "}"}], ",", 
363
+        RowBox[{"Options", "[", "NDSolve", "]"}]}], "]"}]}], ";", 
364
+     "\[IndentingNewLine]", 
365
+     RowBox[{"If", "[", 
366
+      RowBox[{
367
+       RowBox[{
368
+        RowBox[{"Head", "[", "f", "]"}], "===", "List"}], ",", 
369
+       "\[IndentingNewLine]", 
370
+       RowBox[{
371
+        RowBox[{"ifs", "=", 
372
+         RowBox[{
373
+          RowBox[{
374
+           RowBox[{"iCurvaturePlotHelper", "[", 
375
+            RowBox[{"#", ",", 
376
+             RowBox[{"{", 
377
+              RowBox[{"t", ",", "tmin", ",", "tmax"}], "}"}], ",", "p", ",", 
378
+             RowBox[{"Evaluate", "@", 
379
+              RowBox[{"(", 
380
+               RowBox[{"Sequence", "@@", "rlsndsolve"}], ")"}]}]}], "]"}], 
381
+           "&"}], "/@", "f"}]}], ";", "\[IndentingNewLine]", 
382
+        RowBox[{"ParametricPlot", "[", 
383
+         RowBox[{
384
+          RowBox[{"Evaluate", "[", 
385
+           RowBox[{
386
+            RowBox[{
387
+             RowBox[{"#", "[", "tplot", "]"}], "&"}], "/@", "ifs"}], "]"}], 
388
+          ",", 
389
+          RowBox[{"{", 
390
+           RowBox[{"tplot", ",", "tmin", ",", "tmax"}], "}"}], ",", 
391
+          RowBox[{"Evaluate", "@", 
392
+           RowBox[{"(", 
393
+            RowBox[{"Sequence", "@@", "rlsplot"}], ")"}]}]}], "]"}]}], 
394
+       "\[IndentingNewLine]", ",", "\[IndentingNewLine]", 
395
+       RowBox[{
396
+        RowBox[{"if", "=", 
397
+         RowBox[{"iCurvaturePlotHelper", "[", 
398
+          RowBox[{"f", ",", 
399
+           RowBox[{"{", 
400
+            RowBox[{"t", ",", "tmin", ",", "tmax"}], "}"}], ",", "p", ",", 
401
+           RowBox[{"Evaluate", "@", 
402
+            RowBox[{"(", 
403
+             RowBox[{"Sequence", "@@", "rlsndsolve"}], ")"}]}]}], "]"}]}], 
404
+        ";", "\[IndentingNewLine]", 
405
+        RowBox[{"ParametricPlot", "[", 
406
+         RowBox[{
407
+          RowBox[{"Evaluate", "[", 
408
+           RowBox[{"if", "[", "tplot", "]"}], "]"}], ",", 
409
+          RowBox[{"{", 
410
+           RowBox[{"tplot", ",", "tmin", ",", "tmax"}], "}"}], ",", 
411
+          RowBox[{"Evaluate", "@", 
412
+           RowBox[{"(", 
413
+            RowBox[{"Sequence", "@@", "rlsplot"}], ")"}]}]}], "]"}]}]}], 
414
+      "\[IndentingNewLine]", "]"}]}]}], "\[IndentingNewLine]", 
415
+   "]"}]}]}], "Input",
416
+ CellLabel->
417
+  "In[195]:=",ExpressionUUID->"f922cec0-aa84-4593-aff3-3268dbccfdf7"],
418
+
419
+Cell[CellGroupData[{
420
+
421
+Cell[BoxData[
422
+ RowBox[{"CurvaturePlot", "[", 
423
+  RowBox[{
424
+   RowBox[{"FabiusF", "[", "x", "]"}], ",", 
425
+   RowBox[{"{", 
426
+    RowBox[{"x", ",", "0", ",", "4"}], "}"}]}], "]"}]], "Input",
427
+ CellLabel->
428
+  "In[205]:=",ExpressionUUID->"83f1c93d-5075-475d-b9f3-efc604a47ce1"],
429
+
430
+Cell[BoxData[
431
+ GraphicsBox[{{{}, {}, 
432
+    TagBox[
433
+     {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
434
+      1.], FaceForm[Opacity[0.3]], LineBox[CompressedData["
435
+1:eJxd1nc8lf/7B3D7nGOTMiJS9kiSlXNfbykpoyWliIxSFEqKUGRVQshooeyR
436
+PbJ3RglZGWWPjKQI58jvPn2+f/3OH+c8no/3fe73db2u+9z32W7leMKWgY6O
437
+7hD+Rvv8/y8rypamAEFj8G+8ZJt7YELjP9uApRDv2pXoH/v+sws8TLn1LLpX
438
+SkuzxKx0WtQNqlrc796tddLa5PY6U1/SC97bDgmo9IdpLW/9/ckk0huATblq
439
+uSle67/v+0KVxubMjq4d5NY+jZriF/7AnWvPJTimS/7vfA/gjLPel9VmU3JS
440
+zN18oTePYEU5LuDFzovk/84fDLtm4vaJOTiRUYbVyQrjUBji/MspvtuV/N9+
441
+T4CeYbujNq8HOeORn8GPnjBgio9nUR26R/5v/whQlTz68ZDrfbKAfcpBsXNP
442
+IW4tzDro6cP/1RMJVZICh6KpL8m+R1qw41+jQC880/+7Q+b/6osB7rGXajuO
443
+FZMXZObVfC48gwmjhwx97dX/q/c5DIgIDZ9iavxfva9g6KOxoLppB7l5ao/s
444
+2KVYqD/Ec75pfxcZ/tUfB7u/2616d/aQhWzSnzxcioOkQ5PPBoP6yEv/+omH
445
++13Kjcyxg+S2z1qcO9ReA1Hv5LHm8KH/9fca7qoN7RivHSEH6LQ+LL39BvKM
446
+t70y/Dj+v34ToC3kTgnTu2kyOc+CYFySAL1Tf26zBsyT+f/1nwhjWU0OWVsX
447
+yYviP+/PUhLhxJrkPJ3tEvnjvzySoM94IvmV6Co5JcyHzo+cDB8C8oajetfJ
448
+Pv/ySQaYa6hfZmbAzBj4PEXupoBbUknHpwFmbO+/vFIh8kc+f48TK8Z5PXG1
449
+oCoVIhoLIthruLDJf/mlQUn0153qU7xY1bCqqxFDOtTpbr09dW4LFvkvz3QI
450
+66a/KJQnhF053rg4oZMB29GfeX8mMUyTxLM7bywDZuMXHIcVd2Cs1aaOd/0y
451
+IZt7ruBFryTWdZuW/1uwCpqtKqaXw14pzczwv38LzJt/hO5N24VZ/5tHFvhm
452
+Rl8Wc1HGOI9hKmeYsqH12fGDTz32YuPptPlkQ3GsjW7gujqWTwi4vjMxGyQN
453
+r552YiZj7ta0eWXDRsz93VbtCFOt/JS9cDAHni1OpK4762BTQrT55cDUbUXW
454
+Bntd7LGrwI+yiRy43e3YIdd4GOProM0zF3RrHkvJvTLE3BUuKDwIyAX7vshi
455
+jr/HsOJA2nxzwSzq6DTbrZNY02iq/SnpPFDpjS4SQSZYMkabdx5ImwsVHLMw
456
+xYxiFlO3N+WB38SdG7l9ZljJL9r88+Fz0MIxPTNL7KDSkkyOUz7ojtBt+1ho
457
+he1w+Pyw730+cFkf9bhgYYtpJOfMMIoWgJEXHz46O+zacIiBgmsBqLwJ5Akq
458
+sMdShK5lmnwsgDE01vfIyRFrPmHAeW9nIWiO7lJQa3bG0h7IOqbeKYShkG7u
459
+cD4X7GYFsa2joxBiDi3Y1Ma5YjkLE0pUmSKoXqkpP37TDWMRq38i4V0Ex6pk
460
+OFKiPDBBgzeLRr1FEDN4Vzya5R721MX75O1dxaDJGCqXNueNicZY5Mf7F4PP
461
+t1yhSkZfjO8deXPLYDG48bSc3tD3x1I6trr+VnkHbCXMV9NbAjHzsdVukaB3
462
+MNJAEB4JeITVz/aoHRp9Bwmji4XZfsGY0/eCaCfNElg3/32IdzwUm+sPX415
463
+UgJVnn4eEplhWGul89naqRJYSSK/jn4ZgSVGHC2dhVJwzVKwWiyOxCzPKAhv
464
+iSoFlXaF9Eb6GOxezNSg3cEyYNQ2cvWWeYWZcTZgYS/K4IVgovSPgDjMw/JN
465
+bOmvMjDaknBHWPA1lvnoHt34kXLI+T5dI9X8Bqt4ZH6B83U5zF7R4lh4kYh5
466
+mmnWqK2Wg6D9hcvG4cmY+cqWHReOVcDyruc9+7NSMY4Ln8by/lZArlJ8yvML
467
+b7FB/vSDg6cqgT51qPqlVzYW4+CfxJJZCXFXX8gfG8vBNNOyGQUYqmDWpnyz
468
+snUednREJD9DoQoiOTy9Qqn5mNSXhzbaplVgNsFnV5xTiIkF/uHr9q0Cp5vt
469
+tXS+xVhdz6ebG/1VkHeELiPXvwxbOr9PMoJQDR+XFk3jSiow6ytJ3dJ7qkF2
470
+/GK60YMq7MEcd0D5+WrwfmNnubexGhvvd1c78bAa9Ja29Y8J1WK/pccmJwqq
471
+4btgWhrZpw6TbjCIvjNcDdMicySJjXos4t7W1QT1GjBubbBZJzdh85e8UzVs
472
+asDkOClZjaEFq1KeMG0NqQGQvTB0b+gD9pOYUfJnogZ46hfdpm61YZbf2O2D
473
+eGshbs/85tAn7ZiXrMPW7VgtZG28Tbhf0oG1cEl4HHlaCw7RdekNWl3YH2kv
474
++W9VtXBsuej7m6huzCm3c+DGbC0Uz1ydLWDqxYSF3MgvderAFEWTYgX6MU33
475
+hrndjnWg8/P9Y1L1AOZhxP2q4VkdsA8qJX3y+oppn47+++NnHZj4huU2bxvG
476
+zPpETOOF6sGOucg9mXMEK78am3dCpx6E4ypeKpBGMdLKU7uCiHpI1Yow8xId
477
+x44FstZeLK+H4BYn+bl9E9jQGXcRgYl66PP3uGRkM4lN1+t1uKs1gPevDc2G
478
+vmksnpAkL2/ZAB3Tfo6fZGYw1m8U/8HABtgpvnUmyX8Wi1oN3of6GuDDK4E/
479
+ofY/MMPA/QnMnu9B13QxxPvPIqYibvy3MPE9hLarSEQP/MKYk03P2LW+h5d2
480
+pG0Xm39jlgpa7C2ijcBATlKRrl7GCiu2XPTQa4Q+yViv9OY/2HjGUKWCcyP4
481
+Kk9rUAZXMD4h7EZoTSNUbubqF9tBwXabfPqgPdMI18Q05QNOUbGLl/Ulf21q
482
+Au084/q+sHXMNGSj95RtE3yyp5wo4KcDpZN7yVuJzVD/t/ujAJUBSnxXnn5Q
483
+aoZ54V3OvPWMsNwRM+9p2gyo3vBUWQQThAZdix1Ka4YvAoVcrXos4Nz/8s+T
484
+z81wxHXGM0iBAKycb47qUJtBr6bCLEWQCPTjkhuJhi3glK79IpHICnktcSan
485
+XVsAFT1c/MrGBiFOE5nE2BYIcXj3SYafHUplG8/ZL7RA70POZyW6nBDa9yhf
486
+KfwDmBjUTjwL4AEdeVbWkdIPcGN1yUxFnheqYzUtwsc+wLbaR3wvu3jBLDKW
487
+uLz3IyyYMjUdVOMD74sLJqW9H2GXRFQdowY/MFS4pTrQtwJpa4qIAEEAjr4J
488
+pojItkKXiFbWlz4B4A459OrenVbYHfwzszNcCO5J7B88uO0TRD216Zgy2gYq
489
+QUMdsrqfIMBpMjZETxRujw2857r2Cd5xrroe3ikGMgmdWV/KP4FGhus1XsXt
490
+kPjSo7RQsQ2+BxpuPXdlB7idNN+Tur8NpAYFHusw7IQvTz6kPTdpgyDlr/pd
491
+L3dCfrxO9D2vNri+8TN575AE5H7hvHqktQ2WSmyvZYdLA+PTwSGtkTaQmb1e
492
+nXJEBu658BjvWm6D0PTvTR+YZaGLK0idb1s7fIdR6eFAOWB/z7Q6eLUdwjPc
493
+LfbVKYJLdt1xZ44OcKBP/dLPtQd6Y4KKrbd3gOsc8fxG6B6gvNfeZrK3A1rl
494
+Fe+28KmA/V80oWneAYH7nDgDdu6FxuDDl5gyO+CySfzrLFs1uK8qU7dc1QHG
495
+77Te7FtXA9nqSNHpzg542xqdUhulDidvzrZ/pHZAmFyX988uDZjepLEjyuAz
496
+3LRXyJ66pQXvH2M3Hlh+hrptLwXcpMlQ1naj+o7LZ+juZCeYDpCh8cDOM5Yv
497
+PoNIZP+AihGAXGCUg8zsZ2hPGuduU9AG6Yy94qWPOoHdbuNGavgBUGKK3Xw+
498
+vhMixU8vym86CAvf7zDTF3WCXKatA8/Tg9B6QLhPd6QTjgarxgvH6YLbkeaT
499
+Hepd0DwZLM/fqQc8YbFSN426QCyzI9vz0mGQCPu1zG/TBb+7NRV91w+DKa9P
500
+gHlIF8ya5KuG7daHPc7bHabGu+D+xo+rz0oMYayvk/8RpQsshtbSpqyNQDet
501
+v1yBpxuO73gtIch9FDI6969c1+oG8TpzYrz6Mci8cnr7elg3SF0mGHSkHwfp
502
+rFUhbtQDDaz1d3d8NYb9PnQmuad64D7TtMuw/in4/gELNLbvgfjenwYmpafg
503
+97Vb7dGRPXDNUSjfNdYEFPkcF8TmesDWfVM1t+cZYMrWlNr1rBeui3TwpD4x
504
+gyRx+uK2rF7w0GSjWxE2h0vfOvddr++Fow/9jQ6lmcO4rc3WgoVeULjOkbba
505
+fB6GXUuUNA99gbgbGcoxYZZwd/m0nfbvL+CCdC+HiFkDG3uinxOxD1weGQz7
506
+OFuDx3JtWKxwH+i6i0S41lrDko3cnfUDfVBsUxB48YoNlJKC7xQ/7YNfBlhF
507
+bJ0ttDLGzsiq9YPqXf2pXRl2YFkWNHBGvx8eGYV6buK8DCJqXkX+Fv0Q5cqz
508
+tMX5MrR8GJAZCegHE+15Xz/NK+D+4MlSVG8/HKjYQVXvt4croo31f90G4HNT
509
+bG/hKUcQ3Mq6Uy54AJ5av4gMaHaEJjqy7enXA7D8IJ/NQMwJzrz1CM5qHgDP
510
+SHUlFO0ElfFpV89vHQSPClf2zyHOoDe3daqgbBAUQz+L3X91AwR2aNUe2vgK
511
+b++/MGLVvg2cFiNWopu/wbpb5Fex6NtQMS3WvCz7DaRjdnQJLNyGmnMdMwkm
512
+uP0iCbmv3eBqTPqFv5nfIExh+2oG7x2gKAbEnVAcAmNso3Bomxe4rgi6aGkM
513
+wTZP48REXy/Im0vdIXlgCHJFrTUtZ7wg0bqEb9V0CI5fb7lUWnoX3hg5KL30
514
+GwIGpo8vtuTfg5Lujx8GB4aAa2jVP+i2DzAr3d1WPzkEQ7+XflzK84E+LbJO
515
+xuIQNJks6TTO+8AOnzhGd+IwHDjarix06T7Ead402KQyDGebzXL5zvtC7YPh
516
+K1qPhqHBxapswdYfLIeHOG00RsDwpMD+pOGH0BL5NY3nwAi4dyvsmZd/BFOv
517
+mpgrjUbgFrHQu+n2I8i9zr8kYDMCaSEt/lq8QWDXcuJNU/AIrNgnuew0eAxO
518
+HIeDRMZGYKGrvcZzIAT+ak+mPAgeBVt/nb70d2HAYW0VoBAzCruXSUp802FA
519
+iT1Oan8zCr3GGkafBMKhi6Ho15Z3o/BoCzsVcwuH9ZTWQ69GR4G5u7+eDYuA
520
+PUo8PM/Ux6Bxp4ByVM9TWMuRXcVGxsA8fkuDnkEMzEvGKIrOjkGBXtxkrE8M
521
+dJIblv8ujcHa6yFM910MNKSU7isnjUOa8ZET3lLPoDte1ktl9ziMXh88Xkh4
522
+Dg3Mdzdz3BsHzkGRnIM9L0Bqhn7EQmQCgFwuIXw2Dr7Q7XihJDUBub8zN9m5
523
+x8FE5tlmut0T8Dun1u7rszioYOO+G3tgAjS5mWOODMRBi42PQrf9BOi56Gjs
524
+uBAPzWZcJVIlExBmfiF5/PprsM4uOmtsMgmpd9yuyBQlAOtnq6lRy0mwTpSV
525
+2jKUAMMdj9Ou20/CFo/Y/WqkRJCeW294fG8SXI6GfdtilgjarXc1S9ImIX5N
526
+PNmQKQmmVIP6v/+dBLMEz8Tk88kQK733dnzSFAR3hFi47EuDFGueX3w5U9Co
527
+PCHDZo/b7b1rQOkUPMp3EOh9lgYsHAfDL7dNQdqWo4/4KGmQ1Cextn1tCjbS
528
+Y6cEKtLB70mgkZXhNKxSeUROG2VCbdGfMP5f01DRfrRmVj8bND0+MpZQp+HE
529
+tUSzE7bZcP7jq1vnWL5D68Ww6U9e2aDmMmX9XPA7iIcnfuXNzQaJKyy7udB3
530
+qJ7vNiwWzAFm987M+qDvsC5z+pv3XA6Qu/XaL0rMwNGf7STu5DwwU68zQidn
531
+QUC1LWX0QhHE3m9UdjCbhcSJyISEe0WgEjo+Fmk7C4bnPtp4xBbBtYKqrKlb
532
+swCcj2ScBotAP7WhwfPFLGjFPL1jd7YYkoQidl8dn4WhuOFPMWfegXf0g/Kz
533
+rnOwbc8e1RnbUsjrPfscIuZBySLELqa2El7ef3Wn9+U88NNVkdlnKqG8ITvH
534
+MXke1neS3A1IVXC6ZVQopmQektoEVzeUqoDTj7+2Z2geRPgc+ui9q8Dw6o1b
535
+jAo/4Kt6gKzjjmoYPN07xF73A7CZ1wXfnGtAd/bAwinXBbDn7/B9olIPjp/C
536
+g565L0BEWSjd7OF6MFQrOP7VawE0LQQ1jlvUQ659lbF1wAJU+DD07ntYD/wH
537
+FZWtoxeg6tGDJ0+G6qHm6eCsRskC3NN/wU4OaQDV9n4vtL4AWz3N3X1/v4fL
538
+1tt7n9/7CeT532VGX5shcJ2cdyp0ERSTRdhX+tvggObJTauBv4B040d7Ev5c
539
+jpQ8LUV/4TcMK1/x26vZC88bHCa/7VsCYVuT4h9XB6CIzSD4BHUJHNv2bb4K
540
+Q7Bedq79eu0yqHcU1vTcG4HHa3/sBLz/AKk+hDGtcgxsexz0g3atAPm4327J
541
+/gm4eKlAuH9mBTary7PslJiG4b0P6oKfr0LjNdW9dnoz0BRyw7H10Bp8O9bD
542
+O285B1tQZWQGAwWmw5j2rSb9gFWxWi65HApUb9KW3BhZAAm7YxRJRyoM8ro5
543
+5RMXQTLI2dZNfh2shJteqEr9AlHrzduNRtbh/BNK47jib/BIcE+syP4LFYtq
544
+NRq6S1AZp8Sh67kBnx9fZ2jRXoZKu8trb2XokFpz9KO38n9gQEKY9XwSHaqI
545
+LdftF1qBoc4SuSlxenSFe5+Iz8QKmJrz798sQY9OedAdb55eATFXu4n9UvTI
546
+7lcdG8/cCvx8xdMbK0eP0gbO8T37tQKL7+JMLVXo0WCwms0zulXQu7mRSDlI
547
+jw69xyJOCq0CMbD8Q8xleqTw5/rWRINVCMdupV3MpUfK+xPIbzNWQbBE40Bw
548
+Pj16XNeVa521Cv2OcgaFhfTIN225kT93FQ6xVSQSSunR4Zbv3XeKViFHJ8gt
549
+q5YejRv2Oe+pWYX4gc7rm7roUUXe0kXLHny/Ydvtciv06F5gvmMW3RpMmsQt
550
+BgEDygyQeLDp6BqweToSarUZ0E46FRPr42vg/tL+9qoOA3oexFmTc3INeBo4
551
+r13SY0DGqejmkTNroORLjT90nAE9sdPVsb+wBm47jakC1gyILU9H/8qNNZh6
552
+MbC07s+ABspP+ptFrkEHB8qu+8SAbjz24GfpXQMrpfoB7Q4GpCBJMJPsW4MF
553
+XjHbyk4G5Gdb/vPAwBpwHVYILP3CgHwvfObyHFoD9iwfruJRBvTscSr3l6k1
554
+uPlCa7j6DwM6Jem0CqtrELpP6s4WMUYk3uOp0ihAAZGwlyGvxBnRAa91nVwh
555
+CtiInl6WlGBEORFusc+EKSCXY/JOXZYRlSqyal4Uo8DTA/3sliqMSOo8M2VK
556
+ioLfL1fflOsxIpiyeflClQJ+v+nO5jozIh/9bNWyExR4eMtIU8CFEUlOv8k9
557
+YUyBhKN2pl6ujChY5Fbu5CkKOBv9PKF/hxGpy/8kc5hS4G/EqNyULyMamVb1
558
+17WgwPLcrLpCNCNS+d6z5GyP77/2/stIBSNq77Q6numD/w4SP3Acq2ZEykJ/
559
+/fl8KZD4YP5WeS0j8t9986C7H368ntNcdCMjCtSdMdcOpEDI7LtTJzoY0f2y
560
+j4wVjymwMNc42DrOiNIHM62doymwkVz9dZadCRWyxBTWZFBATTSrNYKLCfX6
561
+NZZsfkuBrD9tv7R4mdDxzs2bLmVRAGSMBh7zMyHVL+QaplwKkAVvCiuLM6Fz
562
+Z3bJyhdRoEfcgt1XjQndLRFLkKumQPD7j3r6VkwoN2uo7+dnChC2Bu5dtWFC
563
+nHsPRXN3UeCP5wuD5EtMSHdja6VCNwViagJXGK8yoe12lwyseykgO2iOVd5i
564
+QvsnOT1LByiw65qfBvkxExJOv/BLbJwCjIPjxcbFTAiLuOze8JsC99qSytZK
565
+mFDEkcfvs5YocLk36ltcORNqGp9JiVqmQEXsT++5GibUKasvb71Cgf2cvUqB
566
+H5nQ7kOKx6cp+H2lM2StZoQJjTf1/8xloMK5i8euGHAwI4dJ68b9XFQoqXzS
567
+tsTFjNDqeAQdNxUCA2sNY3mZkeLG6JZy3MdD2YIW+ZlREddHUObF10PyeJ6J
568
+M6N58zcHODZTwc9xkmNOjRmtyH3jCxCiwpcVTC/eihn9uKLS/GQnFaL2aCmJ
569
+2uLHd7NbbZOgwmyZruTLS8zoTR3HWipuu7SxfTEOzMj5nIlihSQVtgUsEsNc
570
+mZH6i2c1fdJU4Ls2QPJ/yIxe1vE7jctTwSuit4rpMTPyTf7jYaVAhQ/aj+/f
571
+D2FGR98axXzFbS0dKecdwYw6Q1WZOhXxep/eZ/B8xYwMBybL85So0PC4/a1r
572
+LjNi1h+MPqRChSuKNTzL+cwoMq2euxB30pKV180ivJ+IiOQde6nQXa7p4lLG
573
+jDY51++l4v6ZMdd6vYEZsV8O/vFajQqG37ZKOfcxo5OuAznvNalw61Z+wg0G
574
+FsRqskK+iagw6djMKMvMgqTUbvq24eZkM7kyRGBBNtqLE7LaVHAYP21oyMGC
575
+ZNzGmQZxv7vVcElKgAX5mrq9V9WhgtmQaM+AAgs65Q1e1QepsHn8SVy4Egu6
576
+NcEqxKVLBX+9D45H9rCg2sTq8XO4q132iBars6B5jjmeX7jjWDdVhuuwoHRH
577
+oSF+PSo8tmRa0DdlQUV+B+y1jlDh2gcxNkYzFrS/yua5J+6llDjZkvMsyGDV
578
+lqsCt27uTVdpGxbkk05q1NKngqu4ETA7siC/Fv9Xuw2oUL6R61fpy4L0f/1Y
579
+WTWkQtsi/1fXABY0aVZO3WWE10Mo01B8iK/XnD1ji/vtbu+1FyEsSPXu+tZW
580
+3M/TDsa5P2NB3CjuT9RRKhxOyHZUzWZBy1LumzmPU2HvE7v6ylwWVHiEf78a
581
+7lkOOZHDBSzotNz+OQvcZc7JHedK8P7V9tVm4VahszH2rsP3/xP64PAJKsx4
582
+WaR96GVBdw3fm188SQVLwV3CJv0s6Jm0yPcA3HsWXEK+DbKgEoEaplTcu4z2
583
+uy+OsKCzhwempnHzi61bCMyxoMwDAQEXjalwM+axrQ09ARVKiSzpn8KvFz2l
584
+mTlGAjpwrezLRdxSlC7nWywEtEyZPeeNO2SDy+chGwE992/QKsB9PD8qM3sz
585
+ARmjsw8FTKhgEZ+qqSlAQD+VfW8q4b6760ljrRABBbhEM+vhVnb+MNEtSkAM
586
+BiICrrj5zlrJr8sQEFV0QrQVd61YaKW/PAElWWfrj+L28LtyknsXAV188XLH
587
+Cu40wc2eO1QIKP/QyX6x01SQnWrvOYwRkMYeWZ9ruH2vOyVHniCgEQvbqxTc
588
+UaLaXptOEVBNbYwT2xkqqH/wPBV6moCAR1VpK+65kV3MD80IaNP7jEkN3FZk
589
+6cueFwnosFKlgQtu8jZWnTU7Atp1w0LPB7eCh7bILXsCKjvnwhKK26cyscPJ
590
+iYDspOk+puEm7SRo27gT0PhAZtQgbl2TkyLDHgT0IFOndBr3NrPRVfO7BHRs
591
+lDF5CfdySkPeaV88r5VPX9hN8fzzLGX1gwlIXEqxSh33PiGj7cqvCaipeF4q
592
+ALdw0R+6rAR8fZVNLBT3yYamIblkAnqJ/n6Pxt1hNRwnkUFAUao/Kam4meiK
593
+xQULCYizpXFrM+6qk3cZI4sJiFIqXdaOO9XIdoy3lIAM7farfMFdu/tBEnsV
594
+Af1I+pU5ifv1DT55umYCWk3y6WE4SwW19/kcnh8IqNV8/CAJd0CO/Y/VVgJ6
595
+q/YmlAs381PBvF+f8bwP+5ZvxZ2bY7VvcpCA1F8l31fG/Sz9tYjNEAENXOcd
596
+U8MtnfBrY2iEgPquc0mQcftu1Nf1TRJQs0DTkUO4na2Fjrb+JKD0P+57zuI2
597
+EW/S9/5NQMOd6iwWuBPr/fRU/hBQfMOnYmvcR75I7H9GJaAuEd4qB9yXGJb2
598
+XiQQke/Jzxc9cZv1Mu4RZCWibOMvet641R8JK31gJ6JrXqe4/HC7v7osq8xL
599
+RKFJP/WDcLMZ2Ir+FSYiqTnX8BjcgrsKhXNEiej8ltaUF7hvveYQshEnogyp
600
+2aRYWh7Mn/iapYho/a6jRSLu8bPqvJ6yRFTE3CqUgnuRLZlLSYGI/iyMV6Xh
601
+djIIZ41UJiLXmyqfsnA/0eYmHt5LRA6GNuq5uMvNnzBT1YjoNBEF5+MuEo+l
602
+syITkfmZAfp3uJnMxpYV9IjoLp8lXzWt3jOev4eOEFHTNf4fNbipHIKL4YZE
603
+9Ord4Ls63B3Lp+dWTxDRngyt7Y24TdvXvmecIqJIwZSKJtycBbFTFmeIKI+h
604
+0bAFt7D8j9F6cyKKDsna34q7KyJm+LYlET0pkUz9hFsi6eA3OWsiYmetYGjH
605
+PXLhdd8TOyJiKE0K/Yz7Sox9u/kNIto39lmsF/eF12KfuF3x/XIrZb7Q+g3v
606
+/lB7m4gseryk+3DPsx5slPEiIhG7DOIA7pN31usH7uH91Cd8p3l7amFtyH0i
607
++twTXDuIu5RNrnIpkIj82I6c+4b7u9REWcojPD/JBKEh3Ifb4kvOBROR8hR9
608
+B81nI4QKq8OJaOBEn8wIbkILd+bjV0QUf9vAbwx3ytsbN3njiWirpjjjOG7o
609
+6iZHvSGi1Mq0OzRf633ZGpdCRG6xnuYTuEPS6aMk0oloqVz4Pc3Vb20t0jKJ
610
+aE1aQH4S91VlxYW8XCISuPpxiuYbqWHF6gVEdIV1AE3hniP/uVdeRETnUhci
611
+aH7eXMXzvoyI5A592j2NW6xaok+/kogUOHvcafbrfPi6rZqIam/ZV9GsrXdq
612
+T18DESnKZml/p10vb0oo55uI6P18tCfNl3jF6kZbiOi2oW8hzcGiM8Zzbfj1
613
+2tYpOoN797tjItc/E9FPJ5djNBuaFY4vdxFR5+uHXjRjBd6udP1ERM0N+Uyz
614
++sVJzG+QiBg53q3RzMRvSGAdIqKEkY+is7jzvQWiN43j+T/ktKF5lOxlGT1J
615
+RI6e5+/T7P53FH9SEZHnhck4mp2Dst5J/iCi109+dNP81HSzT/pPvP+UiB80
616
+Z8neOaL0Gz//gQqWOdyxG0O8BctEdMjgrjDNBr26/RqrRGSQ8F2J5qj8jDcV
617
+FCKa373pAM1WEbwOOn+JyKaPzYRmofNfqQaMJFRJznelOfLQgfp2ZhKSHvH0
618
+o/nNnrTHJkQSsi05Gk7zl+3cJv2sJPRcc28czR95XLdZcpDw/38aGTQLMg5M
619
+jHGRkC/j5SKaTy1pZ13mJSFvldZqmpf6ONANfhLScbHrpPnRxxvEFUESOmGf
620
+P0DztcovbR7CJHROzWaMZrVsiKEXJaH7BvdnaO6KTbzgv52EZmqEF2kuDWGT
621
+ZdtJQlZ71Fdo5rvnvBgiSUJpbf3rNA9cIN+PkSMh/7hOwjxuxZNv9LcpkpDf
622
+WVV2mvMPkPjeKJGQwjENbprNVR0HpPaQ0J760U00C0t3JWTsJaGj6/v4aR4W
623
+3Hd1tzoJqWjpCdH8nC1+b6Emnkc9pwjN5HWWv5pkElIbfCpKc+G8Q0MlkFBV
624
+w+h2mi8fkQ8K2U9CA6c0dtJ8ImnmuMVBEtqlfELy3zpDOv8uPRKyM1WWpjnp
625
+/JXBv0dI6GrnoAzNF/in7V4dI6E700nyNO9qu/SbbEJCQcUfFWkuRrZsnhdI
626
+yM29YDfNydlW4mUOJGRxz2LPP4eaH9O8j89rMFyF5nnHM17FMSR0UTznn5cV
627
+jPryG0hIDC7+8+iMjmrOLxLqnpL55/8DdghmFA==
628
+       "]]},
629
+     Annotation[#, "Charting`Private`Tag$437871#1"]& ]}, {}},
630
+  Axes->{True, True},
631
+  AxesLabel->{None, None},
632
+  AxesOrigin->{0, 0},
633
+  DisplayFunction->Identity,
634
+  FrameLabel->{{None, None}, {None, None}},
635
+  FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
636
+  GridLinesStyle->Directive[
637
+    GrayLevel[0.5, 0.4]],
638
+  ImagePadding->All,
639
+  Method->{
640
+   "DefaultGraphicsInteraction" -> {
641
+     "Version" -> 1.2, "TrackMousePosition" -> {True, False}, 
642
+      "Effects" -> {
643
+       "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, 
644
+        "Droplines" -> {
645
+         "freeformCursorMode" -> True, 
646
+          "placement" -> {"x" -> "All", "y" -> "None"}}}}, "ScalingFunctions" -> 
647
+    None},
648
+  PlotRange->{{0., 3.243990348766134}, {0., 1.7721998270300445`}},
649
+  PlotRangeClipping->True,
650
+  PlotRangePadding->{{
651
+     Scaled[0.05], 
652
+     Scaled[0.05]}, {
653
+     Scaled[0.05], 
654
+     Scaled[0.05]}},
655
+  Ticks->{Automatic, Automatic}]], "Output",
656
+ CellLabel->
657
+  "Out[205]=",ExpressionUUID->"e6db7c3b-6fac-4a3a-b719-f61dc8c48834"]
658
+}, Open  ]]
659
+},
660
+WindowSize->{786, 884},
661
+WindowMargins->{{Automatic, 210}, {-186, Automatic}},
662
+FrontEndVersion->"12.1 for Microsoft Windows (64-bit) (June 9, 2020)",
663
+StyleDefinitions->"Default.nb",
664
+ExpressionUUID->"403bb8c0-0efb-4c0b-a09f-03976a9aa4f6"
665
+]
666
+(* End of Notebook Content *)
667
+
668
+(* Internal cache information *)
669
+(*CellTagsOutline
670
+CellTagsIndex->{}
671
+*)
672
+(*CellTagsIndex
673
+CellTagsIndex->{}
674
+*)
675
+(*NotebookFileOutline
676
+Notebook[{
677
+Cell[558, 20, 8002, 224, 656, "Input",ExpressionUUID->"b6d7bb97-f801-4b79-84e9-03757a7fafc8"],
678
+Cell[8563, 246, 6219, 170, 561, "Input",ExpressionUUID->"f922cec0-aa84-4593-aff3-3268dbccfdf7"],
679
+Cell[CellGroupData[{
680
+Cell[14807, 420, 266, 7, 28, "Input",ExpressionUUID->"83f1c93d-5075-475d-b9f3-efc604a47ce1"],
681
+Cell[15076, 429, 12996, 227, 220, "Output",ExpressionUUID->"e6db7c3b-6fac-4a3a-b719-f61dc8c48834"]
682
+}, Open  ]]
683
+}
684
+]
685
+*)
686
+
687
+(* End of internal cache information *)
688
+