diff --git a/.gitignore b/.gitignore index 01a1f47..9619e59 100644 --- a/.gitignore +++ b/.gitignore @@ -1,3 +1,15 @@ +# General stuff __pycache__/ typst/ +*.o +a.out + +# Some artifacts Hahn_gamma* + +# Seperate out all pdfs for now +*.pdf + +# Just the VL PDFs? +*VL*.pdf + diff --git a/README.md b/README.md index b5b5773..c21750e 100644 --- a/README.md +++ b/README.md @@ -1 +1,4 @@ -bb \ No newline at end of file +# Contains the source for my Studies + +This repo is split into the study semesters. + diff --git a/S1/AGLA/Hausaufgaben/Zettel03.pdf b/S1/AGLA/Hausaufgaben/Zettel03.pdf deleted file mode 100644 index c96ab78..0000000 Binary files a/S1/AGLA/Hausaufgaben/Zettel03.pdf and /dev/null differ diff --git a/S1/AGLA/Hausaufgaben/Zettel08.pdf b/S1/AGLA/Hausaufgaben/Zettel08.pdf deleted file mode 100644 index 15eb62c..0000000 Binary files a/S1/AGLA/Hausaufgaben/Zettel08.pdf and /dev/null differ diff --git a/S1/AGLA/Vorlesungen/VL10.pdf b/S1/AGLA/Vorlesungen/VL10.pdf deleted file mode 100644 index 7318e52..0000000 Binary files a/S1/AGLA/Vorlesungen/VL10.pdf and /dev/null differ diff --git a/S1/AGLA/Vorlesungen/VL11.pdf b/S1/AGLA/Vorlesungen/VL11.pdf deleted file mode 100644 index ff91903..0000000 Binary files a/S1/AGLA/Vorlesungen/VL11.pdf and /dev/null differ diff --git a/S1/AGLA/Zettel/Blatt_03.pdf b/S1/AGLA/Zettel/Blatt_03.pdf deleted file mode 100644 index 13bf5be..0000000 Binary files a/S1/AGLA/Zettel/Blatt_03.pdf and /dev/null differ diff --git a/S1/AGLA/Zettel/blatt_02.pdf b/S1/AGLA/Zettel/blatt_02.pdf deleted file mode 100644 index e7b9cc9..0000000 Binary files a/S1/AGLA/Zettel/blatt_02.pdf and /dev/null differ diff --git a/S1/AGLA/conf.pdf b/S1/AGLA/conf.pdf deleted file mode 100644 index 9922f42..0000000 Binary files a/S1/AGLA/conf.pdf and /dev/null differ diff --git a/S1/ExPhyI/.ipynb_checkpoints/ha3-checkpoint.ipynb b/S1/ExPhyI/.ipynb_checkpoints/ha3-checkpoint.ipynb deleted file mode 100644 index bf1da98..0000000 --- a/S1/ExPhyI/.ipynb_checkpoints/ha3-checkpoint.ipynb +++ /dev/null @@ -1,311 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Hausaufgabe Blatt 3\n", - "## Gleichförmig beschleunigte, geradlinige Bewegung - Revisited\n", - "\n", - "In dieser Aufgabe werden wir die Bahnkurve eines gleichförmig beschleunigten Objektes in einer Dimension berechnen und dieses mal auch visualisieren. Die Position $x$ zum Zeitpunkt $t$ ist, wie auf dem Blatt 2, gegeben durch folgende Gleichung:\n", - "\\begin{equation*}\n", - "x\\!\\left( t \\right) = x_0 + v_0 t + \\frac{1}{2} a t^2 \n", - "\\end{equation*}\n", - "wobei $x_0$ und $v_0$ die Anfangsposition und -geschwindigkeit sind und $a$ die konstante Beschleunigung, die auf das Objekt wirkt. \n", - "\n", - "## 1. Numpy Arrays: Linspace\n", - "Anstelle, dass wir die Einträge in numpy arrays \"per Hand\" definieren, können wir eine nützliche Funktion verwenden. \n", - "\n", - "**a)** \n", - "Machen Sie sich mit der nachstehenden Zelle vertraut. Verstehen Sie die Syntax?" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "ExecuteTime": { - "end_time": "2019-11-01T10:22:27.227336Z", - "start_time": "2019-11-01T10:22:27.100666Z" - } - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[0. 0.25 0.5 0.75 1. ]\n" - ] - } - ], - "source": [ - "import numpy as np # Laden der Numpy Bibliothek \n", - "\n", - "x = np.linspace(0, 1, 5) # Definieren von x\n", - "\n", - "print(x) # Ausgabe x" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "**b)** Erstellen sie ein numpy array für die Zeit `t` indem sie `np.linspace()` korrekt verwenden. Dabei soll gelten $t_0 = 0$ und $t_N = 5$ mit der Anzahl der Einträge $N = 50$." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "**c)** Benutzen Sie die in ha2 Aufgabe 2 definierte Funktion `printBahnkurve()` um sich nun die Bahnkurve für das gerade erstellte array `t` ausgeben zu lassen. Verwenden Sie die Werte $x_0=3$ und $v_0=10$ wie auf Blatt 2." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Return\n", - "\n", - "Bisher hat unsere definierte Funktion lediglich einen `print()` Befehl ausgeführt. Wir wollen nun, dass unsere Funktion einen Wert zurück gibt. Dadurch kann der Wert in einer Variablen gespeichert und somit weiterverarbeitet werden. Dazu verwenden wir das `return` Statement. \n", - "\n", - "**d)** Betrachten Sie die folgenden zwei Funktionen. Beschreiben Sie kurz (1-2 Sätze), was hier geschieht. " - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": { - "ExecuteTime": { - "end_time": "2019-11-01T10:22:27.233313Z", - "start_time": "2019-11-01T10:22:27.230416Z" - } - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "2 4\n" - ] - } - ], - "source": [ - "def identity(x): # definiere Funktion\n", - " return x # definiere Ausgabe\n", - "\n", - "def square(x):# definiere Funktion\n", - " return x**2 # definiere Ausgabe\n", - "\n", - "id2 = identity(2) # definiere id2 über Zugriff auf identity\n", - "square2 = square(2)# definiere id2 über Zugriff auf square\n", - "\n", - "print(id2, square2) # Ausgabe der Werte" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "**e)** Schreiben Sie eine neue Funktion, indem Sie den `print()` Befehl in der Funktion `printBahnkurve()` durch das `return` Statement ersetzen. Wählen Sie einen geeigneten Namen für die neue Funktion. " - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Visualisierung\n", - "Da Sie nun dazu in der Lage sind, viele Datenpunkte zu erzeugen, wollen wir als nächsten Schritt die berechnete Bahnkurve in einem plot mithilfe von `matplotlib.pyplot` visualisieren. `Matplotlib` ist eine beliebte und sehr vielseitige plot Bibliothek, die es uns ermöglicht Daten zu visualisieren. Wer einen Eindruck davon gewinnen möchte, was alles mit `matplotlib` möglich ist, kann ja mal [hier](https://matplotlib.org/3.1.1/gallery/index.html) vorbeischauen!\n", - "\n", - "Wir haben folgendes Grundgerüst vorbereitet, in dem die Funktion $f(x) = x^2$ beispielhaft geplottet wird." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": { - "ExecuteTime": { - "end_time": "2019-11-01T10:22:42.277126Z", - "start_time": "2019-11-01T10:22:42.160402Z" - } - }, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import matplotlib.pyplot as plt # lade matplotlib als Bibliothek\n", - "import numpy as np\n", - "x = np.linspace(-2, 2, 170) # definiere x\n", - "xQuadrat = x**2 # berechen x^2\n", - "\n", - "# ### Anfang Grundgerüst ( mit # kann man Kommentare schreiben )\n", - "\n", - "fig, ax = plt.subplots()\n", - "\n", - "ax.set_title(\"Parabel\") # Titel\n", - "ax.set_xlabel(\"X-Werte\") # x-Achsenbeschriftrung\n", - "ax.set_ylabel(\"y-Werte\") # y-Achsenbeschriftung\n", - "\n", - "ax.plot(x, xQuadrat) # x-Wert hier: x, y Wert hier: xQuadrat\n", - "\n", - "plt.show()\n", - "\n", - "# ### Ende Grundgerüst" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "**a)** Machen Sie sich mit dem Grundgerüst vertraut, indem Sie \n", - " - `x` mit Werten Ihrer Wahl erweitern\n", - " - einen geeigneten Titel\n", - " - geeignete x- und y- Achsenbeschriftung wählen.\n", - " \n", - "Möchte man mehrere Kurven in einem Diagramm darstellen, so muss `ax.plot()` lediglich erneut aufgerufen werden. \n", - "Dabei ist es nützlich diese Kurven in einer Legende zu unterscheiden:" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": { - "ExecuteTime": { - "end_time": "2019-11-01T10:22:27.961375Z", - "start_time": "2019-11-01T10:22:27.514251Z" - } - }, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig, ax = plt.subplots()\n", - "\n", - "ax.set_title(\"Mehrfachplot\") # Titel\n", - "ax.set_xlabel(\"X\") #x-Achsenbeschriftung\n", - "ax.set_ylabel(\"Y\") # y-Achsenbeschriftung\n", - "\n", - "ax.plot(x, xQuadrat, label=\"$x^2$\") # label: Eintrag Legende, versteht auch LaTex!\n", - "ax.plot(x, x**4, label=\"$x^4$\") # label\n", - "\n", - "ax.legend() # Zeige Legende\n", - "plt.show() " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "**b)** Kopieren Sie das Grundgerüst und ersetzen sie die x-Werte durch das oben definierte array `t` und die y-Werte durch die errechnete Bahnkurve. Wählen Sie auch hier einen geeigneten Titel und Achsenbeschriftungen." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "ExecuteTime": { - "end_time": "2019-11-01T10:21:24.775267Z", - "start_time": "2019-11-01T10:21:24.689518Z" - } - }, - "outputs": [], - "source": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "**c)** Variieren Sie nun die Anfangsgeschwindigkeit. Erstellen Sie zwei Kurven mit verschiedenen Bedingungen (z.B. $v_0 = 10$ und $v_0=20$). Vergleichen Sie die Kurven miteinander, indem Sie diese in einem Diagramm darstellen. Benutzen Sie angemessene Beschriftungen!" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "ExecuteTime": { - "end_time": "2019-11-01T10:21:24.776711Z", - "start_time": "2019-11-01T10:21:24.023Z" - } - }, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.11.9" - }, - "latex_envs": { - "LaTeX_envs_menu_present": true, - "autoclose": true, - "autocomplete": true, - "bibliofile": "biblio.bib", - "cite_by": "apalike", - "current_citInitial": 1, - "eqLabelWithNumbers": true, - "eqNumInitial": 1, - "hotkeys": { - "equation": "Ctrl-E", - "itemize": "Ctrl-I" - }, - "labels_anchors": false, - "latex_user_defs": false, - "report_style_numbering": false, - "user_envs_cfg": false - } - }, - "nbformat": 4, - "nbformat_minor": 4 -} diff --git a/S1/ExPhyI/VL10.typ b/S1/ExPhyI/VL/VL10.typ similarity index 100% rename from S1/ExPhyI/VL10.typ rename to S1/ExPhyI/VL/VL10.typ diff --git a/S1/ExPhyI/VL11.typ b/S1/ExPhyI/VL/VL11.typ similarity index 100% rename from S1/ExPhyI/VL11.typ rename to S1/ExPhyI/VL/VL11.typ diff --git a/S1/ExPhyI/VL12.typ b/S1/ExPhyI/VL/VL12.typ similarity index 100% rename from S1/ExPhyI/VL12.typ rename to S1/ExPhyI/VL/VL12.typ diff --git a/S1/ExPhyI/VL17.typ b/S1/ExPhyI/VL/VL17.typ similarity index 100% rename from S1/ExPhyI/VL17.typ rename to S1/ExPhyI/VL/VL17.typ diff --git a/S1/ExPhyI/VL6.typ b/S1/ExPhyI/VL/VL6.typ similarity index 100% rename from S1/ExPhyI/VL6.typ rename to S1/ExPhyI/VL/VL6.typ diff --git a/S1/ExPhyI/VL9.typ b/S1/ExPhyI/VL/VL9.typ similarity index 100% rename from S1/ExPhyI/VL9.typ rename to S1/ExPhyI/VL/VL9.typ diff --git a/S1/ExPhyI/ha3.ipynb b/S1/ExPhyI/ha3.ipynb deleted file mode 100644 index bf1da98..0000000 --- a/S1/ExPhyI/ha3.ipynb +++ /dev/null @@ -1,311 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Hausaufgabe Blatt 3\n", - "## Gleichförmig beschleunigte, geradlinige Bewegung - Revisited\n", - "\n", - "In dieser Aufgabe werden wir die Bahnkurve eines gleichförmig beschleunigten Objektes in einer Dimension berechnen und dieses mal auch visualisieren. Die Position $x$ zum Zeitpunkt $t$ ist, wie auf dem Blatt 2, gegeben durch folgende Gleichung:\n", - "\\begin{equation*}\n", - "x\\!\\left( t \\right) = x_0 + v_0 t + \\frac{1}{2} a t^2 \n", - "\\end{equation*}\n", - "wobei $x_0$ und $v_0$ die Anfangsposition und -geschwindigkeit sind und $a$ die konstante Beschleunigung, die auf das Objekt wirkt. \n", - "\n", - "## 1. Numpy Arrays: Linspace\n", - "Anstelle, dass wir die Einträge in numpy arrays \"per Hand\" definieren, können wir eine nützliche Funktion verwenden. \n", - "\n", - "**a)** \n", - "Machen Sie sich mit der nachstehenden Zelle vertraut. Verstehen Sie die Syntax?" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "ExecuteTime": { - "end_time": "2019-11-01T10:22:27.227336Z", - "start_time": "2019-11-01T10:22:27.100666Z" - } - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[0. 0.25 0.5 0.75 1. ]\n" - ] - } - ], - "source": [ - "import numpy as np # Laden der Numpy Bibliothek \n", - "\n", - "x = np.linspace(0, 1, 5) # Definieren von x\n", - "\n", - "print(x) # Ausgabe x" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "**b)** Erstellen sie ein numpy array für die Zeit `t` indem sie `np.linspace()` korrekt verwenden. Dabei soll gelten $t_0 = 0$ und $t_N = 5$ mit der Anzahl der Einträge $N = 50$." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "**c)** Benutzen Sie die in ha2 Aufgabe 2 definierte Funktion `printBahnkurve()` um sich nun die Bahnkurve für das gerade erstellte array `t` ausgeben zu lassen. Verwenden Sie die Werte $x_0=3$ und $v_0=10$ wie auf Blatt 2." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Return\n", - "\n", - "Bisher hat unsere definierte Funktion lediglich einen `print()` Befehl ausgeführt. Wir wollen nun, dass unsere Funktion einen Wert zurück gibt. Dadurch kann der Wert in einer Variablen gespeichert und somit weiterverarbeitet werden. Dazu verwenden wir das `return` Statement. \n", - "\n", - "**d)** Betrachten Sie die folgenden zwei Funktionen. Beschreiben Sie kurz (1-2 Sätze), was hier geschieht. " - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": { - "ExecuteTime": { - "end_time": "2019-11-01T10:22:27.233313Z", - "start_time": "2019-11-01T10:22:27.230416Z" - } - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "2 4\n" - ] - } - ], - "source": [ - "def identity(x): # definiere Funktion\n", - " return x # definiere Ausgabe\n", - "\n", - "def square(x):# definiere Funktion\n", - " return x**2 # definiere Ausgabe\n", - "\n", - "id2 = identity(2) # definiere id2 über Zugriff auf identity\n", - "square2 = square(2)# definiere id2 über Zugriff auf square\n", - "\n", - "print(id2, square2) # Ausgabe der Werte" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "**e)** Schreiben Sie eine neue Funktion, indem Sie den `print()` Befehl in der Funktion `printBahnkurve()` durch das `return` Statement ersetzen. Wählen Sie einen geeigneten Namen für die neue Funktion. " - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Visualisierung\n", - "Da Sie nun dazu in der Lage sind, viele Datenpunkte zu erzeugen, wollen wir als nächsten Schritt die berechnete Bahnkurve in einem plot mithilfe von `matplotlib.pyplot` visualisieren. `Matplotlib` ist eine beliebte und sehr vielseitige plot Bibliothek, die es uns ermöglicht Daten zu visualisieren. Wer einen Eindruck davon gewinnen möchte, was alles mit `matplotlib` möglich ist, kann ja mal [hier](https://matplotlib.org/3.1.1/gallery/index.html) vorbeischauen!\n", - "\n", - "Wir haben folgendes Grundgerüst vorbereitet, in dem die Funktion $f(x) = x^2$ beispielhaft geplottet wird." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": { - "ExecuteTime": { - "end_time": "2019-11-01T10:22:42.277126Z", - "start_time": "2019-11-01T10:22:42.160402Z" - } - }, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import matplotlib.pyplot as plt # lade matplotlib als Bibliothek\n", - "import numpy as np\n", - "x = np.linspace(-2, 2, 170) # definiere x\n", - "xQuadrat = x**2 # berechen x^2\n", - "\n", - "# ### Anfang Grundgerüst ( mit # kann man Kommentare schreiben )\n", - "\n", - "fig, ax = plt.subplots()\n", - "\n", - "ax.set_title(\"Parabel\") # Titel\n", - "ax.set_xlabel(\"X-Werte\") # x-Achsenbeschriftrung\n", - "ax.set_ylabel(\"y-Werte\") # y-Achsenbeschriftung\n", - "\n", - "ax.plot(x, xQuadrat) # x-Wert hier: x, y Wert hier: xQuadrat\n", - "\n", - "plt.show()\n", - "\n", - "# ### Ende Grundgerüst" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "**a)** Machen Sie sich mit dem Grundgerüst vertraut, indem Sie \n", - " - `x` mit Werten Ihrer Wahl erweitern\n", - " - einen geeigneten Titel\n", - " - geeignete x- und y- Achsenbeschriftung wählen.\n", - " \n", - "Möchte man mehrere Kurven in einem Diagramm darstellen, so muss `ax.plot()` lediglich erneut aufgerufen werden. \n", - "Dabei ist es nützlich diese Kurven in einer Legende zu unterscheiden:" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": { - "ExecuteTime": { - "end_time": "2019-11-01T10:22:27.961375Z", - "start_time": "2019-11-01T10:22:27.514251Z" - } - }, - "outputs": [ - { - "data": { - "image/png": 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m6pNaZkRExFM5W2ZcZ+RfB4WZ+uSco2kTGIa1tYiIiNQnFz0tGxRm6ldUe/D2g9J8OJJmdTUiIiL1o/Ag5B8AbC43YB4ozNQvb9/K5reM9dbWIiIiUl8c32kRbcyzd12Mwkx9a9HNXCrMiIiIp3B8p8V2tbaOGijM1LdYhRkREfEwzjDTzdo6aqAwU98UZkRExNM4w0x3a+uogcJMfXM0weXuhaJD1tYiIiJypsqK4eA2c10tM01EQFjltAaZG6ytRURE5ExlbwajwpzGICTO6mqqZWmYWbhwIWPHjiU+Ph6bzcbnn39e47a33norNpuNF154odHqO2061CQiIp7i+P4yLjaNgYOlYaawsJAePXowderUk273+eef89tvvxEfH99IlZ0hxzHFDLXMiIiIm3Pxzr8APla++JgxYxgzZsxJt9m/fz9//vOf+f7777nwwgsbqbIz5Og3o5YZERFxd47vshYKM6fFbrczYcIE7r//frp06VKrx5SUlFBSUuK8npeX11Dl1cyRXrO3QHkp+Pg1fg0iIiJnym6vPMrgwi0zLt0B+Omnn8bHx4e777671o+ZMmUKYWFhzktiYmIDVliDsESzI7C9zAw0IiIi7ujIbnOKHm9/c8oeF+WyYWblypW8+OKLvP3229jq0OHowQcfJDc313nZu3dvA1ZZA5vtuH4zOtQkIiJuyvEdFtPJnLLHRblsmFm0aBFZWVkkJSXh4+ODj48PaWlp3HfffbRu3brGx/n7+xMaGlrlYgmd0SQiIu7ODQ4xgQv3mZkwYQLnnHNOldvOO+88JkyYwI033mhRVXWgMCMiIu7OxUf+dbA0zBQUFLBjxw7n9dTUVNasWUNERARJSUlERkZW2d7X15fY2FhSUlIau9S6Oz7MGIbLnpsvIiJSIzc4LRssDjMrVqxg5MiRzuuTJk0CYOLEibz99tsWVVVPolLAyxdKcs2pDcKTrK5IRESk9ooOQd4+c71F7c4otoqlYWbEiBEYhlHr7Xfv3t1wxdQ3Hz+I7giZ681kqzAjIiLuxNEq07w1BFjU/7SWXLYDsEdQvxkREXFXbnKICRRmGpbCjIiIuCvHZMku3vkXFGYaljPMrLO2DhERkbpSy4wAlXM0HdkDR49YWoqIiEitlZdUjmCvMNPEBTaHsGMdfzM1g7aIiLiJ7C1gLze/x0ITrK7mlBRmGppm0BYREXfjnCm7q1uMk6Yw09Cc/WbUMiMiIm7CTUb+dVCYaWjqBCwiIu7GTeZkclCYaWiOP4TsLVBeam0tIiIip2IYbnUmEyjMNLzwVuAfChWlcHCr1dWIiIic3JE95lQ83n4Q1cHqampFYaah2WyVyfaADjWJiIiLO7DWXEZ3NKfmcQMKM40hvpe5TF9tbR0iIiKn4viucnx3uQGFmcYQ19NcHlhjZRUiIiKn5viuiu9pZRV1ojDTGBzpNmM9VJRbW4uIiEhNDEMtM1KDiDbgFwLlxZXDQ4uIiLiaI3vg6GHw8oWYzlZXU2sKM43By6uyuU79ZkRExFU5vqNadAEff2trqQOFmcbiCDPqNyMiIq7KDQ8xgcJM43F0AlbLjIiIuCo37PwLCjONx9kJeANUlFlbi4iIyO8ZBqSvMdfVMiPVimgD/mFQUQJZm62uRkREpKrDu6H4iDnyb3Qnq6upE4WZxmKzQXwPc12HmkRExNU4O/92dZuRfx0UZhqTBs8TERFX5ez829PSMk6Hwkxj0rQGIiLiqpydf92rvwwozDQuxx9I5kYoL7W2FhEREQfDgPRjE0wqzMhJNW8NAeFQUQpZm6yuRkRExHRoF5Tkgre/OVu2m1GYaUw2mwbPExER1+Po/hDbDbx9ra3lNCjMNDYNniciIq7GTQfLc1CYaWzOTsBrLC1DRETEyU0Hy3NQmGlsjtSbuRHKSywtRUREBLu9Msw4jh64GYWZxhbeCgKbg73MDDQiIiJWOrQLSvPBJ8AtO/+Cwkzjs9kqm/HUCVhERKzm7PzbHbx9rK3lNFkaZhYuXMjYsWOJj4/HZrPx+eefO+8rKyvj73//O926dSM4OJj4+Hiuv/560tPTrSu4vqgTsIiIuAo37/wLFoeZwsJCevTowdSpU0+4r6ioiFWrVvHwww+zatUqZs2axbZt27j44ostqLSeqROwiIi4Cuc0Bu7Z+RfA0vakMWPGMGbMmGrvCwsLY+7cuVVue/nllznrrLPYs2cPSUlJjVFiw3Ck36xNUFYMvgGWliMiIk2U3Q4Hjo3866adf8HiMFNXubm52Gw2wsPDa9ympKSEkpLKs4Ty8vIaobI6CkuEoEgoyoGsjZDQx+qKRESkKcrZAaUF4BsEUR2srua0uU0H4OLiYh544AGuueYaQkNDa9xuypQphIWFOS+JiYmNWGUt2WzqNyMiItarMvKvW7VvVOEWYaasrIzx48djt9t59dVXT7rtgw8+SG5urvOyd+/eRqqyjjSDtoiIWM3xHeTGh5jADQ4zlZWV8Yc//IHU1FR++umnk7bKAPj7++Pv799I1Z0Bx6GlfSutrUNERJqu/SvMZcu+1tZxhly6ZcYRZLZv3868efOIjIy0uqT64/jDyd4CxS7Yr0dERDxbeUll5183DzOWtswUFBSwY8cO5/XU1FTWrFlDREQE8fHxXHHFFaxatYqvv/6aiooKMjIyAIiIiMDPz8+qsutHsxgIT4IjeyB9FbQZYXVFIiLSlGRsgIpS84SU5slWV3NGLG2ZWbFiBb169aJXL7P/yKRJk+jVqxePPPII+/bt48svv2Tfvn307NmTuLg452Xx4sVWll1/WvYzl/uWW1uHiIg0PY7vnoS+5okpbszSlpkRI0ZgGEaN95/sPo/Qsh9smAn7VlhdiYiINDWOMOP4Ye3GXLrPjMdLOHaMct8K8PTgJiIirsXZ+df9xzpTmLFSXHfw9oOig3B4t9XViIhIU1GQfex7x+YRA7cqzFjJx9+cpRR0qElERBqPo1UmOgUCwqytpR4ozFjNcTrcfoUZERFpJI4f0AnufUq2g8KM1XRGk4iINDZn51+FGakPjj+kA+vMGbRFREQakr0C9q8y1z3gTCZQmLFeeCsIigJ7GWSst7oaERHxdAe3QWk++AZDTCerq6kXCjNWs9l0qElERBqPc7C83uDlbW0t9URhxhU4DjUpzIiISEPzsP4yoDDjGnRGk4iINJZ9K82lh5zJBAozriG+N2AzJ53Mz7S6GhER8VQl+ZC1yVxXy4zUq4DQyk5Yap0REZGGsn8VYEBYEoTEWl1NvVGYcRWO4aQ1ErCIiDQUD5qP6XgKM65CZzSJiEhDc/xg9pDxZRwUZlyF4w8rfbU5oJGIiEh9MozjzmRSmJGGEJ0Cfs2gtACyt1hdjYiIeJoje6AwG7x8Kyc59hAKM67Cy9scwAh0qElEROqf47slthv4BlhbSz1TmHElCRo8T0REGsj+Y+PLeNAp2Q4KM67E2QlYZzSJiEg989D+MqAw41ocf2DZW+HoYWtrERERz1F2FNLXmOtqmZEG1SwaItoCBuzVoSYREakn6avBXgbNWkDzZKurqXcKM66m1UBzuWeJtXWIiIjncHynJA0Em83aWhqAwoyrSVKYERGRepZ2XJjxQAozrsbxh7Z/JZQVW1uLiIi4P3sF7F1mricNsLaWBqIw42oi2kBwNFSUwoE1VlcjIiLuLmszlOSaA7O26Gp1NQ1CYcbV2GyVyVmHmkRE5Ew5vkta9gNvH2traSAKM67I2W9mqbV1iIiI+3N8l3hofxlQmHFNx4cZu93aWkRExH0ZRmXLTCuFGWlMsd3BNxiKj2jSSREROX25eyFvP3j5QEIfq6tpMAozrsjbp3KERvWbERGR0+U4xBTXA/yCra2lASnMuCr1mxERkTO1x7PHl3GwNMwsXLiQsWPHEh8fj81m4/PPP69yv2EYPPbYY8THxxMYGMiIESPYuHGjNcU2NucZTQozIiJympydfz1zfBkHS8NMYWEhPXr0YOrUqdXe/8wzz/D8888zdepUli9fTmxsLOeeey75+fmNXKkFWvYDmzfk7oHcfVZXIyIi7qboEGRtMtfVMtNwxowZw//93/9x2WWXnXCfYRi88MILPPTQQ1x22WV07dqVd955h6KiIj788EMLqm1k/s0grru5rtYZERGpK8eov5HtITjK2loamMv2mUlNTSUjI4PRo0c7b/P392f48OEsXry4xseVlJSQl5dX5eK2NE+TiIicLmd/Gc8+xAQuHGYyMjIAaNGiRZXbW7Ro4byvOlOmTCEsLMx5SUxMbNA6G5T6zYiIyOlqAoPlObhsmHGw/W6qcsMwTrjteA8++CC5ubnOy969exu6xIaTeCzMZG6Eo0csLUVERNxIWTGkrzLX1TJjndjYWIATWmGysrJOaK05nr+/P6GhoVUubiukhTnxJAbsW251NSIi4i7SV5sTFgfHHPse8WwuG2aSk5OJjY1l7ty5zttKS0tZsGABgwYNsrCyRpZ0bF/Tau4nJCIiUsWeY98ZrQaaExh7OEunzywoKGDHjh3O66mpqaxZs4aIiAiSkpK45557ePLJJ2nfvj3t27fnySefJCgoiGuuucbCqhtZ0gBY8776zYiISO01of4yYHGYWbFiBSNHjnRenzRpEgATJ07k7bff5m9/+xtHjx7ljjvu4PDhw/Tv358ffviBkJAQq0pufI4/xP0robwEfPytrUdERFyb3Q57fjPXm0B/GQCbYRiG1UU0pLy8PMLCwsjNzXXP/jOGAc+2g6KDcNP3TeYPU0RETlPGBpg22Jyw+IE95nx/bqgu398u22dGjrHZoNWxfjO7F1lbi4iIuL7dv5jLpP5uG2TqSmHGHSQPM5epCjMiInIKjh++rYdaW0cjUphxB44/yL2/mf1mREREqmOvqGyZcfwQbgIUZtxBdIo5VkB5scabERGRmmWsh+Ij4BcCcT2trqbRKMy4A5sNko+1zuhQk4iI1MRxiKnVoCbTXwYUZtyH41CTOgGLiEhNHD94k5tOfxlQmHEfjmOf+5ZDaZG1tYiIiOupKK8cLb4Jdf4FhRn3EdEGQuLNuTb2/mZ1NSIi4moOrIHSfAgIg9huVlfTqBRm3IXNVtk6o0NNIiLye6kLzWXroeDlbW0tjUxhxp2oE7CIiNSkCY4v46Aw404cf6Dpq6Ak39paRETEdZSXVk4u2cQ6/4LCjHtp3grCk8Berlm0RUSk0v6VUFYEQZEQ3cnqahqdwoy7cU5tsNDaOkRExHUcf4jJq+l9tTe9PXZ3rdUJWEREfsfxA7cJHmIChRn34/hDPbAWjh6xtBQREXEBZcWwd5m53rrpzMd0PIUZdxMaDxFtwbBXDo4kIiJN175lUFECzVpAVHurq7GEwow7StbUBiIickzqcf1lbDZra7GIwow7cnYCVpgREWnyHD9sk5vmISZQmHFPjvFmMtdDYY61tYiIiHVKC2HfCnO9iXb+BYUZ99QsBqI7mutpv1hbi4iIWGfPUrCXQWhLaJ5sdTWWUZhxV47WGY03IyLSdDkPMTXd/jKgMOO+2owwlzt/srQMERGxkOM7wPGd0EQpzLir5GHg5QOHdsGhVKurERGRxlaQbY45BtD2bGtrsZjCjLsKCIWWZ5nrap0REWl6dv1sLmO7mX0pmzCFGXfmSOIKMyIiTc+OH81lE2+VAYUZ99bu2B/wrgVQUWZtLSIi0njs9sofsm1HWVuLC1CYcWdxPSEwAkrzYd9yq6sREZHGkrkBCrPANwiSBlhdjeUUZtyZlze0HWmuO5obRUTE8zlaZVoPBR9/a2txAQoz7s7RvKh+MyIiTcfOYz9g2+kQEyjMuD9Hx6/01ZraQESkKSgtNEf+BfWXOabWYWbfvn0NWYecrtA4iOkCGJWn6YmIiOfa/QtUlEJ4EkS2tboal1DrMNO1a1fee++9hqzlBOXl5fzjH/8gOTmZwMBA2rRpwz//+U/sdnuj1uHy2ukUbRGRJsN5SvaoJj2FwfFqHWaefPJJ7rzzTi6//HJychrncMbTTz/NtGnTmDp1Kps3b+aZZ57h2Wef5eWXX26U13cbx/ebMQxraxERkYal/jInqHWYueOOO1i7di2HDx+mS5cufPnllw1ZFwBLlixh3LhxXHjhhbRu3ZorrriC0aNHs2LFigZ/bbeSNBB8AiH/AGRtsroaERFpKIfTIGcH2LzNaW0EAJ+6bJycnMxPP/3E1KlTufzyy+nUqRM+PlWfYtWqVfVW3JAhQ5g2bRrbtm2jQ4cOrF27ll9++YUXXnihxseUlJRQUlLivJ6Xl1dv9bgs3wBoPRh2zDNbZ1p0sboiERFpCI7uBIlnQUCYtbW4kDqFGYC0tDRmzpxJREQE48aNOyHM1Ke///3v5Obm0rFjR7y9vamoqOCJJ57g6quvrvExU6ZM4fHHH2+wmlxW21FmmNnxIwy6y+pqRESkIezUFAbVqVMSef3117nvvvs455xz2LBhA9HR0Q1VFwCffPIJ77//Ph9++CFdunRhzZo13HPPPcTHxzNx4sRqH/Pggw8yadIk5/W8vDwSExMbtE6X0G4UfA+kLYbSIvALsroiERGpTxXlsGuhua5TsquodZg5//zzWbZsGVOnTuX6669vyJqc7r//fh544AHGjx8PQLdu3UhLS2PKlCk1hhl/f3/8/ZvgaIhRHSC0JeTtMwNN+3OsrkhEROrT/hVQkguBzSG+p9XVuJRadwCuqKhg3bp1jRZkAIqKivDyqlqit7e3Ts2ujs123CnamtpARMTjOE7JbjPSnM5GnGrdMjN37tyGrKNaY8eO5YknniApKYkuXbqwevVqnn/+eW666aZGr8UttB0Fq97VPE0iIp7I0flXp2SfoOF679aDl19+mYcffpg77riDrKws4uPjufXWW3nkkUesLs01tRlhnq53cCsc3g3NW1tckIiI1IvCg7B/pbmu/jIncOkwExISwgsvvHDSU7HlOIHh5pgzab/A1jkw4DarKxIRkfqwfS5gQGx3cxobqUITTXqalDHmctt31tYhIiL1Z/v35rLD+dbW4aIUZjyNI8zs/hWKc62tRUREzlxFWWVfyA7nWVuLi1KY8TSRbSGyPdjL1BFYRMQT7FkKJXkQFAXxva2uxiUpzHiilGPNkNvmWFuHiIicOcf/5e1Hg5e+tqujd8UTdTh2qGn7D+aIkSIi4r62/2AudYipRgozniixvzlC5NHDsG+Z1dWIiMjpytkJB7eBlw+0HWl1NS5LYcYTefuYzZEAW3VWk4iI23K0yrQapFmyT0JhxlM5Tt9TmBERcV+O/8Pb6xDTySjMeKp2o8xmyZztZjOliIi4l6NHIO1Xc73jBZaW4uoUZjxVQBi0Gmyuq3VGRMT9bJ8L9nKI7gQRbayuxqUpzHgy52jAOkVbRMTtbP3GXKpV5pQUZjyZo99M2mLzzCYREXEP5SWwfZ65nnKhtbW4AYUZTxaRbDZPGhWV/yhERMT17V4EpfnQLBbie1ldjctTmPF0ztGA1W9GRMRtbPnWXKacr1F/a0HvkKdzjgY8z5ysTEREXJthVJ64oUNMtaIw4+la9oWgSCjJNfvOiIiIazuwBvLTwTcYkodZXY1bUJjxdF7elWc1bf7S2lpEROTUNn9lLtufA74B1tbiJhRmmoLOl5rLzV+BvcLaWkREpGaGAZuO/fDsdLG1tbgRhZmmIHmYOYheQSbsWWp1NSIiUpPsrebI7d5+lXPsySkpzDQFPn6Vncg2fWFtLSIiUjNHd4C2Z0NAqLW1uBGFmaai8zhzuflLsNutrUVERKrnCDOdxlpbh5tRmGkq2o4E/1DIPwD7lltdjYiI/N6hVMhYDzZvSNEUBnWhMNNU+PhXntW06XNLSxERkWo4zmJqPQSCIqytxc0ozDQljkNNm77QoSYREVfjCDM6xFRnCjNNSduzwa8Z5O2H9FVWVyMiIg65+2DfMsCmMHMaFGaaEt9A6HCeua5DTSIirsNxpmmrQRASa20tbkhhpqnpfIm53PSFOTiTiIhYb8Msc9nlUmvrcFMKM01Nu3PANwiO7IH01VZXIyIih9Ng/wqweWnU39OkMNPU+AVVjiqpAfRERKznPMQ0GEJaWFuLm1KYaYqOP6tJh5pERKy1cba51CGm06Yw0xS1Hw0+AXD42ABNIiJijcO7zbNLdYjpjLh8mNm/fz/XXXcdkZGRBAUF0bNnT1auXGl1We7Nvxm0P9dc11lNIiLWcbTKtB4KzaKtrcWNuXSYOXz4MIMHD8bX15fvvvuOTZs28dxzzxEeHm51ae7PcVbThpk61CQiYpX1M82lDjGdER+rCziZp59+msTERGbMmOG8rXXr1tYV5ElSxoBvsNnEuX8ltOxrdUUiIk1L1mbIXA9evpV9GeW0uHTLzJdffknfvn258soriYmJoVevXrz++usnfUxJSQl5eXlVLlINv2DoeKG5vv5Ta2sREWmK1n9mLtufq7mYzpBLh5ldu3bx3//+l/bt2/P9999z2223cffdd/Puu+/W+JgpU6YQFhbmvCQmJjZixW6m25XmcsMsqCi3thYRkabEMCp/SHa7wtpaPIDNMFy3w4Sfnx99+/Zl8eLFztvuvvtuli9fzpIlS6p9TElJCSUlJc7reXl5JCYmkpubS2hoaIPX7FYqyuC5FCjKgQmzzbmbRESk4e1dDm+eYx7uv3+HOQaYVJGXl0dYWFitvr9dumUmLi6Ozp07V7mtU6dO7Nmzp8bH+Pv7ExoaWuUiNfD2rex0tk6HmkREGo2jVabTRQoy9cClw8zgwYPZunVrldu2bdtGq1atLKrIAzkONW3+CsqOWluLiEhTUFEOG4/NxeT4P1jOiEuHmXvvvZelS5fy5JNPsmPHDj788EOmT5/OnXfeaXVpnqPlWRCWBKX5sPU7q6sREfF8u+ZDYTYERUKbEVZX4xFcOsz069eP2bNn89FHH9G1a1f+9a9/8cILL3DttddaXZrn8PKC7sd+Gaz7xNpaRESagrUfmcuul5uH++WMuXQH4PpQlw5ETdbB7TC1L9i84b4t0CzG6opERDxTcS78uwOUF8Mff4aE3lZX5LI8pgOwNJKo9pDQF4yKynEPRESk/m36wgwyUSkQ38vqajyGwoyYeow3l2s/tLYOERFPtubYIaaeV4PNZm0tHkRhRkxdLzeH1M5YDxkbrK5GRMTzHEqFPYsBG3T7g9XVeBSFGTEFRUDK+eb6uo+trUVExBOt+5+5bDMcwhKsrcXDKMxIpR5Xm8t1/9P0BiIi9ckwKs9i6nGNtbV4IIUZqdTuXAiKgoJM2DHX6mpERDzH7l/gcCr4hZij/kq9UpiRSj5+lR2BV79vbS0iIp7E8X9q18vAL9jaWjyQwoxU1es6c7ltDhRkWVuLiIgnKM41T8kG6H29tbV4KIUZqSqmkznmjL288viuiIicvvWfQflRiO4ICX2srsYjKczIiXpPMJer3jM7rYmIyOlb/Z657DVBY8s0EIUZOVGXy8A3CHK2w95lVlcjIuK+MjZA+mpzHC9Hn0SpdwozcqKAUOhyqbm+6l1raxERcWeOVpmUMRAcZW0tHkxhRqrn6KS2YSYcPWJpKSIibqm0qLLvYe+J1tbi4RRmpHqJ/SGms9lpbd0nVlcjIuJ+Ns42z2QKT4K2Z1tdjUdTmJHq2WzQ9yZzfcVb6ggsIlJXK94yl31uBC993TYkvbtSs+5/MDsCZ2+BPUutrkZExH0cWAf7V5gdfx3jd0mDUZiRmgWEmbNpQ+UvDBERObWVM8xlp4ugWYy1tTQBCjNyco5DTZs+h8IcS0sREXELJfmVM2Q7/g+VBqUwIyeX0BviekJFaeUphiIiUrN1n0BpAUS2g9ZDra6mSVCYkVM764/mcvmbYK+wthYREVdmGLDsdXO93x814m8jUZiRU+t6OQRGQO4e2Pqd1dWIiLiu1AXmSRN+zaDnNVZX02QozMip+QZWDqK3bLq1tYiIuDJHq0yP8eZo6tIoFGakdvrdDDYv81dH1harqxERcT1H9sDWb831s/5kbS1NjMKM1E54EqRcYK6rdUZE5ETL3wDDDm1GQHSK1dU0KQozUnuOXxprP4ajh62tRUTElZQWVk7Mq1aZRqcwI7WXPAxiukBZIax8x+pqRERcx9qPzB95zVtDh/OtrqbJUZiR2rPZYOCd5vpvr0FFmbX1iIi4Arsdlrxqrg+4A7y8ra2nCVKYkbrpdgUEx0B+Omz83OpqRESst/17OLQT/MOg57VWV9MkKcxI3fj4Vx4PXvKyZtMWEVnyirnsewP4N7O0lKZKYUbqru9N4BMAB9ZC2mKrqxERsU76Gti9CLx84Kxbra6myVKYkboLjoQeV5vri1+ythYRESstmWouu1wKYQnW1tKEuVWYmTJlCjabjXvuucfqUmTgnwEbbJsDmZusrkZEpPEdSoUNM831QXdZW0sT5zZhZvny5UyfPp3u3btbXYoARLWDzheb67++aG0tIiJWWDLVHCSv7SiI62F1NU2aW4SZgoICrr32Wl5//XWaN29udTkAGIbBvE2ZGE25A+zge8zl+k/NYbxFRJqKgixY/b65PuRea2uxkGEY/Lg5E7vd2u9Ctwgzd955JxdeeCHnnHPOKbctKSkhLy+vyqUhvL80jVveXcEf313J4cLSBnkNl5fQ2xy226iAxVOtrkZEpPH8Ng3KiyGhL7QeYnU1lsgvLuPuj9dw8zsreG3hLktrcfkw8/HHH7Nq1SqmTJlSq+2nTJlCWFiY85KYmNgwhdls+Hl7MW9zJhe8tIjfduU0zOu4OscvklXvQuFBa2sREWkMxXmw7A1zfci95oCiTcyG/blc9PIvfLU2HW8vGz5e1r4HLh1m9u7dy1/+8hfef/99AgICavWYBx98kNzcXOdl7969DVLbhAGtmHXHIJKjgjmQW8zVry/lhXnbqLC4qa3RJQ+H+F5QfrRyrAUREU+2/HUoyYWoDpUT8DYRdrvBG4t2cdmri0nLKSIhPJD/3TqQPw5rY2ldNsOFO318/vnnXHrppXh7Vw4NXVFRgc1mw8vLi5KSkir3VScvL4+wsDByc3MJDQ2t9xoLS8p55IuNzFy1D4CzkiN4cXxP4sIC6/21XNaWb+Dja8CvGdyzHoIirK5IRKRhlBTAC93g6CG4dDr0uMrqihpNdn4Jf/10LQu2ZQMwunMLnrmiO+FBfg3yenX5/nbplplRo0axfv161qxZ47z07duXa6+9ljVr1pwyyDSGYH8fnvtDD/5zVQ+C/bxZlnqIMS8uYu6mTKtLazwpF0CLblBaAEv/a3U1IiINZ8WbZpCJaANdL7e6mkazYFs2Y15cxIJt2fj7ePGvS7ry2oQ+DRZk6srH6gJOJiQkhK5du1a5LTg4mMjIyBNut9qlvVrSM7E5d3+0mvX7c/njuyu4YVBrHhjTkQBf60NXg7LZYPjf4H8TzE5xA++AQNc460xEpN6UFsGvxwYKHfpX8Hbpr9B6UVJewbNztvLGL6kApLQI4aWre5ESG2JxZVW5dMuMu0mOCmbm7YO4ZUgyAG8v3s0lr/zK1ox8iytrBB0vgpjOUJJnzqgtIuJpVs6AooMQ3gq6/8HqahrcruwCLv/vYmeQuX5gK77482CXCzLg4n1m6kND95mpyc9bsvjrp2vJKSzFz8eLB87vyA2DWuNlcY/vBrVhFnx2ozlz7D3rIDDc6opEROpHaRG81BMKMmHsS9BnotUVNRjDMPh05T4e+3IjRaUVNA/y5ZkrenBu5xaNWofH9JlxZyM7xjDnnmGMTImmtNzOP7/exMQZy8jMK7a6tIbTeRxEdzJ7+S9+2epqRETqz7LpZpAJT6qcm84DHSos5fb3V/G3z9ZRVFrBwDaRfPeXYY0eZOpKYaYBRYf489YN/fjXuC74+3ixaPtBznthIXM2HLC6tIbh5Q1nP2SuL/2vxp0REc9QnAu/vmCuj3gQfFyj02t9+3lrlvkdtTEDHy8b95+Xwvu39Cc2rHZDo1hJYaaB2Ww2JgxszTd3D6FrQihHisq47f1V/O2ztRSWlFtdXv3reBHE9YSyQvjlP1ZXIyJy5pa8CkcPm+PKdPe8U7GLSsv5x+fruXHGcrLzS2gX04zP7xzMnSPb4e0mXSMUZhpJu5gQZt0+mNuGt8Vmg/+t2McFLy1iZdphq0urXzYbnP2wub7sdchLt7YeEZEzUXSockDQkZPNFmgPsmbvES566RfeX2rOr3fj4NZ8fdcQuiaEWVxZ3SjMNCI/Hy8eGNORj/44gPiwANJyirhy2mKe+m4LJeUVVpdXf9qNgqSBUFECC56xuhoRkdP3y/NQmm+OpdVpnNXV1JvyCjsvztvO5f9dzK6DhcSGBvD+zf15dGwXtxxORGHGAgPaRPLdPcO4rFcCdgOmLdjJxS//yob9uVaXVj9sNhj1iLm+6l3I3mZtPSIip+PIHvhturk+6mHw8oyvzB1ZBVwxbQn/OTYFz0Xd45hzz1CGtI+yurTT5hmfjBsKC/Tl+at6Mu26PkQG+7E1M59LXvmVF+dtp6zCbnV5Z67VIOgwxpxR+8fHra5GRKTufnrCbGFuPRTaj7a6mjNWYTd4feEuLnhpEWv2HiEkwIcXx/dk6jW9XWYk39OlMGOx87vG8sO9wxjTNZZyu8F/5m3jslcXsy3TAwbaO+cxsHnBlq9hz1KrqxERqb0D62DdJ+b6uY+7/czYu7IL+MNrS3ji282UltsZ1iGa7+8ZxrieCVaXVi8UZlxAZDN/Xr22Ny+O70lYoC/r9+dy0Uu/8NqCne49C3dMR+g1wVz/4WHw7PEZRcSTzHsUMMz5lxL6WF3NabPbDd78JZUxL5onnDTz9+Gpy7rxzo39iA/3nAmRFWZchM1mY1zPBH6499hAexV2pny3hSumLWZHlhu30ox4EHyDYN8y2PS51dWIiJza9nmw8yfw8q08O9MN7T5YyPjpS/nX15soKbczpF0U3987jPFnJWFz85am31OYcTEtQgN464Z+PH15N5r5+7B6zxEuePEXpv7kpn1pQuNg0N3m+g+PQNlRa+sRETmZijL4/kFzvf+tEJFsbT2nwW43ePvXVM5/cSHLdh8i2M+bJy7tyns3n0WCB7XGHE9hxgXZbDau6pdUpZXm3z9sY9xUNz3jafBfIDQBcvfAkqlWVyMiUrPlb8LBbRAUCcPut7qaOtuRlc+Vry3hsa82UVxmZ1DbSObcM4xr+7fyuNaY4ynMuLD48EDeuqEfL1zVk/AgXzYdyGPcK7/yzJwtFJe50bg0fkFw7j/N9UXPayA9EXFNhTkw/0lz/eyH3Wqy3NJyOy/9uJ0LXvyFlWmHCfbz5l/juvD+zf1JjAiyurwGpzDj4mw2G5f0SmDuvcO5sFscFXaDV+fv5IKXFrFi9yGry6u9rpdDYn8oK4J5j1ldjYjIieY/ac7D1KIb9L7e6mpqbfWew4x9+Reen7uN0go7Z3eMYe6k4UwY2BovN5mO4EzZDMOzTzGpyxTi7mDOhgwe/mID2fkl2GwwYUAr/npeCqEBvlaXdmr7V8HrZwMG3PidORaNiIgrSF8Dr48Eww4Tv4bkoVZXdEpFpeX8+/ttzFicimFARLAfj47tzMU94j3ikFJdvr/VMuNmzu8ay7x7h3Nln5YYBry7JI1zn1/Ad+sP4PK5NKF35a+db+4zO9qJiFjNbjf/TzLsZiuyGwSZhduyGf2fhbz1qxlkLuuVwLxJwxnXM8EjgkxdqWXGjf264yAPzV7P7pwiAM7pFMPj47q6dm/1okPwch84eghGPwGD/mx1RSLS1K18G776C/iFwJ+Xm2dhuqis/GL+7+vNfLnW7HuYEB7IE5d2ZURKjMWV1T+1zDQRg9tFMeeeYdx9djt8vW3M25zFuc8v4I1Fuyh31dO4gyIqOwPPnwK5+62tR0SatsKDMPdRc33kZJcNMhV2g/eWpjHquQV8uTYdL5s5w/UP9w7zyCBTV2qZ8RDbM/OZPHs9y3cfBqBLfChTLutG95bh1hZWHbsdZpwPe3+DjhfB+A+srkhEmqrZt8PaD6FFV/jTAvD2sbqiE2zYn8tDn29g7d4jAHRvGcYTl3SjW8swawtrYHX5/laY8SB2u8GnK/fy5LdbyD1ahtexDsKTRqcQFuhiHYQzNsD04WAvhz+8B50vtroiEWlqdv4E710K2ODmHyDxLKsrqiK/uIzn527jncW7sRsQ4u/D/eencG3/Vng3gbOUdJipifLyMgfb+/G+4VzaKwG7Ae8sSePsf8/n0xV7sbvSPE+xXc3B9AC+vR+OHrG0HBFpYkoLzX4yAGf90aWCjGEYfLv+AOc8v4AZv5pBZmyPeH68bzjXD2zdJIJMXallxoMt3nGQR77cyI6sAgB6J4Xzz3Fd6ZrgIk2TZcUwbTDk7IDeE+Hil6yuSESaiu8fMkckD20Jdy4F/xCrKwLMEXwf+3ITv+w4CECryCD+Oa4rwztEW1xZ49NhpuM05TAD5qiQby9O5YV52ykqrcDLBtcNaMV956YQFuQCh552/wpvX2CuX/8ltBlubT0i4vn2rYA3zzVPxb72M2h/rtUVkV9cxovztvP24t2U2w38vL24bXgb7hjZjgBfb6vLs4TCzHGaephxOJB7lCe+2czX6w4AEBnsx9/HdOSK3i2tHyHy60mw4k0IS4TbF0NA0/2cRKSBlRbBa0PNFuFuf4DLX7e0HLvdYPbq/Uz5bgsHC0oAc5iNhy/qTKvIYEtrs5rCzHEUZqr6/aGnnonhPDK2M72TmltXVEkB/HcQHEmDXhNgnCajFJEGMudBWPoqhMTBHUsg0Lr/+zbsz+WRLzawas8RAJKjgnlkbGdG6lRrQGGmCoWZEzkOPb04bzuFpeaElZf0jOfvYzoSF2bRgHu7f4W3LwQMuOZ/0OE8a+oQEc+Vugjeuchct/Dw0sGCEp77YRsfL9+DYUCQnzd3nd2em4a0xt+naR5Sqo7CzHEUZmqWlVfMs99v5bNV+zAMCPD14rbhbbl1WFsC/Sz4B+XokNeshXm4KTiq8WsQEc9UnAvThsCRPZadcFBSXsGMX3fzyk87yC8pB2Bcz3geHNOJ2LCARq/H1SnMHEdh5tTW78vln19vdA64Fx8WwN/HdGz8ycrKjsJrw+HgVugwBq7+CJrgHCMiUs8MA2beAhs+g/Ak88dSI569ZJ5qncFTczaz99BRALomhPLwhZ3p3yay0epwNwozx1GYqR3DMPhm/QGmfLuF/UfMf2y9k8J5+KLO9GrM/jQZ682ZtStK4YJ/m+M/iIiciTUfwee3gc0bbprTqGPKrN17hH99vYkVaeaPxRah/tx/Xkcu65Vg/ckXLk5h5jgKM3VTXFbB6wt38er8nRwtM/vTXNgtjvvPS6F1VCP1rF86Deb8Hbz94U8/Q4sujfO6IuJ5cnbCa8OgtABG/gOG398oL5t+5CjPfr+V2avN+ecCfL24dVhbbh3ehiA/15sywRUpzBxHYeb0ZOYV8+/j+tP4eNm4tn8Sd49qT2Qz/4Z9ccOAD/8A23+AqBT440/g36xhX1NEPE9ZsTmeTMY6aDUYJn4FXg3bHzD3aBnTFuzkrV9SKSk3J/y9vHdL7j8vRf1i6shjwsyUKVOYNWsWW7ZsITAwkEGDBvH000+TkpJS6+eozZthGAbl5eVUVFTUV+luxdvbGx8fn2r7x2zJyOOp77Ywf2s2AM38fbh9RFtuGpzcsJ2ECw+anfXyD0DXK+DyN9R/RkTq5qt7YOUMCIyA2xZBWMsGe6nisgreXbKbV37eSe7RMgDOah3Bwxd19vgJIRuKx4SZ888/n/Hjx9OvXz/Ky8t56KGHWL9+PZs2bSI4uHaHPE71ZpSWlnLgwAGKiorqu3y3EhQURFxcHH5+ftXe/+uOg0z5bjMb9ucB5nHfSed24Io+iQ03T0jaEvN0baMCLnwO+t3SMK8jIp5n7Scw+0+ADa77DNqd0yAvU2E3mLVqH/+Zu4303GIAOrRoxt/O68ioTjGNexKFh/GYMPN72dnZxMTEsGDBAoYNG1arx5zszbDb7Wzfvh1vb2+io6Px8/Nrcn94hmFQWlpKdnY2FRUVtG/fHi+v6ucftdsNvlqXzrPfb2XfYbOTcNvoYCadm8KYrrEN05nt15dg7sPg7Qc3zoGWfer/NUTEs2RugjdGQVkRDP87jJxc7y9hGAY/bs7ime+3sC3THIQ0LiyASed24LLeLTUZZD2oS5hxq15Iubm5AERERNS4TUlJCSUlJc7reXl5NW5bWlqK3W4nMTGRoKCg+ivUzQQGBuLr60taWhqlpaUEBFR/XNfLy8a4ngmc3zWW95akMfXnHezMLuTOD1fRJT6Uv45OYURKdP0GwkF3wd7fYMvX8Mm18Kf5EBJbf88vIp6l6BB8fLUZZNqMMMNMPVu6K4fnftjqHM4iLNCXO0e25fqBrZvsPEpWc5uWGcMwGDduHIcPH2bRokU1bvfYY4/x+OOPn3B7dcmuuLiY1NRUkpOTa/wCbypO573IKy7jzUWpvLFol3Mk4T6tmvPX0SkMbFuPYycU58Eb55jjz7Q8C274GnwauBOyiLifinL44HLYNR/CW5k/foJq/vFbVyvTDvP83K38uiMHAH8fL24aksxtw9sSFugCE/d6GI88zHTnnXfyzTff8Msvv9CyZc2duKprmUlMTFSYOYUzeS8OFZYybcFO3lm829l7f2j7KP46OoUeieH1U+DBHeb4MyW55vxNF7+sDsEiUpVjFHHfILh5LsR2rZenXbfvCM/P3eY8EcLX28ZV/RL588j2OkOpAXncYaa77rqLL7/8koULF540yAD4+/vj769f7Y0pItiPyRd04uYhyUz9aQcfL9/Dou0HWbT9IKM6xnD3qPZnHmqi2sEVb8GHV8Lq9yCqAwy+u17qFxEPsOItM8gAXDqtXoLMpvQ8np+7jXmbMwHw9rJxRe+W/PnsdiRGNN2uCa7IpcOMYRjcddddzJ49m/nz55OcnGx1SXISLUID+NclXfnTsDa8MG87s1fv48ctWfy4JYsRKdHcPar9mc3O3f4cGP0EfP+g2Sm4eSvoPK7+dkBE3NP2efDNX831EZPP+P+FzQfyePmn7Xy7PgMALxtc0jOBu0e1b7zBQ6VOXDrM3HnnnXz44Yd88cUXhISEkJFh/mGFhYURGGjR7M5uYu/evUyYMIGsrCx8fHx4+OGHufLKKxvltRMjgnjuDz24c2Rbpv68gy/WpDN/azbzt2YztH0UfxnVnr6tT/M49oDb4XAqLJsOs/4EoQnQsm/97oCIuI+MDfDpDeYQDj2ugeF/O+2nWrv3CC//tMPZEmOzmSOg33NOB9rFaOBOV+bSfWZqOitmxowZ3HDDDbV6jpMdc/PkPjMHDhwgMzOTnj17kpWVRe/evdm6dWuN4/M05Hux+2Ahr87fwcxV+6mwm39ug9pG8pdR7U9vkrWKcvj4Gtj+vTkY1k3fQ3SHeq1ZRNzA4d3w5nlQkAGth8J1s8Cn+rGyTmb57kO8/NMOFm4z+8Q4Qsyfz25Hx1iNHG8Vj+wAfLqaapj5ve7du/PNN9+QmJhY7f2N8V7sPVTEq/N38OmKfZQfCzX9Wjfn9hFtGZlSx8GlSgrgnbGQvgpCW8LN3zfo6J4i4mIKsuCt8+DQLojpDDd+C4G1P4xtGAaLd+bw0o/b+S31EGD2ibmkZwJ3jGxL22i1xFjN4zoAy5lZsWKFczwdKyVGBDHlsu7cObId/52/k/+t2Mvy3YdZ/vYKOsaGcNvwtlzUPQ4f7+oH7avCvxlc+ym8dT7kbIf3LoMbv4PgejwlXERcU3EuvH+5GWTCkswWmVoGmQq7wdxNmby2cCer9xwBzLOTruybyO3D26pjr5tSy4yHt8zk5OQwdOhQ3njjDQYNGlTjdla8Fxm5xbz1ayofLE1zjlOTEB7In4a14Q99E2s399ORPWYzc346xHaD67+s13ElRMTFlOSbP172LYOgKPMwc1S7Uz6suKyCWav28/qiXaQeLATMcWKuPiuJW4e3IS5M/TBdTV1aZmrxE1hc0UcffURAQAD79+933nbLLbfQvXt350jJJSUlXHrppTz44IMnDTJWiQ0LYPIFnVj8wCjuPy+FyGA/9h85yqNfbmTw0z/x0o/bOVJUevInCU+C6z+H4GjIWA/vX2b+ahMRz1NaCB/8wQwyAeEwYfYpg8yRolJe/nE7Q57+icmz15N6sJDQAB/uHNmWX/5+No9d3EVBxgOoZcZNW2YMw6Bnz54MHTqUqVOn8vjjj/PGG2+wdOlSEhISMAyDa665hpSUFB577LFTPp8rvBfFZRV8unIf0xfuZO8hc+6nAF8vLu/dkhsHJ5/8bILMTeaklEcPQct+cN1MCNBMtSIeo7QQPhoPqQvBPxSu/wISete4+d5DRbz5Syr/W7GXouNafm8eksxV/RIJ9lcvC1enDsDHqWuYMQyDo2UVjV5noK93nec0+vrrr7niiit45JFH+Pe//82iRYvo0qULAL/88gvDhg2je/fuzu3fe+89unXrVu1zuUKYcSivsPPthgxeW7CTjemVc2uNSInm5iHJDGkXVf17dWCd2Sm4+AjE9TR/temQk4j7K86DD66EvUvBrxlM+BwS+52wmWEYLN99mBm/pvL9xgyOnWdAp7hQbhvehgu6xeFbmz554hIUZo5T1zBTVFpO50e+b/Q6N/3zPIL86v5LoXfv3mzcuJEffviB4cOHn/bru1KYcTAMg99SD/HmL6nM25yJ4y81pUUINw1pzbieCSdO6paxHt4dB0U55hkO138BzWIav3gRqR9Fh8zOvumrzNbW62adMLZUcVkFX61N5+3Fu6v8ABrSLopbh7ep+QeQuDSdzdREfP/992zZsoWKigpatGhhdTn1zmazMaBNJAPaRLL7YCFvL97N/1bsZWtmPn+fuZ5n5mzl6rOSuLp/Egnhx455x3aDG741A03WJnhzNEyYBRFtrN0ZEam73H1mkMneYo4pdf3nENfDeXdmXjHvL03jw9/2kFNo9q/z9/Hist4J3DAomZTYEIsKl8amlhk3Pcy0atUqRowYwSuvvMLHH39MUFAQn3766Wm/viu2zFQn92gZnyzfwzuL09h/xOxX42WDUZ1aMGFAK4a0i8LLywY5O+G9S+FImtk5+NrPIL6ntcWLSO1lbTE79Ofth5A487BxTCfnoaT3l6bx7foDzjGr4sMCmDCwNeP7JdI8uO4D54nr0WGm43hiB+Ddu3czcOBA7rrrLiZPnszKlSvp168fy5cvp0+fPqf1nO72XpRX2Jm7KZP3lqaxeGeO8/bkqGCu7Z/ElX0SCas4BB9cbh568msGV74N7c+1rmgRqZ3URfDJdWb/t6gOcN0scv1jmb1qHx/8toftWQXOTfu1bs6Ng5MZ3blF7caoErehMHMcTwszhw4dYvDgwQwbNozXXnvNefu4ceMoKSlhzpw5p/W87vheOOzIyuf9pXuYuXIf+SXlgHkW1MU94rmuVwTdfrkDW+pCsHnBeVOg/63meOUi4npWvgPfTAJ7OUbLs9g4fDrvrs3jy7XpFJfZAbMl++Ie8UwY2IquCTpr0VMpzBzH08JMQ/GE96KwpJwv1qTz7pLdbMnId97eJSaA55u9S0r65+YNfW6EMc+c1hwuItJAKsph3qOwZCoAu+PGMKnkFlallzg36dCiGdcNaMUlvRIIDfC1qlJpJOoALE1SsL8P1/RP4uqzElm15zDvL93Dt+sPsDGrmPOyruQ232D+5v0hXitnYGRuxPaHdyA03uqyRaQgG+OzG7HtXgTAy/YreC71UqAEPx8vLuwWx7X9k+jTqrnOSpJqKcyIx7HZbPRpFUGfVhE8dnEXvlybzifL9zBt/4VsrYjnBd9XCNu3jMKXB1N40WvE9BhtdckiTVbmxkUEfXETIaVZFBgB3F92K9/Z+9M2Opir+iVyRZ9EItShV05BYUY8WligLxMGtGLCgFZsTM/lf8tbcfXqRJ6z/5tOZXsInPUHvvjhco4OfpAxPVsRFqSma5GGVlhSzg8b0yme/x+uzH0bH5udnfY47rXdT5e+ZzGrb0t6JYarFUZqTWFGmowu8WE8Pi6M4gs6MW/tYA78/A/OLvyOcYWfsXHOcsZ/czetOvbikl4JjOwYjb9PLSa6FJFaKS23s2h7Np+vSWfdpo38i2kM814PNlgcOIJDI5/hk57tajfBrMjvKMxIkxPg681FfdtB3485vHIWAXPupUtZGrNtD/DElmu5beO5hAX6cWH3OC7uEU+/1hF4e+kXokhd2e0GK9IO8/ma/Xy7/gBHikoZ7/0zX/l8QKjtKGVe/uSfPYVBg2/SGYZyRhRmpElr3ucy6DAIPr+DgJ0/8i/ft7nAbw1/K57Ih7+V8eFve4gO8eeCrrFc2D2evq2am4PyiUi1DMNg3b5cvt1wgK/WpJOeWwxAS1sWrwW+SX9jvbldy374jnuViOgOVpYrHkJhRiQk1hwheNl0mPsIAyvWMD9oM/MirmNy9tlk55fwzpI03lmSRkyIPxd0i+PC7nH0SVKwEQGzBWb13sN8uz6DORsynKNzA4T6e/HPuCWMzZ6Od8VR8AmEUQ9j638beOmQktQPjTPj5mOr1Be9F8cc3A7f3AepCwAwItqytvs/eC+rLT9syiC/uNy5aWxoAKO7tODczi3onxyJn49GH5Wmo8JusCz1EHM2HGDOxgwy8yrHgwny82ZkSgzXxe2j/7Z/45Wx1ryj1RC4+CWIbGtR1eJONGjecRRmakfvxXEMAzbMhO8nQ0GmeVvnSygZ+Qi/5jTj63UHmLsx0znaMECIvw/DU6I5t3MLRnaM0YBe4pEKSsr5ZXs28zZn8fOWLOfkjmD+GxjVKYYx3eIYEZWP//zHYfNX5p1+IXDOo9D3ZvBS6JfaUZg5jsJM7ei9qEZxLvw8BZa9BoYdvHyg9/Uw7H5Kglrwy/aDzN2UybzNWRwsqPxV6uNlzvZ9bucWnN0xhsSIIAt3QuTM7DtcxI+bs5i3OZPfdh2itMLuvC88yJdzO7VgTLdYBreLwr8sHxY+C7+9BvYycwqRPjfAiMnQLNq6nRC3pDBzHIWZ2tF7cRIH1sG8x2Dnj+Z1nwDodwsMmQTBkcf6Cxxh7qZM5m7KYGd2YZWHt4kOZkSHGIanRNM/OYIAX/UTENdVWm5n1Z7DLNyWzU9bsqpMDQLQOjKIUZ1aMKpTDP1aR+Dr7QWFOfDbf+G36VCSa27Y9mwY/QS06GzBXognUJg5TlMPM0VFRXTq1Ikrr7ySf//73zVu1xTeizO2+1f46V+wZ4l53a8Z9L3JnLgyrKVzs13ZBczdlMmPm7NYuecwFfbKf2L+Pl4MaBPJiJRohneIJjkqWAODiaUMw2DXwUIWbctm0faDLNmVQ1FphfN+by8bfVo155xOMYzq1II2x//N5mfA4pdhxQwoOxbiozvB6P+D9udYsDfiSRRmjtPUw8xDDz3E9u3bSUpKUpipD4YBO36En/4JB451arR5Q5dLYMCd0LJPlc1zj5axeMdBFmzLZv7WbDLyiqvcHx8WwMC2UQxsG8nAtpEkhAc20o5IU5adX8JvqTn8sv0gi7YfrHL2EUBUMz+GtjcD94iUaMKDfjedQNZm8+y/1R9AxbFDrLHdYdhfoeNY9YuReqGJJgWA7du3s2XLFsaOHcuGDRusLscz2GzmL852o2DbHFjyCuxeZHYY3jATEgdA/z9ByoXgG0BYoC9jusUxplschmGwLbOABduyWLAtm2Wph0jPLWbmqn3MXLUPgFaRQQxsE+kMNzEhCpZy5jLzilm6K4ffUg/x266cEw6F+vl4cVbrCIa2j2Jo+2g6xoacOOxAWTFs/tJshdmzuPL2xAFmiGl3jga+E8sozHiwv/71rzz77LMsXrz41BtL3dhskDLGvBxYB0tfhfWfwd6l5iUgDLpeDj2ugZZ9wWbDZrOREhtCSmwIfxrWlqLSclamHWbxzhyW7Mxh3b4jpOUUkZZTxMfL9wJm/4Q+rSLo27o5fVs1p210M41tIydlGAZpOUWs2nOYZamHWLorh905RVW2sdkgpUUIg9tFMaxDNGe1jqh+GgHDMFth1n5otsIcPXTsCbyh4wXQ/zZoNVghRiynMOOhvvjiCzp06ECHDh0UZhpaXHe4dBqc8xgsfxPWfAh5+2DFW+Ylsh30GA+dxsFxo50G+fkwtH00Q9ubZ3nkF5exfPchFu/IYcmuHDYdyGN3ThG7c4qcLTdhgb70Tgqnb+sI+rRqTreEMIL99c+4KSssKWftviOs3nOEVWmHWb33CIeOO2UazKzRJT6U/smR9E+O4KzkiBMPHR0vextsnAUbZsHBrZW3hyaYZyf1mgChcQ2zQyKnQX1m3LSfyEcffcSNN97Izp07SUhIAOCWW25h2bJlLFq0iKeeeor3338fb29vCgoKKCsr47777uORRx6p9vnc+b1wOXY77F4Iaz4ym+XLjvtVHNkOUi6AjhdCy34nHQE1t6iMVXsOsyLtECvTDrNm7xGKy+xVtvGyQbuYZnRLCKdbQijdWobTOS5Uk/V5qOKyCrZm5LMxPY/1+3NZs/cIWzPysP/uf3E/by86x4dyVnIE/ZMj6Ns6grDAk4x9ZK+A9DWwY575N5t53GFpbz/zEFLv66HdueCt8CyNQx2Aj+OpYcYwDHr27MnQoUOZOnUqjz/+OG+88QZLly51hhuHt99+mw0bNqgDsBVK8mHTl+av3NSFUHHcL+bgaGgzAloPheSh0Dz5pM31ZRV2NqXnsTLtsPPy+w7FYJ590j6mGd1bhtEpLpSU2BA6xoYSEXySX+LicgpKytl8II8N+3PZsD+Pjem5bM8qqHJ2nENCeCA9k8LpndScXknhdIkPPfWs7/mZsPMnM8Ds/KnyEBKYYyq1GWkeKu14gXnYVKSRqQPwmTCMqr+kG4tvUJ2OO9tsNp544gmuuOIK4uPjefHFF1m0aNEJQUYs5h8Cva41L8V55hfH1m9h2w9QmA3rPzUvAKEtzVDTahDE94bojlV+Bft6e9EjMZweieHcNCQZgKy8Ytbvz2Xdvlzn8mBBCVsy8k8YHyQ6xJ+OsSF0jA0hJTaUjrEhtIkOJshP/w1YqbCknB1ZBWzLzGe7Y5lZcMIZRg4RwX50iQ+lS3wYPRPD6JXUnBahp/gBYrdD9hbY+1vl5dCuqtv4h0Kb4dB+NHS8CIIi6mkPRRqeWmZ+3xpRWghPxjd+oZPTwS+4zg/r3bs3Gzdu5IcffmD48OGn/fJqmWlkFWXmeDWpCyF1EexfaY6YejyfQLM/TnxviO8JMZ0gsj341TyisGEYZOaVsG7fEdbvz2XzgXy2Zuax91D1X4wAcWEBtIkOJjkqmOSoZrSJDqZNVDAJ4YH4eOsU2/pQVmFn/+Gj7M4pJC2niN05hew+WMj2rAL2HT75Z+MILl0TwugSH0pcWMDJxyYqLzGDS8YG83BRxnrIWGeOaF2FDeJ6mIeQ2p1jdlT31jQc4jo8rmXm1Vdf5dlnn+XAgQN06dKFF154gaFDh1pdluW+//57tmzZQkVFBS1atLC6HKkLb19IHmZewAzRe5aap3nvW2H2XyjNr/wV7WSD5q3MVpuoDhDRxrwe3grCErH5+BEbFkBsWCyju8Q6H1VQUs62zHy2ZuSz5UAeWzLy2ZqZz5GiMg7kFnMgt5hfd+RUKdHX20ZCeCAtmwcdWwaS0Ny83rJ5IC1CA/DWmVWAGVYy88z3Mf3IUdKPmMu0Q0Wk5RSy7/DRag8POUQ186d9TDM6tGhG+xYhdGgRQvuYZjSv6dBgRTnkHzBbVw7thJyd5nrOTvO6vfzEx/gGm+MgJfY3T6du2RcCw+vnDRCxmMu3zHzyySdMmDCBV199lcGDB/Paa6/xxhtvsGnTJpKSkk75+Dq3zLjJYaZVq1YxYsQIXnnlFT7++GOCgoL49NNPT/vl1TLjYux280tp/ypIX2We/p29pWq/ht+zeUFIPIQlQLMYCI6BZi3MOXGatTh2PcY8fODXDGw2DheWsutgIbuyC0g9WMiu7EJSDxaSmlNIabm95tfCnIMqOsSfmBB/okMCiAl1rPsTExJATIg/EcF+hAf50szfxy1HOi4sKSenoJTsghIOFpSQU1DKwWPrBwtKzCB4pJis/OITOuH+XoCvF60igmkdFUTryGCSIoNoF22Gl4hgP/MzL8mFokNQeBCKco5dDprXc/dB3n7I3Q8FGeZ8YTW+WDjEdoMWXc1lbFeI6aLOu+JWPKoDcP/+/enduzf//e9/nbd16tSJSy65hClTppzy8Z7YAXj37t0MHDiQu+66i8mTJ7Ny5Ur69evH8uXL6dOnz6mfoBru+l40OYUHzVCTvQWyt8Lh3XA4DY7sgfKaD1ecwOZl9ufxD4OAULO/hGPpF4zh409BuTe5ZV4cLvXmUImNnGIb2Uchs8ggoxCOGj5U4EUFXtjxwm54UYEN+/G3HVu3eXkR5O9HcKAfIf6+hAT6ERrgQ6CfD4G+Xvj7ehPo60WAr3k9wM+HAF9vfL298PGy4e1lq7r09sL72CizdruB3TCwG2BwbN0OdsOgtAJKyysoKa+guMyg5Nh6SblBSVkFRaXlFBaXUlhSRlFJGYXFpRSVlFNUYt5WXl6BDQMvDOfSCzu2Y9d9bRX4UY4fZQR4VRAT5EVUIEQF2ogIMIgMsBERYCPC304wxdhKC8xWOMeyJP/YMs8MMUbFKT6443j5mC1ykW0hoq25jGxrttiFJmjsF3F7HnOYqbS0lJUrV/LAAw9UuX306NE1jp1SUlJCSUnlDMZ5eXkNWmNjO3ToEGPGjOHiiy9m8uTJAPTp04exY8fy0EMPMWfOHIsrlAYVHAXBQ6D1kKq3G4bZofhwGuSnQ0HWsUumeXtBJhQcW1aUmL/qi3PNy++7UgA2IOTYpeWJd8PpdK2wA4XHLu7A+9ilLkqPXap5T2vNL8RsPQuKND/voEjzEppgtrqFtjSXwTGaNkDkGJcOMwcPHqy2P0iLFi3IyMio9jFTpkzh8ccfb4zyLBEREcHmzZtPuP2LL76woBpxGTabeQipWczJtzMMKDtqtgQU5x1b5prLknzztrIiKC82O5KWF/9uvfS460fNQyNGhRmO7BXHrdvNpVGBYT/uYtgx7HYMgGMtKZXrlTUax274fbOx47rt93dW0whh+/3SVvU+G2DYvMw7bDZsNi+weWGzmS1JjqXXsds5bltsXuYzePuBj5+5rHLxBR//ynVvf/BvZnby9wsxl/7NzMN9fsFmK1lQJARGgK9aRkXqyqXDjMPvj7UbhlHj8fcHH3yQSZMmOa/n5eWRmJjYoPWJuA2bzTwbyi8IQmJPvX19vCTVZg0RkXrj0mEmKioKb2/vE1phsrKyajx7x9/fH39//8YoT0RERFyASx9w9fPzo0+fPsydO7fK7XPnzmXQoEEWVSUiIiKuxKVbZgAmTZrEhAkT6Nu3LwMHDmT69Ons2bOH2267zerSRERExAW4fJi56qqryMnJ4Z///CcHDhyga9eufPvtt7Rq1crq0kRERMQFuHyYAbjjjju44447rC5DREREXJBL95lpLC4+bmCj0HsgIiLuqkmHGV9fc+SvoiILpi9wMY73wPGeiIiIuAu3OMzUULy9vQkPDycrKwuAoKAgt5w/5kwYhkFRURFZWVmEh4fj7V3XIU9FRESs1aTDDEBsrDlwmCPQNFXh4eHO90JERMSdNPkwY7PZiIuLIyYmhrKyMqvLsYSvr69aZERExG01+TDj4O3trS90ERERN9SkOwCLiIiI+1OYEREREbemMCMiIiJuzeP7zDgGg8vLy7O4EhEREaktx/d2bQZ19fgwk5+fD0BiYqLFlYiIiEhd5efnExYWdtJtbIaHj2Nvt9tJT08nJCSk3gfEy8vLIzExkb179xIaGlqvz+0KtH/uz9P3Ufvn/jx9H7V/p88wDPLz84mPj8fL6+S9Yjy+ZcbLy4uWLVs26GuEhoZ65B+pg/bP/Xn6Pmr/3J+n76P27/ScqkXGQR2ARURExK0pzIiIiIhbU5g5A/7+/jz66KP4+/tbXUqD0P65P0/fR+2f+/P0fdT+NQ6P7wAsIiIink0tMyIiIuLWFGZERETErSnMiIiIiFtTmBERERG3pjBTS7t37+bmm28mOTmZwMBA2rZty6OPPkppaelJH2cYBo899hjx8fEEBgYyYsQINm7c2EhV190TTzzBoEGDCAoKIjw8vFaPueGGG7DZbFUuAwYMaNhCT9Pp7J87fYaHDx9mwoQJhIWFERYWxoQJEzhy5MhJH+Pqn9+rr75KcnIyAQEB9OnTh0WLFp10+wULFtCnTx8CAgJo06YN06ZNa6RKT09d9m/+/PknfFY2m40tW7Y0YsW1t3DhQsaOHUt8fDw2m43PP//8lI9xt8+vrvvoTp/hlClT6NevHyEhIcTExHDJJZewdevWUz7Ois9QYaaWtmzZgt1u57XXXmPjxo385z//Ydq0aUyePPmkj3vmmWd4/vnnmTp1KsuXLyc2NpZzzz3XOWeUqyktLeXKK6/k9ttvr9Pjzj//fA4cOOC8fPvttw1U4Zk5nf1zp8/wmmuuYc2aNcyZM4c5c+awZs0aJkyYcMrHuern98knn3DPPffw0EMPsXr1aoYOHcqYMWPYs2dPtdunpqZywQUXMHToUFavXs3kyZO5++67mTlzZiNXXjt13T+HrVu3Vvm82rdv30gV101hYSE9evRg6tSptdre3T4/qPs+OrjDZ7hgwQLuvPNOli5dyty5cykvL2f06NEUFhbW+BjLPkNDTtszzzxjJCcn13i/3W43YmNjjaeeesp5W3FxsREWFmZMmzatMUo8bTNmzDDCwsJqte3EiRONcePGNWg99a22++dOn+GmTZsMwFi6dKnztiVLlhiAsWXLlhof58qf31lnnWXcdtttVW7r2LGj8cADD1S7/d/+9jejY8eOVW679dZbjQEDBjRYjWeirvv3888/G4Bx+PDhRqiufgHG7NmzT7qNu31+v1ebfXTnzzArK8sAjAULFtS4jVWfoVpmzkBubi4RERE13p+amkpGRgajR4923ubv78/w4cNZvHhxY5TYaObPn09MTAwdOnTgj3/8I1lZWVaXVC/c6TNcsmQJYWFh9O/f33nbgAEDCAsLO2Wtrvj5lZaWsnLlyirvPcDo0aNr3J8lS5acsP15553HihUrKCsra7BaT8fp7J9Dr169iIuLY9SoUfz8888NWWajcqfP70y542eYm5sLcNLvPas+Q4WZ07Rz505efvllbrvtthq3ycjIAKBFixZVbm/RooXzPk8wZswYPvjgA3766Seee+45li9fztlnn01JSYnVpZ0xd/oMMzIyiImJOeH2mJiYk9bqqp/fwYMHqaioqNN7n5GRUe325eXlHDx4sMFqPR2ns39xcXFMnz6dmTNnMmvWLFJSUhg1ahQLFy5sjJIbnDt9fqfLXT9DwzCYNGkSQ4YMoWvXrjVuZ9Vn2OTDzGOPPVZtZ6zjLytWrKjymPT0dM4//3yuvPJKbrnlllO+hs1mq3LdMIwTbmtIp7OPdXHVVVdx4YUX0rVrV8aOHct3333Htm3b+Oabb+pxL2rW0PsH1n6Gddm/6mo6Va1Wf36nUtf3vrrtq7vdVdRl/1JSUvjjH/9I7969GThwIK+++ioXXngh//73vxuj1Ebhbp9fXbnrZ/jnP/+ZdevW8dFHH51yWys+Q58Ge2Y38ec//5nx48efdJvWrVs719PT0xk5ciQDBw5k+vTpJ31cbGwsYCbVuLg45+1ZWVknJNeGVNd9PFNxcXG0atWK7du319tznkxD7p8rfIa13b9169aRmZl5wn3Z2dl1qrWxP7+aREVF4e3tfUIrxcne+9jY2Gq39/HxITIyssFqPR2ns3/VGTBgAO+//359l2cJd/r86pOrf4Z33XUXX375JQsXLqRly5Yn3daqz7DJh5moqCiioqJqte3+/fsZOXIkffr0YcaMGXh5nbxhKzk5mdjYWObOnUuvXr0A8zj5ggULePrpp8+49tqqyz7Wh5ycHPbu3Vvly78hNeT+ucJnWNv9GzhwILm5uSxbtoyzzjoLgN9++43c3FwGDRpU69dr7M+vJn5+fvTp04e5c+dy6aWXOm+fO3cu48aNq/YxAwcO5Kuvvqpy2w8//EDfvn3x9fVt0Hrr6nT2rzqrV6+2/LOqL+70+dUnV/0MDcPgrrvuYvbs2cyfP5/k5ORTPsayz7BBuxd7kP379xvt2rUzzj77bGPfvn3GgQMHnJfjpaSkGLNmzXJef+qpp4ywsDBj1qxZxvr1642rr77aiIuLM/Ly8hp7F2olLS3NWL16tfH4448bzZo1M1avXm2sXr3ayM/Pd25z/D7m5+cb9913n7F48WIjNTXV+Pnnn42BAwcaCQkJLrmPdd0/w3Cvz/D88883unfvbixZssRYsmSJ0a1bN+Oiiy6qso07fX4ff/yx4evra7z55pvGpk2bjHvuuccIDg42du/ebRiGYTzwwAPGhAkTnNvv2rXLCAoKMu69915j06ZNxptvvmn4+voan332mVW7cFJ13b///Oc/xuzZs41t27YZGzZsMB544AEDMGbOnGnVLpxUfn6+898YYDz//PPG6tWrjbS0NMMw3P/zM4y676M7fYa33367ERYWZsyfP7/Kd15RUZFzG1f5DBVmamnGjBkGUO3leIAxY8YM53W73W48+uijRmxsrOHv728MGzbMWL9+fSNXX3sTJ06sdh9//vln5zbH72NRUZExevRoIzo62vD19TWSkpKMiRMnGnv27LFmB06hrvtnGO71Gebk5BjXXnutERISYoSEhBjXXnvtCaeAutvn98orrxitWrUy/Pz8jN69e1c5LXTixInG8OHDq2w/f/58o1evXoafn5/RunVr47///W8jV1w3ddm/p59+2mjbtq0REBBgNG/e3BgyZIjxzTffWFB17ThOQ/79ZeLEiYZheMbnV9d9dKfPsKbvvOP/f3SVz9B2rGARERERt9Tkz2YSERER96YwIyIiIm5NYUZERETcmsKMiIiIuDWFGREREXFrCjMiIiLi1hRmRERExK0pzIiIiIhbU5gREbdSUVHBoEGDuPzyy6vcnpubS2JiIv/4xz8sqkxErKIRgEXE7Wzfvp2ePXsyffp0rr32WgCuv/561q5dy/Lly/Hz87O4QhFpTAozIuKWXnrpJR577DE2bNjA8uXLufLKK1m2bBk9e/a0ujQRaWQKMyLilgzD4Oyzz8bb25v169dz11136RCTSBOlMCMibmvLli106tSJbt26sWrVKnx8fKwuSUQsoA7AIuK23nrrLYKCgkhNTWXfvn1WlyMiFlHLjIi4pSVLljBs2DC+++47nnnmGSoqKpg3bx42m83q0kSkkallRkTcztGjR5k4cSK33nor55xzDm+88QbLly/ntddes7o0EbGAwoyIuJ0HHngAu93O008/DUBSUhLPPfcc999/P7t377a2OBFpdDrMJCJuZcGCBYwaNYr58+czZMiQKvedd955lJeX63CTSBOjMCMiIiJuTYeZRERExK0pzIiIiIhbU5gRERERt6YwIyIiIm5NYUZERETcmsKMiIiIuDWFGREREXFrCjMiIiLi1hRmRERExK0pzIiIiIhbU5gRERERt6YwIyIiIm7t/wGi7Y5FRrg9wgAAAABJRU5ErkJggg==", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig, ax = plt.subplots()\n", - "\n", - "ax.set_title(\"Mehrfachplot\") # Titel\n", - "ax.set_xlabel(\"X\") #x-Achsenbeschriftung\n", - "ax.set_ylabel(\"Y\") # y-Achsenbeschriftung\n", - "\n", - "ax.plot(x, xQuadrat, label=\"$x^2$\") # label: Eintrag Legende, versteht auch LaTex!\n", - "ax.plot(x, x**4, label=\"$x^4$\") # label\n", - "\n", - "ax.legend() # Zeige Legende\n", - "plt.show() " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "**b)** Kopieren Sie das Grundgerüst und ersetzen sie die x-Werte durch das oben definierte array `t` und die y-Werte durch die errechnete Bahnkurve. Wählen Sie auch hier einen geeigneten Titel und Achsenbeschriftungen." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "ExecuteTime": { - "end_time": "2019-11-01T10:21:24.775267Z", - "start_time": "2019-11-01T10:21:24.689518Z" - } - }, - "outputs": [], - "source": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "**c)** Variieren Sie nun die Anfangsgeschwindigkeit. Erstellen Sie zwei Kurven mit verschiedenen Bedingungen (z.B. $v_0 = 10$ und $v_0=20$). Vergleichen Sie die Kurven miteinander, indem Sie diese in einem Diagramm darstellen. Benutzen Sie angemessene Beschriftungen!" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "ExecuteTime": { - "end_time": "2019-11-01T10:21:24.776711Z", - "start_time": "2019-11-01T10:21:24.023Z" - } - }, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.11.9" - }, - "latex_envs": { - "LaTeX_envs_menu_present": true, - "autoclose": true, - "autocomplete": true, - "bibliofile": "biblio.bib", - "cite_by": "apalike", - "current_citInitial": 1, - "eqLabelWithNumbers": true, - "eqNumInitial": 1, - "hotkeys": { - "equation": "Ctrl-E", - "itemize": "Ctrl-I" - }, - "labels_anchors": false, - 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)XBH4A1@J! ery*:h)hEB;t@'tA7@ ze#ցA!IװW\D}HQisט;+!}K߾&&M:ǎ;Sx=u}m˰[^?, -endstream -endobj -startxref -129468 -%%EOF diff --git a/S1/ReMe/RM_WS2425_UE1.pdf b/S1/ReMe/RM_WS2425_UE1.pdf deleted file mode 100644 index 2da6d58..0000000 Binary files a/S1/ReMe/RM_WS2425_UE1.pdf and /dev/null differ diff --git a/S1/ReMe/Uebung.pdf b/S1/ReMe/Uebung.pdf deleted file mode 100644 index 7b5d9d0..0000000 Binary files a/S1/ReMe/Uebung.pdf and /dev/null differ diff --git a/S1/ReMe/VL17.typ b/S1/ReMe/VL/VL17.typ similarity index 100% rename from S1/ReMe/VL17.typ rename to S1/ReMe/VL/VL17.typ diff --git a/S1/ReMe/VL18.typ b/S1/ReMe/VL/VL18.typ similarity index 100% rename from S1/ReMe/VL18.typ rename to S1/ReMe/VL/VL18.typ diff --git a/S1/ReMe/VL19.typ b/S1/ReMe/VL/VL19.typ similarity index 100% rename from S1/ReMe/VL19.typ rename to S1/ReMe/VL/VL19.typ diff --git a/S1/ReMe/VL4.typ b/S1/ReMe/VL/VL4.typ similarity index 100% rename from S1/ReMe/VL4.typ rename to S1/ReMe/VL/VL4.typ diff --git a/S1/ReMe/VL6.md b/S1/ReMe/VL/VL6.md similarity index 100% rename from S1/ReMe/VL6.md rename to S1/ReMe/VL/VL6.md diff --git a/S1/ReMe/VL17.pdf b/S1/ReMe/VL17.pdf deleted file mode 100644 index c6f3001..0000000 Binary files a/S1/ReMe/VL17.pdf and /dev/null differ diff --git a/S1/ReMe/VL18.pdf b/S1/ReMe/VL18.pdf deleted file mode 100644 index 74167a3..0000000 Binary files a/S1/ReMe/VL18.pdf and /dev/null differ diff --git a/S1/ReMe/VL19.pdf b/S1/ReMe/VL19.pdf deleted file mode 100644 index 69dc721..0000000 Binary files a/S1/ReMe/VL19.pdf and /dev/null differ diff --git a/S1/ReMe/VL4.pdf b/S1/ReMe/VL4.pdf deleted file mode 100644 index 4d2c7d1..0000000 Binary files a/S1/ReMe/VL4.pdf and /dev/null differ diff --git a/S1/input.txt b/S1/input.txt new file mode 100644 index 0000000..315fa5a --- /dev/null +++ b/S1/input.txt @@ -0,0 +1 @@ +# Input file for the current file of the semester diff --git a/S2/AGLA/.anki b/S2/AGLA/.anki new file mode 100644 index 0000000..04caf8c --- /dev/null +++ b/S2/AGLA/.anki @@ -0,0 +1 @@ +University::Math::S2 diff --git a/S2/AGLA/.unicourse b/S2/AGLA/.unicourse new file mode 100644 index 0000000..d399ce9 --- /dev/null +++ b/S2/AGLA/.unicourse @@ -0,0 +1,2 @@ +name: Lineare Algebra und Analytische Geometrie II +short: AgII diff --git a/S2/AGLA/VL/AgIIVL1.typ b/S2/AGLA/VL/AgIIVL1.typ new file mode 100644 index 0000000..781c4c1 --- /dev/null +++ b/S2/AGLA/VL/AgIIVL1.typ @@ -0,0 +1,7 @@ +// AGLA template +#import "../preamble.typ": * + +#show: conf.with(num: 1) + += Uebersicht + diff --git a/S2/AGLA/index.typ b/S2/AGLA/index.typ new file mode 100644 index 0000000..705c34d --- /dev/null +++ b/S2/AGLA/index.typ @@ -0,0 +1 @@ += AGLA II diff --git a/S2/AGLA/preamble.typ b/S2/AGLA/preamble.typ new file mode 100644 index 0000000..ab4cc8a --- /dev/null +++ b/S2/AGLA/preamble.typ @@ -0,0 +1,14 @@ +#import "../../default.typ": * + +#let conf(num: none, ueb: false, body) = { + // Global settings + show: default + + // Set the header + [AGLA II \ Vorlesung #(num)] + // Make tcahe outline + outline() + + // load the document + body +} diff --git a/S2/AGLA/template.typ b/S2/AGLA/template.typ new file mode 100644 index 0000000..781c4c1 --- /dev/null +++ b/S2/AGLA/template.typ @@ -0,0 +1,7 @@ +// AGLA template +#import "../preamble.typ": * + +#show: conf.with(num: 1) + += Uebersicht + diff --git a/S2/AnaMech/VL/AnMeVL4.typ b/S2/AnaMech/VL/AnMeVL4.typ new file mode 100644 index 0000000..da4fbee --- /dev/null +++ b/S2/AnaMech/VL/AnMeVL4.typ @@ -0,0 +1,132 @@ +#import "../preamble.typ": * + +#show: conf.with(num: 4) + += Grundlagen der Netwon'schen Mechanik + ++ MP ++ Das Ziel ist die Trajektorie im $RR^n $ (Euklidischer Raum) + +Die Wahl des KS (kartesisch) +- Wahl des Urprungs +- Orietierung der Achsen +$ + arrow(r) (t)= arrow(e)_(x) + y (t) arrow(e)_(y) + z (t) arrow(e)_(z) \ + = vec(x,y,z)_(x y z) \ + arrow(r)= r arrow(e)_(r) \ + r = abs(arrow(r))= sqrt(x^2 + y^2 + z^2 ) +$ + +Wir betrachten die nicht-relativistische Mechanik, sodass die Zeit absolut ist $t = t'$. \ +Wir fordern jedoch die Forminvarianz aller physikalischer Gesetze. + +Beschleunigte Bezugsysteme werden wir nicht verlangen, dass die selben Gesetze entstehen. \ ++ Die Forminvarianz soll in allen Inertialsystemen gelten. ++ $"KS"= "IS"==> "KS' mit" arrow(v)_("rel") "bewegt auch IS"$ + +Es gilt, dass in beiden Koordinatensystemen die Kraft gleich die zeitliche Ableitung des Impulses ist. + +== Wechsel zwischen IS + +Galilei-Tafel +$ + t'= t \ + arrow(r')= arrow(r)-arrow(v)_("rel") t \ + ==> "Newton II invariant" +$ + +== Newtons Prinzip der Bestimmtheit + ++ AWP: $arrow(r) (t_0 ),dot(arrow(r)) (t_0 )==> arrow(r) (t), forall t $ + - Messwerte zur Zeit $t$: $arrow(r) (r),dot(arrow(r)),...,O(arrow(r),dot(arrow(r)),t) "(QM)"$ + $==>$ Euklidischen Raum bei mikroskopischen Kraeften ++ Effektive Probleme mit Reibung + - Dynamik auf gekruemmten Flaechen + +Mathematische Ungenauigkeiten kommen durch eingefuehrte Idealisierungen. + +== Newton II +In der mikroskopischen Physik gilt die Gleichung +$ + m dot.double(arrow(r))= arrow(f) (r,dot(arrow(r)),t). +$ +Die Masse und die Kraefte kommen aus experimentellen Beobachtungen. + +== Kraefte + +Es gibt jetzt $N$ MP mit den Ortsvektoren $arrow(r)_(i) $. +$ + m_i dot.double(arrow(r))_(i) = arrow(f)_(i) (arrow(r)_(j) ,dot(arrow(r))_(j) ,t), j != i. +$ +Das ergibt 3N Gleichungen. + +WICHTIG: Naeherung, welche immer verwendet wurde, die des abgeschlossenen Systems. + +Mikroskopisch ufndamentale Kraefte sind die #underline[Gravitaion] und die #underline[Elektro-/Magnetostatik]. Deren Potential ist Proporitional zu $r^(-1) $, d.h. sie sind ein radial Potiential. \ +Die daraus resultierende Kraft ist eine Paarkraft +$ + arrow(f)_(i j) = arrow(f)_(i j) (abs(arrow(r)_(i) - arrow(r)_(j) )). +$ + +Actio $= $ Reactio: $arrow(f)_(i j) = -arrow(f)_(j i) $. + +Starke Version von Actio gleich Reactio: $arrow(f)_(i j) = f_(i j) (abs(arrow(r)_(i) -arrow(r)_(j) ))arrow(e)_(i j) , space f_(i j) = -f_(j i) , space arrow(e)_(i j) = (arrow(r)_(i) - arrow(r)_(j) ) / (abs(arrow(r)_(i) - arrow(r)_(j) )) $ + + +Die kleinen $f$ sind die Kraefte, welche die MP gegenseitig auf sich ausueben und die grossen $F$ sind die globalen externen Kraefte. \ +Allgemeine Form +$ + arrow(f)_(i) = sum_(j != i)^(N) arrow(f)_(n) + arrow(f)^("ext") _(i). +$ +Fuer ein abgeschlossenes System gilt die Naeherung +$ + arrow(f)^("ext") _(i) = arrow(0) space forall i. +$ + += Abgeschlossene Systeme +- N MP $==>$ $m_i $ +- $m_i != m_i (t)$ Q: Was bedeutet das? +- Starkes Actio gleich Reactio + +== Massenschwerpunkt +$ + arrow(R)= (1) / (M) sum_(i=1)^(N) m_i arrow(r)_(i) , space M = sum m_i \ + M dot.double(arrow(R))= sum m_i dot.double(arrow(r) )_(i) = sum (sum _(j != i) arrow(f)_(i j) + arrow(f)^("ext") _(i) )= sum arrow(f)^("ext") _(i) = arrow(F)^("ext") \ + M dot.double(arrow(R))= arrow(F)^("ext") +$ +nur geschlossen, falls $arrow(F)^("ext") = "const"$. + +$ + arrow(R) (t)= arrow(V)_(0) (r)+ arrow(r)_(0) +$ + +Damit haben wir nur noch $6N - 6$ Gleichungen zu loesen. + += Gesamtimpuls +$ +arrow(p)= sum arrow(p)_(i) = sum m_i dot(arrow(r))_(i) \ +dot(arrow(p))= sum m_i dot.double(arrow(r))_(i) = M dot.double(arrow(R)) +$ + +$ + arrow(F)^("ext") = 0 <==> (dif arrow(p)) / (dif t) = 0 , space arrow(p) "erhalten" +$ + +== Gesamtdrehimpuls + +$ + arrow(L)&= sum arrow(l)_(i) = sum (arrow(r)times arrow(p)) \ + &= sum m_i (arrow(r)_(i) times dot(arrow(r))) +$ + +$ + dif / (dif t) arrow(L)= sum m_i (dot(arrow(r))times dot(arrow(r))+ arrow(r)times arrow(r))= sum arrow(r)times (sum _(i != j) arrow(f)_(i j) + arrow(f)^("ext") _(i) )\ + sum arrow(r)times arrow(f)_(i j) = 1/2 sum (arrow(r)times arrow(f)+ arrow(r)times arrow(f))= 1/2 sum (arrow(r)_(i) - arrow(r)_(j) )times arrow(f)_(i j) = arrow(0) +$ + +Abgeschlossenes System: $(dif arrow(L)) / (dif t) = arrow(0)$ + +$arrow(f)^("ext") _(i) != arrow(0) ==> dot(arrow(L))= sum_(i=1)^(N) (arrow(r)_(i) times arrow(f)^("ext") _(i) )= arrow(N)$ + +Naechsten Montag weiter in den abgeschlossenen Systemen. Danach die zentral Potentiale. + diff --git a/S2/AnaMech/template.typ b/S2/AnaMech/template.typ index 1342ba8..f27b5c1 100644 --- a/S2/AnaMech/template.typ +++ b/S2/AnaMech/template.typ @@ -1,4 +1,4 @@ -#import "./preamble.typ": * +#import "../preamble.typ": * #show: conf.with(num: 1) diff --git a/S2/CWR/template.typ b/S2/CWR/template.typ index 9fcabbf..4a5b8f7 100644 --- a/S2/CWR/template.typ +++ b/S2/CWR/template.typ @@ -1,5 +1,5 @@ // Diff template -#import "./preamble.typ": * +#import "../preamble.typ": * #show: conf.with(num: 1) diff --git a/S2/DiffII/VL/DiIIVL4.typ b/S2/DiffII/VL/DiIIVL4.typ new file mode 100644 index 0000000..5ac7a9b --- /dev/null +++ b/S2/DiffII/VL/DiIIVL4.typ @@ -0,0 +1,198 @@ +// Diff template +#import "../preamble.typ": * + +#show: conf.with(num: 4) + + += Wiederholung + +Im $RR^n $ mit $p >= 1$ gilt $norm(x)_(p) = (sum_(i=1)^(n) abs(x_i )^(p) )^(1/p) $. + +Dabei ist $(RR^n , norm(dot)_(p) )$ ein Banachraum. Ein Spezialfall fuer $p=2$ ist das Skalarprodukt. + +Q: Erzeugt ein Skalarprodukt immer eine Norm? + += Hilbertraeume + +Zur Erinnerung fuer einen Vektorraum $V$ ist ein K-VR mit Skalarprodukt $angle.l dot \, dot angle.r$ und $norm(dot):= sqrt(angle.l dot \, dot angle.r)$, dann gilt: +$ + abs(angle.l x \, y angle.r) <= norm(x)dot norm(y) space forall x,y in V. +$ + +#lemma[ + Sei V ein K-VR mit $K in {RR,CC}$ mit Skalarprodukt $angle.l dot\,dot angle.r$. Dann definiert $norm(x)= sqrt(angle.l x\,x angle.r) , space x in V$ eine Norm auf V. +] + +#proof[ + Dreiecksungleichung anwenden. + $ + norm(x+y)^2 = angle.l x+y \, x+y angle.r = angle.l x \, x angle.r + angle.l x \, y angle.r + angle.l y \, x angle.r + angle.l y \, y angle.r + $ +] + +#definition[ + Sei V ein K-Vr mit $K in {RR,CC}$ mit Skalarprodukt $angle.l dot \, dot angle.r$. Wir nennen V einen *Hilbertraum* falls V unter der erzeugten Norm $norm(x)= sqrt(angle.l x \, x angle.r) , space x in V$, vollstaendig ist. +] + +#example[ + - $RR^n $ mit dem Standardskalarprodukt ist ein Hilbertraum. +] + +Ein weiteres Beispiel ist der Folgenraum $l^2 $. + +Sei $l^2 := {a = (a_n )_(n in NN): a_n in CC space forall n in NN, sum_(i=1)^(oo) abs(a_n )^2 < oo }$.\ +Fuer $a in l^2 $ definiere +$ + norm(a)_(2) = (sum_(n=1)^(oo) abs(a_n )^2 )^(1/2). +$ +Sind $a,b in l^2 , space N in NN$, so gilt +$ + sum_(i=0)^(oo) abs(a_n macron(b_n )) <=^("Cauchy-Schwarz") (sum_(i=0)^(oo) abs(a_n )^2 )^(1/2) (sum_(i=0)^(oo) abs(b_n )^2 )^(1/2) <= norm(a)^(2) norm(b)^(2). +$ +Also ist $angle.l a \, b angle.r = sum_(i=0)^(oo) a_n macron(b_n )$ absolut konvergent. + +Behauptung: $l^2 $ ist ien C-VR, denn sind $a,b in l^2 , space lambda in CC$ so gilt +$ + sum_(i=0)^(oo) abs(a_n + lambda b_n )^2 <= sum_( )^(oo) (abs(a_n )^2 + 2 abs(a_n )abs(lambda b_n )+ abs(lambda b_n )^2 ) \ + <= norm(a)^2 + 2 abs(lambda)norm(a)norm(b)+ norm(b)^2 abs(lambda)^2 < oo. +$ + +T: $angle.l dot \, dot angle.r$ definiert ein Skalarprodukt auf $l^2 $. + +#theorem[ + $l^2 $ ist unter dem Skalarprodukt $angle.l a \, b angle.r = sum_( )^(oo) a_n macron(b_n )$ ein Hilbertraum. +] + +#proof[ + Sei $a^(k) = (a_n ^(k) )_(n in N)$ eine Cauchy-Folge im $l^2 $. \ + Fuer $epsilon > 0$ wahle $N in NN$ sodass $norm(a^(k) - a^(l) )_(2) < epsilon space forall n, l <= N$. \ + Dann gilt fuer $k,l >= N , space n in NN$ + $ + abs(a_n ^(k) - a_n ^(l) ) <= sum_(i=0)^(oo) abs(a_n ^(k) - a_n ^(l) )^2 = norm(a^(k) - a^(l) ) < epsilon^2 . + $ + Es folgt dass $(a_n ^(k) )_(n in NN) $ fuer jeder $n in NN$ eine Cauchy-Folge ist, sei $a_n = lim_(k -> oo) a_n ^(k) in CC , space a = (a_n )^(n in NN) $. + + Betrachte $m in NN$ und $k,l >= NN$. Dann gilt + $ + sum_(i=0)^(oo) abs(a_n^(k) - a_n ^(l) ) ^2 < epsilon^2. + $ + Im Grenzwert $l -> oo$ folgt $sum_(i=0)^(oo) abs(a_n ^(k) - a_n )^2 < epsilon^2 space forall m in NN forall k >= N$. Im Grenzwert $m -> oo$ folgt $sum_(i=0)^(oo) abs(a_n ^(k) - a_n )^2 <= epsilon^2 space forall k >= N $, also $a^(k) - a in l^2 $ und damit $a in l^2 $. Aus der zweiten Ungleichung folgt ausserdem, dass $lim_(n -> oo) a^(n) = a$ in $l^2 $. +] + +Nun folgt eine Anwendung. + +#definition[ + Sei X eine Menge, $(Y,d_(y) )$ eine vollstaendiger metrischer Raum und $f_n: X -> Y , space n in NN$ eine FOlge von Abbildungen. Wir sagen, dass $(f_n )_(n in NN) $ gleichmaessig konvergent ist, falls gilt + $ + forall epsilon > 0 exists N in NN forall x in X forall k,l >= N: d_(y) (f_k (x), f_(l) (x)) < epsilon. + $ +] + ++ Ist $(f_n )_(n in NN)$ gleichmaeig konvergent, so ist $(f_n (x))_(k in NN)$ fuer jedes $x in X$ eine Cauchy-Folge, d.h. $exists f (x) := lim_(n -> oo) f_n (x) space forall x in X $. ++ Ist $(f_n )_(n in NN) $ gleichmaessig konvergent mit $f (x) = lim_(n -> oo) f_n (x) , space x in X$ so gibt es fuer jedes $epsilon>0$ ein $N in NN$ sodass $d_(y) (f (x), f_n (x))= N forall x in X$. + +#proof[ + Bilde den Grenzwert $k -> oo$ in der Definition einer gleichmaessig konvergenten Folge von Abbildungen und verwende + $ + lim_(n -> oo) d_(y) (f_n (x), f_(l) (x))= d_(y) (lim_(n -> oo) f_n (x), f_(l) (x)). + $ + Dabei wird benutzt, dass + $ + abs(d (x_k ,y)- d (y,y)) <= d (x_k x). + $ +] + +#example[ + Sei $P (z) = sum_( )^(oo) a_n z^(m) $ eine Potenzreihe mit $a_n in CC$, Konvergenzradius $r (P) >0$ und $0 < delta CC + $ + #highlight[TODO: finish on why this series converges] +] + +Q: Sei $A in M_(m times m) $. Koennen wir aehnlich $sum_(i=0)^(oo) a_i A^(i) $ definieren? + +_PAUSE_ + += Operatornorm + +Wie kann man eine sinnvolle Norm fuer Matrizen $A in M_(n times m)$ (Operatoren) definieren? + +Wie kann ich eine Konvergez fuer die lineare Abbildung $sum_(i=0)^(oo) a_i A^(i) $ definieren? + +#definition[ + Seien $(V,norm(dot)_(V) ),(W,norm(dot)_(W) )$ normierte K-VR und eine lineare Abbildungen $A: V -> W$ gegeben. Wir nennen A *beschraenkt*, falls es eine positiv reele Konstante $C$ gilt, sodass $norm(A x)_(W) <= C norm(x)_(V) space forall x in V $. \ + Ist A beschraenkt, so defninieren wir die *Operatornorm* von A durch + $ + norm(A) := sup_(x in V \ x != 0) (norm(A x)_(W) ) / (norm(x)_(V) ). + $ +] + +#example[ + Betrachte $A = mat( + 3, 0; + 0, 2; + ) $ als lineare Abbildung $RR^2 -> RR^2 $ mit $norm(dot)_(2) $ auf $RR^2 $. Dann gelten die Aussagen + $ + norm(A x)_(2) = sqrt((3 x_1 )^2 + (2 x_2 )^2 ) <= 3 norm((x_1 ,x_2 ))_(2) space forall x in RR^2 \ + norm(A e_1 )_(2) = norm((3,0))_(2) = 3 norm(e_1 )_(2), + $also ist $norm(A) = 3$. +] + +#remark[ + Eine lineare Abbildung $A: V -> W$ zwischen K-VR $V,W$ nenn wir auch linearen Operator. +] + +#lemma[ + Seien $(V,norm(dot)_(V) ),(W,norm(dot)_(W) )$ normierte K-VR, $dim V < oo$ und $A: V -> W$ eine lineare Abbildung. Dann ist A beschraenkt. +] + +#proof[ + Die erste Intuition ist, dass durch die endliche Dimension und die Linearitaet die Aussage entsteht. + + Fuer $x in V$ sei $norm(x)= norm(x)_(V) +norm(A x)_(W) $. Dann ist $norm(dot): V -> RR^(+) $ eine Norm auf V (Task). + Nach Satz folgt, dass es ein $C>0$ gibt sodass + $ + norm(x) <= C norm(x)_(V) space forall x in V. \ + ==> norm(A x)_(W) <= C norm(x)_(V) space forall x in V. + $ + + Man kann den Beweis von den Aequivalenzen von Normen verwenden. +] + +Ein Beispiel fuer einen unbeschraenkten lineare n Operator ist + +Der Startraum ist hier $V = C^(1) ([0,1])$. Und der Endraum $W = CC$.\ +Mit der verwendeten Norm $norm(f)= sup_(t in [0,1]) abs(f (t))$. + +Nun ist die Abbildung $A: V -> W$ gegeben durch $A f := f'(0)$. Dann ist A nicht beschraenkt, da Oszillierende Funktionen wie $sin (n x)$. Denn $norm(f_n ) <= 1$ aber $abs(f'_(n) (0))= n$. + +#remark[ + Ist $A: V -> W$ ein beschraenkter, linearer Operator, so gilt fuer $x,y in V$: + $ + d_(W) (A x,A y) = norm(A x - A y)_(W) = norm(A (x - y))_(W) <= norm(A) norm(x - y)_(V) = norm(A) dot d_(V) (x,y). + $ +] + +#definition[ + Seien $(X,d_(x) )$ und $(Y,d_(y) )$ metrische Raeume und $f: X -> Y$ eine Abbildung. Wir nennen $f$ Lipschitz-stetig falls es ein $L >=0 $ gibt sodass + $ + d_(y) (f (y_1 ), f (y_2 )) <= L d_(x) (y_1, y_2 ) space forall y_1, y_2 in X. + $ +] + +#theorem[ + Sei $A: V -> W$ ein linearer Operator zwischen normierten Raeumen $W,V$. Dann sind die folgenden Aussagen aequivalent: + + A ist beschraenkt + + A ist stetig + + A ist stetig an der Stelle $x = 0$ $==>$ A ist beschraenkt +] + +#proof[ + Sei A stetig in $x = 0$. Wegen $A dot 0 = 0$ gibt es ein $delta > 0$ sodass $norm(A x)_(W) <= 1$ fuer alle $x in V "mit" norm(x)_(V) <= delta$. Sei $x in V \\ {0}$. Dann ist $norm((delta) / (norm(x)_(V) ) )_(V) = delta$ + und damit $1 >= norm(A (delta) / (norm(x)_(V) ) x_(W) )= norm((delta) / (norm(x)_(V) ) A x )_(W) = (delta) / (norm(x)_(V) ) norm(A x)_(W) $. + + Es folgt $norm(A x)_(W) <= (1) / (delta)norm(x)_(V) space forall x in V $ und A ist beschraenkt. + +] + diff --git a/S2/DiffII/pdfs/DiIIVL4.pdf b/S2/DiffII/pdfs/DiIIVL4.pdf index 22c3b37..7e265a8 100644 Binary files a/S2/DiffII/pdfs/DiIIVL4.pdf and b/S2/DiffII/pdfs/DiIIVL4.pdf differ diff --git a/S2/DiffII/template.typ b/S2/DiffII/template.typ index 9fcabbf..4a5b8f7 100644 --- a/S2/DiffII/template.typ +++ b/S2/DiffII/template.typ @@ -1,5 +1,5 @@ // Diff template -#import "./preamble.typ": * +#import "../preamble.typ": * #show: conf.with(num: 1) diff --git a/S2/Neuro/VL/NeuroVL2.typ b/S2/Neuro/VL/NeuroVL2.typ new file mode 100644 index 0000000..ac66705 --- /dev/null +++ b/S2/Neuro/VL/NeuroVL2.typ @@ -0,0 +1,107 @@ +#import "../preamble.typ": * + +#show: conf.with(num: 1) + += Membrane Potential + +Outside the cells in the brain there is salt. +Inside there is potassium. + +== Prerequisites for a Neuron to fire + +_Watch the embedded movie._ + +There are different potentials build up in the membrane. + ++ The charge is in equillibrium. But there is a gradient of Pr and Cl ++ Cloride will diffuse $==>$ on that side there are too many negative charges ++ The negative charge pushes the potassium to this side ++ Finally a potassium gradient stabilizes + +Why is the resulting potential negative? + +== Nernst and general Nernst eqation +$ + V_(x) = (R T) / (z F) ln ([X]_(o) ) / ([X]_(i) ) \ + V_(x) = (R T) / (z F) ln (P_("K") [K]_(o) + P_("Cl") ["Cl"]_(o) + ... ) / (P_("K") [K]_(i) + P_("Cl") ["Cl"]_(i) + ... ) \ + +$ + +When the permeability for the potassium is low then the other ones play a bigger role. +Potential is only there when permeability is existing. + +Q: What is similar to a low pass filter. + +In reality there are multiple conducters connected in parralel. Also the conductivity of the Na and K channles are changable. + +Q: What does a conductivity of $oo$ mean? + += Hodgkin and Huxley + +Q: What have they done? +A: They used squids to measure the axons, because they are $1"mm"$ thick + +Types of Neuronal Recording Methods +- EEG (on top of the head) +- ECoG (small hole in the head) +- Extracellular (needles in the brain) +- Intra cellular (needles in the cell of the brain) + +== Action Potential + ++ The cell gets excited ++ Chainreaction of channel opening and gradient stabilisation + - Sodium channels open + - K chanels open + - Na channels become refactory + - ... ++ Refactory period ++ ... + +#highlight[TODO: continue the steps] + +Currents can add up to trigger an AP. THe refactory period is the time after an AP when Na channles are inactive. The firing rate is increaed with a highter input strenght. + +The lenght of the potiential depends on the type of cell. Then the refactory period is also longer. \ +The maximum firing rate is limited by the absolute refactory period. + +== The actual model + +$ + I_("inj") = I_(C) + sum I_(k) (t) , space C = Q/u , space I_(C) = C (dif u) / (dif t) = C (dif V) / (dif t) \ + I_(x) = I_(x) \ + C (dif V_m ) / (dif t) = - sum I_(k) + I_("inj") (t) \ + sum I_k = g_("Na") (V_m - V_("Na") )+ g_(K) (V_m - V_(K) )+ g_(L) (V_(m) - V_(L) )\ + C (dif V_m ) / (dif t) = - g_("Na") (V_m - V_("Na") )- g_(K) (V_m - V_(K) )- g_(L) (V_(m) - V_(L) ) + I_("inj") (t) \ +$ + +Now the Equation becomes time dependent + +$ + C (dif V_m ) / (dif t) = - macron(g)_("Na") m^(3) h (V_m - V_("Na") )- macron(g)_(K) n (V_m - V_(K) )- macron(g)_(L) (V_(m) - V_(L) ) + I_("inj") (t). \ + dot(x)= - (1) / (tau_(x) u_(b)) A . +$ + +Capacitance is a biological constant. + +== Voltabe clamp method + +With this method it is possible to stimulate a cell and measure the floating current at the same time. + +There are substances to kill certain types of channels in the cell. If done so the graph of the potential changes. + +Also there is a method to measuer individual channels and their current they leave through.The AP is a positive feedback loop. + +The sodium channels cannot immeadiately open again. It takes about 1ms for them to open again. When measuring one always measurers multiple fibres (Suberposition). + +In the heart there are calcium channels. + +_Max firing frequency is about $1"kHz"$_ + +== Propagation of AP + +There are multiple Methods of propagation the AP. One is to recreate the AP along the way (this takes time but is faster with higher diameter of the axon). + +The other method is the saltatory "jumpy" conduction. This is much faster and the AP jumps between the isolations. + + diff --git a/S2/Neuro/preamble.typ b/S2/Neuro/preamble.typ new file mode 100644 index 0000000..da265ee --- /dev/null +++ b/S2/Neuro/preamble.typ @@ -0,0 +1,20 @@ +#import "../../default.typ": * + +#let rot = math.op("rot") +#let grad = math.op("grad") + +#let conf(num: none, date: "", body) = { + // Global settings + show: default + + // Set the header + [ExPhy II \ Vorlesung #(num) \ #(date) \ Jonas Hahn] + + // Make the outline + outline() + + // load the document + body +} + + diff --git a/S2/Neuro/template.typ b/S2/Neuro/template.typ index 1342ba8..f27b5c1 100644 --- a/S2/Neuro/template.typ +++ b/S2/Neuro/template.typ @@ -1,4 +1,4 @@ -#import "./preamble.typ": * +#import "../preamble.typ": * #show: conf.with(num: 1) diff --git a/S3/input.txt b/S3/input.txt new file mode 100644 index 0000000..315fa5a --- /dev/null +++ b/S3/input.txt @@ -0,0 +1 @@ +# Input file for the current file of the semester diff --git a/S3/links.md b/S3/links.md index 37b9405..3d81a41 100644 --- a/S3/links.md +++ b/S3/links.md @@ -1,3 +1,4 @@ # Links -Preparation for the third semester links +Preparation for the third semester links. +