{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "




\n", "


\n", "# Κεφάλαιο 8\n", "
\n", "




" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 8. Συμβολική κι αριθμητική επίλυση ΣΔΕ" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "\n", "> Για να λύσετε αυτήν την διαφορική εξίσωση, την παρατηρείτε μέχρι να φανερωθεί μια λύση της.

George Pólya (1887 - 1985)

\n", "> " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "\n", "Ας υποθέσουμε ότι μας έχει δοθεί μια Συνήθης Διαφορική Εξίσωση (ΣΔΕ) και η μέθοδος του Pólya δεν είναι και τόσο αποτελεσματική για να βρούμε έστω και μια ειδική λύση της. Τότε το Sage μας παρέχει μια πλειάδα από συμβολικές και αριθμητικές μεθόδους τόσο για την ποιοτική μελέτη των λύσεων της ΣΔΕ, όσο και για να βρούμε (αν είναι εφικτό) την γενική λύση της.

\n", "Συμβολικά, το Sage ενσωματώνει (μέσω του Maxima) όλες τις φαινομενικά αποκλίνουσες μεθόδους επίλυσης μιας ΣΔΕ πρώτης τάξης, που ίσως να σας φάνηκαν ένα ανιαρό συνταγολόγιο στην πρώτη επαφή που είχατε σε ένα προπτυχιακό μάθημα ΣΔΕ. Το γεγονός αυτό μας επιτρέπει να επικεντρωθούμε στα κύρια χαρακτηριστικά των λύσεων μιας ΣΔΕ και κατ' επέκταση του φυσικού-μαθηματικού, φαινομένου-μοντέλου που περιγράφει η αντίστοιχη ΣΔΕ.

\n", "Φυσικά, δεν είναι πάντα εφικτό για να βρούμε αναλυτικά (σε κλειστή μορφή) τις λύσεις μιας ΣΔΕ. Το αντίθετο ισχύει μάλιστα, δοσμένης μιας ΣΔΕ η εύρεση της γενικής της λύσης είναι ένα πολύ δύσκολο εγχείρημα γιατί πολύ απλά οι συναρτήσεις που έχουμε στην διάθεσή μας είναι πολύ λίγες για να περιγράψουν την πολυπλοκότητα του φαινομένου που μοντελοποιεί μια ΣΔΕ. Εδώ έρχεται και πάλι το Sage με μια πλειάδα από πανίσχυρα εργαλεία αριθμητικής επίλυσης ενός προβλήματος αρχικών-συνοριακών τιμών (ΠΑΤ-ΠΑΣΤ) για να μας δώσει μια αρκετά ικανοποιητική αριθμητική προσέγγιση της λύσης του.

\n", "Τόσο τα συμβολικά όσο και τα αριθμητικά εργαλεία που μας παρέχει το Sage για την μελέτη μιας ΣΔΕ, παρέα με τις γραφικές ικανότητες που διαθέτει για την απεικόνιση των διανυσματικών πεδίων και των αντίστοιχων ροών τους, του χώρου των φάσεων, των διαγραμμάτων διακλάδωσης, των περιοδικών και σχεδόν περιοδικών τροχιών και σε τελική ανάλυση του συνόλου των λύσεων μιας ΣΔΕ είναι ένας συνδυασμός που μας επιτρέπει να ισχυριστούμε ότι \n", "\n", "> για να λύσετε αυτήν την ΣΔΕ, την μελετάτε με το Sage μέχρι να απεικονίσετε την λύση της,\n", "\n", "παραφράζοντας τον Pólya." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 8.1 Συμβολική επίλυση ΣΔΕ" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 8.1.1 ΣΔΕ πρώτης τάξης " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "Ας θεωρήσουμε μια βαθμωτή ΣΔΕ πρώτης τάξης, δηλαδή μια εξίσωση της μορφής

\n", "$$ F\\left(\\,x,y(x),y'(x)\\, \\right) =0$$
\n", "Κατ' αρχήν ξεκινάμε με τον καθορισμό της ανεξάρτητης και της εξαρτημένης μεταβλητής" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "x = var('x')\n", "y = function('y')(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "Για να λύσουμε συμβολικά μια ΣΔΕ πρώτης τάξης χρησιμοποιούμε την εντολή desolve η οποία σαν ορίσματα και επιλογές δέχεται τα εξής
\n", "desolve(de, dvar, ics=..., ivar=..., show_method=..., contrib_ode=...)\n", "
\n", "όπου\n", "

" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Γραμμικές ΣΔΕ πρώτης τάξης

\n", "

\n", "Είναι ΣΔΕ της μορφής \n", "$$ y' + P(x)\\,y = Q(x)\\,,$$\n", "όπου $P,Q$ συνεχείς συναρτήσεις σε κάποιο κοινό διάστημα του πεδίου ορισμού τους. Για παράδειγμα με την βοήθεια του Sage θα βρούμε την γενική λύση της \n", "$$ y'+3\\,y = e^x \\,.$$" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "x = var('x')\n", "y = function('y')(x)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1/4*(4*_C + e^(4*x))*e^(-3*x), 'linear']\n" ] } ], "source": [ "sol1a = desolve(diff(y,x) + 3*y == exp(x), y, show_method=True); print sol1a" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "Παρατηρούμε ότι το Sage (ουσιατικά το Maxima) ονομάζει την σταθερή ολοκλήρωσης με _C. Ας θεωρήσουμε τώρα την γραμμική ΣΔΕ\n", "$$ y' + 2\\,y = x^2 -2\\,x+3\\,.$$\n", "Στο Sage μπορούμε να δώσουμε συμβολικά την ΣΔΕ και να του ζητήσουμε την γενική λύση της ΣΔΕ να μας την γράψει σε ανηγμένη μορφή χρησιμοποιώντας την μέθοδο expand" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1/2*x^2 + _C*e^(-2*x) - 3/2*x + 9/4\n" ] } ], "source": [ "SDE = diff(y,x) + 2*y == x^2 -2*x+3\n", "sol1b = desolve(SDE, y).expand(); print sol1b" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "Ας θέσουμε επιπλέον και την αρχική συνθήκη $y(0)=1$ στην προηγούμενη ΣΔΕ" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1/2*x^2 - 3/2*x - 5/4*e^(-2*x) + 9/4\n" ] } ], "source": [ "sol1b_PAT = desolve(SDE, y, ics=[0,1]).expand(); print sol1b_PAT" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

ΣΔΕ με χωριζόμενες μεταβλητές

\n", "

\n", "Είναι ΣΔΕ της μορφής \n", "$$ P(x) =y' \\, Q(y)$$\n", "όπου $P,Q$ συνεχείς συναρτήσεις σε κάποιο κοινό διάστημα του πεδίου ορισμού τους. Για παράδειγμα με την βοήθεια του Sage θα βρούμε την γενική λύση της \n", "$$ y\\,y' = x $$" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1/2*y(x)^2 == 1/2*x^2 + _C, 'separable']\n" ] } ], "source": [ "sol2a = desolve(y*diff(y,x) == x, y, show_method=True); print sol2a" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "Ως ένα άλλο παράδειγμα ας θεωρήσουμε την ΣΔΕ χωριζομένων μεταβλητών $y'\\,\\log y = y\\,x$." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1/2*log(y(x))^2 == 1/2*x^2 + _C, 'separable']\n" ] } ], "source": [ "sol2b = desolve(diff(y,x)*log(y) == y*x, y, show_method=True); print sol2b" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "Το Sage συμφωνεί μαζί μας ότι πρόκειται για μια ΣΔΕ χωριζομένων μεταβλητών. Παρατηρήστε ότι το Sage δεν επιχειρεί να λύσει την εξίσωση ως προς $y(x)$. Αυτό αφήνεται στην διακριτική ευχέρεια του χρήστη να το κάνει αν είναι απαραίτητο, φυσικά με την απαραίτητη διερεύνηση των διαφόρων περιοχών ισχύος της λύσης" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[{y(x): e^(-sqrt(x^2 + 2*_C))}, {y(x): e^(sqrt(x^2 + 2*_C))}]\n" ] } ], "source": [ "sol3b_y = solve(sol2b[0],y,solution_dict=true); print sol3b_y" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "Προσοχή ! Ορισμένες φορές το Sage δεν αναγνωρίζει μια ΣΔΕ ως χωριζομένων μεταβλητών και την χειρίζεται ως ακριβής ΣΔΕ. Για παράδειγμα η ΣΔΕ $y'=e^{x+y}$" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[-(e^(x + y(x)) + 1)*e^(-y(x)) == _C, 'exact']\n" ] } ], "source": [ "sol3 = desolve(diff(y,x) == exp(x+y), y, show_method=True); print sol3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

ΣΔΕ Bernoulli

\n", "

\n", "Είναι ΣΔΕ της μορφής \n", "$$ y' +P(x)\\,y = Q(x)\\, y^a\\,,$$\n", "όπου $P,Q$ συνεχείς συναρτήσεις σε κάποιο κοινό διάστημα του πεδίου ορισμού τους και $a\\neq 0,1$. Για παράδειγμα με την βοήθεια του Sage θα βρούμε την γενική λύση της \n", "$$ y' - y =x\\,y^4$$" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[e^x/(-1/3*(3*x - 1)*e^(3*x) + _C)^(1/3), 'bernoulli']\n" ] } ], "source": [ "sol4 = desolve(diff(y,x)-y == x*y^4, y, show_method=True); print sol4" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Ομογενείς ΣΔΕ

\n", "

\n", "Είναι ΣΔΕ της μορφής \n", "$$ y' = \\frac{P(x,y)}{Q(x,y)}\\,,$$\n", "όπου $P,Q$ ομογενείς συναρτήσεις του ίδιου βαθμού σε κάποιο δοσμένο διάστημα. Για παράδειγμα με την βοήθεια του Sage θα βρούμε την γενική λύση της \n", "$$ x^2\\,y' =y^2+x\\,y+x^2\\,.$$" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[_C*x == e^(arctan(y(x)/x)), 'homogeneous']\n" ] } ], "source": [ "sol5 = desolve(x^2*diff(y,x) == y^2+x*y+x^2, y, show_method=True); print sol5" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "Ας θεωρήσουμε την ομογενή ΣΔΕ \n", "$$\\quad x\\,y'=y+\\sqrt{x^2+y^2}$$ \n", "και ας επιχειρήσουμε να την επιλύσουμε όπως έχουμε μάθει, δηλαδή θεωρώντας την αντικαταστάση $y(x)=x\\,u(x)$ να την μετατρέψουμε σε μια ΣΔΕ χωριζομένων μεταβλητών. Επειδή η ΣΔΕ δεν ορίζεται για $x=0$, την περιορίζουμε στο διάστημα $x\\in (0,\\infty)$. Στο Sage υλοποιούμε τα προηγούμενα ως εξής" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(x*diff(u(x), x) + u(x))*x == x*u(x) + sqrt(x^2*u(x)^2 + x^2)\n" ] } ], "source": [ "u = function('u')(x)\n", "y = x*u\n", "SDE = x*diff(y,x) == y + sqrt(x^2+y^2); print SDE" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x == _C*e^arcsinh(u(x))\n" ] } ], "source": [ "assume(x>0)\n", "sol5b = desolve( SDE , u ); print sol5b" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "Παρατηρούμε ότι η λύση μας δίνεται σε πεπλεγμένη μορφή η οποία όμως μπορεί να απλοποιηθεί μέσω ταυτοτήτων που ισχύουν μεταξύ της συνάρτησης λογαρίθμου και των υπερβολικών τριγωνομετρικών συναρτήσεων και των αντιστρόφων τους. Μπορούμε να χρησιμοποιήσουμε τις ταυτότητες αυτές μέσω της επιλογής logarc του Maxima. Πιο συγκεκριμένα, από το Sage οδηγούμε το Maxima που εκτελεί την ολοκλήρωση να χρησιμοποιήσει υπερβολικές τριγωνομετρικές ταυτότητες ως εξής" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x == _C*(sqrt(u(x)^2 + 1) + u(x))\n" ] } ], "source": [ "S = desolve(SDE,u)._maxima_().ev(logarc=True).sage(); print S" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "Η γενική λύση της ΣΔΕ για την μεταβλητή $u(x)$ είναι λοιπόν πιο απλή και έχει την μορφή\n", "$$ c^2 \\, (u^2+1) = (x - c\\,u)^2 $$\n", "και επιστρέφοντας στην αρχική μεταβλητή $y(x)$ έχουμε ότι " ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x == _C*(sqrt(y^2/x^2 + 1) + y/x)\n", "[\n", "y == -1/2*(c^2 - x^2)/c\n", "]\n" ] } ], "source": [ "reset('y'); var('y , c');\n", "lysh = S.subs({u(x):y/x}); print lysh\n", "eq = c^2*( (y/x)^2 +1)==(x-c*y/x)^2 ; print solve(eq,y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "Δηλαδή η γενική λύση της αρχικής μας ΣΔΕ έχει την απλή μορφή\n", "$$ y(x) = \\frac{x^2-c^2}{2\\,c} $$\n", "Οπότε από το παράδειγμα αυτό συμπεραίνουμε ότι ορισμένες φορές είμαστε υποχρεωμένοι να βοηθήσουμε εμείς το Sage έτσι ώστε να βρούμε την γενική λύση μιας ΣΔΕ. Αυτό συμβαίνει επειδή το λογισμικό δεν αντιλαμβάνεται ότι ουσιαστικά δουλεύουμε σε ένα διάστημα και στο διάστημα αυτό ισχύουν επιπλέον υποθέσεις για την λύση που αναζητούμε." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Ακριβείς ΣΔΕ

\n", "

\n", "Είναι ΣΔΕ που γράφονται ως ένα ακριβές διαφορικό, δηλαδή ΣΔΕ της μορφής \n", "$$ \\frac{\\partial f}{\\partial x} \\, {\\mathrm d} x + \\frac{\\partial f}{\\partial y} \\, {\\mathrm d} y = 0\\,,$$\n", "όπου $f$ διαφορίσιμη συνάρτηση στο πεδίο ορισμού της. Για παράδειγμα με την βοήθεια του Sage θα βρούμε την γενική λύση της \n", "$$ y' = \\frac{\\cos y - 2\\,x}{y+x\\,\\sin y}\\,, \\qquad f(x,y) = x^2-x\\,\\cos y +\\frac{y^2}{2}\\,.$$" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[x^2 - x*cos(y(x)) + 1/2*y(x)^2 == _C, 'exact']\n" ] } ], "source": [ "reset()\n", "x = var('x')\n", "y = function('y')(x)\n", "sol6 = desolve(diff(y,x) == (cos(y)-2*x)/(y+x*sin(y)), y, show_method=True); print sol6" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

ΣΔΕ Riccati

\n", "

\n", "Είναι ΣΔΕ της μορφής \n", "$$ y' = P(x)\\,y^2 + Q(x)\\,y + R(x)\\,,$$\n", "όπου $P,Q,R$ συνεχείς συναρτήσεις σε κάποιο κοινό διάστημα του πεδίου ορισμού τους. Για παράδειγμα με την βοήθεια του Sage θα βρούμε την γενική λύση της \n", "$$ y' = x\\,y^2 + \\frac{1}{x}\\,y + \\frac{1}{x} \\,.$$\n", "Σε αυτό το παράδειγμα πρέπει το όρισμα contrib_ode να το αλλάξουμε σε True, έτσι ώστε το Sage να χρησιμοποιήσει πιο περίπλοκες μεθόδους ολοκλήρωσης ΣΔΕ " ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[y(x) == -(_C*cos(x) - sin(x))/((_C + x)*cos(x) + (_C*x - 1)*sin(x))], 'riccati']\n" ] } ], "source": [ "sol7 = desolve(diff(y,x) == x*y^2+y/x+1/x, y, contrib_ode=True, show_method=True); print sol7" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

ΣΔΕ Lagrange και Clairaut

\n", "

\n", "Μια ΣΔΕ της μορφής\n", "$$ y = x\\,P(y') + Q(y')\\,,$$\n", "όπου $P,Q$ διαφορίσιμες συναρτήσεις σε κάποιο κοι διάστημα, ονομάζεται τύπου Lagrange. Ειδικότερα, όταν η συνάρτηση $P$ είναι η ταυτοτική συνάρτηση, η ΣΔΕ καλείται τύπου Clairaut. Για παράδειγμα, η ΣΔΕ \n", "$$ y = x\\,y' - y'^2 \\,.$$\n", "είναι τύπου Clairaut, και με την βοήθεια του Sage η γενική λύση της ΣΔΕ και η ειδική λύση της είναι" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[y(x) == -_C^2 + _C*x, y(x) == 1/4*x^2], 'clairault']\n" ] } ], "source": [ "sol8 = desolve(y == x*diff(y,x)-diff(y,x)^2, y,contrib_ode=True, show_method=True); print sol8" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "Ας παραστήσουμε γραφικά την παραμετρική οικογένεια ευθειών καθώς και της παραβολής που απαρτίζουν την γενική και την ειδική λύση, αντίστοιχα, της παραπάνω ΣΔΕ τύπου Clairaut" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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9v4XP5s3AqFH8NzVyrAuFfA/CP/4IdOrEX5YKFfjGvXVrfn9KZBOoI22kO/3l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\nWAfhv/+Gt5FWr093J+CW6J+Cend37jT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BWOHDiY60kJBMSbEf68Rj2ImzEiCvJw04Wykt\n2zsskF0xLdD3E48e7UxIy+foVFUEXA7CRGk+5yIn+/v9d9j2/wayeDEvbJJ1CZLtCQacrYgG+IFQ\nRicacOaY5MQ7GOB1cjJSmQqFHhWEFT6c6Eh7vUCtWnKOMoC8xzAg76wEyOtJA86zYdneYYHsimn9\n8fj1Ex+Ve9/589xOfN11fO4xMRyEy5ZN82XHssj2/+rRr4SWMfNw0hMMOMuCnehEA/KOSYAz7+Cj\nR+VnBRQKPSoIK/yQ1ZEGOJNr2lRurKzHMODMWQmQ15MGnGXDgL3vcCB2GtNGGPUTG7F5M7d8lS/P\nnyGy3hMnOAgnJ6f5suPrr+fs06xckJUF6f5fPbKa0HpkfIIFTrNgJzrRThyTAHnvYACYNYuPQ+Yc\nFQo9Kggr/HBSFxY6zgcP2o914jEMyDsr6Y/DTk8acJ4Ny/gOB2KnMW2EWZ1YZL1WtV69WIdV7VgQ\nSv0X4EDdvj3XPa00ofXI+gQLnGTBAM+wyOhE649FNmDLegcDwH338XEoFE7JUxDOycnBU089hWbN\nmiE+Ph41a9bEwIED8U/AvNapU6dwzz33oFy5cqhQoQKGDBmCczK6cooCY968eejatSsqV64Ml8uF\nTRfn3PR14czMTIwYMQKVKlVC2bJl0adPHxzVzZmePCk/fQ3IewwDzpyVnOhJA86zYRnfYT0yGtNG\n6OvEd98NjBgRnPUa1XrNFLMCa8fXX8+SnzVqOKv/Av6a0L/8IvceWZ9ggdMs2IlONODMMcmJd7DH\nww9HZvXxlStXokePHqhZsyZcLhcWGLhAjB8/HjVq1EDp0qXRqVMn7N692/6DFQXKiy++iFatWiEh\nIQFVq1ZF7969sTNACcbuHilDnoJwWloaunTpgq+//hq7du3CmjVr0Lp1a7Rq1cpv3C233IKrr74a\na9euxerVq3HppZdiwIABefloRR757LPP8Pzzz+Ojjz6C2+32BWF9XXjYsGFISkrC8uXLsX79erRp\n0wbt2rXz20/r1kC/fnKf6cRj2ImzEiCvJw04z4YBOd9hPU5XTAOc9c6cyYGCa72cxdpNhYsg3K1b\nN/To0SNIqk9kx02a8H6jolh21Ent2MlKaIGsT7DAaRbsRCfaiWMS4Mw7eMMGa430JUuWYPz48fj2\n22/hdruDgvBLL72EihUrYuHChdiyZQt69eqFBg0aIEu2RqAoELp164ZPP/0U27dvx+bNm3Hbbbch\nKSkJF3Q1Hpl7pB35Ph29du1auN1uHDp0CACwfft2uFwurF+/3jfmhx9+QFRUFI6oAkqRs3//fr9M\nGODgdOedaYiNjcU8nSHwjh074HK5sEZnUj9hAjslySzQceIxDMg7KwH+etIyOM2GZX2H9ciumDaq\n9T7/PGewdnViwN7AQV//7d+fSw6ytWPA+UpoQN4nWOA0C87I4AVWMjrRgDPHJEDeOxjghXvx8XJ1\ndaNMuEaNGnhd1zqQlpaGuLg4fPnll3IHoCgUjh8/DpfLhVWrVgHgv5PMPdKOfA/CP/30E6KiopCe\nng4AmDlzJhITE/3G5ObmIjo6GvPnz8/vj1c4xCgIP/EEULnyUrjd7qAbe1JSEt58803fz6tX883t\nt9/kPk/WYxhw5qwEaHrSMtltKNmwk95hgdmKaZlar2w/sVUQNqv/ytSOAecroQHnPcGA8yxYtDzJ\n6EQDzhyTnHgHA0DHjlybliEwCO/bty/o+gOADh06IDk5WW6nikJh9+7dcLvd2LZtGwBg6VK5e6Qd\n7jzLhujIysqisWPH0j333ENly5YlIqLU1FSqWrWq37ioqChKTEykVDuBV0WR0LEj0YkTqRQTExsk\nuVatWjW/v9u117KqUUqK3L5792YFqNxc+7HduxOVK8d6vDKMHEn0119Ey5fbj3W5iCZNIlq3jhW6\nZBg+nKhVK6KhQ1kDWYaOHVkF7P33Wa94yxai0aNZf3vQIKKEBNbAPnSIFbQaNNDeW7s20YoVRAMG\nsO70I4/Ify4R0Zo1RC1bslrZihWsiCaIjSXq14/op59YO3noUFabuuIK1uX+7DM+ph49WB981ixW\n+ZJh1ixWmpo61V5RiIjVsSZPJrrpJqL27eU+4733iDp3ZtUiO86cIVq0iOjee+X2vWABH3fnzvZj\nz50jWr2aqGtXuX0HkpqaSi6Xi6oFyHEFXmeKogUAJScnU7t27ahp06ZExH+72Fj7e6QdjoLw7Nmz\nKSEhgRISEqhcuXK0evVq37bc3Fzq168fuVwumjp1qu2+ANjLeSnyBau/mxHt2nGQ8nqDtwX+3aKj\n+WblJAifPk20apX92Lg4or59OQjLiKt26EDUtCnfoGW48UaiG27gYCyz/6goliT86y+i116T+wwi\nonvu4d/RqFFEzZuzzOaIEUR79/LvrU8fopgY4/fGxRHNmMHn9P77LKV57Jj9Z370EQe0evVYstNK\nqrNhQ5bzPHSI5RlLlyYaOJCofn2i1FQ+14QEuXM9eZLlQe++Wz4wLVhAtGkT0cSJcuP//JMfMEaM\nkBv/9df80Ne/v9z4+fP52EuXth+7bBk/GIUahM1Q98fixYgRI2j79u00Z84c27GO/3ZO0vFz585h\n7969vn+ZmZkAeJV07969cdVVV+FUwMoVNR1d9Jj93QDj6WgAaNRoKVwuuakWYQsns2hJ7zEsw9Kl\nPDUou5L33Xe5NnxxSYItTmvDgHzvcGCtt1IloEwZ+YVKgZj1Ewe2KIXS/6vH6+Wp/agonqaWrR0D\nznqCAee1YPEZderILZoCeLq4c2e5sewdLL8AbeRI+RXXgJqODkdGjhyJunXr4sCBA36v59d0dJ5r\nwiIAN2/eHCcNloH+9ddfcLvdfguzUlJS1MKsYsL+/fv9VkcLRo9OA1EsvvlGW3Swc+dOw0UHBw/y\njWvuXLnPFB7DMjcuj4eVuUaMkNu3Ez1pILTasFXvsFWtN5QV04EY1YlFEN61Ky2k/t9A9CuhZWvH\ngPOeYMB5LdipTrT4bspqdE+bxg8fMt7BANCwoXxrHOBsYdZc2QtKUWCMHDkStWvXxl6DJ26jhVlm\n90gr8hSEc3Nz0bNnT9StWxebN29Gamqq71+2bjlot27d0LJlS/zxxx/45Zdf0KhRI9wrK8ukKBBO\nnTqFjRs3YvHixXC5XPjyyy+xceNGpF4U4OV+4eGoXbseli1bhnXr1qFt27amy++bNOG2Fxn++1++\nMeqeyyx58knOImX1kJ3oSQOhZcOBvcNmalaBx+xUY9qIQN1poZhVvXqa4/7fQKxWQhv1HYvs2GlP\nMBBaFuxEJxoAXn6ZJVBlWtcA7u++8Ua5sXv38u/h22+tx507dw4bN27Ehg0b4HK58MYbb2Djxo04\neFHl5uWXX0ZiYiIWLlyIzZs3o1evXmjYsKFqUSpihg8fjgoVKmDlypV+sS0jI8NvTL16cvdIM/IU\nhEUWpf/ncrngdruxQvdoe/r0aQwYMMAn1vHggw/ivOyySUWB8Mknn/j+Vvp/ky+q1Z85A7hcmbjp\nplG+RvS+ffuaNqInJ8srbWVnc0Ylm606cVYCnOlJA6FlwwDQqxdQrhwbPThxLnKqMW12zEJ3ukED\nDsLXXpsmrf9shOxKaKPs+LrrnPUEA86zYKc60YAzx6S0NA7wb70lN37qVD5nuwC/fPlyw2ttkK4H\nauLEiT6xji5duiixjmKA0d/M7XbjP7paRWZmJkaNkrtHmqFkKxWmONGRFhq+F1fv23LvvUDz5nJj\nnTorAc70pAFn2bDIesuV4/fUru3cuSgUjelAsrK4l5qIg/B11xmLdcgQiiY0wNnxQw/xuTipHYeS\nBTvRiQacOSYB/NBGJC/J2auXs++YQmGECsIKU5zoSJ8/L29XCDjzGAacOSsBzvSkAfts2KzWO3Gi\n895hQSga0wJ9/+/kyRyEY2PTpGufekLRhBaInuD69YHPPpOrHQPOs2DAmU404MwxCXDmHZyVxWsP\nZGvTCoUZKggrTHHiLwzwCtSuXeXGOvEYBpw7KznVkwaMs2G7Wq9T32E9oWpMB/r/ioVZ996b5tif\nOBRNaD1GPsFWtWMgtCzYqU60U8ckp97BYhHaunVy4xUKM1QQVpjixF8Y0LSh7aYiBU48hgFnzkqA\nMz1pQMuGr76aNZyt1Kz0OPUd1uN0xbSR/68IwmfOpDn2Jw5FE1pg5xNstrL6zTedZ8FOdKIBZ45J\ngDPvYIC/D1WqyC9CUyjMUEFYYYmTurBYEJWSIjfeiccw4MxZCXCuJ715s6ix2jsXBeLUd1iPzIpp\nq/7fQNlKWX/iUDSh9TjpCRbZcZUqfA7ly8vVjgHnOtGAM8ckwJl3MMASmE4WiCkUZqggrLDESV3Y\n6+WeXlkPVqcew06dlQB7PWmjWm+dOrxAyclK6VB8h/VYrZi28/810o62050ORRNaTyg9wQBnxkRs\nzCFTOwac60Q7dUxy6h189GjoswcKRSAqCCsscVoXHjwYaNpUfv9OPIYBZ85KAAc3I5s5q1pvKH3D\ngHPf4UCMVkwH1n+NMDNwCOwnFll2qCuhBaH0BAPBtWC72rGgdWt5xSvAuWOSE+9gAJg1i8crrSFF\nfqCCsMISp3VhsSr5og6BLU48hgHnzkpeLz8U9Okj51wk3hNK3zDg3Hc4EP2KaaP6rxFWLkr6fuL2\n7TlDDnUltMCpT7DAbEW0lSrXunVyghh6nDgmAc68gwHgvvv4YUKhyA9UEFbY4qQufPKks6Dt1GM4\nI4P7c8ePlxsPcKB1ubS+Xplab6jZcCi+w3pycvj4YmPl9Z/t/IQBrhNXrcra1TExoa2EBpz7BAtk\nV0QHZsdVq3K9XDZjP32af3eyq+4BZ97BHg8/ZIVaR1coAlFBWGGLk7owwNOH/frJ79+JxzDAU6wN\nGlgfT2DW63LxdKfswqm8ZMOh+A4Ljhxh9SkRgGRWTIsg3K2btVjH+PG83+hoeS1lPaH4BAuc9gVn\nZfFaAbdbvnYMaGYissphTr2DN2zg8T//LDdeobBDBWGFLU7rwhMmABUryi/4GTeOx8tOB1o5K5nV\neh9+2JmeNBB6Nhxq77C+/jt3rrzGtEwmLFZCjxljXCeWwagnWIZQ+oIBTSf6t9/kaseAM8ckAHjp\nJZ4dkG2re+klbnvTGZEpFHlCBWGFLU7rwqtX883yt9/kxou6X+DiKTMCnZVkar1O9aSBvGXDTnuH\njeq/shrTdkE4cCV0YJ1Ypp/YrifYilDUsYx0ou0cnZw6JgE863D77fLjO3bk/naFIr9QQVghhZO6\ncE4OZ6KTJsmNd+oxDLCzUvnyHIjtnIsETvWkgdCzYUCud9jO/1dGY9oqCFuthJbtJwac+wQLQs2C\n7XSijVZW33WXM8ckp97B6emcmcv2nSsUMqggrJDCaV24b1/OTGWR9RgWWW/z5lo2JONcBDjXkwby\nlg3b9Q7b9f8K7DSmzYKwjCa0XT8xEHpPMBBaFgzI60QHZscxMXK1Y8C5d/DChfwZu3bJjVcoZFBB\nWCGF07qwWCAj26pj5zFsVOutUwe48065/QOh6UkDecuGzXqHZfp/BXYa00ZB2IkmtFk/MRB6TzAQ\nehbsVCca0ByT+vSRqx0DzryDAWDkSGeqWgqFDCoIK6RwWhcW9bm5c+XGG3kM29V6nTorAc71pIG8\nZcNAcO+wbP+vHiuNaaMg7FQT2qxOHGpPMBB6FuxUJ1q8Rzgm2dWOAefewQDQsKHzBziFwg4VhBXS\nOKkLAxw0hgyRHy88hu2ciwROnZUA53rSgrxkw6J3+MEHreu/dphpTAcG4bxoQuvrxF9/HVpPMBB6\nFhyKTrSVY5KZKpdY6S0rWLJ3r3PREIVCBhWEFdI4rQsnJzvzIx45UjNPsHMuEjh1VgLs9aSNyGs2\n/MILWo+uk2nWQIxWTOuDcF41oQGuE7dqxVPCVao47wkGQs+CnepEA3KOSUa14ypV5GrHADB1Kv/e\nncygKBQyqCCskMZpXViscN22zXxMYNbrcgH33y/fv+rUWQkw15O2I9RsWNR/Y2JY6MKp73AggSum\nRRC++eZuKFOmB+rUmR2SJrSejz7SHoic9hOHmgUDznWiAeeOSVu3cjkgPl6udgwAvXrxQ5hCkd+o\nIKyQxmld+Px5ns4MlBC0qvU69RgOxVlJryfthFCyYX3998cfQ/cdDkS/YloE4bZt0/KkCS3Q9wQ7\n7ScGQs+CQ9GJduqYBGjewevW2deOAc6iExJ4NkOhyG9UEFY4wmlduHNnbtEB5Gq9Tj2GAefOSgBn\nkVFRPPXqBNls2Kz/Ny++w3r0K6bXruUgHBOTFrImtJ7AnmAn/cR5yYIHD+barqxyGuDcMQkw9g62\ncnQS093r1sl/hkIhiwrCCkc4rQu/+CJnUq1by9V6nXoMA86dlQCu7ZUt678aWwaZbNis/3fevHno\n1Kkr3O7KIHJh48ZNQe/NzMzEiBEjUKlSJZQtWxZ9+vTBUZMUVKyYTkzkIDxtWt4LlmY9wTL9xEDo\nWfDJk/xw4jTbdOqYZOcdbLSy+ppreEGc0xYthUIGFYQVjpCtC4usNyGBx7dsae9cJHDqMfz/7Z1/\nkFTVlcdv96DBzA8YXFijRjSCQpmoQJQii7AaCZAwMmWYWiOLWX5sFQlJJFmTxVQKcbUsTbQSdysG\nU0rFCIMSY7FEraVcAtSGIMpPS4ZIdlYkqQgpQMeBOJmB+e4f1zv95vW9991zXg/963yqphTo1+81\nw/S3zzvnfL+cZCVAV6pUP2nAXw379n+ffvpp3HffffjGN56EUlk8+GC+CC9evBgjR47Eli1bsHv3\nbkyaNAmTJ092XssTTwBKaRE+diydCCftBPv2iYF0VbDxiT5yJPwYTmISJTvYVMeDBoX3jgWBioiw\nQMLXF7b1epct0/91VR42qBnDQFiyUhyOnzTgroZD938PHToEpTIYNmxfPzOTjo4OnHvuuXg+kuv4\nu9/9DplMBjt27LBef309cP31WoQXLkwnwiE7wT7faW4VbPOJDoGamATQs4OPHtWvacmS5N6xIHAQ\nERbIxPvCSb3eBQv0IFQo1IxhwJ+s5IPjJw30r4aT/J/jHDp0CJlMBh/96L5+ucO//vWvkc1m8+wn\nR44ciR/96Ef9fi/qCf3HP2oRVqrD6zHtg5oTHO8Tp6mCk3yiXVATkwBadjAArF6tr830x329Y0Hg\nICIskLnrLn3LddUqf3KRwXg2Hz4cfg5qxnA8WSkUjp80kKuGr7kmzP85ihHhZcv29ROf1tZWDB48\nOO/x119/PZYtW9b367gntJmO/spXOrwe077XwskJjvaJv/51XhUMhPtER+EkJlGzgwFg3jx9bXFC\nXLkEIQQRYYHE66/rN02zQ5qUXATooRvKahNAzxgGdLLS+efTdlq5ftKAnrBWSg/txCvwNWvWoK6u\nDnV1daivr8dvImPLRoR3797XL3fYJcLXXXcd7v6wRLV5QhsRPn68w+sx7YKbEwzoPvH8+fr4iy+m\n70BzfKIB4KGHaIlJAD07+MwZ/eEyyXlMqmMhDSLCQiLxXq95s6Hsu06cCLS0hD+emjEMAHv36mN+\n9avwYwCen7Tp/zY0aKvNeBV38uRJtLe39311RVLgjQjv27evX+5wyO1omye0EeGZM2dixowm1NU1\noba2CTNmNKG1tdX7OtLkBBvMmlBNDW2fGOD5RAP6Nvw//APtGGp28J49+nVt2hT2eKmOBQ4iwoIT\nX6+Xui+8fLmubEOtFDkZw729wFVXAbfdFn4MQPOTjvd/jfEDxUXr0KFDyGaz2LdPT0eb3eG9e/MH\ns958882+wSyXJ3TcO9rlMW2DmxNsiPaCKfvEAM8nGsglJm3YEH4MNTsY0JVzba2eGqci1bEQioiw\n0I+k5CIDdV942zb9fNu3h19LaMZwFE6yEhDmJ23b/6W4aJ04cQJ79+7Fiy++iEwmg2effRZ79+5F\ne/uRvtzhxYu/gksvvRSbN2/Gzp078ZnPfAaTJ0/2ekLbUpRsHtNx0uQEG+IT0aH7xADPJxron5gU\nCjU7GNCDX7Nm0a4tjlTHQhIiwgKA8OQiA9VHuqdHP/eKFeHXlJQxbIOTrAQk+0n79n9DXbR+9rOf\nIZPJIJvN9vu69957+3KHf/7zLnzta1/rM+uYM2cO2tqO9k1C2z5c2EQYyPeYjpImJ9jgmohO2ic2\ncHyifYlJPqjZwZ2d+sMWNW3Lh1THgg0R4SomtOq1QfWRBnS1OWlS+ONtGcMhcJKVfH7SSfu/aROW\nDPHcYSB/EtqGS4SB/h7TUdLkBBt8e8G+fWKA5xMNhCUmxeFkB2/YoM9z8CDt+kKQ6liIIiJchVCr\nXhfUvrAxV4iKTBImY5gCJ1kJyPeTpuz/pskbNpjcYbM7bJuEtuET4ajHtJmYpu4E2wjdC3b1iTk+\n0QA9MQnQZiyU7GBAm3NQz8NBqmNBRLhKSFP1uqD2hc1u57p14ed47jl9DOU6OclKQH8/aZf/s4tC\nVcP/8R+5Ss82CW2/brcIAzmP6dGjdU+UsxMch+KOFe8Tc32iOYlJgB7UGzeOdsyoUby1NS5ScqfG\niAAAIABJREFUHVcvIsIVTqGqXhvUvjCgxWDhwvDHd3ba4xCT4CQrAbryHTbM3f/1UYhq+PRp4Lrr\ngJEj7ZPQNpJEGMhNTI8dy98JNnDcsaJ9YvPhhuITDfASk7q69N2Fe+8NP6a9nXervFBIdVxdiAhX\nIANR9drg9IWXLqVVzwA9YxjgJSsB+s1aKeCKK2iexEDhqmFT/Y8dG7bSFSLCALB+vX7eUaP41wbw\nPaJ7e3OV/vDhtH1igJ6YBORWyPblZ2U4eewx3cum7I0PBFIdVwciwhXEQFa9Lqh9YeMTvH9/+DGc\njGFqslK0//uxj+kkJw5pq2HjCf03f6PvAIR8cIqadTQ1uQ06FizQjlGuiekQ0nhEA7nvf2Nj+D4x\nwEtMAuzZwUnMnq0/TJUSUh1XLiLCZc7ZqnpdUPvCp07Rby9zMoaB8GSleP+X6ycNpKuGo5PQ+/ej\nb3c46XlCKuHoTrBrYjoEbhVsMD7Rhw+H7xMDvMSkpOxgG3/9q759Te1Xny2kOq48RITLlGJUvTY4\nfeFp07S4UKBmDANhyUq2/d80ftIArxq2TUKb3eG1a/3HJolwfCfYNjEdQtoqOO4THbpPDPASkyjZ\nwQbzYWXnTtq5ioFUx5WBiHAZUeyq1wanL2zygilvFpyM4aRkJd/+L8dP2sCphl2T0Lbd4ThJImzb\nCY5OTB8/HnaNaatgm0900j4xwEtMAujZwYD+eRo+nG9gUgykOi5vRITLgFKpel1Q+8JvvKFfx8aN\n4cdwMoYBe7JSyP4vxU/aBqUadnlCm+uI7g7b8ImwbyeY4jGdtgpO8on2+U5zEpMAenYwoAe/br+d\ndkwpIdVx+SEiXKKUYtXrgtoX7u3VFSqlVwfQM4aB/GQlyv5viJ+0i9Bq2OcJbYjuDttwiXBITnCI\nxzSQvgoO8Yl2+U5zEpM42cFHj/IsT0sRqY7LBxHhEqPUq14bnL7wggXaJpICJ2M4mqzk83+2keQn\nnURSNWwmoV2e0AazO2xyh+O4RDg0J9jnMQ2kr4KBcJ/oeJ941y56YhJAzw4GgNWr9bm4iVKlilTH\npY2IcAlQTlWvDU5f2EwgHz4cfgwnYxjQyUrnnOP3f7bh85MOPd5VDYd4QkeJ5g7HsYkwNSfYNzGd\ntgqm+kRH+8Qf/7i+ZU5JTALo2cEAMG+e/rBRqUh1XJqICBeRcqx6XVD7wseP04WbkzH817/q61JK\np+hQ38zjftJUbNVwqCd0HJM7HP9wZtsTpuYEuyamC1EFc32it27V/0Zqa8P3iQFedvCZM/rDb4hD\nWSUg1XHpICJ8lin3qtcFtS8M6FuULS2081AyhqP939Gj6clKQH8/aQ62ajjUEzpOZ6d9dzheCXNz\ngm0T02mrYK5PNJB7HWPHhu8TA7zs4D179Lk2baJfZzkj1XHxERE+S1RS1WuD0xdevlz3eEOsGQ2h\nGcPx/i83WQnQQ0sXXECvog3Ratg3CR2CbXc4KsJpc4KjE9NdXemr4Icf5vlEA7nEpL/8JXyfGKBn\nBwO6h1xbq19ztSLVcXEQER5AKrXqtcHpC2/bpv9etm8PPyYkY9i2/8tNVgJyK1XPPEM/FshVw1dd\nlTwJHUJ8dzgqwoXICTYT09Onp6uCz5wBLr+ct/ITT0wK2ScGeNnBgDYDmTWLfp2ViFTHZxcR4QGg\n0qteF9S+cE+P/jtasYJ2HlfGcNL+LzdZCQCmTqWHSEQxt3UvvdQ/CR1CfHfYiPCuXR2pc4INjz+e\nC7LgYnyiXatVPlyJSb59YoCXHdzZqYWbuxNeyUh1PPCICBeIaqp6XXD6wnPm6L8zCraM4ZD9X26y\nEpDOT9pMQp9zjl5HKkRQfHR32IjwlCkdqXOCDeZDQzbL85gGcj7RnNfrS0xy7RMDvOzgDRv0az14\nkH6d1YJUxwOHiHBKqrXqtcHpCxtjfp8tY5x4xnDo/i81WSkK1086Ogn96KPpEpaiRHeHjx3TIqxU\nR6qcYIOZiL7xRp7HNJDvE00hJDHJ5jvNyQ4GgCVL6ElL1YxUx4VFRJiBVL12OH1h4wu8bh3tXCZj\n2Of/bCM0WckGx086OgldqLxhg9kd/va3tQjPmVOYANzoRDTHYxqw+0SHEpqYFO8Tm1vRlOxgQOcr\nc8M6qhmpjguDiDABqXqTofaFAf0mv3Ah7ZiVK/X3wOf/bCMkWckF1U/aNgmdNm84zr/8C5DNahE+\neDC9CNv2gike00CyT3QS1MQk0yeurdV3RCgfcNrbaUYigh2pjvmICCcgVS8NTl946VLaMe+8o3uC\nSgFf/jLt+pKSlZII9ZN2eUIXuhrWw09ahGfMyJl1cHHtBYd6TANhPtEuuIlJb7+te+41NbRjH3tM\nvy5OWpaQj1THdESEHUjVy4PTFzZTtPv3Jz822v+9+mp6xjBgT1YKJcRPOskTulDVsNkJvuIKLcJP\nPplOSZLcsZI8pg2hPtE2uIlJJjv4858P3ycGgNmz9YciofBIdRyGiHAEqXrTw+kLnzrVf9DKRbz/\ny8kYBvKTlSgk+UmHeEIXqho2O8Hbt2sRHj68gzTgFifEHcvnMQ3QfaLjcBKTgFx2cHd32D4xoL9X\n9fU8Ny8hHKmO/YgIQ6reQsPpC0+bps0hbLj2f7kZw9FkJQ4uP2mKJ3TaajiaE2xWlOrqOry5wz5C\nPaJdHtMGrk80oH8OOYlJQH52cNI+MZCzxdy5k34+gYdUx/lUrQhL1TtwcPrCjzyiq9r4D2PS/i8n\nYxjQaUTnncczznD5SVM8odNUw/GcYCPC3/9+B9scg+IR7ZqYTuMTDeg35/PPp9uDurKDffvEgP55\nHz6cZ+8ppEOq4xxVJ8JS9Q48nL6wsYaM7rmG7P9yMoYBfas4TYB73E+a4wnNrYbjOcFGhE+c6PDm\nDrvgJCXZJqbT+ESfOaMr6JDBrzi+7GDbPrFh/HiepaZQWKq9Oq4KEZaq9+zC6Qv39uqp5W9+U/86\ndP+XmzEM6J4hJ1kJ6O8n7ZqEToJTDdtygqPe0b7cYRfcpKToxHQan2ggd2uYU8UnZQfbfKePHk33\nIUwoPNVaHVe0CEvVWzw4feEFC/RtTp//cxxOxrAhTbISoP2kJ03yT0InQa2GbTnB8ShDV+6wjbR5\nwWZi+qtf5YsokEtMot6ap2QHR/vE//Zv+jju914YWKqpOq44EZaqtzTg9IVNaIDP/9kGJWM4Sppk\nJQBYs0Zfb2MjLTAgCqUaduUEx0XYlTtsI21eMKAnppXiO5HFE5MoULODTZ84m9W3v4XSphqq44oR\nYal6SwtqX/iVV3SPVSl6ClBoxrANbrJSby/wT/+kzzt7Nv34KCHVsC8n2IjwzJk5sw5b7nCctFWw\nwUypn3ceLxzDlZgUAic7+NQpfa2UfWKh+FRqdVzWIixVb+lC6QtH+7/jxgEtLbRzhWQMu+AmK5lJ\n6OZmup90nJBq2JcTHK+EDfHc4TiFqIIB/cbY0ABceSXdYxrwJyb54GYH79mjX/c3vhG2TyyUFpVW\nHZelCEvVWx4k9YVt+7/Ll+vbu9TQe1fGcBKcZKXoJDTVT9qFrxqO7gTbcIlwPHc4SqGq4KhPNNVj\nGghLTHLByQ4GctPUXV1h+8RC6VIJ1XHZiLBUveWHry/s2v/dtk1/f7dvp53LljEcCiVZyTYJHeon\n7cNVDcd3gm24RBjonzscpVBVcNwnmuIxDYQnJtngZAcD+vb1rFm5XyftEwulTzlXxyUvwlL1li+u\nvrBv/7enR/8ArVhBO1c8Y5hCaLKSyxM6xE+6p6cH3/nOd/CpT30KtbW1uPDCC3HHHXfgTxH10dXw\nCUydejsaGhowdOhQTJ26EEqd9OYE+0Q4mjtsfmYKVQUDdp/oUI9pgJ6YZOBmB3d26g9+8TsXvn1i\nobwot+q4JEVYqt7KwNYXDtn/nTNH735SMRnDVEKSlXye0El+0oAWys997nN47rnncPDgQezYsQMT\nJ07Edddd1+95Ghtn4KMfHYdXX30NL720DdnsaIwcOdd7/T4RBpC3O1yoKtjnE53kMQ3wE5MAbVTC\nyQ7esEEfd/Bg/p/Z9omF8qVcquOSEmGpeisP0xd2+T/bMLcoqWEETzyhj/vzn+nX6UtWCvGEdvlJ\n+3jttdeQzWbxhw8PamtrQyaTgVK78cIL+py1tf+FmpoavONZaE0SYSC3O/z73xeuCvb5RCd5TAP8\nxCQAWLyYt1e8ZEnycdInrjxKuTouughL1VvZ3HWXvu3s83+OYyqkdeto5zp6FMhkgFWr6NfpS1YK\n8YR2+Un7ePnll1FTU4POzk4AwKpVqzBs2DDccIOeNFYK+MlPTmPQoEFYv36959zJImx2h6+9tjBV\ncIhPtMtj2sBNTDpzRv+bMu5qFEaN0gKehPSJK5NSrI6LJsJS9VYHRsBGjEjuuUYZOxZYuJB+vsmT\neRnDrmQliid03E/aR1dXFyZMmIB58+b1/d4DDzyAMWPG9OUrjx2rBWfEiBFYuXKl87lCRBjQAQdK\n6deZllCfaNfEdJrEJJMdTP0g0d5Oi1mUPnFlUyrV8VkVYal6qwvT/1VKv2lTWLqU7rgF8DOGgfxk\nJaondNRPes2aNairq0NdXR3q6+vxm8h97J6eHjQ1NeHTn/50XxUM5ET43nt1RX/VVfr1Dx8+HI/H\nbbIixM06ol+tra19jzO94MZG+q3+KFSfaNvENDcxCchlB1NDOx57TF8H5fa39Ikrn2JXx2dFhKXq\nrS7i/d/x4+k+0qYa3L+fdhw3Yxjon6zkmoROYupU/WZ98uRJtLe39311dXUB0ALc3NyMa6+9Fidi\nSrhq1SoMHToMH/mIDmjQ8XyFuR1tJqL/7u/cu8OhmO8NxSc6OjGdJjEJyM8ODmX2bL0GxkH6xNVB\nMarjARNhqXqrE9v+L8dH+tQp/soRN2MY0AJ6883uSegknn1W/3t//fX8PzMCfPXVV+O4pUna1nYA\nSmVx0UW7cfKkFozRozcWZDArOhHt2h0OZdYsLejUuxRmYvrhh/nnd2UHJ9HdrT983H8//ZwG6RNX\nD2ezOi64CO/fL1VvteLa/+XkCwN6f3T6dPp1cDOGAR0IoJR/EtpHd7d+/fHhn9OnT+OWW27BJZdc\ngtdffx1Hjhzp++r+8IdDG1/MxOjRE/Dqq6/i0Ud/A6WuwI03+m8jJIlwfC/Ytjscyltv6VvllIAN\ng5mYPuccXqsB8GcH+9i6VX9fd+6knzOK9ImrD1t1/NRTvFaKjYKL8H33SdVbjfj2fzn5woAe6ho8\nmP6GmyZj+L779LFpwt7vuSffT/rQoUPIZrP9vjKZDLLZLLZu3dqXE/zFL76LuXPn9pl1XHDBIowb\nd8orWEkibNsL5uQOA/rNaMgQXs8d0INc2awe1qJ6TAPJ2cEu7r5b39mIh19wkD5xdRKtjs8/v3C3\nqAsuwidPyqfDaiJ0/5eTL2wGnXxuUTa4GcNmEnr0aF6ykoHjJ23LCQbCEpZ8Iuxzx6LkDgP9faK5\nmMSkIUNoHtMALTs4zvjx6T5Y2ZA+cfXy7ruFe66i7wkL5YvL/9kGpy/c26udrDj7oNSM4egktAkG\n4MTyGSh+0q6cYCAsYcknwj53LEruMJDvE83BJCZRPaYBenaw4ehRvngnIX1iIS0iwgILn/+zDW5f\neMECbQlJhZIxHJ+E5iQrxQnxkwb8OcGGpGrYJcIhHtEhucMGm080hXhiEsVjGuBlBwPA6tX6PJ7Z\ntlRIn1hIg4iwQCbE/zkOty9spo0PH6YdF5ox7PKEpiQr2Qjxkwb8OcHR5/JVwy4RDvWITsodBvw+\n0aHYEpNCPKYBfnYwAMybpz+MDCTSJxa4iAgLwVD8n21w+sLHj/PEG0jOGPZ5QocmK/lI8pNOygmO\n4quG42Ydra2tpKQkX+6wwecTHYotMSnEYxrgZwefOaM/YIQ4nhUC6RMLVESEhSAo/V8XnL4woG+D\ntrTQz5eUMezzhA5JVkrC5ycdkhMcf7yrGrZVwtSkJN/ucIhPdBK+xKQkj2mAnx28Z48+76ZN9GO5\nSJ9YoCAiLCRC7f+64PaFly/Xe78h1pFRfBnDIZ7QvmSlUFx+0mbIiTL57aqG4yLMyQv27Q6H+kT7\nSEpMcnlMA/zsYCC3V/yhYdlZQ/rEQigiwoIXTv/XBbcvvG2bfjPbvp1+TlvGcKgntC9ZKZSon7TB\n7AR/6Uu053JVw3ER5uYF23aHqT7RLkISk1wT09zsYEAPcs2aRT+uEEifWAhBRFiwkrb/64LTF+7p\n0UNWK1bQzxfPGKZ4QruSlagYP2mDayc4BFs1HBVhThUcJb47zPGJjkNJTLJNTHOzgzs7dQVP2dce\nCKRPLPgQERbyKET/1wW3LzxnjnZLohLNGHZNQvuIJytxiPpJ+3aCQ7BVw1ER5lbBhvjuMNcnOgo1\nMSk6MZ0mO3jDBv13cfAg/dhCI31iwYWIsNCPQvV/XXD7wma9hRPBN3ky0NTknoT2EU1W4mL8pP/5\nn5N3gkOIV8NGhN99tyNVFWwwu8P//u98n2gDJzEpOjFtPsBwPlQsWcKroAcK6RMLNkSEhT4K2f91\nwe0Lm+nadevo53z4Yd2X44rplCk6iCQN99yj7ywk7QSHEK+GjQivXt2RqgqO8sUv6oGmhga+TzSQ\nq/ypt7PNxHRjo66iOatRo0blB2kUG+kTC3GySqh6uruV+upXlVq0SKn585XavFmpj31sYM41ZIhS\n48crtWUL7biPf1ypsWOV2riRd87Tp5Vqblbqjjvox8+dq9R//7dSR47QjzV89rNK9fQodeONSn3y\nk/znUUqpTEapFSuU2rlTqZdeyv3+gw8qddNNSk2Zku75lVLqoYeU+uADpS65RKnaWv7zrF6t1GWX\nKTVpEu24IUOU+tWvlOroUOrcc5UCaMf/3/8p9b//q9T06bTjBppMRv+sbd6s1JtvKjVhgv4+CtWL\niHCVc+SIfuN+4gmlfvpTpVau1G96A8nf/70WYeob6/TpWoQpx+3fr9S3vqVUfb1SdXW08xlaWpQa\nNEipZ57hHQ9o0aytVerwYfrrtnHjjUrdcIN+XvN8b7xxm+rqukWtXbs29fP/9rf6ed94Q/8/h64u\npX7xC/0hJpOhH9/To1Rvr1JHjyp15520Yzdu1N+zm26in/dsMHmyFt8LL9T//9RTxb4ioWgUuxQX\nisdA939dcPvCZlJ3//6wx0cnob/9bX7GMAA0N/OTlcxO8EMP8SMWbZje8DPP6NvRU6Y4lnAZTJyo\nI9u4ucNALjHpwAHeNZgd3x//mOYxDQCzZ+tb9qWO9IkFEeEq5Wz0f11w+8KnTrnNN+LEJ6HTZAwD\nwC9+wUtWiu4Eh/pJh2J6w5ddpkX4pZcKI8JRn2hu7jCQS0ziEs0ODvWYBrSQ1dcD99/PP/fZRPrE\n1Y2IcJUxUPu/VDj7woD2Hp4+3f8Ymyc0N2PYwE1Wiu8EJ/lJU3n5ZUApd5Qhh7hPNDV3GMhPTKIS\nzw4O9ZgG9GCaUvrDRDkh+8TViYhwFTGQ+79UuPvCjzyiBeEvf/E/xjYJTc0YjkNNVrLtBPv8pDno\nW75ahN97L70I23yiqbnDgD0xiYItOzjEYxrQgRjDh6dbAysWsk9cfYgIVwnF6v+64PaFjQ2ky3PZ\n5wlNyRi2QUlW8uUEu/ykqRh3rKuv1iK8bl16EXb5RFNyhwF7YhIFV3awz2PaMH58epvNYiJ94upC\nRLgKKGb/1wW3L9zbq9ONbA5KSZ7QoRnDLijJSr6cYJufNAfjjvXii1qEx43rSGVMkeQTHZI7DPgT\nk0JIyg52eUwDup+a1lylFJA+cfUgIlzBlEr/1wW3L7xggR5wihLqCZ2UMZxESLJSSE5w3E+aStQj\n2ph1KNVhzRsOJcknOiR3GEhOTEoiJDvY5jENAKtX69/n+HKXItInrnxEhCuUUur/uuD2hY2V4eHD\n+tcUT+ikjOEkkpKVQnOCo37SHKIe0UaEGxtnYsiQJqxZ08p6zhCfaF/usCEkMclHaHawbWJ63jz9\nGioJ6RNXNiLCFUip9X9dcPvCx4/nbmXbJqF9+DKGQ0hKVgrNCTZ+0hxbxXhSkhHhDRs6rHnDIbz1\nVphPtC93GKAlJtmgZAfHJ6bPnNFVoy8julyRPnHlIiJcYZRi/9cFty8MaDOJlhb3JLQPW8YwBVey\nEjUn+J57gNpa+m3beFKSEeH33uuw5g2H8K//qsUsxCfatztMTUyKQ80Ojk5Mm2n0TZt45y51pE9c\nmYgIVwil3v91we0LL1+uV31ck9A+4hnDVFzJStSc4D/+UYsZJe/WlhccjTK05Q0n8cEHWjjvvDP8\nGNvuMCcxKQ4nO9hMTF9+uXbY6urin78ckD5xZSEiXAGUQ//XBbcv/PTTWmxuuME+Ce0jmjHMJZ6s\nxM0JnjNHV3Khr9+WFxwVYVvecBLmFvqbb4Zft213mJuYZEiTHbx5s/6ejhzJO3e5IX3iykFEuMwp\nl/6vC05f2ExCZ7P+CWQfkyfrVSYujz+uz//OO/6d4CQ2bw6307RVwUB/EQby84aTmDiRt9Mb3x1e\ntChdfu8rr/Czgzs79V0Fqsd0OSN94spARLiMKaf+rwtqXzg6CT1zpvYX5vDww/p2Kjcr98QJ/Xf/\nwx/6d4KToPhJ26pgIF+EKdVw1Ceag9kd/tOfdE/5e9/jPQ8ALFume+qckI0NG/Tr+PKXwz2mKwHp\nE5c/IsJlSLn2f12E9oXjk9DGGjHJPMLG73+v//6ef55+rKG5WU9KJ+0EJxHiJ+2qgoF8EQbCq+G4\nTzQVszs8bVq6xCRA302YP5937JIlugrv7g73mK4kpE9cvogIlxnl3P91EdoXjk9CG2emdet45/3k\nJ4E77uAdC+jzKqVFzLcTnESIn7SrCtbH54twSDVs84nmYHaHr7yS/xwHDujn+M//5B0/alRu3SvU\nY7rSkD5xeSIiXEaUe//XRUhf2OUJPXYssHAh77zf+166jOEnn9TXXQifYp+ftK8KBnIiPHPmTDQ1\nNaG1VZt1JFXDLp9oKseO6aGoCy7g9yVNdrAvmMNFe3v+LfUQj+lKRPrE5YeIcJlQCf1fF0l9YZ8n\n9NKlvOlqIF3GsNkJ/sQnaMlKLnx+0r4qGLBXwoC/Gk7yiaZg2gLZLC93GOifHUzlscd0TzS+b+3z\nmK5kpE9cXogIlziV1v914eoLJ3lCG7/j/fvp50yTMWx2go0NZiHuTNj8pJOqYMAtwoC7Gk7yiaZg\nEpM4ucNAfnYwldmz9YcNGy6P6WpA+sTlgYhwCVOJ/V8Xtr5wiCf0qVPpbCg5GcPRnWBKslISNj/p\npCoY8IuwqxoO8YkOIZqYxMkdBuzZwaF0d+u7JPff736MzWO6WpA+cekjIlyiVGr/10W8L0zxhJ42\nTb/xc6BmDNt2gkOSlQBgxYoVGDNmDGpra9HY2Iibb74ZO3bs6Pvz7m7gb//2BEaNuh0NDQ0YOnQo\nhg1biKlT/XtUPhEG8qvhUJ/oEOKJSdTcYcCdHRzC1q36fDt3uh8T95iuNqRPXNqICJcgldz/dRHv\nC1M8oR95RN8G5Qz1UDOGbTvBSclKhrVr12LTpk1466230NbWhkWLFmHIkCE4FikBR42agWx2HDZv\nfg0PPLANSo3GtGlzvc+bJMLxapjiE52ELTEpNHdYX7s/OziJu+/Wd0qSTFKqdWLaIH3i0kVEuISo\nlv6vC9MXdk1CuzBDTUnJRS5CM4ZdOcFJyUou3n//fWQyGfz6w8mwtrY2ZDIZZLO78eij+nbxNdf8\nF2pqavCOx5A6SYSBXDX8/PN0n2gXrsSk0NxhICw72Mf48eHDZdU6MR1F+sSlh4hwiVBN/V8Xd92l\n3yBck9Auent1X5bjOQyEZQwn5QS7kpVcdHd34wc/+AEaGxtx/MPSbNWqVRg2bBjmzNGvR09un8ag\nQYOwfv1653OFiLCphi+7jO4T7cKXmBSSOwyEZwfbOHqUPtBVrRPTUaRPXFqICJcA1db/dbFmTc70\nIVTMDAsWaPtHDiEZw0k5wa5kpTgvvPAC6urqkM1mcfHFF2NnpJn5wAMPYMyYMX1VqxGnESNGYOXK\nlc7nDBFhAHnPm4akxKSk3GGAlh1sY/Vq/XpCU6sM1TwxbZA+cemQVUJRefJJpaZMUerSS5XatUup\nSZOKfUXFobtbqR//WP//ggVK1dfTjp8+Xam2NqX+8Af6uevqlJo2Tan16+1/fvy4Ut/6llJf+pI+\nj42RI/X3cc0a/evW1lZVX1+v6uvrVUNDg9q2bZtSSqmbbrpJ7du3T23fvl3NmDFDtbS0qGPHjvV7\nrvfe0/81fwcAVCaTSXwdt912m7rlllv6fa1du7bvzxsa9H/ff18pIPHpvPzP/+i/63/8R/uf19Qo\n9dOfKnXggFKPPGJ/zJYtSnV2KtXczLuGjRuVuuYapS64gHbcokVKLV2q1J13KvXyy7xzlzuDByv1\nxBP6Z+4nP1Hq5puV+vOfi31VVUqxPwVUK9Xe/40SnYS+8kpevvDx47QgiDi+jOHQnOBostLJkyfR\n3t7e99XlCLkdPXo0HnzwQQC529HXXANccYVeqzl0qDC3o83rGDGCnjdsIzQxybc7zMkONpw5o1sX\n1CxpQ7VPTEeRPnFxEREuAtL/7U90EpqbLwzoSL6WFt41uDKGKTnB0WSlUC6//HLc++H92AMHDiCb\nzUKp3XjpJe0nPXfuxoIMZhmf6Pvvp+cNx/ngg/DEJNfucJrsYADYs0d/XzZt4h0PyMR0FOkTFw8R\n4bOM9H/7E5+E5uQLG5Yv117QoQNdceIZw5yc4OZmYMKE/N8/deoUvvvd7+KVV17B22+/jV27dmH+\n/Pk477zz0NbWBkCfo75+JurrJ+DVV19Fc/NvUFNzBW6/3X9rIESEoz7R1LzhOL/8JS0xybY7nCY7\nGMh5TTtuMAQjE9M5pE9cHESEzyLVuP/rw3hCNzXlhJOaLxzlt7/VbyDbt/OuJ54xzMnx2pt3AAAA\n8klEQVQJNpPWcYHq6urCrbfeiosvvhiDBw/GRRddhObmZuzatavvMdod611MmzYXDQ0NaGgYCqUW\n4amn/BFNSSIc94mm5A3buPVWvRpEIb47nCY7GNDmHl/4Au/YOFu26O/z4sXpHcTKHdknPvtkgLQj\nGoIgFJP3339fDRkyRHV0dKgGM30lCEJZICIsCGUOANXZ2anq6+uDpqgFQSgdRIQFQRAEoUjInrAg\nCIIgFAkRYUEQBEEoEiLCgiAIglAkRIQFQRAEoUiICAuCIAhCkRARFgRBEIQiISIsCIIgCEVCRFgQ\nBEEQioSIsCAIgiAUif8HtSV6s3ZJZfkAAAAASUVORK5CYII=\n", "text/plain": [ "Graphics object consisting of 21 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt = Graphics()\n", "var('c')\n", "f = -c^2+c*x \n", "for j in range(0,20,1):\n", " plt += plot(f(c=-10 + j) ,-20,20,thickness=1)\n", "plt2 = plot(1/4*x^2,-20,20,color='red',thickness=2)\n", "(plt+plt2).show(ymin=-30,ymax=30,figsize=5,aspect_ratio=0.4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

ΣΔΕ με παραμέτρους - Το λογιστικό πληθυσμιακό μοντέλο

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\n", "Το 1838 ο Βέλγος µαθηµατικός Pierre François Verhulst διατύπωσε το λογιστικό μοντέλο πληθυσμιακής ανάπτυξης. Σύμφωνα με το μοντέλο αυτό ο πληθυσµός P συχνά αυξάνεται εκθετικά στα αρχικά στάδια ζωής του όµως σταδιακά φτάνει στο όριο χωρητικότητας, εξαιτίας περιβαλλοντικών πιέσεων και περιορισµένων διατροφικών πόρων. Για να περιγράψουµε το γεγονός ότι η σχετική ανάπτυξη µειώνεται καθώς ο πληθυσµός αυξάνει και γίνεται αρνητικός αν το P ξεπεράσει την φέρουσα χωρητικότητα Κ του περιβάλλοντος, δηλαδή τον µέγιστο πληθυσµό που είναι ικανό να υποστηρίξει το περιβάλλον µακροπρόθεσµα, θεωρούµε ότι ο σχετικός ρυθµός ανάπτυξης δίνεται από την ΣΔΕ

\n", "$$ \\frac{1}{P}\\,\\frac{\\mathrm{d}\\,P}{\\mathrm{d}\\, t} = r\\,(1-\\frac{P}{K})\\quad \\Leftrightarrow \\quad \\frac{\\mathrm{d}\\,P}{\\mathrm{d}\\, t} = r\\,P\\,(1-\\frac{P}{K}) $$
\n", "όπου $r,K$ παράμετροι με τιμές στους θετικούς πραγματικούς αριθμούς. Ας επιλύσουμε την ΣΔΕ αυτή με την βοήθεια του Sage" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [], "source": [ "reset()\n", "var('t r K');\n", "assume(r>0); assume(K>0);\n", "P = function('P')(t);" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "diff(P(t), t) == -r*(P(t)/K - 1)*P(t)\n" ] } ], "source": [ "SDE = diff(P,t) == r*P*(1-P/K); print SDE" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-(log(-K + P(t)) - log(P(t)))/r == _C + t\n" ] } ], "source": [ "sol = desolve( SDE,[P,t]); print sol" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "Παρατηρούμε ότι το Sage μας δίνει την λύση σε πεπλεγμένη μορφή όπου εμφανίζεται και πάλι η συνάρτηση λογαρίθμου. Για να μπορέσουμε να λύσουμε ως προς την εξαρτημένη μεταβλητή $P$ θα πρέπει να χρησιμοποιήσουμε μεθόδους του Sage που γνωρίζουν ταυτότητες που ισχύουν για την συνάρτηση του λογαρίθμου. Η μέθοδος αυτή είναι η simplify_log. Με τις παρακάτω διαδοχικές εντολές οδηγούμε το Sage να μας δώσει την λύση ως προς την μεταβλητή $P$" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-_C - t - (log(-K + P(t)) - log(P(t)))/r\n" ] } ], "source": [ "Sol = sol.lhs() - sol.rhs() ; print Sol" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-(_C*r + r*t + log(-(K - P(t))/P(t)))/r\n" ] } ], "source": [ "Sol2 = Sol.simplify_log(); print Sol2" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "P(t) == -K/(e^(-_C*r - r*t) - 1)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Sol3 = solve(Sol2, P)[0].simplify() ; Sol3.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "Οπότε η γενική λύση της ΣΔΕ του λογιστικού πληθυσμιακού μοντέλου είναι η

\n", "$$ P(t) = \\frac{K}{1-e^{-r\\,(t+c)}} \\,.$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 8.1.2 Γραφική απεικόνιση των λύσεων μιας ΣΔΕ - ολοκληρωτικές καμπύλες " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "Ας θεωρήσουμε την αμέσως προηγούμενη ΣΔΕ του λογιστικού πληθυσμιακού μοντέλου και ας υποθέσουμε ότι θέλουμε να απεικονίσουμε γραφικά την λύση μας για διάφορες τιμές της σταθερής ολοκλήρωσης. Πρώτα απ'όλα ας δούμε ποιές θεωρεί το Sage ως συμβολικές μεταβλητές στην παραπάνω λύση." ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(K, _C, r, t)\n" ] } ], "source": [ "print Sol3.variables()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "Το Sage θεωρεί ως μεταβλητές την σταθερή ολοκλήρωσης _C, την ανεξάρτητη μεταβλητή t, καθώς και τις παραμέτρους $r,K$. Την $P$ το Sage δεν την θεωρεί μεταβλητή γιατί η $P$ δηλώθηκε ως συνάρτηση του t παραπάνω. Η σταθερή ολοκλήρωσης _C έρχεται από την διαδικασία ολοκλήρωσης της ΣΔΕ που εκτελεί το Maxima, και για να έχουμε πρόσβαση σε αυτή θέτουμε την δεύτερη συνιστώσα στο αποτέλεσμα .variables() σε μια συμβολική έκφραση. Έπειτα αντικαθιστουμε τόσο την συνάρτηση y(x) όσο και την _C σε νέες συμβολικές εκφράσεις π.χ. w και c αντίστοιχα, με σκοπό να τις χειριστούμε κατάλληλα για την γραφική απεικόνιση της λύσης μας. Τα προηγούμενα υλοποιούνται στο Sage με τις ακόλουθες εντολές." ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "p == -K/(e^(-c*r - r*t) - 1)\n" ] } ], "source": [ "k = Sol3.variables()[1]\n", "var('c p')\n", "lysh = Sol3.subs({P(t):p, k:c}); print lysh" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "Ας υποθέσουμε τώρα ότι ο αρχικός πληθυσμός είναι $P(0)=P_0$. Θέτοντας $t=0$ στην λύση που βρήκαμε έχουμε" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "p0 == -K/(e^(-c*r) - 1)\n" ] } ], "source": [ "var('p0')\n", "lysh0 = lysh(t=0,p=p0) ; print lysh0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "Οπότε η σταθερή ολοκλήρωσης c μπορεί να εκφρασθεί ως συνάρτηση της αρχικής συνθήκης $P_0$ και της παραμέτρου K. Πραγματικά" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "p == K*p0*e^(r*t)/(p0*e^(r*t) + K - p0)\n" ] } ], "source": [ "c_sub = solve(lysh0,c,solution_dict=true);\n", "lysh_p0 = lysh.subs(c_sub).simplify_full() ; print lysh_p0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "Δηλαδή η λύση παίρνει την μορφή\n", "$$ P(t) = \\frac{K\\,P_0 \\, e^{r\\,t}}{P_0\\,e^{r\\,t} + K - P_0}$$\n", "όπου τώρα μπορούμε να θέσουμε διάφορες τιμές στην συμβολική μεταβλητή που εκφράζει την αρχική συνθήκη $P_0$. Πράγματι" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [], "source": [ "plt = Graphics()\n", "for j in range(0,10,1):\n", " plt += plot(lysh_p0.rhs()(K=1,r=0.5,p0=j/4),0,9,thickness=1.3)" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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pMtfSG28AH34IVFfL98eMkfdcsMD3HdKJiIgChcHIR5qaZCbqN9+UWiS1UO2Y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\nidE7WtfVSXA5e1bKrIKTMUS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7+8w/aIgokCya5mo5yuBx7hyQn2/DJZdYUVVVhcTExEAX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\n", "text/plain": [ "Graphics object consisting of 10 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.show(figsize=6,ymin=0,ymax=2.5,aspect_ratio=2, axes_labels=['$t$','$P(t)$'], \\\n", " ticks=[[],[1,0.5]], tick_formatter=[[],[\"$K$\",\"$K/2$\"]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "Παρατηρούμε, όπως αναμέναμε άλλωστε, ότι υπάρχουν δυο λύσεις ισορροπίας, η $P=0$, και η $P=K$. Επίσης παρατηρούμε από το σχήμα ότι αν $ 0 < P_0 < K $, ο πληθυσμός αυξάνεται γρηγορότερα όταν φτάσει στο μισό της φέρουσας χωρητικότητας. Πράγματι, η δεύτερη παράγωγος $P''(t)$ υπολογίζεται από την ίδια την ΣΔΕ και είναι " ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(K - P(t))*(K - 2*P(t))*r^2*P(t)/K^2\n" ] } ], "source": [ "print diff(SDE.rhs(),t).subs({diff(P,t) : SDE.rhs()}).factor()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "Αφού $P(t)=0$, και $P(t)=K$, είναι λύσεις ισορροπίας, από την δεύτερη παράγωγο που υπολογίσαμε αμέσως παραπάνω, συμπεραίνουμε ότι ο ρυθμός αύξησης του $P'(t)$ έχει ακρότατη τιμή (μέγιστο) όταν $P(t)=K/2$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "Ας θεωρήσουμε τώρα την ΣΔΕ χωριζομένων μεταβλητών \n", "$$y'\\,\\log y = y\\,\\sin x\\,.$$ \n", "Θα βρούμε πρώτα συμβολικά την γενική της λύση με το Sage, κι έπειτα θα απεικονίσουμε γραφικά την γενική λύση (δηλαδή θα βρούμε τις ολοκληρωτικές καμπύλες της ΣΔΕ) για διάφορες τιμές της σταθερής ολοκλήρωσης." ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1/2*log(y(x))^2 == _C - cos(x)\n" ] } ], "source": [ "reset()\n", "x = var('x')\n", "y = function('y')(x)\n", "sol = desolve(diff(y,x)*log(y) == y*sin(x), y); print sol" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "Θα πρέπει τώρα να βρούμε πως έχει διαχειριστεί το Sage την σταθερή ολοκλήρωσης." ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(_C, x)\n" ] } ], "source": [ "print sol.variables()" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1/2*log(w)^2 == c - cos(x)\n" ] } ], "source": [ "k = sol.variables()[0]\n", "var('c w')\n", "lysh = sol.subs({y(x):w, k:c}); print lysh" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [], "source": [ "P = Graphics()\n", "for j in range(1,20,1):\n", " P += implicit_plot(lysh(c=-3+j/4),(x,-3*pi,3*pi),(w,0,3),plot_points=350)" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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6vpJt8WZn47viyFEkYld1P3hQn7K1RTq5w4ZIJqzn08nzla/goPnP/+Tv++AD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\nstJdkK31XursxDXLlsmfnbF3LxyntKLyjG9+E3PB2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84558OHc167tnu2r7RyDxw5SWws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\naD0sDM64Vy84nN9+w19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"text/plain": [ "Graphics object consisting of 19 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "P.show(figsize=6,aspect_ratio=4)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "### 8.1.3 ΣΔΕ δεύτερης τάξης" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

ΣΔΕ 2ης τάξης με σταθερούς συντελεστές

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\n", "Ας θεωρήσουμε τώρα ΣΔΕ δεύτερης τάξης με σταθερούς συντελεστές, για παράδειγμα την ΣΔΕ \n", "$$ y'' + y = \\sin x+ x\\, \\cos x $$\n", "Για να βρούμε την γενική της λύση εκτελούμε τις παρακάτω εντολές" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": true }, "outputs": [], "source": [ "x = var('x'); y = function('y')(x)\n", "SDE = diff(y,x,2) + y == sin(x) + x*cos(x) " ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[_K2*cos(x) - 1/4*x*cos(x) + 1/8*(2*x^2 - 1)*sin(x) + _K1*sin(x), 'variationofparameters']\n" ] } ], "source": [ "sol2d = desolve(SDE, y,show_method=True); print sol2d" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "Η μέθοδος που χρησιμοποιεί το Maxima για την εύρεση της γενικής λύσης της παραπάνω ΣΔΕ είναι η μέθοδος μεταβολής των παραμέτρων, ή μέθοδος Lagrange. Αν μας δίνεται το ΠΑΤ που απαρτίζετια από την ΣΔΕ και τις αρχικές συνθήκες $y(0)=1$, $y'(0)=2$, τότε για την επίλυση του ΠΑΤ εκτελούμε" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-1/4*x*cos(x) + 1/8*(2*x^2 - 1)*sin(x) + cos(x) + 19/8*sin(x)\n" ] } ], "source": [ "sol2d_pat = desolve(SDE, y, ics=[0,1,2]); print sol2d_pat" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "ενώ για το πρόβλημα συνοριακών τιμών (ΠΣΤ) $y(0)=0$, $y(1)=0$, η λύση που μας δίνει το Sage είναι" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-1/4*x*cos(x) + 1/8*(2*x^2 - 1)*sin(x) + 1/8*(2*cos(1) - sin(1))*sin(x)/sin(1)\n" ] } ], "source": [ "sol2d_pst = desolve(SDE, y, ics=[0,0,1,0]); print sol2d_pst" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "Όμως δεν έχει υλοποιηθεί ακόμα συμβολικός αλγόριθμος στο Sage που να επιλύει προβλήματα συνοριακών τιμών με μικτές συνοριακές συνθήκες, για παράδειγμα συνοριακές συνθήκες της μορφής $y(0)-y(1)=0$, $y'(0)-y'(1)=0$. Μια μέθοδος για να επιλύσουμε τέτοιου είδους ΠΣΤ είναι μέσω της αναλυτικής κατασκευής της λεγόμενης συνάρτησης Green, η οποία (αν υπάρχει) κατασκευάζεται με αλγοριθμικό τρόπο, αρκεί ο χρήστης να έχει τις κατάλληλες γνώσεις. Μια τέτοια αναλυτική διαπραγμάτευση είναι έξω από τους στόχους των σημειώσεων αυτών." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

ΣΔΕ Euler

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\n", "Πρόκειται για γραμμικές ΣΔΕ 2ης τάξης της ακόλουθης μορφής\n", "$$ a\\,x^2\\,y'' + b\\,x\\,y' + c\\,y = f(x) $$\n", "\n", "όπου $x\\neq 0$ και $f(x)$ συνεχής συνάρτηση σε κάποιο κατάλληλο διάστημα. Για παράδειγμα" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1/10*x^2*cos(log(x))^2 + 1/10*x^2*sin(log(x))^2 + (_K2*cos(log(x)) + _K1*sin(log(x)))/x\n" ] } ], "source": [ "reset()\n", "x = var('x'); y = function('y')(x)\n", "SDE = x^2*diff(y,x,2) + 3*x*diff(y,x) + 2*y == x^2\n", "sol = desolve(SDE, y); print sol" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Ειδικές συναρτήσεις

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\n", "Το Sage γνωρίζει πάρα πολλές (αν όχι όλες) ΣΔΕ οι λύσεις των οποίων ορίζουν τις λεγόμενες ειδικές συναρτήσεις. Για παράδειγμα, οι συναρτήσεις Airy του πρώτου και δεύτερου είδους στο Sage είναι οι συναρτήσεις airy_ai και airy_bi, και οι οποίες είναι δυο γραμμικώς ανεξάρτητες λύσεις της ΣΔΕ $y'' + x\\,y=0$. Πράγματι" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0\n" ] } ], "source": [ "reset()\n", "var('x c1 c2')\n", "y = c1*airy_ai(x) + c2*airy_bi(x)\n", "SDE = diff(y,x,2) - x*y ; print SDE.expand()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "Το όριο καθώς $x\\rightarrow \\infty$ των αντίστοιχων συναρτήσεων είναι" ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0\n", "+Infinity\n" ] } ], "source": [ "print limit(airy_ai(x),x=oo);\n", "print limit(airy_bi(x),x=oo);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "και η γραφική τους παράσταση ακολουθεί" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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x148/xpAhQwCQe/of/6DtFhMT6TxOcdk7YCFmGKb3sGkT8H//B3z6KRAUBFxz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BaxQCBQpKiIMnlOnwYeeUTlwIkTqcXWL35Be6v/+q9UoUQxHDzwLFniCdzW4vhxTw1wAOaEmA0Y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\nRU5ErkJggg==\n", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_ai = plot(airy_ai(x), (x, -20, 5) , color='blue', legend_label='Ai(x)') ;\n", "plot_bi = plot(airy_bi(x), (x, -20, 5) , color='red' , legend_label='Bi(x)') ;\n", "(plot_ai + plot_bi).show(ymin=-0.5,ymax=1,figsize=5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "Ένα πολύ ενδιαφέρον πρόβλημα της φυσικής, η κβαντική μπάλα, ανάγεται στην επίλυση της παραπάνω ΣΔΕ και οι συνοριακές συνθήκες του προβλήματος αυτού επιβάλλουν οι τιμές της ενέργειας $q_Ε$ να είναι κβαντισμένες $n=1,2,3,\\ldots$, και οι οποίες υπολογίζονται από τις ρίζες της συνάρτησης Ai(x)=0. Στο Sage μπορούμε να βρούμε τις ρίζες τις συνάρτησης Ai(x) μέσω του SciPy, ως εξής" ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "import pylab\n", "from scipy.special import airy, ai_zeros" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ -2.33810741 -4.08794944 -5.52055983 -6.78670809 -7.94413359\n", " -9.02265085 -10.04017434 -11.0085243 -11.93601556 -12.82877675\n", " -13.69148904 -14.52782995 -15.34075514 -16.13268516 -16.905634\n", " -17.66130011]\n" ] } ], "source": [ "a = ai_zeros(int(16)) ; print a[0] # οι πρώτες 16 ρίζες της συνάρτησης Ai(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "Στο παρακάτω γραφικό απεικονίζουμε τις πρώτες 16 ρίζες της Ai(x) παρέα με την συνάρτηση Ai(x)." ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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yVeAVfvYzym+Jtm0mYxVHhbjjHKcUYtXzfB3X8sWKIw62e4384uuaAwwlhk6U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\nLQL+/W/pbVtRIeHEVJOdLaIUCEhBgGAQmD079eMonMeymprkVpfwA+L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"text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ppoints = [ (a[0][i],0) for i in range(16) ] ; \n", "plotp = points(ppoints,color='red',size=30) ; (plotp+plot_ai).show(figsize=5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "Είναι περιττό να πούμε ότι στο Sage υπάρχουν διαθέσιμες σχεδόν (αν όχι) όλες οι ειδικές συναρτήσεις όπως οι υπεργεωμετρικές, Ηermite, Laguerre, Legendre, Chebyshev, οι ελλειπτικές συναρτήσεις Jacobi, κτλ." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 8.1.4 Μετασχηματισμός Laplace" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "Ο μετασχηματισμός Laplace μετατρέπει μια γραμμική ΣΔΕ και τις αρχικές συνθήκες σε μια αλγεβρική εξίσωση για την εξαρτημένη μεταβλητή σε έναν παραμετρικό χώρο $y(s)$, και με τον αντίστροφο μετασχηματισμό Laplace ανακτούμε την λύση $y(x)$ της ΣΔΕ οι οποία ικανοποιεί τις δοσμένες αρχικές συνθήκες.
\n", "Ειδικότερα, αν η συνάρτηση $f(t)$ ορίζεται για $t \\geq 0$, και ικανοποιεί τις συνθήκες που θα αναφερούμε παρακάτω, ο μετασχηματισμός Laplace της $f(t)$ ορίζεται από την σχέση

\n", "$$ \\mathcal{L}[f(t)]= F(s) = \\int_0^\\infty e^{-s\\,t}\\,f(t) \\, {\\mathrm{d}}\\, t \\,. $$
\n", "Πρόκειται για έναν ολοκληρωτικό μετασχηματισμό, και συνεπώς το παραπάνω γενικευμένο οφείλει να συγκλίνει για να έχει νόημα ο παραπάνω ορισμός. Ισχύει το ακόλουθο

\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "Θεώρημα : Έστω ότι\n", "

    \n", "
  • Η $f(t)$ είναι τμηματικά συνεχής στο διάστημα $ 0 \\leq t \\leq A$, για οποιονδήποτε θετικό πραγματικό $A$.
  • \n", "
  • $\\left|\\,f(t)\\,\\right| \\leq K \\, e^{a\\,t}$, όταν $t \\geq M$, όπου $K,a,M$ πραγματικές σταθερές, αναγκαστικά $ K, M > 0 $

  • \n", "Τότε ο μετασχηματισμός Laplace $\\mathcal{L}[f(t)]= F(s)$, που ορίστηκε παραπάνω, υπάρχει για κάθε $s > a$.

    \n", "Στο Sage ο μετασχηματισμός Laplace υλοποιείται με την εντολή laplace. Για παράδειγμα, στα παρακάτω βρίσκουμε τον μετασχηματισμό Laplace των συναρτήσεων $i)\\,\\, e^{a\\,t}$, $ii)\\,\\, \\sin a\\,t$ και $iii)$ της αλματικής συνάρτησης unit_step που γνωρίζουμε από προηγούμενα κεφάλαια." ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-1/(a - s)\n" ] } ], "source": [ "var('s t a')\n", "f = exp(a*t)\n", "print f.laplace(t,s)" ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "a/(a^2 + s^2)\n" ] } ], "source": [ "f = sin(a*t)\n", "print f.laplace(t,s)" ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1/s\n" ] } ], "source": [ "f = unit_step(t)\n", "print f.laplace(t,s)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "

    \n", "Αν $f_1$ και $f_2$ είναι τμηματικά συνεχείς συναρτήσεις των οποίων ο μετασχηματισμός Laplace υπάρχει για $s>a_1$ και $s>a_2$ αντίστοιχα, τότε για $s>\\max (a_1,a_2)$ ισχύει ότι

    \n", "$$ \\mathcal{L}[c_1\\,f_1(t) + c_2\\,f_2(t)] = c_1\\,\\mathcal{L}[f_1(t)] + c_2\\,\\mathcal{L}[f_2(t)] $$
    \n", "που σημαίνει ότι ο μετασχηματισμός Laplace είναι ένας γραμμικός τελεστής στον χώρο των τμηματικά συνεχών συναρτήσεων. Αυτή η ιδιότητα του μετασχηματισμού Laplace είναι πολύ χρήσιμη για την επίλυση γραμμικών ΣΔΕ. Επιπλέον ισχύει το εξής

    \n", "Θεώρημα : Αν η $f$ είναι συνεχής και η $f'$ είναι τμηματικά συνεχής σε οποιοδήποτε διάστημα της μορφής $0 \\leq t \\leq A$, και υπάρχουν σταθερές $K,a$ και $M$ τέτοιες ώστε $\\left| f(t) \\right| \\leq K\\,e^{a\\,t}$ για $t \\geq M$, τότε ο μετασχηματισμός Laplace $\\mathcal{L}[f'(t)]$ της $f'$ υπάρχει και ισχύει ότι \n", "$$ \\mathcal{L}[f'(t)] = s\\,\\mathcal{L}[f(t)] - f(0)\\,. $$\n", "Γενικότερα, με τις κατάλληλες τροποποιήσεις στα παραπάνω, επαγωγικά ισχύει ότι

    \n", "$$ \\mathcal{L}[f^{(n)}(t)] = s^n\\,\\mathcal{L}[f(t)] - s^{n-1}\\,f(0) - s^{n-2}\\,f'(0) - \\cdots - s\\,f^{n-2}(0) - f^{n-1}(0) \\,. $$
    \n", "Ειδικότερα ισχύει ότι \n", "$$ \\mathcal{L}[f''(t)] = s^2 \\mathcal{L}[f(t)] - s\\, f(0) - f'(0)\\,. $$\n", "Χρησιμοποιώντας τα προηγούμενα και εφαρμόζοντας τον μετασχηματισμό Laplace σε μια γραμμική ΣΔΕ 2ης τάξης με σταθερούς συντελεστές, η ΣΔΕ μετατρέπεται σε μια αλγεβρική εξίσωση για τον μετασχηματισμό Laplace της άγνωστης συνάρτησης. \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

    \n", "Παράδειγμα: Ας θεωρήσουμε το ΠΑΤ \n", "$$ y'' -3\\,y' -4\\,y = \\sin t \\,, \\qquad y(0) = 1 \\,, \\quad y'(0)=-1$$\n", "Εφαρμόζοντας τον μετασχηματισμό Laplace στην προηγούμενη ΣΔΕ και χρησιμοποιώντας την γραμμικότητα του τελεστή $\\mathcal{L}$ και πως μετασχηματίζονται οι παράγωγοι παίρνουμε ότι\n", "

    \n", "$$ (s^2 - 3\\,s-4)\\, \\mathcal{L}[y(t)] - s\\, y(0) - y'(0) + 3\\,y(0) = \\mathcal{L}[\\sin t] \\qquad\\qquad (*)$$\n", "
    \n", "Αν δεν γνωρίζουμε, ή έχουμε ξεχάσει τον μετασχηματισμό Laplace, στοιχειωδών συναρτήσεων όπως της συνάρτησης ημιτόνου, μπορούμε να ζητήσουμε από το Sage να μας βοηθήσει" ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "t |--> 1/(s^2 + 1)\n" ] } ], "source": [ "var('t s'); \n", "f = function('f')(t)\n", "f(t) = sin(t); print f.laplace(t,s)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

    \n", "Με βάση τα προηγούμενα, και χρησιμοποιώντας τις αρχικές συνθήκες $y(0)=1$ και $y'(0)=-1$ η σχέση $(*)$ γίνεται

    \n", "$$ \\mathcal{L}[y(t)] = Y(s) = \\frac{1}{(s^2-3\\,s-4)(s^2+1)} + \\frac{s-4}{s^2-3\\,s-4} $$
    \n", "Οπότε χρησιμοποιώντας τον αντίστροφο μετασχηματισμό Laplace στο Sage βρίσκουμε την λύση του παραπάνω ΠΑΤ" ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3/34*cos(t) + 1/85*e^(4*t) + 9/10*e^(-t) - 5/34*sin(t)\n" ] } ], "source": [ "Y(s) = 1/(s^2-3*s-4)/(s^2+1) + (s-4)/(s^2-3*s-4)\n", "print Y(s).inverse_laplace(s,t)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

    \n", "Αν βέβαια το επιθυμούμε μπορούμε να διασπάσουμε το παραπάνω κλάσμα σε απλά κλάσματα" ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1/34*(3*s - 5)/(s^2 + 1) + 9/10/(s + 1) + 1/85/(s - 4)\n" ] } ], "source": [ "print Y(s).partial_fraction()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

    \n", "και να βρούμε τον αντίστροφο μετασχηματισμό Laplace από τους σχετικούς πίνακες. Όμως αυτό δεν είναι απαραίτητο, αφού στο Sage έχουν ήδη υλοποιηθεί όλα τα παραπάνω με μια εντολή. Για παράδειγμα, το παραπάνω ΠΑΤ λύνεται πολύ απλά ως εξής:" ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1/85*(17*y(0) + 17*D[0](y)(0) + 1)*e^(4*t) + 1/10*(8*y(0) - 2*D[0](y)(0) - 1)*e^(-t) + 3/34*cos(t) - 5/34*sin(t)\n" ] } ], "source": [ "reset()\n", "t = var('t'); \n", "y = function('y')(t)\n", "eq = diff(y,t,t) - 3*diff(y,t) - 4*y - sin(t) == 0\n", "sol_laplace = desolve_laplace(eq, y); print sol_laplace" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

    \n", "όπου οι αρχικές συνθήκες δεν έχουν συγκεκριμένες τιμές. Αν θέλουμε να λύσουμε ένα συγεκριμένο ΠΑΤ, πχ την προηγούμενη ΣΔΕ μαζί με τις αρχικές συνθήκες $y(0)=1$, $y'(0)=-1$, τότε εκτελούμε " ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3/34*cos(t) + 1/85*e^(4*t) + 9/10*e^(-t) - 5/34*sin(t)\n" ] } ], "source": [ "sol_pat = desolve_laplace(eq, y, ics=[0,1,-1]); print sol_pat" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 8.1.5 Εφαρμογές στις ηλεκτρικές ταλαντώσεις" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

    \n", "Από τις πιο ενδιαφέρουσες εφαρμογές των μη ομογενών γραμμικών ΣΔΕ δεύτερης τάξης με σταθερούς συντελεστές, είναι στις ταλαντώσεις ηλεκτρικών κυκλωμάτων που περιλαμβάνουν αντίσταση, πηνίο, πυκνωτή (RLC) και μια πηγή, ή στην παλμική κίνηση μηχανικών συστημάτων κα. \n", "

    \n", " \n", "

    \n", "Η ΣΔΕ που περιγράφει την χρονική εξέλιξη του ηλεκτρικού φορτίου $y=Q(t)$ στο ένα φύλλο του πυκνωτή (στο άλλο φύλλο του πυκνωτή το φορτίο είναι $-Q(t)$) σε ένα απλό ηλεκτρικό κύκλωμα RLC,\n", "είναι της μορφής

    \n", "$$ y''(t) + 2\\,k\\, y'(t) + \\omega_0^2 \\, y(t) = g(t)\\,,$$
    \n", "όπου $k=\\frac{R}{2\\,L}$, και $\\omega_0 = \\frac{1}{\\sqrt{L\\,C}}$, και $g(t)$ είναι ο όρος πηγών και περιγράφει την εξωτερική ηλεκτρική διέγερση του κυκλώματος από μια μπαταρία ή μια γεννήτρια. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

    Κύκλωμα LC - Περιοδικές ταλαντώσεις

    \n", "

    \n", "Ας υποθέσουμε ότι δεν υπάρχει εξωτερική διέγερση από πηγές ($g(t)=0$) και το κύκλωμα αποτελείται μόνο από ένα πηνίο και έναν πυκνωτή, δηλαδή δεν υπάρχει αντίσταση και κατά συνέπεια όρος απόσβεσης. Αν η αρχική τιμή του φορτίου στο ένα φύλλο του πυκνωτή είναι $y(0)=1$, και η αρχική ένταση του ρεύματος $y'(0)=0$, τότε η λύση του ΠΑΤ είναι" ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "cos(t*w0)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "reset()\n", "var('t w w0'); \n", "assume(w0>0);\n", "y = function('y')(t)\n", "eq = diff(y,t,t) + w0^2*y == 0\n", "sol = desolve(eq, y, ivar=t , ics=[0,1,0]); sol.show()" ] }, { "cell_type": "code", "execution_count": 59, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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tzaP/zW3aAF27qq2LGf785z9jyJAhiI+PR0pKCiZNmoRtZ20qf/r0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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt1 = plot(sol(w0=1),(t,0,20), \\\n", " legend_label='$\\,\\,\\cos(t)$', thickness=2);\n", "(plt1).show(figsize=5,ymin=-1.5,ymax=1.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

    \n", "Όπως φαίνεται από το σχήμα, το ηλεκτρικό φορτίο στα άκρα του πυκνωτή μεταβάλλεται περιοδικά. Ουσιαστικά, καθώς το φορτίο αποκακρύνεται από τους οπλισμούς του πυκνωτή, η μεταβολή στο φορτίο αλλάζει το μαγνητικό πεδίο στο πηνίο, ή με άλλα λόγια η αποθηκευμένη ηλεκτρική ενέργεια στους οπλισμούς του πυκνωτή μετατρέπεται σε μαγνητική ενέργεια στο πηνίο. Η διαδικασία συνεχίζεται μέχρι οι οπλισμοί να φορτισθούν με αντίθετο φορτίο και μετά η διαδικασία συνεχίζεται αντίστροφα. Ο φορτισμένος πυκνωτής αποφορτίζεται και κάποια στιγμή επανέρχεται στην αρχική του κατάσταση και η όλη διαδικασία επαναλαμβάνεται από την αρχή." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

    Εξαναγκασμένη ταλάντωση

    \n", "

    \n", "Ας υποθέσουμε τώρα ότι υπάρχει εξωτερική διέγερση και είναι περιοδική, για παράδειγμα $g(t)= \\cos \\omega\\,t$, με $\\omega>0$, και ότι και πάλι δεν υπάρχει όρος απόσβεσης (δηλαδή αντίσταση στο κύκλωμα $k=0$). Τότε η ΣΔΕ παίρνει την μορφή

    \n", "$$ y''(t) + \\omega_0^2 \\, y(t) = \\cos \\omega \\, t\\,.$$
    \n", "Η γενική λύση της ΣΔΕ είναι η" ] }, { "cell_type": "code", "execution_count": 60, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "_K2*cos(t*w0) + _K1*sin(t*w0) - cos(t*w)/(w^2 - w0^2)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "reset()\n", "var('t w w0'); \n", "assume(w0>0); assume(w>0);\n", "y = function('y')(t)\n", "eq = diff(y,t,t) + w0^2*y - cos(w*t) == 0\n", "sol = desolve(eq, y, ivar=t); sol.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

    \n", "όπου $K_1$, $K_2$ σταθερές ολοκλήρωσης που καθορίζονται από τις αρχικές συνθήκες.\n", "Υπάρχουν δυο ενδιαφέρουσες περιπτώσεις: α) $\\omega_0 \\neq \\omega\\,$, αλλά $\\left|\\,\\omega_0 - \\omega\\,\\right| $ πολύ μικρό, και β) $\\omega_0 = \\omega$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

    Διαμόρφωση πλάτους

    \n", "

    \n", "Ας υποθέσουμε ότι αρχικά $y(0)=y'(0)=0$ τότε" ] }, { "cell_type": "code", "execution_count": 61, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-cos(t*w)/(w^2 - w0^2) + cos(t*w0)/(w^2 - w0^2)\n" ] } ], "source": [ "sol_lap = desolve_laplace(eq, y, ivar=t,ics=[0,0,0]); print sol_lap" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

    \n", "που σημαίνει ότι μεταβολή του ηλεκτρικού φορτίου είναι η διαφορά δυο περιοδικών ταλαντώσεων με διαφορετικές συχνότητες $\\omega_0$ και $\\omega$, αλλά με ίσο πλάτος $A = \\frac{1}{\\omega_0^2-\\omega^2}$. Χρησιμοποιώντας την τριγωνομετρική ταυτότητα\n", "$$ \\cos A - \\cos B = 2\\,\\sin(\\frac{A-B}{2}) \\, \\sin(\\frac{A+B}{2}) $$" ] }, { "cell_type": "code", "execution_count": 62, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0\n" ] } ], "source": [ "var('A B')\n", "eq = cos(A) - cos(B) - 2*sin((B-A)/2)*sin((A+B)/2)\n", "print eq.trig_reduce()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

    \n", "η λύση του ΠΑΤ γράφεται ως εξής\n", "$$ y(t) = \\left[ \\frac{2}{\\omega_0^2 - \\omega^2}\\,\\sin \\frac{(\\omega_0-\\omega)\\,t}{2} \\right] \\,\\sin \\frac{(\\omega_0+\\omega)\\,t}{2} \\,. $$\n", "Αν ο αριθμός $\\left|\\,\\omega_0 - \\omega\\,\\right| $ είναι πολύ μικρός, τότε ο αριθμός $\\left|\\,\\omega_0 + \\omega\\,\\right| $ είναι πολύ μεγαλύτερος από τον $\\left|\\,\\omega_0 - \\omega\\,\\right| $. Συνεπώς ο όρος $\\sin \\frac{(\\omega_0+\\omega)\\,t}{2}$ ταλαντώνεται πολύ γρηγορότερα από τον όρο $\\sin \\frac{(\\omega_0-\\omega)\\,t}{2}$, οπότε συνολικά η ταλάντωση που υπερισχύει είναι αυτή με συχνότητα $\\frac{(\\omega_0+\\omega)}{2}$, αλλά με αργή ταλάντωση (διαμόρφωση) πλάτους \n", "$$ P = \\frac{2}{\\omega_0^2 - \\omega^2}\\,\\sin \\frac{(\\omega_0-\\omega)\\,t}{2} \\,.$$" ] }, { "cell_type": "code", "execution_count": 63, "metadata": { "collapsed": false }, "outputs": [], "source": [ "P = 2/(w0^2-w^2)*sin((w0-w)*t/2)" ] }, { "cell_type": "code", "execution_count": 64, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ff4C3HjCbzSZL8wiWkJmZydNPP80DDzzA77//Tt++fQ23HOmFkWoxAq0NpaTA\n6dOGXrJEvBZGN998M4sWLWLz5s188MEHHD16lM6dO5OVlWVE/a5ovvvuO9q2bcvGjRsd21588UW+\n//572umDgLxEbxFShRFAbKz9/5wcEK0rBCKJiYm0a9eOhIQEx7bevXuzbNkyQ6+jF0ZXX619vuYa\n7bMPBtlFOH78uM9cHcKVycGDB2nfvj3z5s1zbKtZsybZ2dmGXue337TP+vyp+rG0vp35Eq+FUffu\n3Xn44Ydp2bIld955Jxs2bCAtLY2VK1caUb8rliVLlnDrrbeSlJQE2B/ELVu2MGPGDLcC2lxBtRhF\nR2tmS9CEETg/tL4iJyeHV199lYyMDN9fTCj3LFu2jA4dOnD06FEAqlatyvLly1m5cmWxmd+9Qe2w\ng4KgUSNtu14kHTli6CWLkJqaym233Ub37t05c+aMby8mXBGsXbuWm266iV9//RWASpUqMW/ePNas\nWUNUVMlLd3iCfuBw1VXaZzPbkIrhS4KoCyUeLkPaxcXFERLifPn4+HgJLCygcePGjs8dOnRg5cqV\n1K9f3/Dr5ORAgfYiNhb04QuFhdGddxp+eSeGDBnCBx98wMcff8z69etpovryBMFNfvjhB/r06eP4\nfsMNN/Dxxx/ToEEDw6+lKJowatAAwsO1fWZ26k888QRHjx7l6NGj3Hjjjaxfv15mCAseoSgKkyZN\nYsyYMY5trVq14uOPP+YavRnUQFRhVKsW6D3GepFkhtUVMH5JkPPnzyvVqlVT3n333WL3Sx4j11mx\nYoXywgsvKDk5OT67xuHDWp6IRx5x3vfVV9q+F1/0WRUURVGU5ORkpWrVqo58LTVq1FC+/vpr315U\nKNeMGTNGAZQnn3xSuXDhgs+uk5KitZM77nDe98032r5nnvFZFRRFUZTt27crtWvXdsqa/dlnn/n2\nokK5JC8vT+ndu7fjWYqLi1MyMzN9dr3sbK2ddOjgvO/nn7V9ffr4rApOeO1KGzFiBNu2bePYsWN8\n/fXXPPjgg4SEhIjlxwDi4uKYOXOmI4eJL1CtRWAf7erRGa2cyvmCunXrsmfPHsfinCkpKXTt2pXV\nq1f79sJCuWX8+PGsX7+eefPmUaFCBZ9dR28cL2zk1FuMfB0fceutt7Jnzx7aFOQLSE9Pp0ePHixZ\nssS3FxbKHUFBQSxZsoSOHTsyadIkli9f7tPA/4L1yQFnCxE4u6bNshh5LYxOnDjBY489RtOmTYmL\ni6NmzZokUIetAAAgAElEQVR88803VK9e3Yj6CT6mYMFjoKgwqlPHPjsNfC+MAK666ip27NjB7bff\nDsDFixfp3bu3U9CfILhKUFAQ99xzj8+nt+tdZIWFUfXqoIZimBEfUa9ePbZt28a9994L2HPO9O/f\nn9mzZ/v+4kK5omLFinz55ZeMGjXK1DZUWBhVqmR/FxUu50u8FkYrVqzgxIkTXLhwgaSkJJYvX+4U\nHyP4N3rB07Ch876QEKhXr2g5X1KlShU2bdpE3759Abuv++mnn2b+/PnmVEAQ3EQ/2i3c9dls2rbj\nxyEvz/f1qVy5Mv/973959tlnHdsWL17MpUuXfH9xoVxROA7YV5QUeF142+nTYMaEd8m0ZyE///wz\nx/QmGwsozZWm35aSYs4DCRAWFsbixYsZPnw4YBdLRqYnEAQjOXFC+/y3vxXdr267fBn++sucOgUH\nBzNr1ixGjRpFq1at2LhxI6GhoeZcXBDcRN+GinsP6Qft+rK+QoSRRSQmJtKlSxduv/12TpjxS5eA\nXpcVthgV3mZmLiObzcbUqVN5/fXX2bp1qyNuQhBUfvnlFwYMGOBIfGoVycna5+Imjuq3mdnUbTYb\nkyZN4uuvv5bVCIRiSU1NRTErnXQpuNOG9GV9hQgjC9i3bx9du3YlJSWFo0ePMmLECMvqolqMIiKg\natWi+/Xq3Sx3morNZmPs2LG0b9/e3AsLfs/Bgwe57bbbWLx4MXFxcZa6iVSxExzsnAdMxSphpCLZ\nsoXi+OOPP2jdujUTJ060uipO7UIN39Cj3yYWo3LI/v37ufPOO0lNTQXsOYo++OADS+qiKJrYadDA\nOYeRipXCSBCK4/Dhw9xxxx38VeCXOnbsGOfV1SctQO2o9ZMV9FgtjAShMCdPnqRbt26cOHGC1157\njQULFlhaH9UKFB3tnMNIxew2JMLIRJKSkujevTtnz54FoGPHjmzevJno6GhL6nPmDKheiOLcaOAc\nMyHLgghWk5ycTLdu3Th58iQAbdq04YsvvrDMVZSbq8UNlZR/VYSR4E+kpqbSvXt3jhRM8WratCn3\n33+/ZfVRFE0YFWctAnGllVtSU1O5++67+fPPPwFo3749GzZsIDIy0rI66YVOcUGjoE2TBPMW8HOH\n3Nxcq6sgmERaWho9evRwTFi47rrr2Lp1K1WL8wGbREFzBkru1PVty9+E0ccff8zy5cutroZgEpmZ\nmdx77738VLBia8OGDdm6dSsxMTGW1SktTRugl9SGxJVWThk1ahQHDhwAoEmTJmzYsMHwtWbc5dQp\n7XPdusWXqV1b+1wwSPcb9u/fT9OmTdm6davVVRF8zIULF7j//vvZv38/YM95tWXLFsvzpek76ZIs\nRvpO3Z+srnPnzuXRRx+lf//+bNiwwerqCD7m4sWL9OrVi2+++QaAWrVqsXXrVp8sNeUOegtQScKo\ndm3NTS3CqBzx5ptvcvvttxMTE8PmzZupWbOm1VVyEkZ6AaQnJkaLPdKXt5pff/2VTp06cfToUR56\n6CH27NljdZUEH3L06FHHQpZqG6pd0kNrImXNpgF7zESVKvbP/mQx+uGHH1AUhcuXL/Pwww+zY8cO\nq6sk+AhFUXj88cf5/PPPAXsKlC1btvhs3TN3cEUYBQdr3gtxpZUjoqOj2bhxI9u3b+eq4jJYWYAr\nwigkBFQN50/C6Oqrr6ZLly6A3Tx8zz33cOjQIWsrJfiM5s2bs2PHDq677jo2btzoNwsMlzWbRkXt\n1P3JHf3uu+/y6KOPAnZrwn333UdiYqLFtRJ8gc1m4/777yckJISIiAg2btxIq1atrK4W4Jow0u87\nfRp8PQlVhJGJhIeHE6tfst5iXBFG+n2nTtkD5fyBkJAQli9fTqdOnQA4c+YMd911F2fOnLG4ZoKv\nuPbaa/nhhx9o27at1VVxoG9D+ni8wqjT+LOzITPTt3VyleDgYJYuXcpdd90F2NdWu+eeeyzNqyb4\njgEDBrB582ZWr17NzTffbHV1HLg6uNCnwvB1Ny/CyEd88gm0bw+dO8N331ldm+JxVxjl5toD5fyF\nihUrsm7dOlq2vA6w5+Vo2/ZhMjMlILs8sGMH3Hor3HKL1oaCgvyry9Jnsi4uh1Fx+/zJahQWFsbq\n1au56Sb7i/LPP/+kTZv7SUnxE/UmeMXXX0PHjvY29Pnn0LVrV4cQ9hf0sauuCiNftyH/6mXKCT/9\nBA8/DHv3wvbtcM899iU1/A29MCqtU9ePhP0tALtKlSq0bbsRsFfyxIntdOjwnF9kcxU858gR6NED\ndu6EXbvgzjv9S1Co6IVRaRN79AMPf3JJgz0B5E03rQPsLv6UlB/o1WuZtZUSvCY52d6Gvv7a3oZ6\n9jRvEVZ38GRw4euldUQYGUxeXh5Tpzr7QFNSwB/XQFU76OhoqFix5HL+3KkfPw7LltUD1gLhAPz8\ncxJ//JFjab0E75g0yXltvvR0+L//s64+JaGKtZCQ4jPHq/irxQggIwP+/e+awHogBpjD11//AwnZ\nC2ymTAF93tPsbPs2f0MvckqbkyQWowAlOzubm27qyLJlc4rsmzMH8vMtqFQpqCKnrMk9/iyMVq5U\nVyy/EVgADEFR1vPRRxWsrZjgEbm5ufz44+8Ul1pn2TL7Qqz+hNqp16wJpXn5/LkNLV2qxj01BX4H\nnkZRYNEiS6sleEFurv13LczHH/s+cNld1DYUHQ3h4SWX01tkRRgFCIqiMGjQIPbu/Zb8/GeA8Qwf\nbncBAPzxBxSkYPELMjO1INCyhJE/u9I2b9Y+r1//ODAdCGHtWqtqJHiKoig8++yz3HJLOy5etOem\neuYZeOgh+/6//rK71vwFRdE69bLy4/mzxejTT7XPmzdHOATeunXW1EfwjtmzZ7Np01nS0+3fH3vM\n/g/g3Dn48kvLqlYs/tiGRBgZxPTp03UZZCsDvbn/frj3Xq1MQQoJv0D/YAWqxSgrC776yv65YUO4\n+25QZ6B++y0UrLwiBAgzZ85kwYIFZGWdAx4CztKrF/TqpZX54guraleU9HRt9F1Wp+6vbSg3F7Zt\ns3+uW9c+kGvXzv59/37/E3FC6cyfP5/nnnuO/v1vBOwj8bvv1gYXAOvXW1O34sjNxSHgykrtJ8Io\nwPjss88YMWKEbstiKlduQYcOcMcd+nKmV61EXJ1mDP7bqX/1lb1hgT3I0GZzvt/+ZF0QSmfbtm0M\nHz5ct2UuYWHV6dwZbr9d2/q//5letRJxNfAa/Ndi9M039tgTgG7d7G2oa1dtv79ZF4SS2b17N889\n9xwA5879DtiT3t51l/NvumuXBZUrAf20e3fakARf+zlHjx7l73//O/mOAKIxwEN06gRhYdCiBdSo\nYd+ze7f/5AFydap+4f3+5Er7+mvtc7du9v8L0hoB9hmBgv9z+vRp4uLiyLMHiwGjgHhuuME+KaB+\nfWjc2L5n717/iTNyRxjp9/vT4EKfSuS22+z/6wcX/mShE0rm7Nmz9O7dW7d25AvAAFq1sj97VatC\n06b2Pfv2aWuTWY07bahKFQgNtX8utxajuLg4evbsyYoVK6yqgtfk5OTw6KOPkpqaCkDbtvcB4wG4\n4QZ7GZtNM02npPjPkgD6B6usBzIqSguK86f8iXv3ap/V+33rrdq2b791Lq/+ToL/kJeXx2OPPcbJ\nAsXdunVXYAIA+hx07dvb/8/Ohl9+MbmSJeBOpx4aCuqybv5kMdq3T/us5s285RYtkFxtY6mpqdx3\n332OJSUE/0FRFAYMGMDxgoX4WrXqCLwFaP0iaO3p0iX4/nuTK1kC7rQhm00rU26FUUJCAuvWrSM+\nPt6qKnjNZ5995lijq0mTJtx664eot1TtyEHrcMB/Hkh9XqWyfLs2m2b18pd8TIqiddrVq0ODBvbP\nNWtqq5n/8IN9JmBOTg7PPfccrVu3JsVf/gABgPHjx/NFgVmiTp063HvvcsC+WuT112vl1MEFOAti\nK3GnUwfNFeBPwuiHH+z/h4ZC8+b2zxERoCbo378f/vgjmfbt27N+/Xr+/ve/c+zYMWsqKxTL22+/\nzacFEfQ1atSgd++PALtpRf8euvFG7bNeEFuJp23ozBnfzvIWV5oX3HvvvWzatIn69euzcuVKfvop\n2rFP35HrhZG/PJB6faCKntLQCyN/cAempGjWq9attYVuQbvf58/D77/D8OHDmT17NidOnKBPnz46\nt6dgJYqikJSUBNiXp0hISODIES2QQC+M9J9//tmsGpaOq4npVNQByIULWlyPlVy4oFnfmje3u/5V\n1PudkwPnztWmWbNmgN1lEx8fzyV/m/N9hfLtt9/yyiuvOL4vXbqUI0e09NH691DLltrnAwfMqF3Z\neCqM8vLAlw4AEUZe0r17d44cOUKbNm0cHXZMjH2Gh4r+gfQXN4B+xpYrwkjt1C9dck4aZhUFC60D\nmu9cpU0b7fO+ffDqq68SU9DqNm/ezBtvvGFCDYWysNlsLFy4kHnz5jF16lQ6d+6MuoZpWBhce61W\nVv9Z/9tbiTvuaHBuZ/4wY/Lnn9UcYM5tBpyF6E8/BbNs2TIaFwR67dq1i3/9618m1VIojYYNG3Jb\nQXDYK6+8Qo8ePRxeiZAQuO46raxqEQT/HFy4I4zAt5ZXEUYGEBYWRlqa9iMXDK4cXHUVBNu9A/z2\nm7l1Kwm9xUiNfSgNfafuD96o0oRRixbO5erUqcOKFSsc62yNGzeO7RKZ7RfYbDaeeuophg4dSlaW\n9ru2bKkFWoLdVVqhIGenvwgjdzt1fTvzhzZ08KD2Wf8CBWdhtG+ffemdhIQEQkJCAJgyZQpbt241\noZZCadSuXZvNmzczf/58JkyYQF6e9o6JjdXaDNifP1VY+IvFSB+zWlZIB4gwCjhKe1GHhWmzan77\nzX9cUWAXbNHRpZcFZ2HkDwHYesub3ppQ+Lv6u3Tt2pVx48YBkJ+fz+OPP06aP62IK3DggNY2Wrd2\n3hcUpMW9HDniH9l7XV3KQMXfBhf6JT+uucZ5X3FW7htvvJHJkycDdjdo3759Oe1PAVNXKMHBwTz5\n5JOEhITwxx929ycUfQ+BNmg8c8Y/+nF3Bxf6dubLNiTCyCD0L+riHkj1ZZ2VZV/cz2rUh6p69dKX\nMlDxt05dL0QLC6MmTbSYI3250aNH06VLFwCOHz/OoEGDZLFZP0JvTS1sdQXtd7582R47ZjVqp165\nMlSqVHZ5f2tDhw9rn5s0cd5Xt6797wLnNjRs2DB69OgB2NMsDBkyxMe1FNyhrPeQ3p2mtxhahdqG\nbDbXPBf6Mr50R4swMoiyHkh1tAv+4U5TO2ZX4osKl/OHTl3trCtW1GahqVSsaM+EDc4WuuDgYJYu\nXUq1atUA2LRpE4f1bwfBUvQWDH17UfG3OCNXlzJQ8bcYI/XRt9ns7n49Npv2G+itEEFBQSxevJja\ntWtzzz33MH36dNPqK5RNWe8hvWXQnwYXNWpo4SalYZY7WoSRCyiKwhtvvFHqNNXSXGngX526flaM\nKyod/EsY5eba3Slg77yLs3ip9zs93dlcW79+fRYsWEC7du3Yt28f1xT2IQg+oyzrnH7AUNzP4k9t\n6NIlbVaMJ8LI6jYEmjBq0KD4xTvV+52fr7U3gJiYGHbv3s2nn35K7bKywwqmUpYw0gtgq4WRO2sN\nqojFyI/48MMPGTNmDK1atWLlypXFllEfyAoVtJw6evzJYuTujLTC5azu1P/4Q5tNU9iNpqK/34Vf\nor169eLbb78VUWQiq1atonfv3pwtpTdTLUbFWTDAuaO3Whi5kwdMxZ+Cr1NTQQ2xK+xGUymtDf3t\nb3/Dps+RIficdHVRsVIoLfYS/EsYZWXZB+ngf1ZXEUZlcOzYMZ5//nkAMjIyHDOb9Fy6pI2+SrJg\n6B/IP/7wQUXdwN0cRoXLWd2p6+9fcS9QKNu6EOyK3VYwhBMnTvD000+zevVqWrVqxali1sRQFE0Y\nNWzoPJtG5eqrtc9W5xjU51AJxDZUWnyRir4NWT2Yu9JJT0+ndevWPPvss2RlZZVYTm1DtWvbVywo\njDoJCKwXRp68h8Ri5Afk5eXRr18/MjIyAOjXrx+9e/cuUu6PP7T1m0qyYNSrp/lQC3LaWYYnD6RZ\nswFcQX//irPOgX+5Xa5kFEVh0KBBnDt3DoBOnTpRq5hsiCkp2irbJRnyqlTRAoKtbkN6YVQQslYm\n/hRj5Iow0v8OEopnLYMHD+bYsWO8//77joF6YbKztSnsJQ0YK1bUcuzp3aNWoG8DroZ0VKmiTayR\nGCOLeOutt9i2bRtgT6Q1c+bMYsvpLRj6Ua2ekBC7OALrR7uePJD+5AbQvxTVIOvC6IWRPqhXMJeF\nCxeyadMmAOrWrcv7779frAumtKnjKjabJoSTkqxNe6FvQ64Ko8hILTeT1W3o6FHtc0kvUb11weo+\n60pmzZo1LF68GIDIyEhH2pHC6N9D+t+uMOrv/ddfkJlpTB09QT+4cPU9FBxsXxAXxGJkCT///DNj\nx44F7Enoli5dSnQJCX/0D2RJL2rQOvWzZ+3+VavwxGIUHm7v2AsfbwX6Troki1HdunYxWri8YB7H\njx9n6NChju9z586lqtqrFUJv1i9pcAHa733xorV5WDzp1P1pzcGC9UaBkttQtWqahc4d9/8v/pLe\nvxxw+vRpnn76acf3mTNn0rCEl4xe7JYmjBo10j5baXn1ZHABWnsTYWQyly9fZuDAgeTm5gLw0ksv\n0alTpxLL6zsN/UNXGP3zbOUD6Ykw0pe1ulN3xZUWHKxN43dHGO3cuZMf1JU1BY9RXWiqG3rAgAHc\ne++9JZbX/6altSH9721lG/LElQZap271moMnTmifC6e7ULHZtN/i2LGyF+1MS0tjwIABNG/enB07\ndhhSzysZtQ2pC1/36tWL/v37l1jeVWGk/731AtlsPBlcgPYeSk/3XaJXEUbFcPHiRa4t8MU0bdqU\n119/vdTy+hevq8LISiuGt8IoNVWbFWYF6r2rUqX4AEMV9X6fOwcF7+cSycnJYeTIkXTq1InHH3+c\nixcvGlPZK5SFCxeyefNmAOrVq1dmvhtXxC74z+DC09Gu2oYuXrR2IVn1hRgaWvqsOrU/y82FYmLm\nnVi2bBmLFy9GURSeeOIJsv1hpdwAZuHChXzyySeAPUXC3LlzS50J6Ikw0gtks/HWYgS+W0hWhFEx\nVK5cmSVLlvDJJ5+waNEiKhQ3RUaH3mJUWqfuL6NdT2KMQOvU8/PtYsMK8vK0xlzavQb3hKjNZmPr\n1q0oisKBAwccblTBM7p37+6wEM2bN48qVaqUWt5VYeQvbcjb0S5YG4CtCqP69UvPfK8f6JXlTvvn\nP/9Jhw4dADh8+DBjxozxqo5XMhcvXmT06NGO7/Pnz6dmGXkhrhSLkRkz00QYlcJ9993HTTfdVGY5\ntcOIiSl9aYDyYjEC6+I7Tp/WzKelxXMV3l/W/Q4LC2PJkiWEhYUB9sB7cQd4Tr169fjkk0/Yvn07\nd999d5nl1d+nQoXSLRj+KIw8sRiBdS7prCwth1FJbjQVd4RRcHAwCxcuJLwgW+Q777wjbchDKlSo\nwLZt2+jcuTP9+/fn/vvvL/MYVRgFB9sFb0no9/mLMPLUYiTCyE/JzYU//7R/dudF7Q8xRq4uIKvi\nD526K4HXKu4K0ZYtWzJx4kRA8+/nqGshCG5js9m49dZbyyynKFp7aNBAm45bHPrf3MrBhbeuNLCu\nDelfhmUJI73lwZUA7GuvvdapDQ0cOFBcah4SGxvL//73P2bPnu1SeVUYNWigTTwpDn90pYnFqJxx\n/LgWRFlafBFo0/VBE1NWoF8nzZ3ktWb4dsvCnU5d/3u4+hIdNmyYw0r4yy+/OFYTF3zHuXPatOGy\nxG69eprrx0phpD7/YWEQEeH6cf6Q9kL/MizNsgDuWYxUhg4dys033wzAoUOHxC3tBUFBQVRyYYXi\njAwtD1hZA/Rq1ez5jMB/LEYlTFYtFjMGFyKMvMTVwGuwT3dXn/GTJ31WpTJRHyZ3VDo4P7yqKd5s\n9AGgaqKykvDEdRkcHMzcuXMJKRhyTZo0iYP+sAx1OcYdK2BoKKj5Ia0cXKiderVq7g0u/CHGyNPB\nhavCqLBLbcGCBaUuBSN4jyuzDFVsNq2MP1iMoqNLt3AVRixGAYCrOYzA/kCqL3OrOvXsbG19Gnfi\ni8BZGFllMdILyjp1Si/7t79pLy13rAutWrVixIgRju/ffvutGzUU3MWVhJ161DZ0+rR1syPVDtkd\nNxr4h8XIHWFUtapnuYyaNm3KhAkTuPPOO/nxxx+p7u4oTHALd6yA+jLnz5c9Y9dX6AcX7lCuhVFc\nXBw9e/ZkxYoVVlUBgJMnTzJw4EBOemjC0b9wXenU1Zd5ero103U9WUBWRf8AW2UxckcYhYVpZdx1\nu4wdO5bHH3+cffv2MWDAAPcOvsLILyvBTRm4OiNNRf1N8/OtmQSgn2rv7vveH9pQcrL2uayXqM2m\nlUlOdi/30vDhw9m8eTMNXPlRBa/Qi11XhJG+7ywrDYMvyM/XhJG7bahcC6OEhATWrVtHfHy8VVUA\n7P7whQsX0qxZM7744gu3j9dbflx5IPXuHyvcaZ7OBAD/c6XVrl12eVWsnjplf6G5SsWKFfnwww9p\n0aKFexW8Ahk0aBCDBg0izcOHwh1XGjh36la0If2fGehtqKzBBWixkdnZWhyLKwQFBZWad0fQSNar\nVQ9w12Kk7zutEEYZGVrCUH+0ul7RrrRNmzbx0UcfARASEkKrVq3cPoe7L2q9MLLCnabvjN0JeAPn\nB9hqV1pYmGsNSu8qsDImpbzyxRdf8O9//5v58+fToUMH8jzwbbnrSrNaGJWXwYXNVnpqBBX9pBEv\n399CMXz33Xc0btyYYcOGkeXhWlHuxBiB87vKijbk6Yy0wuXLncXIarKzs3n22Wcd39966y1quOtb\nQutkgoJc62Ss7tT1iRnLyLlXBH/o1NV7Vru2a0GvVgvR8syFCxf4xz/+4fg+ZMgQgoOD3T6PXhi5\n6wYItE5d3+asHlzUrOla0Kv+NxFhZCy5ubk8+eSTXLp0ienTp7NgwQKPzuOuxchqV5o3g4vwcG0m\nqAgjg5kwYQJHCxI/dOnShX79+nl0HrWTiYmx5wUqC6tf1Hph5K7FyOpO/dIlzXTqinUOZLTrSyZO\nnMjhw4cB6Nixo9Nil+6gCqPate2dXlnoO3Ur2pA3nXpoqBbMbMXgQlG0F6ErbjRwbkNWzmIqj7z9\n9tv89NNPAFx//fX885//9Og86u8SFuZa7KjVrjRvBhegvbt8tQLDFSmMfvrpJ6ZNmwbYMx5/8MEH\nHvnC8/PtM2PA9U7Gn4SRuxYjfUJIKzr1v/7Sgj8D5X6XVw4cOMCbb74JQGhoKHPnziWotLUlSiAv\nT+uY9S/g0gjkOD39MVa0odRULXO8lYOLQ4cOGXOiAObYsWNMmDABsMdjzZ8/n9DQUI/OpQqj+vVd\ns6RbLYy8bUOqMPJVG7rihFF+fj7/+Mc/uHz5MgCjRo1yLBjrLmfPQsFpXO5krHYDeCOMwPcPZGm4\nMyNNxRed+g8//MDevXuNOVkAoigKzz33nKMNjRw5kubNm3t0rpQULQjT1d/U6jZk1Gg3Lc29WV5G\n4G7gNRjbhtLS0vjHP/7Btdde69Fkl/LEkCFDHFnBn3vuOdq1a+fReTIztX7dFTcaBHaMEWhtKCdH\nSz9jJFecMMrKyqJuwZAzNjaWV155xeNzuRt4DdZbMPSCxhthlJpqbafuyf32tlPPyclh5MiRtG/f\nnoEDBzqEwZXG8uXL+fLLLwFo3Lix02KX7qLvlF39TWvV0kbFgWgxUttQbq5vOvXS8KQNGSmMVq9e\nzdy5c1EUhWeeeYaL7kwVLUds2LCBtWvXAlCrVi2H5cgT3I0vAvszqBqnAtliBL4ZpF9xwigyMpKP\nP/6YTz75hPnz51OhQgWPz+WJBSMyUkvHrrrhzMRbi5H6EOflacs4mIUn99tIIRoSEsJnn31GXl4e\nP/74I++//753JwxQbrjhBrp16wbArFmzqKg+0B7gyYs6NFSLowhkYVT4XGbgiRDVx096K4yeeOIJ\nOnbsCNjdaVOmTPHuhAFIfn4+Q4cOdXyfNm0a0e4sWlkId2ekgX2ykJpB3mph5InFSP/u8kWc0RUn\njFTuu+8+OnXq5NU5POnUbTZ7RwP2mBmz8Sb4uvAxVnbqrgqjiAgtLsrbTj04OJhZs2Y5vo8dO5bT\nVqhbi4mNjWXLli1s27aNe+65x6tzeeLa0Zc9edJ8y6VRbgAw3yXtyf0ODtYGGN4GXwcFBTFnzhzH\nkjtTpkzh999/9+6kAUZQUBCrVq2iY8eO3HbbbTz++ONenc8TixFo76wzZ8zPIO/pOmnFHSMWIz/D\n005dFUYpKeY/kEZZjMDaTt1VIQqaK+DPP71/iXbo0IEnnngCgPT0dK9csYGMzWbzemABnv+m6mj3\n0iX3kg4agVHB1xB4bejMGXtchze0aNGCIUOGAHb39ODBg707YQDSqlUrtm3bxpo1a7xOgqm3hJe1\nfqQeKzPIGzlAF2HkZ3hilgZNGCmK+QtJqg9keDh44kW0crTricUItM7iwgVjzK5TpkyhSoGqXLRo\nEbt27fL+pFconr6o9TnDzO7UVWEUFqYtCu0OgdiG9HFGRrgvX3vtNUes56effsq6deu8P2mAERQU\nRFVPVEEh9EZrd35TKwOw9f2wJ15EEUZ+jLcWIzDfnaY+RJ5Yi8B/XGmqxcAV9J26EQHvMTExTsGS\nzz77rEcZnwXPhZGVbUgdzFSv7trU6MJY2Yb0L1FP25ARszsjIyOZPn264/uIESO8XnPvSsXTNmTl\nlH1VGFWqZB9guIsIIz/G0xe1lZ26+kB6Koz8wQ1Qo4Y2o8IVjJyZpvLMM8/QunVrAH788Ud27txp\nzImvMDxtQ/5gMfLEjQbWWozUexUWZp8I4iq+SPL4yCOPcMcdd3DnnXfyySefeJQHS3AWNe60IX8Q\nRi/2U1oAACAASURBVEYM0CX42gMWLlzIWR/5q9SHqXJlLZutK1gljC5fhvPn7Z89teBaOdpVO3X9\n/XMFX+QyCgkJ4b333uPWW29l7969dO7c2ZgTX2GobSgyUkvz7wpWtaGcHPtiquB5G7JycKG2oZo1\n3bN2+aIN2Ww21qxZw+bNm4mNjTXmpFcg+jbkjms3kIWR/jixGLnJtm3bGDhwILGxsSxZssTw87ub\nWl/Fqk49I0P7bIRSN7NTz87WXkiurEmnx1e5ozp27Mi2bdu4/vrrjTupn7Fnzx5GjBhBhv7hMRBP\n25BVFiN9oLcRgwsz25CiaEvquLsspK+yjUdGRnodfOzv+NpFqLYhd9xoYF0bunxZS/Xir++hciuM\nLl++zPPPPw9AamqqI8OoUVy4oHWS7j6QemFk5gPp7Yw0sG60q3bo4H6n7sv10spzp64oCi+++CLT\npk0jNjaWn3/+2dDzZ2drYj1QOnVvE6SCdVbXjAxtORB3BxdWLzoaqCiKwr333surr75q+DsIArMN\n6QcX/iqMXFhbOTCZPXu2Y3G+tm3bMmjQIEPP72ngNVhnMQrkTl0vjPzFYlTeWbZsmWPGXdWqVQ13\nd+gDgb0ZXJjZhowYXFhlMdK//NxtQ1YvIRGorF69mk2bNrFp0yZ27dpl+DIo3rQh/TOg7199TSC0\noXJpMTpz5gyvvfaa4/t7771HsJq61SA8naoP0ql7gr5Td9dipA9IvALzMXrE+fPnefnllx3fZ8yY\n4fEClyXh6WwasG60623+FfB9fERJeCOMoqO19B4ijFzjwoULDB8+3PH9xRdfNPwa3rShqlXtGbAh\n8DwXFSpoz6MEX7vIa6+9RnqBvW7AgAHcfPPNhl/DG4uR/sVulTDytFOPitKWB7DKleZupx4aqmUo\nFjeAa7zxxhucLHgDPvDAA9x1112GX8ObwUVUlDbNN9AGF8HBWu6WQBFGNpvWz5nVhhSzU5obzLRp\n0zh27BgA3bp144EHHjD8Gt4Io6AgrV8MNGEEvl3QvNwJo8TERObOnQtA5cqVmTx5sk+u402nHham\n/aiB1qnbbNqxZrrSvLEYgfYbnTplzhIS53wxjDGJQ4cOOXLMhIeH8/bbb/vkOt506jab9nIP5E7d\nqjbkrjACTRilpnqf/bo00tPTGTZsGE8//bTvLuJjjh8/7nj3BAcHM2PGDJ/EI3rThqB8tCERRi6w\nfPlyxyyAsWPHUtuTp8UFvH0grVgvzagHUg3ADhSLEWi/0cWLWsoCX5CZmcmYMWOoX7++I8Yt0Bg2\nbBi5ubkADB8+nKuuuson1/HG6grOnbpZxgVfdOpm1d1bYWTG9O78/Hxuvvlmpk+fzvz58/nmm298\ncyEf8/LLL3PhwgUAnn/+eZo3b+6T6xgljC5cgKwsY+pUFka1IfXYrCxtUoFRWCaM4uLi6NmzJytW\nrDD0vFOmTGH16tXceeedPl2Dx9tOXRVGGRn2l7UZGBF8DVqnfu6ceWu9eWsx0scZ+dIVMG/ePN54\n4w2ysrIYOnRowLkDMjMzSS0wY9SrV49Ro0b57FpGDS4uX/ZNnEFxGC2M8vK0qcu+xts2ZMbMtKCg\nIJ577jnH9xdffDHgMmJv27aNhIQEAGrUqMG4ceN8di2jhBGYZzUy+j1U+JxGYJkwSkhIYN26dcTH\nxxt6XpvNxoMPPsiWLVsIDw839Nx6vHGlgTVT9o3u1MG8BTy9ma4P5iUz++c//0njxo0B+PzzzwNu\nDajKlSuzY8cOPvzwQ9577z0qu5O51E0CsVP3RRsyy/LqrdVVL4x8GYD9zDPP0LJlSwC+++47n+Sg\n8yURERG0a9cOsMfqVfHmQSkDb2algTUz03zRhoweGJU7V5pZqJ16cLBnL2orZqYZEXwNzrmMzIqR\nMCrGCHwrjCpUqMDUqVMd34cPH06OLwMyfIDNZuPxxx/3SbCoHvXlGhTk2Yva6jZkhDsarGlD3rrS\nfCmMQkJCmDlzpuP76NGjyTLLz2MA7dq1Y/fu3axcuZInn3zSp9dS+zJ9zJ07yOCieEQYeYjaMcTE\naLO03EH/QAZap64/1iwXhjqaiYiAihXdP97MKfsPPfQQt912GwBHjhzh3Xff9e0FAxS1U69Z0/s2\nJG6AslHvUVCQZ+u8mZnk8fbbb6dXr14AnDx5kjfffNO3FzSYoKAgHnnkEcPTxBTG0/UjVUQYFY8I\nIw/Iz9derp7EF4Gz1cNHS7kVQf9AqtOFPcHXC/gVh36NJ08wc10gm83GO++845iFMmHCBP4ye7Vg\nP0ffhjydH2H14CIqyvPzWNmGqlfX8te4g1muNJU333yTkBB7DuKpU6dywqjVa8sJiqL1Ze4sHqvH\namHkjedChJGfcfasFnTsaaeu5o9Qz2cG6sNTqZKWA8YTzE5Ql5enuRs8caOB+QsmXn/99Q4zekZG\nBmPGjPH9RQOItDRtJomngwsr4/T0+bw8wYokj4E0uAC45pprHMs6tW3blkyzotQDhPR0LW2Cp+8h\nfX9qhTDyZoDuyzYU0MJIURSfrD9TFt4GXoPzA2l20Ju3sYBmj3bT0uwWBvC8U7ci+/XEiROJjIyk\nXbt29O/f35yLBgjeBl6DtaNdb0a6hY83ow15swizSs2a9lgWMK8Nvfbaa6xatYrt27fTtGlTcy4a\nIAR6G4qI8Mz9pyLB1yXw8ccfc80117Bo0SJTp3R6O1UfrLEYGdWpmz3a9XZGmnqc6j4wK3NvrVq1\n2LVrF7t376Zjx47mXNRNfv/9d0e+FTMJ9E7d28GF2XF63k5eAAgJ0e65WW2oatWq9O7du1wv1uwp\nV3obEldaMeTk5DBy5Ej+/PNPnnjiCf73v/+Zdm0jLEZ6YWSGxSg3VxsxBprFyNvZNGB3e6iuFzOX\nBWnRogVBngR0mEBeXh4PP/wwzZo1Y8WKFabmXDK6DZkxuLh4UXNdBLIw8rQNgfkZ5P0dRVFYvHix\nJTNPjRBG5cVzIcKogHfffZejR48CcMcdd9C1a1fTrm2Excjs4Gt9vqFA69SNsBiB5k776y/NNXcl\ns2TJEn744QeOHTvGtGnTTBVGRnTq0dGaFdCMKe9GzaYpfLzZVlcjhFFurnlB4/7MRx99xIABA2je\nvDlbt2419dpGtKHQUO1ZNMNidOmSlmFbhJHBpKSkMHHiRMA+A+itt94y1dRqxGg3IkILgDZDGBk1\nzRjMn2pshBsAtN/q0iVzlzPxRzIzMxk9erTj+1tvvWWqZcuITl0/7dyMNmSkMApEqyuYH4Dtz1y4\ncIGRI0cCdpd0nlnLABRgRBsCzfIaaAN0EUaFGD9+POkFd/iJJ56gdevWpl7fCIuRzaY9kGaYMH01\n2jXbYiSdujG8+eabnCq4Cb169aJLly6mXt+INgSBK4z0s3FEGAUm06dPJykpCYDu3bvTo0cPU69v\ntDAyY4knI9tQpUr2uLfC5zWCgBNGv/zyC++//z5gT70+YcIE0+ugfyA9zR8BmvXj7Fnf++uNyh0B\nzp16IFmMrJiZ5o8cP36cadOmARAaGmpJ8jyjO/WMDOMXkiyMkVbX8HAtUakII/fJzs5m48aNll3/\n1KlTTJ48GbAnc3zrrbcsqIP22Yg2pCi+fxaNFEY2m/NizEYScMLo5ZdfdpgsX375ZerWrWt6HVRX\nWmSk3SXmKeoDefGiFhjtK4x8IIODteR2YjFyn5ycHN566y1HjJzZvPrqq04rf19zzTWm10G9/xUr\n2tuRp+gDsH0t0o1sQ+C7Tr049BY1/T1zF39oQytXriQ2Npb777+fgwcPWlKHsWPHOvIqPf3007Ro\n0cL0OqiDu9BQ45Z48rXlNVDaUIixp/MtiqLw8MMPs3fvXmw2G8OHD7ekHmqH4I0LAIrOqvFGZJWF\n0Q9klSr2UXogWYz8oVNPTEzkwQcf5OjRo+zZs4cVK1aYev19+/axdOlSAKpVq8bYsWNNvb6KOrio\nXVvLjeMJhTt1fdJHo/FFG/rzT3MGF/rg9EAXRocOHSI5ORmAl156ifXr15t6/cTERBYsWABAVFQU\n48ePN/X6Kvqs196EB+qfB19PYjC6DfXvbz+nJ0vclEZAWYxsNhv9+/fnt99+49NPPyXCl0qiBLKz\n7YIAvDNfgrkz03yl1M+d870bULUYBQV5NzLSu9Ks6tQbNWrE+fPnAUhISODbb7819frXXXcd77//\nPjVr1mTcuHFU9dav6gE5OVoH7G0bCuROXT1HVpbv3YD6e+PNS8QfhNGwYcP429/+BsCGDRvYsmWL\nqdd/5513HDM4X331VWJ8qcZLIC9PWwbH2zYUyBaj0aPhzTfhlVe8P5eegBJGKhEREVx//fWWXNuo\noFEwN5eRkfER+nPk5oKv8wN6u8aTir4DsSrGKDo6mnHjxjm+v/TSS6ZOkw8JCeGZZ57h0KFDPPPM\nM6ZdV49+XTMjhVGgdepmTmJQhVFYmD1o1VP8QRhVrFjREd8DMHz4cC5fvmza9efMmcPMmTO58cYb\nefHFF027rp6UFC3lyJXchnxFQAojKzEq4A2seyCNMBKYOd1YvTfeuADAPzp1sMckXHvttQDs2LGD\ntWvXmnp9RbELtFBv8vF7gZGDC6tGu4HWhlRhVK2ad67LKlW0NCNWtqH4+HhuuOEGAPbv3+9wbZlB\nWFgYL7zwAt988w0VKlQw7bp6jJoABOZaXY0eoPuKgBBGeXkwcSI0bgyVK0NcnHnpywujz2EUSBaj\nQB3t5uRoCcG8FUZVq2pr81jVqSsK/PvfoWRlaTPBhgx5mdzcXJ9eNz8fpk6Fq66CChXgoYfs8S1W\nUB4GF4HUhsBZGHmDzaa9iK0URsuWBZGcPN3x/dVX/+XzRWYVBWbMgKuvts/MfeghGwWz9U3HyDYU\nyK40X+H3wigvzy6Exo6FP/6wvyQ/+gi6dwcrFls28oEsDzFG4NsAbP25jezUrXKlTZoEzzwDJ07c\nD9wGQFLSYcaO/cBn18zPhyefhJdfhqNH7e7PNWvg1lvNWwZAj6+EUaDGGBU+t9HoBxdGBKmqv9mZ\nM2CiB8vBrFnQrx/8+WdHoDcAZ8+e5vXXfWc1UhR47jkYMgR+/90eZ7p2LdxyizV9iQwufIvfC6Np\n0+Djj7XvwcH2//fts3f0ZmNE1msVqx5Idaq9N5jVqRsVNKqi79RNTlTL99/Da6+p32yEhk5z7Jsx\nI4Hz530TazRjBixapH1Xrf9Hj8ILL/jkkqViZBuyYrRrs3mXYkDFrGVB9Of21uoK2m+mKOZb7g8c\nAP1k5IiISUBDYB4JCc/57D4uXgwF6fMAzR2ZnAyDBvnmmqXhK4tRoA0ufIVfC6PNmw/x6qvrAAWb\nDdavhx9/tLvTAObOhUOHzK1ToAdfR0Zq2UK9waxO3WhhpFqM8vPN79RHjtQCJseNg9TU9sTEvAjM\nIifnKyZPNn5Zm6Qk+8wNlVWr4PBh7dlLSIDERMMvWyqBOtpVn3P9Gm3eYFaMka8GF2C+O23cOLvF\nE2DYMDhz5hpuuOEI8BTHj4egm9dgGGfOwODB2vfFi+3iXu3/P/kEvvzS+OuWRqC2If1zrk8U7G9Y\nJozi4uLo2bNnqXlcnnzyFfLyHgBu4+mnj3HPPdC8OYwYYd+fl2efqmcmRo52rXClGTU7uzx06maa\nwPfsgc8+s3+++mq7WKlcGXbunEFY2HNAKG+/bXcXG0nPnhO4eHEToPDCC9C7N9Srp7dcwTvvGHvN\nsgh0V5pRI12zrK76viWQhdGhQ5r3oFYte9xpxYrwn/8EO2bavfceGJ3zcfJkLUVLv372f7Vq2ber\nmJ342sg2FBWleWLMakMREVq8pz9imTBKSEhg3bp1xMfHF7t/8eKvSU5eDUBQ0CHGj9dUxNChmik7\nIUHzn5uB+kAGB3uXbBCcR55mBV/7olMPJIuRVZ36nDna55df1jqFJk3scQtgjwUxUuhv2PAjiYn/\nAu4mNPRRXn9d2zdwoPYbLlvmPIXe1xg5o6ZSJXMWY9YvlxBowqg8tSE1s8WQIdqSKn/7m90aC/bB\n8v+zd97xURTvH//cpZJCSCih90BoAlKkiIUiypciRUQ6AtIVQZogwk8wEBAEEQuIKC2ogKAICKGI\niPQgvXcMRSAhvdz8/tjbm7mUu+17G/b9evFiL9mdnezNM/vMM09hFRa5/PXXVXz6aVMAO+Dv79x2\nr17cvQFuN0PpRY0rlFSMLBbtag4qLUNq4ZFbaYQQjOPNQgC6dZuO8HCazDE4GHj9de44KQlYt067\nvimVbRTQrjp4Whr30gWUG5BGtRjpkeQxI4PbwgI4K1HPns6/nzCBZj1ftky5fg0bNgEA9yZp2bKJ\n03cfFAQMGsQdZ2YC69crc08h8H9f0aJUqZEKW4xZTRlKTaVJGNWQIXNx4RqbjQu6AThXgJx+PWPH\n0r9t9Wrg2jVl7jt48Acg5G8AbfD880vBVqDy9gaGDOGOCeEW6VrBW7sDA6lriRy0kCHAVIxksXLl\nRty79xcAwGqNxNKlb+Y6Z8AAesy/dNQmO5sOSLn+RTxsIVm1UMPhrSCsdrXaStu1C0hI4I47dco9\nkYWFAcOGccfp6ZzvnFzWrYvF9etbAQAWSwUsWzYi1zmssVarxQUh9GUqd6XLw0/qam4DmDJE0UOG\n9u0Dbt7kjtu2ze1EHhhIAwmys7mAA7n89dcxnD690v6pKD777LVc57AyxCtuWqC0DPHjIimJ+nAp\nTUYGrQmqQ8J9UXicYpSZmYmxYyc4PrdvPwvBwbm9hZs0ocrJjh3qF2EFOOWFj2Qy0oBUI6mWudoV\nzoYN9Lhz57zPGTWKWiC//lpeGLTNZsM779CQzZdemoHSpXMnoqtfH6hYkTvetUv91SLA+WrwmdKV\nlqHUVPWysJuKEUVvGerRI+9zRo4E/Py44+XL5Y+FgQOpDDVqNAUREbm9hStXBux5JhEXR5U3NUlP\np3Ou0osLQL0FBr84BEyLkWiWLPkG9+6dt39qjtmzO+Z5ntUK/O9/3HFaGjexq42Sjtc8WgxIpTP2\nAsad1LXeSiME2LSJO/bz41a7eVG+PB3Pt24BGzdmI1tiPoHVq2Nw69ZR+6d6WLiwZ57nWSxA167c\ncXY2sHWrpNuJQknfCB4tomrUUIzYqBwjLS702I7my6Gx835OihXjXSwIHj7chGbNOiFTYhG6bdt+\nx9mz9mgJVMJnnw3L99xXXqHHfICFmrBWuiddhtTCoxQjm82GWbOoDbRBgzmIjMw/hLl9e3r8229q\n9oxDyVB9Hi3ysKgxIAMCqAOxkSZ1rbcBzp6lCvWLL7r2BxjmmHt/x4ABDSSVOUhPT8e4cZMdn+vV\ni0a1avmLebt29Dg2VvTtRKO2YmSkxYWXF80pZqTFRWAgDX7RQjG6eRM4dYo7btzY9fMfPhwAxgLo\nhLi4TVi6dKno+9lsNowcSa1FEREz8cwzfvme36YNPdZCMVJDhrTIZWQqRhKxWq146qk/AbwLoCcm\nTmzq8vyWLWmY4Z49qnevQEzqSg1Ii4W2pcWkbrUqk5gyOJhGs2gxqbOWzJYtXZ/bti1QpsxJAG3x\n+PFxTJkivsxBXFwc7jtCHF/CpEltXJ7ftCndfoiNpVE/amEuLpzRUoYAZRQjgM5/WsjQ9u30+KWX\nXJ/buDFQrRrda5syZRoeP34s6n6rVq3CxYt8cq8GeP/9112e/8wzdMGzY4e2MmRajNTBoxSjW7eA\nrVuLApiH8PCV6NTJ9fnBwcDTT3PHp06pH/KuZJ00noIwqWthMQoNVSapnta1nljF6MUXXZ9rtQKj\nRtUG0AUAcO9ePObNmyfqfpUqPQPgEoARCA2djVdfdX1+oUJA8+bc8fXrXLkDNTHqpK5W8UstFSNv\nb2UydgP0u0tIUM+vi2fvXnrcurXrcy0W4L33GgPgHKUfPLiLuXPnur4oB3fuJALgwkQDA6PRvbvr\nicfHB3jhBf5a4MQJUbcTjZLpLnhMi5EzHqUYffMNdW4ePNgiKAHU88/TY1aA1MCoFiO1JnXepJ2Y\nSDM6K41SxS9Z+O/uwQP1HN4BbuXIWzJDQjhnZ3e8+Sbg4xMFgAs4iI6Oxh0Re37ffQdkZZUAsAiD\nB9cTFA7PWrL++EPwrSRREPz01JCh9HT1FAxWhiwKJVfXckt6/37uf29voGFD9+f37AkEBX0MXobm\nzp2Lf9mB5wZ//xEALgJYiP79WzqSR7qCVdjUliGjLi5MxUgCWVk0TNlqFV5/5rnn6LGWk7oaFiMj\n+UcAdHAT4hxxoBRZWbRdNRQjQN1J/fJlWnakeXO67euK4sWB7t2rAeASpCQnJ2OawDoHNptzqL9Q\nGeItRgDw99/CrpGK2v4RRpvUtQhiUHNxAahreX3wgPPTA7iFBb8N7orAQGDAgKoAOKe9lJQUwTJE\nCF8TrSSAUY48Re4wugyZipEzHqMY/fILt5UGcFEH5csLu65ZM3p86JDy/WJRw4Rp5AGpdpJHtk0l\nil/yaKUYseOxcWPh13FO2FMBcI4LS5YswVn+7eCC3bu5OmgA0KoVl1VbCI0a0W1KfnWuFuak7oza\nilFmJi1noaRipFVk2oED9Lipa5dTJ4YOBYAPAHB7h0uXLsUZAbVC9u7lCtUCnLJTp46w+z31FC3O\nbETFyNxKc8ZjFKPPPqPHXGSBMIoWBSpV4o6PHVO3YjpvMSpcGILMq0Iw8oBUe1JXw2kU0G61e/Ag\nPRajGDVrBtSpUwIAl88rOzsbkyZNcnsdW/37rbeE3y8wkJvYAeDkSfoiVQP+efv4KPedGnkrTW0Z\nYrfRjShDrJIhRjGqWRN44YXi4GWoUKFgQYsLVoaG5R+hnwtfX6BBA+740iV1C1Szz7tECWXaNLKf\nnhp4hGJ08iR1Uo2IcB95kBN+QKakULOrGvADUqltNMDYq121kzwaXTFiLUZ8EjghWCz8pPwugFLw\n8QnC008/DZsLR66bN2kSvJIl4dbpOif8S4cQdS2vbMZepfxdjLyVZsqQa1gLphjFCGBlaDJatryE\nzvllV7Vz5w7NAF+sGFdwWQxNmtBjdlGkNPzzDgujEaVyMbIMqYGuitHGjRvRuXNnzJhBtZmRI8VH\nH7EOeYcPK9S5HCQnA3zUp1LmS0AbixE/4VosykWlAAXDYiTCJ1MUWVnAUXuOxYoVxRcc7t0bCAoK\nBPAjfHwu4p13PoA1D8FItXvsfvkltZYOGSK+BhmruMXFibtWKNnZdCWtpAxpubiwWpWpTcVTEGRI\nLcXIZqNbaaVKCXev4Hn1VSA8PADADGzZUhS3b7s+f9kyWg/vzTfFKx3PPEOP1dpOI4Ru/yspQwEB\n9O81mtVVDXRTjLKysjBhwgT8/PPPWLu2NoB/EBQE9O8vvi3eYgQAR44o1UNn1Mi/AnDbGGpXB2cL\n9ykR8s7DDm4jrXbZ70+tSf30aVqmRsw2Gk9wMKccAc2RkhKOb7/NfY7NZkOLFi3QpcvrWLjwEgAu\nckfMNhpP3br0+Pjx/M+Tw927NHpRyUnd15cqK2pP6iEh6smQqRg5c+kS3dZt3Fi8hdHXlwYgZGUB\nS5bkfd65c+eQlgYsXMh9tlgg2OmahV1cHDsm/nohJCXReUVJGdKiGDM7vkNyV1fxKHRTjL7//nuc\nO3fO/qkpgDro319aEj9WMVLLYqSGwxsAxMSscUxYak/qSmvpSjpfr1mzJtfPjDypS91GA+izGMHU\nfY2O5krfsMTExODIkSPYsOEHPH7Mlf3o0wdOFcCFUrMmp1QB6lmMxMpQXmMiP/jxocXiQkmEbqWJ\neRYsaskQ69uilgyxCnq9etz/Yp/DW29RRfbTT3M/499//x2RkZFo0aIX4uOvAAC6dOFqoImlQgX6\nwldrccE+67Q0aWMiP7R6DwUF0blGKaTKR37ophh9/PHHzKc58POzYMKEfE93SWgoUKUKdxwXJ68A\nZ36oEaoPcF+ompo6IepN6kpajLRUjLSIqGEVdKmKUe3acCQ5vX3bOUAhPT0dkydPZq6aCYsFmDhR\nWn/9/YHISO74zBkur47SqKkY8TL04IHymYe1kiFXiwtPU4x8fOj2sBaKEW/RFPscypUD+vbljh89\nAmbPpr+z2WwYP54r/XH48GoAnEOTk1iJwGKhQQw3b6ozn7PPOj5eWWWAl6G0NHWKsqslQ0ABUozu\nOdz2uwFogmHDgLJlpbfHW41SU7mJXWnUshgB6lYHT0mhiqInW4zyQq1J3c+P9l2tSf2ff+gxv9qV\nwrRpdAvh//6PprRYvHgxrl69aj/rJQCt0bMnUK2a9Hvx/czKoiHLSqKmDPGTelYW9QVUCjVlyKhb\naYBzWRA1ymDkpRhJYfp06j+zYAHN7r5q1Socd9zkaQA90KmTsESs+cHKuhpWI1aGlHK85lHbAVtN\nxUhpNFeM7t69y3zyBvAxQkLcr3TdaYTsdhq7vytFk8zrGneTuhyNVWy4sZh7UUvOGkkD0tW98pvU\nldLehUzqUr9fsZO6mPsQQssCFCu2RtZ+er161GcoKYmrHn737iPMmDHDfoYFwGz4+KyBkxFWADn/\nJnZSd7WdJvWZq+WnBziPj2+/VUbmefJzGpU6ztnr1FSM1qxZI0kxEvp38TKUng58842yzxygikVw\nMBfAIJXy5YFWrbh7paVxmbEfPkzDRKeXTjT8/KxgK/BI+X7Z7S0xipHQe7EyxOdNEoOr+7gKYpD7\nHmUzu7t6Dylt+ZGKpopRRgbw9tuzmJ8MARCB+fPdJ0x098B4EybAhf8LvU7ovdxtpcn5QsVGpom5\nF51s10jKeu3qXvn5RxhJMUpJ4RQOIdcI5do1arXw8pL/LGbOpNbUffuAp56ahQeOh9MHQD1Ur75G\ndNROzr9JqAO2EoqRWhYjAFi3zjiKkZrh+jkVI6FJUsUqRgCwerWyz/zhQ652H8DN7XId3glZ48h3\nd+DAWZQu3RC3HWFqLwNohWnTnH2LpHy/Z89qpxhJsRi5ug87x+Yci3Lfo2xlBCMoRoq5QBFCF6nj\nvQAAIABJREFU3FYxXrqUYMsW/i3kA+BdDBiQiC5d3CeVy8rKQqKLkypUoMfHjtH23F0n9F43btDj\nwMDc/ZVyH/66oCB63fXrzn+L0P7lB7/1AmShUKFE0cn7XN2LjRK5f1/5Z84aF63WvMeI1HsVK0av\nuXiR+qiJ6V9+sKG6QUHyn4WPD/D998ArrwDp6Udx5060/TdWAOPx2muJePxY/n3Yl8Lhw/nLpNRn\nfv06vSYvGZJzHzaEPjVVmfHHQ2WIK0khZ5znvI4QTo4I4VbpSj/zu3fpNd7ewpJ3Cr0Xq9QlJyv7\nzNn8RTVqyH/mQBa++y4Rr7wCJCfPRlraKeZ3H6B9+0QMHer8fKTcq1ChLFgsiSCES9ch9HKh9+KV\nRQDw8lL2mbNJi2/elP8s2Gtu3nS+j5LjXOx1wcHBsLgJcbQQoszucGJiIkI8PQbPxMTExMTE5Ikl\nISEBhd2EvyumGAmxGAFAkyYjcebMCgDA4MGDMXfuXCVuDwBo25au1q9fVzZXQrVqXGKtUqWUz669\nfDnwzjvc8YIF0nI55cfatdRHZfZsvoaQctSowUVMhYcD588r23bFipxJt2JF5R0ZFywApk7ljpcv\nB9wkxRVFv37Azz9zx4cOyXOIzklmJjB+/KdYtuxDAECbNm3w008/KdZ+t27A9u3c8YkT4pPquaJ+\nfc7xNTjYeQWpBKtX0xIOc+cKL6ArBLVlqF494MoVzgLj8KdXiLp1uTbVaJt9LrNmiSuh4Y4RI4CV\nK7nj2FjnJL5yuXDhErp27YVr17gonf/9739YvXq1Yu0PHAjwIrlvHxddqhQtWnCBHVYrZ2FUMqfW\nxo00gm/aNODdd5VrOzaWS4MAAOPGAVOmKNe2WIRYjBTbSrNYLG61MADYtGkqIiI4xejbb7/FuHHj\nEBERoUgf6tVzVozYisdyYDP2likjLdeSK8qUocepqcq2z+a+KVVK+b6HhXGKUUKCsm3bbHRfulgx\n5fvNOnMmJirbPq8g+vlxY1LpnB2LFo3D9u1LcePGDWzfvh2HDx9Gy5YtFWm7YUOqGF25ouykzm+N\nqjEO1ZShjAx6XLKkOjJ05Qo3DoODlSuVAlD/KDVkiN16ffRI2fYvXKDHzzzDbb0qRYMG9XHq1CFU\nqVIFd+7cwebNm3HixAk0V+iFUb8+VYxu3HAudC4XXoZKllQ+uouNCk9JUfb75DOKA9wiWumxqDSa\nR6WVYDKDZWVl4f3331esbXYSZx2w5XL/vjoZe3nULGnAOo5Kcb52B99mWlruBIRySEykz1zpMGNA\nvbIgWVl0Uq9WTXmlCAAKFSrERKUB48aNc1lHTQw1a9JjJdNeJCVRJ3elI9IAdUvrqF3KgG8zO1tY\nIIBQsrNp39WWISXTXhBCrfIVKiirFPEEBgbmkiGFNk+cZEjJtBfZ2c6LC6XRSobUeA8pjW55jIoX\nLw4A+Omnn3CAL4gjkzp16LGSipGa0TRAwZjUc95LLmrmXwHUm9QvX6arIz5hohr07t0bde1hZEeP\nHkVMTIwi7aqlGLHKp5TM3O4wZSg3bFtGkqH4eGotrlFDuXZz0r9/f9Sw32D//v34md//lgnbZyVl\niC2pY2TFyMxj5AI2h4RS2jprMeLzyCgBO6mrrRipaTFSY0CqleTRqIoR63+mpmJktVoxZ84cx+dp\n06YpYjWKjKRbOUqudtkCnmooRmJzgYlBSxlSMmRfbRkKDaUWUSPKkLe3N2bNmgWLxYI+ffrg6aef\nVqTdKlW4SFJAWRlSq/oCj6kYUXRTjPr164dqdq/Uv/76CycVMPGEhdF8SEZa7Rp5UjeqxahoUWNP\n6gDneN22bVu8/vrr2LJlC6wKeGIGBFD/qzNnlMtorPakzioXpgxxqC1DViudb40qQx06dMDp06fx\n/fffo4K7PCkC8famARfnzytXokptGQoIoAXNjSZDSqObYuTj44OoqCh07twZp06dQh12H0wGvBnz\n7l3lvlw5q929e/eiY8eOKFOmDKxWKzZt2pTrnKioqQBKAwjAkSNtcPHiRVn9ZWFXoHqvdqOiotC4\ncWMULlwY4eHh6Ny5M87nCGVLT0/HiBEj0LVrMQDBALrBx+dunu3JQc9J/csvv0TdunUREhKCkJAQ\nNGvWDFu3bnX8nn8GxYoVQ0BAANq3b58jYzxl06ZNiImJQRV3iZhEwMvQ48fOOXzkIESGoqKiYLVa\nMWbMGMfP2GcRHByMbt265fksfHw4x2XAeFZXrs3pAKx44QUrrFbuX01mX1Poc2BRWzECqOX17l3O\nB0YJuEXtbQB9MH48JwN169bF0aNHnc6bOnUqSpcujYCAALRpI23etFgsiFRB++JlKDOTliARS6VK\nlRxjwWq1okMHK7hX9iiUKiVtTLjCYlGvkKxcGbLZbPjggw9QuXJlBAQEoGrVqk4+YjxKjAlAR8UI\nALp06YL169ejevXqirXJ7u8qFVYvRzFKTk5GvXr18Pnnn+cZIjh79mwsWrQIYWFfATiIrKxAtG3b\nFhlsKIwM+AHp7a2OE6OY1e7evXsxatQoHDhwADt27EBmZiZeeuklpDIF4kaPHo3Nmzdj0KB1AP4A\ncBurVnVVvuNQZ1Jnx1x+w7pcuXKYPXs2jhw5giNHjqBly5bo1KkTztjNnPwz+O677+Dr64stW7ag\nUaNGeW43+/JLPAVRw3nU3Wr30KFDWLJkicNviod/FuvWrcMff/yB27dvo2vXvMeD2pO61eqcSFIp\nqAzVxsKFdxAfH4/4+Hj8+eefjnPEPAceLRUjm40LUlGCEyceAWgOwA8//bQNZ86cwSeffIJQZhXG\nz5tfffUVDh48iMDAvOfNtLQ0TJkyhanNqQ1KyNDhw4cdYyE+Ph59+24HVwKoO0qVkjYm3KGWDMld\noM+aNQtfffUVFi9ejLNnzyI6OhrR0dFYtGiR4xyhY0IQRGMSEhIIAJKQkKBK+wsWEMJtABCydKky\nbXbqRNu8eVN6OxaLhWzcuNHpZ6VKlSLz5s0jdepw7fv6JhB/f3+ydu1amb3mqFSJa7dYMUWay8Xy\n5fTZfP65uGvv3btHLBYL2bt3LyGEGxu+vr5k/fr15KOP+HbPEovFQg4cOKB43//3P9r3O3fkt2ez\nERIayrVXvry4a8PCwsiyZcucnsHEiRMJAMc/NZ5BXixbRp/L/PnKtNmzJ23z3Dnn3z1+/JhUq1aN\nxMbGkhdeeIG8++67hBDn8cBz9mz+46F+fa59b2/uu1CKqlW5dkNDlWuTZdUqQoBpBKhPPv009+/F\nPgeehQvpM1+5Uo2eEzJwIL1HXJwybQYHTyDAcyQ0NP/vkZ83eRIS8p43586dSwCQ4OBgxeZUIaxZ\nQ5/Lxx8r02adOu8QIIIAhMTGShsT7nj2Wdrv1FQles3RpAltNzNT/PXt27cngwYNcvpZ165dSZ8+\nfRyfhY4JIehqMVIDNSICeIsRu/2iBFeuXEF8fDxatWrl8DPKyCiMhg2fwX42J74M1K5oLMc/4tGj\nR7BYLAizL1OOHDmCrKwstGrVilmxVEd4eHnFngeL0g7Yd+/SlZFQ67zNZkNMTAxSUlLQtGlTxzOI\njIzEp59+CoCzCpUpU0aVZ5AXakSmubIYjRgxAh06dMiVi+nw4cOO8cBTvXp1lC+f93jgV7tZWcqG\nvWsnQxfwwQdlUKVKFfTu3Rs37HWIWLngcfUceLS0GAHKyFBSEvD48S8AGsJq7Y6SJcPx9NNPY+nS\npY5z2HmTp3DhwnjmGed58+HDh5g5c6a93SRVtszyQ2kZyszMxLlzqwAMBADcvStONoTiql6aHHgZ\nCg6WlsKkWbNmiI2NxQV7LpTjx49j3759aNeuHQDhY0IoKmRZ0Rc1FaPwcGXz0sTHx8NisSA8PNxp\nQBYpEo54BWYZNkmiFoqRGEEihGD06NF49tlnHb4U8fHx8PX1ReHChZ0m9eLFlXkeOck5qbOFiKUg\nxmn05MmTaNq0KdLS0hAcHIwNGzYgMjISx44dg6+vL+bMmYM0e2KokSNH4s8//1TlGeQF23elttJ4\nGQoKor5AABATE4O4uDgcPnw41zV37txxjAeW8PC8x0POqBr2PlIhRCvFqAmA5ejUqTr69v0X06ZN\nw3PPPYeTJ086yQVLfs+Bx4iK0blzAHAZwBcoW3YsvvtuMg4cOIC3334b/v7+6N27t9O8yZLzeURF\nReGhfVLq27cvnpIr4CKoVo1bSNtsysjQhg0bkJmZAKAfACAzU5xsCCWnDCnl5C1XhiZOnIjExERE\nRkbCy8sLNpsNM2fORI8ePQBA8JgQSoGzGJUpQ/0AlFCMsrOpwKsRkcbDRqalpxO3KcuF8PgxzXuh\n1qQuNVx/+PDhOH36dL7VlNlJ3ctLmeeRE1bolUjyKEYxioyMxPHjx3HgwAEMGzYMffv2xVl7A4QQ\nfPfddwCAIkWKYPLkySBEnWeQFyEhdKwr5afHP1/2md+8eROjR4/GypUr4cPHNwsgv2ehRrhxSgqN\nKlJXhtoC6Apv79po06YNfvvtNzx8+BA//PBDvte5GxOsE7pRFCNuvNkANECvXh+hbt26eOuttzB4\n8GB88cUXLq9ln8e1a9ewcOFCAICfnx8++ugjUf24ffs2vvzySwl/AYe/P80MfvYsnYelsmzZMvj7\nvwKgJIoVy3+BLneeUCtkX65itHbtWqxevRoxMTE4duwYvvvuO8yZMwcrVqxweZ3U5+GxihGRGCds\nsdCX0tWrXHkAOdy7Rx1zlVaMSpYsCUII7ty54zQg7969m0vzlYIW2UalbKWNHDkSv/32G3bv3o3S\nzEMtWbIkMjIykJiY6CSUDx8q8zxywn6fSkRfiVGMvL29UblyZTz99NOYOXMm6tatiwULFqBkyZJI\nT0935CSaNGkSwsLCRI2Ju3fvYuTIkdi2bZvUP8Vheb1/X75TbXIyrabNPvMjR47g3r17aNCgAXx8\nfODj44M9e/ZgwYIF8PX1RXh4ONLT03NVzc7vWaiR9kKLMOO8rK4hISGoVq0aLl686CQXLO7GhBEt\nRpwMlQJQw0mGatSogev20vLsvMnCPo/JkycjPT0dAOekXK5cOcF9mDdvHqpWrYphw4bhb77GlAR4\nGUpO5kqDSOX69ev2YBWuAGCpUpA8JtyhhmLEVkWQKkPjx4/HpEmT8Nprr6FWrVro1asX3n33XURF\nRQEQNibE4HGK0X///YcxY8agv4xKqvyAJMS55o4U1ExMV6lSJZQsWRKxsbHMpJ6I06cPoJkCBXa0\nmNTFJqcbOXIkNm7ciF27dqF8jgqlDRo0gLe3N2JjYx1CGRBwHtevX0fTpk0V7DUHW19La8UoJzab\nDenp6fDy8nL8rGzZshg1ahTOnxf+DM6cOYMqVarg888/x7hx45AtMdyO7T+3vSGd/PyLWrdujRMn\nTiAuLg7Hjx/H8ePH0bBhQ/Tu3dtx7OPjg9jYWMc1rp6FGpO61ooRf7+kpCRcunQJpUuXdpILHiFj\ngn0GavVdacWIs/I3B3Auxxg858gzxM6bPImJiThwgJs3Dx8+jFWrVgEAihYtikmTJonqQ2BgoCNS\ndvz48ZIX6Uq5dSxbtgzFi4cjK4vzpylZEpLHhDvUkCHenQOQPg5TUlJyWX6sVqtjAeluTIhGtLu2\nTFxFpWVnZ5Nq1ao5onAOHjwo6R4zZ1IP+JgYef395Rfa1vTp4q9PSkoicXFx5NixY8RisZD58+eT\nuLg4cv36dUIIIbNnzyZhYWFk5MhNBPiHAJ1I8eJVSXp6uryOE0J276Z9HzdOdnN5YrMR4uXF3aNB\nA9fnDhs2jBQpUoT88ccfJD4+3vEvlQl/GDZsGKlYsSIJDd1FgMPE17cZefbZZ1Xp+82b9Pl07Ci/\nvYoVubZCQlxHRb3//vtk79695OrVq+TEiRNk4sSJxMvLi8TGxhJCuAgMX19fMmHCBHL48GHSrJnw\nZ2Cz2UijRo0cMvTtt99K+ls++4w+myVLJDXhYM8e2taYMa7PZaPSCKHjYdeuXW6fBRtN98UX8vrM\ns28fbZPplqLYbIRYre8RYA+pUeMq2bdvH2ndujUpUaIEuX//PiFE3HPgiYjg+l2kiDr9JoSQx4/p\n83nhBfnt1apFCHCIAL5kxoyPycWLF8mqVatIUFAQWbNmjeM8ft7ctGkT+eeff0inTp1I1arcvDl+\n/HjH+F+wYIHoPmRmZpLq1as72sgZSSyUb7+lzyavaEMh2Gw2UqFCBTJ48PuOtvr25X4nZUy4IyaG\n9nnuXFlNOTh7lrbJBJGJon///qRcuXJk8+bN5OrVq2T9+vWkePHiZNKkSY5zXI0JsXiUYkQIIYsW\nLXIMyOeff57YJMTdrltHv4hp0+T196uv5L0gdu/eTSwWC7FarU7/BgwY4Djnww8/JKGhpQhQiAAv\nkTFjLsjrtJ2ff6Z9nzlTkSbzpGhR7h6VK7s+L6/nYLVayXfffec4Jy0tjYwYMZIARQkQREJCupE7\nSsTS50FWlnClzh3JyYRYLFxbzzzj+tyBAweSSpUqEX9/fxIeHk7atGnjUIoI4Z/BCFK0aFESFBRE\nunUT9wx2797tkKEyZcqQlJQU0X/P9u107IwdK/pyJ9jJds4c1+e++OKLTopRWloaGTlypKBnocZ4\n37xZ3sJIKH5+PQhQhlgs/qRcuXLkjTfeIJcvX3b8Xsxz4BEql3IJDOTuExkpr53MTEJ8ffl0F5tJ\nnTp1SKFChUjNmjXJN998k+v8Dz/8kJQqVYoUKlSIvPTSS+TCBW7etNlsZPPmzaRDhw6SF5jr1693\nyFCNGjVIpoQY8/376dgZOlRSN8jvv/9OrFYrWb78gqOtCRO430kZE+7vR/v8/vuymnLw99+0zVGj\npLWRlJRE3n33XVKxYkUSEBBAqlatSqZOnZrre8lvTIjF4xSjjIwMEhER4RiUv/76q+h7nDpFv4ge\nPeT198MPaVubN8tryxXsqlrui4iHXbGIzTEkhipVuHuEhSnTHrsKbdlSmTbzo0wZ7j4lS8pr59gx\n2ud+/RTpmiw6dOjgkKGoqCjR19+4Qf+e//1PXl/mzaNtrVolry1X/PGH8jLE5Rji/kkwPgimenXu\nHoULK9NedjYhVivXZsOGyrSZH7z8y7VMXbhAn3XXrsr0TSo2m400a9bMIUNff/216DYePFDOmsbO\n5QsXymvLFYcPy1fmcrJ1K23zgw+UaVNtPM7HyMfHBx9//LHj84QJE0T7SVStCvCuGnKjatQufsnD\nOo4qVdJAC+drtu1Hj+RHXwDaOI3y8H5Gd+5w6fulomV9JyHMmjXLUTstKioK90V6ULPRnXJlSO0a\nTzxG9TFi205MVCYLe2IilUW1ZYj/Th894qL4pML64egtQxaLBdHR0Y7PH374IZKTk0W1ERpK897J\nlSHWB7JsWXltucLIMqQkHqcYAUDXrl3xzDPPAABOnTrlCF0Wiq8vV+EY4BxH5bystVKMjDwg+bZt\nNmUS6+mhGBEiL2Tf0xSjmjVrYuBALhlcYmJinnWFXMFGd165QqNKpGDKkHvYhUuOQCNJaClD7Ita\nThCDp8lQ8+bN8eqrrwIA/v33X2zcuFF0G/zfER8vr0Aw+1zZoBGlUUOG2KAcNRfoSuKRipHFYsGc\nOXMcnz/44AOkiFyK8AMyNRWwR3lKgp/Uvb2BYsWkt+MOdkCqYTHSQjEClMmWak7qyjB9+nQEBAQA\n4CJWbCJXCPzfYbMBcuoaa2UxYiddoylGasoQa41WA1aGbt6U3g4rQ2xEl55ERUWhSZMm2LlzJ3r2\n7Cn6eqWiO9nnqqbFqHBhuttiNBlSEo9UjACgRYsW6NChAwCgatWqorcC2AEpx4zJK0alSnGZTNXC\nz48WeTXagJSa5DE/2BeDVhYjQBnFyNubWiv1plSpUvj000+xZcsWbN682bG1JhRWhuSEG/MyFBio\nTDbq/PD3B+x6oCoyFBKiTJt5Iae0Tl5oubhgUwTJydfDjjEF64rLIjIyEvv378eLL74o8Xp6LOc9\nxM9NXl7KlqXKicVC53OjvYeURDfFqEePHujYsWO+mY8BIDo6Gps2bcLu3btz5bxxB7vikDogMzO5\n+leAulsAPPzKTimLkdyKxkIx8qTOKkZSV7s2G10NVqkCiEjijPfeew+LFi1CphwHJxcMHjwYL7/8\nsqTsr0pP6qVKcROvmvAyZLRJ3cgypITFiBA6xsqWpf5tQlBLdpRADRliUp2pAj9enuStNN1qpcXE\nxOSq85KTyMhIyYX/lBiQd+5wAgtooxiFhXHbfg8ecPeV+xLRw2JktK00JSxG169THxwxWwBxcXGY\nN28eCCFYtWoV/vrrL83KfghBCRlKSOBK0wDOlgW1CAvjrBb//WdcGVJCMdKiHAiPEorRvXviCzAD\nXM3Btm3bYurUqRg4cCC8lSxmqQBKyFBGBvcuAtT1L+Lhx0tiImccELPQywvTYuRBsKZYqQNSK6dR\nHn61m5VFXyZy4CcaPz+gUCH57eVHQVntSlWMpETTEEIwduxYR1bd1157zaOUIoCL7uR336TKEPui\n1EoxAriXiZwIKR5+PFss6m4DFhQ/PamKkVT/ovHjx+P27dsYOnQolixZIu3mKlK+PLfFC0iXIdZH\nT03/Ih52vCjtGmEqRjrDhkpK9Y9ghVwrixGPEmZMfkCqbb580i1GUhyvf/31V+zcuRMAULlyZYwY\nMULazVXEz4/6S0kthMn6nGipGAHKyBD/YggJUdfH0MiLi/BwWtRUqo+RlMXFjh07sGXLFgBAuXLl\nZJWRUgurlS7SL16UlhKEfQ9paTEClJUhi4Vz7jYCBVYxAqiA3b0r7Qu+do0e28v0qIrSuYy0UoyU\nntTZv13tvgcE0P4rsdoVMqlnZmZi3Lhxjs/R0dHw8/OTdnOV4f+elBRpimNBUYzUXukqvZWmpWLk\n5UUXjlrJkM1mc5KhmTNnopCaZvF8+iAE/u/JygIuXxZ/H61C9XmMurhQEoN0UxqsSVZKqCQb5i/S\n91sSSg7IzEyuqjNgbIuR2qHGAJ1sbt2iPmViYCd1IdE0X331Fc7ZB+Szzz6LLl26iL+pTB4/fiwo\nBYbcyDRWMdJ6G0CuDBGinWJk5K00gH639+9Ly3l1+jQ9FrKVtnLlSsTFxQEA6tevj169eom/qUQy\nMjIwf/581K9fX7QMSdlO0yq5I49aOxdG2UYDDKoYJScn48iRI27PkzsgWYuRFoqRkhYjLR3e1LIY\n+fur6xvFw0826enSJgJ+bJUs6f5ZP3r0CNOmTXN8/uSTTzT1LcrMzMTixYtRtWpVp1xh+SFXhoxs\nMUpNpVsfRpUhQBvFiP1upVgWeaU7JISTI1ekpqZiypQpjs9z5swRnYpCDqNGjcKYMWPwzz//YN68\neW7PlytD7ALdaIoRu7gwSkQaYDDFiBCCZcuWISIiAu3bt0eSmzTLcle7/IC0Wo1nwtQyRFIt/wgt\nrEWAvJD9Bw9oSgchWwBXr151RGP27NkTjRs3FndDmVy7dg3vvPMO7t69izlz5iA+Pt7l+XIndb2c\nrwH5MmTkxQX/txcuTP1/1IR9YYv1M0pKotfUqOE+knDBggW4Yb+gXbt2aNWqlbgbymT06NHwssfM\nz5o1S3UZ0tqlQ0kZSknhthAB02KkGhaLBb/++iv+/fdfxMfHO9WyyQulBmSZMtpMLqwiYFTFSO42\nACF0tavFShdwfmGLzZLObtEK2QKoV68ezpw5g7lz5zrVBNSKqlWrYsiQIQA4y+v06dNdnq+UxSgw\nUJuJUUkZMrJipLUMyYlMY8dVzZruz69SpQrKly8Pq9Xq9h2gBjVq1MBbb70FgJOhqVOnujy/WjV6\nLOc95OVl7AW6qRipyOzZs+FjT6wwd+5c3HQhheXK0Uy4YgdkSgq3Xw5oo6UDypYF0VIxYtMByJ3U\nU1O5LS1AO4tRxYr0+OpVcddKydbr5+eHsWPHooJWAysHU6dORZA9g96SJUtw1oVwhIUBJUpwx2Jl\niBCqGJUrp35yR0BZGdJSMfLxoZnv5S4ubDbtra5yFCOx/kWvvfYazp07h19//RW1atUSdzOFmDZt\nGoLt+Ru++eYbnDx5Mt9zAwLoO+TsWfF+jFov0NWyuppbaSoSERHhCG1OTU3F5MmT8z2XDZW8fJm+\ncIWgteM1YFyLEXsPuZO61r4RgDzF6NQpeqzTHC2aEiVKYMKECQCA7OxsTJw40eX5vNXo33+5hI1C\nefCA5hLSwjcCMO5WGnsPuYuLx49pagU9rK5it9LYxYXQHEb+/v545ZVXxN1IQUqUKIH3338fABed\n9t5777k8n5ehR4/o1rsQkpPpnKjHAt1oMqQUhlOMAK6obKj9Tfz999+7dMTmB2R2NnDpkvB7aL2v\nCxjXYgQoN6lrHZEGAJUq0eMrV8Rdy652hWwDeApjxoxBaXuM9caNG7F37958z5W6ncY+S/YZq4mR\nJ3VeTuXKEDt3aCVD7OJRjtXVSDI0evRoR6mqbdu2Ydu2bfmeK1WG9H4PmVtpBiIsLMxpX5fNIJwT\nqQ7YeliMlKwOrrUJk79HcrK0JGY8eliMypSh9YekWoxCQtStHK80AQEB+L//+z/H53HjxgmSITGT\nOvssTcXIPfw9UlK4zN1S0TpUH+AiyfgMz2IXF/y8XKiQdi9/JfD390dUVBQAbifDVTkSIylG7Fg3\n2ntIKQypGAHA8OHDUbVqVQDAnj17sH379jzPM9KA9PGhmUGNajEC5K149bAYeXvTrQAxilFiIt02\nqFVLGx8aJenXrx9q1aqFChUq4O2331ZcMWJfkOx2pZoUKkRf0EZVjHLeWyx6LC4sFvodX70q3I8m\nPZ3LCA1wbg9GSQDI06NHD6xYsQInT550GR1npPeQlxcdi0aTIaUw2DCk+Pr6Ijo6GqVLl8by5cvR\nunXrPM9j96zFDEg9LEaAcpWN9fIxynlvsegxqQPUovHwoXA/GiHRNGfOnBGcIVdrvL1Rppg5AAAg\nAElEQVS9sXHjRpw7dw49e/bMNxeMkbbSAOVkyKiKkR6LC4B+x6mptOipOy5coP5QRtpG47Farejd\nuzd8fX1dnmckxQhQ5z1kKkYa8eqrr+LChQvo169fvpN6RARdyUsdkFoqRvxE9uCBtNpUPFoPSKNP\n6lIcsN05Xt+7dw9NmjRB48aN8ccff8jpnmpUqVLFbTmSChWkFcI0FSNxKFUWRI+tNECar547x+sH\nDx4gJiYmX2umUQgP57bbAWMpRg8fynsPmVtpOmCxWBDAx+Png78/FVgxoZL8yzE0VN2q2jnhB6TN\nxm3VSMWoW2l6WYykKEbuHK+nTZuGxMREHDlyBCtWrJDTPV2RWgiTfzkGBNCQfy3gFerUVO6fVNhx\nzL/U1ESpfGB6OF8DzjIkVDFyF6o/bdo0vPHGG2jevLnLtBKejsVCrUbXrtFoTXewz1GPnQtCxEWi\n5sS0GHkw/IBMShKWrj4tjfqO8NXFtUKpsiD8gPT2pvlR1ESprTS9twEA4ZO6K4vRiRMn8OWXXwIA\nAgMD8dFHH8nsob6whTCFRHfabFTBrFhRW/8rpRyw2XGshZKuhtXVyBajM2fOYPHixQCA48ePO/IG\nGRVehggBzp8Xds2FC9z/ZctqUx6JRykZMi1GHoxYP6MrV6hlKSJCnT7lh9KTemioNi+lJ9liVLgw\nrS4OcKVrRo8e7fAtmjx5Mkq6KwDl4Yj1kYiPp3nDtHK85lFKhvhrvby0sRobXYbkKEbe3oA9lsbB\nmDFjkJ2dDQCYOHEiymiR9llFWKuyi3yQDh48oN8lmz1bC9RQjEyLkYfBTuqs6TY/eC0dyC2saqO0\nxUgrLV0Ni5EnT+pJSXT/P2dE2oYNG7Bz504AQOXKlfHuu+8q2FN9YGWItZTlx+XL9FhL/yLAuIsL\nNXyMtLS6Vq5Mj4VYFbOzaUmdqlUB1n/5t99+w9atWwEA5cqVw9ixYxXsqfpkZ2cjJibGodgBwFNP\n0d8fP+6+DfY9ZPQFuo+PthYvuTwRilGdOvRYyIDkw0cBYw7I7Gzqn6SVYqT0ajcwkCs1ohWlS1MH\nYyFm7vyS0qWmpjpN4p988gn8+YYNAiEEq1atwrp16xw/Y2Xon3/ct8HWkDPqape/VisFXSkfI/Zv\n1nKVHhoKFCvGHbPff35cuUKtiqxVPzMzE2PGjHF8jo6OdutL6kkcOnQIDRs2xBtvvIGlS5c6fs4q\nRkJkiJ2HjC5DRYsaK51JgVOMCCFYv349WrZsiVS752WdOjQ/Rlyc+zaMbjFineWMajHScqULcOOD\nV4IvXaIVofODtZqwitHixYtx1b4X17p1a3Tq1EnZjqpMcnIymjdvjt69e2PkyJF4/PgxAM75mldU\nhSwu2Bej0BpySqHU4oKXI6MuLooU0aa2Fgv/Xf/7L1eaxBXsOKpdmx4vXrwY5+wDqGnTpnj99dcV\n7qW6pKenI87+opkyZQoe2b/MUqWo4ihWMTLiAp291kj+RYCOilGPHj3QsWNHrFmzRtF2J0+ejK5d\nu2LXrl345JNPAHBRMbzAnjzpPqrG6BYjrSPSAGUmdUK0rwrOwo+RzEz322knTtBj1vF66NChmDJl\nCoKCgrBgwQJYjLRMAucozvtDxcfH4+OPPwbAvWD5l9f581yGc1ewk7oRFSN2DGs1FpXeStNThgD3\nlld2kVq/Pve/zWZzBC0AMKQMPfvss+jRowcA4P79+44M8xYLtRrFx7uvmcYu0I1oMcrIoPOEHmNR\nDropRjExMdi0aRPeeOMNRdvt1asXvOz1HaKionDTXuq5Xj3u9xkZ7kuD8AMyJER7y4USFiM9FCMl\nJvWkJGqp0fq5A86TurutgGPH6DE/tgAagXbjxg3UNGLGOgBz5851JKybN28eLtsdhurW5X5PiHvn\nUf75+ftrG2YMKDOps9cZaXFhs1H511sxcidDrMWIH1tWqxUHDhzA+PHjMXjwYDRq1Ej5TmrA7Nmz\nUcjuVPPZZ5/hjP2lI2Y7jVcsvbyM6aendVSnkhS4rbRatWphxIgRAICUlBSMHz8egPPLy9V2GutU\nW7269vuiRrUYBQfTZyV1K02vaBoeoZM6IVQxKlWKS96WkyJGCsHIQeXKlR0+HhkZGY7K4fzLC3C9\nncaG9EdEaF/mQenFhVZjsXBh+TKUkEAT8nn64oKfhwsXdo5cLFy4MGbPno2vvvpK8f5pRfny5R3v\nnqysLEfJHVaGXClGhNAFesWKzo7pWqD04sJUjDyAadOmoah9VlizZg327t3rMNUCrhUjdiXMOpxq\nhdKTulbvZ6uVJsGTutrVK5qGR+ikfu0a/RvZcVWQeP/99x1bahs2bEBsbKzgxcXVq3S7WustAMC4\nFiOrldZKVEKG9HgZsd+3q620Bw9orri6dfNWno22hZaT8ePHo4I9XfWOHTuwbt06wZFp8fHcIh0w\nZUgPCqRiFBoaipkzZzo+v/3226hdm4ZNstsgOWF9R/RQjIoUoatGI1mM2HsVBIuRq5B0dvwUVMUo\nODgYs2bNcnweNWoUatSgznmuJnVWhvLKZqw2Rt4G4GVIqmKkV9ZrnipVuK0fwLUMsYo1q3AXJAIC\nAvDpp586Pi9cuBA1a9Ln4+o9xLp76KEYse8N02JUgBg0aBDq2SUuLi4Ov/zyjSMJX1xc/qVB9FaM\n2MrGUi1GemUb5fv96JHw0isseluMQkJoPaJ//sm/RtDRo/S4oCpGANCnTx8888wzAIBHjx7h3r0L\nDl+HY8fyD2LQW3EMCKBbD0ab1HkZevhQvgzp8TLy9aVRmqdPc1UE8uLgQXpckGWoU6dO6Ny5M6ZO\nnYpt27bB35++V06dyj9yj91m0+M95OsLBAVxx0aTISUosIqRl5cXFi5cCAAICwuDn5+fY2Xy6FH+\n2Y31VowA+UUw9bYYZWW5j1rKC70tRgBdvSYlOScpZPn7b3rcoIGxi1u6wmq1YvHixRg9ejTOnj2L\nmjVrwq4nITU1fx8JvRUji8W4MsQrRpmZ0uq8eYIM8d95dnb+TvqsDDVtqn6f9MJisWDdunWYPn26\nwxm7SRPudzYbcPhw3texssVuv2mJkjJkKkYeRIsWLbBs2TJcuHAB/fr1Q+PG9Hd//ZX7fEKoYlSy\nJFC8uDb9zAlvLXn0iJtcxKL3pA5I2wrQ22IEOJv189ouys4GDhzgjosVO4BevZ515CwpiDz99NOY\nP38+CtudX9iXGPtyY+EVoyJFtC8HwiN3UtdrtSs3utMTZIhVhvPaLiKEjp2QkERERBTcxQWQ21eK\nV4wAYP/+vK/h5x6rNXcdRq1gZciI1ks5FGjFCAAGDBiAMPu30qwZ/fm+fbnPjY+nKy69rEWAc2Vj\nKZOj3hajnH0Qiiesdtmokbz0ndOnefN3NrKyhuOvv/5CgwYNsHv3bo16qC+sYpTXpH7vHi3UXK+e\nftlu+fGTnEyzK4uhICwu9LYYAXkrRteuAXfuAACBl9eraNu2jSOc/UnA3eIiPZ1a2iIiuK1hPeDH\nT1aW+2SdeWE6XxuEJk1o9ENeitGhQ/SYfUFqDbvSk7LiLQiTuidYjI4cyf17qgx8iUePOGej2rVr\n49lnn1W9b55A3bq0dEpeipHe22g8rFIgRUnX28cIkL+48AQZyksxouPmRzx4sAuxsbHo3Lmzo+hy\nQScigs7L+/fntsYcP87l2wMAPdM48Vm6AeD+ffHXe4KSLpUnSjEKDqb7tSdO5H55s9treu57s4NI\nigO21lXBeeRuA3iCxahiRbqF+tdfubcy9+wBgHgAkx0/W7x4Mby1rr2gE76+QMOG3PHly9Q6xOMp\njuly017otdotCBajkBBaUPb48dxO+lx95SQAtKbgnDlzYNU64ZVOWCx0O+3+/dxpDfitesB5201r\nTMXoCeL557n/CQF27HD+HbsC1lMxkmsx4l8EWhfuk7va9QRBsliA557jjhMSnJ3xbTbg998BYBwA\nrpDWgAED0Lx5c627qSutWtHjLVucf7d3Lz3Wc7UrN2SfH78BAdoWM5a7uGBfYHpZjAD6Qk9Ndba8\nEgJs2wYA0wFwVQnatWuH9u3ba91FXXnhBQCwAUjA9u3Ov2PfQ3ywgx6wPrb37om/npchi4XmuDMK\nT5xi9PLL9Jid1JOT6X5vxYpcRmO9kGsx4idHrSdGuatd/m8tXFj74pcsvGIEAH/8QY+PHAHu398N\nYCUALl/W7NmzNe2bJ9CuHQAQAHvx22/051lZVDEKD9e+RhqLXMVIr+KXcmWIf4GxaT/0gF+AAryV\nlePsWeDGjX8AzAcA+Pn5GbIemlzKlTsKoDmAN7BtG91LIwSIjeWOg4L0delgFSM5FqOQEJq7ySg8\ncYrR88/zPhK/YuPGXY5cNbt3033dl17SqXN25FiM0tNpqDxrCtUCuc7X/N+q50oXcJ7UWaviL79k\nABjh+BwVFYXieoUu6khw8Dn4+LwE4Dls2bLFITcHDlAnzeef18/xGlDOYqS15VKu1ZVdFOm5M8VZ\nRDg4CxHHb7/ZAAwBwO1RT548GVWrVtWya7qTmZmJiRM7A/gbwBZs2/ajQ25OnKDFZV94AfDx0amT\ncH5/SLEY6VnMWC5PnGKUnZ2EkJAuADrgv/8GYft2LlnIL7/Qc1irkh7IsRjp6XwpZ7Wbne05ilGd\nOly6BoCb1PmElT/8kA2gHQAv1K3bGIMGDdKzm7px5MghZGZyGmNa2ihs2cLJ0IYN9BzOqqQfrAyJ\nXe2mptLEhFpP6nK30vgXmN76ekQElwUb4KyuvGx//vlycAoBUKlSdUc9sScJHx8fzJ8/3/E5M/Md\nLF/Ofdnr19Pz2rTRumfOyNlK07uYsVyeOMUoMDAQYWH8EvIyxo79GKmpQEwM95NChYDWrXXrHgB5\nFiM9fQzkWIwePKCZpvWe1K1WoHt37jgjg3vhHzwInDtXCMAc1K8fh5Urv4GX0ezDCtGrVy/UrMnv\nN17ChAkzkJlJZcjLC+jQQbfuAQBKlKDHYid1PcOM2cWFWNlPSaFJIbW2FufEYgFefZU7zs7mxsap\nU8CVK10ADAdgxTfffAE/LR24PIjOnTujRYuO9k/x+Pjj92GzAatXcz+xWICuXXXrHgB5W2kJCTTa\nzlSMDIDFYsHq1YsBcE4sp07NxtCh55DA+dKie3dtI7ny4km0GLEvL70VIwB44w16PHs2MGkS/Txi\nRG3Url1b+055CJwMfQGAs/OfOxeNgQP/cUSotWun/2QoZ7XLvgS0VjDY+4mVfU+Tob596fH8+cC4\ncQBQBMDnmDz5Al588UWdeqY/FosFK1Z8BoslEAAQH/8levfejwsXuN8//zxQpoyOHYS8rTQjZ70G\nnkDFCADq1auJZs3es3/KxPffDwfnTAqMHKlbtxzIsRixk6mePkZGV4yeeQbgg83OnQN27eKOK1QA\nevfWr1+eQt26NdG69fv2T1lYsWIQeL+R0aN165YDOYqRnjLEyr7YVbqeCl1ePPUUwOs+Fy/SYJfw\ncGDChMr6dcxDqFChPLp0mWH/RLBmzRAAXG4DT9hhlBOub+TkjsATqhgBwPr1H8Dbu6L9004AqzFw\nIM3RoieFC1PHSbGrRj230vz9aWiz2K00T1OMLBZgwYLc0RTz5mkbvu3J/PjjJPj51bB/OgRgEV5/\nHWjZUs9ecbCpKnhnVqHoqWD4+NDQZrEvI0+TIYCToZzy8skn+lvlPYUVK0YiIOBp+6cTAL5E+/b6\n+7kC3FjkdwHkLC5Mi5GBCA8PwNdff+b4HBAwBjNnSiyspDBWK9Wy5ViM9HBi5vttdIsRADRowDnl\nN2rErX5XrQK6dNG7V55DkSJ+WLv2a8fnkJDPsGRJposrtMPLi45/OVtpesgQr4wZ3WIEcIEM27dz\nkb5NmwJr1wK9eundK8+hUCFvbNr0NaxWP4SGjkf//m9izRp9IzpZ+HEkR4Y8ZT4Xw5ORrjcfBgxo\nj02bXsXPP/8MP79MXLhwGuHhnlHaoWhRTsmR42Okx+RYpAhXc87oFiOeV17h/pnkTadOz2L48OHI\nyMhAdHQ0goN1jC/OQfHi3ARtpK00/p6XLnEylJUlPKeXp8pQixbOIfsmzrRq1QC3bl1FST4U1oMo\nXpzbBk1I4DKYC00f4IlKuhieWIsRz6JFi9CrVy+cOnXKo+pd8ebHxMTcKfVdofdqlze9Pn7MTepC\nYSd1NqJIL9LS0tCnTx+cOnVK7654PJ999hmWLFmCUA9zJuCVg+RkLmJLKHpP6vw9CRG3wNC73znJ\nzs4GkVKW/QnEE5UiQHpkGjufe8JYFItuilGPHj3QsWNHrFmzRq8uAADKlCmDlStXopSeqa7zgFVq\nxEyOem+lsUIgZhvQ01a7M2fOxMqVK1G/fn18++23enfHo/HUGldSQ/b1XlxIdXr1NBmKiopCmzZt\ncOXKFb27YiIRqZFp5laaRGJiYlC4cGG9bu/x5MzcK9SKwipGeizgcwqS0H570qR+4sQJzJo1CwBA\nCEEjPYt+mUgmZ2RahQrCrtPb8iJVMdK73yynTp3CRx99hIyMDNSrVw9Xr171OIuiiXukWow8aSxK\nwTOXeiaSq4PzAzI0VJ96Y1LDpPnIIT8/rkaQXmRnZ2PQoEHIsu8DTpo06YnOWWRkpI5FXt68vPQp\nfqmExUjPl1F2djbefPNNZNhrxQwbNsxUigyKVBkyFSMTVZBa64mf1PUqqyFVkNhSBnpGZMyfPx8H\nDx4EAERGRmLy5Mn6dcZEFuxYFBOyz0/qYWH61BuTqxgFBfH1IPXh008/dchQ9erV8eGHH+rXGYOT\nnZ2Nx3whNR2QOxYDArh/RsNUjDwUKRajrCwaJm8kxchmo0Kn5zbaqVOnHIqQxWLBkiVLntiSBUpA\nCMH+/ft1u79cHyO9Vrpyt9L0lKELFy5gypQpADgZ+uabb1CoUCH9OmRgzp07hxYtWuDNN9/UrQ9y\nLUZGtBYBpmLkks2bN+OPP/7Q5d5SyoKwliUjTeqPHnH1lAD9JvXMzEz07dvXYf4fM2aMR0UpGo3b\nt2+jQ4cOaNasGWJjY3Xpg5RJPS2Ni2IDjCVDbBFmvfpts9kwaNAgpNkr8I4aNQrN+fTxJqLIzMxE\n69atsX//fvz000/48ccfdemH1IUu/87S219UKqZilAcpKSno27cv2rdvj379+iEpKUnzPkgZkHpH\npAHS+u0JjteEELRu3RoWiwU1atTAjBkz3F9kki8bN27E5s2bAQBvvvkmEhMTNe+DUWVIimL04AEt\n2qmXDC1btsyxkKxUqRI+/vhjfTpSAPDx8cHcuXMdn4cPH457YhNyKYDcha5pMSpA+Pv749q1awCA\nq1evYhJbQVQjwsPp8Z07wq7xhEndqIqRr68vZs+ejb1792LVqlXw19NJowAwZMgQR5HQ69evY8yY\nMZr3gd1KE+pj5AlOo1JeRp7geN2tWzcMGjQIALBkyRIEBgbq05ECQvfu3dHFnmr//v37GKlDIU8p\n87knyJBcTMUoD6xWq9Pe+KJFi7B3715N+8Dm+4qPF3aNqRjJp3nz5qhfv76+nSgAWK1WLFu2DEH2\nEMNvvvkGv/32m6Z9YOulGWlSDw2l/RaqGHlC3pgiRYpgyZIlOHPmDFq1aqVPJwoQFosFixcvRpjd\nr+KHH37ATz/9pGkfAgOpI7+RxqJcTMUoH6pWrYqZM2c6Pvfv31/T6ICwMFrAVKjFSO/EdAAXEePr\nm7s/rvAkxchEOSpWrIh58+Y5Pg8ePBgPxdaKkYGXF/XVk7KVppdixPbbSBYjnsjISH07UIAIDw/H\nokWLHJ+HDh2K27dva3Z/i0V8vTRPGotSMRUjF7z99tto1qwZAODy5ct4++23Nbu31Uq304RajFgF\nit2K0xKLhSo3RrQYmSjLoEGD8LK9VPjt27cxdOhQTctE8ONJ6FYae56ekzrfb6GKkSfIvok69OjR\nw7Gl9t9//+Gjjz7S9P7sWBQiup5gdZWLqRi5wMvLCytWrHBsByxfvhw//PCDZvfnJ7i7dzlPf3d4\nyuQoVpDYl5GpGBUsLBYLli5diiL2Inr79u3DHaEmUAXg/YySk4HUVPfne4oM8S+UxETAHijpEnbx\n5KFlt0wkYrFY8PXXX6N06dIYNWqUkxVWC/g5OSuLKybrDnMr7QmgcuXK+PzzzwEAhQsX1rQuFD/B\nZWcLC9n3lEmdF4bMTGGCpIfFKJsPmzBRnTJlymDJkiXo3Lkzjh8/rmnBTLE+b54iQ2IdsFnFyMPK\nPpooQNGiRXHq1CksXLhQ87xQ7FgUYnk1LUZPCH369MGMGTNw/PhxdOvWTbP7io1M85RJXezLSGvF\n6Oeff0aTJk1w/vx59W9mAoCLWFq3bh2Kauz8JnYssgqGpyhGQl5GWluMLl68CJsQM7aJYvBWV61h\nx5OQ91BBcI0wFSMBWCwWTJ48GRUrVtT0vmIHJH9OQIC+9cakrnb9/AC1Zf/WrVsYNGgQDh8+jPr1\n65vKkYZYdKj1IjZkn5ch1ldOD8TK/r//cv9brer3+/bt22jatClefvllTbdFTfSBHYv8OHOF6Xxt\noirsilWIAzY/R+ntfCm2RhUvbCVLqlsnLSsrC2+88Qb+s+9Ltm3bFhEREerd0ER3xI5FXoaKFgV8\nfNTpkxDEpuvgzylenEazqkF2djZ69+6N+/fvY/v27ZgwYYJ6NzPxCNitWTFj0ctLv+houZiKkQcj\nZtWYmUlLAuitGIlR6DIyqP+U2r4RU6dOdeSjKleuHJYsWaKLFcNEO8QoGIR4zuJCTL9tNtpvtbfR\nZs6ciV27dgHgfMfY7MwmBROpSnp4uD5FmJXAoN1+MhCjYLCrYb0ndVbBcWd6Zf+u0qXV6Q8AbN26\nFVFRUQAAb29vrF27VnN/FxPtYceUu/Qvjx9ztdIA/WVIzMvo4UNuYQSou7jYs2cPpk+fDoBL4Llm\nzRoUM+peSQEiKysLX3zxBTL5QaAwYrbStFTS1cRUjBQgVUgcsATEWIw8xfEaEKcYsS8rtSb1mzdv\nok+fPo7PUVFRaNq0qTo3MxEFIQTLly93RH4qjVQl3UgypIXj9b1799CzZ0+Hw/X06dPRokULdW5m\nIpj4+Hi0adMGw4cPV610lZittPv3aZ00I0dHmoqRTLZu3YrKlStj//79irctZtVoVMWI/b1agjRz\n5kzct3uBd+jQAWPHjlXnRiaisNls6NWrFwYMGIB33nnHUYBUSdgx5c5ixMqQ3qtdMdZitRUjm82G\n/v37OzIut2zZUpf6kSa5uX79Ovbt2wcA+OSTT7BhwwbF7xEWRv3tPEFJ1wJTMZLB77//jnbt2iE+\nPh7du3dXvPpxkSK0vIaRLEYlSlAnak9QjObPn48RI0agfPnyWL58uelX5CFYrVZHpGd2dja6d++u\neLkDf3+u9hjgfix6kgwFBgLBwdyx3orRv//+i1OnTgEAihcvjpUrV8JLTQ9vE8E0btzYKeFj//79\ncenSJUXvYbHQcaX3WNQKUzGSQcuWLR3m5Js3b6Jnz56KJg60WISXBWEndTZEWQ+8vWkfPEEx8vf3\nx6JFixAXF+coyGjiGXz00Udo3bo1AODOnTt47bXXkCEk1bMIeD+j27ddZ2L3JMUIEP4yYmVIjZdR\nmTJlcOzYMXTr1g0rVqxAKSPvkRRARowYge7duwMAEhMT8dprryGNd5ZTCH5c3b3LZcDOD1MxkkmP\nHj3QsWNHrFmzRq8uyMbb2xsxMTGOTL47duzAtGnTFL0HP0Hfu0f3bvPCk5yvAark3LnjupyJFooR\nTyhvOjDxGLy8vLB69WqUK1cOAPDXX39h3Lhxit6DH1dpaa4zsXuqYpSQ4LqciRYvo9DQUPz4449o\n27atOjcwkQxfdqdatWoAgGPHjuGdd95R9B68DBHiOlGqqRjJJCYmBps2bcIbb7yhVxcUoVSpUli7\ndq3DtDxjxgxs3rxZsfb5wWWzuc7D4kmOowAVpKws10keWcVIzag0E8+lePHiWLduHXzt+8YLFy7E\n6tWrFWtfaGSap8oQ4NpqZJYDMQkODsZPP/3kKBfy9ddfY8WKFYq1zyo5QmXIVIyecJ577jnMmjXL\n8blPnz64ePGiIm2XLUuPb97M/7xbt+ixJygYQh2w+d95exs3S6qJfBo1aoRFixY5Pg8ZMsSRiFMu\nQseip03qQoMv2BeVJ/TbRB/q1KmDL774AgAQERGBxo0bK9Z2mTL0mH3X5ETtbV2tMBUjhRg7diy6\ndOkCAHj48CF++uknRdq17zAAAG7cyP88fnIMDqZOm3oiVjEycjIwE2UYNGgQ3nzzTce2jVJ5poRa\njPiFh5eXZ1iMhCpG/LxQuDD3z+TJpV+/fvjss8/w999/o3r16oq1K/Q95GmLC6mYryKFsFgs+Pbb\nb/HUU09h8eLFmDhxoiLtsgMyP4sRIVSLZzV7PRGiGGVl0e1BJbYANmzYgPfeew9ZrrwDTTwWi8WC\nRYsW4dixY3j55ZcVa1doyD4vQ6VLq1tWQyhCEusRQl9U7FwhlYcPH8pvxERXRo4cqXiQiVDFiJeh\noCB963XKxVSMFKRw4cI4fPgwhg0bplib7FZafgMyIQFISeGOjaQY/fsvdcxm/04pHDx4EL169cIn\nn3yCl19+GcnJyfIaNNGFQoUKoUKFCoq2ycpEfjKUnk6VdE+Uofy2L+7d4/oOyFeM/vnnH1SuXFm1\nZJsmxkWIYsQq6eXLq98nNTEVI4XxUbjypJAByU6anjip56cYXb9Oj+UI0tWrV9GhQwdHBvJSpUoh\nICBAeoMmBQp7qiQAwLVreZ/DWpLkKulKwcpEfrLP/lyODN29excdOnTAo0ePMHLkSCxfvlx6YyYF\nDiHvofv3aUkdUzEyURUhztfszz1FMRJi6WIVI6mr3UePHqFdu3a4a1/uP/fcc1i6dKmZxNHEQcmS\nNFFqfooRK0OeqBjl129WtqTKUHJyMjp27IjrdoFs1KgRXn/9dWmNmRRIAgK4DID5FxkAABPxSURB\nVNiAsPncVIxMVMXfn0Zr5Tcg2UlT4V0IyZQuzUWaAcDVq3mfI3e1m5GRga5du+LMmTMAgOrVq2PD\nhg3w8/MT35iJISCuMjTmg9VKlYZr1/JO8shaXT1FMQoKoi8j9qXDIndxwcvQgQMHAAClS5fGzz//\n7Aj7NilYbNmyBVu3bpV0LS8Xt27lnZvOVIxMJJGeni4pjJ+f8G7dyjvJI6t4sNsGeuLlRYUjP8VI\nzqRus9kwYMAA7Ny5EwBQrFgxbN682cxsXYC5cOECGjdu7ChPIQZeLhITgUePcv/eEy1GAJWhmzfz\nln05FiNehrZt2wYACAkJwZYtW1DaE/J9mCjO8uXL0aFDB3Tr1g2HDh0SfT0/vjIz886pp8QOgKdg\nKkYakZCQgFdeeQUtWrTAlStXRF3LD7Ls7LzDdj1RMQJoXxISgLyCXVhLl1hBunr1qmPl4+fnh02b\nNqFKlSrSOmri8Rw/fhxNmjTB4cOH8dJLL+Fqftp2PrCW1Ly2pdifeaJilJWVt+zLWaW/9957jkSa\n/v7++OWXX/DUU09J7KmJJ0MIwW+//Ybs7GwkJyejXbt2OH36tKg23PkZKeXv5gmYipFGvPfee9i1\naxfi4+PRtm1bUQVnK1Wix3nVB2TfEZ40INl+5/Ue4/8WPz/xSSkrV66MPXv2oFy5cvjxxx/RtGlT\nyf008XyqVKmCypUrAwBu376N1q1bI95dETEGd4oRu1ax38YjYPud13Ya+zISq9DVqlULVqsVXl5e\nWLt2raPuo0nBw2Kx4Pvvv8dzzz0HALh//z5atWqF8+fPC26DXXRfvpz79+ZWmoloZs2ahcjISADc\nlkC7du3wKC+bfh5UrUqP89qJ45WOkiUBT3INYAUpp2Jks1HhqlxZWnLH2rVr4/z58+jQoYPULpoY\nhKCgIGzZssUhQ5cuXUKbNm0cTvfucKcY8WPR39+zEtO5c8Dm54PSpbm+i2HgwIFYv349li5dio4d\nO0rvpIkh8Pf3x8aNG9GgQQMAQHx8PFq2bIlLea2288Dde4hXjCwWzwkCkoqpGGlE0aJFsW3bNsf+\nPb8lIEQ5cjUg09JoODxrofEEXClGt2/T/Cvs3ycWf7FvAxPDUqxYMWzfvh3l7drCyZMn8eKLLwqy\nHLlT0nmLUeXK3MTuKbhSjBISaEFPqTLUqVMn9O/fX9rFJoajSJEi+P3331G3bl0AwK1bt9CyZUtc\nyy/skYEdYxcu5P4930R4OLcLYGRMxUhDypcvj99//x3FixcHABw6dAht2rRxm23WlWLEmi89yb8I\ncP0yYv8O0zXIRChly5ZFbGwsytr3jU6fPo0XXnjBreWIHYs5F8jx8TT/iidtowGu+83KUESEJt0x\nKQCEhYVh+/btqFWrFgDg+vXr+PXXX91ex87TOd9DiYnUB07OQtdTMBUjjalVqxZ27dqFEiVKAOAs\nR0OGDHF5TYUKtERBzgHJ+kYYSTFiJ3lTMTIRQ9WqVbFnzx6H5ahatWooUqSIy2vKleNysQCAPbuD\nA9ZfwtOsrmy5q7NnnX/HrtpNxchEDMWLF8eOHTtQvXp1REdHY8SIEW6vCQqiiXtzWozOnaPH9t1u\nQ2MqRjpQq1Yt7Ny5EyVKlEClSpUwd+5cl+f7+FAl4+JF5zws7GTpaQpGqVI0sV5OhY5VjFytMKKj\no3Hw4EHlO2diaHjn+7feegs//vgjfPmBlg9WK52wL12iFiL+M4+nKUYhIfRllFMxYmXKlQwlJSUp\n3zETw1OyZEkcPXoU48aNE3wNP87u3uWsRDzs2FSwdq1uyFaMBgwYAKvV6vSvXbt2SvStQMNbjnbv\n3u1Y+bqCH5CPHzvnkDh5kh7Xrq1wJ2Xi5QVUq8YdX7jA5b/gYVcYeU3qNpsNEyZMwIQJE9C2bVvE\nxcWp21kTw1GxYkV89dVXghN61qzJ/W+zAWwwDhu17ImrXb5P9+4B//1Hf+7OYkQIwfvvv49GjRrh\n/v376nbSxJCILZ2Un1uHaTHKg1deeQV37txBfHw84uPjsWbNGiWaLfDUrFlTkFIEUAUDcJ7I2Vx3\n/MTvSdi3sZGZ6SxIx49z/wcE5F6lZ2RkoG/fvoiOjgbAlf3Yt2+fBr01KcjUqEGP2e00Vob48epJ\nsC8a9gXEzwMWS25rcXZ2NoYMGYKoqCicPXsW//vf/5DJrkxMTCTAvodYGWItRqZiZMfPzw/FixdH\niRIlUKJECYSEhCjRrAmDPYgAAMAbTwihFqMKFYDgYO375Q72RcO/gB4/ptsXtWtT/ymAJsJctWoV\nAMBqteKLL74QtAduYuIKduGQ1+IiONgzM/ayLxr+BZSVBZw4wR1HRACBgfScx48fo2vXrliyZAkA\nLodNv379FC9wbVLwSWP3nOH8Hjp6lB7z49LX1/N8XaWgiGK0e/duhIeHIzIyEsOHD8eDBw+UaNaE\noV49eswrRjducEoG4HnbaDx5KUb8hA44C9qlS5fw7LPPOsp8+Pv7Y/369Rg6dKgGPTUpaBBCsGHD\nBkd9NdZixCtGSUk0MKBmTc8K1edhFSO+3+fO0XQXrAxduXIFzZo1w8aNGwEAPj4+WL16NYYPH65R\nb00KCikpKWjevDk++OAD2OzF0ewpkAAAR45w/2dl0W3dqlVpjUwjI1sxeuWVV/D9999j586diI6O\nxp49e9CuXTtJxR5NnFm5ciXefvttZGRkoFYtalnhFSNP3wIAgDp16DEvSP/8Q3/GT+q3bt1Co0aN\ncNJuAitatCh27tyJTp06adRTk4LGhx9+iC5dumDAgAFIT09HlSo0vwovQ6zrmqcuLlgZ4lfp/FY0\nQBdNu3fvdpKhIkWKYPPmzejRo4dGPTUpKBBCMHDgQBw9ehQzZszAq6++isTERJQoQTOsHz3K+eud\nOgVkZHA/Y8eqoSEiWLVqFQkKCiJBQUEkODiY/Pnnn7nOuXz5MrFYLGTnzp15tpGQkEAAkISEBDG3\nfuL4888/ia+vLwFAGjZsSC5evEjq1CEEIMTbm5CkJEKmTeM+A4SsXKl3j/PGZiOkaFGuj0WLcp8H\nDKD93ruXnjt06FACgERGRpLz58/r12kTw3Py5ElisVgIAAKANG7cmFy7do00bUrH3t27hMyeTT8v\nWaJ3r/OnbFmuj8HBhGRlETJqFO335s3cOe3bt3f8vdWrVyfnzp3Tt9MmhsVms5H58+cTq9XqGFM1\natQg58+fJ5060bF37hwnN/znuXP17rkyiLIYderUCcePH8fx48cRFxeHhg0b5jqnUqVKKFasmNsq\n8j169EDHjh2d/plO2xS2SObhw4dRv359lCgRA4AzXe7eDbD+yM2aads/oVgstG///cdtAWzfzn32\n9wfYIbRgwQJMmTIFBw4cQISZmMVEBrVq1cIPP/zgyIx+8OBB1K9fH8WKbXCc8+efwP799JrmzbXu\npXAaN+b+f/yYsxbFxnKfrVYqXytWrEC1atXw8ssv4++//0Y11lPWxEQEFosFo0ePxtatWxEaGgoA\nOHPmDBo2bAhf3xjHeX//DfzxB72OH6eGR2lN68aNG8RqtZJffvklz9+bFiPhHDlyhERERDg0du7f\nQAIkkYEDCfHz47T0smU5S4ynMmsWXVGMHEmPX3pJ756ZFHSO/n97dxca1ZnHcfw3GTesiTNjxKBD\nRZCKEi1SBa2tQhOKL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"text/plain": [ "Graphics object consisting of 3 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt1 = plot(sol_lap(w0=0.8,w=1),(t,0,80), \\\n", " legend_label='$\\,\\,5.5555 \\, \\sin \\, (0.1\\,t) \\,\\, \\sin \\, (0.9\\,t)$', thickness=2);\n", "plt2 = plot(P(w0=0.8,w=1) , (t,0,80) , linestyle=\"--\" ,color='black' , \\\n", " legend_label='$\\,\\, 5.5555 \\, \\sin \\, (0.1\\,t)$', thickness=2);\n", "plt3 = plot(-P(w0=0.8,w=1) , (t,0,80) , linestyle=\"--\" ,color='black' , thickness=2);\n", "(plt1+plt2+plt3).show(figsize=6,ymin=-9,ymax=9)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

    Συντονισμός

    \n", "

    \n", "Στην περίπτωση αυτή η συχνότητα της εξωτερικής διέγερσης είναι ίση με την ιδιοσυχνότητα του συστήματος, $\\omega=\\omega_0$." ] }, { "cell_type": "code", "execution_count": 65, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "1/2*t*sin(t*w0)/w0" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "reset()\n", "var('t w w0');\n", "w = w0;\n", "assume(w0>0);\n", "y = function('y')(t)\n", "eq = diff(y,t,t) + w0^2*y - cos(w*t) == 0\n", "sol = desolve(eq, y, ivar=t, ics=[0,0,0]); sol.expand().show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

    \n", "Εξαιτίας της ύπαρξης του όρου $t\\,\\sin \\omega_0\\,t$ στην λύση του ΠΑΤ, το πλάτος της ταλάντωσης δεν είναι φραγμένο καθώς $t\\rightarrow \\infty$, και αυτό ισχύει ανεξάρτητα από τις αρχικές τιμές. Αυτό το φαινόμενο ονομάζεται συντονισμός. Ουσιαστικά, προσθέτουμε συνέχεια ενέργεια στο σύστημα στην ιδιοσυχνότητα του συστήματος και εξαναγκάζουμε το πλάτος της ταλάντωσης να μεγαλώνει μέχρι που το σύστημα καταρρέει. Βέβαια στην πραγματικότητα, αυτό είναι δύσκολο να συμβεί γιατί πάντα υπάρχουν απώλειες στο κύκλωμα και η τροφοδοτούμενη ενέργεια από την πηγή μετατρέπεται σε άλλες μορφές ενέργειας, πχ. θερμότητα." ] }, { "cell_type": "code", "execution_count": 66, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1/2*t/w0\n" ] } ], "source": [ "P = 1/(2*w0)*t ; print P" ] }, { "cell_type": "code", "execution_count": 67, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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MREWxjFLHjqkXMTB1rl0TgrK6d9fuWtXzr1wRzyZDI7XtSQCJMEEQEubFF1/E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\nv18ZhENCzO+PGmgEW87F1FNRURG8vb1RWFjIc8JEZDd79+7F4MGDTV8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rKBEREdkJc0cT\nERHZCYMwERGRnTAIExER2Ykq14QFQcC1a9fg6enJhB5EROS0VBmEiYiI7gScjiYiIrITBmEiIiI7\nYRAmIiKyEwZhIiIiO2EQJiIishMGYSIiIjthECYiIrKT/wfjeLFkj0rdZwAAAABJRU5ErkJggg==\n", "text/plain": [ "Graphics object consisting of 3 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt1 = plot(sol(w0=1),(t,0,40), \\\n", " legend_label='$ 0.5 \\,t\\,\\sin \\, (t) $', thickness=2);\n", "plt2 = plot(P(w0=1) , (t,0,40) , linestyle=\"--\" ,color='black' , \\\n", " legend_label='$ 0.5\\,t$', thickness=2);\n", "plt3 = plot(-P(w0=1) , (t,0,40) , linestyle=\"--\" ,color='black' , thickness=2);\n", "(plt1+plt2+plt3).show(figsize=5,ymin=-30,ymax=30)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 8.1.6 Ηλεκτρικές ταλαντώσεις με ασυνεχείς όρους εξαναγκασμού" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "

    \n", "Μια από τις πιο ενδιαφέρουσες εφαρμογές του μετασχηματισμού Laplace είναι σε ΣΔΕ που διέπουν RLC κυκλώματα όπου ο όρος πηγής είναι μια ασυνεχής συνάρτηση. \n", "Για παράδειγμα, θεωρούμε την ΣΔΕ

    \n", "$$ 2\\,y''+y'+2\\,y = g(t) \\,, \\qquad \n", "g(t) = \\left\\lbrace \\begin{array}{cc} 1\\,, & 5\\leq t \\leq 20 \\,,\\\\\n", "0 \\,, & 0 \\leq t < 5\\,,\\,\\, t \\geq 20 \\,. \\end{array} \\right. $$
    \n", "\n", "Από φυσική άποψη, μια ΣΔΕ αυτής της μορφής περιγράφει την μεταβολή του ηλεκτρικού φορτίου σε έναν κύκλωμα RLC και το κύκλωμα περιλαμβάνει και μια μπαταρία ή γεννήτρια που δίνει μοναδιαίο φορτίο μόνο για $5 \\leq t < 20$.

    \n", "Αν και το Sage γνωρίζει τον μετασχηματισμό Laplace της αλματικής συνάρτησης (ή κατανομής Heaviside)" ] }, { "cell_type": "code", "execution_count": 68, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "e^(-5*s)/s\n" ] } ], "source": [ "reset()\n", "var('s,t')\n", "f = unit_step(t-5);\n", "un_lap = f.laplace(t,s) ; print un_lap" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

    \n", "δεν γνωρίζει τον αντίστροφο μετασχηματισμό Laplace της παραπάνω συνάρτησης" ] }, { "cell_type": "code", "execution_count": 69, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "ilt(e^(-5*s)/s, s, t)\n" ] } ], "source": [ "print inverse_laplace(un_lap,s,t)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

    \n", "Μέχρι να βελτιωθεί ο αλγόριθμος που εκτελεί τον αντίστροφο μετασχηματισμό Laplace συναρτήσεων μετατόπισης που προέρχονται από αλματικές συναρτήσεις, μπορούμε για τον σκοπό αυτό να χρησιμοποιούμε την εξής ιδιότητα του μετασχηματισμού Laplace

    \n", "$$ \\mathcal{L} [ \\, \\mathbf{u}(t-c)\\, f(t-c) \\, ] = e^{-c\\,s} \\, F(s)\\,,\\qquad \\mbox{όπου} \\qquad F(s) = \\mathcal{L}[f(t)] \\,.$$
    \n", "Οπότε, για να λύσουμε την παραπάνω ΣΔΕ με την μέθοδο του μετασχηματισμού Laplace, εργαζόμαστε ως εξής" ] }, { "cell_type": "code", "execution_count": 70, "metadata": { "collapsed": false }, "outputs": [], "source": [ "reset()\n", "var('s t'); \n", "y = function('y')(t)\n", "eq = 2*diff(y,t,t) + diff(y,t) + 2*y == unit_step(t-5) - unit_step(t-20) ; " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

    \n", "Παίρνουμε τον μετ. Laplace της ΣΔΕ και έχουμε" ] }, { "cell_type": "code", "execution_count": 71, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2*s^2*laplace(y(t), t, s) + s*laplace(y(t), t, s) - 2*s*y(0) + 2*laplace(y(t), t, s) - y(0) - 2*D[0](y)(0) == e^(-5*s)/s - e^(-20*s)/s\n" ] } ], "source": [ "eq_LT = eq.laplace(t,s); print eq_LT" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

    \n", "Λύνουμε την προηγούμενη ως προς την $\\mathcal{L}[y(t)]$ " ] }, { "cell_type": "code", "execution_count": 72, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[\n", "laplace(y(t), t, s) == (2*s*e^(20*s)*D[0](y)(0) + (2*s^2*y(0) + s*y(0))*e^(20*s) + e^(15*s) - 1)*e^(-20*s)/(2*s^3 + s^2 + 2*s)\n", "]\n" ] } ], "source": [ "Y = solve(eq_LT, laplace(y(t),t,s)) ; print Y" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

    \n", "Όπως αναμέναμε οι αρχικές συνθήκες δεν έχουν προσδιορισθεί, οπότε ας υποθέσουμε επιπλέον ότι το αρχικό φορτίο $y(0)=Q(0)$ και η ένταση $y'(0)=I(0)=Q'(0)$, για $t=0$, είναι $y(0)=0$ και $y'(0)=0$. " ] }, { "cell_type": "code", "execution_count": 73, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "e^(-5*s)/(2*s^3 + s^2 + 2*s) - e^(-20*s)/(2*s^3 + s^2 + 2*s)\n" ] } ], "source": [ "YY = Y[0].rhs().subs({y(0):0, diff(y,t)(0):0}).expand() ; print YY" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

    \n", "Όπως παρατηρούμε ο μετασχηματισμός Laplace της άγνωστης συνάρτησης απαρτίζεται από δυο όρους

    \n", "$$ \\mathcal{L} [ y(t) ] = Y(s) = e^{-5\\,s}\\,H(s) + e^{-20\\,s}\\,H(s)\\,,\\qquad H(s)=\\frac{1}{2\\,s^3+s^2+2\\,s}$$
    \n", "Οπότε, σύμφωνα με την προαναφερόμενη ιδιότητα του μετασχηματισμού Laplace και του αντιστρόφου του, ο αντίστροφος μετασχηματισμός Laplace της $Y(s)$ είναι

    \n", "$$ y(t) = \\mathcal{L}^{-1} \\, [Y(s)] = \\mathbf{u}(t-5)\\, h(t-5) - \\mathbf{u}(t-20)\\, h(t-20) $$
    \n", "όπου $h(s)$ είναι ο αντίστροφος μετασχηματισμός Laplace της $H(s)$" ] }, { "cell_type": "code", "execution_count": 74, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-1/30*(sqrt(15)*sin(1/4*sqrt(15)*t) + 15*cos(1/4*sqrt(15)*t))*e^(-1/4*t) + 1/2\n" ] } ], "source": [ "h(t) = inverse_laplace(1/(2*s^3+s^2+2*s),s,t); print h(t)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

    \n", "Συνεπώς η λύση του προβλήματος αρχικών τιμών είναι η παρακάτω συνάρτηση" ] }, { "cell_type": "code", "execution_count": 75, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "t |--> -1/30*((sqrt(15)*sin(1/4*sqrt(15)*(t - 5)) + 15*cos(1/4*sqrt(15)*(t - 5)))*e^(-1/4*t + 5/4) - 15)*unit_step(t - 5) + 1/30*((sqrt(15)*sin(1/4*sqrt(15)*(t - 20)) + 15*cos(1/4*sqrt(15)*(t - 20)))*e^(-1/4*t + 5) - 15)*unit_step(t - 20)\n" ] } ], "source": [ "ysub(t) = unit_step(t-5)*h(t-5) - unit_step(t-20)*h(t-20) ; print ysub" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

    \n", "Η γραφική παράσταση της λύσης του ΠΑΤ δίνεται στο επόμενο σχήμα" ] }, { "cell_type": "code", "execution_count": 76, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ms2fPxq1bt/Dxxx/Dt4p0UampqbU2xaW9DNSqTMOGwD/+IX7Idpo3Bxo3Bq5d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\nWU4pLyVFSaIAAAAASUVORK5CYII=\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt_ysub = plot(ysub(t),(t,0,40),thickness=2,ymin=-0.4,ymax=1) ; \n", "plt_ysub.show(figsize=5, axes_labels=['$t$','$Q(t)$'] )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

    \n", "Παρατηρούμε ότι η λύση χωρίζεται σε τρεις περιοχές:\n", "

    • $0 < t < 5$, στην οποία ισχύει η το ΠΑΤ \n", "$$ 2\\,y''+y'+2\\,y = 0 \\,, \\qquad y(0)=y'(0)=0\\,.$$
    • \n", "Από το θεώρημα ύπαρξης και μοναδικότητας η λύση του ΠΑΤ στο διάστημα αυτό είναι η $y(t)=0$.\n", "
    • $5 < t < 20$, στην οποία ισχύει η το ΠΑΤ \n", "$$ 2\\,y''+y'+2\\,y = 1 \\,, \\qquad y(5)=y'(5)=0\\,,$$
    • \n", "Είναι το άθροισμα μιας σταθερής (η απόκριση στην σταθερή εξωτερική τάση) και μιας φθίνουσας ταλάντωσης λόγω της ύπαρξης όρου απόσβεσης $y'$ στην αντίσταση R (η λύση της ομογενούς ΣΔΕ).\n", "
    • $t > 20$, στην οποία ισχύει το ΠΑΤ \n", "$$ 2\\,y''+y'+2\\,y = 0 \\,, \\qquad y(20)=y_1\\,,\\quad y'(20)=y_2\\,,$$
    • \n", "που παριστάνει μια φθίνουσα ταλάντωση γύρω από την ευθεία $y=0$. Οι τιμές $y_1=y(20)$, και $y_2=y'(20)$, δηλαδή το αρχικό φορτίο και η ένταση του ρεύματος, αντίστοιχα, στο ένα άκρο του πυκνωτή, υπολογίζονται ως εξής\n", "\n", "
    " ] }, { "cell_type": "code", "execution_count": 77, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.501620577296880\n", "0.0112485659727303\n" ] } ], "source": [ "print ysub(20).n() ; \n", "print diff(ysub,t)(20).n()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

    \n", "Μια εναλλακτική αντιμετώπιση του μειονεκτήματος του Sage να μην μπορεί να υπολογίζει τον αντίστροφο μετασχηματισμό Laplace συναρτήσεων μετατόπισης είναι να χρησιμοποιήσουμε το ελεύθερο ΣΣΥ giac , το οποίο περιλαμβάνεται στο Sage. Για παράδειγμα στο Sage εκτελούμε την εντολή" ] }, { "cell_type": "code", "execution_count": 78, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "-1/30*(sqrt(15)*e^(-1/4*t + 5/4)*sin(1/4*sqrt(15)*(t - 5)) + 15*cos(1/4*sqrt(15)*(t - 5))*e^(-1/4*t + 5/4) - 15)*Heaviside(t - 5)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "inv_lap = giac('invlaplace(exp(-5*s)/(2*s^3+s^2+2*s),s,t)').sage() ; inv_lap.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 8.1.7 Γραμμικά συστήματα ΣΔΕ" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

    \n", "Με ανάλογους αλγόριθμους όπως για ΣΔΕ πρώτης τάξης, το Sage μπορεί να επιλύσει συμβολικά και ΠΑΤ για γραμμικά συστήματα ΣΔΕ με σταθερούς συντελεστές. Για παράδειγμα, το ΠΑΤ για το σύστημα ΣΔΕ

    \n", "$$\\left(\\begin{array}{c} y_1'(t) \\\\ y_2'(t) \\\\y_3'(t) \\end{array} \\right) = \n", "\\left( \\begin{array}{rrr} 2 & -2 & 0 \\\\ -2 & 0 & 2 \\\\ 0 & 2 & 2 \\end{array} \\right) \\, \n", "\\left(\\begin{array}{c} y_1(t) \\\\ y_2(t) \\\\y_3(t) \\end{array} \\right) \\,, \\qquad\n", "\\left(\\begin{array}{c} y_1(0) \\\\ y_2(0) \\\\y_3(0) \\end{array} \\right) = \n", "\\left(\\begin{array}{r} 2 \\\\ 1 \\\\ -2 \\end{array} \\right)\n", "$$
    \n", "λύνεται με την χρήση της εντολής desolve_system" ] }, { "cell_type": "code", "execution_count": 79, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[y1(t) == e^(4*t) + e^(-2*t), y2(t) == -e^(4*t) + 2*e^(-2*t), y3(t) == -e^(4*t) - e^(-2*t)]\n" ] } ], "source": [ "var('t'); \n", "y1 = function('y1')(t); \n", "y2 = function('y2')(t);\n", "y3 = function('y3')(t); \n", "y = vector([y1,y2,y3])\n", "A = matrix([[2,-2,0],[-2,0,2],[0,2,2]])\n", "system = [diff(y[i], t) - (A*y)[i] for i in range(3)]\n", "sol = desolve_system(system, [y1,y2,y3] , ivar=t, ics=[0,2,1,-2]); print sol" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "

    \n", "όπου οι αρχικές συνθήκες δίνονται στη μορφή ics = [t0,y1(t0),y2(t0),y3(t0)]. Η λύση όπως παρατηρούμε παράγεται από εκθετικές συναρτήσεις της μορφής $e^{\\lambda\\,t}$, όπου $\\lambda$ όπως γνωρίζουμε είναι οι ιδιοτιμές του πίνακα A." ] }, { "cell_type": "code", "execution_count": 80, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[4, 2, -2]\n" ] } ], "source": [ "print A.eigenvalues()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

    \n", "Στο παρακάτω σύστημα ΣΔΕ οι ιδιοτιμές του πίνακα A είναι μιγαδικές" ] }, { "cell_type": "code", "execution_count": 81, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[y1(t) == 2*cos(2*t)*e^(3*t), y2(t) == e^(3*t)*sin(2*t)]\n" ] } ], "source": [ "reset()\n", "var('t'); \n", "y1 = function('y1')(t); \n", "y2 = function('y2')(t);\n", "y = vector([y1,y2])\n", "A = matrix([[3,-4],[1,3]])\n", "system = [diff(y[i], t) - (A * y)[i] for i in range(2)]\n", "sol = desolve_system(system, [y1, y2], ivar=t, ics=[0,2,0]) ; print sol" ] }, { "cell_type": "code", "execution_count": 82, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[3 - 2*I, 3 + 2*I]\n" ] } ], "source": [ "print A.eigenvalues()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

    Συζευγμένοι ταλαντωτές

    \n", "

    \n", "Ας θεωρήσουμε δυο μάζες που συνδέονται με δυο ελατήρια όπως στο παρακάτω σχήμα και ας σημειώσουμε με $x_1$, $x_2$ την απομάκρυνσή τους από την θέση ισορροπίας. \n", "

    \n", " \n", "

    \n", "Στην μάζα $m_1$ ασκούνται δυνάμεις και από τα δυο ελατήρια. Το πρώτο ελατήριο με σταθερή απόσβεσης $k_1$ ασκεί δύναμη στην $m_1$ ίση με $-k_2\\,x_1$. Το δεύτερο ελατήριο διαστέλλεται ή συστέλλεται ανάλογα με την σχετική θέση των δυο μαζών. Οπότε το δεύτερο ελατήριο ασκεί μια δύναμη στη μάζα $m_1$, ίση με $k_2\\,(x_2-x_1)$.
    \n", "Με παρόμοιο τρόπο η μόνη δύναμη που ασκείται στην μάζα $m_2$ είναι η δύναμη επαναφοράς από το δεύτερο ελατήριο, άρα η δύναμη αυτή είναι ίση με $-k_2\\,(x_2-x_1)$. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

    \n", "Θέτοντας όλα τα παραπάνω στον δεύτερο νόμο του Newton, παίρνουμε τις εξισώσεις της κίνησης

    \n", "$$ \\begin{array}{rcl}m_1 \\, x_1''(t) & = & -k_1\\,x_1 + k_2\\,(x_2-x_1)\\,, \\\\\n", "m_2 \\, x_2''(t) & = & -k_2\\,(x_2-x_1)\\,, \\end{array}$$
    \n", "δηλαδή ένα συζευγμένο σύστημα δυο γραμμικών ΣΔΕ δεύτερης τάξης με σταθερούς συντελεστές. Το σύστημα αυτό μπορεί να γραφεί ως ένα σύστημα τεσσάρων ΣΔΕ πρώτης τάξης με την εισαγωγή των εξαρτημένων μεταβλητών (ταχυτήτων) $x_3 = x_1'$ και $x_4 = x_2'$. Η εισαγωγή αυτή οδηγεί στο σύστημα ΣΔΕ

    \n", "$$\\left(\\begin{array}{c} x_1'(t) \\\\ x_2'(t) \\\\x_3'(t) \\\\ x_4'(t) \\end{array} \\right) = \n", "\\left( \\begin{array}{cccc} \n", "0 & 0 & 1 & 0 \\\\ \n", "0 & 0 & 0 & 1 \\\\ \n", "-\\frac{k_1+k_2}{m_1} & \\frac{k_2}{m_1} & 0 & 0 \\\\\n", "\\frac{k_2}{m_2} & -\\frac{k_2}{m_2} & 0 & 0 \n", "\\end{array} \\right) \\, \n", "\\left(\\begin{array}{c} x_1(t) \\\\ x_2(t) \\\\x_3(t) \\\\ x_4(t) \\end{array} \\right) \\,.\n", "$$
    " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

    \n", "Ας υποθέσουμε ότι οι αδιάστατες μάζες και σταθερές των ελατηρίων είναι $m_1=2$, $m_2=1$, $k_1=4$ $k_2=1$, αντίστοιχα, και οι αρχικές απομακρύνσεις και ταχύτητες των μαζών είναι \n", "$x_1(0)=1$, $x_2(0)=x_1'(0)=x_2'(0)=0$. Το ΠΑΤ αυτό λύνεται στο Sage όπως παρακάτω" ] }, { "cell_type": "code", "execution_count": 83, "metadata": { "collapsed": false }, "outputs": [], "source": [ "var('t m1 m2 k1 k2'); \n", "x1 = function('x1')(t); \n", "x2 = function('x2')(t);\n", "x3 = function('x3')(t); \n", "x4 = function('x4')(t);\n", "x = vector([x1,x2,x3,x4])\n", "k1=4;k2=2;m1=2;m2=1;\n", "A = matrix([[0,0,1,0],[0,0,0,1],[-(k1+k2)/m1,k2/m1,0,0],[k2/m2,-k2/m2,0,0]])\n", "system = [diff(x[i], t) - (A*x)[i] for i in range(4)]\n", "sol = desolve_system(system, [x1,x2,x3,x4] , ivar=t, ics=[0,1,0,0,0])" ] }, { "cell_type": "code", "execution_count": 84, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[x1(t) == 2/3*cos(2*t) + 1/3*cos(t), x2(t) == -2/3*cos(2*t) + 2/3*cos(t), x3(t) == -4/3*sin(2*t) - 1/3*sin(t), x4(t) == 4/3*sin(2*t) - 2/3*sin(t)]\n" ] } ], "source": [ "print sol" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

    \n", "Πρόκειται για περιοδικές κινήσεις με περίοδο $2\\,\\pi$. \n", "Για να έχουμε μια γραφική εποπτεία της λύσης του προβλήματος δυο συζευγμένων ταλαντωτών, παρακάτω προβάλλουμε την λύση στο χώρο των φάσεων $(x_1,x_1')$, και τις απομακρύνσεις $x_1(t)$, $x_2(t)$ ως συναρτήσεις του χρόνου $t$ στο ίδιο γράφημα." ] }, { "cell_type": "code", "execution_count": 85, "metadata": { "collapsed": false }, "outputs": [], "source": [ "ph1 = parametric_plot( [ sol[0].rhs(), sol[2].rhs() ] , (t,0,2*pi),xmin=-1,xmax=1, ymin=-2,ymax=2, \\\n", " fontsize=12,color='blue',thickness=2,aspect_ratio=1,figsize=5 , \\\n", " axes_labels=['$x_1$','$x^\\prime_1 $'] )\n", "ph2 = parametric_plot( [ sol[1].rhs(), sol[3].rhs() ] , (t,0,2*pi),xmin=-1,xmax=1, ymin=-2,ymax=2, \\\n", " fontsize=12, color='red', thickness=2, aspect_ratio=1.2,figsize=5 ,\\\n", " axes_labels=['$x_2$','$x^\\prime_2 $'])" ] }, { "cell_type": "code", "execution_count": 86, "metadata": { "collapsed": true }, "outputs": [], "source": [ "ga = graphics_array([ph1, ph2])" ] }, { "cell_type": "code", "execution_count": 87, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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TpgUf16wJXH+9nljCFRcHDB6sjt99V18shdGxo1r4OnOmPbeQJbI0n08W3wT0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\n3dGS8x8Tph9/E7UvjsXY7hPrfcXqd9ZkPBYX0tGWbbDJf/3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GRK3DjthKdOxI5UwAOWIhQApahg+wTkfrLS5O/pIbz4qt0PeUYWzC1q0kEAAA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\n", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pos1 = plot( sol[0].rhs(),(t,0,2*pi),color='blue',legend_label='$ x_1(t) $',thickness=2);\n", "pos2 = plot( sol[1].rhs(),(t,0,2*pi),color='red' ,legend_label='$ x_2(t) $',thickness=2);\n", "(pos1+pos2).show(figsize=5,axes_labels=['$t$','$x(t)$'] , legend_loc='lower right' )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 8.2 Αριθμητική ολοκλήρωση ΣΔΕ

    \n", "\n", "

    \n", "Όπως έχει γίνει ήδη φανερό από τα θέματα που έχουμε διαπραγματευτεί μέχρι εδώ, το Sage είναι ένα σύνολο από αλγεβρικούς και αριθμητικούς αλγόριθμους που επιλύουν πολλά μαθηματικά προβλήματα και ταυτόχρονα μας παρέχει την δυνατότητα να έχουμε την γραφική αναπαράσταση της λύσης τους. Ειδικότερα στη μελέτη των διαφορικών εξισώσεων ο συνδυασμός αυτός είναι ένα από τα μεγαλύτερα πλεονεκτήματα του Sage. Για πολλά και πολύ ενδιαφέροντα προβλήματα που μοντελοποιούνται από ένα σύστημα μη-γραμμικών ΣΔΕ δεν είναι δυνατόν να βρούμε την λύση του συστήματος ΣΔΕ σε κλειστή μορφή, και συνεπώς δεν υπάρχει συμβολική επίλυση στο Sage. Για αυτά τα προβλήματα το Sage μας παρέχει ένα πλήθος από αριθμητικούς αλγόριθμους για να επιλύσουμε το πρόβλημα αρχικών-συνοριακών τιμών αριθμητικά.\n", "

    \n", "Ο λόγος που έχουμε στην διάθεσή μας ένα μεγάλο πλήθος από τέτοιου είδους αριθμητικούς αλγόριθμους είναι επειδή ένας αλγόριθμος μπορεί να είναι καλά προσαρμοσμένος για ΣΔΕ ενός τύπου, ενώ σε προβλήματα διαφορετικού τύπου (π.χ. προβλήματα με περιοδικές ή σχεδόν περιοδικές τροχιές, χαοτικά κτλ.) να είναι καλύτερα προσαρμοσμένος ένας διαφορετικός αλγόριθμος. \n", "Επιπλέον, το Sage μας επιτρέπει να έχουμε πρόσβαση στην βιβλιοθήκη GSL (GNU Scientific\n", "Library) η οποία μας δίνει την δυνατότητα να χρησιμοποιήσουμε ακόμα περισσότερους αριθμητικούς αλγόριθμους. Γενικά το ζήτημα της αριθμητικής ολοκλήρωσης ενός συστήματος μη-γραμμικών ΣΔΕ είναι αρκετά ευρύ και για να μην χαθούμε θα παρουσιάσουμε στο παρόν εδάφιο τα βασικά αριθμητικά εργαλεία - εντολές που μας παρέχει το Sage." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

    \n", "

    • desolve_odeint
      Ο αριθμητικός αλγόριθμος για επίλυση ΣΔΕ με την εντολή odeint του συστήματος scipy, το οποίο με την σειρά του χρησιμοποιεί το πρόγραμμα lsoda από το πακέτο odepack της Fortran.
    • \n", "
    • desolve_rk4
      Ο κλασικός αλγόριθμος Runge-Kutta 4ης τάξης από το Maxima για βαθμωτές ΣΔΕ
    • \n", "
    • \n", "desolve_system_rk4
      Ο αλγόριθμος Runge-Kutta 4ης τάξης από το Maxima για συστήματα ΣΔΕ.
    • \n", "
    • desolve_mintides, desolve_tides_mpfr
      \n", "Το πακέτο tides. Πρόκειται για αλγόριθμο που ολοκληρώνει αριθμητικά το σύστημα ΣΔΕ με την μέθοδο σειρών Taylor. Το κύριο χαρακτηριστικό του πακέτου είναι ότι εκτελεί ολοκλήρωση του συστήματος ΣΔΕ με όση ακρίβεια δεκαδικών ψηφίων θέλουμε! Για να το χρησιμοποιήσουμε χρειάζεται να το εγκαταστήσουμε με την εντολή: sage -i tides αν έχουμε εγκαταστήσει το Sage ως root σε όλο το λειτουργικό σύστημα, ή ./sage -i tides στο directory του Sage στον λογαριασμό που έχουμε εγκαταστήσει το Sage τοπικά ως user.
    " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

    \n", "Ας δούμε πως μπορούμε να χρησιμοποιήσουμε τα εργαλεία αυτά στην επίλυση απλών και πιο σύνθετων δυναμικών συστημάτων." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 8.2.1 Πληθυσμιακό μοντέλο θηρευτή - θηράματος " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

    \n", "Ας υποθέσουμε ότι σε ένα περιβάλλον όπου οι διατροφικοί πόροι είναι πεπερασμένοι υπάρχουν δυο βιολογικά είδη από τα οποία το ένα είναι ο θηρευτής και το άλλο το θήραμα. Για παράδειγμα, οι πληθυσμοί φώκιες και πιγκουίνοι, καρχαρίες και ψάρια, πασχαλίτσες και μελίγκρες, αλεπούδες και λαγοί είναι κάποιοι πληθυσμοί της κατηγορίας θηρευτής-θήραμα.

    \n", "Το πιο απλό μοντέλο ΣΔΕ που περιγράφει τον πληθυσμό του θηράματος $x(t)$, και του θηρευτή $y(t)$ δίνεται από το σύστημα μη-γραμμικών ΣΔΕ" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

    \n", "$$ \\frac{d \\,x}{d\\,t} = a\\,x\\, - b\\,x\\,y\\,, \\qquad \\frac{d \\,y}{d\\,t} = -c\\,y\\, + d\\,b\\,x\\,y\\,, $$
    \n", "όπου $a,b,c,d$ θετικές αταθερές και ο χρόνος $t$ μετριέται σε χρόνια, και αναφέρεται ώς μοντέλο Lotka-Volterra.
    \n", "

      \n", "
    • Ο όρος $a\\,x$ παριστάνει την αύξηση του πληθυσμού του θηράματος όταν δεν υπάρχουν θηρευτές.\n", "
    • \n", "
    • Οι όροι $-b\\,x\\,y$ και $d\\,b\\,x\\,y$ παριστάνουν την αλληλεπίδραση των δυο ειδών. Ο πληθυσμός του θηράματος υποφέρει και ο πληθυσμός του θηρευτή αυξάνεται από την αλληλεπίδραση των ειδών.\n", "
    • \n", "
    • Ο όρος $-c\\,y$ παριστάνει την μείωση του πληθυσμού του θηρευτή όταν δεν υπάρχουν θηράματα.
    • " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

      \n", "Αν και το σύστημα ΣΔΕ μπορεί να ολοκληρωθεί (η ΣΔΕ που προκύπτει διαιρώντας το παραπάνω σύστημα είναι χωριζομένων μεταβλητών) θα το λύσουμε αριθμητικά. Ο λόγος είναι ότι το ολοκλήρωμα που προκύπτει είναι δύσκολο να το χρησιμοποιήσουμε για να περιγράψουμε τους πληθυσμούς παραμετρικά από τον χρόνο $t$. Όμως η αριθμητική επίλυση μας δίνει τόσο την λύση παραμετρικά ως προς $t$, όσο και ως προς τις μεταβλητές $x,y$.

      \n", "\n", "Πρώτα απ' όλα ορίζουμε τις μεταβλητές και θέτουμε συγκεκριμένες τιμές στις σταθερές $a,b,c,d$. Μετά ορίζουμε την ΣΔΕ σε διανυσματική μορφή και θεωρούμε μια αρχική τιμή, πχ $x(0)=10$, $y(0)=5$, δηλαδή αρχικά υπάρχουν 10 λαγοί και 5 αλεπούδες. Μετά θεωρούμε το διάστημα διάστημα που θα λύσουμε την ΣΔΕ καθώς και το βήμα ολοκλήρωσης. Με αυτές τις πληροφορίες είμαστε έτοιμοι να εκτελέσουμε την εντολή που ολοκληρώνει αριθμητικά το σύστημα ΣΔΕ. Αυτά που πειγράψαμε με λόγια υλοποιούνται στα παρακάτω." ] }, { "cell_type": "code", "execution_count": 89, "metadata": { "collapsed": false }, "outputs": [], "source": [ "reset()\n", "var('t x y')\n", "(a, b, c, d) = (1., 0.1, 1.5, 0.75)\n", "f=[ a*x - b*x*y , -c*y + d*b*x*y ]\n", "x0y0 = [10 , 5]\n", "ts = 0.01;\n", "tt=srange(0., 15.,ts);\n", "sol = desolve_odeint(f, x0y0 , tt , [x , y] , ivar=t)\n", "l1 , l2 = sol.T" ] }, { "cell_type": "code", "execution_count": 90, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "print type(l1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

      \n", "H λύση είναι στην μορφή ενός πίκανα που οι γραμμές αποτελούνται από τα ζευγάρια αριθμών που αντιστοιχούν οι πληθυσμοί $(x(t_i), y(t_i))$, στους χρόνους $t_i$, στους οποίους έχουμε ζητήσει να υπολογισθεί η λύση. Στο συγκεκριμένο παράδειγμα τα $t_i$ διατρέχουν το διάστημα $[0,15]$ με\n", "βήμα $h=0.01$. Παίρνοντας το ανάστροφο του πίνακα μπορούμε να αποσυμπλέξουμε τους πληθυσμούς και να τους θέσουμε στα ξεχωριστά διανύσματα l1 και l2, αντίστοιχα. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

      \n", "Με τις παρακάτω εντολές δίνουμε μια γραφική παράσταση των πληθυσμών $x(t_i)$ και $y(t_i)$ στους αντίστοιχους χρόνους $t_i$, στο ίδιο γραφικό " ] }, { "cell_type": "code", "execution_count": 91, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Tpk0DUJ72ZLVaERkZiebNmzulQMXFxWHZsmUO22w2G6xWK3Jzcx22L1iwAAsX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SAAAG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\nkUgkEokGkAZZIpFIJBIN8P/Ynj5LXIIE4wAAAABJRU5ErkJggg==\n", "text/plain": [ "Graphics object consisting of 4 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "p1 = line(zip(tt, l1), color='red')\n", "p1 += text(\"rabbits\" ,(12,37), fontsize=10, color='red')\n", "p2 = line(zip(tt, l2), color='blue')\n", "p2 += text(\"foxes\" ,(12,7), fontsize=10, color='blue')\n", "(p1+p2).show(figsize=5,axes_labels=[\"t\",\"population\"],ticks=2, gridlines=true)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

      \n", "Για να έχουμε γενικότερη εποπτεία των λύσεών μας στα παρακάτω σχεδιάζουμε το πεδίο διευθύνσεων και λύνουμε αριθμητικά το σύστημα ΣΔΕ για διάφορες αρχικές τιμές των πληθυσμών, και τέλος απεικονίζουμε όλα μαζί τα γραφικά στο xy επίπεδο." ] }, { "cell_type": "code", "execution_count": 92, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def g(x,y):\n", " v = vector(f) \n", " return v/v.norm()" ] }, { "cell_type": "code", "execution_count": 93, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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LCHzp3Lx5ExkZGcx1X716hYULF+L8+fNMO2wBwJYtW+Dh4YGjR48ybZSRl5eHli1bwsPD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\n0zukMe+jqZ88eQJ7e3ukpqbC19eXK1+1ahWuXLnSKiG/Hm32+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"text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "q = plot_vector_field(g(x, y), (x, 0, 60), (y, 0, 36)); q.show(figsize=5)" ] }, { "cell_type": "code", "execution_count": 94, "metadata": { "collapsed": false }, "outputs": [], "source": [ "n = 11; L = srange(6, 18, 12 / n); R = srange(3, 9, 6 / n)\n", "CI = zip(L, R)\n", "for j in range(n):\n", " X = desolve_odeint(f, CI[j] , tt, [x , y] , ivar=t) \n", " q += line(X, color=hue(.8-float(j)/(1.8*n)))" ] }, { "cell_type": "code", "execution_count": 95, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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AgAMHDmRKSooozZMnTxYoqzpq1CjRlfWOHDlSoMLcggULRFe02r59u1qvXLly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z16vXf5KIvQzfBJvv67kRgl10cHsSiP8VwrIxXdXRguYfunC6Zs0ai7z0mZmZbNu27X9TE05M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\nN6d///6aAdTrkvnz5+Pn50fjxo1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"text/plain": [ "Graphics object consisting of 12 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "q.show(figsize=5,axes_labels=[\"rabbits\",\"foxes\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

      \n", "Για τις τιμές των σταθερών $a,b,c,d$ που δώσαμε, παρατηρούμε ότι οι δυο πληθυσμοί συνυπάρχουν αρμονικά στο περιβάλλον. Στα δυναμικά συστήματα θα μάθετε πως να βρίσκετε και να χαρακτηρίζετε ποιοτικά τα δυο σημεία ισορροπίας του παραπάνω συστήματος ΣΔΕ $(x,y)=(0,0$ και $(x,y)=(\\frac{c}{b\\,d},\\frac{a}{b})$ και ότι υπάρχουν τιμές των παραμέτρων που ένα από τα δυο είδη μπορεί να εξαφανισθεί." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 8.2.2 Οριακοί κύκλοι - Ο ταλαντωτής Van der Pol " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

      \n", "Ένας οριακός κύκλος είναι μια απομονωμένη περιοδική τροχιά ενός δυναμικού συστήματος. Οριακοί κύκλοι εμφανίζονται σε δυναμικά συστήματα στο επίπεδο τα οποία μοντελοποιούν τεχνολογικά και φυσικά φαινόμενα. Για παράδειγμα, το παρακάτω ηλεκτρικό κύκλωμα αποτελείται από μια τρίοδο, ένα κύκλωμα RLC, του οποίου το πηνίο είναι σε αμοιβαία επαγωγή με ένα άλλο πηνίο M. \n", "

      \n", " \n", "
      " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

      \n", "Η μη-γραμμική ΣΔΕ που περιγράφει την μεταβολή του φορτίου στο ένα άκρο του πυκνωτή

      \n", "$$ \\frac{d^2\\,x}{d\\,t^2} + \\varepsilon\\,(x^2-1)\\,\\frac{d\\,x}{d\\,t} + x =0\\,, $$
      \n", "και διατυπώθηκε το 1926 από τον Balthasar Van der Pol. Eισαγάγοντας την μεταβλητή $y=x'(t)$, η παραπάνω ΣΔΕ μπορεί να γραφεί ισοδύναμα ως το ακόλουθο σύστημα

      \n", "$$ \\frac{d\\,x}{d\\,t} = y \\, , \\qquad \\frac{d\\,y}{d\\,t} = -x - \\varepsilon\\,(x^2-1)\\,y \\,. $$
      \n", "Θα λύσουμε αριθμητικά το παραπάνω μη-γραμμικό σύστημα ΣΔΕ για την τιμή της παραμέτρου $\\varepsilon=10$ και με αρχικές τιμές $x(0)=1$, $y(0)=0$." ] }, { "cell_type": "code", "execution_count": 96, "metadata": { "collapsed": false }, "outputs": [], "source": [ "reset()\n", "var('t x y')\n", "epsilon = 10.\n", "f = [ y , -x -epsilon*(x^2-1)*y ]" ] }, { "cell_type": "code", "execution_count": 97, "metadata": { "collapsed": true }, "outputs": [], "source": [ "var('t x y')\n", "P=desolve_system_rk4( f , [x,y] , ics=[0,1,0], ivar=t, end_points=100, step=0.05)\n", "Q=[ [i,j] for i,j,k in P]\n", "xy = [ [j,k] for i,j,k in P]\n", "LP=line(Q)" ] }, { "cell_type": "code", "execution_count": 98, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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4uCUfLVsCe/fStZLhjG13L1myBN27d0d6ejoiIiIwS9db7CuAW2m6Xj1atKWL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\nVGXEb79Nd+e2bu3te51GRVY3cSKdgKfr4koTyYg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"text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "LP.show(figsize=5,axes_labels=[\"$t$\",\"$x(t)$\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

      \n", "Για μικρό χρόνο μετά από $t=0$, στο σύστημα εκτελεί περιοδική ταλάντωση με σταθερό πλάτος. Ο οριακός κύκλος φαίνεται στο χώρο των φάσεων $xy$. Πιο συγκεκριμένα, στο παρακάτω γραφικό απεικονίζουμε το πεδίο διευθύνσεων που ορίζει το σύστημα ΣΔΕ, μαζί με την λύση που βρήκαμε αριθμητικά στο επίπεδο των φάσεων $x-y$." ] }, { "cell_type": "code", "execution_count": 99, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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F3kev9TNkDZ06dULPnj2F65YvXx4fffQRatSoIVz7888/R506dYTryuVy/PDD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\nffr0QWpqKsLCwiCVSuHv74+6deuif//+7JVlbkoKwseNA1auBJj9We/cu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"text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def g(x,y):\n", " v = vector(f) \n", " return v/v.norm()\n", "van_vf = plot_vector_field(g(x, y), (x, -3, 3), (y, -15, 15)); \n", "xy_plot = list_plot(xy, color='red' , size=10);\n", "(van_vf+xy_plot).show(figsize=5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 8.2.3 Μη γραμμικές διαταραγμένες ταλαντώσεις" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

      \n", "Όπως θα δείτε στα δυναμικά συστήματα, οι τροχιές ενός αυτόνομου δυναμικού συστήματος δεν μπορούν να τέμνονται, και συνεπώς το θεώρημα Poincare-Bendixson συνεπάγεται ότι δεν μπορεί να υπάρχει χάος σε δυο διαστάσεις. Ωστόσο, χάος μπορεί να εμφανισθεί σε αυτόνομα τρισδιάστατα συστήματα και σε δισδιάστατα μη-αυτόνομα (ή διαταραγμένα) συστήματα της μορφής\n", "$$ x''(t) = f(x(t),x'(t),t)\\,,$$
      \n", "όπου η συνάρτηση $f$ εξαρτάται με ρητό τρόπο από τον χρόνο $t$. Για τέτοια συστήματα οι τροχιές επιτρέπεται να τέμνονται στο επίπεδο. Οι λεγόμενες τομές Poincaré μας επιτρέπουν να μελετήσουμε τις περίπλοκες τροχιές που ακολουθεί το μη-αυτόνομο δυναμικό σύστημα.

      \n", "Για παράδειγμα, θεωρούμε την εξίσωση Duffing η οποία είναι η μη-γραμμική μη-αυτόνομη ΣΔΕ δεύτερης τάξης \n", "$$ \\frac{d^2\\,x}{d\\,t^2} + k\\,\\frac{d\\,x}{d\\,t}+ ( x^3-x ) = \\Gamma \\, \\cos \\omega\\,t \\,.$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

      \n", " \n", "
      \n", "

      \n", "Η ΣΔΕ αυτή μοντελοποιεί ένα περιοδικά διαταραγμένο ταλαντωτή του οποίου η δύναμη επαναφοράς είναι κυβική, το $x(t)$ παριστάνει την απομάκρυνση της μάζας $m$ από την θέση ισορροπίας, το $k$ είναι μια σταθερή απόσβεσης, $Γ$ και $\\omega$ είναι το πλάτος, και η συχνότητα της δύναμης της διαταραχής, αντίστοιχα." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

      \n", "Οι τροχιές του παραπάνω διαταραγμένου μη-αυτόνομου δυναμικού συστήματος, μπορούν αντιστοιχιστούν στις τροχιές ενός αυτόνομου συστήματος σε έναν τόρο. Η αντιστοιχία αυτή είναι δυνατή, εισαγάγοντας μια τρίτη μεταβλητή $\\theta = \\omega\\,t$. Οπότε η ΣΔΕ του Duffing μετατρέπεται στο παρακάτω αυτόνομο σύστημα ΣΔΕ

      \n", "$$ \\frac{d\\,x}{d\\,t} = y\\,, \\, \\qquad \\frac{d\\,y}{d\\,t} = x - k\\,y - x^3 + \\Gamma \\, \\cos \\theta \\,, \\qquad \\frac{d\\,\\theta}{d\\,t} = \\omega\\,.$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

      \n", " \n", "
      \n", "

      \n", "Μια τροχιά του δυναμικού συστήματος Duffing αντιστοιχεί σε με μια τροχιά γύρω από έναν τόρο με περίοδο $\\frac{2\\,\\pi}{\\omega}$. Η αντιστοιχία αυτή μας οδηγεί με φυσικό τρόπο στην λεγόμενη απεικόνιση Poincaré ενός επιπέδου με $\\theta=\\theta_0$ στον εαυτό του. Στο διπλανό σχήμα απεικονίζεται η πρώτη βόλτα της τροχιάς με αρχικό σημείο $P_0$, η οποία τέμνει το επίπεδο $\\theta=\\theta_0$ στο σημείο $P_1$. Η συγκεκριμένη τροχιά καθώς και όλες οι άλλες με διαφορετικά αρχικά σημεία ξεδιπλώνονται στο εσωτερικό του τόρου στον τρισδιάστατο χώρο.



      \n", "Θα λύσουμε το παραπάνω σύστημα για συγκεκριμένες τιμές των παραμέτρων $k=0.3$ και $\\omega=1.25$, και για διάφορες τιμές του πλάτους της διαταραχής $Γ$, με την odeint του scipy." ] }, { "cell_type": "code", "execution_count": 100, "metadata": { "collapsed": false }, "outputs": [], "source": [ "reset()" ] }, { "cell_type": "code", "execution_count": 101, "metadata": { "collapsed": false }, "outputs": [], "source": [ "var('t x y')\n", "Gamma=0.5;omega=1.25;k=0.3;\n", "f=[ y , x - k*y - x^3 + Gamma*cos(omega*t) ]\n", "ci=[0.4,0.]\n", "ts = n(2.*pi/omega/100.);\n", "tt=srange(0.,900.,ts);\n", "sol=desolve_odeint(f,ci,tt,[x,y],ivar=t)" ] }, { "cell_type": "code", "execution_count": 102, "metadata": { "collapsed": false }, "outputs": [], "source": [ "X, Y = sol.T\n", "pe=line(zip(X[0:len(X)],Y[0:len(Y)]),thickness=1,xmin=-1.5,xmax=1.5,ymin=-1.5,ymax=1.5)" ] }, { "cell_type": "code", "execution_count": 103, "metadata": { "collapsed": false }, "outputs": [], "source": [ "poi= [ [ sol[i,0] , sol[i,1]] for i in range(0,len(tt),100)];\n", "pmape = points(poi[10:len(poi)],size=2, color='black',xmin=-1.5,xmax=1.5,ymin=-1.5,ymax=1.5)" ] }, { "cell_type": "code", "execution_count": 104, "metadata": { "collapsed": false }, "outputs": [], "source": [ "gb = graphics_array([pe, pmape]); " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
      \n", "
      \n", "

      \n", "Μια έκθεση πορτρέτων φάσης (αριστερά) και η αντίστοιχη τομή Poincaré στο επίπεδο $\\theta=0$ (δεξιά), του δυναμικού συστήματος Duffing, με τιμές των παραμέτρων $k = 0.3$ και $ω = 1.25$: (α) Г = 0.2 διαταραγμένη τροχιά με περίοδο ένα, (β) Γ = 0.3 μια υποαρμονική τροχιά περιόδου δύο, και (γ) Г =0.31 μια μόλις εμφανιζόμενη υποαρμονική τροχιά περιόδου 4.\n", "

      \n", "
      " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
      \n", "
      \n", "

      \n", "Μια έκθεση πορτρέτων φάσης (αριστερά) και η αντίστοιχη τομή Poincaré στο επίπεδο $\\theta=0$ (δεξιά), του δυναμικού συστήματος Duffing, με τιμές των παραμέτρων $k = 0.3$ και $ω = 1.25$: (δ) Г = 0.37 Διαταραγμένη υποαρμονική τροχιά περιόδου πέντε, (ε) Γ = 0.5 (χάος) Στην τομή Poincaré, κάθε \"γλώσσα\" κάτω από αλλαγή κλίμακας δημιουργείται από διαφορετικές νέες γλώσσες, και (στ) Г =0.8 Διαταραγμένη τροχιά περιόδου ένα.\n", "

      \n", "
      " ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "### 8.2.4 Ο παράξενος ελκυστής του Lorenz
      \n", "\n", "

      \n", "Το 1963 o μετεωρολόγος Edward Lorenz κατασκεύσασε ένα μαθηματικό μοντέλο μεταφοράς αερίων μαζών. Πρόκειται για ένα αρκετά απλό σύστημα μη-γραμμικών ΣΔΕ, που όμως οι τροχιές του δυναμικού αυτού συστήματος παρουσιάζουν χαοτική συμπεριφορά. Το σύστημα του Lorenz δίνεται από τις εξισώσεις.

      \n", "$$ \\frac{d\\, x}{d\\,t} = \\sigma\\,(y-x)\\,, \\phantom{y} \\\\ \\quad\n", " \\frac{d\\, y}{d\\,t} = x\\,(\\rho-z)-y \\,, \\\\ \\qquad\n", " \\frac{d\\, z}{d\\,t} = x\\,y-\\beta\\,z\\,, \\qquad\\phantom{y}\n", " $$
      \n", "όπου το $x$ μετρά την ταχύτητα του αέρα, το $y$ μετρά την αλλαγή της θερμοκρασίας στην οριζόντια διεύθυνση, ενώ το $z$ την κάθετη, $\\sigma$ είναι ο αριθμός Prandtl, $\\rho$ ο αριθμός Rayleigh, και $\\beta$ ένας παράγοντας αλλαγής κλίμακας.\n", "Για τις τιμές των παραμέτρων $\\sigma=10$, $\\beta=\\frac{8}{3}$, και $\\rho=28$, ο Lorenz ανακάλυψε την ύπαρξη ενός παράξενου ελκυστή. Με την βοήθεια το Sage και του πακέτου tides θα λύσουμε το παραπάνω σύστημα ΣΔΕ, αριθμητικά, για να εντοπίσουμε τον παράξενο ελκυστή του Lorenz." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

      \n", "Για την επίλυση του συστήματος ΣΔΕ μπορείτε να χρησιμοποιήσετε την εντολή desolve_odeint, όπως παραπάνω ή την Runge-Kutta 4ης τάξης του Maxima. Για τους εκπαιδευτικούς σκοπούς του μαθήματος αρκούν οι αλγόριθμοι αυτοί.

      \n", "Όμως το Sage μας παρέχει την δυνατότητα να χρησιμοποιήσουμε τον αλγόριθμο tides. Πρόκειται για έναν αλγόριθμο αριθμητικής ολοκλήρωσης συστημάτων ΣΔΕ που βασίζεται στην μέθοδο σειρών Taylor. Το κύριο του χαρακτηριστικό του πακέτου είναι η εκτέλεση αριθμητικής ολοκλήρωσης με όση υπολογιστική ακρίβεια θέλουμε, μέσω της χρήσης της βιβλιοθήκης MPFR. Το πακέτο tides έχει ενσωματωθεί στο Sage μέσω της εντολής desolve_tides_mpfr, και μέχρι την ώρα που γράφονται οι σημειώσεις αυτές είναι ο μαναδικός συνδυασμός ΣΣΥ που μας επιτρέπει να χρησιμοποιήσουμε το tides με μια μόνο εντολή!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

      \n", "Με τις παρακάτω εντολές ολοκληρώνουμε το σύστημα του Lorenz για $t\\in[0,T]$ κατά μήκος μιας τροχιάς περιόδου 10 με ακρίβεια 100 δεκαδικών ψηφίων." ] }, { "cell_type": "code", "execution_count": 105, "metadata": { "collapsed": true }, "outputs": [], "source": [ "reset()" ] }, { "cell_type": "code", "execution_count": 106, "metadata": { "collapsed": false }, "outputs": [], "source": [ "var('t x y')\n", "s = 10; r = 28; b = 8/3;\n", "f(t,x,y,z)= [s*(y-x),x*(r-z)-y,x*y-b*z]\n", "x0 = -13.7636106821342005250144010543616538641008648540923684535378642921202827747268115852940239346395038284\n", "y0 = -19.5787519424517955388380414460095588661142400534276438649791334295426354746147526415973165506704676171\n", "z0 = 27\n", "T = 15.586522107161747275678702092126960705284805489972439358895215783190198756258880854355851082660142374" ] }, { "cell_type": "code", "execution_count": 107, "metadata": { "collapsed": false }, "outputs": [], "source": [ "sol = desolve_tides_mpfr(f, [x0, y0, z0], 0, T, T, 1e-100, 1e-100, 100)" ] }, { "cell_type": "code", "execution_count": 108, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000, -13.7636106821342005250144010543616538641008648540923684535378642921202827747268115852940239346395038, -19.5787519424517955388380414460095588661142400534276438649791334295426354746147526415973165506704676, 27.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000], [15.5865221071617472756787020921269607052848054899724393588952157831901987562588808543558510826601424, -13.7636106821342005250144010543616538641008648540923684535378642921202827747268115852940239346470530, -19.5787519424517955388380414460095588661142400534276438649791334295426354746147526415973165506634524, 27.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000345574]]\n" ] } ], "source": [ "print sol" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

      \n", "Αλλάζοντας τις αρχικές συνθήκες σε $(x_0,y_0,z_0) = (-1,-1,2)$, και για χρόνο $Τ=50$ με βήμα $0.01$, και με την προεπιλεγμένη ακρίβεια του MPFR (16 δεκαδικών ψηφίων) μπορούμε να ολοκληρώσουμε το σύστημα του Lorenz ως εξής:" ] }, { "cell_type": "code", "execution_count": 109, "metadata": { "collapsed": true }, "outputs": [], "source": [ "x0 = -1\n", "y0 = -1\n", "z0 = 2" ] }, { "cell_type": "code", "execution_count": 110, "metadata": { "collapsed": true }, "outputs": [], "source": [ "sol1 = desolve_tides_mpfr(f, [x0, y0, z0], 0 , 50, 0.01)" ] }, { "cell_type": "code", "execution_count": 111, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0.0000000000000000000000000000000000000000000000000, -1.000000000000000000000000000000000000000000000000, -1.000000000000000000000000000000000000000000000000, 2.000000000000000000000000000000000000000000000000]\n", "\n", "5001\n" ] } ], "source": [ "print sol1[0]; print type(sol1); print len(sol1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

      \n", "Το πακέτο μας επιστρέφει μια λίστα αριθμών στην οποία η πρώτη στήλη (0) είναι οι τιμές του χρόνου t, και στις στήλες 1,2,3 οι τιμές των μεταβλητών $x,y,z$, αντίστοιχα, υπολογισμένες στα χρονικά βήματα που εκτελείται η αριθμητική ολοκλήρωση. Το αποτέλεσμα μπορούμε να το απεικονίσουμε σε ένα τρισδιάστατο γραφικό κατά τα γνωστά. Όμως υπάρχει στην διάθεσή μας και η πανίσχυρη βιβλιοθήκη γραφικών matplotlib για ένα αρκετά ευπαρουσίαστο γραφικό.\n", "Μπορούμε να μεταφέρουμε τα αριθμητικά αποτελέσματα που πήραμε από το Sage στην matplotlib και να τα σχεδιάσουμε με την την matplotlib ως εξής:" ] }, { "cell_type": "code", "execution_count": 112, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Φορτώνουμε το numpy, την matplotlib κι ένα εργαλείο της για τρισδιάστατους άξονες.\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from mpl_toolkits.mplot3d import Axes3D" ] }, { "cell_type": "code", "execution_count": 113, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Δημιουργούμε 3 np.array με τις τιμές των x, y, z\n", "xs = np.empty((len(sol1)))\n", "ys = np.empty((len(sol1)))\n", "zs = np.empty((len(sol1)))" ] }, { "cell_type": "code", "execution_count": 114, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Μεταφέρουμε τα δεδομένα μας στα αντίστοιχα np.array\n", "for i in range(len(sol1)):\n", " xs[i] = sol1[i][1]\n", " ys[i] = sol1[i][2] \n", " zs[i] = sol1[i][3]" ] }, { "cell_type": "code", "execution_count": 115, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 115, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Δημιουργούμε το γραφικό με την matplotlib\n", "fig = plt.figure()\n", "ax = fig.gca(projection='3d')\n", "ax.plot(xs, ys, zs, lw=0.001,color='blue',linewidth=1.5)\n", "# Εδώ μπορείτε να προσθέσετε άλλο ένα γραφικό πχ μια τροχιά περιόδου ένα \n", "# ax.plot(xs1, ys1, zs1, lw=0.001,color='red',linewidth=1.5)\n", "ax.set_xlabel(\"X Axis\")\n", "ax.set_ylabel(\"Y Axis\")\n", "ax.set_zlabel(\"Z Axis\")" ] }, { "cell_type": "code", "execution_count": 116, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Σώζουμε το γραφικό για μελλοντική χρήση\n", "fig.savefig('lorenz.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

      \n", "Η γραφική αναπαράσταση της αριθμητικής λύσης του συστήματος ΣΔΕ φαίνεται στα ακόλουθα σχήματα." ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "

      \n", " \n", "
      \n", "

      \n", "α) (Γραφικό από την matplotlib) Ο παράξενος ελκυστής του Lorenz για τις τιμές των παραμέτρων $\\sigma = 10$, $\\rho = 28$, και $\\beta = 8/3$ (μπλέ χρώμα), και μια περιοδική τροχιά που περικλείει τα δυο ασταθή σημεία ισορροπίας (εκτός της αρχής (0,0,0) ) ακριβώς μια φορά (κόκκινο χρώμα). \n", "β) (Γραφικό από το πακέτο mayavi) Ο παράξενος ελκυστής του Lorenz, από τα ίδια αριθμητικά αποτελέσματα, διαμορφωμένος όμως με το εξειδικευμένο πακέτο τρισδιάστατων γραφικών mayavi, σε αλληλεπίδραση με την matplotlib (interactive mode).\n", "

      \n", "
      \n", "
      " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
      \n", " \n", "
      \n", "

      \n", "(Γραφικά από το πακέτο mayavi) Προβολές του παράξενου ελκυστής του Lorenz α) στο $xy$ επίπεδο β) στο $xz$ επίπεδο και γ) στο $yz$ επίπεδο, για τις τιμές των παραμέτρων $\\sigma = 10$, $\\rho = 28$, και $\\beta = 8/3$.\n", "

      \n", "
      \n", "
      " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Την αλλαγή χρωματισμού της τροχιάς όταν αυτή γυροφέρνει τα ασταθή σημεία ισορροπίας την επιτύγχαμε ως εξής. Πρώτα απ' όλα βρίσκουμε στο Sage τα σημεία ισορροπίας (σημεία στα οποία μηδενίζονται οι παράγωγοι, $x'(t)=y'(t)=z'(t)=0$) για τις δοσμένες τιμές των παραμέτρων." ] }, { "cell_type": "code", "execution_count": 117, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[\n", "[x == 6*sqrt(2), y == 6*sqrt(2), z == 27],\n", "[x == -6*sqrt(2), y == -6*sqrt(2), z == 27],\n", "[x == 0, y == 0, z == 0]\n", "]\n" ] } ], "source": [ "print solve([ f[0](t,x,y,z)==0,f[1](t,x,y,z)==0,f[2](t,x,y,z)==0],x,y,z )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "και στην συνέχεια για συνάρτηση χρωματισμού στο πακέτο mayavi θεωρούμε την εξής:" ] }, { "cell_type": "raw", "metadata": {}, "source": [ "orbit_col = (np.array(x)+8.5)*np.sign(np.array(x)+8.5)/17.0 - (np.array(x)-8.5)*np.sign(np.array(x)-8.5)/17.0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Ουσιαστικά χρωματίζουμε την τροχιά με την συνάρτηση

      \n", "$$ \\frac{(x+6\\,\\sqrt{2})}{{12\\,\\sqrt{2}}} \\, {\\rm sign} \\left(\\,x+6\\,\\sqrt{2}\\,\\right) - \n", "\\frac{(x-6\\,\\sqrt{2})}{{12\\,\\sqrt{2}}} \\, {\\rm sign} \\left(\\,x-6\\,\\sqrt{2}\\,\\right)\\,, $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "η οποία έχει πεδίο τιμών το $[-1,1]$, όπου ${\\rm sign}$ η συνάρτηση προσήμου. Με αυτόν τον τρόπο όταν η τροχιά βρίσκεται κοντά στο ένα ασταθές σημείο γίνεται κόκκινη, ενώ κοντά στο άλλο παίρνει ιώδες χρώμα και χρωματίζεται με τα ενδιάμεσα χρώματα του ουράνιου τόξου όταν περνάει κοντά από το τρίτο ασταθές σημείο, δηλαδή την αρχή των αξόνων $(0,0,0)$. " ] } ], "metadata": { "kernelspec": { "display_name": "SageMath 7.5.1", "language": "", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.13" } }, "nbformat": 4, "nbformat_minor": 0 }