From e97916f988651d046e93cc0a14f47c93b77d3ccc Mon Sep 17 00:00:00 2001 From: Andrew Lorimer Date: Sun, 25 Aug 2019 20:03:14 +1000 Subject: [PATCH 01/16] [chem] results & calculations for ascorbic acid titration --- chem/ascorbic-acid-titration.xls | Bin 0 -> 6656 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 chem/ascorbic-acid-titration.xls diff --git a/chem/ascorbic-acid-titration.xls b/chem/ascorbic-acid-titration.xls new file mode 100644 index 0000000000000000000000000000000000000000..58c03aec30ca1cdade060c9187a3abc61758e589 GIT binary patch literal 6656 zcmeHLX>3$g6h3b@rnE3^rHWLik4j4mEwx~x#MBOSKuN4LZCzrFI<&8)GHrD_Zi!1l zP1LAS`C&vN5W&P?P(uP5QK$d>A!3Y;Xfy%+p+t=17MBR)_nr5Kj*m{58lur~Ud~<4 zy=S@Sp1Zvd4wN0*_S&4o;(|-XE5|cM63C$&C{NGUOGP{=lXg6l$z;hWo`L_62aY+m zat?i%L_d&oJ`ETI76I8-?BxHUp`9_c01tG^FutUivO%Rmz12_{H0^$geGGICIEZ{6)1@LU( zIl$S#bAfY!mB90W=L5sQDxe9R3#14R zsbA#e6W%yeI+X{Cf|$jCU*4SY9=Ckm`wt@`UiFP>TzmoA4RR}Eqb(NiG5;x8t~SIB 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\(\rightarrow\) \verb;normCdf;. + + For function in domain \(a \le x \le b\): + + \[ \operatorname{E}(X) = \int^b_a x f(x) \> dx \] + + \[ \operatorname{sd}(X) = \sqrt{\operatorname{Var}(X)} = \sqrt{\oepratorname{E}(X^2)-[\operatorname{E}(X)]^2} \] + \end{document} -- 2.49.0 From c0dc70858af633fbee6fd88e78c4f4caef925996 Mon Sep 17 00:00:00 2001 From: Andrew Lorimer Date: Wed, 28 Aug 2019 08:58:13 +1000 Subject: [PATCH 03/16] [spec] variable forces and right angle pulleys --- spec/dynamics.pdf | Bin 167234 -> 178283 bytes spec/dynamics.tex | 5 +++++ 2 files changed, 5 insertions(+) diff --git a/spec/dynamics.pdf b/spec/dynamics.pdf index 031b21cd32c0cd89736ff69428b20b2166924064..ca06d3747805d82297d78caf4cf3f3f531790f1d 100644 GIT binary patch delta 88315 zcmV(+K;6H>nhNXi3b6VK12!`>lhNfUf9+gZj~mI6e(zsVZ_9?a%6T6H_(2+L1RKJ7 zb-;^-W*#_fN}|nUM0Ss?f4^TuX4b_bo1*;Ezyc$YN=8M-9gz`PBdU*;s9xSYe|Pi8 zpF$Oz=#;D8eWyXyVye{X}HE$92&T5CO%Dt*5F?Y357wp^^{f9uuZ 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zu@xrF#N~C0c)8u<+oxgNVq=#*A$~2GyVcI@Ar(RGR?vWRgxKj|WbAoqG@t0;I1H}V zv#i@RgjBjgACG!Ak1He2TKfMJhyug1uc*yqY{UL}!oH@7R9?axbMRFDfPGksf4why z)b-Z!{?5@{!_cxR<_-#ekYv>}(8briL^EoWtfloGUHL8u;ZU1|YCcuCNNCI6zbZ)B zB&K?V*Hw8)$cwLG&Cf8l_K%QUDv>cBidQfg&2-LUkX^|1&GaA~Bwas# zt6E5+h5fYhGt+=X5!bTZ0{;WQb8~kEm^%Dt^dEH{uA955tGl-= Vz!HI-hliJo8-bcyN<|vse*j-OKj{Df diff --git a/spec/dynamics.tex b/spec/dynamics.tex index 83eb5a2..5891f4e 100644 --- a/spec/dynamics.tex +++ b/spec/dynamics.tex @@ -161,6 +161,7 @@ A mass of \(m\) kg has force of \(mg\) acting on it \begin{itemize} \item \textbf{Suspended pulley:} tension in both sections of rope are equal \item \textbf{Linear connection:} find acceleration of system first + \item \textbf{Pulley on right angle:} \(a = \frac{m_2g}{m_1+m_2}\) where \(m_2\) is suspended (frictionless on both surfaces) \item \textbf{Pulley on edge of incline:} find downwards force \(W_2\) and components of mass on plane \end{itemize} @@ -245,4 +246,8 @@ Three methods: \colorbox{cas}{On CAS:} use Geometry, lock known constants. +\section{Variable forces (DEs)} + +\[ a = \dfrac{d^2x}{dt^2} = \dfrac{dv}{dt} = v\dfrac{dv}{dx} = \dfrac{d}{dx} \left( \frac{1}{2} v^2 \right) \] + \end{document} -- 2.49.0 From 93eb70a4067f707438d4162bcef4943141871e43 Mon Sep 17 00:00:00 2001 From: Andrew Lorimer Date: Wed, 28 Aug 2019 14:03:45 +1000 Subject: [PATCH 04/16] [spec] confidence intervals/limits --- spec/statistics.pdf | Bin 169004 -> 125628 bytes spec/statistics.tex | 47 ++++++++++++++++++++++++++++++++++++++++++++ 2 files changed, 47 insertions(+) diff --git a/spec/statistics.pdf b/spec/statistics.pdf index 9f5622dac1bf0227761d302c031f05abbae46a6b..cd372e03102e64ca47503e671c4d85109ed599e9 100644 GIT binary patch delta 89716 zcmV)9K*hhTs0zH*2e8Ws0y8+5A%y`H5;ih33NK7$ZfA68G9WQ9HZwVwL0JM71Ti)_ zGnY_=0w;fsv;|O{%N8vR1a}V_26uONcPID&gTo+$1$TE3P6%#6g9LYXg1ZwS0fNKh z$i4U6`~Ow%)l_}cYg_l)y>?TRt7$TeTY$|#GGIptGdl~L06C5CVCNBF=M`XM 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\pgfmathparse{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))}% + \pgfmathparse{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))} } -{\begin{center} \begin{tikzpicture} +\begin{tikzpicture} \pgfplotsset{set layers} \begin{axis}[every axis plot post/.append style={ mark=none,domain=-3:3,samples=50,smooth}, @@ -138,7 +138,7 @@ every axis x label/.style={at={(axis description cs:1,-0.25)},anchor=south west}] \addplot {gauss(0,0.75)}; \end{axis} -\end{tikzpicture}\end{center}} +\end{tikzpicture} \section{Central limit theorem} @@ -151,12 +151,13 @@ \item \textbf{Interval estimate:} confidence interval for population mean \(\mu\) \end{itemize} - \subsection*{95% confidence interval} + \subsection{95\% confidence interval} - \[ \left( \overline{x} \pm 1.96 \dfrac{\sigma}{\sqrt{n}} \] + The 95\% confidence interval for a population mean \(\mu\) is given by + + \[ \overline{x} \pm 1.96 \dfrac{\sigma}{\sqrt{n}} \] where: \\ - \(\mu\) is the population mean (unknown) \\ \(\overline{x}\) is the sample mean \\ \(\sigma\) is the population sd \\ \(n\) is the sample size from which \(\overline{x}\) was calculated @@ -170,11 +171,11 @@ \subsection*{Interpretation of confidence intervals} - 95% confidence interval \(\implies\) 95% of samples will contain population mean \(\mu\). + 95\% confidence interval \(\implies\) 95\% of samples will contain population mean \(\mu\). \subsection*{Margin of error} - For 95% confidence interval for \(\mu\), margin of error \(M\) is: + For 95\% confidence interval for \(\mu\), margin of error \(M\) is: \begin{align*} M &= 1.96 \times \dfrac{\sigma}{\sqrt{n}} \\ @@ -183,12 +184,57 @@ \subsection*{General case} - A confidence interval of \(C\)% is given by + A confidence interval of \(C\)\% for a mean \(\mu\) s given by + + \[ x \in \left( \overline{x} \pm k \dfrac{\sigma}{\sqrt{n}} \right) \quad \text{ where } k \text{ is such that } \Pr(-k < Z < k) = \frac{C}{100} \] + + \subsection*{Confidence interval for multiple trials} + + For a set of \(n\) confidence intervals (samples), there is \(0.95^n\) chance that all \(n\) intervals contain the population mean \(\mu\). + + \section{Hypothesis testing} + + Note hypotheses are always expressed in terms of population parameters + + \subsection*{Null hypothesis \(H_0\)} + + Sample drawn from population has same mean as control population, and any difference can be explained by sample variations. + + \subsection*{Alternative hypothesis \(H_1\)} + + Amount of variation from control is significant, despite standard sample variations. + + \subsection*{\(p\)-value} - A 95% confidence interval for \(\mu\) will have \(M\) when - \[ \overline{x} \pm k \dfrac{\sigma}{\sqrt{n}} \] + Probability of observing a value of the sample statistic as significant as the one observed, assuming null hypothesis is true. - where \(k\) is such that \(\Pr(-k < Z < k) = \frac{C}{100}\) + % table of p-values for strength of evidence + \subsection*{Distribution of sample mean} + + If \(X \sim \operatorname{N}(\mu, \sigma)\), then distribution of sample mean \(\overline{X}\) is also normal with \(\overline{X} \sim \operatorname{N}(\mu, \frac{\sigma}{\sqrt{n}}\). + + \subsection*{Statistical significance} + + Significance level is denoted by \(\alpha\). + + If \(p<\alpha\), null hypothesis is \textbf{rejected} \\ + If \(p>\alpha\), null hypothesis is \textbf{accepted} + + \subsection*{\(z\)-test} + + Hypothesis test for a mean of a sample drawn from a normally distributed population with a known standard deviation. + + \subsubsection*{\colorbox{cas}{\textbf{On CAS:}}} + + Menu \(\rightarrow\) Statistics \(\rightarrow\) Calc \(\rightarrow\) Test. \\ + Select \textit{One-Sample Z-Test} and \textit{Variable}, then input: + \begin{itemize} + \item \(\mu\) condition - same operator as \(H_1\) + \item \(\mu_0\) - expected sample mean (null hypothesis) + \item \(\sigma\) - standard deviation (null hypothesis) + \item \(\overline{x}\) - sample mean + \item \(n\) - sample size + \end{itemize} \end{document} -- 2.49.0 From ac176d3d2464068ad19adb01a74f54d61c442562 Mon Sep 17 00:00:00 2001 From: Andrew Lorimer Date: Sun, 1 Sep 2019 22:03:21 +1000 Subject: [PATCH 06/16] [spec] reorganise notes for sac --- spec/dynamics.pdf | Bin 178283 -> 163504 bytes spec/dynamics.tex | 152 +++++++++++++--------------- spec/spec-collated.pdf | Bin 377933 -> 449594 bytes spec/spec-collated.tex | 75 +++++++++----- spec/statistics.pdf | Bin 203428 -> 212441 bytes spec/statistics.tex | 218 +++++++++++++++++++++++++---------------- 6 files changed, 257 insertions(+), 188 deletions(-) diff --git a/spec/dynamics.pdf b/spec/dynamics.pdf index ca06d3747805d82297d78caf4cf3f3f531790f1d..dc59835e128918c05f5f7faeb3a93f4cea6c7a8f 100644 GIT binary patch delta 99341 zcmZU4Q*hu<&~3P}ZQHhO+qSjgFSc!OY}?7k8*c24Z728t)vd4Y!|jKzu6dlAo^$5( zne!XihEJG8GH?zy_KZO*P->u7cP$>T6T^Q+Ye|oMq_~p_=0}v(=^(si?y93XbHi~_ zP2E*`$!PkLVIc8N{;(-V486)(+W}O&EV{S%idzP2ts|}OC->`<>)p$cW<2+dhljTT zjY11rngv+F@}b6~>)ZQuw2j)er5nje>g~B<+_*LluF 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zOc;t*M#$8WHxFi}{%VK}DMz%9;6xUF8)$&9BR(1`S4V}-*JTcE91R7C&Jm}Js2&JM zn4{a|>o|pWl85G>5KD&mY>D7(wzh{=kf|ZsKc7${UmsWN?sc4;5jpBr`_$i^{U&&J z)d@Jb4YCUD>~w}tu$!qyzB~RNCnw5qjba$bT46W3US#QGe|3^!EElV;Up3g&3%GR% g)+^Q|t^Ysl)s$Et5HvV8Ha2z^7!nc@IZ>GZ0nG{+hyVZp diff --git a/spec/dynamics.tex b/spec/dynamics.tex index 5891f4e..b6a1af8 100644 --- a/spec/dynamics.tex +++ b/spec/dynamics.tex @@ -1,105 +1,58 @@ -\documentclass[a4paper, tikz, pstricks]{article} -\usepackage[a4paper,margin=2cm]{geometry} -\usepackage{array} -\usepackage{amsmath} -\usepackage{amssymb} -\usepackage{tcolorbox} -\usepackage{fancyhdr} -\usepackage{pgfplots} -\usepackage{tikz} -\usetikzlibrary{arrows, - calc, - decorations, - scopes, - angles -} -\usetikzlibrary{calc} -\usetikzlibrary{angles} -\usetikzlibrary{datavisualization.formats.functions} -\usetikzlibrary{decorations.markings} -\usepgflibrary{arrows.meta} -\usetikzlibrary{decorations.markings} -\usepgflibrary{arrows.meta} -\usepackage{pst-plot} -\psset{dimen=monkey,fillstyle=solid,opacity=.5} -\def\object{% - \psframe[linestyle=none,fillcolor=blue](-2,-1)(2,1) - \psaxes[linecolor=gray,labels=none,ticks=none]{->}(0,0)(-3,-3)(3,2)[$x$,0][$y$,90] - \rput{*0}{% - \psline{->}(0,-2)% - \uput[-90]{*0}(0,-2){$\vec{w}$}} -} - -\usepackage{tabularx} -\usetikzlibrary{angles} -\usepackage{keystroke} -\usepackage{listings} -\usepackage{xcolor} % used only to show the phantomed stuff -\definecolor{cas}{HTML}{e6f0fe} - -\pagestyle{fancy} -\fancyhead[LO,LE]{Year 12 Specialist - Dynamics} -\fancyhead[CO,CE]{Andrew Lorimer} - -\setlength\parindent{0pt} - +\documentclass[spec-collated.tex]{subfiles} \begin{document} -\title{Dynamics} -\author{} -\date{} -\maketitle +\section{Dynamics} -\section{Resolution of forces} +\subsection*{Resolution of forces} \textbf{Resultant force} is sum of force vectors -\subsection*{In angle-magnitude form} +\subsubsection*{In angle-magnitude form} \makebox[3cm]{Cosine rule:} \(c^2=a^2+b^2-2ab\cos\theta\) \makebox[3cm]{Sine rule:} \(\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\) -\subsection*{In \(\boldsymbol{i}\)---\(\boldsymbol{j}\) form} +\subsubsection*{In \(\boldsymbol{i}\)---\(\boldsymbol{j}\) form} Vector of \(a\) N at \(\theta\) to \(x\) axis is equal to \(a \cos \theta \boldsymbol{i} + a \sin \theta \boldsymbol{j}\). Convert all force vectors then add. To find angle of an \(a\boldsymbol{i} + b\boldsymbol{j}\) vector, use \(\theta = \tan^{-1} \frac{b}{a}\) -\subsection*{Resolving in a given direction} +\subsubsection*{Resolving in a given direction} The resolved part of a force \(P\) at angle \(\theta\) is has magnitude \(P \cos \theta\) To convert force \(||\vec{OA}\) to angle-magnitude form, find component \(\perp\vec{OA}\) then \(|\boldsymbol{r}|=\sqrt{\left(||\vec{OA}\right)^2 + \left(\perp\vec{OA}\right)^2},\quad \theta = \tan^{-1}\dfrac{\perp\vec{OA}}{||\vec{OA}}\) -\section{Newton's laws} +\subsection*{Newton's laws} \begin{tcolorbox} - \begin{enumerate} - \item Velocity is constant without a net external velocity + \begin{enumerate}[leftmargin=1mm] + \item Velocity is constant without a net external force \item \(\frac{d}{dt} \rho \propto \Sigma F \implies \boldsymbol{F}=m\boldsymbol{a}\) \item Equal and opposite forces \end{enumerate} \end{tcolorbox} -\subsection*{Weight} +\subsubsection*{Weight} A mass of \(m\) kg has force of \(mg\) acting on it -\subsection*{Momentum \(\rho\)} +\subsubsection*{Momentum \(\rho\)} \[ \rho = mv \tag{units kg m/s or Ns} \] -\subsection*{Reaction force \(R\)} +\subsubsection*{Reaction force \(R\)} \begin{itemize} \item With no vertical velocity, \(R=mg\) - \item With upwards acceleration, \(R-mg=ma\) + \item With vertical acceleration, \(|R|=m|a|-mg\) \item With force \(F\) at angle \(\theta\), then \(R=mg-F\sin\theta\) \end{itemize} -\subsection*{Friction} +\subsubsection*{Friction} \[ F_R = \mu R \tag{friction coefficient} \] -\section{Inclined planes} +\subsection*{Inclined planes} \[ \boldsymbol{F} = |\boldsymbol{F}| \cos \theta \boldsymbol{i} + |\boldsymbol{F}| \sin \theta \boldsymbol{j} \] \begin{itemize} @@ -122,9 +75,7 @@ A mass of \(m\) kg has force of \(mg\) acting on it pulley/.style={thick} } -\begin{figure}[!htb] - \centering - \begin{tikzpicture} + \begin{center}\begin{tikzpicture} \pgfmathsetmacro{\Fnorme}{2} \pgfmathsetmacro{\Fangle}{30} @@ -153,17 +104,9 @@ A mass of \(m\) kg has force of \(mg\) acting on it \end{scope} \draw[force,->] (M.center) -- ++(0,-1) node[below] {$mg$}; \draw (M.center)+(-90:\arcr) arc [start angle=-90,end angle=\iangle-90,radius=\arcr] node [below, pos=.5] {\footnotesize\(\theta\)}; - \end{tikzpicture} -\end{figure} + \end{tikzpicture}\end{center} -\section{Connected particles} - -\begin{itemize} - \item \textbf{Suspended pulley:} tension in both sections of rope are equal - \item \textbf{Linear connection:} find acceleration of system first - \item \textbf{Pulley on right angle:} \(a = \frac{m_2g}{m_1+m_2}\) where \(m_2\) is suspended (frictionless on both surfaces) - \item \textbf{Pulley on edge of incline:} find downwards force \(W_2\) and components of mass on plane -\end{itemize} +\subsection*{Connected particles} \def\boxwidth{0.5} \tikzset{ @@ -172,8 +115,7 @@ A mass of \(m\) kg has force of \(mg\) acting on it } -\begin{figure}[!htb] - \centering +\begin{center} \begin{tikzpicture} \matrix[column sep=1cm] { @@ -231,22 +173,68 @@ A mass of \(m\) kg has force of \(mg\) acting on it \\ }; \end{tikzpicture} -\end{figure} + \end{center} + +\begin{itemize} + \item \textbf{Suspended pulley:} tension in both sections of rope are equal \\ + \(|a| = g \frac{m_1 - m_2}{m_1 + m_2}\) where \(m_1\) accelerates down \\ + With tension: \\ + \[ \begin{cases}m_1 g - T = m_1 a\\ T - m_2 g = m_2 a\end{cases} \\ \implies m_1 g - m_2 g = m_1 a + m_2 a \] + \item \textbf{String pulling mass on inclined pane:} Resolve parallel to plane \\ + \[ T-mg \sin \theta = ma \] + \item \textbf{Linear connection:} find acceleration of system first + \item \textbf{Pulley on right angle:} \(a = \frac{m_2g}{m_1+m_2}\) where \(m_2\) is suspended (frictionless on both surfaces) + \item \textbf{Pulley on edge of incline:} find downwards force \(W_2\) and components of mass on plane +\end{itemize} + +\hspace{2em}\parbox{8em}{In this example, note \(T_1 \ne T_2\):} + \begin{tikzpicture} + + \begin{scope} -\section{Equilibrium} + \coordinate (O) at (0,0); + \coordinate (A) at ($({3*cos(\iangle)},{3*sin(\iangle)})$); + \coordinate (B) at ($({3*cos(\iangle)},0)$); + \coordinate (C) at ($({(1-0.25*\boxwidth)*cos(\iangle)},{(1-0.25*\boxwidth)*sin(\iangle)})$); % centre of box + \coordinate (D) at ($(C)+(\iangle:\boxwidth)$); + \coordinate (E) at ($(D)+(90+\iangle:0.5*\boxwidth)$); + \coordinate (F) at ($(B)+(0,{1.5*sin(\iangle)})$); + \coordinate (G) at ($(A)+(\iangle:-2*\boxwidth)$); + \coordinate (H) at ($(G)+(90+\iangle:0.5*\boxwidth)$); + \coordinate (I) at ($(H)+(\iangle:-0.5*\boxwidth)$); + \coordinate (J) at ($(H)+(\iangle:\boxwidth)$); + \coordinate (X) at ($(A)+(\iangle:0.5*\boxwidth)$); % centre of pulley + \coordinate (Y) at ($(X)+(90+\iangle:0.5*\boxwidth)$); % chord of pulley + + \draw[plane] (O) -- (A) -- (B) -- (O); + \draw (O)+(\arcr,0) arc [start angle=0,end angle=\iangle,radius=\arcr] node [right, pos=.75] {\footnotesize\(\theta\)}; + + \draw [rotate=\iangle, m] (C) rectangle ++(\boxwidth,\boxwidth) node (z) [rotate=\iangle, midway, font=\footnotesize] {\(m_1\)}; + \draw [rotate=\iangle, m] (G) rectangle ++(\boxwidth,\boxwidth) node (l) [rotate=\iangle, midway, font=\footnotesize] {\(m_2\)}; + \draw [pulley] (A) -- (X) ++(0.5*\boxwidth, 0) arc[rotate=\iangle, start angle=0, delta angle=360, x radius=0.25, y radius=0.25] node(r) [midway, rotate=\iangle] {}; + \draw [string] (E) -- (H) node [midway, above, font=\footnotesize, rotate=\iangle] {\(T_2\)}; + \draw [string] (J) -- (Y) node [midway, above, font=\footnotesize, rotate=\iangle] {\(T_1\)} arc (90+\iangle:0:0.25) -- ++($(0,{-1.5*sin(\iangle)})$) node [midway, above right, font=\footnotesize] {\(T_1\)} node[m] {\(m_3\)}; + + \end{scope} + + \end{tikzpicture} +\subsection*{Equilibrium} \[ \dfrac{A}{\sin a} = \dfrac{B}{\sin b} = \dfrac{C}{\sin c} \tag{Lami's theorem}\] +\[ c^2 = a^2 + b^2 - 2ab \cos \theta \tag{cosine rule} \] Three methods: \begin{enumerate} \item Lami's theorem (sine rule) - \item Triangle of forces or CAS (use to verify) + \item Triangle of forces (cosine rule) \item Resolution of forces (\(\Sigma F = 0\) - simultaneous) \end{enumerate} -\colorbox{cas}{On CAS:} use Geometry, lock known constants. + \begin{cas} + \textbf{To verify:} Geometry tab, then select points with normal cursor. Click right arrow at end of toolbar and input point, then lock known constants. + \end{cas} -\section{Variable forces (DEs)} +\subsection*{Variable forces (DEs)} \[ a = \dfrac{d^2x}{dt^2} = \dfrac{dv}{dt} = v\dfrac{dv}{dx} = \dfrac{d}{dx} \left( \frac{1}{2} v^2 \right) \] diff --git a/spec/spec-collated.pdf b/spec/spec-collated.pdf index 2af5693473797d195b23dfaba30384137b9a4b4f..7aa2159ebf421d89567fbb2924c33b3875b71986 100644 GIT binary patch delta 385608 zcmZU)V{j!*^Zy;&wr$&Xvf;+I?VQ+7Ha0f4ZQI${KC$^+_w#%CpI2QqRbACxHT|9W zbk9sAc4s?23Z;sK6eBAWCmiMc^2jsCN1+}#RbsQuDvU)*PLoSGM8^(+gfEP zFwX6{`2@7_y&Lj0{JEnqOxA8M%B6r(abj2T%0hAZ{;b>m24*w=ObLGx|GWXQ4SW5< zl=J=Hw*M(xV)V<3lSf00k{4<3z3<{G(xG7jN6ZuI!b%z__&2dL5;?8;2doYX{?zmw;ci$1+Q7E37kL zOMrh2jzo2uMDfvXca6m&aRI;|5{Woy@a0G(631(w4Q2<2+c=)SzAkUS_JY&Pu9+|5 zPc7Swx-P4*z_zxS%O{Hle_>gEMhVLk>oE|;Du4vVPNW(J19-q%tox)@!gI? zHqk;p5%#8rGNW9|SPRs_p_iWQ&#fbo9Cu|?7JeI}2;@d&{9=IedWL#E*-$nY=zBFA zVees3LCl7NLIoka^&VpG%wyT4LaJNxC{WPo7j8FzQV#mNW43 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