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% Replace ABCDEF in the next line with your chosen problem
% and replace 1111111 with your Team Control Number
\newcommand{\Problem}{ABCDEF}
\newcommand{\Team}{1111111}
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\usepackage{newtxmath} % must come after amsXXX\usepackage[pdftex]{graphicx}
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\lhead{Team \Team}
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\cfoot{}\newtheorem{theorem}{Theorem}
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\begin{document}
\graphicspath{{.}} % Place your graphic files in the same directory as your main document
\DeclareGraphicsExtensions{.pdf, .jpg, .tif, .png}
\thispagestyle{empty}
\vspace*{-16ex}
\centerline{\begin{tabular}{*3{c}}\parbox[t]{0.3\linewidth}{\begin{center}\textbf{Problem Chosen}\\ \Large \textcolor{red}{\Problem}\end{center}}& \parbox[t]{0.3\linewidth}{\begin{center}\textbf{2021\\ MCM/ICM\\ Summary Sheet}\end{center}}& \parbox[t]{0.3\linewidth}{\begin{center}\textbf{Team Control Number}\\ \Large \textcolor{red}{\Team}\end{center}} \\\hline
\end{tabular}}
%%%%%%%%%%% Begin Summary %%%%%%%%%%%
% Enter your summary here replacing the (red) text
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\begin{center}
\textcolor{red}{%
Use this template to begin typing the first page (summary page) of your electronic report. This \newline
template uses a 12-point Times New Roman font. Submit your paper as an Adobe PDF \newline
electronic file (e.g. 1111111.pdf), typed in English, with a readable font of at least 12-point type. \\[2ex]
Do not include the name of your school, advisor, or team members on this or any page. \\[2ex]
Papers must be within the 25 page limit. \\[2ex]
Be sure to change the control number and problem choice above. \\
You may delete these instructions as you begin to type your report here. \\[2ex]
\textbf{Follow us @COMAPMath on Twitter or COMAPCHINAOFFICIAL on Weibo for the \newline
most up to date contest information.}
}
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%% MCM/ICM LaTeX Template %%
%% 2021 MCM/ICM %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\documentclass[12pt]{article}
\usepackage{geometry}
\geometry{left=1in,right=0.75in,top=1in,bottom=1in}%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Replace ABCDEF in the next line with your chosen problem
% and replace 1111111 with your Team Control Number
\newcommand{\Problem}{C}
\newcommand{\Team}{111111}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\usepackage{newtxtext}
\usepackage{amsmath,amssymb,amsthm}
\usepackage{newtxmath} % must come after amsXXX\usepackage{graphicx}
\usepackage{xcolor}
\usepackage{fancyhdr}
\lhead{Team \Team}
\rhead{}
\cfoot{}\newtheorem{theorem}{Theorem}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{definition}{Definition}%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\usepackage{enumerate}%\item 需要
\usepackage{tabularx}% \table
\usepackage{booktabs}% \toprule
\usepackage{float}%圖片浮動
\usepackage{graphicx}
\usepackage{bm}% reference
\usepackage{indentfirst}
\setlength{\parindent}{2em} %2em代表首行縮進(jìn)兩個字符
\usepackage{listings}%代碼
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\begin{document}
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\thispagestyle{empty}
\vspace*{-16ex}
\centerline{\begin{tabular}{*3{c}}\parbox[t]{0.3\linewidth}{\begin{center}\textbf{Problem Chosen}\\ \Large \textcolor{red}{\Problem}\end{center}}& \parbox[t]{0.3\linewidth}{\begin{center}\textbf{2021\\ MCM/ICM\\ Summary Sheet}\end{center}}& \parbox[t]{0.3\linewidth}{\begin{center}\textbf{Team Control Number}\\ \Large \textcolor{red}{\Team}\end{center}} \\\hline
\end{tabular}}%==========================================
\renewcommand{\abstractname}{Summary}%=====================================
%%%%%%%%%%% Begin Summary %%%%%%%%%%%
% Enter your summary here replacing the (red) text
% Replace the text from here ...\begin{center}\large\textbf{ { A System of Interstate Energy Cooperation Goals Based on Data Insight}}\end{center}
\begin{abstract}To address the above-mentioned challenge, we propose.... Then a XX model is proposed as ....
We propose ... based on .... Then we employ an XX model as .... The results show .... Lastly, we analyze ... to find ....According to our empirical results, we propose some confident (sales) strategies and recommendations for .... We write a letter to (the marketing director of Sunshine Company) to summarize our analysis and results, together with our recommendations./ to assist with ..., we propose ...Our framework shows a strong accuracy, robustness. It can be easily implemented to other data with our source codes.\textbf{Keywords}: ext-Based Measure, Informative Text Selection, Reputation Quantification, Sales Strategy Formation
\end{abstract}
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\clearpage
\pagestyle{fancy}
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\tableofcontents
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\section{Introduction}
\subsection{Problem Background}
To solve this problem, we need to construct the time-space based bathtub temperature model to
determine the optimal strategy which could achieve the following three objectives:
\begin{enumerate}[\quad\bf1.]\item To keep the temperature \textbf{even} throughout the bathtub;\item To keep the temperature as close as possible to the \textbf{initial} temperature;\item \textbf{Not to waste} the water too much.
\end{enumerate}
\subsection{Our work}
\begin{enumerate}[\bf 1.]\item work1.\item work2.\item work3.\item work4.
\end{enumerate}
\section{Preparation of the Models}\subsection{Assumptions}
To simplify our model and eliminate the complexity, we make the following main assumptions in this literature. All assumptions will be re-emphasized once they are used in the construction of our model:
\begin{enumerate}[\bfseries 1.]\item e assume that the data given by official can fully solve the problem of the topic and do not need to obtain additional data as auxiliary information.\item Assumption2.\item Assumption3.
\end{enumerate}
\subsection{Notations}
In this work, we use the nomenclature in \textbf{Table \ref{Ntt}} in the model construction. Other nonefrequent-used symbols will be introduced once they are used.\begin{table}[H]\begin{center}\caption{Notations}\begin{tabular}{cl}\toprule\multicolumn{1}{m{3cm}}{\centering Symbol}&\multicolumn{1}{m{8cm}}{\centering Definition}\\\midrule$I$&The Intensity of the Heat Source\\$k$&The Material's Conductivity\\$h$&The Heat Transfer Coefficient\\$c$&The Heat Capacity of Water (=4200 J/(kg$\cdot^\circ$C))\\$\rho$&The Density of Water (=10$^3$ kg/m$^3$)\\\bottomrule\end{tabular}\label{Ntt}\end{center}
\end{table}
\section{Data Preprocessing}
\begin{figure}[!htbp]\small\centering\includegraphics[width=7cm]{./pictures/11.png}\includegraphics[width=7cm]{./pictures/13.png}\caption{analysis of customers}\label{nt}
\end{figure}\subsection{Default Value Processing}
\subsection{Abnormal Value Processing}
\subsection{Data Synthesis and Classification}
\section{Model Construction}
\textbf{Partial Differential Equation Method} (\textbf{PDE-Method}) \cite{10} is very uesful.We use \textbf{PDE-Toolbox} in \textbf{MATLAB} software to solve .... \textbf{Figure \ref{jj}} shows the structure of our model, which can be
divided into two parts: \textbf{PDE Solving Model} and \textbf{Analysing Model}.
\begin{figure}[H]%\usepackage{float}\small\centering\includegraphics[width=14cm]{./pictures/model.png}\caption{The Structure of Model}\label{jj}
\end{figure}
\section{Targets and Action}
\section{Senitivity Analysis}\label{condition}
\section{ Strengths and Weaknesses}
\subsection{Strengths}
\begin{itemize}\item Strength1.\item Strength2.\item Strength3.
\end{itemize}
\subsection{Weaknesses}
\begin{itemize}\item Weakness1.\item Weakness2.
\end{itemize}
\section{conclusion}
Different methods may show different ranks of effect according to the users' demand, the conditions
outside the bathtub and of the bathtub, and so on. However, according to our research in Section
\ref{condition}, these recommended methods are still useful under various conditions, if the details
(e.g. the temperature and the time of period) are properly adjusted. So the users can choose and
adjust the bath strategy based on the rules below:\paragraph{Rule I}
\emph{High temperature and large flux can make the water attach the optimum temperature earlier,meanwhile it may cause uneven temperature and waste of water.}
\paragraph{Rule II}
\emph{Evenness comes from continuous inflow with appropriate temperature, a little higher than theoptimum temperature in usual.}
\paragraph{Rule III}
\emph{The best strategy to have an excellent bath is to heat up the water before it cool down.}\clearpage
\section*{Memo}\addcontentsline{toc}{section}{Memo}\begin{flushleft}Dear users:\end{flushleft}Thank you very much for choosing our bathtubs. Each piece of your support is our valuable treasurewhich can encourage us to develop better bathtubs.We express our sincere thanks to you and yourfamily!For this kind of bathtub, we have some suggestions for you:\begin{enumerate}[\bf 1.]\item You don't have to worry about the full-water condition, because when the bathtub is fullof water, the overflow drain can drain out the excess water.\item With the consideration that you will have your special demands on the bath water, we giveyou some suggestion through so that you can choose what you prefer(or just freestyle you bath).\end{enumerate}
\clearpage
\begin{thebibliography}{99}\addcontentsline{toc}{section}{References} %引用部分標(biāo)題（"Refenrence"）的重命名\bibitem{5}Bailyn M., A Survey of Thermodynamics. \emph{American Institute of Physics}, 1997:23.\bibitem{6}Louis C.B., Convective Heat Transfer (2nd ed.). \emph{Wiley-Interscience}, 2003:107.\bibitem{7}Frank I., Theodore L.B., David D., Adrienne S.L., Fundamentals of Heat and Mass Transfer(6th ed.). \emph{John Wiley \& Sons.}, 2007:260-261.\bibitem{8}Marek R., Straub J., Analysis of the Evaporation Coeffcient and the CondensationCoeffcient of Water. \emph{International Journal of Heat and Mass Transfer}, 2001(44):39-53.\bibitem{9}Tao W.Q., Heat Transfer (4th ed.) (in Chinese). \emph{Higher Educational Press},2006:2-5.\bibitem{10}Lu J.A., Shang A., Xie J., Gu P., MATLAB-Solution of Partial Differential Equations (inChinese). \emph{Wuhan University Press}, 2001.\end{thebibliography}\clearpage\section*{Appendices}\addcontentsline{toc}{section}{Appendices}\noindent Appendix1：%下面的是配置是可以寫中文注釋的python環(huán)境:%\usepackage{listings}%\usepackage{color}\definecolor{dkgreen}{rgb}{0,0.6,0}\definecolor{gray}{rgb}{0.5,0.5,0.5}\definecolor{mauve}{rgb}{0.58,0,0.82}\lstset{ frame=shadowbox, % shadowbox framedrulesepcolor= \color{gray},%框的顏色language=Python,aboveskip=3mm,belowskip=3mm,showstringspaces=false,columns=flexible,basicstyle={\small\ttfamily},numbers=left,%設(shè)置行號位置none不顯示行號%numberstyle=\tiny\courier, %設(shè)置行號大小 numberstyle=\tiny\color{gray},keywordstyle=\color{blue},commentstyle=\color{dkgreen},stringstyle=\color{mauve},breaklines=true,breakatwhitespace=true,escapeinside=``,%逃逸字符(1左面的鍵)，用于顯示中文例如在代碼中`中文...`tabsize=4,extendedchars=false %解決代碼跨頁時，章節(jié)標(biāo)題，頁眉等漢字不顯示的問題 }\begin{lstlisting}from sklearn.svm import SVCclassifier = SVC(kernel = 'rbf',C=0.8, random_state = 0,class_weight={0:20,1:24})#classifier = SVC(kernel = 'rbf',C=1.2, random_state = 0)classifier.fit(X_train, y_train)# Predicting the Test set resultsy_pred = classifier.predict(X_test)\end{lstlisting}%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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