[161] | 1 | %% |
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| 2 | %% Copyright 2007, 2008, 2009 Elsevier Ltd |
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| 3 | %% |
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| 4 | %% This file is part of the 'Elsarticle Bundle'. |
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| 5 | %% --------------------------------------------- |
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| 6 | %% |
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| 7 | %% It may be distributed under the conditions of the LaTeX Project Public |
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| 8 | %% License, either version 1.2 of this license or (at your option) any |
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| 9 | %% later version. The latest version of this license is in |
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| 10 | %% http://www.latex-project.org/lppl.txt |
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| 11 | %% and version 1.2 or later is part of all distributions of LaTeX |
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| 12 | %% version 1999/12/01 or later. |
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| 13 | %% |
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| 14 | %% The list of all files belonging to the 'Elsarticle Bundle' is |
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| 15 | %% given in the file `manifest.txt'. |
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| 16 | %% |
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| 17 | %% Template article for Elsevier's document class `elsarticle' |
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| 18 | %% with harvard style bibliographic references |
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| 19 | %% SP 2008/03/01 |
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| 20 | |
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| 21 | \documentclass[preprint,12pt,authoryear]{elsarticle} |
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| 22 | |
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| 23 | %% Use the option review to obtain double line spacing |
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| 24 | %% \documentclass[authoryear,preprint,review,12pt]{elsarticle} |
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| 25 | |
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| 26 | %% Use the options 1p,twocolumn; 3p; 3p,twocolumn; 5p; or 5p,twocolumn |
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| 27 | %% for a journal layout: |
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| 28 | %% \documentclass[final,1p,times,authoryear]{elsarticle} |
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| 29 | %% \documentclass[final,1p,times,twocolumn,authoryear]{elsarticle} |
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| 30 | %% \documentclass[final,3p,times,authoryear]{elsarticle} |
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| 31 | %% \documentclass[final,3p,times,twocolumn,authoryear]{elsarticle} |
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| 32 | %% \documentclass[final,5p,times,authoryear]{elsarticle} |
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| 33 | %% \documentclass[final,5p,times,twocolumn,authoryear]{elsarticle} |
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| 34 | |
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| 35 | %% For including figures, graphicx.sty has been loaded in |
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| 36 | %% elsarticle.cls. If you prefer to use the old commands |
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| 37 | %% please give \usepackage{epsfig} |
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| 38 | |
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| 39 | %% The amssymb package provides various useful mathematical symbols |
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| 40 | \usepackage{amssymb} |
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[166] | 41 | \usepackage{multimedia} |
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| 42 | \usepackage{amsfonts} |
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| 43 | \usepackage{amsmath} |
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| 44 | \usepackage{multimedia} |
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| 45 | \usepackage{graphics} |
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| 46 | \usepackage{bbm} |
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| 47 | \usepackage{pstricks} |
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| 48 | \usepackage{amsthm} |
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| 49 | \usepackage{graphics} |
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| 50 | \usepackage{pgf} |
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| 51 | \usepackage{wrapfig} |
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| 52 | \usepackage{mathtools} |
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| 53 | \newcommand{\vectornorm}[1]{\left|\left|#1\right|\right|} |
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| 54 | \newcommand{\bo}[1]{\mathbf{#1}} |
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| 55 | %\newcommand{\vectornorm}[1]{\left|\left|#1\right|\right|} |
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| 56 | \newcommand{\dif}[2]{\frac{\partial #1}{\partial #2}} |
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| 57 | \newcommand{\diff}[2]{\frac{\partial^2 #1}{\partial {#2}^2}} |
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| 58 | \newcommand{\odif}[2]{\frac{d #1}{d #2}} |
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| 59 | \newcommand{\odiff}[2]{\frac{d^2 #1}{d #2^2}} |
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| 60 | |
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[161] | 61 | %% The amsthm package provides extended theorem environments |
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| 62 | %% \usepackage{amsthm} |
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| 63 | |
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| 64 | %% The lineno packages adds line numbers. Start line numbering with |
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| 65 | %% \begin{linenumbers}, end it with \end{linenumbers}. Or switch it on |
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| 66 | %% for the whole article with \linenumbers. |
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| 67 | %% \usepackage{lineno} |
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| 68 | |
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[165] | 69 | \journal{Ocean Modellling} |
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[161] | 70 | |
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| 71 | \begin{document} |
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| 72 | |
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| 73 | \begin{frontmatter} |
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| 74 | |
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| 75 | %% Title, authors and addresses |
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| 76 | |
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| 77 | %% use the tnoteref command within \title for footnotes; |
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| 78 | %% use the tnotetext command for theassociated footnote; |
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| 79 | %% use the fnref command within \author or \address for footnotes; |
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| 80 | %% use the fntext command for theassociated footnote; |
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| 81 | %% use the corref command within \author for corresponding author footnotes; |
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| 82 | %% use the cortext command for theassociated footnote; |
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| 83 | %% use the ead command for the email address, |
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| 84 | %% and the form \ead[url] for the home page: |
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| 85 | %% \title{Title\tnoteref{label1}} |
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| 86 | %% \tnotetext[label1]{} |
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| 87 | %% \author{Name\corref{cor1}\fnref{label2}} |
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| 88 | %% \ead{email address} |
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| 89 | %% \ead[url]{home page} |
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| 90 | %% \fntext[label2]{} |
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| 91 | %% \cortext[cor1]{} |
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| 92 | %% \address{Address\fnref{label3}} |
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| 93 | %% \fntext[label3]{} |
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| 94 | |
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[165] | 95 | \title{Modeling Surface Currents in the Eastern Levantine Mediterranenan Using Surface Drifters and Satellite Altimetry Data} |
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[161] | 96 | |
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| 97 | %% use optional labels to link authors explicitly to addresses: |
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| 98 | %% \author[label1,label2]{} |
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| 99 | %% \address[label1]{} |
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| 100 | %% \address[label2]{} |
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| 101 | |
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[165] | 102 | \author{Leila Issa, Julien Brajard, Pierre-Marie Poulain, Laurent Mortier, Dan Hayes, Milad Fakhri} |
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[161] | 103 | |
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| 104 | \address{} |
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| 105 | |
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| 106 | \begin{abstract} |
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| 107 | %% Text of abstract |
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| 108 | |
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| 109 | \end{abstract} |
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| 110 | |
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| 111 | \begin{keyword} |
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| 112 | %% keywords here, in the form: keyword \sep keyword |
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| 113 | |
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| 114 | %% PACS codes here, in the form: \PACS code \sep code |
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| 115 | |
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| 116 | %% MSC codes here, in the form: \MSC code \sep code |
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| 117 | %% or \MSC[2008] code \sep code (2000 is the default) |
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| 118 | |
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| 119 | \end{keyword} |
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| 120 | |
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| 121 | \end{frontmatter} |
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| 122 | |
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| 123 | %% \linenumbers |
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| 124 | |
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| 125 | %% main text |
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[165] | 126 | \section{Introduction} |
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[161] | 127 | \label{} |
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[165] | 128 | \section{Data} |
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| 129 | \section{Method} |
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[166] | 130 | \begin{itemize} |
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| 131 | |
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| 132 | \item $\vec{U_0}=\vec{U}_{b}+\vec{\delta U},$ $\vec{U}_b=\textcolor{red}{\vec{U}_{alt}}$ and $\vec{r}=\vec{r}^{\,b}+\vec{\delta r}$ |
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| 133 | \item Model and Linear tangent (forward Euler for the numerical integration, and bilinear Lagrange interpolation in space for instance): |
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| 134 | \small{ |
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| 135 | \begin{align} \notag |
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| 136 | &\vec{r}^{\,b}_i(k\delta t)=\vec{r}^{\,b}_i((k-1)\delta t)+2\delta t \, interp(\vec{U}^b, \vec{r}^{\,b}_i((k-1)\delta t)),\,\,\,\,\, \text{\textcolor{blue}{model}} \\ \notag |
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| 137 | &\vec{\delta r}_i(k\delta t) = \vec{\delta r}_i((k-1)\delta t) + 2 \delta t \, \{ interp(\textcolor{green}{\vec{\delta U}},\vec{r}^{\,b}_i((k-1)\delta t)) \\ \notag |
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| 138 | &+ \vec{\delta {r}}_i((k-1)\delta t) \cdot \partial _{(x,y)} interp (\vec{U}^b,\vec{r}^{\,b}_i((k-1)\delta t))\} \,\,\, \text{\textcolor{blue}{tangent}} \notag |
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| 139 | \end{align} |
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| 140 | initialized with observations, for $k=1,2,3, \cdots $ and $i=1, \cdots N_{drift}$ |
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| 141 | } |
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| 142 | %\vec{r}(0)= \vec{r}^{o}(0)$ |
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| 143 | \item Perform sequences of optimization |
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| 144 | \[\mathcal{J}(\textcolor{green}{\delta \vec{U}})= \frac{1}{2} \left \{ \sum _i \sum_{m=1}^{P} \vectornorm{\vec{r}^{\,b}_i+\delta \vec{r}_i(\textcolor{green}{\delta \vec{U}}) -\vec{r}_i^{\,o}(m\Delta t) }^2 +\vectornorm{ \textcolor{green}{\vec{\delta U}} }^2_{\bo{B}} \right\} \] |
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| 145 | $P$ depends on $T_{L}/\Delta t$. $T_L$ characteristic of autocorrelation of drifters (typical 1-3 days) |
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| 146 | |
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| 147 | %+\sum_{i,m=1}^{m=P} \vectornorm{\vec{r}^{\,b}+\delta \vec{r}(\textcolor{green}{\delta \vec{u}}) -\vec{r}_i^{\,o}(m\Delta t) }^2 \right] \] |
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| 148 | \end{itemize} |
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| 149 | |
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| 150 | |
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| 151 | |
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| 152 | |
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[165] | 153 | \section{Twin Experiments} |
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| 154 | \section{Experiment with Real Data} |
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[161] | 155 | %% The Appendices part is started with the command \appendix; |
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| 156 | %% appendix sections are then done as normal sections |
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| 157 | %% \appendix |
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| 158 | |
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| 159 | %% \section{} |
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| 160 | %% \label{} |
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| 161 | |
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| 162 | %% If you have bibdatabase file and want bibtex to generate the |
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| 163 | %% bibitems, please use |
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| 164 | %% |
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| 165 | %% \bibliographystyle{elsarticle-harv} |
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| 166 | %% \bibliography{<your bibdatabase>} |
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| 167 | |
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| 168 | %% else use the following coding to input the bibitems directly in the |
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| 169 | %% TeX file. |
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| 170 | |
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| 171 | \begin{thebibliography}{00} |
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| 172 | |
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| 173 | %% \bibitem[Author(year)]{label} |
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| 174 | %% Text of bibliographic item |
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| 175 | |
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| 176 | \bibitem[ ()]{} |
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| 177 | |
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| 178 | \end{thebibliography} |
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| 179 | \end{document} |
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| 180 | |
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| 181 | \endinput |
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| 182 | %% |
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| 183 | %% End of file `elsarticle-template-harv.tex'. |
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