118 lines
3.0 KiB
TeX
118 lines
3.0 KiB
TeX
\documentclass[11pt]{report}
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\usepackage{setspace}
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\doublespacing
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\usepackage[toc,page]{appendix}
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\usepackage[]{amsmath}
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\usepackage[]{amsthm}
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\usepackage{mathtools}
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\numberwithin{equation}{section}
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\usepackage[]{amssymb}
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\usepackage[margin=1in]{geometry}
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\usepackage[]{soul}
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\usepackage[]{bbm}
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\usepackage[]{cancel}
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\usepackage[]{xcolor}
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\usepackage[]{enumitem}
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\usepackage{mathrsfs}
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\usepackage{hyperref}
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\usepackage[capitalise]{cleveref}
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\usepackage{natbib}
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\usepackage{neuralnetwork}
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\usepackage{witharrows}
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\usepackage{listings}
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\usepackage{graphicx}
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\DeclareMathAlphabet{\mymathbb}{U}{BOONDOX-ds}{m}{n}
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% \usepackage[]{enumerate}
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\setlength\parindent{0pt}
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\DeclareMathOperator{\Trace}{Trace}
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\DeclareMathOperator{\Hess}{Hess}
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\DeclareMathOperator{\supp}{supp}
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\DeclareMathOperator{\domain}{Domain}
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\DeclareMathOperator{\lip}{Lip}
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\usepackage{tikz-cd}
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\DeclareMathOperator{\rect}{Rect}
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\DeclareMathOperator{\param}{Param}
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\DeclareMathOperator{\inn}{In}
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\DeclareMathOperator{\out}{Out}
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\DeclareMathOperator{\neu}{NN}
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\DeclareMathOperator{\hid}{Hid}
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\DeclareMathOperator{\lay}{Lay}
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\DeclareMathOperator{\dep}{Dep}
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\DeclareMathOperator{\we}{Weight}
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\DeclareMathOperator{\bi}{Bias}
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\DeclareMathOperator{\aff}{Aff}
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\DeclareMathOperator{\act}{Act}
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\DeclareMathOperator{\real}{Rlz}
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\DeclareMathOperator{\id}{Id}
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\DeclareMathOperator{\mult}{Mult}
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\DeclareMathOperator{\wid}{Wid}
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\DeclareMathOperator{\sm}{Sum}
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\DeclareMathOperator{\trn}{Trn}
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\DeclareMathOperator{\cpy}{Copy}
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\DeclareMathOperator{\ex}{Ex}
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\DeclareMathOperator{\lin}{Lin}
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\DeclareMathOperator{\relu}{ReLU}
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\DeclareMathOperator{\zero}{Zr}
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\DeclareMathOperator{\obj}{obj}
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\DeclareMathOperator{\dom}{dom}
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\DeclareMathOperator{\cod}{cod}
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\newcommand{\bbP}{\mathbb{P}}
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\newcommand{\E}{\mathbb{E}}
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\newcommand{\R}{\mathbb{R}}
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\newcommand{\Z}{\mathbb{Z}}
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\newcommand{\N}{\mathbb{N}}
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\newcommand{\p}{\mathfrak{p}}
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\newcommand{\mft}{\mathfrak{t}}
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\newcommand{\f}{\mathfrak{f}}
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\newcommand{\C}{\mathfrak{C}}
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\newcommand{\n}{\mathscr{N}}
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\newcommand{\lp}{\left(}
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\newcommand{\rp}{\right)}
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\newcommand{\rb}{\right]}
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\newcommand{\lb}{\left[}
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\newcommand{\lv}{\left|}
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\newcommand{\rv}{\right|}
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\newcommand{\la}{\langle}
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\newcommand{\ra}{\rangle}
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\newcommand{\ve}{\varepsilon}
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\newcommand{\les}{\leqslant}
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\newcommand{\ges}{\geqslant}
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% Input layer neurons'number
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\newcommand{\inputnum}{3}
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% Hidden layer neurons'number
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\newcommand{\hiddennum}{5}
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% Output layer neurons'number
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\newcommand{\outputnum}{2}
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\newtheorem{theorem}{Theorem}[section]
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\newtheorem{corollary}{Corollary}[theorem]
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\newtheorem{lemma}[theorem]{Lemma}
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\newtheorem{definition}[theorem]{Definition}
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\newtheorem{remark}[theorem]{Remark}
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\newtheorem{claim}[theorem]{Claim}
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\title{Reformulation without f}
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\author{Shakil Rafi}
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\begin{document}
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\maketitle
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\begin{theorem}
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Consider the following diffeq:
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\begin{align}
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\lp \frac{\partial }{\partial t} u \rp \lp t,x \rp + \la \mu \lp t,x \rp, \nabla_x \lp t,x \rp \ra + \frac{1}{2} \lp \Trace \lp \Hess_x u_d \rp \lp x \rp \rp -V\lp t,x \rp u \lp t,x\rp +f\lp t,x \rp = 0
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\end{align}
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\end{theorem}
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\end{document} |