# waves-16-arma

Simulation of Standing and Propagating Sea Waves with Three-Dimensional ARMA Model
git clone https://git.igankevich.com/waves-16-arma.git
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preamble.tex (2250B)

      1 \usepackage{amsmath}
2 \usepackage{cite}
3 \usepackage{latexsym} % \Box macro
4 \usepackage{mathtools} % fancy dots in matrices
5 \usepackage{graphicx}
6 \graphicspath{{figures/}}
7
8 % custom mathematical expressions
9 \newcommand{\Var}[1]{\sigma_{#1}^2}
10 \newcommand{\Fourier}[1]{\mathcal{F}\left\{#1\right\}}
11 \newcommand{\InverseFourier}[1]{\mathcal{F}^{-1}\left\{#1\right\}}
12 \newcommand{\Fun}[1]{\mathcal{D}_1\left(x,#1\right)}
13 \newcommand{\FunSecond}[1]{\mathcal{D}_2\left(x,#1\right)}
14 \newcommand{\FunThird}[1]{\mathcal{D}_2\left(x,#1\right)}
15 \newcommand{\FunThreeD}[1]{\mathcal{D}_3\left(x,y,#1\right)}
16 \newcommand{\Sinh}[1]{\cosh\left(#1\right)}
17 \newcommand{\SinhX}[1]{\sinh\left(#1\right)}
18
19 \newcommand{\FourierY}[2]{\mathcal{F}_{#2}\!\left\{#1\right\}}
20 \newcommand{\InverseFourierY}[2]{\mathcal{F}^{-1}_{#2}\!\left\{#1\right\}}
21
22 \newcommand{\FourierX}[3]{\mathcal{F}_{#2}\!\left\{#1\right\}\!\left(#3\right)}
23 \newcommand{\InverseFourierX}[3]{\mathcal{F}^{-1}_{#2}\!\left\{#1\right\}\!\left(#3\right)}
24
25 % properly aligned version of sqrt for \zeta_y^2
26 \newcommand{\SqrtZeta}[1]{\sqrt{\vphantom{\zeta_x^2}\smash[b]{#1}}}
27
28 % wave vector
29 \newcommand{\Kvec}{\vec{k}}
30 \newcommand{\Kveclen}{\lvert\smash[b]{\Kvec}\rvert}
31
32 % springer template
33 \usepackage{mathptmx}       % selects Times Roman as basic font
34 \usepackage{helvet}         % selects Helvetica as sans-serif font
35 \usepackage{courier}        % selects Courier as typewriter font
36 \usepackage{type1cm}        % activate if the above 3 fonts are
37                             % not available on your system
38 %
39 \usepackage{makeidx}         % allows index generation
40 \usepackage{graphicx}        % standard LaTeX graphics tool
41                              % when including figure files
42 \usepackage{multicol}        % used for the two-column index
43 \usepackage[bottom]{footmisc}% places footnotes at page bottom
44
45 % see the list of further useful packages
46 % in the Reference Guide
47
48 \institute{Ivan Gankevich \at Saint Petersburg State University, Universitetskii prospekt 35, Petergof, Saint Petersburg, Russia 198504, \email{i.gankevich@spbu.ru}%
49 \and Alexander Degtyarev \at Saint Petersburg State University, Universitetskii prospekt 35, Petergof, Saint Petersburg, Russia 198504, \email{a.degtyarev@spbu.ru}%
50 }