#LyX 2.1 created this file. For more info see http://www.lyx.org/
\lyxformat 474
\begin_document
\begin_header
\textclass article
\begin_preamble
\usepackage{etex}
\usepackage[all, knot]{xy}
\xyoption{arc} 
\usepackage{qtree}
\usepackage{tipa}
\usepackage{pstricks}
\usepackage{pst-plot}
\usepackage{rotating}
\usepackage{tikz}
\usetikzlibrary{scopes}
\end_preamble
\use_default_options false
\maintain_unincluded_children false
\language english
\language_package default
\inputencoding auto
\fontencoding global
\font_roman lmodern
\font_sans default
\font_typewriter default
\font_math auto
\font_default_family default
\use_non_tex_fonts false
\font_sc false
\font_osf false
\font_sf_scale 100
\font_tt_scale 100
\graphics default
\default_output_format pdf
\output_sync 0
\bibtex_command default
\index_command default
\paperfontsize default
\spacing single
\use_hyperref false
\papersize default
\use_geometry false
\use_package amsmath 1
\use_package amssymb 1
\use_package cancel 0
\use_package esint 1
\use_package mathdots 1
\use_package mathtools 0
\use_package mhchem 1
\use_package stackrel 0
\use_package stmaryrd 0
\use_package undertilde 0
\cite_engine basic
\cite_engine_type default
\biblio_style plain
\use_bibtopic false
\use_indices false
\paperorientation portrait
\suppress_date false
\justification true
\use_refstyle 0
\index Index
\shortcut idx
\color #008000
\end_index
\secnumdepth 3
\tocdepth 3
\paragraph_separation indent
\paragraph_indentation default
\quotes_language english
\papercolumns 1
\papersides 1
\paperpagestyle default
\tracking_changes false
\output_changes false
\html_math_output 0
\html_css_as_file 0
\html_be_strict true
\end_header

\begin_body

\begin_layout Section
Introduction
\end_layout

\begin_layout Standard
In order to properly typeset the document and have instant preview working,
 the following packages have to be installed:
\end_layout

\begin_layout LyX-Code
xy, qtree, tipa, pstricks, pst-plot, rotating, tikz, pgf, etex
\end_layout

\begin_layout Standard
Due to the use of postscript specials in Section 
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:PSTricks"

\end_inset

, only the Postscript or PDF (ps2pdf) output formats will correctly render
 the included images.
 However, the PDF (XeTeX) output seems to also work, while trying to typeset
 the document with 
\family typewriter
pdflatex
\family default
 or 
\family typewriter
pdflualatex
\family default
 will generate errors.
\end_layout

\begin_layout Section
Diagrams by XY(-pic)
\end_layout

\begin_layout Standard
Few examples of diagrams were taken from Aaron Landa's archive of xy-pic
 examples, see 
\begin_inset Flex URL
status collapsed

\begin_layout Plain Layout

http://www.math.columbia.edu/~lauda/xy/
\end_layout

\end_inset

.
\end_layout

\begin_layout Description
Braid
\end_layout

\begin_layout Standard
\begin_inset Preview

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
xy
\end_layout

\begin_layout Plain Layout

(5,10)*{}; (-10,-10)*{} **
\backslash
crv{(6,-2)&(-12,4)}
\end_layout

\begin_layout Plain Layout


\backslash
POS?(.25)*{
\backslash
hole}="x" 
\backslash
POS?(.45)*{
\backslash
hole}="y" 
\backslash
POS?(.6)*{
\backslash
hole}="z";
\end_layout

\begin_layout Plain Layout

"y"+(0,-1); (2,-10)*{} **
\backslash
crv{}
\backslash
POS?(.2)*{
\backslash
hole}="M";
\end_layout

\begin_layout Plain Layout

(-10,10)*{}; "z" **
\backslash
crv{(-9,0)};
\end_layout

\begin_layout Plain Layout

"z"; "M" **
\backslash
crv{};
\end_layout

\begin_layout Plain Layout

"M"; "x" **
\backslash
crv{(5,0)};
\end_layout

\begin_layout Plain Layout

"x"; "y" **
\backslash
crv{(0,7) & (-5,6)};
\end_layout

\begin_layout Plain Layout


\backslash
endxy 
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Description
Knots
\end_layout

\begin_layout Standard
\begin_inset Preview

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
xy
\end_layout

\begin_layout Plain Layout

(6,9)*{}="1";
\end_layout

\begin_layout Plain Layout

(-8.5,-1)*{}="2";
\end_layout

\begin_layout Plain Layout

"1";"2" **
\backslash
crv{~*=<.5pt>{.} (0,30)}?(.75)*
\backslash
dir{>}+(-2,2)*{z};
\end_layout

\begin_layout Plain Layout

(-6.5,8)*{}="1";
\end_layout

\begin_layout Plain Layout

(-.5,-9)*{}="2";
\end_layout

\begin_layout Plain Layout

"1";"2" **
\backslash
crv{~*=<.5pt>{.} (-28.5,9.3)}?(.7)*
\backslash
dir{>}+(-2,-2)*{u};
\end_layout

\begin_layout Plain Layout

(-9.5,-3.35)*{}="1";
\end_layout

\begin_layout Plain Layout

(8.5,-3)*{}="2";
\end_layout

\begin_layout Plain Layout

"1";"2" **
\backslash
crv{~*=<.5pt>{.} (-17.67,-24.19)}?(.7)*
\backslash
dir{>}+(-1,-3)*{x};
\end_layout

\begin_layout Plain Layout

(1,-10)*{}="1";
\end_layout

\begin_layout Plain Layout

(6.5,7.13)*{}="2";
\end_layout

\begin_layout Plain Layout

"1";"2" **
\backslash
crv{~*=<.5pt>{.} (17.67,-24.19)}?(.7)*
\backslash
dir{>}+(3,-1)*{y};
\end_layout

\begin_layout Plain Layout

(11,-1)*{}="1";
\end_layout

\begin_layout Plain Layout

(-4,8)*{}="2";
\end_layout

\begin_layout Plain Layout

"1";"2" **
\backslash
crv{~*=<.5pt>{.} (28.5,9.3)}?(.93)*
\backslash
dir{>}+(1,2)*{w};
\end_layout

\begin_layout Plain Layout


\backslash
endxy
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Description
Circles
\end_layout

\begin_layout Standard
\begin_inset Preview

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
xy
\end_layout

\begin_layout Plain Layout

(0,0)*
\backslash
xycircle(14,8){++
\backslash
dir{<}};
\end_layout

\begin_layout Plain Layout

(0,0)*
\backslash
xycircle<10pt>{{.}};
\end_layout

\begin_layout Plain Layout

(0,0)*
\backslash
xycircle(5,2){:};
\end_layout

\begin_layout Plain Layout

(0,15)*
\backslash
xycircle(10,4){--};
\end_layout

\begin_layout Plain Layout


\backslash
endxy 
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Description
Cobordism
\end_layout

\begin_layout Standard
\begin_inset Preview

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
xy
\end_layout

\begin_layout Plain Layout

(0,0)*
\backslash
ellipse(3,1){.};
\end_layout

\begin_layout Plain Layout

(0,0)*
\backslash
ellipse(3,1)__,=:a(-180){-};
\end_layout

\begin_layout Plain Layout

(-6,-8)*
\backslash
ellipse(3,1){.};
\end_layout

\begin_layout Plain Layout

(6,-8)*
\backslash
ellipse(3,1){.};
\end_layout

\begin_layout Plain Layout

(0,-8)*
\backslash
ellipse(3,1){.};
\end_layout

\begin_layout Plain Layout

(-6,-8)*
\backslash
ellipse(3,1)__,=:a(-180){-};
\end_layout

\begin_layout Plain Layout

(6,-8)*
\backslash
ellipse(3,1)__,=:a(-180){-};
\end_layout

\begin_layout Plain Layout

(0,-8)*
\backslash
ellipse(3,1)__,=:a(180){-};
\end_layout

\begin_layout Plain Layout

(-3,6)*
\backslash
ellipse(3,1){-};
\end_layout

\begin_layout Plain Layout

(3,6)*
\backslash
ellipse(3,1){-};
\end_layout

\begin_layout Plain Layout

(-3,12)*{}="1";
\end_layout

\begin_layout Plain Layout

(3,12)*{}="2";
\end_layout

\begin_layout Plain Layout

(-9,12)*{}="A2";
\end_layout

\begin_layout Plain Layout

(9,12)*{}="B2";
\end_layout

\begin_layout Plain Layout

"1";"2" **
\backslash
crv{(-3,7) & (3,7)};
\end_layout

\begin_layout Plain Layout

(-3,0)*{}="A";
\end_layout

\begin_layout Plain Layout

(3,0)*{}="B";
\end_layout

\begin_layout Plain Layout

(-3,1)*{}="A1";
\end_layout

\begin_layout Plain Layout

(3,1)*{}="B1";
\end_layout

\begin_layout Plain Layout

"A";"A1" **
\backslash
dir{-};
\end_layout

\begin_layout Plain Layout

"B";"B1" **
\backslash
dir{-};
\end_layout

\begin_layout Plain Layout

"B2";"B1" **
\backslash
crv{(8,7) & (3,5)};
\end_layout

\begin_layout Plain Layout

"A2";"A1" **
\backslash
crv{(-8,7) & (-3,5)};
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\begin_layout Plain Layout

%REFLECT
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(3,-16)*{}="1";
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\begin_layout Plain Layout

"1";"2" **
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crv{(3,-10) & (9,-10)};
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\begin_layout Plain Layout

(-3,-16)*{}="1";
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(-9,-16)*{}="2";
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\begin_layout Plain Layout

"1";"2" **
\backslash
crv{(-3,-10) & (-9,-10)};
\end_layout

\begin_layout Plain Layout

(-15,-16)*{}="A2";
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\begin_layout Plain Layout

(15,-16)*{}="B2";
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(3,0)*{}="B";
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\begin_layout Plain Layout

(-3,-1)*{}="A1";
\end_layout

\begin_layout Plain Layout

(3,-1)*{}="B1";
\end_layout

\begin_layout Plain Layout

"A";"A1" **
\backslash
dir{-};
\end_layout

\begin_layout Plain Layout

"B";"B1" **
\backslash
dir{-};
\end_layout

\begin_layout Plain Layout

"B2";"B1" **
\backslash
crv{(13,-6) & (2,-8)};
\end_layout

\begin_layout Plain Layout

"A2";"A1" **
\backslash
crv{(-13,-6) & (-2,-8)};
\end_layout

\begin_layout Plain Layout


\backslash
endxy
\end_layout

\end_inset


\end_layout

\end_inset

 
\begin_inset Preview

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
xy 0;/r.18pc/:
\end_layout

\begin_layout Plain Layout

(20,2)*{
\backslash
bullet}="RU"+(1,3)*{x^{
\backslash
ast}};
\end_layout

\begin_layout Plain Layout

(16,-3)*{
\backslash
bullet}="RD"+(2.5,2)*{x^{
\backslash
ast}};
\end_layout

\begin_layout Plain Layout

(-16,2)*{
\backslash
bullet}="LU"+(-1,2)*{x};
\end_layout

\begin_layout Plain Layout

(-20,-3)*{
\backslash
bullet}="LD"+(-1,2)*{x};
\end_layout

\begin_layout Plain Layout

"RU";"RD" **
\backslash
crv{(4,2) & (4,-1)}; ?(.1)*
\backslash
dir{<}; ?(.85)*
\backslash
dir{<};
\end_layout

\begin_layout Plain Layout

"LD";"LU" **
\backslash
crv{(-4,-2) & (-4,1)};
\end_layout

\begin_layout Plain Layout

?(.08)*
\backslash
dir{<}; ?(.85)*
\backslash
dir{<};
\end_layout

\begin_layout Plain Layout

(7.5,0)*{}="x1"; (-7.5,0)*{}="x2";
\end_layout

\begin_layout Plain Layout

"x1"; "x2" **
\backslash
crv{(7,-10) & (-7,-10)};
\end_layout

\begin_layout Plain Layout

(16,-20)*{
\backslash
bullet}="RDD"+(2.5,-1)*{x^{
\backslash
ast}};
\end_layout

\begin_layout Plain Layout

(-20,-20)*{
\backslash
bullet}="LDD"+(-1,-3)*{x};
\end_layout

\begin_layout Plain Layout

(20,-12.5)*{
\backslash
bullet}="RUD"+(3.5,1)*{x^{
\backslash
ast}};
\end_layout

\begin_layout Plain Layout

(-16,-15)*{
\backslash
bullet}="LUD";
\end_layout

\begin_layout Plain Layout

(-16,-2.5)*{}="A"; (16.1,-14.9)*{}="B";
\end_layout

\begin_layout Plain Layout

"RD"; "RDD" **
\backslash
dir{-};
\end_layout

\begin_layout Plain Layout

"LD"; "LDD" **
\backslash
dir{-};
\end_layout

\begin_layout Plain Layout

"A"; "LUD" **
\backslash
dir{.};
\end_layout

\begin_layout Plain Layout

"RDD"; "LDD" **
\backslash
crv{(0,-17)}; ?(.57)*
\backslash
dir{>};
\end_layout

\begin_layout Plain Layout

"RU"; "RUD" **
\backslash
dir{-};
\end_layout

\begin_layout Plain Layout

"LU"; "A" **
\backslash
dir{-};
\end_layout

\begin_layout Plain Layout

"B"; "RUD" **
\backslash
crv{(18,-14.15)};
\end_layout

\begin_layout Plain Layout

"B"; "LUD" **
\backslash
crv{~*=<4pt>{.}(0,-18)}; ?(.4)*
\backslash
dir{<};
\end_layout

\begin_layout Plain Layout


\backslash
endxy
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Description
Strings
\end_layout

\begin_layout Standard
\begin_inset Preview

\begin_layout Standard
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
xy (-15,0)*{};(15,0)*{};
\end_layout

\begin_layout Plain Layout


\backslash
endxy
\end_layout

\begin_layout Plain Layout


\backslash
qquad = 
\backslash
qquad 
\backslash
xy
\end_layout

\begin_layout Plain Layout

(-10,12)*{}; (-10,-12)*{}; **
\backslash
dir{-}?(.5)*
\backslash
dir{<}+(-4,0)*{F(x)};
\end_layout

\begin_layout Plain Layout

(-2,12)*{}="1";
\end_layout

\begin_layout Plain Layout

(6,-7) *{}="2";
\end_layout

\begin_layout Plain Layout

(14,-7) *{}="3";
\end_layout

\begin_layout Plain Layout

(14,-13)*{}="3'";
\end_layout

\begin_layout Plain Layout

(18,0) *={}="";
\end_layout

\begin_layout Plain Layout

"1";"2" **
\backslash
crv{(-4,-21)&(5,-15)};
\end_layout

\begin_layout Plain Layout

?(.15)*
\backslash
dir{<}+(5,10)*{
\backslash
overline{F(x)}};
\end_layout

\begin_layout Plain Layout

"2";"3" **
\backslash
crv{(6,1)&(14,1)};
\end_layout

\begin_layout Plain Layout

?(0)*
\backslash
dir{<}+(4,8)*{
\backslash
widetilde{F(i_x)}} ;
\end_layout

\begin_layout Plain Layout

?(.95)*
\backslash
dir{<}+(5,-2)*{F(
\backslash
overline x)};
\end_layout

\begin_layout Plain Layout

"3";"3'" **
\backslash
dir{-};
\end_layout

\begin_layout Plain Layout

(-2,6)*{}="X1";
\end_layout

\begin_layout Plain Layout

(-10,6)*{}="X2";
\end_layout

\begin_layout Plain Layout

"X1";"X2" **
\backslash
crv{~*=<2pt>{.}(-2,-1)&(-10,-1)};
\end_layout

\begin_layout Plain Layout

(-2,-6)*{}="XA";
\end_layout

\begin_layout Plain Layout

(-10,-6)*{}="XB";
\end_layout

\begin_layout Plain Layout

"XA";"XB" **
\backslash
crv{~*=<2pt>{.}(-2,1)&(-10,1)};
\end_layout

\begin_layout Plain Layout


\backslash
endxy
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Description
Categories
\end_layout

\begin_layout Standard
\begin_inset Preview

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
xymatrix{
\end_layout

\begin_layout Plain Layout

(x 
\backslash
otimes 1) 
\backslash
otimes y
\end_layout

\begin_layout Plain Layout


\backslash
ar[rr]^{a_{x,1,y}}
\end_layout

\begin_layout Plain Layout


\backslash
ar[dr]_{r_x 
\backslash
otimes 1_y}
\end_layout

\begin_layout Plain Layout

&& x 
\backslash
otimes(1 
\backslash
otimes y)
\end_layout

\begin_layout Plain Layout


\backslash
ar[dl]^{1_x 
\backslash
otimes
\backslash
ell_y } 
\backslash

\backslash

\end_layout

\begin_layout Plain Layout

& x 
\backslash
otimes y }
\end_layout

\end_inset


\end_layout

\end_inset

 
\begin_inset Preview

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
xy
\end_layout

\begin_layout Plain Layout

(-9,0)*+{
\backslash
bullet}="1";
\end_layout

\begin_layout Plain Layout

(0,0)*+{
\backslash
bullet}="2";
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/^.9pc/ "1";"2"};
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/_.9pc/ "1";"2"};
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/^2pc/ "1";"2"};
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/_2pc/ "1";"2"};
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@{=>} (-4.5,1.5)*{};(-4.5,-1.5)*{}} ;
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@{=>} (-4.5,7.25)*{};(-4.5,4.75)*{}} ;
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@{=>} (-4.5,-4.75)*{};(-4.5,-7.25)*{}} ;
\end_layout

\begin_layout Plain Layout

(0,0)*+{
\backslash
bullet}="1";
\end_layout

\begin_layout Plain Layout

(9,0)*+{
\backslash
bullet}="2";
\end_layout

\begin_layout Plain Layout

(18,0)*+{
\backslash
bullet}="3";
\end_layout

\begin_layout Plain Layout

{
\backslash
ar "1";"2"};
\end_layout

\begin_layout Plain Layout

{
\backslash
ar "2";"3"};
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/^1pc/ "1";"2"};
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/_1pc/ "1";"2"};
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@{=>} (4.5,3)*{};(4.5,.75)*{}} ;
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@{=>} (4.5,-.75)*{};(4.5,-3)*{}} ;
\end_layout

\begin_layout Plain Layout


\backslash
endxy 
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Description
Transformations
\end_layout

\begin_layout Standard
\begin_inset Preview

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
xy %FIG.19.
 Natural transformation between functors.
\end_layout

\begin_layout Plain Layout

(-26,-2)*+{
\backslash
bullet}="a";
\end_layout

\begin_layout Plain Layout

(-12,3)*+{
\backslash
bullet}="b";
\end_layout

\begin_layout Plain Layout

(-16,-5)*+{
\backslash
bullet}="c";
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/^.25pc/ "a";"b"};
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/_.25pc/"a";"c"};
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/_.15pc/ "b";"c"};
\end_layout

\begin_layout Plain Layout

%START TOP
\end_layout

\begin_layout Plain Layout

(12,10)*+{
\backslash
bullet}="ta";
\end_layout

\begin_layout Plain Layout

(26,15)*+{
\backslash
bullet}="tb";
\end_layout

\begin_layout Plain Layout

(22,8)*+{
\backslash
bullet}="tc";
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/^.25pc/ "ta";"tb"};
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/_.25pc/ "ta";"tc"};
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/_.15pc/ "tb";"tc"};
\end_layout

\begin_layout Plain Layout

%START bottom
\end_layout

\begin_layout Plain Layout

(12,-10)*+{
\backslash
bullet}="ba";
\end_layout

\begin_layout Plain Layout

(26,-5)*+{
\backslash
bullet}="bb";
\end_layout

\begin_layout Plain Layout

(22,-12)*+{
\backslash
bullet}="bc";
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/^.25pc/@{.>} "ba";"bb"};
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/_.25pc/ "ba";"bc"};
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/_.15pc/ "bb";"bc"};
\end_layout

\begin_layout Plain Layout

%START CONNECT
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/_.15pc/ "ta";"ba"};
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/_.15pc/ "tb";"bb"};
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/_.15pc/ "tc";"bc"};
\end_layout

\begin_layout Plain Layout

%START ARROWS AND LABELS
\end_layout

\begin_layout Plain Layout

(-12,6)*{}="DF";
\end_layout

\begin_layout Plain Layout

(6,10)*{}="CF";
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/^.35pc/^F "DF";"CF"};
\end_layout

\begin_layout Plain Layout

(-12,-6)*{}="DF";
\end_layout

\begin_layout Plain Layout

(6,-10)*{}="CF";
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/_.35pc/_G "DF";"CF"};
\end_layout

\begin_layout Plain Layout

(-2,5)*{}="DF";
\end_layout

\begin_layout Plain Layout

(-2,-5)*{}="CF";
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@{=>}^{
\backslash
alpha} "DF";"CF"};
\end_layout

\begin_layout Plain Layout

(29,3)*{D};
\end_layout

\begin_layout Plain Layout

(-23,3)*{C};
\end_layout

\begin_layout Plain Layout


\backslash
endxy 
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Section
IPA
\end_layout

\begin_layout Standard
\begin_inset Preview

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textipa{Ekspl@"neIS@n}
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Section
QTree
\end_layout

\begin_layout Standard
\begin_inset Preview

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
Tree[.S [.N This ] [.V is ] [.NP [.Det a ] [.N test ] ] ] 
\end_layout

\end_inset


\end_layout

\end_inset


\begin_inset Preview

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
Tree [.$
\backslash
sigma$ $
\backslash
mu$ $
\backslash
mu$ ]
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Section
PSTricks
\begin_inset CommandInset label
LatexCommand label
name "sec:PSTricks"

\end_inset


\end_layout

\begin_layout Standard
Some simple graphing examples.
\end_layout

\begin_layout Subsection
Function plotting
\end_layout

\begin_layout Standard
\begin_inset Preview

\begin_layout Standard
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
begin{pspicture*}(-1,-3.5)(10.5,3.5)
\end_layout

\begin_layout Plain Layout


\backslash
psaxes{->}(0,0)(0,-3)(10,3)
\end_layout

\begin_layout Plain Layout


\backslash
uput[-90](10,0){$x$}
\backslash
uput[0](0,3){$f(x)$}
\end_layout

\begin_layout Plain Layout


\backslash
psplot[linecolor=red,linewidth=1pt]{0.1}{10}{ x ln }
\end_layout

\begin_layout Plain Layout


\backslash
end{pspicture*}
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Subsection
Inline data plotting
\end_layout

\begin_layout Standard
\align center
\begin_inset Preview

\begin_layout Standard
\align center
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
begin{pspicture*}(-1.5,-1.5)(11,5)
\end_layout

\begin_layout Plain Layout


\backslash
psaxes{->}(0,0)(0,0)(10,5)
\end_layout

\begin_layout Plain Layout


\backslash
psset{linewidth=2.5pt}
\end_layout

\begin_layout Plain Layout


\backslash
rput(5.0,-1.0){Speed [MPH]}
\end_layout

\begin_layout Plain Layout


\backslash
rput(-1.0,1.0){
\backslash
begin{rotate}{90}Cost [Dollars]
\backslash
end{rotate}}
\end_layout

\begin_layout Plain Layout


\backslash
savedata{
\backslash
mydata}[{{0,0},{1.3,0.32},{5.5,1.1},{6.5,1.15},{8.1,1.28},{10,4}}]
\end_layout

\begin_layout Plain Layout


\backslash
dataplot[plotstyle=curve,showpoints=true,dotstyle=triangle,linecolor=blue]{
\backslash
mydata} 
\end_layout

\begin_layout Plain Layout


\backslash
end{pspicture*}
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Subsection
Lissajous curves
\end_layout

\begin_layout Standard
\begin_inset Preview

\begin_layout Standard
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
\end_layout

\begin_layout Plain Layout


\backslash
parametricplot[plotstyle=line,plotpoints=50,linecolor=red]{0}{8}{50 t mul
 cos 100 t mul sin}
\end_layout

\begin_layout Plain Layout


\backslash
end{pspicture*}
\end_layout

\end_inset


\end_layout

\end_inset


\begin_inset space \hfill{}
\end_inset


\begin_inset Preview

\begin_layout Standard
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
\end_layout

\begin_layout Plain Layout


\backslash
parametricplot[plotstyle=line,plotpoints=100,linecolor=red]{0}{8}{150 t
 mul cos 100 t mul sin}
\end_layout

\begin_layout Plain Layout


\backslash
end{pspicture*}
\end_layout

\end_inset


\end_layout

\end_inset


\begin_inset space \hfill{}
\end_inset


\begin_inset Preview

\begin_layout Standard
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
\end_layout

\begin_layout Plain Layout


\backslash
parametricplot[plotstyle=line,plotpoints=150,linecolor=red]{0}{8}{150 t
 mul cos 200 t mul sin}
\end_layout

\begin_layout Plain Layout


\backslash
end{pspicture*}
\end_layout

\end_inset


\end_layout

\end_inset


\begin_inset space \hfill{}
\end_inset


\begin_inset Preview

\begin_layout Standard
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
\end_layout

\begin_layout Plain Layout


\backslash
parametricplot[plotstyle=line,plotpoints=200,linecolor=red]{0}{8}{250 t
 mul cos 200 t mul sin}
\end_layout

\begin_layout Plain Layout


\backslash
end{pspicture*}
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Section
TikZ
\end_layout

\begin_layout Standard
\begin_inset Flex URL
status collapsed

\begin_layout Plain Layout

http://www.texample.net/media/tikz/examples/TEX/free-body-diagrams.tex
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Preview

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
def
\backslash
iangle{35} % Angle of the inclined plane
\end_layout

\begin_layout Plain Layout


\backslash
def
\backslash
down{-90}
\end_layout

\begin_layout Plain Layout


\backslash
def
\backslash
arcr{0.5cm} % Radius of the arc used to indicate angles
\end_layout

\begin_layout Plain Layout

\end_layout

\begin_layout Plain Layout


\backslash
begin{tikzpicture}[
\end_layout

\begin_layout Plain Layout

    force/.style={>=latex,draw=blue,fill=blue},
\end_layout

\begin_layout Plain Layout

    axis/.style={densely dashed,gray,font=
\backslash
small},
\end_layout

\begin_layout Plain Layout

    M/.style={rectangle,draw,fill=lightgray,minimum size=0.5cm,thin},
\end_layout

\begin_layout Plain Layout

    m/.style={rectangle,draw=black,fill=lightgray,minimum size=0.3cm,thin},
\end_layout

\begin_layout Plain Layout

    plane/.style={draw=black,fill=blue!10},
\end_layout

\begin_layout Plain Layout

    string/.style={draw=red, thick},
\end_layout

\begin_layout Plain Layout

    pulley/.style={thick},
\end_layout

\begin_layout Plain Layout

]
\end_layout

\begin_layout Plain Layout

\end_layout

\begin_layout Plain Layout


\backslash
matrix[column sep=1cm] {
\end_layout

\begin_layout Plain Layout

    %% Sketch
\end_layout

\begin_layout Plain Layout

    
\backslash
draw[plane] (0,-1) coordinate (base)
\end_layout

\begin_layout Plain Layout

                     -- coordinate[pos=0.5] (mid) ++(
\backslash
iangle:3) coordinate (top)
\end_layout

\begin_layout Plain Layout

                     |- (base) -- cycle;
\end_layout

\begin_layout Plain Layout

    
\backslash
path (mid) node[M,rotate=
\backslash
iangle,yshift=0.25cm] (M) {};
\end_layout

\begin_layout Plain Layout

    
\backslash
draw[pulley] (top) -- ++(
\backslash
iangle:0.25) circle (0.25cm)
\end_layout

\begin_layout Plain Layout

                   ++ (90-
\backslash
iangle:0.5) coordinate (pulley);
\end_layout

\begin_layout Plain Layout

    
\backslash
draw[string] (M.east) -- ++(
\backslash
iangle:1.5cm) arc (90+
\backslash
iangle:0:0.25)
\end_layout

\begin_layout Plain Layout

                  -- ++(0,-1) node[m] {};
\end_layout

\begin_layout Plain Layout

\end_layout

\begin_layout Plain Layout

    
\backslash
draw[->] (base)++(
\backslash
arcr,0) arc (0:
\backslash
iangle:
\backslash
arcr);
\end_layout

\begin_layout Plain Layout

    
\backslash
path (base)++(
\backslash
iangle*0.5:
\backslash
arcr+5pt) node {$
\backslash
alpha$};
\end_layout

\begin_layout Plain Layout

    %%
\end_layout

\begin_layout Plain Layout

\end_layout

\begin_layout Plain Layout

&
\end_layout

\begin_layout Plain Layout

    %% Free body diagram of M
\end_layout

\begin_layout Plain Layout

    
\backslash
begin{scope}[rotate=
\backslash
iangle]
\end_layout

\begin_layout Plain Layout

        
\backslash
node[M,transform shape] (M) {};
\end_layout

\begin_layout Plain Layout

        % Draw axes and help lines
\end_layout

\begin_layout Plain Layout

\end_layout

\begin_layout Plain Layout

        {[axis,->]
\end_layout

\begin_layout Plain Layout

            
\backslash
draw (0,-1) -- (0,2) node[right] {$+y$};
\end_layout

\begin_layout Plain Layout

            
\backslash
draw (M) -- ++(2,0) node[right] {$+x$};
\end_layout

\begin_layout Plain Layout

            % Indicate angle.
 The code is a bit awkward.
\end_layout

\begin_layout Plain Layout

\end_layout

\begin_layout Plain Layout

            
\backslash
draw[solid,shorten >=0.5pt] (
\backslash
down-
\backslash
iangle:
\backslash
arcr)
\end_layout

\begin_layout Plain Layout

                arc(
\backslash
down-
\backslash
iangle:
\backslash
down:
\backslash
arcr);
\end_layout

\begin_layout Plain Layout

            
\backslash
node at (
\backslash
down-0.5*
\backslash
iangle:1.3*
\backslash
arcr) {$
\backslash
alpha$};
\end_layout

\begin_layout Plain Layout

        }
\end_layout

\begin_layout Plain Layout

\end_layout

\begin_layout Plain Layout

        % Forces
\end_layout

\begin_layout Plain Layout

        {[force,->]
\end_layout

\begin_layout Plain Layout

            % Assuming that Mg = 1.
 The normal force will therefore be cos(alpha)
\end_layout

\begin_layout Plain Layout

            
\backslash
draw (M.center) -- ++(0,{cos(
\backslash
iangle)}) node[above right] {$N$};
\end_layout

\begin_layout Plain Layout

            
\backslash
draw (M.west) -- ++(-1,0) node[left] {$f_R$};
\end_layout

\begin_layout Plain Layout

            
\backslash
draw (M.east) -- ++(1,0) node[above] {$T$};
\end_layout

\begin_layout Plain Layout

        }
\end_layout

\begin_layout Plain Layout

\end_layout

\begin_layout Plain Layout

    
\backslash
end{scope}
\end_layout

\begin_layout Plain Layout

    % Draw gravity force.
 The code is put outside the rotated
\end_layout

\begin_layout Plain Layout

    % scope for simplicity.
 No need to do any angle calculations.
 
\end_layout

\begin_layout Plain Layout

    
\backslash
draw[force,->] (M.center) -- ++(0,-1) node[below] {$Mg$};
\end_layout

\begin_layout Plain Layout

    %%
\end_layout

\begin_layout Plain Layout

\end_layout

\begin_layout Plain Layout

&
\end_layout

\begin_layout Plain Layout

    %%%
\end_layout

\begin_layout Plain Layout

    % Free body diagram of m
\end_layout

\begin_layout Plain Layout

    
\backslash
node[m] (m) {};
\end_layout

\begin_layout Plain Layout

    
\backslash
draw[axis,->] (m) -- ++(0,-2) node[left] {$+$};
\end_layout

\begin_layout Plain Layout

    {[force,->]
\end_layout

\begin_layout Plain Layout

        
\backslash
draw (m.north) -- ++(0,1) node[above] {$T'$};
\end_layout

\begin_layout Plain Layout

        
\backslash
draw (m.south) -- ++(0,-1) node[right] {$mg$};
\end_layout

\begin_layout Plain Layout

    }
\end_layout

\begin_layout Plain Layout

\end_layout

\begin_layout Plain Layout


\backslash

\backslash

\end_layout

\begin_layout Plain Layout

};
\end_layout

\begin_layout Plain Layout


\backslash
end{tikzpicture}
\end_layout

\begin_layout Plain Layout

\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\end_body
\end_document
