First part of the cosmology paper

Signed-off-by: Riccardo Finotello <riccardo.finotello@gmail.com>

sciencestuff.sty

@@ -266,58 +266,58 @@
 
 %---- dot, bar, tilde, hat
 
-\providecommand{\da}{\ensuremath{\dot{a}}\xspace}
-\providecommand{\db}{\ensuremath{\dot{b}}\xspace}
-\providecommand{\dc}{\ensuremath{\dot{c}}\xspace}
-\providecommand{\dd}{\ensuremath{\dot{d}}\xspace}
-\providecommand{\de}{\ensuremath{\dot{e}}\xspace}
-\providecommand{\df}{\ensuremath{\dot{f}}\xspace}
-\providecommand{\dg}{\ensuremath{\dot{g}}\xspace}
-\providecommand{\dh}{\ensuremath{\dot{h}}\xspace}
-\providecommand{\di}{\ensuremath{\dot{i}}\xspace}
-\providecommand{\dj}{\ensuremath{\dot{j}}\xspace}
-\providecommand{\dk}{\ensuremath{\dot{k}}\xspace}
-\providecommand{\dl}{\ensuremath{\dot{l}}\xspace}
-\providecommand{\dm}{\ensuremath{\dot{m}}\xspace}
-\providecommand{\dn}{\ensuremath{\dot{n}}\xspace}
-\providecommand{\do}{\ensuremath{\dot{o}}\xspace}
-\providecommand{\dp}{\ensuremath{\dot{p}}\xspace}
-\providecommand{\dq}{\ensuremath{\dot{q}}\xspace}
-\providecommand{\dr}{\ensuremath{\dot{r}}\xspace}
-\providecommand{\ds}{\ensuremath{\dot{s}}\xspace}
-\providecommand{\dt}{\ensuremath{\dot{t}}\xspace}
-\providecommand{\du}{\ensuremath{\dot{u}}\xspace}
-\providecommand{\dv}{\ensuremath{\dot{v}}\xspace}
-\providecommand{\dw}{\ensuremath{\dot{w}}\xspace}
-\providecommand{\dx}{\ensuremath{\dot{x}}\xspace}
-\providecommand{\dy}{\ensuremath{\dot{y}}\xspace}
-\providecommand{\dz}{\ensuremath{\dot{z}}\xspace}
-\providecommand{\dA}{\ensuremath{\dot{A}}\xspace}
-\providecommand{\dB}{\ensuremath{\dot{B}}\xspace}
-\providecommand{\dC}{\ensuremath{\dot{C}}\xspace}
-\providecommand{\dD}{\ensuremath{\dot{D}}\xspace}
-\providecommand{\dE}{\ensuremath{\dot{E}}\xspace}
-\providecommand{\dF}{\ensuremath{\dot{F}}\xspace}
-\providecommand{\dG}{\ensuremath{\dot{G}}\xspace}
-\providecommand{\dH}{\ensuremath{\dot{H}}\xspace}
-\providecommand{\dI}{\ensuremath{\dot{I}}\xspace}
-\providecommand{\dJ}{\ensuremath{\dot{J}}\xspace}
-\providecommand{\dK}{\ensuremath{\dot{K}}\xspace}
-\providecommand{\dL}{\ensuremath{\dot{L}}\xspace}
-\providecommand{\dM}{\ensuremath{\dot{M}}\xspace}
-\providecommand{\dN}{\ensuremath{\dot{N}}\xspace}
-\providecommand{\dO}{\ensuremath{\dot{O}}\xspace}
-\providecommand{\dP}{\ensuremath{\dot{P}}\xspace}
-\providecommand{\dQ}{\ensuremath{\dot{Q}}\xspace}
-\providecommand{\dR}{\ensuremath{\dot{R}}\xspace}
-\providecommand{\dS}{\ensuremath{\dot{S}}\xspace}
-\providecommand{\dT}{\ensuremath{\dot{T}}\xspace}
-\providecommand{\dU}{\ensuremath{\dot{U}}\xspace}
-\providecommand{\dV}{\ensuremath{\dot{V}}\xspace}
-\providecommand{\dW}{\ensuremath{\dot{W}}\xspace}
-\providecommand{\dX}{\ensuremath{\dot{X}}\xspace}
-\providecommand{\dY}{\ensuremath{\dot{Y}}\xspace}
-\providecommand{\dZ}{\ensuremath{\dot{Z}}\xspace}
+\providecommand{\dota}{\ensuremath{\dot{a}}\xspace}
+\providecommand{\dotb}{\ensuremath{\dot{b}}\xspace}
+\providecommand{\dotc}{\ensuremath{\dot{c}}\xspace}
+\providecommand{\dotd}{\ensuremath{\dot{d}}\xspace}
+\providecommand{\dote}{\ensuremath{\dot{e}}\xspace}
+\providecommand{\dotf}{\ensuremath{\dot{f}}\xspace}
+\providecommand{\dotg}{\ensuremath{\dot{g}}\xspace}
+\providecommand{\doth}{\ensuremath{\dot{h}}\xspace}
+\providecommand{\doti}{\ensuremath{\dot{i}}\xspace}
+\providecommand{\dotj}{\ensuremath{\dot{j}}\xspace}
+\providecommand{\dotk}{\ensuremath{\dot{k}}\xspace}
+\providecommand{\dotl}{\ensuremath{\dot{l}}\xspace}
+\providecommand{\dotm}{\ensuremath{\dot{m}}\xspace}
+\providecommand{\dotn}{\ensuremath{\dot{n}}\xspace}
+\providecommand{\doto}{\ensuremath{\dot{o}}\xspace}
+\providecommand{\dotp}{\ensuremath{\dot{p}}\xspace}
+\providecommand{\dotq}{\ensuremath{\dot{q}}\xspace}
+\providecommand{\dotr}{\ensuremath{\dot{r}}\xspace}
+\providecommand{\dots}{\ensuremath{\dot{s}}\xspace}
+\providecommand{\dott}{\ensuremath{\dot{t}}\xspace}
+\providecommand{\dotu}{\ensuremath{\dot{u}}\xspace}
+\providecommand{\dotv}{\ensuremath{\dot{v}}\xspace}
+\providecommand{\dotw}{\ensuremath{\dot{w}}\xspace}
+\providecommand{\dotx}{\ensuremath{\dot{x}}\xspace}
+\providecommand{\doty}{\ensuremath{\dot{y}}\xspace}
+\providecommand{\dotz}{\ensuremath{\dot{z}}\xspace}
+\providecommand{\dotA}{\ensuremath{\dot{A}}\xspace}
+\providecommand{\dotB}{\ensuremath{\dot{B}}\xspace}
+\providecommand{\dotC}{\ensuremath{\dot{C}}\xspace}
+\providecommand{\dotD}{\ensuremath{\dot{D}}\xspace}
+\providecommand{\dotE}{\ensuremath{\dot{E}}\xspace}
+\providecommand{\dotF}{\ensuremath{\dot{F}}\xspace}
+\providecommand{\dotG}{\ensuremath{\dot{G}}\xspace}
+\providecommand{\dotH}{\ensuremath{\dot{H}}\xspace}
+\providecommand{\dotI}{\ensuremath{\dot{I}}\xspace}
+\providecommand{\dotJ}{\ensuremath{\dot{J}}\xspace}
+\providecommand{\dotK}{\ensuremath{\dot{K}}\xspace}
+\providecommand{\dotL}{\ensuremath{\dot{L}}\xspace}
+\providecommand{\dotM}{\ensuremath{\dot{M}}\xspace}
+\providecommand{\dotN}{\ensuremath{\dot{N}}\xspace}
+\providecommand{\dotO}{\ensuremath{\dot{O}}\xspace}
+\providecommand{\dotP}{\ensuremath{\dot{P}}\xspace}
+\providecommand{\dotQ}{\ensuremath{\dot{Q}}\xspace}
+\providecommand{\dotR}{\ensuremath{\dot{R}}\xspace}
+\providecommand{\dotS}{\ensuremath{\dot{S}}\xspace}
+\providecommand{\dotT}{\ensuremath{\dot{T}}\xspace}
+\providecommand{\dotU}{\ensuremath{\dot{U}}\xspace}
+\providecommand{\dotV}{\ensuremath{\dot{V}}\xspace}
+\providecommand{\dotW}{\ensuremath{\dot{W}}\xspace}
+\providecommand{\dotX}{\ensuremath{\dot{X}}\xspace}
+\providecommand{\dotY}{\ensuremath{\dot{Y}}\xspace}
+\providecommand{\dotZ}{\ensuremath{\dot{Z}}\xspace}
 
 \providecommand{\bara}{\ensuremath{\overline{a}}\xspace}
 \providecommand{\barb}{\ensuremath{\overline{b}}\xspace}

sec/part1/introduction.tex

@@ -85,11 +85,11 @@ implies
   - \frac{1}{2 \pi \ap}
   \infinfint{\tau}
   \finiteint{\sigma}{0}{\sigma}
-  \sqrt{\dX \cdot \dX - \pX \cdot \pX}
+  \sqrt{\dotX \cdot \dotX - \pX \cdot \pX}
   =
   S_{NG}[X],
 \end{equation}
-where $S_{NG}[X]$ is the Nambu--Goto action for the classical string, $\dX = \ipd{\tau} X$ and $\pX = \ipd{\sigma} X$.
+where $S_{NG}[X]$ is the Nambu--Goto action for the classical string, $\dotX = \ipd{\tau} X$ and $\pX = \ipd{\sigma} X$.
 
 The symmetries of $S_P[\gamma, X]$ are the keys to the success of the string theory framework~\cite{Polchinski:1998:StringTheoryIntroduction}.
 Specifically~\eqref{eq:conf:polyakov} displays symmetries under:

thesis.bib

@@ -1003,6 +1003,23 @@
   number = {1-2}
 }
 
+@article{Estrada:2012:GeneralIntegral,
+  title = {A {{General Integral}}},
+  author = {Estrada, Ricardo and Vindas, Jasson},
+  date = {2012},
+  journaltitle = {Dissertationes Mathematicae},
+  shortjournal = {Dissertationes Math.},
+  volume = {483},
+  pages = {1--49},
+  issn = {0012-3862, 1730-6310},
+  doi = {10.4064/dm483-0-1},
+  abstract = {We define an integral, the distributional integral of functions of one real variable, that is more general than the Lebesgue and the Denjoy-Perron-Henstock-Kurzweil integrals, and which allows the integration of functions with distributional values everywhere or nearly everywhere. Our integral has the property that if \$f\$ is locally distributionally integrable over the real line and \$\textbackslash psi\textbackslash in\textbackslash mathcal\{D\}(\textbackslash mathbb\{R\}\%) \$ is a test function, then \$f\textbackslash psi\$ is distributionally integrable, and the formula\% [{$<\backslash$}mathsf\{f\},\textbackslash psi{$>$} =(\textbackslash mathfrak\{dist\}) \textbackslash int\_\{-\textbackslash infty\}\^\{\textbackslash infty\}f(x) \textbackslash psi(x) \textbackslash,\textbackslash mathrm\{d\}\% x\textbackslash,,] defines a distribution \$\textbackslash mathsf\{f\}\textbackslash in\textbackslash mathcal\{D\}\^\{\textbackslash prime\}(\textbackslash mathbb\{R\}) \$ that has distributional point values almost everywhere and actually \$\textbackslash mathsf\{f\}(x) =f(x) \$ almost everywhere. The indefinite distributional integral \$F(x) =(\textbackslash mathfrak\{dist\}) \textbackslash int\_\{a\}\^\{x\}f(t) \textbackslash,\textbackslash mathrm\{d\}t\$ corresponds to a distribution with point values everywhere and whose distributional derivative has point values almost everywhere equal to \$f(x).\$ The distributional integral is more general than the standard integrals, but it still has many of the useful properties of those standard ones, including integration by parts formulas, substitution formulas, even for infinite intervals --in the Ces\textbackslash `\{a\}ro sense--, mean value theorems, and convergence theorems. The distributional integral satisfies a version of Hake's theorem. Unlike general distributions, locally distributionally integrable functions can be restricted to closed sets and can be multiplied by power functions with real positive exponents.},
+  archivePrefix = {arXiv},
+  eprint = {1109.2958},
+  eprinttype = {arxiv},
+  file = {/home/riccardo/.local/share/zotero/files/estrada_vindas_2012_a_general_integral.pdf;/home/riccardo/.local/share/zotero/storage/34MFYX8V/1109.html}
+}
+
 @article{Figueroa-OFarrill:2001:GeneralisedSupersymmetricFluxbranes,
   title = {Generalised Supersymmetric Fluxbranes},
   author = {Figueroa-O'Farrill, José and Simón, Joan},

thesis.tex

@@ -70,6 +70,10 @@
 
 %---- coordinates
 \newcommand{\pX}{\ensuremath{X'}\xspace}
+\newcommand{\kmkr}{\ensuremath{\qty{k_+,\, l,\, \vb{k},\, r}}}
+\newcommand{\kmkrN}[1]{\ensuremath{\qty{k_{\qty(#1)\, +},\, l_{\qty(#1)},\, \vb{k}_{\qty(#1)},\, r_{\qty(#1)}}}}
+\newcommand{\mkmkr}{\ensuremath{\qty{-k_+,\, -l,\, -\vb{k},\, r}}}
+\newcommand{\mkmkrN}[1]{\ensuremath{\qty{-k_{\qty(#1)\, +},\, -l_{\qty(#1)},\, -\vb{k}_{\qty(#1)},\, r_{\qty(#1)}}}}
 
 %---- BEGIN DOCUMENT