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| __TOC__
| | [[File:SpanishFlag.png|24px|right|link=Bienvenido]] |
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| <strong>MediaWiki has been installed.</strong>
| | =Welcome!= |
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| Consult the [//meta.wikimedia.org/wiki/Help:Contents User's Guide] for information on using the wiki software.
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| Let's add a link to my [[Blog|blog]]
| | Welcome to my personal website. |
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| | I set up this website in October 2016, mainly as the answer to an |
| | everlasting craving to express my thoughts in a written form. |
| | Writing, as any other expression of art, must be cultivated. The |
| | style can only be improved by practicing: every writer has to |
| | find the adequate voice to put to words that what is on its mind. |
| | I'm searching for my voice, and my [[Blog|blogs]] are the |
| | platform that supports such quest. In them I discuss day-to-day |
| | events, as well as scientific topics that are related to my |
| | scientific career. |
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| $\newcommand{\Re}{\mathrm{Re}\,}
| | I'm glad to announce that [[Thesis|my doctoral thesis]] was awarded the <b style="color:brown"> prize for the best theoretical thesis of 2020</b> by the [http://gefes-rsef.org/juan-camilo-lopez-carreno-premio-gefes-2020-a-la-mejor-tesis-teorica/ Real Sociedad Española de Física] (the Spanish Royal Society of Physics). |
| \newcommand{\pFq}[5]{{}_{#1}\mathrm{F}_{#2} \left( \genfrac{}{}{0pt}{}{#3}{#4} \bigg| {#5} \right)}
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| \newcommand{\ket}[1]{\vert #1\range}$
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| Take a look at this beautifully typesetted equation:
| | This site also contains pages about the technical details of the |
| \begin{equation}
| | tools I use on a daily basis, such as [[Emacs|emacs]], |
| p(n) = \mathcal{C}_n\times
| | [[Latex|$\LaTeX$]] and [[Mathematica|Mathematica]]. Please, feel |
| {}_1\!F_2\left(n+1;\frac{2n+1}{2}+\frac{\Gamma_\sigma}{\Gamma},
| | free to visit them. |
| n+\frac{\Gamma_\sigma}{\Gamma};
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| -\frac{P_\sigma} {2\Gamma}
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| \right)\times \ket{\alpha}
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| \end{equation}
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| | The language of this website is the universal language of science |
| | and technology: English. However, as my native language is |
| | Spanish, some pages are going to be written Spanish (too). |
|
| |
|
| | | You may want to go directly to the [[Curriculum_Vitae|science]] |
| We consider, for various values of $s$, the $n$-dimensional integral
| | section. Perhaps the [[Contact|contact]] page? Or maybe you |
| \begin{align}
| | want to try a [http://camilopez.org/wiki/Special:Random random page]. |
| \label{def:Wns}
| |
| W_n (s)
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| &:=
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| \int_{[0, 1]^n}
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| \left| \sum_{k = 1}^n \mathrm{e}^{2 \pi \mathrm{i} \, x_k} \right|^s \mathrm{d}\boldsymbol{x}
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| \end{align}
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| which occurs in the theory of uniform random walk integrals in the plane,
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| where at each step a unit-step is taken in a random direction. As such,
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| the integral \eqref{def:Wns} expresses the $s$-th moment of the distance | |
| to the origin after $n$ steps.
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| | |
| By experimentation and some sketchy arguments we quickly conjectured and
| |
| strongly believed that, for $k$ a nonnegative integer
| |
| \begin{align}
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| \label{eq:W3k}
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| W_3(k) &= \Re \, \pFq 32{\frac12, -\frac k2, -\frac k2}{1, 1}{4}.
| |
| \end{align}
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| Appropriately defined, \eqref{eq:W3k} also holds for negative odd integers.
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| The reason for \eqref{eq:W3k} was long a mystery, but it will be explained
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| at the end of the paper.
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| | |
| == First Section ==
| |
| | |
| === First Subsection ===
| |
| | |
| ==== First subsubsection ====
| |
| | |
| <m>x^2</m>
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| <i class="fa fa-file-pdf-o fa-2x" aria-hidden="true"></i> CV file
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| <i class="fa fa-camera-retro"></i> fa-camera-retro
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| | |
| <a class="list-group-item" href="#"><i class="fa fa-home fa-fw" aria-hidden="true"></i> Home</a>
| |
| <a class="list-group-item" href="#"><i class="fa fa-book fa-fw" aria-hidden="true"></i> Library</a>
| |
| <a class="list-group-item" href="#"><i class="fa fa-pencil fa-fw" aria-hidden="true"></i> Applications</a>
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| <a class="list-group-item" href="#"><i class="fa fa-cog fa-fw" aria-hidden="true"></i> Settings</a>
| |
| | |
| <div class="list-group">
| |
| <a class="list-group-item" href="#"><i class="fa fa-home fa-fw" aria-hidden="true"></i> Home</a>
| |
| <a class="list-group-item" href="#"><i class="fa fa-book fa-fw" aria-hidden="true"></i> Library</a>
| |
| <a class="list-group-item" href="#"><i class="fa fa-pencil fa-fw" aria-hidden="true"></i> Applications</a>
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| <a class="list-group-item" href="#"><i class="fa fa-cog fa-fw" aria-hidden="true"></i> Settings</a>
| |
| </div>
| |
| | |
| <ul class="fa-ul">
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| <li><i class="fa-li fa fa-check-square"></i>List icons</li>
| |
| <li><i class="fa-li fa fa-check-square"></i>can be used</li>
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| <li><i class="fa-li fa fa-spinner fa-spin"></i>as bullets</li>
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| <li><i class="fa-li fa fa-square"></i>in lists</li>
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| </ul>
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| | |
| | |
| <i class="fa fa-quote-left fa-3x fa-pull-left fa-border" aria-hidden="true"></i>
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| ...tomorrow we will run faster, stretch out our arms farther...
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| And then one fine morning— So we beat on, boats against the
| |
| current, borne back ceaselessly into the past.
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| | |
| == Getting started ==
| |
| * [//www.mediawiki.org/wiki/Special:MyLanguage/Manual:Configuration_settings Configuration settings list]
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| * [//www.mediawiki.org/wiki/Special:MyLanguage/Manual:FAQ MediaWiki FAQ]
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Welcome!
Welcome to my personal website.
I set up this website in October 2016, mainly as the answer to an
everlasting craving to express my thoughts in a written form.
Writing, as any other expression of art, must be cultivated. The
style can only be improved by practicing: every writer has to
find the adequate voice to put to words that what is on its mind.
I'm searching for my voice, and my blogs are the
platform that supports such quest. In them I discuss day-to-day
events, as well as scientific topics that are related to my
scientific career.
I'm glad to announce that my doctoral thesis was awarded the prize for the best theoretical thesis of 2020 by the Real Sociedad Española de Física (the Spanish Royal Society of Physics).
This site also contains pages about the technical details of the
tools I use on a daily basis, such as emacs,
$\LaTeX$ and Mathematica. Please, feel
free to visit them.
The language of this website is the universal language of science
and technology: English. However, as my native language is
Spanish, some pages are going to be written Spanish (too).
You may want to go directly to the science
section. Perhaps the contact page? Or maybe you
want to try a random page.
