Juan L. Varona
Dept. of Mathematics and Computation
University of La Rioja (Logroño, Spain)
Sorry for my English in this page.
I know that it is very bad, and I'm sure that a lot of
grammar and spelling corrections should be added.
I was born in Tudela (Navarra, Spain) in 1962, although by chance;
it can be said that I am of
(La Rioja, Spain),
where I lived when a child.
I received the master's degree in Mathematics by the University of Zaragoza in 1985,
and read the doctoral thesis
in the University of Cantabria in 1988, under the
direction of professor José J. Guadalupe (Chicho).
I am Full Professor in the
Universidad of La Rioja.
Usually, I teach Numerical Analysis, Mathematical Analysis
and Theory of Numbers in the Degree of Mathematics,
as well as some courses of TeX.
Approximation Theory and Fourier Analysis:
Most of my research work belongs to this field.
Fundamentally, it deals on convergence of Fourier series in Lp
spaces with weights, as well as weak convergence.
We have taken care of the following types of series:
If you have more details, or you are interested in this subjects,
you can download my Ph. D. thesis (in Spanish) and the most part of
my papers pushing here.
- Fourier series of orthogonal polynomials, both classic polynomials
and modifications of the measurement adding deltas of Dirac.
- Fourier-Bessel Series.
- Series of Neumann type, and its relation with
Hankel transform and the dual integral equations.
- Fourier series related to the Dunkl transform,
as well as sampling theorems and uncertainty.
Fractals and Chaos:
I have written some papers about fractals related with iterative methods.
Most of them are divulgative papers, and they have the necessary code
(in Mathematica) to reproduce the pictures involved.
If you are interested, you can download the papers and
the corresponding code from here.
On the other hand, years ago,
I developed several applications for Macintosh that allow to draw
fractals or drawings coming from dynamic systems. But for a
long time I have not been updating them; as a consequence, they are
not Power Macintosh native and they seem poor if compared
with more modern others. Someday I will retake this.
I have been working in several subjects related to
elementary number theory.
I no longer continue with them but,
for years, most part of my research on number theory was devoted to aliquot sequences.
If a positive integer number n is taken, we denote
sigma(n) the sum of its divisors (including 1 and n), and s(n) =
sigma(n)-n the sum of its divisors without n. By iterating the function,
it appears the so called aliquot sequence. For instance, n = 20,
s(20) = 1+2+4+5+10 = 22, s(22) = 1+2+11 = 14, s(14) = 1+2+7 =
10, s(10) =... Then, the conjecture of Catalan-Dickson assures that
all these sequences finish in 1 (being the previous term a prime number),
a perfect number, a pair of amicable numbers, or a cycle. No counterexample is
known nor the conjecture is proved. In this subject I have worked in
collaboration with Manuel Benito
(who, by the way, also has written
a book on Brocot sequences).
We have obtained a computation record: The
aliquot sequence that begins in 3630 converges to 1 in 2624
iterations after to have reached a maximum of 100 digits (in base 10)
in iteration 1263.
If you are interested in this,
click here to find more information on
our work (in English). In Spanish, you can read
that is an enlargement of the one that appeared published in La Gaceta de la RSME.
Also you can accede directly from here to the table
with the present state of the sequences that begin in a
number smaller than 10000 and whose end is (still) not known, and to
the tables of 80 digits, 90 digits
and 100 digits.
Now, my research work related to number theory is not so divulgative, and can be found in the page with my
Book on Differential Equations:
I have written a book entitled Classic methods of
resolution of ordinary differentials equations (in Spanish),
published by the Service of Publications of the University of La Rioja
(ISBN: 84-88713-32-0); it is sold by 3 euros.
You can get it
with format dvi of TeX or pdf of Adobe. It can also be downloaded
from the server
Although, considering its price, perhaps is seem better to buy it instead of
printing it. The book studies, as much theoretically as by means
of examples, the different methods to solve ordinary differentials equations.
It allows, at sight of the aspect
of an equation, to easily identify his type with the target to find
its solutions. In separate files, there are a summary of the methods treated
in the book, what I have named recetas (in English, prescriptions):
servidor ftp server.
Book in memory of Chicho:
Unexpectedly, on april 1, 2000,
our college José Javier Guadalupe Hernández
(also known as Chicho) died in a car accident.
Chicho Guadalupe was initially my teacher, later on we became
collaborators. His untimely death has meant the end of our joint
work. But much more than his scientific presence, we shall miss
his friendship and his warm personality.
The Department of Mathematics and
Computation of the University of La Rioja has published a book
in honour of him (for historial interest, this is
of the page with the call).
The publishers of the book have been
Memoir on Differential Equations:
Actually, this is not a published book, but a memoir on
ordinary differential equations (in Spanish); it is devoted to be a
guide on this subject to be used in the classes in the degree in
mathematics. I wrote this memoir in 1992.
Perhaps it will be useful for somebody.
For more info, and for download it,
push here (in Spanish).
Book on Number Theory:
Encouraged by years of experience teaching courses on number theory, I have written a book on the subject.
The title is Routes across the Theory of Numbers (in Spanish), it has more than 700 pages and it has been copublished by
Electolibris and the Real Sociedad Matemática Española in its collection Universitary Texts.
For more info, push here (in Spanish).
Miscellany: Other activities and subjects of personal interest
Seminario Permanente de Actualización en Matemáticas:
Together with José Manuel Gutiérrez,
I coordinated the seminary of my department during many years.
Its activities consist in divulgative talks
of mathematics with diverse subjects.
For more info, and to see the complete list of talks since it began in 1978,
push here (in Spanish).
The digital journal
Matematicalia has published an article (in Spanish) about our Seminario Permanente,
the oldest divulgative mathematical seminary in Spain.
You can also download it in
self-contained web page.
International Congress of Mathematicians Madrid-2006:
I collaborated in the organization of the International
Congress of Mathematicians
(Madrid, from 22 to 30 of August of 2006),
as a member of the
Committee of Publications.
Together with M. Sanz-Solé, J. Soria and J. Verdera,
I were editor of
Proceedings of the International Congress of Mathematicians,
European Mathematical Society Publishing House, 2006 (Vol. II and III)
and 2007 (Vol. I).
TeX and LaTeX:
TeX is a mixture between text processor and programming language; it
is devoted, fundamentally, to write high-quality printed
documents of scientific content. It was developed by
Donald E. Knuth
and at the moment are implementations for all type of computers.
Many of them are free.
LaTeX es a more powerful and easy of use language;
it is based on TeX.
I have collaborated in the activities of the
Spanishspeaking TeX User Group, a.k.a.
of whom I am a member.
Time ago, I participated actively in the writing of its
I have always been interested in the developments of TeX to write in Spanish.
I have collaborated making dictionaries, keyboard layouts, packages,
collecting utilities and information, etc.
Also, I support the server
where you can found many material to download.
For more info, push here (in Spanish).
If you are looking how to use TeX/LaTeX in a Macintosh computer
(and how to install it), read the next item.
Usually, I use
mainly now, with
Mac OS X,
that has a powerful and useful Unix kernel.
I'm sure that I would also had enjoyed with Linux,
but I'm very confortable with mac, and I don't find a powerful reason
that incite me to dedicate all the time
necessary to dominate a new computer platform.
With Mac OS X, I recommend you the following material related with TeX
(everything is free and can be downloaded in the corresponding links;
but read up to the end of this section before to install):
The best way of achieve the installation in a Mac is to go to the web page
where you can find MacTeX, an
easy-to-install TeX distribution for MacOSX,
that has been built by the MacTeX TeXnical Working Group of the TeX Users Group (TUG).
It includes (among another utilities) all the programs cited in the previous items, with the exception of CocoAspell (if you want to get it, you must download it from its page).
- The front-end, i.e., the user interface to write the .tex file in it,
to use the typeset button, to print, ...:
by Richard Koch and the help of many people.
In particular, I make the localization in Spanish.
Important: TeXShop is not useful without installing TeX Live
(see in the in the next item).
- The kernel (TeX itself):
that has been developed by collaboration between many
TeX users groups
in the world.
(teTeX and the i-Installer,
from Gerven Wierda, is now obsolete).
- A spell checker (i.e., a dictionary) based on aspell:
by Anton Leuski.
It acts as a service of Mac OS X and can be used not only with TeXShop, but by any
other Cocoa application.
I also made the localization into Spanish.
- Another spell checker:
by Rick Zaccone.
I wrote the Spanish dictionary (it has 292 thousand words).
Finally, it will perhaps be usefull for you a keyboard layout developed by myself; it is particularly well adapted to write
TeX/LaTeX in a Mac with a Spanish keyboard.
Push here to read more information,
or download it;
it includes a file "Readme" with instruccions of how to use and how to install it. Check it!
I am a amateur developer.
Working with Macintosh computers, I have developed several
programs, and collaborated in the development of others. Of course,
no of them is commercial.
I have already made reference to some of these programs in
As a general rule, software should be free.
There exists free software of a great quality (adn, moreover, there are
awful comercial software).
In particular, I advocate you for using free software when possible.
There are powerful reasons that can incite you:
Here there is a link to GNU, the main
organization of free software.
- It is economically profitable, and you contribute to avoid that some people
to enrich with your money.
- If you collaborate with the developers, you can help to improve the product.
- You will avoid the problems of proprietary and close formats.
- You will contribute to a more free world.
- You will enjoy with all of this.
For mathematics, I suggest you try Sage,
whose target is "Creating a viable free open source alternative to Magma, Maple, Mathematica and Matlab".
"Alfarense" to "Alfareño":
As I have already mentioned, I am from
a village on
La Rioja (Spain).
A person from Alfaro is said to be an "Alfareño";
however, in the edition 21 (year 1992) and previous of the Diccionario
of the Real Academia Española (RAE),
such word does not exist. In its place, there appears "Alfarense",
a word that has never been used (at least, with this meaning).
When I noticed the error, I take the initiative in get the change
from "Alfarense" to "Alfareño". After contact with the
RAE (actually, with its Instituto de Lexicografía)
and realize a lot of efforts, some of them with the help of the
Ayuntamiento de Alfaro,
I had success.
In the edition 22 (year 2001) of the Diccionario of the RAE
already appears "Alfareño" (and "Alfarense" has been removed).
|I cannot finish without advocate you for visiting
It is an eminently agricultural village with about 10 thousand people.
But it is internationally known because it has
the biggest urban colony of storks in the world,
a big part of it in the roofs of
San Miguel's Church.
It is marvelous to observe them from the balcony.
I am member of
- The Real Sociedad Matemática Española
and Editor-in-Chief of
La Gaceta de la RSME.
- The Sociedad Española de Matemática Aplicada
- The Sociedad Riojana de Profesores de Matemáticas
- The American Mathematical Society (AMS).
- Former member of the Comisión de Información y Comunicación Electrónicas
of the Comité Español de Matemáticas
- The Grupo de Usuarios de TeX Hispanohablantes
CervanTeX (president between May 2005 and February 2016).
- The TeX Users Group TUG.
- The Agrupación Astronómica de La Rioja
- The Community of Neighbors of my house (web page under construction).
To contact myself
Juan Luis Varona
Matemáticas y Computación
Universidad de La Rioja
Edificio J. L. Vives
Calle Luis de Ulloa s/n
26004 Logroño, Spain
Tel.: 34 - 941 299 451. Fax: 34 - 941 299 460
Last modification of
April 13, 2016