Editor-in-Chief: Sergei Tabachnikov |
Managing Editor: Maxim Arnold |
A Journal of the IMS, |
Stony Brook University |
Published by |
Let $ \nu_0(t),\nu_1(t),\ldots,\nu_n(t)$ be the roots of the equation $ R(z)=t$, where $ R(z)$ is a rational function of the form
$\displaystyle \begin{eqnarray*} R(z)=z-\sum\limits_{k=1}^n\frac{\alpha_k}{z-\mu_k}, \end{eqnarray*}$ |
$ \mu_k$ are pairwise distinct real numbers, $ \alpha_k> 0,\,1\leq{}k\leq{}n$. Then for each real $ \xi$, the function $ e^{\xi\nu_0(t)}+e^{\xi\nu_1(t)}+\,\cdots\,+e^{\xi\nu_n(t)}$ is exponentially convex on the interval $ -\infty< t< \infty$.
where the sum runs by all $ a,b,c,d\in{\mathbb{Z}}_{\geq 0}$ such that $ ad-bc=1$. We present a proof of these formulae and list several directions for the future studies.
This journal intends to present mathematics so that it would be understandable and interesting to mathematicians independently on their narrow research fields. We invite articles exercising all formal and informal approaches to "unhide" the process of mathematical discovery.
The name of the journal is not only a dedication to the memory of Vladimir Igorevich Arnold (1937-2010), one of the most influential mathematicians of the twentieth century, but also a declaration that the journal hopes to maintain and promote the style which makes the best mathematical works by Arnold so enjoyable and which Arnold implemented in the journals where he was an editor-in-chief.
The ArMJ is organized jointly by the Institute for Mathematical Sciences (IMS) at Stony Brook, USA, and Springer Verlag, Germany.
The journal intends to publish interesting and understandable results in all areas of Mathematics. The following are the most desirable features of publications that will serve as selection criteria:
The journal articles should be accessible to a very wide community of mathematicians. Not only formal definitions that are necessary for understanding must be provided but also informal motivations even if they are well-known to the experts in the field. If a general statement is given, then the simplest examples of it are also welcome.
Interdisciplinary and multidisciplinary mathematics
We would like to have many research expositions that connect different mathematical subjects. Connections that are useful in both ways are of particular importance. Multidisciplinary research (even if the disciplines all belong to pure mathematics) is generally hard to evaluate, except for the most popular combinations such as algebraic geometry and mathematical physics, analysis and dynamical systems, algebra and combinatorics, and the like. For this reason, this kind of research is often under-represented in specialized mathematical journals. The ArMJ will try to compensate for this.
Problems, objectives, work in progress
Most scholarly publications present results of a research project in their "final" form, in which all posed questions are answered. Some open questions and conjectures may be even mentioned but the very process of mathematical discovery remains hidden. Following Arnold, we will try to unhide this process and made it public by encouraging the authors to include informal discussion of their motivation, possibly unsuccessful lines of attack, experimental data and close by research directions. The journal intends to publish well-motivated research problems on a rather regular basis. Problems do not need to be original; an old problem with a new and exciting motivation is worth re-stating. Following Arnold's principle, a general formulation is less desirable than the simplest partial case that is still unknown.
The most important requirement is that the article be interesting. It does not have to be limited by original research contributions of the author; however, the author's responsibility is to carefully acknowledge the authorship of all results. Neither does the article need to consist entirely of formal and rigorous arguments. It can contain parts, in which an informal author's understanding of the overall picture is presented; however, these parts must be clearly indicated. Including motivations, informal parts, descriptions of other lines of research, possibly conducted by other mathematicians, should serve this principal objective: being interesting.
This is the classical format: a short (usually up to 20 pages) account of a research project containing original results and complete proofs of them. However, all of the above applies. Contributions containing very technical arguments may not be suitable for the ArMJ.
This is an exposition of a broad mathematical subject containing a description of recent results (proofs may be included or omitted), historical overview, motivations, open problems. A research exposition may take 60 pages or more.
This is a description of an open problem. The problem must be well-motivated, illustrated by examples, and the importance of the problem must be explained. Alternatively, and closer to the original style of Arnold, a problem contribution may consist of a set of several problems that take very short space to state. Problems do not need to be original, however, the authorship must be carefully acknowledged. A problem contribution is meant to be short (normally, up to 4 pages, but exceptions are possible).
We feel that the following journals have objectives somewhat similar to those of the ArMJ.
However, each of these journals complies with only a part of our objectives list.
There are many great mathematicians of the twentieth century. The choice of the name may look random (why not, say, "Gelfand Mathematical Journal"? - we are often asked) but we have very specific reasons for using the name of Vladimir Arnold.
The principles, according to which the journal operates, are most accurately associated with Vladimir Arnold. He had been actively promoting these or similar principles.
For many years, V. Arnold had been the Editor-in-Chief of the journal Functional Analysis and its Applications (FAA). In 2006, V. Arnold launched a new journal, Functional Analysis and Other Mathematics (FAOM). The initial composition of the ArMJ Editorial Board consists mostly of former editors of the FAOM.
Despite the close connections with the FAA and the FAOM, we decided to avoid mentioning "Functional Analysis" in the name of the journal. These names have appeared historically, and have nothing to do with scientific principles of the journals. More than that, the names are even confusing: not all mathematicians could guess that, say, Functional Analysis and its Applications welcomes papers in all areas of mathematics, including algebra and number theory. On the other hand, we wanted to have an indication of these connections in the name of the journal. The name of Vladimir Arnold serves as this indication.
The journal is published quarterly, every issue consists of 100-150 pages. Manuscripts should be submitted online at http://www.editorialmanager.com/armj. Accepted file formats are LaTeX source (preferred) and MS Word.
Submission of a manuscript implies: that the work described has not been published before; that it is not under consideration for publication anywhere else; that its publication has been approved by all co-authors, if any, as well as by the responsible authorities - tacitly or explicitly - at the institute where the work has been carried out.
Authors wishing to include figures, tables, or text passages that have already been published elsewhere are required to obtain permission from the copyright owner(s) for both the print and online format and to include evidence that such permission has been granted when submitting their papers. Any material received without such evidence will be assumed to originate from the authors.
Editor-in-Chief:
Askold Khovanskii,
Toronto
e-mail: askold@math.toronto.edu
Managing Editor:
Vladlen Timorin, Moscow
e-mail: vtimorin@hotmail.com
Andrei Agrachev, Trieste
e-mail: agrachevaa@gmail.com
Edward Bierstone, Toronto
e-mail: bierston@math.toronto.edu
Gal Binyamini, The Weizmann Institute of Science, Israel
e-mail:
gal.binyamini@weizmann.ac.il
Felix Chernous'ko, Moscow
e-mail: chern@ipmnet.ru
David Eisenbud, Berkeley
e-mail: de@msri.org
Uriel Frisch, Nice
e-mail: uriel@oca.eu; uriel@obs-nice.fr
Dmitry Fuchs, UC Davis, CA, USA
e-mail: fuchs@math.ucdavis.edu
Alexander Gaifullin, Steklov Mathematical Institute,
Russian
Academy of Sciences, Moscow, Russia
e-mail: agaif@mi-ras.ru
Alexander Givental, Berkeley
e-mail: givental@math.berkeley.edu
Victor Goryunov, Liverpool
e-mail: Victor.Goryunov@liverpool.ac.uk
Sabir Gusein-Zade, Moscow
e-mail: sabirg@list.ru
Yulij Ilyashenko, Moscow and Cornell
e-mail: yulijs@gmail.com
Oleg Karpenkov, Liverpool
e-mail: O.Karpenkov@liverpool.ac.uk
Sergei Kuksin, Paris
e-mail: kuksin@gmail.com
Evgeny Mukhin, Indiana University-Purdue University
Indianapolis, IN, USA
e-mail: emukhin@iupui.edu
Anatoly Neishtadt, Loughborough
e-mail: A.Neishtadt@lboro.ac.uk
Sergei Tabachnikov, Pennsylvania State University, University
Park, PA, USA
e-mail: sot2@psu.edu
Alexander Varchenko, Chapel Hill
e-mail: anv@email.unc.edu
Oleg Viro, Stony Brook
e-mail: oleg.viro@gmail.com
Advisor
Eduard Zehnder, Zurich
e-mail: eduard.zehnder@math.ethz.ch
Editorial Council
Askold Khovanskii, Toronto (Editor-in-Chief)
Vladlen Timorin, Moscow (Managing Editor)
Oleg Viro, Stony Brook (A representative of the IMS)
Sabir Gusein-Zade, Moscow
Yulij Ilyashenko, Moscow and Cornell
Alexander Varchenko, Chapel Hill