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Peer Review Process

The reviewing process is simple anonymous, that is the reviewers are kept anonymous while the authors are not. The authors are asked to provide the names of one or two potential associate editors who will manage their article. Then, the editor in chief assigns the article to an associate editor who seeks reviewer(s). Once the reviews are available, the associate editor reports his decision to the whole editorial board which takes the final decision regarding the acceptance of the article.

Open Access Policy

The North-Western European Journal of Mathematics adheres to the principles of Fair Open Access, and is a member of the Free Journal Network. No charges are levied on authors. Articles are freely available to anyone as soon they are accepted. Hard copies of a volume are available at the cost of the paper and delivery.

Copyright Notice

Authors keep their copyrights. Thus they can reuse figures, article parts or any material they need for subsequent work. The contract license is the Creative Commons License CC-BY which is the most flexible contract maximising the readership on publication.

Current Volume:

The current volume is the volume of 2023.

• Dans la perspective de construire une théorie de Galois infinie pour les extensions non extérieures, nous montrons dans ce texte que le monoïde des endomorphismes d'une $Z$-extension intérieure filtrée s'identifie à la complétion procentrale du groupe de ses automorphismes intérieurs. En particulier, ce monoïde a une structure topologique naturelle qui fait de lui un espace complet et totalement discontinu.
  In order to build an infinite Galois theory for non-outer extensions, we show that the monoïd of endomorphisms of a filtered inner $Z$-extension identifies with the procentral completion of the group of its inner automorphisms. In particular, this monoid has a natural topological structure for which it is a complete and totally discontinuous space.
• Let $H$ be a Hilbert space and $(\Omega,\mathcal{F},\mu)$ a probability space. A Hilbert point in $L^p(\Omega; H)$ is a nontrivial function $\varphi$ such that $\|\varphi\|_p \leq \|\varphi+f\|_p$ whenever $\langle f, \varphi \rangle = 0$. We demonstrate that $\varphi$ is a Hilbert point in $L^p(\Omega; H)$ for some $p\neq2$ if and only if $\|\varphi(\omega)\|_H$ assumes only the two values $0$ and $C>0$. We also obtain a geometric description of when a sum of independent Rademacher variables is a Hilbert point.
• In this paper we consider sequences of nonlinear functionals of Gaussian random fields. We prove their convergence to multifractional processes which generalize Hermite processes.
• In this work, we numerically investigate how a defect can affect the behavior of traveling explosive solutions of quintic NLS equation in the one-dimensional case. Our numerical method is based on a Crank-Nicolson scheme in the time, finite difference method in space including a Perfectly Matched Layer (PML) treatment for the boundary conditions. It is observed that the defect splits the incident wave in one reflected part and one transmitted part; hence the dynamics of the solution may be changed and the blow-up may be prevented depending on the values of the defect amplitude $Z$. Moreover, it is numerically found that the defect can be considered as a barrier for large $Z$.
• Given an unbalanced open quantum graph, we derive a formula relating sums over its scattering resonances with integrals on horizontal lines in the complex plane. We deduce lower bounds on the number of resonances (in bounded regions of the complex plane) that are independent of the size of the graph. We also deduce partial results indicating that Benjamini-Schramm convergence of open quantum graphs should imply convergence of the empirical spectral measures.

Acknowledgements

This journal owes much to the following persons: Denis Bitouzé for LaTex support, Nadine Demarelle for printing service, Mohammed Khabzaoui for computer engineering issues and Omar Aouadi for secretarial tasks.

Supports

The Paul Painlevé Laboratory and the Department of Mathematics of Lille provide financial support which ensures that this journal stays open access. The French Mathematical Society (SMF), the Dutch Mathematical Society (KWG), the Luxembourg Mathematical Society (SML) and the Fields Institute support this project, of a mathematics journal by a non-profit publisher, making research available free of charge for readers and authors.