North-Western European Journal of Mathematics

ISSN=2496-5170

The Lille Main Square

## Aims and scope

The North-Western European Journal of Mathematics publishes research articles and surveys in all areas of pure and applied mathematics including history of mathematics. Articles can be submitted in Dutch, English, French or German.

## Policies

### Peer Review Process

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.

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.

## Author Guidelines

Articles submission: At the initial stage, the authors have only to provide a file in the pdf format. Only when the article is accepted or subject to minor revisions are they asked to ensure it complies with the journal format.

LaTeX details:

• LaTeX class: We strongly encourage the authors to prepare their article to appear in the NWEJM journal with the dedicated nwejmart' LaTeX class (currently, documented only in French), available with up to date MiKTeX 2.9 and TeX Live 2016 distributions.
• Incompatibilities:>
• Our production system is not compatible with the xypic' bundle. For commutative diagramms, please use instead the user-friendly and modern tikz-cd' package.
• We much more prefer graphics not created with PSTricks' and derived. Consider using PGF'/TikZ' or derived packages. In case you really need one of these packages, please contact us.
• Bibliography: The bibliography must be provided as a .bib' file in the format of the biblatex' package.
• Figures: The figures must be provided in PDF or EPS formats.

Here you can find an example of a LaTEX and a biblatex file. The template and the documentation (for the time being only in French). Articles should be sent by mail to the managing editor (nicolas.wickerNOSPAMATuniv-lille.fr) or you can submit them online.

## Current Volume:

The current volume is the volume of 2020.
• Given the notion of suborbifold of the second author (based on ideas of Borzellino/Brunsden) and the classical correspondence (up to certain equivalences) between (effective) orbifolds via atlases and effective orbifold groupoids, we analyze which groupoid embeddings correspond to suborbifolds and give classes of suborbifolds naturally leading to groupoid embeddings.
• Let $\left(\mathcal{H},\left(.,.\right)\right)$ be a Hilbert space and let $\mathcal{L}\left(\mathcal{H}\right)$ be the linear space of bounded operators in $\mathcal{H}$. In this paper, we deal with $\mathcal{L}(\mathcal{H})$-valued function $Q$ that belongs to the generalized Nevanlinna class $\mathcal{N}_{\kappa} (\mathcal{H})$, where $\kappa$ is a non-negative integer. It is the class of functions meromorphic on $C \backslash R$, such that $Q(z)^{*}=Q(\bar{z})$ and the kernel $\mathcal{N}_{Q}\left( z,w \right):=\frac{Q\left( z \right)-{Q\left( w \right)}^{\ast }}{z-\bar{w}}$ has $\kappa$ negative squares. A focus is on the functions $Q \in \mathcal{N}_{\kappa} (\mathcal{H})$ which are holomorphic at $\infty$. A new operator representation of the inverse function $\hat{Q}\left( z \right):=-{Q\left( z \right)}^{-1}$ is obtained under the condition that the derivative at infinity $Q^{'}\left( \infty\right):=\lim\limits_{z\to \infty}{zQ(z)}$ is boundedly invertible operator. It turns out that $\hat{Q}$ is the sum $\hat{Q}=\hat{Q}_{1}+\hat{Q}_{2},\, \, \hat{Q}_{i}\in \mathcal{N}_{\kappa_{i}}\left( \mathcal{H} \right)$ that satisfies $\kappa_{1}+\kappa_{2}=\kappa$. That decomposition enables us to study properties of both functions, $Q$ and $\hat{Q}$, by studying the simple components $\hat{Q}_{1}$ and $\hat{Q}_{2}$.
• We provide a tool how one can view a polynomial on the affine plane of bidegree $(a,b)$ -- by which we mean that its Newton polygon lies in the triangle spanned by $(a,0)$, $(0,b)$ and the origin -- as a curve in a Hirzebruch surface having nice geometric properties. As an application, we study maximal $A_k$-singularities of curves of bidegree $(3,b)$ and find the answer for $b\leq 12$.
• We establish necessary and sufficient conditions for boundedness of composition operators on the most general class of Hilbert spaces of entire Dirichlet series with real frequencies. Depending on whether or not the space being considered contains any nonzero constant function, different criteria for boundedness are developed. Thus, we complete the characterization of bounded composition operators on all known Hilbert spaces of entire Dirichlet series of one variable.
• Hugo Steinhaus (1966a, b) has asked whether inside each acute angled triangle there is a point from which perpendiculars to the sides divide the triangle into three parts of equal areas. In this paper, we prove that $f:\mathbb{D} \rightarrow \mathbb{D}$ is a gyroisometry (hyperbolic isometry) if, and only if it is a continuous mapping that preserves the partition of a gyrotriangle (hyperbolic triangle) asked by Hugo Steinhaus.

## Acknowledgements

This journal owes much to the following persons: Denis Bitouzé for LaTex support, Jean-Jacques Derycke for printing service, Sébastien Huart for wicker computer engineering issues and Aurore Smets for secretarial tasks.

## Supports

The department of Mathematics of Lille 1 provides 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.

## Auxiliary Material

A slide to present the journal.

## Friends

We provide a tentative list of journal friends, i.e. diamond open access journals free of charge for authors and readers.