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Aims and scope
The NorthWestern 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.
Editorial Committee
Editor in Chief: Olivier Goubet
Associate Editors:
Universität der Bundeswehr München, Germany Numerical analysis for partial differential equations Karine Beauchard (*)
ENS Rennes, France Joachim von Below (*)
Université du Littoral Côte d'Opale, France Partial differential equations, operator theory, graph theory Christophe Biernacki (*)
Université de Lille, France Statistical, modelbased data analysis Claire ChainaisHillairet (*)
Université de Lille, France Numerical analysis for partial differential equations Monique Dauge (*)
Rennes I, France Spectral theory, high order methods, singularities in partial differential equations Sinnou David (*)
Université Paris VI, France Arithmetic Youri Davydov (*)
Université de Lille, France Stochastic processes, limit theorems, stochastic geometry Pierre Dèbes (*)
Université de Lille, France Number theory, galois theory and arithmetic geometry Jérôme Droniou (*)
Monash University, Australia Elliptic and parabolic equations (theoretical and numerical study) Aziz El Kacimi (*)
Université de Valenciennes et du Hainaut Cambrésis, France Geometry, global analysis on manifolds Shalom Eliahou (*)
Université du Littoral Côte d'Opale, France Discrete mathematics Peter Fleischmann (*)
University of Kent, United Kingdom Algebra, group theory, representation theory, invariant theory Benoît Fresse (*)
Université de Lille, France Algebraic topology, operad theory Emmanuel Fricain (*)
Université de Lille, France Functional analysis, operator theory, complex analysis of one variable Eamonn Gaffney (*)
Oxford University, United Kingdom Applied mathematics in the life sciences and low Reynolds flows Antoine Gloria (*)
Université Sorbonne, France Homogenization of partial differential equations Gilles Godefroy (*)
Université Paris VI, France Functional analysis Karl GrosseErdmann (*)
Université de Mons, Belgium Functional analysis, operator theory, linear dynamics BaoZhu Guo (*)
Academy of Mathematics and Systems Science, Academia Sinica, Beijing, China System control, partial differential equation, semigroup of linear operators Pascal Lambrechts (*)
Université Catholique de Louvain, Belgium Algebraic topology
Université d'Artois, France Functional analysis André Leroy (*)
Université d'Artois, France Non commutative ring theory, module theory, error correcting codes JeanJacques Loeb (*)
Université d'Angers, France Complex analysis, in particular when related to group theory Florian Luca (*)
University of Witwatersrand, Johannesburg, SouthAfrica Analytic and diophantine number theory Kaisa Matomäki (*)
University of Turku, Finland Analytic and combinatorial number theory Christian Michaux (*)
Université de Mons, Belgium Mathematical logic Ieke Moerdijk (*)
University of Utrecht, Netherlands Algebraic topology, category theory Alejandro Murua (*)
Université de Montréal, Canada Statistical learning, clustering, pattern recognition Hiroaki Nakamura (*)
Osaka University, Japan Arithmetic geometry Jan van Neerven (*)
Delft University of Technology, Netherlands Functional analysis, stochastic analysis Johannes Nicaise (*)
Katholieke Universiteit Leuven, Belgium Algebraic and arithmetic geometry Serge Nicaise (*)
Université Polytechnique HautsdeFrance, France Partial differential equations, numerical analysis, control theory Rimas Norvaisa (*)
Vilnius University, Lituany Probability theory and stochastic processes, nonlinear functional analysis Giovanni Peccati (*)
University of Luxembourg, Luxembourg Random fields, stochastic analysis, stochastic geometry, noncommutative probability Teimuraz Pirashvili (*)
University of Leicester, United Kingdom Homological algebra and polynomial functors Olivier Ramaré (*)
Université d'AixMarseille, France Analytic number theory Sylvie Roelly (*)
University of Potsdam, Germany Stochastic differential equations, statistical mechanics, branching processes Isar Stubbe (*)
Université du Littoral Côte d'Opale, France Category theory, order theory Charles Suquet (*)
Université de Lille, France Rossana Tazzioli (*)
Université de Lille, France History of mathematics Jie Wu (*)
Institut Élie Cartan, Nancy, France Analytic number theory and modular forms
Fields Editor: Deirdre Haskell Managing Editor: Philippe Heinrich
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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 NorthWestern 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.
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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 CCBY which is the most flexible contract maximising the readership on publication.
Author Guidelines
Articles submission:
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Current Volume:
The current volume is the volume of 2022.

In this paper, we study the Cauchy problem of Boltzmann equation with soft potential in modulation spaces. Our aim is to obtain the global existence of solution to the spacehomogeneous Boltzmann equation. To realize this goal, the boundedness of Boltzmann operator in modulation space is established. In addition, Banach fixedpoint theorem is applied with careful estimate of time integral for the contraction mapping.

In this article, we develop the geometry of canonical stratifications of the spaces $\overline{\mathcal{M}}_{0,n}$ and prepare ground for studying the action of the Galois group $Gal ({\overline{\mathbb{Q}}} /\mathbb{Q})$ upon strata. We define and introduce a version of a gravity operad constructed for a class of moduli spaces $\overline{\mathcal{M}}_{0,n}$, equipped with a hidden holomorphic involution. This additional symmetry is associated to a split quaternionic structure. We introduce a categorical framework to present this object. Interaction between the geometry, physics and the arithmetics are discussed. An important feature is that 0divisors of the split quaternion algebra imply additional singular points, and lead to investigations concerning the geometry and mixed Hodge structures.

Building on a result by Tao, we show that a certain type of simple closed curve in the plane given by the union of the graphs of two $1$Lipschitz functions inscribes a square whose sidelength is bounded from below by a universal constant times the maximum of the difference of the two functions.

The aim of this note is to provide a Master Theorem for some discrete divide and conquer recurrences: \[X_{n}=a_n+\sum_{j=1}^m b_j X_{\lfloor\frac{n}{m_j}\rfloor},\] where the $m_i$'s are integers with $m_i\ge 2$. The main novelty of this work is there is no assumption of regularity or monotonicity for $(a_n)$. Then, this result can be applied to various sequences of random variables $(a_n)_{n\ge 0}$, for example such that $\sup_{n\ge 1}\mathbb{E}(a_n)<+\infty$.

We are interested in a sufficient condition given in an article by P. Lefèvre, É. Matheron and A. Primot to obtain the BlumHanson property and we then partially answer two questions asked in this same article on other possible conditions to have this property for a separable Banach space.

We give alternative computations of the Schur multiplier of $Sp(2g,\mathbb{Z}/D\mathbb{Z})$, when $D$ is divisible by 4 and $g\geq 4$: a first one using $K$theory arguments based on the work of Barge and Lannes and a second one based on the Weil representations of symplectic groups arising in abelian ChernSimons theory. We can also retrieve this way Deligne's nonresidual finiteness of the universal central extension $\widetilde{Sp(2g,\mathbb{Z})}$. We prove then that the image of the second homology into finite quotients of symplectic groups over a Dedekind domain of arithmetic type are torsion groups of uniformly bounded size. In contrast, quantum representations produce for every prime $p$, finite quotients of the mapping class group of genus $g\geq 3$ whose second homology image has $p$torsion. We further derive that all central extensions of the mapping class group are residually finite and deduce that mapping class groups have Serre's property $A_2$ for trivial modules, contrary to symplectic groups. Eventually we compute the module of coinvariants $H_2(\mathfrak{sp}_{2g}(2))_{Sp(2g,\mathbb{Z}/2^k\mathbb{Z})}=\mathbb{Z}/2\mathbb{Z}$.

We discuss here a classical CrankNicolson numerical scheme to approximate the solutions of a nonlinear equation Schrödinger that reads \begin{equation*} u_ti\partial_x\left( \nu(x)\partial_x u\right)iu\log u^2=0. \end{equation*}
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 nonprofit publisher, making research available free of charge for readers and authors.