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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.

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Current Volume:

The current volume is the volume of 2021.

• We obtained a moment estimate for the sum of Rademacher random variables under condition that they are dependent in the way that their sum is zero.
• Let $A$ be a nonempty finite subset of $\mathbb{Z}^d$ which is not contained in a hyperplane, $q\in\mathbb{Z}$ with $|q|>1$ and $m\in \mathbb{Z}$ such that $|q|+2d-1\leq m\leq (|q|+2d-1)^2$. In this paper it is shown that \begin{equation*} |A+q\cdot A|\geq \left(\frac{m}{|q|+2d-1}\right)|A|-c \end{equation*} where $c$ depends only on $q,d$ and $m$. In particular, taking $m=(|q|+2d-1)^2$, this results confirms a conjecture of A. Balog and G. Shakan.
• In this paper, we study a class of convolution operators on the space of distributions that enlarge the well-studied class of passive operators. In this larger class, we are able to associate, to each operator, a holomorphic function in the right half-plane with a specific constraint on its range, determined by the operator. Afterwards, we investigate whether the properties of causality and slow growth hold automatically in our larger class of convolution operators. Finally, an alternative class of convolution operators is also considered.
• In this paper, we consider the space of entire functions of minimal type growth for a proximate order. We study the surjectivity of corresponding infinite order differential equations in the cases of regular singular type and of Korobeǐnik type.
• We obtain expected number of arrivals, absorption probabilities and expected time until absorption for an asymmetric discrete random walk on a graph in the presence of multiple function barriers. On each edge of the graph and in each vertex (barrier) specific probabilities are defined.
• Les E- et G-fonctions de Siegel ont été définies en deux sens, strict et large, conjecturalement équivalents. En reprenant et complétant une esquisse d’André, nous énonçons et démontrons l’analogue au sens large du théorème d’André-Chudnovsky-Katz, qui est un théorème de structure sur les G-opérateurs au sens strict (il s’agit d’opérateurs différentiels annulant les G-fonctions au sens strict). Nous en déduisons un théorème de structure sur les E-opérateurs au sens large, qui sont des opérateurs différentiels annulant les E-fonctions au sens large. En application de ce dernier théorème, nous donnons une nouvelle preuve d’une généralisation par André du théorème de Siegel-Shidlovskii sur l’indépendance algébrique des valeurs des E-fonctions au sens large.
• In Coulombel (2015) a multiplier technique, going back to Leray and Gård- ing for scalar hyperbolic partial differential equations, has been extended to the context of finite difference schemes for evolutionary problems. The key point of the analysis in Coulombel (2015) was to obtain a discrete energy-dissipation balance law when the initial difference operator is multiplied by a suitable quan- tity (the so-called multiplier). The construction of the energy and dissipation functionals was achieved in Coulombel (2015) under the assumption that all modes were separated. We relax this assumption here and construct, for the same multiplier as in Coulombel (2015), the energy and dissipation functionals when some modes cross. Semigroup estimates for fully discrete hyperbolic initial boundary value problems are deduced in this broader context.

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.

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