Sghiar, Mohamed

Inspired by the article [3], the introduction of the function $\hat{\circledS}$ whose integer zeros are the prime numbers, will allow me to demonstrate analytically the Goldbach's conjecture [6], the De Polignac's Conjecture [7], the Legendre's conjecture [9], and Landau's conjecture [10] .

Sghiar, Mohamed

Inspired by the article [3], the introduction of the function $\hat{\circledS}$ whose integer zeros are the prime numbers, will allow me to demonstrate analytically the Goldbach's conjecture [6], the De Polignac's Conjecture [7], the Legendre's conjecture [9], and Landau's conjecture [10] .

Lev, Felix

Following the book [1] we discuss on a popular level different aspects of classical and finite mathematics and explain why classical mathematics is a special degenerate case of finite one.

Beuzart-Plessis, Raphaël

This paper contains two results concerning the spectral decomposition, in a broad sense, of the space of nondegenerate Hermitian matrices over a local field of characteristic zero. The first is an explicit Plancherel decomposition of the associated $L^2$ space thus confirming a conjecture of Sakellaridis-Venkatesh in this particular case. The secon...

Lunz, Davin Batt, Gregory Ruess, Jakob Frédéric Bonnans, Joseph

The chemical master equation and its continuum approximations are indispensable tools in the modeling of chemical reaction networks. These are routinely used to capture complex nonlinear phenomena such as multimodality as well as transient events such as first-passage times, that accurately characterise a plethora of biological and chemical process...

Beuzart-Plessis, Raphaël Chaudouard, Pierre-Henri Zydor, Michał

In this paper, we prove the Gan-Gross-Prasad conjecture and the Ichino-Ikeda conjecture for unitary groups $U_n\times U_{n+1}$ in all the endoscopic cases. Our main technical innovation is the computation of the contributions of certain cuspidal data, called $*$-generic, to the Jacquet-Rallis trace formula for linear groups. We offer two different ...

Le Quentrec, Étienne Mazo, Loïc Baudrier, Étienne Tajine, Mohamed

Our study is about perimeter estimation of continuous shapes based on their digitization (i.e. their pixelated representation). To study the estimation error, we are led to propose the notion of monotonically sampling back-digitization, a mapping between the boundary of a digitized Jordan curve and the Jordan curve itself. This mapping ensures that...

Bagayoko, Vincent Van Der Hoeven, Joris Mantova, Vincenzo

Conway's class No of surreal numbers admits a rich structure: it forms a totally ordered real closed field with an exponential functions and a derivation. The aim of this note is to construct a surreal solution E to the functional equation E (a + 1) = exp E (a) with good properties.

Rioul, Olivier

A framework for deriving Rényi entropy-power inequalities (REPIs) is presented that uses linearization and an inequality of Dembo, Cover, and Thomas. Simple arguments are given to recover the previously known Rényi EPIs and derive new ones, by unifying a multiplicative form with constant c and a modification with exponent α of previous works. An in...

Sghiar, Mohamed

The aim of this article is to solve a problem opened more than 2 millennia ago (300 BC) : There is no odd perfect number.