Here's a correction of the second Maths composition in MP for the X competitive entrance exam. It's a very difficult subject, in 4 parts. The main object is the study of linear differential equations with periodic coefficients: we are looking for class \…

With the competitive entrance exam season in full swing, today we turn our attention to the prestigious X competitive entrance exam, with this problem A section MP common to the Ecole Normale competitive entrance exam. Linear algebra is really reduced …

A classical bit can contain either 0 or 1; a quantum bit (qubit) can be in an intermediate state, which is neither 0 nor 1, or both at the same time, a superposition of the two states. Mathematically modeled by: \[ \ket\psi = \alpha\ket0 + \beta\ket1 …

In this Centrale Supelec problem , we studied the Perron-Frobenius theorem. This theorem has many applications, one of which is at the heart of the Google search engine. We say that \(M>0\) if \(\forall i,j,\quad m_{ij}>0\) et \(\rho(A)=\max\{\abs{\lambda}…

The following exercise will help you apply and better understand Abel transform. It's also an example of a series of functions that converges uniformly on a subset of \(\mathbb{C}\), but not necessarily normally. Exercise: Let \((a_n)_{n\in\mathbb{N…