Pisot numbers, primitive matrices and beta-conjugates. We show that given a Pisot number β, for any integer n large enough, there is a nonnegative primitive square matrix whose order is equal to the degree of β, and the matrix admits β for eingenvalue. Let β = a1/β + a2/β + · · ·+ an/β + · · · be the β-expansion of β. For any Pisot number β, the sequence (an)n≥1 is ultimately periodic i.e., for...

In this paper, we present an upwinding methodology for systems of conservation laws. Our aim is to construct upwind schemes which do not require the extraction of the eigensystem of the jacobian matrix (but just the knowledge of the eigenvalues) and rely on the introduction of an appropriate polynomial approximation. @U @t + @F(U) @x = 0; t > 0; x 2 I R ; (1) avec U(x; t) un etat de l'espace de...

Let Γ be an n×n matrix, whose entries are independent identically distributed (i.i.d.) random variables satisfying the subgaussian tail estimate. We obtain polynomial type lower estimates of the singular numbers of Γ, which hold with probability close to 1. We also show that if A is an N × n matrix with N > n, whose entries are i.i.d. subgaussian random variables, then with high probability the...