Let ‖ · ‖ be the euclidean norm on R and γn the (standard) Gaussian measure on R with density (2π)e 2/2. Let θ (≃ 1.3489795) be defined by γ1([−θ/2, θ/2]) = 1/2 and let L be a lattice in R n generated by vectors of norm ≤ θ. Then, for any closed convex set V in R with γn(V ) ≥ 1 2 and for any a ∈ R, (a + L) ∩ V 6= φ. The above statement can be viewed as a “nonsymmetric” version of Minkowski The...

0. Introduction. Even though the question answered in this note has its roots in denotational semantics for the differential λ-calculus ([2] and [1], see also [4]), no background in proof-theory is necessary to understand the problem. In the end, it boils down to a question about a special kind of polynomials in 2n variables over an arbitrary field k. This note is almost “self-contained”, assum...

In this paper, we study the motion of rigid bodies in a perfect incompressible fluid. The rigid-fluid system fils a bounded domain in R3. Adapting the strategy from Bourguignon and Brezis [1], we use the stream lines of the fluid and we eliminate the pressure by solving a Neumann problem. In this way, the system is reduced to an ordinary differential equation on a closed infinite dimensional ma...

In a recent paper, E. Steingŕımsson associated to each simple graph G a simplicial complex ∆G denoted as the coloring complex of G. Certain nonfaces of ∆G correspond in a natural manner to proper colorings of G. Indeed, the h-vector is an affine transformation of the chromatic polynomial χG of G, and the reduced Euler characteristic is, up to sign, equal to |χG(−1)| − 1. We show that ∆G is cons...

Identification of all the electrical parameters of Induction Machines (IMs) is a prerequisite for successful model-based control and/or fault detection. Various approaches have been proposed previously: off-line experiments under alternating stationary conditions, least squares batch and on-line estimation, to name only a few. Both continuous and discrete time have been considered, all of them ...