\(C_{1}^{k},\,k \leq \infty \), is the class of k times continuously differentiable real-valued functions of period 1. Q denotes the Hill’s operator − d2∕dx2 + q(x) with a fixed q of class… Expand

This article studies the Schrödinger equation for an electron in a lattice of ions with an external magnetic field. In a suitable physical scaling the ionic potential becomes rapidly oscillating, and… Expand

The periodic Schrodinger operator and electrons in a crystal preliminaries one dimensional algebraic bloch varieties compactification and consequences the potential zero separable bloch varieties… Expand

We prove that for any incomplete market and any concave utility function the marginal propensities to consume and to save are always positive. Furthermore, we introduce a class of incomplete markets… Expand

Soit q=(α,β,q)∈(0,π) 2 ×L R 2 [0,1]. Le probleme de Sturm-Liouville −y''+q(x)y=λy, 0≤x≤1, y(0) cos α+y'(0) sin α=0; y(1) cos β+y(1) sin β=0, a un spectre discret de valeurs propres simples ν 0 (q)<ν… Expand