“Magnetic Force Microscopy and Energy Loss Imaging of Superparamagnetic Iron Oxide Nanoparticles”

We present quantitative, high spatially resolved magnetic force microscopy imaging of samples based on 11 nm diameter superparamagnetic iron oxide nanoparticles in air at room temperature. By a proper combination of the cantilever resonance frequency shift, oscillation amplitude and phase lag we obtain the tip-sample interaction maps in terms of force gradient and energy dissipation. These physical quantities are evaluated in the frame of a tip-particle magnetic interaction model also including the tip oscillation amplitude. Magnetic nanoparticles are characterized both in bare form, after deposition on a flat substrate, and as magnetically assembled fillers in a polymer matrix, in the form of nanowires. The latter approach makes it possible to reveal the magnetic texture in a composite sample independently of the surface topography

Sur la suite des opérateurs Bernstein composés (On the sequence of composite Bernstein operators)

We consider a sequence of composite Bernstein operators and the quadrature formulae associated with them. Upper bounds for the approximation error of continuous functions and for the approximation of integrals of continuous functions are given. The bounds are described in terms of moduli of continuity of order one and two. Two inequalities of Tchebycheff-Grüss-type are also included

On differential operators associated with Markov operators

In this paper we introduce and study a new class of elliptic second-order differential operators on a convex compact subset K of R^d, which are associated with a Markov operator T on C(K) and which degenerate on a suitable subset of K containing its extreme points. Among other things, we show that the closures of these operators generate Markov semigroups. Moreover, we prove that these semigroups can be approximated by means of iterates of suitable positive linear operators, which are referred to as the Bernstein-Schnabl operators associted with T. As a consequence we show that the semigroups preserve polynomials of a given degree as well as Holder continuity which gives rise some spatial regularity properties of the solutions of the relevant evolution equations

On Markov operators preserving polynomials

The paper is concerned with a special class of positive linear operators acting on the space C(K) of all continuous functions defined on a convex compact subset K of R^d, having non-empty interior. Actually, this class consists of all positive linear operators T on C(K) which leave invariant the polynomials of degree at most $1$ and which, in addition, map polynomials into polynomials of the same degree. Among other things, we discuss the existence of such operators in the special case where K is strictly convex by also characterizing them within the class of positive projections. In particular we show that such operators exist if and only if the boundary of K is an ellipsoid. Furthermore, a characterization of balls of R^d in terms of a special class of them is furnished. Additional results and illustrative examples are presented as well