“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

Magnetic properties and magneto-birefringence of magnetic fluids

Static magnetic properties of a large variety of magnetic fluids with magnetite particles is studied. A qualitative study of magnetization curves was performed to establish the influence of interactions or the presence of agglomerations in each sample. Improved equations for magneto-granulometric analysis, for ideal ferrofluids, were proposed. Better results for the mean magnetic diameter than in the case of using the known equations were obtained. A quantitative study using several models for ideal and interacting particles was performed to select the best method and dimensional distribution function for magneto-granulometric analysis as well as for accurately determining macroscopic quantities of samples (initial susceptibility, saturation magnetization, particle number density or magnetic volume fraction) and properties of nanoparticles (mean magnetic diameter, thickness of the nonmagnetic layer and particle distribution). A new model for magneto-birefringence was proposed and discussed as well as applied for diluted and concentrated ferrofluids. The Langevin behaviour of samples was investigated and compared with the investigation based on magnetic properties. Nanoparticles parameters like mean "magneto-optical" diameter, effective anisotropy constant, Shliomis diameter and the real part of the electrical permittivity of particles were accurately determined

Some Functionals and Approximation Operators Associated with a Family of Discrete Probability Distributions

A certain discrete probability distribution was considered in [“A discrete probability distribution and some applications”, Mediterr. J. Math., 2023]. Its basic properties were investigated and some applications were presented. We now embed this distribution into a family of discrete distributions depending on two parameters and investigate the properties of the new distributions

Some Functionals and Approximation Operators Associated with a Family of Discrete Probability Distributions

A certain discrete probability distribution was considered in ["A discrete probability distribution and some applications", Mediterr. J. Math., 2023]. Its basic properties were investigated and some applications were presented. We now embed this distribution into a family of discrete distributions depending on two parameters and investigate the properties of the new distributions

Dilution series approach for investigation of microstructural properties and particle interactions in high-quality magnetic fluids

The aim of the paper is to study the deviation of magnetic properties of the magnetic fluids prepared for this study, from ideal (Langevin) behaviour, i.e. to estimate particle interaction influence and dimensions and influence of particle aggregates, as well as to explain the related effects observed. We also determine the particle coupling parameter, the particle nonmagnetic layer thickness, and the particle distribution, which are fundamental for sample characterization. A comparison of the studied magnetic fluids with each other, with respect to microstructure formation and particle interaction strength is finally done. For these purposes, a concentration dependence study, following the proposed “dilution series approach”, is performed. Three series of dilutions of three types of magnetic fluids were prepared and analyzed

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