Haematite natural crystals: non-linear initial susceptibility at low temperature

Several works have reported that haematite has non-linear initial susceptibility at room temperature, like pyrrhotite or titanomagnetite, but there is no explanation for the observed behaviours yet. This study sets out to determine which physical property (grain size, foreign cations content and domain walls displacements) controls the initial susceptibility. The performed measurements include microprobe analysis to determine magnetic phases different to haematite; initial susceptibility (300 K); hysteresis loops, SIRM and backfield curves at 77 and 300 K to calculate magnetic parameters and minor loops at 77 K, to analyse initial susceptibility and magnetization behaviours below Morin transition. The magnetic moment study at low temperature is completed with measurements of zero field cooled-field cooled and AC susceptibility in a range from 5 to 300 K. The minor loops show that the non-linearity of initial susceptibility is closely related to Barkhausen jumps. Because of initial magnetic susceptibility is controlled by domain structure it is difficult to establish a mathematical model to separate magnetic subfabrics in haematite-bearing rocks.

Finding the set of k-additive dominating measures viewed as a flow problem

n this paper we deal with the problem of obtaining the set of k-additive measures dominating a fuzzy measure. This problem extends the problem of deriving the set of probabilities dominating a fuzzy measure, an important problem appearing in Decision Making and Game Theory. The solution proposed in the paper follows the line developed by Chateauneuf and Jaffray for dominating probabilities and continued by Miranda et al. for dominating k-additive belief functions. Here, we address the general case transforming the problem into a similar one such that the involved set functions have non-negative Möbius transform; this simplifies the problem and allows a result similar to the one developed for belief functions. Although the set obtained is very large, we show that the conditions cannot be sharpened. On the other hand, we also show that it is possible to define a more restrictive subset, providing a more natural extension of the result for probabilities, such that it is possible to derive any k-additive dominating measure from it.