Fluoride technology of obtaining REM magnetic alloys and master alloys

Rare earth permanent magnets (REPM) based on neodymium-Fe-boron system are the most promising, since they have the highest magnetic and satisfactory mechanical characteristics. The paper covers physical-chemical principles and shows the results of experimental studies of the process of obtaining REM alloys and master alloys using fundamentally new fluoride technology based on ladle calciothermal REM fluorides and Fe reduction

Curve cuspless reconstruction via sub-Riemannian geometry

We consider the problem of minimizing {formula omitted} for a planar curve having fixed initial and final positions and directions. The total length L is free. Here s is the variable of arclength parametrization, K(s) is the curvature of the curve and ¿>0 a parameter. This problem comes from a model of geometry of vision due to Petitot, Citti and Sarti. We study existence of local and global minimizers for this problem. We prove that if for a certain choice of boundary conditions there is no global minimizer, then there is neither a local minimizer nor a geodesic. We finally give properties of the set of boundary conditions for which there exists a solution to the problem