Decomposing numerical ranges along with spectral sets

This note is to indicate the new sphere of applicability of the method developed by Mlak as well as by the author. Restoring those ideas is summoned by current developments concerning $K$-spectral sets on numerical ranges

On the number of branches of real curve singularities

There is presented a method for computing the number of branches of a real analytic curve germ from $R^n$ to $R^m$, where m is greater or equal to n, having a singular point at the origin, and the number of half--branches of the set of double points of an analytic germ from $R^2$ to $R^3$