In this paper, we give necessary and sufficient conditions for the matrix [ a 0 b d ] , over a *-regular ring, to have a Moore-Penrose inverse of four different types, corresponding to the four cases where the zero element can stand. In particular, we study the case where the MoorePenrose inverse of the matrix flips. Mathematics subject classification (2010): 15A09, 16E50, 16W10.

This paper is concerned with the Penrose{Fife phase{ eld model and some Stefan problems, in which the heat ux is proportional to the gradient of the inverse absolute temperature. Recently, Colli and Sprekels proved that, as some parameters in the Penrose{Fife equations tend to zero, the corresponding solutions converge against the solutions to these Stefan problems. Following their approach, we...