We give a corrected version of Theorem 3, Lemma 4, and Proposition 9 in the above-mentioned paper, which are incorrect as stated (as was pointed out by O. Gabber).

We study the effect of magnetic field in an implosion process achieved by radiation. A time-varying sinusoidal magnetic field is seen to affect the continuous transition of space-like detonation to time-like detonation at the core of implosion region. The oscillating varying magnetic field has a significant effect in increasing the volume of the time-like detonation of the core of implosion and also modifies the time of the implosion process. This transition can have significant outcome both theoretically and experimentally in the areas of high-energy hadronization of quark–gluon plasma matter and inertial confinement fusion efforts of fuels.

The complete set of minimal obstructions for embedding graphs into the torus is still not determined. In this paper, we present all obstructions for the torus of connectivity 2. Furthermore, we describe the building blocks of obstructions of connectivity 2 for any orientable surface.

We obtain a removal lemma for systems of linear equations over the circle group, using a similar result for finite fields due to Král′, Serra and Vena, and we discuss some applications.

We describe the maximal torus and maximal unipotent subgroup of the Picard variety of a proper scheme over a perfect field.