Related papers: Particle in Cell (PIC): Error Estimates for Adapti…

This paper has been withdrawn to address an omission. It will be resubmitted in the near future.

This paper has been withdrawn by the author(s), due an error in the proof.

This paper has been withdrawn by the author due to a serious mistake on Lemma 2.4.

This paper has been withdrawn by the author. There is an error on page 3 in the last inequality before Lemma 1.1.

This paper has been withdrawn by the author due to a sheaf-theoretic error, in the end of the proof of the main theorem.

This paper has been withdrawn by the author(s), due a crucial i-number error in Eqn. 18.

The paper has been withdrawn by the author.

This paper has been withdrawn by the author due to a crucial problem in Lemma 3. This equation must be changed.

This paper has been withdrawn by the authors due to a crucial error in calculation.

This paper has been withdrawn by the author: it was a too preliminary version.

This paper has been withdrawn by the author, since now all four parts of the review are available as a single file 0804.1639. I also made some revision of the text in order to avoid misprints and some inaccurate expressions.

This paper has been withdrawn by the author.

This paper has been withdrawn by the author due to an erro thereon line -2 of page 4.

This paper has been withdrawn by the author due to a mistake in the section 4.

This paper has been withdrawn by the author.

This paper has been withdrawn by the author.

This paper has been withdrawn by the author.

The paper has been withdrawn by the author, due to a critical error stemming from the defined template.

This paper has been withdrawn by the author.

This paper has been withdrawn by the authors. Our basic argument on the gauge invariance presented in this paper cannot withstand the criticism which has been drawn to our attention by several colleagues.