Related papers: Counterexamples for the convexity of certain matri…

This paper has been withdrawn as the proof of Lemma 4.1 is incomplete.

This paper has been withdrawn by the authors, due a crucial mistake in Lemma 2

This paper is withdrawn because of an error in Lemma 3.1

This paper has been withdrawn by the author.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This paper is withdrawn due to some errors, which are corrected in arXiv:0912.0071v4 [cs.LG].

This paper has been withdrawn by the author due to a crucial error in Lemma 3.5.

This paper has been withdrawn by the author, due to a crucial error in the proof of Lemma 3.1.

This paper has been withdrawn by the author due to errors.

This paper has been withdrawn by the author due to an error.

This paper has been withdrawn by the author

This paper has been withdrawn by the author due to a crucial error in the proof of Lemma 2.2.

This paper has been withdrawn by the author due to a serious mistake on Lemma 2.4.

The paper is withdrawn.

This paper was withdrawn by the authors. Lemma 5.1 is wrong.

The paper has been withdrawn due to a crucial error in section 3.

This paper is withdrawn.

Paper withdrawn - lemma 4.1 was false. Quite a lot of changes need to be made!

This paper has been withdrawn by the author due to incomplete interpretation for the results.

This paper has been withdrawn by the author, due to an error in the proof of Theorem 3.8.

This paper has been withdrawn by the author due to an erro thereon line -2 of page 4.