Related papers: Cliff-wall surgery and vanishing of basic phase fu…

This paper has been withdrawn by the author due to a crucial error in the proof of Theorem 1.

This paper has been withdrawn, because the argument for generation of Goldstone modes is incorrect.

This paper has been withdrawn due to an error in the proof of the main theorem.

This paper was withdrawn by the authors.

This paper has been withdrawn.

The author has removed this paper, following the publication of a more complete version.

This paper has been withdrawn due to errors in the analysis of data with Carrier Access Rate control and statistical methodologies.

Two recent papers by Kawarabayashi, Thomas and Wollan, "A New Proof of the Flat Wall Theorem" (arXiv:1207.6927) and "Quickly Excluding a Non-Planar Graph" (arXiv:2010.12397) provide major improvements over Robertson and Seymour's original…

This article has been withdrawn due to a mistake which is explained in version 2.

This paper has been withdrawn. See v1 still available to understand the problem: Proposition 2.2 is false. The error in the proof is in claim (3). Then, the whole paper collapses. We do not have any correction for now. We apologize to…

This paper has been withdrawn by the author due to a crucial error in last part of proof.

The paper has been withdrawn by the author, due to a fatal error. A horse stumbles that has four legs.

This paper has been withdrawn by the author due to a gap in the proof of the main result.

This submission is being withdrawn due to serious errors in the achievability proofs. The reviewers of the journal I had submitted to had found errors back in 2006. I had forgotten about this paper until I saw the CFP for a JSAC issue on…

This paper has been withdrawn by the author due to an error in the proof.

This paper has been withdrawn. See quant-ph/9806031 for a discussion.

This paper has been withdrawn by the authors due to several major changes in concepts and results. New version will follow briefly as a new e-print.

This submission to arXiv has been withdrawn by the authors

Classic complex analysis is built on structural function $K=1$ only associated with Cauchy-Riemann equations, subsequently various generalizations of Cauchy-Riemann equations start to break this situation. The goal of this article is to…

The paper has heen withdrawn.