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This paper was withdrawn by the authors. The mistake in math.AG/0209223 affects also this paper.

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The paper has been withdrawn.

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This paper has been withdrawn by the author(s), due a crucial sign error in Thm. 11.

Information Theory · Computer Science 2007-10-29 Zhengbang Zha , XueLi Wang

This paper has been withdrawn by the author due to an erro thereon line -2 of page 4.

Commutative Algebra · Mathematics 2010-12-09 Yongbin Li

This submission has been withdrawn by arXiv admins due to fraudulent affiliation claims by the original submitter.

Number Theory · Mathematics 2014-08-18 Yuanyou Cheng , Glenn J. Fox , Mehdi Hassani

This paper has been withdrawn by the author because there are some typos in proofs.

Commutative Algebra · Mathematics 2013-07-30 M. J. Nikmehr , F. Heydari

This paper has been withdrawn.

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This paper has been withdrawn by author due to an error in the proof.

Geometric Topology · Mathematics 2007-05-23 Qing Zhou

This paper has been withdrawn

Quantum Algebra · Mathematics 2009-02-11 Kyousuke Uchino

The paper was withdrawn because of its significant overlap with a paper appeared recently.

Combinatorics · Mathematics 2008-06-30 Marilena Barnabei , Flavio Bonetti , Matteo Silimbani

This paper has been removed by arXiv administrators because of excessive overlap with gr-qc/0506062.

General Relativity and Quantum Cosmology · Physics 2019-10-21 Murat Korunur , Ali Havare

Withdrawn by arXiv administration because authors have forged affiliations and acknowledgements, and have not adequately responded to charges [hep-th/9912039] of unattributed use of verbatim material.

High Energy Physics - Theory · Physics 2009-09-25 N. Mebarki , A. Maireche

This paper has been withdrawn by the author due to a gap in the proof of Lemma 3.4

Operator Algebras · Mathematics 2007-05-23 Volker Runde

This paper has been withdrawn by the first author due to incomplete bibliography and incorporation of multiple formats in the same file.

Information Theory · Computer Science 2009-12-24 Sahand Ahmad , Cem Tekin , Mingyan Liu , Jianwei Huang , Yunnan Wu

This paper was withdrawn by the authors.

Strongly Correlated Electrons · Physics 2007-05-23 L. Borda , A. Halbritter , A. Zawadowski

Although the results are correct, it was pointed out that the results follow from some previously known results. Accordingly, this version of the paper is withdrawn by the authors.

Computational Complexity · Computer Science 2012-12-03 Bhaskar DasGupta , Lakshmi Kaligounder

This paper was withdrawn by the authors.

High Energy Physics - Theory · Physics 2007-05-23 Subir Ghosh

Admin note: withdrawn by arXiv admin because of the use of a pseudonym, in violation of arXiv policy.

General Mathematics · Mathematics 2014-07-18 Asia Furones