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This paper has been withdrawn by the author due to a crucial error in the definition of homomorphism.

Dynamical Systems · Mathematics 2007-05-23 Maria A. Avino-Diaz , Gabriela Bulancea

This paper has been withdrawn by the author(s), due a crucial sign error in Thm. 11.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This paper has been withdrawn by the author, due to a significant error in section 4.3.1.

Geometric Topology · Mathematics 2009-01-26 Chan-Ho Suh

This submission has been withdrawn by arXiv administrators due to inappropriate text reuse from external sources

General Relativity and Quantum Cosmology · Physics 2022-04-22 M. Aygun , S. Aygun , I. Yilmaz , H. Baysal , I. Tarhan

This paper has been withdrawn by the author(s)

High Energy Physics - Experiment · Physics 2007-05-23 A. Rosowsky

This paper has been withdrawn to address an omission.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

High Energy Physics - Theory · Physics 2008-02-03 J. R. Shepard , J. A. McNeil

This paper has been withdrawn by the authors due to some fatal errors in the analysis.

General Relativity and Quantum Cosmology · Physics 2008-03-05 Seungjoon Hyun , Jaehoon Jeong , Wontae Kim , John J. Oh

This paper has been withdrawn by the author(s), due to the existence of a much better paper in http://arxiv.org/abs/cs.CR/0207027

Cryptography and Security · Computer Science 2007-05-23 Boaz Tsaban

This paper has been withdrawn by the author, due to obsolete reference [4], insufficient discussion in sec. 4, and major conceptual error in sec. 5.

High Energy Physics - Theory · Physics 2010-01-13 K. Odagiri

This paper has been withdrawn by the authors due to a major rewriting.

Neural and Evolutionary Computing · Computer Science 2008-01-07 Manuel Cebrian , Manuel Alfonseca , Alfonso Ortega

arXiv admin comment: This version has been removed by arXiv administrators as the submitter did not have the rights to agree to the license at the time of submission

Neurons and Cognition · Quantitative Biology 2025-07-17 Sanjana Shankar

This paper has been withdrawn by the author, due to an error in Proposition 2.2.

Differential Geometry · Mathematics 2007-05-23 Albert Borbely

This paper ("Two-Level Chromophore and Irreversibility", which can be found at arXiv:0804.0086) has been withdrawn by the author due to too many errors and misleading statements. This paper has been superseded by Section 2.11 and Chapter 7…

Chemical Physics · Physics 2009-12-16 Erich N. Wolf

This paper has been withdrawn by the author due to similarity to Author's other paper

General Relativity and Quantum Cosmology · Physics 2009-04-13 Erez M. Yahalomi

Withdrawn due to error. See D. Lowe, L. Susskind and J. Uglum, hep-th/9402136, for correct treatment. Apologies to all recipients.

High Energy Physics - Theory · Physics 2008-02-03 David A. Lowe

This paper has been withdrawn by the author due to a new work in [arXiv:0901.0456v4] which can contain the results in this paper.

Soft Condensed Matter · Physics 2009-06-10 Xiaohua Zhou

This paper has been withdrawn, as it is superseded by arXiv:0806.2122 (Bloch-Kato exponential maps for local fields with imperfect residue fields), which is a more recent version of the same paper.

Number Theory · Mathematics 2010-05-06 Sarah Livia Zerbes

This paper has been withdrawn

Quantum Algebra · Mathematics 2007-05-23 Frederick Leitner

This paper has been withdrawn by the author due to its main result being included in cond-mat/0403309 by the same author.

Mathematical Physics · Physics 2007-05-23 Z. C. Tu