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This paper has been withdrawn by the authors, since it has been merged with Part I (ID 0802.3570)

Information Theory · Computer Science 2016-08-14 Øyvind Ryan , Merouane Debbah

This paper was withdrawn by the author.

High Energy Physics - Phenomenology · Physics 2007-05-23 Leonard Susskind

This paper has been withdrawn because the content has been substantially improved in a later paper, arXiv:0806.1165.

General Physics · Physics 2008-06-11 David J. BenDaniel

There have been comments on the starting paper, hep-th/0106074, which point out unclear motivation and definition of noncommutative momentum introduced. This paper is withdrawn by the author for more clear presentation.

High Energy Physics - Theory · Physics 2007-05-23 C. Shio

This paper has been withdrawn. Its new version has been published.

Geometric Topology · Mathematics 2007-05-23 Rustam Sadykov

This paper has been withdrawn by the author(s). Please see arXiv:0711.3910 for revision.

High Energy Physics - Phenomenology · Physics 2007-11-25 Swarup Kumar Majee , Amitava Raychaudhuri

This paper has been withdrawn by the author due to a crucial error in the proofs. The error has been corrected and the paper has been expanded in arXiv:0910.5327

Algebraic Geometry · Mathematics 2010-01-14 Mario Maican

This paper has been withdrawn by the author due to the unsure solution to the Dyson-Schwinger equation.

High Energy Physics - Phenomenology · Physics 2007-05-23 Hongting Yang

This submission has been withdrawn by the author and superseded by arXiv:0804.0744.

Differential Geometry · Mathematics 2008-07-16 Graham Smith

This paper has been withdrawn.

Combinatorics · Mathematics 2011-03-04 Golnaz Ghasemiesfeh

This paper has been withdrawn by arXiv administrators because of disputed claims of authorship among former collaborators

General Topology · Mathematics 2015-06-11 Ben Ntatin , William Glunt

This paper has been withdrawn due to disagreement of suggested results and methods between authors.

High Energy Physics - Phenomenology · Physics 2008-11-26 Alexei M. Frolov , Farrukh A. Chishtie

The aim of this article is to provide a complementary understanding to some results of the second author using the machinery of Koszul complexes, and to explain how this approach can provide a new description of projective derived…

Algebraic Geometry · Mathematics 2025-06-27 Tristan Bozec , Julien Grivaux

The paper contains a description of the links of complex surface germ.

Algebraic Geometry · Mathematics 2026-02-04 Francoise Michel

The paper has been withdrawn

Mathematical Physics · Physics 2009-10-31 Alexander I. Olemskoi , Alexei D. Kiselev

This paper withdrawn since it has been published in an updated version in Biophysical Reviews and Letter Vol. 2, No. 2 (2007) 155-166

Soft Condensed Matter · Physics 2007-07-18 Sarah Köster , Holger Stark , Thomas Pfohl , Jan Kierfeld

There have been comments on the starting paper, hep-th/0106074, which point out unclear motivation and definitions on noncommutative momentum introduced. This paper is withdrawn by the author for more clear presentation.

High Energy Physics - Theory · Physics 2007-05-23 C. Shio

This paper has been withdrawn by the author due to some problems.

Quantum Physics · Physics 2008-11-28 Peng Li

This paper has been withdrawn by the authors because it has been combined with "Higher Auslander Algebras Admitting Trivial Maximal Orthogonal Subcategories" (arXiv:0903.0761) together. Please see the new version of the latter paper for the…

Representation Theory · Mathematics 2009-03-25 Zhaoyong Huang , Xiaojin Zhang