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There have been comments on the starting paper, hep-th/0106074, which point out unclear motivation and definitions on noncommutative momentum introduced. Therefore, to give more clear presentation, this paper is withdrawn.

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

This paper has been withdrawn

Quantum Algebra · Mathematics 2007-05-23 Frederick Leitner

This paper has been withdrawn by the author due to a necessity of further editing. (Will be resubmitted here or elsewhere in editted form.)

Materials Science · Physics 2008-11-05 Yoichi Murakami

This paper has been withdrawn by the author(s) for revision.

Information Theory · Computer Science 2010-02-10 Chinmay S. Vaze , Mahesh K. Varanasi

This paper has been withdrawn

History and Overview · Mathematics 2010-05-18 Giorgio Spada

This paper has been withdrawn by the author.

General Relativity and Quantum Cosmology · Physics 2007-05-23 Lukasz Andrzej Glinka

This paper has been withdrawn by the author(s), due the following reasons. A similar system for a different purpose has already been studied in Phys.Rev.D60:083001,1999 (astro-ph/9904315). Moreover, our analysis was wrong because we have…

High Energy Physics - Phenomenology · Physics 2007-05-23 Tomohiro Matsuda

This paper has been withdrawn

Soft Condensed Matter · Physics 2007-05-23 This paper has been withdrawn

This paper is withdrawn because the results in the paper are included in a paper to be published in Mathematical and Computer Modelling.

Classical Analysis and ODEs · Mathematics 2011-05-02 Huseyin Cakalli

This paper has been withdrawn by the author due to its main result being included in cond-mat/0403309 by the same author.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

This paper has been withdrawn. It was an early draft submitted prematurely in error. A complete version is to be submitted shortly.

This paper has been withdrawn by the authors because the paper is largely revised and improved, and to appear in Mechanics Research Communications.

Classical Physics · Physics 2007-05-23 Y. C. Huang , Z. X. Liu , X. G. Li

This paper has been withdrawn by the authors.

Quantum Physics · Physics 2007-05-23 Goong Chen , Zijian Diao

This paper has been withdrawn by the authors.

This paper has been withdrawn by the author

Mathematical Physics · Physics 2008-12-30 Alireza Khalili Golmankhaneh

This paper has been withdrawn by the author.

Statistical Mechanics · Physics 2007-05-23 Sumiyoshi Abe

This paper has been withdrawn by the author.

Quantum Physics · Physics 2007-05-23 Oscar Chavoya-Aceves

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

General Relativity and Quantum Cosmology · Physics 2011-01-07 Naonori Suma Sugiyama , Toshifumi Futamase

This paper has been withdrawn by the author.

Computation and Language · Computer Science 2015-03-14 Juan-Manuel Torres Moreno , Silvia Fernandez , Eric SanJuan