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This paper has been withdrawn by the author(s), due a crucial sign error in Eqn. 1.
This paper has been withdrawn by the author because there are some typos in proofs.
This paper has been withdrawn by the authors
this paper has been withdrawn. A crucial estimate on a Lipschitz variant of the Kakeya maximal function has an incomplete proof.
Paper withdrawn because of a gap in the proof of Proposition 3 of Thomas Schick: "Integrality of L2-Betti numbers", Math. Ann. 317, 727-750 (arXiv.org/abs/math.gt/0001101). Most results of the withdrawn paper were based on this proposition.
This paper has been withdrawn by the author, due to a significant error in section 4.3.1.
The paper has been withdrawn by the author due to crucial error in formula (14) which does not satisfy conditions for S(x,y) domain if only d>2.
This paper has been withdrawn by the author due to a error in attachment of source file.
This paper has been withdrawn while the author verifies the literature.
The paper is suspended. The reason: as was noted by prof. H. Esnault, Theorem 2.1.1 of the previous version (as well as the related Theorem 6.1.1 of http://arxiv.org/PS_cache/math/pdf/9908/9908037v2.pdf of D. Arapura and P. Sastry) is wrong…
This paper has been withdrawn by the author(s), due the final version in math.QA/0604564
This paper has been withdrawn by the author due to serious flaws in certain proofs. For instance, the method used to construct certain automorphic representations is flawed.
This paper has been withdrawn by the author(s), due a crucial sign error in Eqn. 1.
We derive the discrete version of the classical Helmholtz condition. Precisely, we state a theorem characterizing second order finite differences equations admitting a Lagrangian formulation. Moreover, in the affirmative case, we provide…
The paper has benn withdrawn because the computation of the external virial contains an error which invalidate the main result.
This paper has been withdrawn by the authors due to a gap in the proof of the main result (in 5.3).
This paper has been withdrawn by the author, due to errors in the figures.
This paper has been withdrawn by the author due to a crucial error in the last lines in the proof of Lemma 3.3.
There have been comments on this paper which point out unclear motivation and definitions on noncommutative momentum introduced. Therefore, this paper is withdrawn by the author for more clear presentation.
This paper has been withdrawn by the author due to an error in section 7. There is a new version: arXiv:1011.3352.