Related papers: Phase Coherence Analysis of Insect Flight

This paper has been withdrawn by the author.

This paper has been withdrawn by the authors due to crucial error in the main proof (located in Section 2.4). The authors apologize for any inconveniences.

This paper was withdrawn by the author.

This paper has been withdrawn by the authors.

This paper has been withdrawn by the author due to imprecisions which must conduce to wrong results.

This paper has been withdrawn by the author

This paper was withdrawn (temporarily?) by the author since an error needs to be corrected.

This paper has been withdrawn by the authors, as it has been rejected in November 2007.

This paper has been withdrawn by the author. The proof of the main result has a gap that the author does not know how to fix it.

This paper has been withdrawn by the corresponding author because the newest version is now published in Journal of Discrete Algorithms.

The paper is withdrawn due to mistakes in the proofs for Proposition 1.2 and Theorem 2.2.

This paper has been temporarily withdrawn, due to an error in Eq. (3).

This paper has been withdrawn by the author due to an error in the sufficient condition given for the proof of the Tate conjecture for Catanese surfaces.

This paper has been withdrawn by the author.

This paper has been withdrawn by the author due to a serious mistake on Lemma 2.4.

This paper has been withdrawn by the author due to the incorrect argument for the security.

This paper has been withdrawn by the author. The most updated version can be accessed by arXiv:1806.07290.

This paper has been withdrawn by the author due to a crucial sign error in some equations

This paper has been withdrawn by the author, because a better treatment is given in the author's Phd. thesis (Sections 3.4.6 and 4.4), now available on the arxiv.

This paper is withdrawn because the results in the paper are included in a paper to be published in Mathematical and Computer Modelling.