Related papers: Linearizability of cubic polynomials at irrational…

The paper has been withdrawn by authors. The issues studied in this paper were changed so much that we have published a new paper considering these issues. See hep-th/0406074

This paper has been withdrawn by the authors due to the inconsistency of the computations used for extra dimensions and the fractal dimensional approach of the paper. An updated version of the paper will be published under a different…

The paper has been withdrawn.

For positive integers $n>k$, let $P_{n,k}(x)=\displaystyle\sum_{j=0}^k \binom{n}{j}x^j $ be the polynomial obtained by truncating the binomial expansion of $(1+x)^n$ at the $k^{th}$ stage. These polynomials arose in the investigation of…

The paper is being withdrawn since the authors felt that the submission is a little premature after a careful reading by some of the experts in this field.

This paper has been withdrawn by the author, due to a crucial error in the proof of Thm.1

This paper has been withdrawn by the authors, due to the requirement of the Journal where a modified version will be published.

This paper has been withdrawn by the author, because a better treatment is given in the author's Phd.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This paper has been withdrawn while the author verifies the literature.

This paper has been withdrawn by the author because there are some typos in proofs.

This paper has been withdrawn by the authors due to its publication

In 1991, one of the authors showed the existence of quadratic transformations between the Painleve' VI equations with local monodromy differences $(1/2,a,b,\pm 1/2)$ and $(a,a,b,b)$. In the present paper we give concise forms of these…

This paper has been withdrawn by the authors due to a mistake in the proof of Theorem 1.

Consider a hierarchical log-linear model, given by a simplicial complex, $\Gamma$, and integer matrix $A_\Gamma$. We give a new characterization of the rank of $A_\Gamma$ given by a logarithmic transformation on the exponential Hilbert…

Let K be a field of characteristic 0 and let n be a natural number. Let Gamma be a subgroup of the multiplicative group $(K^\ast)^n$ of finite rank r. Given $A_2,...,a_n\in K^\ast$ write $A(a_1,...,a_n,\Gamma)$ for the number of solutions…

This paper has been withdrawn by the authors, due a crucial mistake in Lemma 2

This paper has been withdrawn by the authors. Our basic argument on the gauge invariance presented in this paper cannot withstand the criticism which has been drawn to our attention by several colleagues.

This paper has been withdrawn by the authors because the results obtained here had been corrected and appeared in hep-th/0306008.

This paper was withdrawn by the author due to an edition's rights

This paper is being withdrawn because an error was discovered in lemma 4.3. Although the rest of the paper appears to be correct, this error invalidates the proof of theorem 3.1 and theorem 3.3.