Related papers: Fractals and the two dimensional Jacobian Conjectu…

We attempt to prove the Razumov-Stroganov conjecture using a bijectional approach. We have been unsuccessful but we believe the techniques we present can be used to prove the conjecture.

We analyze examples of projected two dimensional fractals for the case where the objects studied have a Schechter luminosity function. Our results indicate that two dimensional catalogues of sources could be of value in detecting the…

In this paper we have defined one function that has been used to construct different fractals having fractal dimensions between 1.58 and 2. Also, we tried to calculate the amount of increment of fractal dimension in accordance with the base…

In this paper, we will give an extension of Mok's theorem on the generalized Frankel conjecture under the condition of the orthogonal bisectional curvature.

Fractal dimension constitutes the main tool to test for fractal patterns in Euclidean contexts. For this purpose, it is always used the box dimension, since it is easy to calculate, though the Hausdorff dimension, which is the oldest and…

We use contraction method in probabilistic metric spaces to prove existence and uniqueness of selfsimilar random fractal measures.

Topological defects in the framework of effective quantum gravity model are investigated, based on the hypothesis of an effective fractal dimension of the universe. This is done by using Caputo fractional derivatives to determine the…

In this paper, we study a so-called Condition C1 and a weaker Condition C2. For Druzkowski maps Condition C2 is equivalent to the Jacobian conjecture. Main results obtained: - Stating new equivalent formulations of the Jacobian conjecture.…

We investigate potential spaces associated with Jacobi expansions. We prove structural and Sobolev-type embedding theorems for these spaces. We also establish their characterizations in terms of suitably defined fractional square functions.…

The determination of Jacobi sums, their congruences and cyclotomic numbers have been the object of attention for many years and there are large number of interesting results related to these in the literature. This survey aims at reviewing…

We find explicit equations for two-coverings of Jacobians of genus two curves over an arbitrary ground field of characteristic different from two.

We construct a non-proper set of two variables polynomial maps and study the nowhere vanishing Jacobian condition of the Jacobian conjecture for this set. We obtain some classes of polynomial maps satisfying the 2-dimensional Jacobian…

In this paper we present an equivalent statement to the Jacobian conjecture. For a polynomial map F on an affine space of dimension n, we define recursively n finite sequences of polynomials. We give an equivalent condition to the…

We look for spectral type differential equations satisfied by the generalized Jacobi polynomials which are orthogonal on the interval [-1,1] with respect to a weight function consisting of the classical Jacobi weight function together with…

Making use of the theory of infinitesimal canonical transformations, a concise proof is given of Jacobi's identity for Poisson brackets.

The fact that galaxy distribution exhibits fractal properties is well established since twenty years. Nowadays, the controversy concerns the range of the fractal regime, the value of the fractal dimension and the eventual presence of a…

Fractals are ubiquitous natural emergences that have gained increased attention in engineering applications, thanks to recent technological advancements enabling the fabrication of structures spanning across many spatial scales. We show how…

I review the basis and limitations of plausible inference in cosmology, in particular the limitation that it can only provide fundamentally true inferences when the hypotheses under consideration form a set that is exhaustive. They never…

The famous Jacobian conjecture asks if a morphism $f:K[x,y]\to K[x,y]$ having an invertible Jacobian is invertible ($K$ is a characteristic zero field). We show that if one of the following three equivalent conditions is satisfied, then $f$…

The fractal structure of real world objects is often analyzed using digital images. In this context, the compression fractal dimension is put forward. It provides a simple method for the direct estimation of the dimension of fractals stored…